thesis
TRANSCRIPT
AUTOIGNITION OF KEROSENE BY DECOMPOSED HYDROGEN PEROXIDE
IN A DUMP COMBUSTOR CONFIGURATION
A Thesis
Submitted to the Faculty
of
Purdue University
by
James C. Sisco
In Partial Fulfillment of the
Requirements for the Degree
of
Master of Science in Aeronautics and Astronautics
August 2003
ii
iii
ACKNOWLEDGEMENTS
iv
TABLE OF CONTENTS
Page
LIST OF TABLES ............................................................................................................ vii
LIST OF FIGURES ............................................................................................................ix
ABSTRACT ...............................................................................................................xiv
CHAPTER 1: INTRODUCTION .................................................................................. 1
1.1 Hydrogen Peroxide ..............................................................................................3
1.1.1 Benefits of Hydrogen Peroxide as a Propellant ...........................................4
1.1.2 Catalyst Bed Design ....................................................................................6
1.2 Background on Hydrogen Peroxide Bipropellant Engines..................................7
1.2.1 Hypergolic Bipropellant Engines ................................................................7
1.2.2 Staged-Bipropellant Engines .......................................................................8
1.3 Design of Staged-Bipropellant Engines.............................................................11
1.3.1 Advantages of Staged-Engines ..................................................................12
1.3.2 Challenges in Staged Engine Design .........................................................17
CHAPTER 2: INJECTOR DESIGN ............................................................................ 20
2.1 Engine Design....................................................................................................21
2.2 Transverse Injector Design Considerations .......................................................22
2.2.1 Orifice Sizing .............................................................................................23
2.2.2 Decomposed Gas Flow Calculations .........................................................27
2.2.3 Rearward-Facing Step Sizing ....................................................................29
2.2.4 Trajectory Model .......................................................................................32
2.2.5 Baseline Injector Design............................................................................35
CHAPTER 3: AUTOIGNITION.................................................................................. 40
3.1 Basic Chemistry of Autoignition.......................................................................40
v
Page
3.1.1 Composition of Kerosene Fuel..................................................................41
3.1.2 Combustion of Hydrocarbons ....................................................................43
3.1.3 Kinetics of Autoignition............................................................................45
3.2 Autoignition Studies of Kerosene Fuel in Air ...................................................47
3.3 Dump Combustor Autoignition.........................................................................51
3.4 Autoignition Studies in Staged Combustors ......................................................52
3.5 Goals of this Autoignition Study.......................................................................56
CHAPTER 4: EXPERIMENTAL SETUP................................................................... 58
4.1 Test Facility Overview ......................................................................................58
4.2 Cavitating Venturi Flow Control.......................................................................60
4.3 Data Acquisition and Control............................................................................63
4.4 Instrumentation..................................................................................................65
4.5 Test Article and Setup .......................................................................................65
4.6 Hydrogen Peroxide Dilution..............................................................................71
4.7 Pressure Budget .................................................................................................72
4.8 Test Procedure ...................................................................................................74
4.9 Firing Sequence .................................................................................................77
CHAPTER 5: EXPERIMENTAL RESULTS.............................................................. 81
5.1 Test Plan Overview............................................................................................81
5.2 Data Reduction ..................................................................................................84
5.2.1 Pressure Transducer Data ..........................................................................84
5.2.2 FFT and Filtering .......................................................................................86
5.2.3 Calculations using Measured Data ............................................................88
5.3 Uncertainty Ana lysis .........................................................................................93
5.4 Data Summary ...................................................................................................96
5.4.1 Strong Autoignition...................................................................................96
5.4.2 Weak Autoignition...................................................................................101
5.4.3 No Autoignition.......................................................................................104
5.4.4 Trends in Autoignition Data ....................................................................107
vi
Page
5.4.5 Temperature Data ....................................................................................109
5.5 Catalyst Bed Performance ...............................................................................111
5.6 DMAZ Fuel .....................................................................................................116
5.7 Data Analysis ...................................................................................................118
5.7.1 Pressure Effects .......................................................................................118
5.7.2 Jet Trajectory ...........................................................................................120
5.7.3 Shear Layer Residence Time ...................................................................123
5.7.4 Autoignition Correlation..........................................................................123
CHAPTER 6: SUMMARY AND CONCLUSIONS ................................................. 125
LIST OF REFERENCES ................................................................................................ 131
APPENDICES
Appendix A: Part Drawings ............................................................................... 137
Appendix B: DMAZ Material Safety Data Sheet .............................................. 159
Appendix C: Test Cell P&ID............................................................................. 165
Appendix D: Data Reduction............................................................................. 167
Appendix E: Uncertainty Analysis .................................................................... 183
Appendix F: Test Data ....................................................................................... 189
vii
LIST OF TABLES
Table Page
Table ?1.1: Performance comparison of 90% H2O2/JP-8 system to common rocket propellant combinations. Specific impulse calculated assuming a chamber pressure of 1000 psia and equilibrium expansion to sea level pressure of 14.7 psia. ............... 2
Table ?1.2: Properties of liquid and decomposed hydrogen peroxide with concentration.3-5
..................................................................................................................................... 4
Table ?2.1: RBCC engine operating conditions. 26 ............................................................. 22
Table ?2.2: Fuel orifice and manifold geometry of transverse injector design including flow parameters at baseline operating conditions. .................................................... 36
Table ?2.3: Oxidizer port geometry and flow parameters in baseline monopropellant and bipropellant operational modes. ................................................................................ 36
Table ?3.1: Basic hydrocarbon families as found in kerosene-based fuels.51 ................... 42
Table ?3.2: Physical properties of JP-8 fuel. All properties stated at ambient temperature and pressure unless indicated otherwise.47,50 ............................................................ 42
Table ?3.3: Comparison between some physical properties of DMAZ and JP-8............... 57
Table ?4.1: List of cavitating venturis available at APCL. ................................................ 63
Table ?4.2: Comparison between catalyst bed designs used during testing. ..................... 66
Table ?4.3: Typical instrumentation list for autoignition testing. ...................................... 70
Table ?4.4: Pressure budget for a test at baseline design conditions using the GK catalyst bed, see Chapter 2.................................................................................................... 74
viii
Table Page
Table ?4.5: Typical valve firing sequence for each catalyst bed design. ........................... 80
Table ?5.1: Variation in chamber gas properties based on chamber contraction ratio. ..... 91
Table ?5.2: Decomposition properties of hydrogen peroxide as a function of concentration.................................................................................................................................... 92
Table ?5.3: Estimated random error for all measured variables. ........................................ 95
Table ?F.1: Measured and calculated test data during bipropellant operation. ................ 190
Table ?F.2: Measured and calculated bipropellant test data (cont.) ................................. 191
Table ?F.3: Measured and calculated monopropellant test data. ...................................... 192
Table ?F.4: Calculated decomposed gas and fuel flow conditions................................... 193
Table ?F.5: FFT results for bipropellant portion of each test including maximum range of pressure oscillations. ............................................................................................... 194
Table ?F.6: FFT result for monopropellant section of each test including maximum range of pressure oscillations............................................................................................ 195
Table ?F.7: Calculated uncertainty in densities and mass flow rates. .............................. 196
Table ?F.8: Calculated uncertainty in equivalence ratio and bipropellant performance parameters. .............................................................................................................. 197
Table ?F.9: Calculated uncertainty in monopropellant performance parameters. ............ 198
Table ?F.10: Calculated uncertainties in fuel and oxidizer flow parameter as well as momentum ratio and residence time. ...................................................................... 199
ix
LIST OF FIGURES
Figure Page
Figure ?1.1: Typical staged-bipropellant engine using H2O2/kerosene. This is commonly called a ‘dump’ combustor configuration. ................................................................ 11
Figure ?1.2: Comparison of C* vs. mixture ratio curves of 90% H2O2/JP-8 to common rocket propellant combinations.4 C* calculated assuming a chamber pressure of 1000 psia and equilibrium expansion. ...................................................................... 13
Figure ?1.3: Schematic of a Gamma class research engine indicating gas ports and fuel injection points.15 ...................................................................................................... 14
Figure ?1.4: Picture of a Gamma class gas port injector.15 ................................................ 15
Figure ?1.5: Early injector design used in thermal ignition research.11 This injector uses a combination of basic injection concepts such as swirl and gas port injectors. ......... 15
Figure ?1.6: Comparison of chamber temperature vs. mixture ratio of 90% H2O2/JP-8 against other common propellant combinations.4 Combustion temperature calculated assuming a chamber pressure of 1000 psia and equilibrium expansion. . 16
Figure ?2.1: Schematic of a transverse injector indicating important design parameters. . 23
Figure ?2.2: Dependence of discharge coefficient on orifice length over diameter ratio for a full flowing square-edged inlet.44........................................................................... 26
Figure ?2.3: Reacting flow behind a rearward-facing step showing turbulent eddies.45 .... 29
Figure ?2.4: Schematic of injector assembly indicating important geometry and dimensions. All dimensions are in inches. ............................................................... 37
x
Figure Page
Figure ?2.5: Comparison between JP-8 jet trajectories produced by transverse injector design during monoprop and biprop operation. Fuel orifices are located at x = 0, y =0 and x = 0, y = 1.707 inches centerline is at y = 0.854 inches............................... 38
Figure ?4.1: Schematic of a cavitating venturi indicating important parameters. ............. 62
Figure ?4.2: Simplified schematic of test stand with instrumentation locations. .............. 68
Figure ?4.3: Photos of installed test article for: a) GK catalyst bed and b) PCI catalyst bed assemblies. ................................................................................................................ 68
Figure ?4.4: Comparison of engine assemblies for each catalyst bed design. Axial locations of instrumentation are indicated in schematic. .......................................... 69
Figure ?5.1: Plot of pc2 from an autoignition test using PCI catalyst bed. Test conditions: 98% H2O2, φ = 1.84, CR = 3.0. ................................................................................. 85
Figure ?5.2: Plots of pc2 in a) unfiltered and b) filtered form. Test conditions: 87.5% H2O2, φ = 1.40, and CR = 3.0. ............................................................................................. 87
Figure ?5.3: a) Full and b) partial power spectrum of monoprop chamber pressure data shown boxed in Figure ?5.2a)..................................................................................... 88
Figure ?5.4: Variation in C* with φ for H2O2 combusting with JP-8.................................. 92
Figure ?5.5: Plots of pfu_inj and pc2 at the point of injection for a strong autoignition test using: a) the GK catalyst bed using 90% H2O2 at φ = 1.59 and CR = 3.0 and b) the PCI catalyst bed using 90% H2O2 at φ = 1.58 and CR = 3.0..................................... 98
Figure ?5.6: Frame-by-frame view of a strong autoignition test using GK catalyst bed. Test conditions: 90% H2O2, φ = 1.59, CR = 3.0. ...................................................... 99
Figure ?5.7: Frame-by-frame view of a strong autoignition test using PCI catalyst bed. Test conditions: 90% H2O2, φ = 1.58, CR = 3.0. .................................................... 100
Figure ?5.8: a) Unfiltered and b) filtered plots of pfu_inj and pc2 at the point of injection for a weak autoignition test using the GK catalyst bed. Test conditions: 87.5% H2O2, φ = 1.62, and CR = 3.0. ........................................................................................... 101
xi
Figure Page
Figure ?5.9: Frame-by-frame view of a weak autoignition test using GK catalyst bed. Test conditions: 87.5% H2O2, φ = 1.62, CR = 3.0. ......................................................... 102
Figure ?5.10: Plot of pfu_inj and pc2 at the point of injection for a test using PCI catalyst bed. Test conditions: 94% H2O2, φ = 2.15, and CR = 3.0. ............................................. 105
Figure ?5.11: Frame-by-frame view of a test with no autoignition using PCI catalyst bed. Test conditions: 94% H2O2, φ = 2.15, CR = 3.0. .................................................... 106
Figure ?5.12: Autoignition of JP-8 as a function of φ and H2O2 concentration at CR = 3.0.................................................................................................................................. 108
Figure ?5.13: Autoignition of JP-8 as a function of equivalence ratio and contraction ratio at a constant H2O2 concentration of 85%................................................................ 109
Figure ?5.14: Measured Td over the course of tests run at a) 90% H2O2 at φ = 1.59 and CR = 3.0 with GK bed and b) 98% H2O2 at φ = 1.84 and CR = 3.0 with PCI bed. 110
Figure ?5.15: Comparison in decomposition efficiency produced by GK and PCI catalyst beds using 90% H2O2 at approximately equivalent monoprop operating conditions.................................................................................................................................. 112
Figure ?5.16: Comparison in pressure drop across GK and PCI catalyst beds using 90% H2O2 at approximately equivalent monoprop operating conditions. ...................... 113
Figure ?5.17: Plot of the chamber pressure noise parameter against the dominant frequency during the monoprop mode each autoignition test................................. 114
Figure ?5.18: Plot of the chamber pressure noise parameter against the dominant frequency during the biprop mode each autoignition test....................................... 114
Figure ?5.19: Comparison of DMAZ autoignition points to those of JP-8 using the GK catalyst bed at a CR = 3.0. ...................................................................................... 117
Figure ?5.20: Autoignition of JP-8 as a function of equivalence ratio and decomposition temperature at a contraction ratio of 3.0. ................................................................ 119
Figure ?5.21: Autoignition of JP-8 as a function of pc2_tot_mono and decomposition temperature at a contraction ratio of 3.0. ................................................................ 120
xii
Figure Page
Figure ?5.22: Trajectory variations in tests run at a contraction ratio of 3.0.................... 122
Figure ?5.23: Trajectory variations in tests run at a contraction ratio of 5.0.................... 122
Figure ?A.1: Engine assembly using GK catalyst bed, page one. .................................... 138
Figure ?A.2: Engine assembly using GK catalyst bed, page two. .................................... 139
Figure ?A.3: Extension piece for GK catalyst bed, allows temperature and pressure measurement upstream of the fuel injector. ............................................................ 140
Figure ?A.4: Mounting plate for engine assembly using GK catalyst bed. ...................... 141
Figure ?A.5: Page one of transverse fuel injector drawing, indicates manifold dimensions.................................................................................................................................. 142
Figure ?A.6: Page two of transverse fuel injector drawing, indicates orifice dimensions.................................................................................................................................. 143
Figure ?A.7: Transverse fuel injector seat, the fuel feed line is attached to this piece..... 144
Figure ?A.8: Drawing of fuel film cooling injector seat, fuel feed line was capped for autoignition testing. ................................................................................................. 145
Figure ?A.9: Drawing of fuel film cooling injector, fuel was not flowed through this piece during autoignition testing. ..................................................................................... 146
Figure ?A.10: Page one of combustion chamber part drawing. ....................................... 147
Figure ?A.11: Page two of combustion chamber part drawing. ....................................... 148
Figure ?A.12: Page three of combustion chamber part drawing. ..................................... 149
Figure ?A.13: Page four of combustion chamber part drawing. ....................................... 150
Figure ?A.14: Drawing of nozzle piece with a contraction ratio of 3.0. .......................... 151
Figure ?A.15: Drawing of nozzle piece with contraction ratio of 5.0. ............................. 152
xiii
Figure Page
Figure ?A.16: Drawing of nozzle piece with contraction ratio of 6.5. ............................. 153
Figure ?A.17: Assembly drawing of water cooled deflection plate, water cooling apparatus not shown. ............................................................................................................... 154
Figure ?A.18: Engine assembly using PCI catalyst bed. .................................................. 155
Figure ?A.19: Mounting plate used for engine assembly using PCI catalyst bed, this piece was attached to the top of the catalyst bed.............................................................. 156
Figure ?A.20: Page one of drawing of transition piece between PCI catalyst bed and transverse fuel injector. This piece also allowed the measurement of pressure and temperature at the exit of the catalyst bed............................................................... 157
Figure ?A.21: Page two of drawing of PCI transition piece, indicates dimension of V-shaped groove for metal o-ring. .......................................................................... 158
Figure ?C.1: Plumbing & Instrumentation Diagram of Test Cell A at APCL. ................ 166
xiv
ABSTRACT
Sisco, James C. M. S., Purdue University, August, 2003. Autoignition of Kerosene by Decomposed Hydrogen Peroxide in a Dump Combustor Configuration. Major Professor: William E. Anderson.
In staged-bipropellant rocket combustors that use decomposed hydrogen peroxide as
the oxidizer, a liquid fuel is injected into the hot decomposition products comprising
oxygen and water vapor. The oxidizer is at a sufficiently high temperature to vaporize
and to autoignite the liquid fuel. Although the need for a separate ignition system is
eliminated with this configuration, two other issues arise: it is difficult to efficiently mix
a relatively small amount of liquid fuel into a large volumetric flow of oxidizer at the
performance-optimized mixture ratios of about eight; and the combustor design must
provide residence times sufficient for autoignition. The latter issue typically results in the
use of high combustion chamber contraction ratios with their attendant higher weight and
surface area cooling requirements. In this study a transverse injector was used in a dump
combustor configuration, which incorporates a rearward-facing step, to investigate the
autoignition characteristics of JP-8 in decomposed hydrogen peroxide. The goals of the
investigation were to develop a greater understanding of the autoignition process and, if
possible, develop autoignition model for a staged combustor. The chamber contraction
ratio was varied between three and five to evaluate the effects of chamber gas Mach
number, and the hydrogen peroxide concentration was varied from 85 to 98% to evaluate
the effects of oxidizer temperature. Results showed that as hydrogen peroxide
concentration and/or contraction ratio was increased the fuel-rich equivalence ratio which
defined the autoignition boundary increased as well. At a contraction ratio of 3.0, no
autoignition was achieved down to an equivalence ratio of 1.37 using 85% hydrogen
xv
peroxide, but at 98% hydrogen peroxide autoignition occurred up to an equivalence ratio
of 2.06. When the contraction ratio was increased to 5.0 autoignition was achieved at an
equivalence ratio of 1.38 using 85% hydrogen peroxide. More data is needed rega rding
the effects of pressure and decomposed gas Mach number to develop an accurate
autoignition model. However, the use of flame stabilization provided by the
rearward-facing step improved the autoignition range of the combustor according to past
engine data.
1
CHAPTER 1: INTRODUCTION Hydrogen peroxide and kerosene rocket engines have a long history of use in
propulsion systems dating back prior to World War II.1-3,11 Although the performance of
this propellant combination is not as high as liquid oxygen/liquid hydrogen, LOx/LH2, or
nitrogen tetroxide/mono-methyl hydrazine, NTO/MMH, systems it is still a very
appealing option for a number of reasons. Hydrogen peroxide, H2O2, is a very versatile,
highly reactive, high density, storable, and non-toxic oxidizer. The versatility of
hydrogen peroxide is, in a way, a result of its reactivity. It can be decomposed and used
as a monopropellant for reaction control, to drive a turbine, or as a pressurant. Kerosene
based fuels such as Jet-A, JP-8, and RP-1 are very commonly used in the aviation and
rocket industries. These fuels are also storable and non-toxic. An important feature of
this propellant combination is its high density specific impulse, which is defined as the
total impulse delivered per unit volume of propellant. The density specific impulse of
H2O2/kerosene when compared to typical rocket propellant combinations is exceeded
only by the NTO/MMH system. Table 1.1 outlines performance parameters of common
rocket systems operating at similar conditions.4,5
Spacecraft reaction control, RCS, and orbital maneuvering systems, OMS, have
typically used hydrazine and NTO/MMH rocket systems since the 1960’s.6 This was due
to the storability of the propellants, hydrazine’s high performance as a monopropellant,
and the fact that nitrogen tetroxide and mono-methyl hydrazine are hypergolic or ignite
on contact. These factors made hydrazine and NTO/MMH systems very simple and
reliable.6 However, all three propellants are toxic and corrosive while hydrazine is a
carcinogen. This creates significant safety hazards when trying to handle the propellants.
As a result, there is significant interest in developing rocket systems using non-toxic
propellants to replace hydrazine and NTO/MMH systems.6 There is also increased
2
interest to develop low cost, reusable satellite launch vehicles to replace the expendable
vehicles currently used in industry.19 Many of these expendable vehicles use toxic or
cryogenic propellants, such as liquid oxygen and hydrogen. Storable, non-toxic
propellants are also preferred for these launch vehicle applications for ease of handling
on the ground.
Table 1.1: Performance comparison of 90% H2O2/JP-8 system to common rocket propellant combinations. Specific impulse calculated assuming a chamber pressure of
1000 psia and equilibrium expansion to sea level pressure of 14.7 psia.
Oxidizer Fuel
90% H2O2 JP-8
NTO MMH
LOx LH2
LOx RP-1
Optimum O/F Ratio 7.8 2.2 3.5 2.6
Characteristic Velocity, C* (ft/s) 5300 5710 7940 5890
Chamber Temperature, Tc (°F) 4600 5650 4450 6160
Specific Impulse, Isp (sec)
267 288 386 300
Density Specific Impulse, Density Isp (sec) 344 346 101 308
Hydrogen peroxide and kerosene rocket systems have the potential to replace
their toxic and cryogenic predecessors. Table 1.1 shows that both NTO/MMH and
H2O2/kerosene systems have comparable density specific impulse, density Isp, and are
both higher than cryogenic systems. This means that per unit volume of propellant a
H2O2/kerosene systems offer similar if not superior performance compared to
conventional propellant combinations. On a per unit mass basis hydrogen peroxide
systems are not quite as good performers. As a monopropellant hydrogen peroxide has a
lower specific impulse, Isp, than hydrazine and a bipropellant H2O2/kerosene system also
has lower Isp than NTO/MMH, LOx/RP-1, and LOx/LH2. However, analyses have
shown that hydrogen peroxide/kerosene systems may be the most cost effective for future
launch vehicles regardless of mass-based performance.19
3
There are some technical issues associated with these bipropellant systems that
must be resolved to make it a viable replacement for NTO/MMH and current launch
vehicle propellants. Since NTO and MMH are hypergolic it makes the system very
simple in design, it is desired that a H2O2/kerosene system have similar simplicity as
well.6 Hydrogen peroxide and kerosene are not hypergolic by themselves, and there is
research being done make these propellants ignite on contact.6,7,12,13 Alternatively, an
H2O2/kerosene engine can operate in a staged configuration. In this configuration the
hydrogen peroxide is decomposed in a catalyst bed and the kerosene fuel is injected into
the hot decomposed gases. If conditions are correct the oxidizer/fuel mixture can
autoignite eliminating the need for a complex ignition system. However, autoignition is
dependent on a number of different factors such as fuel injector design, hydrogen
peroxide concentration, decomposed gas velocity, chamber pressure, and mixture
ratio.8-11 A better understanding of the autoignition process in these staged
H2O2/kerosene rocket engines is required. The goals of the research described in this
thesis include; outlining a design method for a staged engine injector, generating
experimental data on autoignition under varying engine operating conditions, and
creating a model to aid in the prediction of autoignition. Results of this research may
make the staged-bipropellant H2O2/kerosene rocket a lighter, more reliable, and higher
performing engine in the future.
1.1 Hydrogen Peroxide
Hydrogen peroxide is an inherently unstable chemical compound that
exothermically reacts, or decomposes, into hot oxygen gas and water vapor. Hydrogen
peroxide is miscible in water and is commercially manufactured as an aqueous solution in
a variety of concentrations. Concentrations are usually designated as percent H2O2 by
weight of solution. Propellant-grade H2O2, or HTP, is greater than 70% in concentration
and most modern engines tend to use 85, 90, or 98%. The decomposition rate of
propellant-grade H2O2 is less than 0.1% per year over normal atmospheric temperature
and pressure ranges.3 Decomposition is significantly accelerated as the temperature of the
4
H2O2 and/or its environment is increased and/or when the liquid is in contact with certain
materials or contaminants. These factors can potentially cause a chain reaction of
decomposition since the heat released during a reaction can provide the energy necessary
to decompose the surrounding H2O2 and so on. This is a very dangerous situation in most
cases, however, when controlled it can be advantageous quality. Table 1.2 outlines the
variation in physical and decomposition properties of hydrogen peroxide with
concentration.3,4
1.1.1 Benefits of Hydrogen Peroxide as a Propellant
There are many properties of hydrogen peroxide that make it an appealing choice
as an oxidizer in a rocket propulsion system.1 The density of hydrogen peroxide at a
concentration of 90%, for example, is equivalent to or greater than most common rocket
oxidizers. It has a specific gravity of approximately 1.4, see Table 1.2, whereas liquid
oxygen and nitrogen tetroxide have specific gravities of 1.14 and 1.44 respectively.5
High density propellants are extremely beneficial in rocket systems because more
propellant mass can be stored in a smaller volume. This generally reduces tank volume
and also system mass.
Table 1.2: Properties of liquid and decomposed hydrogen peroxide with concentration.3-5
Concentration 70 % H2O2 80 % H2O2 90 % H2O2 98 % H2O2 Liquid Properties (@ STP)
Molecular Weight 26.86 28.89 31.29 33.42 Specific Gravity 1.283 1.333 1.387 1.432 Boiling Point (F) 257 -- 287 299
Vapor Pressure (psia) 0.137 -- 0.065 0.045 Heat Capacity (Btu/lbm-R) 0.738 -- 0.663 0.633
Decomposed Gas Properties Temperature (F) 504 952 1393 1746
Molecular Weight 21.04 21.56 22.11 22.56 Specific Heat Ratio 1.315 1.287 1.265 1.251 Mass Fraction O2 0.341 0.376 0.423 0.461
Mass Fraction H2O 0.659 0.624 0.577 0.539
5
Hydrogen peroxide has a low vapor pressure, as Table 1.2 shows, on the order of
one-tenth of a psi. This is significantly lower than the vapor pressure of other common
oxidizers such as liquid oxygen, 735 psia at -193 °F, and nitrogen tetroxide, 110 psia at
160 °F.5 It is advantageous to use a propellant with a low vapor pressure in rocket
system for several reasons.1,14 In turbo-pump systems the propellant can be fed to the
pumps at a low pressure without risking cavitation. In addition, only a low absolute
pressure is required in the propellant tank to prevent the liquid from vaporizing. As a
result, use of a propellant with a low vapor pressure leads to low tank and system
pressures which reduce tank and system mass. Another attractive feature of hydrogen
peroxide is its high heat capacity, 0.66 Btu/lbm-R for 90% H2O2 as shown in Table 1.2.
This is comparable to the heat capacity of water, 1.0 Btu/lbm-R, which is considered a
very good coolant and is used for a number of applications. The high heat capacity of
hydrogen peroxide suggests that it would be an excellent coolant for a rocket system.
Hydrogen peroxide also possesses the properties of a storable propellant. It is a
stable liquid over a reasonable range of temperature and pressure, and it is sufficiently
non-reactive with tank material, when properly passivated, for significant lengths of time,
although the concentration will gradually decrease.1-3 It is considered to be a non-toxic
propellant as well. Toxic propellants are poisonous to humans through inhalation or
contact with the body tissue. However, hydrogen peroxide solutions and vapors are
irritating to body tissue. Solutions can cause skin burns and vapors can inflame the
respiratory tract, however, exposure is only lethal in extremely high doses especially
through ingestion.3
The most important feature of hydrogen peroxide as propellant is its reactivity.
The hot gases produced when H2O2 is decomposed contain a significant amount of
energy, see Table 1.2. This makes hydrogen peroxide an excellent monopropellant.
Monopropellant thrusters are typically used for low thrust applications such as reaction
control systems (RCS). Hydrogen peroxide of 85 or 90% concentration has been used in
RCS systems in the past, such as the Mercury space capsule, and new systems using
H2O2 are currently in development.1,27 These gases can also be expanded through a row
of turbine blades imparting its energy to generate turbine rotation. This is important
6
since many rocket systems use turbo-pumps driven by turbines to feed propellants to the
combustion chamber. Decomposed hydrogen peroxide could potentially be used as a
tank pressurant as well. The reactivity of H2O2 also makes it a versatile propellant that
can be used for a number of different propulsion systems. Using hydrogen peroxide as an
oxidizer in a bipropellant main engine as well as a monopropellant for reaction control
and turbine power eliminates the need for separate systems for each of these applications.
This greatly simplifies the overall propulsion system design.
1.1.2 Catalyst Bed Design
Hydrogen peroxide is typically decomposed using a catalyst bed. Most modern
catalyst beds consist of many layers of wire mesh screens, typically stainless steel or
nickel, coated with a catalyst material, typically silver.1,2 Initially, before ‘dry’ catalyst
beds were used, liquid catalysts such as potassium permanganate were injected with
liquid hydrogen peroxide to accelerate decomposition.2,6,11 These liquid catalysts worked
quite well however the need for separate systems for supplying the liquid catalyst made it
operationally cumbersome. Later, ‘dry’ catalyst beds used beads or pellets impregnated
with a catalyst material to react with the hydrogen peroxide.1,11 These catalyst beds also
worked well, but had a very limited operational life.11 A significant drawback to silver
plated catalyst beds is that they are limited to concentrations of approximately 92% or
less. At higher concentrations the decomposition temperature of the H2O2 exceeds the
melting temperature of silver, which is approximately 1760°F, and leads to screen
degradation. Catalyst beds have been tested with catalytic materials with higher melting
temperatures, such as platinum and silver-palladium, for use with up to 98% H2O2.28
In many cases only the first third to half of the screens are coated with silver.2
This is due to the unstable nature of the H2O2, as the peroxide begins to decompose on
the first few screens it releases hot gases. These hot gases heat the surrounding liquid
hydrogen peroxide and this H2O2 begins to decompose and so on. Thus as the hydrogen
peroxide makes its way through the catalyst bed screens the decomposition process relies
more and more heavily on thermal decomposition rather than catalyst material. This is a
7
very complex design dependent on a number of parameters such as hydrogen peroxide
concentration, bed loading (mass flow rate/cross-sectional area), screen mesh or open
area, screen wire diameter, catalyst coating process, and back pressure among others.28
Ideally a good catalyst bed design should produce highly decomposed peroxide at as
small of a pressure drop as possible such that it is still isolated from oscillations in back
pressure.
1.2 Background on Hydrogen Peroxide Bipropellant Engines
1.2.1 Hypergolic Bipropellant Engines
There are two main configurations that have been used in the past and that are
currently being considered for bipropellant hydrogen peroxide engines. The most
simplistic type is a hypergolic configuration whereby a fuel is used that ignites with
liquid hydrogen peroxide on contact in the combustion chamber. In fact, this
configuration was used on the first bipropellant rocket developed using hydrogen
peroxide in Germany in 1935.1,2,6,11 The purpose of this engine, developed by Hellmuth
Walter, was to provide additional thrust at takeoff for an early jet-powered aircraft, the
Messerschmidt 163B.2 At that time only 80% H2O2 was available and its decomposition
temperature was too low to ignite kerosene-based fuels. Therefore Walter developed a
fuel, called C-Stoff, consisting of 30% hydrazine hydrate and 70% methanol, which was
hypergolic with H2O2.2,6,11 Since that time hydrogen peroxide has become available in
higher concentrations. As a result, most engine designers chose to use decomposed
hydrogen peroxide as an ignition source rather than hypergolic fuels.
Recently there has been increased interest in developing rocket systems that use
fuels hypergolic with hydrogen peroxide to replace NTO/MMH systems. These fuels
have been mainly kerosene or methanol based containing additives that make them
hypergolic with H2O2.6,7,12,13 Typically, complex injector designs are required in these
hypergolic engines in order to adequately atomize the propellants. In addition, the
8
injector must deliver the propellants in such a way that they can mix readily. Recent
studies have used pintle, splash plate, and coaxial swirl designs to achieve the necessary
mixing and atomization.12,13 To this date there has been no hypergolic hydrogen peroxide
engine used in a flight-rated system.
1.2.2 Staged-Bipropellant Engines
The second major bipropellant configuration, and also the most often used to date,
is the staged design. This configuration uses a catalyst bed to decompose the hydrogen
peroxide creating hot oxygen gas and water vapor. Further downstream kerosene fuel is
injected into the high velocity gas where it is atomized, vaporized, and, under the correct
conditions, autoignited in the combustion chamber. This engine configuration grew in
popularity following the development of the silver screen catalyst bed.
1.2.2.1 Staged Engine Development in the United Kingdom
Work on these types of engines began in the United Kingdom, U.K., in the late
1940’s following World War II and was derived from the pre-war work done in Germany.
Early research centered on 80% H2O2 decomposed using catalyst stones and aviation
kerosene fuel.10,11 Much of this early development work was done to better understand
how these rocket systems operated and more importantly what conditions were necessary
for autoignition. By the end of 1950 silver screen catalyst beds had been developed and
were being used to decompose 80% hydrogen peroxide.10 These rocket systems were
designed to provide thrust augmentation for jet-powered manned interceptor aircraft and
to power ground-to-air missiles.2,11 Since the interceptor aircraft bearing these systems
were fueled by kerosene it was only logical to use kerosene as a rocket fuel as well.
Two engine classes came out of these early efforts in the United Kingdom were
designated as the KP and Gamma series. The KP-3 engine, developed for the Red Shoes
ground-to-air missile, used kerosene fuel and a silver screen catalyst bed to decompose
9
83% H2O2 and produced a maximum thrust of approximately 3300 lbf.11 The Gamma
class of engines was developed as a backup to the de Havilland Spectre engine, which
used H2O2 and kerosene, designed for the Saunders-Roe SR 53 interceptor.1,2 The early
Gamma engines used 85% H2O2 and silver screen catalyst beds.2,11 The Gamma class
was very successful and numerous variants of the engine were developed most notably
the Gamma 2, Gamma 201, Gamma 301, Gamma 304, Gamma 8, BS 606, and BS
625.1,14,15 Each of these engines was developed for use on the U.K.’s Black Knight re-
entry vehicle and/or the Black Arrow satellite launch vehicle. The engines ran on 85 or
87% H2O2 decomposed in a silver screen catalyst bed. These engines are considered the
highest performing hydrogen peroxide engines ever put into production.1 The Black
Arrow was the only launch vehicle, until the late 1990’s, ever to be developed using
hydrogen peroxide as its oxidizer. The U.K. drew on its wealth of experience, gained
from the late 1940’s through the early 1970’s, to produce these high performance
H2O2/kerosene engines. Gradually these engines were replaced by NTO/MMH,
LOx/RP-1, and LOX/LH2 systems. Currently, there is new work being done in the U.K.
to develop small thrusters for satellite propulsion using a staged-bipropellant design and
kerosene fuel.16,17
1.2.2.2 Staged Engine Development in the United States
In the United States, U.S., as in the U.K. work on hydrogen peroxide engines
began in the 1950’s to develop rocket-assist systems for jet-powered aircraft.1
Rocketdyne, through the U.S. Air Force, developed the AR series of engines that used
90% H2O2 and kerosene. The final result of this effort was the AR2-3 engine which
developed approximately 6000 lbf thrust and had impressive records of reliability and
reusability.1 Independently, at the same time Reaction Motors Incorporated, through the
U.S. Navy, developed the LR-40 engine for use on the F8U.1,18 This engine also used
90% H2O2 and kerosene fuel and generated somewhere between 3500 and 10000 lbf
thrust.18 As aircraft jet engines became more powerful these engines were gradually
phased out of use.
10
Bipropellant hydrogen peroxide engine research and development remained
dormant in the U.S. until the mid 1990’s. At that time low cost launch vehicles were in
demand to replace existing launch systems. Cost analyses, such as that done by Frazier
and Moser, showed that hydrogen peroxide/kerosene systems could be a less expensive
alternative.19 In 1998, Beal Aerospace was formed with a goal to develop both an
expendable and reusable satellite launch vehicle, named the BA-1 and BA-2R
respectively.20 Both launchers were of a three-stage configuration and used a
staged-bipropellant rocket design, using 90% hydrogen peroxide and kerosene, for each
stage.20 Testing began in 1998 with the first firing of the BA-44 third stage engine,
44,000 lbf vacuum thrust.21 Then, in early 2000, Beal ground tested its 810,000 lbf
vacuum thrust second stage engine, the BA-810.21 This engine was the second largest
liquid rocket engine fired in the United States since the Apollo program.21 The first stage
engine was designed to produce 4.1 million- lbf vacuum thrust and would have been the
largest rocket engine ever developed.21 However, in late 2000 the company was
dissolved due to financial reasons and Beal was never able to fire neither a launch vehicle
nor a first-stage engine.
At the roughly the same time the National Aeronautics and Space Administration,
NASA, commissioned the Orbital Sciences Corporation to begin development of a
10,000 lbf vacuum thrust hydrogen peroxide/kerosene stage-bipropellant engine for the
Upper Stage Flight Experiment, USFE.22,23 The purpose of the USFE was to focus on
key technical issues and to demonstrate the operation of a hydrogen peroxide/kerosene
system for a low cost liquid upper stage rocket system.23 Some of these key issues
included catalyst bed design for use with 90% H2O2, kerosene fuel injector design, and
ablative chamber design.22,23 Tests proved that the engine was able to meet project
requirements.23 Currently, the U.S. is still in the midst of staged-bipropellant engine
development and a complete system has yet to be flown.
11
1.3 Design of Staged-Bipropellant Engines
A staged-bipropellant rocket using hydrogen peroxide and kerosene has a number
of design related advantages. As previously described, in these staged engines the H2O2
is decomposed in a catalyst bed. Downstream of the catalyst bed liquid kerosene is
injected into the high velocity decomposed gas flow. The fuel is atomized and vaporized
creating a mixture of fuel vapor, oxygen gas, and water vapor. Depending on the
operating conditions the fuel/oxidizer mixture can autoignite in the combustion chamber.
A typical staged combustor design is shown in Figure 1.1. In this design all of
the decomposed hydrogen peroxide flows through a central gas or steam port. Liquid
kerosene is injected perpendicularly, or transversely, to the gas flow in the port through a
number of circumferentially arranged orifices. The momentum possessed by the gas
causes the liquid fuel jets to deflect and enhances atomization. Downstream of the fuel
injection point the gas port is suddenly expanded to match the combustion chamber
diameter. The expansion is commonly called a rearward-facing step. This step acts as a
flame holder and creates a recirculation zone that continually feeds reactants to the flame.
Figure 1.1: Typical staged-bipropellant engine using H2O2/kerosene. This is commonly called a ‘dump’ combustor configuration.
12
1.3.1 Advantages of Staged-Engines
1.3.1.1 Combustion Performance
An important aspect of the hydrogen peroxide/kerosene propellant combination is
its relatively flat characteristic velocity, C*, versus mixture ratio curve. Mixture ratio is
defined as the ratio of the oxidizer to fuel flow rate. Characteristic velocity is a measure
of propellant, or combustion, performance in the chamber independent of the rest of the
engine. The shape of the C* curve infers that a H2O2/kerosene system can provide
similar combustion performance over a wide range of mixture ratios. Figure 1.2 shows a
plot of C* versus mixture ratio for 90% H2O2/JP-8, NTO/MMH, LOx/RP-1, and
LOx/LH2.4 The figure shows that the 90% H2O2/JP-8 curve has a very flat, gradual peak
while the remaining propellants combinations have a sharp peak in their C* curves. The
decay of the curve for 90% H2O2/JP-8 at high mixture ratios is also less than the other
propellant combinations. This offers significant flexibility when designing a wall cooling
scheme for these engines. In a fuel or oxidizer film cooling scheme some of the fuel or
oxidizer is used as a buffer flow to maintain the chamber wall at a low temperature. A
majority of this propellant may not mix and combust with the core flow affecting the
overall reacting mixture ratio in the chamber. These small deviations in actual
combusting mixture ratio will not have a large affect on engine performance in a
hydrogen peroxide/kerosene system.
13
2000
3000
4000
5000
6000
7000
8000
0 2 4 6 8 10 12 14 16 18 20
Mixture Ratio, O/F (--)
Ch
arac
teri
stic
Vel
oci
ty, C
* (f
t/s)
90% H2O2/JP-8NTO/MMHLOx/RP-1LOx/LH2
Figure 1.2: Comparison of C* vs. mixture ratio curves of 90% H2O2/JP-8 to common rocket propellant combinations.4 C* calculated assuming a chamber pressure of 1000
psia and equilibrium expansion.
1.3.1.2 Injection Techniques
In many liquid- liquid systems impinging injector elements are required to atomize
and mix the propellants. These injectors perform very well, but require precise
machining and complicated design methods. In a staged engine design the high velocity
gas flow enhances the atomization of the liquid fuel. As a result a more simplistic
injector design, which in some cases may not provide as good atomization as an
impinging element, can be used to obtain similar engine performance. Good atomization
is important in a rocket engine because smaller fuel drops require less time to vaporize.
As a result, the fuel vapor and gaseous oxidizer have more time to mix and burn in the
chamber producing higher combustion performance. In the past designers have used
swirl, 8-10,24,25 gas port,15,29 or ring injector22,23 designs or combinations thereof. Figure
1.3 shows an engine schematic of a Gamma class engine.15 This engine uses a gas port
design with kerosene fuel injected at an angle to the gas flow from the downstream side
14
of the injector face. A picture of the injector is shown in Figure 1.4.15 There are 49 gas
ports in the injector and the fuel is well dispersed throughout the chamber by numerous
injection orifices located on the injector face. An injector design that was used in early
thermal ignition research done by Walder and Purchase is shown in Figure 1.5.11 This
injector uses a combination of injection concepts. A fuel swirl element is located in a
central gas port with a small mixing chamber downstream. A number of
circumferentially arranged orifices are used to inject a portion of the decomposed gases
perpendicularly to this central flow. The remaining gas flows through an array of large
gas ports located on the periphery of the injector. A thin annular gap located behind
these ports deflects the gas flow toward the center of the chamber.
Figure 1.3: Schematic of a Gamma class research engine indicating gas ports and fuel injection points.15
15
Figure 1.4: Picture of a Gamma class gas port injector.15
Figure 1.5: Early injector design used in thermal ignition research.11 This injector uses a
combination of basic injection concepts such as swirl and gas port injectors.
16
1.3.1.3 Thermal Benefits
Another advantage of this system that may often be overlooked is the relatively
low combustion temperature of the propellants even at the stoichiometric mixture ratio,
see Figure 1.6.4 Although a cooling scheme is still required in the chamber and throat to
prevent damage to wall materials, the overall heat load compared to LOx/RP-1, LOx/LH2,
and NTO/MMH systems may be significantly lower. This could make the lifetime of a
robustly designed H2O2/kerosene engine significantly longer than an engine using
industry standard propellants.
1000
2000
3000
4000
5000
6000
7000
0 2 4 6 8 10 12 14 16 18 20
Mixture Ratio, O/F (--)
Co
mb
ust
ion
Tem
per
atu
re, T
c (F
)
90% H2O2/JP-8NTO/MMHLOx/RP-1LOx/LH2
Figure 1.6: Comparison of chamber temperature vs. mixture ratio of 90% H2O2/JP-8 against other common propellant combinations.4 Combustion temperature calculated
assuming a chamber pressure of 1000 psia and equilibrium expansion.
17
1.3.1.4 Autoignition
An important benefit of a staged combustor is that the decomposed hydrogen
peroxide eliminates the need for a complex ignition system, such as a torch igniter.
Difficulties in obtaining ignition in the vacuum of space are reduced as well because the
decomposed H2O2 provides a pre-pressurized/pre-heated chamber environment prior to
fuel injection. However, a challenge exists in determining what engine operating
conditions and geometry are sufficient to cause autoignition. In some cases, designers
have found that the propellants will not ignite under certain temperature, pressure, and
chamber geometry conditions.8-10,17,22
1.3.2 Challenges in Staged Engine Design
1.3.2.1 Fuel Distribution and Thermal Management
There are also other challenges that arise when designing a staged-bipropellant
rocket using H2O2 and kerosene. Depending on the concentration of H2O2, the optimum
mixture ratio for this propellant combination is on the order of eight-to-one. This means
that 88% of the total mass in the combustion chamber is decomposed hydrogen peroxide.
A problem can arise, as a result, in distributing the relatively small amount of fuel
uniformly in the chamber. This is especially difficult when attempting to fuel film cool
the combustion chamber wall. Chamber cooling, or thermal management, is also a
problem associated with these engines. Due to the lack of large amounts of fuel
conventional cooling techniques are difficult.
An example of the thermal management problems associated with these engines
was encountered during the development of Orbital Sciences Corporation’s Upper Stage
Flight Experiment, USFE, hydrogen peroxide/kerosene engine.23 The engine design
utilized a silica phenolic chamber liner and as such a cool wall was required to prevent
18
severe ablation of the liner. A ring injector was developed to provide fuel film cooling
along the chamber wall.23 A picture of this injector is shown in Figure 1.7.23 The
injector design is quite complex and is an example of the types of injection techniques
required to keep a cool chamber wall in these engines. A variation of this injector was
used in a prior study using a ‘dump’ combustor configuration.22 In this study additional
kerosene fuel was injected axially along the chamber wall by orifices on the face of the
rearward step.22 A similar ‘dump’ combustor was developed for a rocket-based
combined cycle application and used an axial injector to provide fuel film cooling.26
The combustion chambers of the U.K.’s Gamma class H2O2/kerosene engines
were regeneratively cooled with hydrogen peroxide.14,15,29 This method of cooling is
potentially dangerous. The walls of the coolant channels can become too hot causing
local H2O2 decomposition in the passages. This phenomenon has been observed in the
U.K. in the past and had not caused any significant failures, but it has caused minor
structural and thermal damage to the coolant channels.2 Interestingly enough, the
decomposition temperature 85, 90, and 98% H2O2 are less than most common chamber
wall materials, such as copper and stainless steel. Alternate designs have be proposed
and tested where decomposed gases are used to provide wall film cooling.17,24
1.3.2.2 Performance and Weight
In the end, the low mass-based performance of these propellants may its biggest
disadvantage. The low specific impulse of this propellant combination translates to a
large mass of propellant. This increases structural weight and makes the overall system
very heavy. Catalysts beds, specifically screen beds, are typically heavy as well and their
weight scales with mass flow and chamber pressure. In the past these engines have had
uncommonly large combustion chambers as well. Nearly all past staged engines have
used long chamber lengths and high contraction ratios, which is the ratio of the chamber
to throat cross-sectional area. A paper by Wu et al reports the contraction ratios used by
several past engines at 4.0 or greater.22 A parameter that is commonly used to describe
the chamber geometry is characteristic length, L*. Characteristic length is defined as the
19
ratio of the chamber volume to the throat area. The characteristic lengths of past engines
have ranged from 30 to 75 inches.17,22,25 The propellant mixture requires significant time
in the chamber to vaporize and react necessitating a long chamber and low gas velocity.
This not only a problem from the stand point of chamber weight but it also creates a
larger chamber area to cool.
Figure 1.7: Picture of USFE ring injector.23 The tubes and crescent-shaped manifolds
are used to feed fuel along the chamber wall.
20
CHAPTER 2: INJECTOR DESIGN
In a staged H2O2/kerosene engine simple injection concepts can be designed to
use the decomposed gas flow to enhance fuel atomization. In the past swirl injectors
have seen extensive use in staged engine systems.8-10,24,25 One reason for this is that the
swirl injector produces a thin hollow cone-shaped spray of liquid fuel that is finely
atomized by the decomposed gas flow. In addition, these injectors also have a well
established design methodology.31-33 The geometry of the swirler directly influences the
velocity, thickness, and cone angle of the fuel spray. In a typical design the swirl
geometry is contained in the center of the combustion chamber acting as a bluff body.
Decomposed gas flows co-centrically around the swirler section (sometimes referred to
as a swirl-coaxial design). This bluff body creates a recirculation zone and acts as a
flame stabilizer. An interesting benefit to this injector is it ability to keep the wall of a
combustor cool without additional injector hardware.24 Since the decomposed peroxide
flows along the outside of the injector, or the inside wall of the chamber, it acts as a film
coolant protecting the wall from the hot combustion gases.
Another simple injector design that was used in Gamma class engines is the gas
port injector.15,29 In this design the decomposed gas flows through multiple ports having
large cross-sectional areas. Liquid fuel is injected into the gas flow from orifices located
on the walls of the gas ports or on the injector face. These injectors rely heavily on the
decomposed gas for atomization. A variation of this design is the transverse or crossflow
injector, which has also been used in the past.22 In a typical transverse injector design
multiple jets of liquid fuel are injected normal to the flow of decomposed gas. Drag
forces are exerted on the liquid jet by the gas as it tries to flow around it. These
aerodynamic forces cause the liquid jet to be deflected changing the bulk liquid trajectory.
Numerous empirical studies have been performed to attempt to predict the trajectory of
21
the liquid stream in non-reacting flow situations.34-36 Past experience has also shown that
jet trajectory can have an effect on engine performance.30 Drag forces create
aerodynamic instabilities along the surface of the liquid jet eventually causing jet breakup
and the formation of ligaments and droplets. Jet breakup can be classified into several
regimes,35,37,38 and empirical relations for average drop size have been developed.39,40 A
rearward-facing step is typically used in tandem with this type of injector configuration.
The step acts as a flame-holder creating a recirculation zone that promotes mixing and
combustion at relatively low velocity. This type of combustor configuration is usually
referred to as a dump combustor. Experimental and theoretical studies have identified an
optimal step height at which one obtains highest combustion efficiency.41-43
The transverse injector was chosen for this autoignition study because of its
heritage, simple design, and well characterized performance. This chapter will explain
the models and analyses used to design a transverse injector for a staged-bipropellant
rocket engine. The theory and methodology used to size the rearward-facing step is
discussed as well.
2.1 Engine Design
The staged combustor that was used for this autoignition study was initially
developed for a Rocket-Based Combined Cycle, RBCC, application.26 In this design a
silver screen catalyst bed was used to decompose 90% H2O2 and JP-8 was used as the
fuel. Design requirements called for a ten-second test firing of the engine. To achieve
this without damaging the combustion chamber and nozzle the engine was designed to
incorporate fuel film cooling, FFC. Two injectors were used; a transverse injector to
provide the core fuel flow and an axial injector to provide the film cooling flow. The
axial injector provided the geometry to create a rearward-facing step for flame
stabilization. The engine design is shown in Figure 1.1. The operating and geometrical
parameters of the RBCC engine are shown in Table 2.1. Mass flow and chamber
pressure conditions for the engine were used as a baseline for the injector design used in
this autoignition study.
22
Table 2.1: RBCC engine operating conditions. 26
Chamber Pressure (psia) 525 Core Mixture Ra tio (--) 5.0
Overall Mixture Ratio (--) 2.0 90% H2O2 Flow Rate (lbm/s) 2.23 Core JP-8 Flow Rate (lbm/s) 0.45 FFC JP-8 Flow Rate (lbm/s) 0.65
Chamber Diameter (in) 2.56 Chamber Length (in) 7.70 Contraction Ratio (--) 6.5 Expansion Ratio (--) 5.0
Thrust (lbf) 600
2.2 Transverse Injector Design Considerations
A schematic illustrating the important design parameters of the transverse injector
is shown in Figure 2.1. These parameters include the diameter, do, number, No, and the
length, lo, of the fuel orifices as well as the cross-sectional area of the fuel manifold, Am,
the fuel velocity exiting the orifice, Vf, the velocity of the decomposed gases, Vox, the
diameter of the gas port, Aox, the rearward step thickness, h, and the distance between the
injection point and the edge of the step, ls. A number of design considerations contribute
to determining a final value for each of these variables. One of the primary goals of the
design is to ensure that the injector delivers a reasonable jet trajectory and good
atomization. In addition, the injector must provide sufficient pressure drop to avoid
instabilities resulting from pressure fluctuations in the chamber. Also, the
rearward-facing step must be large enough to provide adequate flame holding but not so
large as to produce a large pressure loss. The transverse injector design methodology
described here centers around all three of these requirements.
23
Figure 2.1: Schematic of a transverse injector indicating important design parameters.
2.2.1 Orifice Sizing
Sizing of the fuel orifices begins by considering the pressure drop across the
orifice. As previously discussed the pressure drop across the injector is an important
parameter in a transverse injector design, or any other injector design for that matter.
Typically, the pressure drop is set to be 20% of the expected engine chamber pressure to
prevent combustion instabilities from affecting injector performance.44 The design
chamber pressure of the staged engine used in this study is about 525 psia, see Table 2.1,
which puts the design injector pressure drop at approximately 100 psid. The equation for
the pressure drop across an injector orifice is derived from Bernoulli’s equation.
Assuming no losses and neglecting gravity Bernoulli’s equation gives the following:
022
22
=−−+ i
f
ie
f
e VpVpρρ
, (2.1)
The properties at the inlet of the orifice are denoted with the subscript ‘i’ and
those at the exit with the subscript ‘e’. The cross-sectional area of the injector manifold
is typically designed to be much larger than that of the injector orifice to produce a very
low fuel velocity in the manifold. Therefore, for this analysis the inlet velocity, Vi, is
24
assumed to be zero. Equation 2.1 can then be solved for the pressure drop, ?pf, across
the injector orifice:
2
21
efeif Vppp ρ=−=∆ , (2.2)
Here ?f is the fuel density which is approximately 50.6 lbm/ft3 at room
temperature.47 Note that the right-hand side of equation 2.2 represents the dynamic
pressure of the fuel exiting the orifice. Since the design pressure drop has been set and
the fuel density is also known equation 2.2 can be solved for the fuel velocity. The
effective orifice area, ∗oA , is related to the fuel velocity through the mass flow rate
equation: ∗= offf AVm ρ& , (2.3)
The fuel velocity at the exit of the orifice is shown as Vf in equation 2.3 and will
be used in the remainder of the analysis to replace Ve. Fuel mass flow rate is denoted
here as fm& and is set for this injector design, see Table 2.1. Therefore, equation 2.3 can
be used to solve for the required effective orifice area. The reason why it is called the
effective orifice area is due to the fact that the velocity profile of the liquid exiting the
orifice is non-uniform. Typically the physical orifice area is multiplied by a constant
called the discharge coefficient, CD, to account for this effect. As a result of this
phenomenon the effective orifice area is related to the physical orifice area as follows:
2
4 ooDoDo dNCACAπ
==∗ , (2.4)
There are an infinite number of combinations of both orifice diameter and number
of orifices that could be used to satisfy a particular total effective area requirement. One
method of proceeding is to specify the number of orifices and then calculate the diameter.
In many cases the diameter that results may need to be modified slightly to match a
common drill bit diameter. If this is required it is advisable to go backwards through the
calculations to determine the pressure drop using the modified diameter. To be
conservative it would be better to adjust to a smaller diameter to make the actual pressure
drop slightly larger to avoid instability.
25
2.2.1.1 Discharge Coefficient
When a liquid enters an orifice from a large manifold it can separate from the
walls of the orifice creating a recirculation zone. In some cases the liquid does not
reattach before it is expelled from the orifice or if it does reattach a sizable boundary
layer exists. This effect is largely dependent on the orifice inlet geometry. The boundary
layer creates a non-uniform velocity profile in the orifice which remains when the liquid
is expelled from the orifice. The physical orifice area is multiplied by a constant term
called the discharge coefficient to account for non-uniform exit velocity.
The discharge coefficient for a full- flowing circular orifice is dependent on its
inlet type and length. Well-rounded inlets with a radius of one-half of the orifice
diameter or greater produce discharge coefficients approaching unity.44 For square-edged
inlets the discharge coefficient is primarily a function of the orifice length. Figure 2.2
shows the variation in discharge coefficient for a full- flowing orifice with a square-edged
inlet as a function of orifice length over diameter, lo/do.44
As this factor approaches a
value of 3.0 the discharge coefficient steadies out to a value of approximately 0.8. This
value is used a first approximation in the present analysis. Typically, an injector is
water-flowed to determine the actual discharge coefficient of its orifices.
Note that for a square-edged orifice the discharge coefficient does not reach unity.
Although the flow is attached to the wall for these high lo/do orifices a sizable boundary
layer still exists causing the velocity profile at the orifice exit to be largely non-uniform.
The flow through a well-rounded inlet follows the wall very smoothly and a very minimal
boundary layer is created resulting in a nearly uniform velocity profile at the exit.
Chamfered or gradually contracting inlets such as that shown in Figure 2.1 are also used
to reduce inlet losses.
26
Figure 2.2: Dependence of discharge coefficient on orifice length over diameter ratio for a full flowing square-edged inlet.44
2.2.1.2 Manifolding
In a multi-orifice transverse injector such as that shown in Figure 2.1 manifolding
the liquid properly is an important issue. It is crucial that the pressure losses in the
manifold be kept to a minimum to keep the injector feed pressure low. High feed
pressures require high tank pressures and generally make system operation more difficult.
Typically a ring manifold fed by a single orifice (or downcomer) is used. A low
downcomer exit velocity is required to minimize pressure loss as the fuel enters the
manifold. In addition, the downcomer should be aligned between two injector orifices to
supply uniform flow to the remaining orifices, as shown in Figure 2.1. The velocity in
the manifold should also be low to minimize pressure loss and to provide uniform flow.
A common rule of thumb is to make the cross-sectional area of the manifold ten times
that of the total orifice area. This will guarantee the manifold velocity to be sufficiently
low. Poor distribution of liquid will lead to unstable engine performance during startup
and shutdown and hot streaks along the combustor wall.
27
2.2.2 Decomposed Gas Flow Calculations
The decomposed gas flow properties must also be determined to calculate the
trajectory of the fuel jet. Hydrogen peroxide decomposition products consist of high
temperature oxygen gas and water vapor. In this analysis the decomposition products are
treated as an ideal gas mixture. Since the Mach number of the gas may be in the high
subsonic regime it is treated as a compressible fluid and compressibility effects are
included in the design equations. The most important part of this analysis is to determine
the velocity and Mach number of the decomposed gas. For now, it is assumed that the
flow area of the gas, Aox, is known. In fact, the flow area is set through flame
stabilization requirements. The oxidizer flow rate, oxm& , can be described using the mass
flow rate equation:
oxoxoxox AVm ρ=& , (2.5)
Unlike the liquid fuel the gas density is not a constant but is a function of the
static pressure and temperature of the decomposed gases. Using the ideal gas law the
following equation is used to determine the gas density, ?ox, for subsonic flow:
oxu
oxoxox TR
MWp=ρ , (2.6)
Here pox is the static pressure, Tox is the static temperature, and MWox is the
molecular weight of the decomposed gas. The universal gas constant is represented by Ru
and is equal to 1545 ft- lbf/lbm-mol-°R. An alternate form of equation 2.6, which
includes compressibility effects, can be found using the isentropic relations for stagnation,
or total, properties of ideal gases. Using the isentropic relation for total density, ?tox,
equation 2.6 becomes:
11
21
1
2
21
12
11
−−−−
−
+=
−
+=γγ γγ
ρρ oxtoxu
oxtoxoxtoxox M
TRMWp
M , (2.7)
Total properties are represented by a subscript ‘t’ while Mox is the gas Mach
number and ? is the specific heat ratio of the decomposed gases. Going back to equation
28
2.5 the velocity of the decomposed gas can be alternately expressed using the definition
of the Mach number and the speed of sound:
ox
oxuoxoxoxox MW
TRMaMV
γ== , (2.8)
The speed of sound in the decomposed gas is represented by aox. Substituting the
isentropic relation for total temperature the gas velocity is as follows:
21
2
21
1−
−
+== oxox
toxuoxoxoxox M
MWTR
MaMVγγ
, (2.9)
Substituting equations 2.7 and 2.9 into equation 2.5 and rearranging gives the
following result:
( )( )12
1
2
21
1−
+−
−
+==γ
γγ
γ oxoxox
toxu
oxtox
oxox MM
MWTR
Apm
M&
, (2.10)
Each of the parameters on the left-hand side of equation 2.10 is a known quantity.
Decomposed gas mass flow rate and flow area are set. The terms under the square-root
are properties of the decomposed gas and can be determined using a thermo-chemistry
code, these properties are dependent on H2O2 concentration.4 The total pressure of the
decomposed gas can be set equal to the chamber pressure of the engine. This assumes
that the gases do not suffer a total pressure loss as they expand around the
rearward-facing step. The chamber pressure can be calculated using the following
equation:
ct
totthCctox gA
mCpp
&∗
== *η, (2.11)
Here pc is the chamber pressure, ∗thC is the theoretical characteristic velocity
determined using a thermochemistry code, ?C* is the assumed combustion efficiency,
totm& is the total mass flow rate, and gc is the gravitational constant. An iterative method,
such as Newton’s method, can be used to solve equation 2.10 for the gas Mach number
since all the other parameters are known. Once the Mach number has been calculated it
can be used in equations 2.7 and 2.9 to solve for the gas density and velocity
respectively.
29
It is important to note that the total pressure of the oxidizer will change when fuel
is injected into the chamber. In other words, during bipropellant operation the total mass
flow rate will include the fuel flow rate and the characteristic velocity will change as well.
Using the baseline conditions and assuming a combustion efficiency of 98% the chamber
pressure with decomposed gas flow only is about 265 psia, this is also called
monopropellant operation. During bipropellant operation using baseline conditions and
an efficiency of 98% the chamber pressure rises to 533 psia. This demonstrates the
significant change in gas pressure depending on the operating mode of the engine.
2.2.3 Rearward-Facing Step Sizing
The rearward-facing step serves as a flame stabilization mechanism in the
combustion chamber. It creates a recirculation zone that feeds the incoming mixture of
fuel vapor and decomposed gases with hot products to sustain the combustion reaction.
In addition, a turbulent shear layer exists between the free-stream and the recirculating
flow creating large-scale turbulent eddies. A photo of this interaction is shown in Figure
2.3.45 It has been suggested that these hot eddies must ignite before they are cooled by
the free-stream flow or the flame will blow-off.42 Therefore, the turbulent mixing time
must be maximized to create a stable flame.
Figure 2.3: Reacting flow behind a rearward-facing step showing turbulent eddies.45
30
The turbulent mixing time is usually taken to be equal to the characteristic
breakdown time of the eddies.42 Knowledge of the characteristic length scale of the
turbulent eddies is required to determine the breakdown time. Experimental results have
shown that the length scale is be equal to the width of the flameholder.42 Using the
notation of Figure 2.1 the flameholder width is equal to twice the height of the
rearward-facing step, 2h. The shear layer characteristic time, t sl, can then be written as:42
gV
hsl
2=τ , (2.12)
Vg is the gas velocity at the edge of the step. The gas velocity is not equivalent to
the velocity of the decomposed gases, Vox, since a mixture of fuel vapor and decomposed
gas exists at the edge of the step. To determine an optimum value for the height of the
step some manipulations must be made to equation 2.12. Using the mass flow equation
the gas velocity can be written as:
oxg
totg A
mV
ρ&
= , (2.13)
Compressibility effects are eliminated by assuming subsonic flow in this analysis.
The oxidizer flow area can be rewritten in terms of the chamber diameter, Dc, and the
step height:
( )224
hDA cox −=π
, (2.14)
Substituting equations 2.13 and 2.14 into equation 2.12 results in the following:
( )222
hDhm c
tot
gsl −=
&
ρπτ , (2.15)
Assuming that the gas density and the total mass flow rate are not functions of the
step height the derivative of equation 2.15 with respect to the step height is:
( ) ( )[ ]hDhhDmdt
dcc
tot
gsl 2422
2 −−−=&
ρπτ, (2.16)
Setting the derivative equal to zero and solving for step height gives the following
relation for the optimum step height, hopt:
31
6c
opt
Dh = , (2.17)
The second derivative of equation 2.15 is taken to confirm that this step height
does indeed maximize the shear layer characteristic time:
( )[ ]hDhDmdh
dcc
tot
gsl 1642422
2
+−−−=&
ρπτ, (2.18)
Substituting equation 2.17 into equation 2.18 for all h:
tot
gc
sl
mD
dhd
&
ρπ
τ2
2
2
−= , (2.19)
The second derivative at hopt is negative meaning that the shear layer
characteristic time curve is concave downward or a maximum at that point. This
confirms that equation 2.17 does represent the value of the optimum height for a
rearward-facing step. This result has been derived mathematically by others and
confirmed through experimental results.41-43 The relation for optimum step height was
used to size the rearward step in this autoignition study.
A dimensionless geometric parameter, called blockage ratio, BG, is often used to
describe the size of the obstruction created by the rearward step in the flow path of the
gas:
c
oxc
AAA
BG−
= , (2.20)
Combustion chamber cross-sectional area is denoted as Ac. The optimum
geometric blockage ratio assuming the step height described in equation 2.17 is 0.56 for
this injector configuration. This means that the rearward-step takes up over 50% of the
total chamber flow area.
Another parameter of interest concerning the rearward-facing step is the length of
the recirculation zone. This has been studied both numerically and experimentally in
both reacting and non-reacting flows.45,46 Typically the flow reattachment length, la, is
specified in terms of number of step heights downstream of the face of the step. For
non-reacting flows the reattachment length is 6 to 8 step heights downstream of the step
face.45,46 In a reacting flow situation the reattachment length drops to 4 to 6 step heights
32
downstream.45,46 This averages at an attachment length of approximately one chamber
diameter downstream assuming an optimum step height.
2.2.4 Trajectory Model
There has been a good deal of past research aimed to predict the trajectory of a
liquid jet injected transversely into a crossflow of subsonic gas in non-reacting systems.
Lin et al34 summarized and compared many of the empirical correlations as well as the
measurement techniques used to obtain them. One must exercise caution when using
these empirical correlations in reacting flow situations. This is especially true following
the breakup of the liquid column into ligaments and droplets where vaporization begins
to play important role, i.e., high x/do.
Unfortunately, many experimental studies undertaken to develop jet trajectory
correlations are done far from the injection point, high x/do (> 50).34 A study done by Wu
et al35 evaluated jet trajectory at x/do < 10 using a range of liquids. The testing was
conducted over a wide range of liquid and gas flow conditions as well. Wu et al’s
correlations are most applicable to reacting flow situations encountered in rocket
combustors for these reasons.
The trajectory for a liquid jet in crossflow, from Wu et al, is stated as follows:
oDjo dx
QCd
y π= , (2.21)
Here x and y are the axial and transverse directions respectively, CDj is the drag
coefficient of the liquid jet, and Q is the liquid to gas momentum ratio. Wu et al also
developed a correlation for determining the drag coefficient for any liquid based on its
viscosity:35 364.0
984.0
=
w
f
Dw
Dj
C
C
µ
µ, (2.22)
CDw is drag coefficient for water, µw is the viscosity of water, and µf is the
viscosity of the liquid of interest. Wu et al determined the drag coefficient of water to be
33
1.51.35 At room temperature the viscosity of water is 1.87*10-5 lbf-s/ft2 while the
viscosity of JP-8 fuel is 2.56*10-5 lbf-s/ft2.47 Using these properties the drag coefficient
for a JP-8 fuel jet is 1.67. Substituting this result into equation 2.21 the trajectory of a
JP-8 jet is described by the following equation:
oo dx
Qdy
37.1= , (2.23)
It is important to note that the jet trajectory is primarily dependent on the liquid to
gas momentum ratio. The higher the momentum ratio the greater the jet will penetrate
into the gas stream at a given axial position. The momentum ratio for this analysis is
defined as:
2
2
oxox
ff
V
VQ
ρ
ρ= , (2.24)
Each of the parameters needed to determine momentum ratio can be calculated
using equations 2.2, 2.7, and 2.9.
2.2.4.1 Jet Breakup
A fuel jet exiting from the orifice of a transverse injector relies heavily on the gas
flow for atomization. Considerable work has been done in analyzing the primary
atomization or breakup processes of a nonturbulent liquid jet.35,37,38 In general there are
two parameters which are most important in dictating the jet breakup regime; the
momentum ratio and the Weber number. Weber number, Wegd, is a non-dimensional
variable relating aerodynamic forces of the free-stream gas to the surface tension forces
of the liquid and is defined here as:
f
ooxoxgd
dVWe
σρ 2
= , (2.25)
The surface tension, s f, of JP-8 fuel is approximately 1.57*10-3 lbf/ft. There are
four generally accepted primary breakup regimes for nonturbulent jets separated by
Weber number.35,37,38 According to Mazallon et al37 at Wegd < 5 aerodynamic forces are
34
small compared to surface tension forces in the liquid column. Instabilities within the
liquid column itself will dominate in this regime, which is referred to as the column
breakup regime. As Weber number increases the aerodynamic forces play a greater role.
In the bag breakup regime, 5 < Wegd < 60, the liquid column deforms into large baglike
structures with interconnecting liquid columns. Multimode breakup occurs at 60 < Wegd <
110 where the column is broken into baglike droplets and liquid ligaments are formed
due to shearing forces acting on the perimeter of the column. At Wegd > 110, the shear
breakup regime, aerodynamic forces are dominant and liquid ligaments are stripped from
the liquid column. Wu et al35 also investigated the different primary jet breakup regimes
noting that at large momentum ratios surface breakup occurs before breakup of the liquid
column. Wu et al also found that the breakup point in the trajectory of a nonturbulent jet
always occurs at an x/do = 8.0.35 This was also confirmed by Salaam et al.38 This result
can be used as a guideline during transverse injector design. It is preferred that the fuel
jet undergo breakup and begin to vaporize prior to passing the rearward-facing step. To
guarantee this the edge of the rearward step should be at least eight step heights
downstream of the fuel injection point.
2.2.4.2 Drop Size
Much work has also been done in determining empirical correlations for average
drop size in a crossflow injection scheme. Ingebo39 developed two mass median drop
diameter (MMD) correlations based on the column wave regime, i.e. capillary or
acceleration waves. Hautman and Rosfjord40 developed an empirical MMD correlation
using Malvern analysis techniques that was dependent on gas density, gas velocity, and
liquid surface tension. Hautman and Rosfjord compared the developed correlation to past
MMD empirical correlations including that of Ingebo. This comparison served mainly to
investigate the various exponents used on the density, velocity, and surface tension terms.
Kihm et al48 developed a correlation for Sauter mean drop diameter (SMD) based on flow
properties as well as axial and transverse position downstream of the injection point.
35
Due to the multiplicity of jet breakup regimes and limits in measurement
techniques there are no completely comprehensive drop size correlations. However,
according to Hautman and Rosfjord many of the past drop size correlations for liquid jets
in a crossflow use a similar dependency:
pox
nox
mf
VCSMD
ρ
σ∝ , (2.26)
Here C, m, n, and p are all constants. This equation shows that drop size is
directly proportional to surface tension and inversely proportional to gas density and
velocity. The denominator term is similar in form to gas momentum or dynamic pressure,
which is normally defined as ρoxVox2. According to Hautman and Rosfjord, the constant
exponent p is larger than n making the gas velocity the more dominant factor in
determining drop size. This result can be used to qualitatively compare the atomization
of a transverse jet operating under varying flow conditions.
2.2.5 Baseline Injector Design
The important fuel flow parameters and fuel geometry for the transverse injector
design used in this study are shown in Table 2.2. Twelve orifices were chosen for this
design to provide significant fuel distribution. Assuming an orifice discharge coefficient
of 0.8 and designing for a pressure drop of 100 psid an orifice diameter of 0.0355 inches
was required to provide the necessary effective area. A final orifice diameter of 0.036
inches was chosen to match a common drill bit diameter, which slightly decreased the
design pressure drop to 94 psid. Due to design limitations the cross-sectional area of the
injector manifold came out to be approximately seven times the total orifice area
resulting in a manifold velocity of about 15 ft/s. The manifold velocity is significantly
lower than the velocity of the fuel exiting the orifice, 130 ft/s, and should not produce any
significant pressure loss. In addition a 45° contraction was used to smoothly transition
the fuel from the manifold to the orifices. The orifice length came out to be slightly
greater than four times its diameter putting the discharge coefficient close to 0.8
according to Figure 2.2. Dimensioned injector drawings are contained in Appendix A.
36
Table 2.2: Fuel orifice and manifold geometry of transverse injector design including flow parameters at baseline operating conditions.
Fuel Mass Flow Rate, fm& (lbm/s) 0.45
Fuel Density (JP-8), ?f (lbm/ft3) 50.6
Number of Orifices, No 12
Orifice Diameter, do (in) 0.036
Assumed Discharge Coefficient, CD 0.80
Orifice Exit Velocity, Vf (ft/s) 131
Orifice Pressure Drop, ?pf (psid) 93.9
Orifice Length/Diameter Ratio, lo/do ~ 4.0
Manifold Area/Orifice Area Ratio, Am/Ao ~ 7.0
Table 2.3: Oxidizer port geometry and flow parameters in baseline monopropellant and bipropellant operational modes.
Chamber Diameter, Dc (in) 2.56
Oxidizer Port Diameter, Dox (in) 1.707
Rearward Step Height, h (in) 0.427 Orifice-to-Step Distance, ls (in) 1.75
Monopropellant Bipropellant Oxidizer Mass Flow Rate, oxm& (lbm/s) 2.23 Gas Mach Number, Mox 0.21 0.10
Gas Velocity, Vox (ft/s) 473 235
Gas Density, ?ox (lbm/ft3) 0.290 0.594
The oxidizer port geometry and decomposed gas flow parameters for
monopropellant, monoprop, and bipropellant, biprop, operation of this injector are shown
in Table 2.3. Using equation 2.17 and a chamber diameter of 2.56 inches, from Table
2.1, the optimum step thickness was determined to be 0.427 inches. This set the oxidizer
port diameter, Dox, at 1.707 inches. Breakup of the fuel jet should occur approximately
0.30 inches downstream of the injection point from the finding of Wu et al and Salaam et
al.35,38 The edge of the rearward step was located 1.75 inches downstream of the
injection point due to the presence of the axial injector. This is approximately 50 orifice
37
diameters downstream which should give the jet significant time to atomize and vaporize.
A schematic of the injector assembly including some important dimensions in shown in
Figure 2.4, dimensioned hardware drawings are contained in Appendix A. The solution
for the gas flow properties depends on the mode of engine operation and the properties of
the decomposed gas, which are shown in Table 1.2. As Table 2.3 shows the gas velocity
decreases by half, from 470 to 235 ft/s, and the density doubles upon switching from
monoprop to biprop mode.
Figure 2.4: Schematic of injector assembly indicating important geometry and dimensions. All dimensions are in inches.
Figure 2.5 compares the fuel jet trajectory produced by this transverse injector in
monoprop and biprop mode. The plots show the variation in trajectory with changes in
gas velocity. In monoprop mode the fuel- to-oxidizer momentum ratio is 13.4 while in
biprop mode it increases to 26.5. This suggests, as Figure 2.5 shows, that the fuel
penetrates deeper into the gas flow in bipropellant mode. The vertical line in Figure 2.5
indicates the axial position of jet breakup. The trajectories produced in both operational
modes intersect after the breakup point. The Weber numbers in monoprop and biprop
modes are approximately 3850 and 1950 respectively. According to the Mazallon et al37
38
this puts the jet breakup well into the shear regime. Since the gas velocity is higher in
monoprop mode it suggests that the average fuel drop size is smaller than during biprop
operation.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Axial Direction, x (in.)
Tra
nsv
erse
Dir
ecti
on
, y (
in.)
Biprop TrajectoryMonoprop TrajectoryAxial Fracture PointChamber WallsChamber Centerline
Figure 2.5: Comparison between JP-8 jet trajectories produced by transverse injector design during monoprop and biprop operation. Fuel orifices are located at x = 0, y =0 and
x = 0, y = 1.707 inches centerline is at y = 0.854 inches.
Typically staged-bipropellant engines operate in monoprop mode prior to fuel
injection. From the point at which the fuel is injected until the combustion reaction
occurs in the chamber to increase the chamber pressure the fuel will follow the monoprop
trajectory curve. (There will be a slight chamber pressure rise due to fuel vaporization
but it does not alter the trajectory significantly). As a result the monoprop trajectory is
crucial in dictating the initial atomization characteristics of the flow and could potentially
affect autoignition as well. It is important that the trajectory be monitored very carefully
such that fuel penetration is not too small or too large, especially at off-design conditions.
If the momentum ratio is too small the liquid will not be dispersed well within the
chamber and will tend to hug tightly to the chamber wall causing a fuel-rich periphery
39
and an oxidizer-rich core. If the momentum ratio is too large the streams will collide and
coalesce at the centerline of the chamber, resulting in a fuel-rich core and possibly poor
vaporization. This can be seen in Figure 2.5 downstream of the breakup point. Both
cases result in poor dispersion of the liquid within the chamber and a significant decrease
in performance. Data obtained by Helms et al30 using two different transverse injector
designs flowing H2O2 showed performance losses when trajectory analysis indicated
liquid stream collision. Analysis of the predicted trajectories shows that opposing fuel
jets do not appear to collide prior to breakup while fuel penetration seems to be sufficient
enough to produce reasonable fuel dispersion.
40
CHAPTER 3: AUTOIGNITION
One of the primary advantages of a H2O2/kerosene staged-bipropellant rocket
engine is that the hot decomposed hydrogen peroxide gases can be used as an ignition
source. This eliminates the need for a separate ignition system, such as a torch igniter,
and greatly reduces the complexity of the engine. One drawback to this ignition
approach is that the conditions required for autoignition are not well understood. Past
research has shown that autoignition of kerosene in decomposed hydrogen peroxide is
dependent on temperature, pressure, gas velocity, and injector design.8-11,17,22 This
chapter will attempt to outline the basics of autoignition in hopes of creating a better
understanding of the process occurring in a staged engine. In addition past work on
autoignition of kerosene in air will be discussed as well as autoignition studies of
kerosene in decomposed hydrogen peroxide. Also included is a model for determining
flame stability and autoignition in dump combustor with a rearward-facing step. The
goals of this autoignition study will be outlined as well.
3.1 Basic Chemistry of Autoignition
Autoignition, also known as spontaneous or thermal ignition, is defined as the
initiation of a self-sustained exothermic reaction without the aid of an external energy
source. In other words, the reactants themselves have enough energy to start and
continue a reaction. Ignition is a term commonly used in reference to combustion or
oxidization of a mixture of gases, which in this study is kerosene fuel vapor and
decomposed hydrogen peroxide. In many cases an external energy source is required for
ignition if the energy of the reactants is insufficient to begin the reaction. Typically an
41
electric spark, laser, or torch is used to provide additional energy for ignition.
Autoignition, by definition, is an event not a process. However, chemical kinetics, in
general, dominates the process which occurs prior to autoignition. This process is
complex and not well understood, but a basic understanding of it may help in determining
which factors are most important to achieving autoignition.
3.1.1 Composition of Kerosene Fuel
Before going into the kinetics of the processes leading to autoignition it helps to
understand the properties and composition of kerosene fuel. Kerosene is a distillate
fraction of petroleum that boils between 300 and 570°F.47,49,50 It contains thousands of
different hydrocarbon molecules and can have many different formulations as a result.
Common kerosene fuel formulations used in the aviation and rocket industries are Jet-A,
JP-4, JP-5, JP-8, and RP-1. Many of these kerosene derivatives were developed for
specific applications that may have required lower freezing point, higher flash point, or
lower concentrations of specific hydrocarbons than available kerosene-based fuels at the
time. These properties are achieved by varying the composition or introducing additives
to the fuel. JP-8 is currently the most widely used fuel for aircraft in the U.S. Army and
Air Force.49,50 It is basically Jet-A, which is the most common commercial aircraft fuel,
with three military specified additives that inhibit corrosion and improve lubricity,
dissipate static, and inhibit fuel system icing.49,50 Since kerosene-based JP-8 is so widely
used in military aviation it was chosen for this autoignition study.
JP-8 is composed of a number of paraffins, naphthenes, aromatics, and olefins of 50,
30, 18, and 2 percent by volume respectively on average.47,49,50 These different families
of hydrocarbons are classified according to their molecular formula, molecular structure,
and type of carbon-carbon bonding. A summary of the properties of each family of
hydrocarbons is shown in Table 3.1.51 The molecular formula of JP-8 is C11H21 which is
an average based on the composition of hydrocarbons found in the fuel. Some important
physical properties of JP-8 are shown in
Table 3.2.47,49,50
42
Table 3.1: Basic hydrocarbon families as found in kerosene-based fuels.51
Family Name Other Names Molecular
Formula Carbon-Carbon
Bonding
Primary Molecular Structure
Alkanes Paraffins CnH2n+2 Single bonds only Straight or
branched open chains
Alkenes Olefins CnH2n One double bond, all others single
Straight or branched open
chains
Alkynes Acetylenes CnH2n-2 One triple bond, all others single
Straight or branched open
chains
Cyclanes Cycloalkanes, Cycloparaffins,
Naphthenes
C2H2n or (CH2)n
Single bonds only Closed rings
Aromatics Benzene Family
CnH2n-6 Resonance hybrid
bonds Closed rings
Table 3.2: Physical properties of JP-8 fuel. All properties stated at ambient temperature and pressure unless indicated otherwise.47,50
Average Molecular Formula C11H21 Average Molecular Weight 153.3
Boiling Range (°F) 330-510 Freezing Point (°F) -60
Critical Temperature (°F) 770 Critical Pressure (psia) 340
Density (lbm/ft3) 50.6 Kinematic Viscosity (lbf-s/ft2) 2.56e-5
Surface Tension (lbf/ft) 1.57e-3 Vapor Pressure (psia @ 120°F) 0.190
43
3.1.2 Combustion of Hydrocarbons
Kerosene-based fuels such as JP-8 contain a number of different aromatics,
naphthenes, paraffins, and olefins. The molecular formula of JP-8 suggests that it is
made up of hydrocarbon molecules containing eleven carbons on average. These
molecules are very large with numerous atomic bonds of different types and strengths.
Breaking down such large molecules cannot be done in a single reaction but must occur
in a series of smaller reactions until only simple molecules remain. For example, Turns51
describes the combustion of paraffins, with greater than two carbon atoms, as a sequence
of three processes.
In the first step of the combustion process the paraffin fuel molecule is
bombarded by hydrogen, H, and oxygen, O, atoms and splits into mainly olefins and
diatomic hydrogen, H2. The diatomic hydrogen is oxidized to form water assuming there
is oxygen available. The second step of the reaction involves the oxidation of the olefins
to carbon monoxide, CO, and diatomic hydrogen. Olefins are unsaturated molecules
meaning hydrogen atoms do not occupy all of the carbon’s available bonds. Also, in this
step, all the diatomic hydrogen is converted to water. Finally, in the third step the carbon
monoxide is consumed to form carbon dioxide, CO2. The consumption of carbon
monoxide accounts for most of the heat release produced by the overall combustion
process. The high heat release is usually accompanied by a luminous flame. In a
reacting flow ignition is usually defined to occur at the point in which a flame is visible,
hot- flame ignition. Since this is the point of highest heat release the energy generated
sustains the reaction.
Combustion or oxidation of a JP-8 is a complex multi-step process as described
above, however, to simplify things somewhat the overall reaction is typically written
instead. The overall combustion reaction of JP-8 with 1 gram of hydrogen peroxide at
concentration 100*X % assuming complete combustion can be expressed as follows:
( ) ( ) ( ) ( ) ( )gglOH
lOH
l OcHbCOOHMW
XOH
MWX
HaC 2222
2222
21111
+→−
++ , (3.1)
44
Here MWH2O2 is the molecular weight of hydrogen peroxide, 34.016 g/mol, and
MWH2O is the molecular weight of water, 18.016 g/mol. Note there is no oxygen, O2(g), or
water vapor, H2O(g), term on the left side of equation 3.1 to represent decomposed
hydrogen peroxide gas. The chemical reaction describing the decomposition of 100*X%
H2O2 has been combined with the complete combustion reaction of JP-8 with the
decomposed gas to form an equivalent overall reaction. The moles of JP-8, carbon
dioxide, CO2(g), and water vapor are represented by a, b, and c respectively in equation
3.1 and are determined from the following equations:
22652
OHMWX
a = , (3.2)
226522
OHMWX
b = , (3.3)
OHOH MWX
MWX
c222
16586 −
+= , (3.4)
The stoichiometric mixture ratio, O/Fs, for JP-8 combusting with hydrogen
peroxide as a function of concentration can be found from:
8
22
265
−
=JP
OHs MW
MWX
FO , (3.5)
MWJP-8 is the molecular weight of JP-8 fuel, 153.3 g/mol as shown in
Table 3.2. For 90% H2O2 the stoichiometric mixture ratio is approximately equal
to 8.01 while for 98% H2O2 it is 7.36. The relative amounts of fuel and oxidizer present
in a reaction is most often expressed in terms of equivalence ratio, φ, and is defined as
follows:
FOFO s=φ , (3.6)
The actual oxidizer to fuel mixture ratio is represented by O/F. When operated at
stoichiometric mixture ratio the equivalence ratio is equal to one. At fuel rich conditions,
or O/F < O/Fs, the equivalence ratio is greater than one and at oxidizer rich conditions it
is less than one. Representation of mixture ratio in terms of equivalence ratio allows a
45
comparison between staged engine autoignition test data and much of the past kerosene
autoignition work done in air.
3.1.3 Kinetics of Autoignition
The previous section outlined the basic chemical processes which must occur
prior to ignition of a hydrocarbon fuel such as kerosene. In order for these reactions to
occur the energy of the gaseous fuel and oxidizer mixture must increase by a specific
amount, called the activation energy, before the reactants can be converted to products.
The collision theory of chemical reactions is used to model a reacting mixture by
supposing the system is a collection of molecules of finite size and velocity moving
randomly in space.51-53 As a molecule in the mixture moves in space it will eventually
collide with another molecule. A chemical reaction may occur at the point of collision
depending on the energy and orientation of each molecule. If the energy of the collision
is too low no reaction will occur at all, it will not activate a reaction. If the temperature
and pressure of the mixture are increased the energy of the molecules will increase as
well. Now, at the point of collision the molecules have more energy allowing stronger
molecular bonds to be broken and potentially releasing more energy to the system.
Eventually the energy of the moving molecules and their molecular composition may
become sufficient to activate the final step in the combustion reaction and autoignite the
mixture.
Collision theory can be also used to explain how the rate of a combustion reaction
is affected by the conditions of a system. In the collision theory model molecules gain
more energy with increasing temperature and pressure. As molecular energy increases so
does the velocity of the molecule and the number of collisions occurring in the mixture.
If collisions occur more frequently and at higher energy then reactions will also occur at a
faster rate. The Arrhenius relation states that the rate, kR, at which a chemical reaction
occurs is dependent on the activation energy of the reaction, Ea, and the temperature, T,
of the system:51-53
46
=
TRE
Zku
aR exp , (3.7)
Here Ru is the universal gas constant, and Z is the pre-exponential factor which is
dependent on the number of collisions between molecules calculated from collision
theory. Equation 3.7 agrees with collision theory in that the higher the temperature of
the mixture and the lower the activation energy of the reaction the faster the reaction rate.
Due to the temperature dependence of the reaction rate it may change significantly over
the course of a reaction as heat is released to the system.
As collision theory suggests and the previous section described a number of
elementary and chain reactions can occur in a system. Hydrocarbons, such as kerosene,
typically contain a significant number of elementary reactions in addition to the three
major steps described previously. The sum of these reactions describes the overall
reaction or reaction mechanism of the system. For such complex cases a global
activation energy is determined experimentally to approximate the kinetics of the system.
It is important to note that the energy of the gaseous mixture determines what reactions
will occur, the rate of these reactions, and the path of subsequent reactions. Thus, the
final result of the reaction depends on the initial conditions of the reactants and may not
necessarily lead to complete combustion or autoignition. This is demonstrated by the fact
that hydrocarbons reacting at low temperatures, < 800°F at ambient pressure, emit a
bluish flame.54,55 Commonly called cool- flame ignition this reaction is characterized by a
relatively low heat release, as compared to hot- flame ignition, and as such the reaction is
not self-sustainable.
The period of time from which a gaseous fuel and oxidizer mixture is formed to the
point of autoignition is termed the ignition delay. Ignition delay is governed by the
chemical kinetics of the reactions leading to carbon monoxide consumption assuming a
well mixed combination of fuel and oxidizer. From collision theory and the Arrhenius
relation one would expect the ignition delay to decrease with increasing temperature and
pressure as the reaction rate increases. One would also expect the concentration of the
reactants to affect the delay as well. Understanding ignition delay in practical
combustion systems is extremely important. In the case of the staged combustor used in
47
this study the mixture of decomposed peroxide and kerosene must be supplied at the
appropriate conditions to make the ignition delay as short a possible. Since the gases are
flowing at high velocity in the engine if the delay is too long the reactants will not
autoignite in the chamber. There is an added effect in ignition delay for a staged
combustor in that the fuel does not atomize, vaporize, and mix instantaneously. This
process takes some time and this time varies based on operating conditions. Chemical
reactions begin as soon as fuel vapor is present in the mixture and as such the rate of
vaporization may play an important role in the overall ignition delay. The rearward step
in a dump combustor is used to increase the time that the mixture spends in the chamber.
3.2 Autoignition Studies of Kerosene Fuel in Air
Since the 1970’s there has been significant research conducted on the autoignition
behavior of kerosene fuel in air. Many of these studies were performed initially to
simulate conditions in lean, premixed gas turbine engine combustors.55-58 In these
combustors the fuel and air are mixed prior to entering the main combustion chamber and
therefore autoignition must be avoided to prevent engine damage. More recently
research has been focused on autoignition in supersonic flows as encountered in scramjet
combustors.59 Ignition delay must be as short as possible in such engines to minimize
length and weight. Experimental research was aimed, for both engine cases, at
developing correlations and models for predicting ignition delay based on operating
conditions.
There are a number of methods used in determining the ignition delay of a
gaseous fuel and oxidizer combination. These include the constant volume bomb, rapid
compression, reciprocating engine, shock-tube, and continuous flow methods. In gas
turbine combustor research the continuous flow method was most often used because it
most accurately represented the actual flow field in a combustor. There are many
variations to this technique, but the basic concept is the same for all. The setup usually
consists of a tube or duct through which heated air flows at high subsonic velocity. One
of the benefits of such an arrangement is that the temperature, pressure, and/or velocity of
48
the air can be controlled independently. The fuel is injected into the air stream where it
mixes and reacts with the air. The method of injection is extremely important, especially
for liquid fuels, in minimizing effects of vaporization on ignition delay and for obtaining
a uniform mixture of fuel and air. Ignition is verified through the direct visual
observation of a flame inside the duct, for windowed setups, or exiting the chamber.
Alternate methods include the use of temperature or pressure measurements or
photodectors to indirectly verify the ignition event. Ignition delay is calculated using the
air velocity and the distance from the injection point to the position of the visible flame.
The correlations used to calculate ignition delay vary as much as the test
apparatus used to obtain them, but they too have a common form. Ignition delay
correlations are derived from chemical kinetics and make use of the Arrhenius relation.
The reaction is treated as a whole using the global activation energy determined from
experimental data. Correlations for ignition delay, t i, of hydrocarbons usually take the
following form:57
[ ] [ ] nmj
u
ai pOFuel
TRE
A 2exp
=τ , (3.8)
Here [Fuel] and [O2] are the concentrations of gaseous fuel and oxygen
respectively. The static pressure and temperature of the incoming air is denoted as p and
T. The parameter A is a constant and Ea is the global activation energy as in equation 3.7.
Exponents j, m, and n are constants determined through experimental data. Values of the
constants in equation 3.8 vary from experiment to experiment for a particular fuel, but
the trends are generally similar.57
There have been several autoignition studies performed to date with
kerosene-based fuel and air in a continuous flow apparatus. One such study was
performed by Spadaccini and TeVelde55 with Jet-A fuel for equivalence ratios ranging
from 0.3 to 0.7, temperatures from 800 to 1350°F, pressures from 150 to 450 psia, and air
velocities from 65 to 330 ft/s. In this experiment the pressure and velocity of the air were
set as well as the length of the duct. The temperature of the air was gradually increased
until a visible flame was seen at the exit of the duct. This was considered the point of
autoignition. Ignition delay was assumed equal to the residence time of the gases in the
49
duct, which was calculated by dividing the velocity of the air by the duct length. The
study resulted in the following general correlation for ignition delay:
=
TRE
pA
u
ani expτ , (3.9)
For Jet-A fuel the coefficient A is equal to 1.68e-8, n is equal to 2.0, Ea is equal to
37.78 kcal/mol, and p is in atmospheres. Equation 3.9 indicates that equivalence ratio
does not affect ignition delay, at least for φ < 1.0. In addition, ignition delay is shown to
be inversely proportional to the square of the air static pressure. Spadaccini and TeVelde
point out that most ignition delay correlations are fitted with a pressure exponent of unity,
n = 1.0, but their data suggests that an exponent of 2.0 is a better fit especially at high
temperatures. The effect of fuel concentration distribution was also investigated in this
study and was found to influence the ignition delay for short residence times. However,
as the residence time was increased the effect became negligible. Spadaccini and
TeVelde also investigated the effects of the temperature, up to 260°F, of the Jet-A fuel
prior to injection and found it had no influence on ignition delay.
A second study was performed by Freeman and Lefebvre56,57 with Jet-A at
atmospheric pressure. Tests were conducted at equivalence ratios from 0.2 to 0.8,
velocities from 30 to 130 ft/s, and temperatures up to 1450°F. Test were conducted
similarly to Spadaccini and TeVelde in that the flow conditions of pressure, velocity, and
equivalence ratio were prescribed and the air temperature was gradually increased until a
stable flame was observed exiting the duct. Freeman and Lefebvre observed that as the
air temperature increased autoignition initially arose as flashes of flame at a small
distance downstream of the duct exit. Gradually as the temperature increased the flame
front moved upstream to the duct exit at which point the air temperature was recorded
and the test was terminated.
The correlation developed by Freeman and Lefebvre was modeled after Equation
3.8. Since the pressure was kept constant during the investigation the value of n was set
equal to zero. A value of 40.9 kcal/mol was determined for Ea which compares very well
with the value of 37.78 kcal/mol determined by Spadaccini and TeVelde. Freeman and
Lefebvre also found that the equivalence ratio has a negligible effect on ignition delay for
50
φ < 1.0 also in agreement with Spadaccini and TeVelde. Increasing the oxygen
concentration of the incoming air was found to decrease the ignition delay and Freeman
and Lefebvre set the exponent m equal to -0.65 based on experimental data. The fuel
temperature was also found to have negligible effect on ignition delay consistent with
Spadaccini and TeVelde.
Both Spadaccini and TeVelde and Freeman and Lefebvre compared the
autoignition characteristics of kerosene to other fuels, including other hydrocarbons. In
general, kerosene was found to exhibit a shorter ignition delay in air than other typical
gas turbine fuels55 as well as gaseous fuels such as propane.56,57 In addition, the
experimentally determined activation energy of kerosene fuel has also been found to be
lower than other fuels.55 These results are attributed to the large concentration of
paraffins in the fuel. Paraffins, which are straight-chain hydrocarbons (see Table 3.1),
tend to autoignite more quickly than other types of hydrocarbons.55
The last study on the autoignition of kerosene fuel in air that will be discussed
was done by Mestre and Ducourneau.58 The experimental setup for this study differed
slightly from the previous two in that the had a cocentric design whereby a secondary
flow of air heated the main test section. Tests were conducted over a wide range of
equivalence ratios from approximately 0.8 to 8.0, pressures from 80 to 160 psia, an
average air ve locity of 215 ft/s, and temperatures up to 1500°F. As in the previous
studies the air temperature was gradually raised until autoignition was verified by a visual
detection of a flame exiting the duct. A unique correlation was developed to determine
the autoignition temperature based on pressure and equivalence ratio and is stated as
follows:
( )( )φ
φφφ
4.022.09.845000
16.0432.03
2
++−
++=pp
T , (3.10)
Here T is in degrees Celcius and p is in bars. Experimental results of Mestre and
Ducourneau showed that the autoignition temperature plotted as a function of
equivalence ratio for constant pressure had a minimum that varied with pressure. This
minimum temperature moves from an equivalence ratio of almost 3.0 at 5.4 bars to
approximately 1.0 at 11 bars. Data also showed that the required autoignition
51
temperature decreased with increasing pressure but the decrease became smaller as
pressure neared approximately 10 bars. The study also found that the required
autoignition temperature decreased with increasing residence time. Use of the secondary
air flow to heat the primary tube did not have a significant effect on the autoignition
temperature.
3.3 Dump Combustor Autoignition
As discussed in Chapter 2 in order for a stable flame to exist in a dump
combustor the rearward-facing step must provide sufficient shear layer residence time or
the flame will blow off. A study by Plee and Mellor42 outlines the development of a
model to predict blow off for various flame holder geometries under oxidizer rich
conditions. The model basically states that if the shear layer residence time is greater
than the ignition delay then a stable flame will exist in the shear layer. If the residence
time is to small then the shear layer flame will be unstable and blow off will occur. For
an oxidizer rich, premixed flow the relation can be stated as follows:
bm isl += ττ , (3.11)
The slope and intercept of the equation for the blow off limit are denoted by m
and b respectively. These values are determined through experimental data. Shear layer
residence time is calculated using equation 2.12 for a rearward-facing step configuration.
Plee and Mellor suggest the use of the following relation for ignition delay for oxidizer
rich equivalence ratios:
φτ
1exp
=
TRE
TT
Ku
a
ini , (3.12)
Here T is the adiabatic flame temperature at equivalence ratio φ, Tin is the inlet
temperature of the premixed gases, and K is a constant. The T/Tin term is used to
decouple fluid mechanics from thermochemistry. Data from Mestre and Ducourneau
showed that autoignition temperature increases with increasing equivalence ratio for fuel
rich mixture ratios. This suggests that the ignition delay increases with equivalence ratio
52
for fuel rich mixtures. Equation 3.12 would show the opposite trend if used for fuel rich
conditions and for that reason can only be used for oxidizer rich equivalence ratios. Note
that this relation for ignition delay does not include a pressure term.
In situations where vaporization may still play an important role in the
recirculation region behind a bluff body a modification to equation 3.11 is required:
bam visl ++= τττ , (3.13)
A constant, a, is multiplied by the vaporization characteristic time, t v, to give a
best fit to the experimental data. The vaporization characteristic time or fuel droplet
lifetime is determined from the D2 law for droplet vaporization:
λτ
2o
v
d= , (3.14)
The vaporization coefficient, ?, is determined through heat and mass transfer
considerations, see Turns,51 and the droplet diameter, do, is determined through
experimental data or correlations. A blow off model based on equation 3.13 has been
developed by Plee and Mellor based on experimental data for Jet-A reacting in air for
several different types of flameholder configurations. However, a model of flame
stability for Jet-A reacting with air behind a rearward-facing step was not developed in
the study by Plee and Mellor. This model is fairly simplistic, especially when
vaporization effects are not important, in that one can compare the calculated values of
shear layer time and ignition delay to determine whether a stable flame or autoignition
will occur.
3.4 Autoignition Studies in Staged Combustors
Research into the autoignition characteristics of kerosene fuel in decomposed
hydrogen peroxide has not been as substantial as it has been in air. Much of the data
concerning autoignition in staged engines are the result of problems encountered during
engine design. Typically the baseline engine design is tested and does not achieve
autoignition.17,22 Design changes are made, usually in residence time, and then the
53
engine is retested to verify autoignition. The studies do not go into much more depth
than stating the operating conditions and geometry of each design. There were, however,
a series of papers written in the early 1950’s on autoignition of kerosene fuel in
decomposed hydrogen peroxide by Walder,8,9 Walder and Purchase,10 and Walder and
Broughton.25 A summary of this research is found in a paper by Harlow.11
The most extensive of these autoignition studies by Walder is found in his earliest
paper.8 In this study 80% H2O2 was decomposed in a catalyst stone bed giving a
decomposition temperature of approximately 950°F, see Table 1.2. Tests to determine
autoignition temperature were conducted similarly to those done with kerosene in air.
Initially water is mixed with the liquid hydrogen peroxide to drop the decomposition
temperature below 750°F. The water flow was gradually reduced to increase the
decomposed gas temperature until autoignition was verified by visual detection of a
flame exiting the chamber throat. Aviation kerosene fuel was fed to the chamber through
twelve swirl injectors and the residence time of the gas in the chamber was modified by
varying the chamber length and throat diameter. The contraction ratio was varied from
approximately 6.5 to 20.0. All tests were conducted at a mixture ratio of 9.1, which is
approximately stoichiometric for 80% H2O2 according to equation 3.5.
Walder developed a correlation for the autoignition temperature of kerosene in
decomposed hydrogen peroxide similar in form to equation 3.9. The main difference
was that Walder supposed that the ignition delay was proportional to the characteristic
length, L*, of the engine. The basic form of the correlation is as follows:
=∗
TC
pC
Ln
12 exp , (3.15)
Here p is the chamber pressure, T is the decomposition temperature, and n, C1,
and C2 are constants. The constant C1 is basically equivalent to the constant Ea/Ru term
found in equation 3.9. Walder manipulates equation 3.11 by taking the logarithm of
both sides of equation 3.11 and arrives at the following:
( ) DTC
pL n +=∗log , (3.16)
54
The slope of a line describing autoignition pressure versus characteristic length at
constant temperature gives the value of the exponent n. Walder found n to be equal to
1.15 based on test data. This value is close to unity, which Spadaccini and TeVelde
suggested worked well for autoignition of kerosene in air at low temperatures. The
constants C and D are the slope and intercept of a line plotting autoignition temperature
as a function of L* at constant pressure. Walder found these constants to be equal to 3720
and -2.62 respectively based on test data. From this relation one can see that as L* and/or
chamber pressure are increased the temperature required for autoignition decreases. This
agrees with the results from Mestre and Ducourneau. Walder also investigated the effect
of equivalence ratio on the autoignition temperature at constant pressure of 100 psia and
L* of 50.4 inches. It was found that the required autoignition temperature rose to a value
of about 830°F at an equivalence ratio of 1.25 from 805°F at the stoichiometric value. At
an equivalence ratio of approximately 0.8 the required autoignition temperature fell to
770°F. The trend in these results also agrees with that of Mestre and Ducourneau for fuel
rich equivalence ratios.
A subsequent study by Walder further investigated the effect of L* on
autoignition.9 In this study the characteristic length was artificially increased by placing
a restrictor plate on the throat of the combustion chamber using the same setup as in the
previous study.8 The pressure would gradually increase as the fuel and decomposed gas
entered the chamber until autoignition occurred and blew out the restrictor plate. Another
study, by Walder and Purchase,10 investigated the affect of injector design on autoignition
temperature. A number of complex injector designs were tested which made use of swirl
jet, straight orifice, and combined swirl and straight orifice injection techniques. All tests
were conducted at a stoichiometric mixture ratio of 9.1 for 80% H2O2 and L* ranging
from 68 to 100 inches using the same test setup and procedure as in the previous
investigations.8 Average autoignition temperature was found to vary with injector design,
the injector requiring the lowest temperature is shown in Figure 1.5. The results suggest
that autoignition is dependent on the atomization and vaporization processes which occur
following fuel injection. A fourth study, performed by Walder and Broughton,25
investigated autoignition in larger, hydrogen peroxide cooled chambers. A silver screen
55
catalyst bed was used during this test series to decompose 80% H2O2. The engine ran at
approximately stoichiometric mixture ratio and a biprop chamber pressure of 400 psia. A
characteristic length of 30 inches was used, corresponding to a contraction ratio of
approximately 6.5, to provide a thrust of approximately 92% of the theoretical value.
A study by Wu et al22 on the development of staged-bipropellant engines using
hydrogen peroxide and JP-8 noted some problems obtaining autoignition. The test
engine was very similar in design to that presented in Chapter 2 of this thesis. A silver
screen catalyst bed was used to decompose 85% H2O2 at 95% efficiency and the engine
used a transverse type injector design with a rearward step. Autoignition was not
achieved at a monoprop chamber pressure of 340 psia and a contraction ratio of 5.4. The
mixture ratio used during this test is unclear but other data from the study suggests that it
was somewhere between 6.0 and 11.0, corresponding to equivalence ratios between 0.8
and 1.4. The contraction ratio was increased to 7.11 to establish reliable autoignition.
In a study by Coxhill et al17 autoignition problems were also experienced during
staged engine development. This engine design used kerosene fuel jet injectors angled at
55° to the decomposed gas flow and did not incorporate flame holding geometry. A
silver screen catalyst bed was used to decompose 90% H2O2 and the engine operated at
mixture ratios from about 6.0 to 10.0, equivalence ratios from 0.8 to 1.3. Autoignition
did not occur at a contraction ratio of approximately 13.0 at chamber pressures less than
160 psia even for fully decomposed hydrogen peroxide. It is unclear as to what the
mixture ratio was during these autoignition tests. At a contraction ratio of about 20.0
autoignition was achieved for all tested conditions and was subsequently used in the final
engine design.
It is interesting to note the high contraction ratios used during autoignition testing
of kerosene in hydrogen peroxide. From the data presented above the smallest
contraction ratio used was at a value of 6.5. Flight -rated engines such as the Gamma Mk
201 and Mk 301 had contraction ratios of approximately 7.529 and the Orbital Sciences
USFE engine had a contraction ratio of about 7.1.23 It is generally desired that the
contraction ratio be as small as possible to minimize the size of the combustion chamber.
56
This reduces weight as well as cooling requirements. Typical values of contraction ratio
for many other engines and propellant combinations are on the order of 2.0 or 3.0.
3.5 Goals of this Autoignition Study
The primary goal of this autoignition study is to develop a model for autoignition
to aid in the design of staged H2O2/JP-8 engines. Past research on autoignition of
kerosene fuel in air and decomposed hydrogen peroxide has shown good agreement on
the effect of temperature on ignition. The exponential effect of temperature on ignition
delay as derived from chemical kinetics and the Arrhenius relation, equation 3.7, is
agreed upon by most researchers. Most correlations suggest that ignition delay is
dependent on the inverse of pressure while some suggest that this dependence changes at
higher temperatures. It is also generally agreed that mixture ratio does not play a
significant role in autoignition at oxidizer rich equivalence ratios, φ < 1.0. However,
there is little data on the effect of fuel rich equivalence ratios on autoignition. It is also
unclear whether equivalence ratio effects are the result of changes in the chemical
kinetics of the reaction or of changes in the atomization properties of the injector, which
affects vaporization time. In addition, many studies mention that autoignition is
dependent on the residence time of the gaseous mixture, but there are few correlations
that actually take this effect into account. This effect is especially important when bluff
body flame stabilization is used in a combustor. In relation to rocket combustors
residence time, especially contraction ratio, seems to be extremely important to
autoignition. As a result, a design model for autoignition in a H2O2/JP-8 engine should
include the effects of fuel rich equivalence ratios and contraction ratio.
It is proposed that the blow off model derived by Plee and Mellor42 be used as a
model for autoignition for the engine used in this study. It will be assumed that
vaporization is complete prior to entering the recirculation zone behind the
rearward-facing step to eliminate the need for the droplet lifetime term. This may not be
a good assumption but it greatly simplifies the analysis. To use this model the ignition
57
delay equation, equation 3.12, must be modified to deal with fuel rich equivalence ratios.
The proposed modification is as follows:
j
u
a
ini TR
ETT
K φτ
= exp , (3.17)
The exponent, j, on the equivalence ratio term will need to be determined through
experimental data. The activation energy can be taken as an average of the results of
Spadaccini and TeVelde55 and Freeman and Lefebvre.56,57 Temperature effects on
autoignition can be determined by varying the hydrogen peroxide concentration and thus
the decomposition temperature. Shear layer residence time will be modified by changing
the chamber contraction ratio and thus the chamber pressure and gas velocity. The
rearward-facing step height will remain constant through testing.
A secondary goal of this study is to compare the autoignition characteristics of
JP-8 in decomposed hydrogen peroxide with that of an experimental fuel called DMAZ.
DMAZ is an acronym for Dimethylamino-2-ethyl azide or Dimethyl-2-Azidoethylamine.
Due to its experimental status there is a limited amount of data regarding the physical
properties of DMAZ. Some of the physical properties of the fuel can be found in its
Material Safety Data Sheet, MSDS, which is contained in Appendix B. The known
properties of DMAZ are compared to JP-8 in Table 3.3. DMAZ will be run under
similar test conditions as JP-8 in terms of equivalence ratio, hydrogen peroxide
concentration, and contraction ratio to make the comparison.
Table 3.3: Comparison between some physical properties of DMAZ and JP-8.
Fuel DMAZ JP-8 Molecular Formula (CH3)2NCH2CH2N3 C11H21 Molecular Weight 114.2 153.3
Boiling Point/Range (°F) 275 330-510 Freezing Point (°F) -92 -60 Density (lbm/ft3) 58.2 50.6
Kinematic Viscosity (lbf-s/ft2) < 2.09e-4 2.56e-5 Vapor Pressure (psia) 0.21-0.97 (@ 68°F) 0.190 (@ 120°F)
Flash Point (°F) 86 127 O/Fs with 90% H2O2 4.32 8.02
58
CHAPTER 4: EXPERIMENTAL SETUP
Autoignition testing was conducted in Test Cell A of Purdue University’s
Advanced Propellants and Combustion Lab, APCL, located at Maurice J. Zucrow
Laboratories. Over the past two years this facility has seen extensive use in testing of
hydrogen peroxide in monopropellant and bipropellant systems.12,13,24,30 An excellent
description and history of the test stand located in Test Cell A is contained in a thesis by
B.J. Austin.60
4.1 Test Facility Overview
Test Cell A at APCL houses a test stand rated to a maximum operating thrust of
1000 lbf. The existing bipropellant system contains two stainless steel tanks, a four-
gallon capacity fuel tank and four-gallon capacity oxidizer tank. The oxidizer tank is
devoted exclusively for use with hydrogen peroxide. Nitrogen is used to pressure-feed
the propellants to the test article and each of the propellant tanks are rated to a maximum
pressure of 2000 psia. Two 6000 psia storage cylinders supply nitrogen to the entire
system and are located outside of the test cell. This nitrogen supply is run through the
test cell to a regulator panel in the control room. Dome-loaded regulators, which are
tapped into the 6000 psi nitrogen supply line, are used to regulate the ullage pressure in
both the fuel and oxidizer tanks. These provide rapid response and maintain the tanks at
a very steady ullage pressure during a test run. Hand- loaded regulators located on the
panel in the control room are used to set the operating pressures of the dome-loaded
regulators as well as the purge pressures for the fuel and oxidizer lines. Typical tank
ullage pressures range from 800 to 1800 psia.
59
Propellant feed lines as well as nitrogen supply lines consist of a combination of
½” and ¼” diameter stainless steel tubing. Stainless steel, grades 304 or 316, is used
throughout the system due its compatibility with hydrogen peroxide.3 Flow control is
accomplished using a wide range of cavitating venturis for use in both ½” and ¼” feed
line. Propellants are vacuum loaded through fill lines connected to the bottoms of the
tanks. Suction pressure is provided by a 1/3 hp vacuum pump, which can move 1.23
ft3/min of air, and the vacuum system is controlled by manual ball valves. All of the
controllable valves in the system, excluding purge valves, are pneumatically actuated ball
valves that use helium, supplied at 100 psia, for fast response. Solenoid valves are used
to control nitrogen flow through the purge lines.
Each propellant system, fuel and oxidizer, contains six remotely operated valves.
A pressurization valve is used to control the flow of nitrogen pressurant to the tank. The
tank vent valve releases the pressurant to the environment following a test or in the case
of emergency. This is the only normally open valve in each system. A dump valve
provides a means of draining propellant from the tank. This is used if propellant remains
in the tank following a test or to safely drain the tank in emergencies. Drained hydrogen
peroxide is collected in a plastic bucket that is half full of water. This dilutes the H2O2 to
a lower concentration making it safer to handle. Drained fuel is collected in an empty
aluminum bucket. An isolation valve, located downstream of the dump valve, is used to
isolate the tank from the test article. This is only used during a test in the case of a
catastrophic failure. Downstream of the isolation valve is the main valve which controls
the flow of the propellant to the test article. This is the only timed valve in each system.
A complete plumbing and instrumentation diagram, P&ID, of the test facility is shown in
the Appendix C.
The test stand is outfitted with two parallel lengths of Unistrut metal framing
downstream of the oxidizer and fuel main valves. A mounting plate is attached to this
framing and the test article is secured to the plate. Typically the test article is mounted
vertically, but the valve box can be easily reoriented to a horizontal position to
accommodated longer test articles. The metal framing is attached to a pair of flexures
which transfers the thrust produced by the engine to a load cell.
60
4.2 Cavitating Venturi Flow Control
As previously mentioned flow control at this test facility is accomplished using
cavitating venturis. The internal contour of a cavitating venturi does not vary
significantly from a typical venturi flow meter, but it functions in a distinctly different
manner. The job of a cavitating venturi is to provide a large enough pressure drop to
push the local pressure of a fluid below its vapor pressure. Usually this occurs at or just
downstream of the venturi throat. When the fluid cavitates in the venturi tiny pockets of
vapor are formed that effectively create a choke point in the flow. The choke point
prevents variations in downstream pressure from propagating upstream to affect the mass
flow rate through the venturi. However, if the downstream pressure becomes too large it
will push the venturi out of cavitation and create an unstable flow rate. Generally, if the
back pressure rises to above 75% of the venturi inlet pressure cavitation will not occur.
In a venturi, as in an orifice, the flow does not exactly follow the wall contour and
often separates from the wall downstream of the throat. The separating flow creates a
vena contracta, which acts as a flow restriction and creates a fluid dynamic throat of
smaller diameter. To account for this phenomenon a constant discharge coefficient term
is used in cavitating venturi mass flow rate calculations. A well designed cavitating
venturi contour will have a discharge coefficient equal to unity. Water flows are
performed to determine the discharge coefficient for a particular venturi. The general
water flow procedure consists of flowing water through a venturi of a specific throat
diameter at a constant inlet pressure for some length of time. This information is used to
calculate what the total mass flowed would be assuming a discharge coefficient equal to
one. It is very difficult to maintain a completely constant pressure at the inlet to the
venturi so the mass flow rate is calculated based on inlet pressure at each instant in time
for the duration of the test. The mass flow rate history is integrated in time over the
entire test duration to determine the total theoretical mass. The water is collected in a
bucket and the total mass is recorded. Dividing the mass of the collected water by the
theoretical mass of water gives the discharge coefficient. Typically three water flows are
done to obtain a good average.
61
Mass flow through a cavitating venturi can be calculated from Bernoulli’s
equation for incompressible flow. Writing Bernoulli’s equation from the venturi inlet to
the throat of the vena contracta gives the following:
022
22
=−−+ cv
ii
Vp
Vp
ρρ, (4.1)
Here pi is the venturi inlet or supply pressure, Vi is the inlet velocity, ? is the
liquid density, pv is the vapor pressure of the liquid, and Vc is the velocity at the throat of
the vena contracta. The crude schematic of a cavitating venturi is shown in Figure 4.1.
The inlet and exit diameter of a cavitating venturi are equal to the inner diameter of the
stainless steel tubing, which is 0.18” for ¼” tubing and 0.37” for ½” tubing. Substituting
the equations for mass flow rate at the inlet and vena contracta throat into equation 4.1
results in the following after some manipulation:
( )21
2
12−
−−=
i
cvic A
AppAm ρ& , (4.2)
The cross-sectional area of the venturi inlet is denoted by Ai, Ac represents the
cross-sectional area of the vena contracta throat, and m& is the mass flow rate of liquid.
Typically the square of the ratio of the area of the contracta to the inlet is a very small
number and as such is usually neglected in mass flow calculations. Also, when compared
to the required supply pressure the vapor pressure of many liquids is extremely small and
is usually neglected as well. The vapor pressure of JP-8 is 0.190 psia at 120°F47 and the
vapor pressure of 90% H2O2 is 0.065 psia at 77°F.3 Since the cross-sectional area of the
vena contracta is not known it is usually represented as in terms of a constant discharge
coefficient, CDcv, and the physical throat cross-sectional area. Substituting this into
equation 4.2 results in the following equation:
( )21
2
12−
−−=
i
tDcvvitDcv A
ACppACm ρ& , (4.3)
Neglecting the area ratio and vapor pressure terms gives an alternate form:
itDcv pACm ρ2=& , (4.4)
62
This form of the cavitating venturi mass flow rate equation was used during
autoignition testing for both JP-8 and hydrogen peroxide. Typical oxidizer and fuel flow
rates can range from 0.1 to 2.5 lbm/s and 0.1 to 0.5 lbm/s respectively depending on the
venturi and supply pressure. The effective diameter, deff, of a cavitating venturi can be
written as follows:
Dcvteff Cdd = , (4.5)
The effective diameter is an alternate name for the vena contracta throat diameter
of the venturi. A list of venturis available for use at APCL including physical and
effective throat diameters as well as flow rate of water for a 1000 psia supply pressure is
shown in Table 4.1. During testing the 0.111 and 0.094 inch throat diameter venturis
were used to control the flow of H2O2 while the 0.058 inch venturi was used to control
JP-8 flow rate.
Figure 4.1: Schematic of a cavitating venturi indicating important parameters.
63
Table 4.1: List of cavitating venturis available at APCL.
Throat Diameter,
dt (in.)
Discharge Coefficient,
CDcv (--)
Effective Diameter, deff (in.)
Tubing Diameter
(in.)
Water Mass Flow, m& (lbm/s)
0.018 1.851 0.024 ¼ 0.076 0.019 -- 0.019 ¼ 0.047 0.022 0.998 0.022 ¼ 0.064 0.028 0.934 0.027 ¼ 0.096 0.030 0.814 0.027 ¼ 0.096 0.032 -- 0.032 ¼ 0.134 0.034 0.833 0.031 ¼ 0.126 0.036 -- 0.036 ½ 0.170 0.038 0.705 0.032 ¼ 0.134 0.040 1.018 0.040 ¼ 0.210 0.054 0.861 0.050 ¼ 0.328 0.054 0.807 0.049 ¼ 0.315 0.058 0.844 0.053 ¼ 0.369 0.062 -- 0.062 ½ 0.504 0.068 0.935 0.066 ¼ 0.572 0.078 0.839 0.071 ¼ 0.661 0.094 0.994 0.094 ½ 1.160 0.111 0.989 0.110 ½ 1.588
4.3 Data Acquisition and Control
A LabVIEW, version 6.1, virtual instrument (VI) is used for valve control and
data acquisition at the facility. The program is run on a PC operating Windows 2000
with a Pentium IV 2.0 GHz processor. During a test a VI is used to open and close
valves, to set and carry out valve firing sequences, as well as to monitor and acquire data.
The program creates a file which contains a number of rows and columns of data. Each
column corresponds to a particular channel of temperature or pressure data and each row
represents the data collected from each channel at a particular instant in time.
To actuate a valve in the system the VI is used to command a five volt
(TTL/CMOS) digital ON/OFF signal be generated by the 32-bit high-speed digital I/O
card, National Instruments (NI) model number PCI-6533 (PCI-DIO-32HS). This digital
signal is sent to a 32-channel relay board which transmits a 24 volt signal to the
64
appropriate valve. In a pure solenoid valve, as used in the purge lines, the 24 volt signal
actuates the solenoid which moves the valve stem and opens the valve. The valve will
remain open as long as the 24 volt signal is in place. In a pneumatic valve the signal
actuates a solenoid which allows helium at 100 psia to enter a chamber forcing the valve
stem to rotate to its open position. When the 24 volt signal is turned off the solenoid
closes and the helium is vented from the chamber.
A 16-bit resolution data acquisition (DAQ) card, NI model number PCI-6052E, is
used for a total collection capability of 333,000 samples per second of 8 differential
inputs. The analog input must be within ±0.05 and ±10.0 volts. A NI SCXI-1000 chassis
is connected to the DAQ card to expand the total channel capacity. The chassis consists
of four modules of up to 32 channels a piece for a maximum of 128 analog inputs. This
sets the maximum scan rate for sampling 128 channels at approximately 2600 samples
per second. During testing all data channels are sampled at 1000 samples per second.
Currently one module in the chassis is set up to collect thermocouple data, NI model
number SCXI-1102. The thermocouples are plugged into a terminal block, NI model
number TC-2095, which is connected to the module. The terminal block can
accommodate up to 32 channels. The voltage signal generated by the thermocouples is
automatically converted to temperature using LabVIEW and the terminal block which
contains cold junction compensation circuitry. Two of the remaining three modules, NI
model number SCXI-1102C, are set aside for pressure transducer data as well as any
other input signals of less than 10 volts, such as load cell, valve position, or heat flux
transducer data. The transducer wires are connected to a terminal block, NI model
number SCXI-1303, one of which is connected to each of the two modules in the chassis.
Each terminal block can accept up to 32 channels of data. Typically pressure
measurements are recorded as voltage in a data file and converted to units of pressure by
a data reduction code.
65
4.4 Instrumentation
Pressure measurements are made using 3000 psi absolute pressure transducers
manufactured by Druck, model number PMP 1260 or 1265. These transducers follow a
linear calibration curve and output one volt at a pressure of 0 psia and five volts at 3000
psia. Using these two points the slope of the calibration curve is 750 psia per volt. The
transducers are accurate to within ±0.25% of the full scale pressure, which corresponds to
an accuracy of ±7.5 psia. At APCL the transducers are powered by a 24 volt DC supply,
the excitation voltage must be between 8 and 30 volts DC for normal operation. These
transducers can withstand an overpressure of up to 6000 psia and operate nominally
within -40 and 185°F.
Temperature measurements are made using type K thermocouples made by
Omega Engineering, Inc. The temperature sensing junction of these thermocouples is
formed by Chromega and Alomega wire, which are nickel/chromium and
nickel/aluminum alloys respectively. These wires are contained in a stainless steel, SS
304, sheath and are attached to a two-prong connector. Insulation is used to isolate the
wires from each other and the sheath material. This combination of junction and sheath
material gives thermocouple an operating temperature range of up to 1700°F. The probe
diameter is 1/16 inch and is 12 inches in length. Exposed and grounded junctions were
used for this testing. In a grounded thermocouple the wires are actually attached to the
sheath material inside the tip of the probe. The sensing junction protrudes from the tip of
an exposed thermocouple probe leaving it exposed to the environment.
4.5 Test Article and Setup
A simplified schematic of the test stand including the location of pressure
transducers and thermocouples is shown in Figure 4.2. Pressure transducers are located
at the top of both propellant tanks to measure and monitor the ullage pressure.
Temperature of the liquid hydrogen peroxide in the oxidizer tank is measured using a
66
grounded thermocouple. This temperature is routinely monitored when the tank contains
H2O2 for safety purposes in the event of fluid decomposition. Transducers are also
located just upstream of the fuel and oxidizer cavitating venturis to measure the inlet
pressure. This pressure is used in for mass flow rate calculations, equation 4.4. A
pressure transducer is placed just upstream of the inlet to the fuel injector manifold. This
measurement is used along with chamber pressure to calculate the pressure drop across
the injector. Another transducer is positioned just upstream of the inlet to the catalyst bed.
Pressure drop across the catalyst bed is calculated using this measurement and the
pressure measured downstream of the catalyst bed.
Two different catalyst beds were used during the course of autoignition testing.
The baseline catalyst bed is a silver screen design and was made by General Kinetics,
LLC. Due to its silver screen design hydrogen peroxide concentration is limited to 92%
or less. This bed was designed to operate at a flow rate of 2.5 lbm/s of 90% H2O2 or a
bed loading of approximately 0.38 lbm/in2-s. Bed loading, G, is defined as the mass flow
rate divided by the cross-sectional area that the flow sees in the catalyst bed. The
diameter of the flow path through this bed is about 2.9 inches. A second bed, made by
Precision Combustion, Inc., has a different internal design which allows it to operate
using hydrogen peroxide concentrations up to 98%. This bed was also designed to
operate at a flow rate of approximately 2.5 lbm/s of 90% H2O2, but the loading is double
that of the baseline bed at about 0.80 lbm/in2-s. The diameter of the flow path through
the bed is about 2.0 inches. Table 4.2 shows a comparison between the two catalyst bed
designs.
Table 4.2: Comparison between catalyst bed designs used during testing.
Catalyst Bed General Kinetics, LLC. (GK)
Precision Combustion, Inc. (PCI)
General Design Silver Screen Proprietary H2O2 Concentration Up to 92% Up to 98%
Design Flow Rate (lbm/s) 2.50 2.50 Design Loading (lbm/in2-s) 0.38 0.80
Internal Diameter (in) 2.90 2.00 Exit Diameter (in) 2.90 1.75
67
Since the catalyst beds have different exit geometry two different engine
assemblies were used during the course of autoignition testing. The difference between
the two is in the method and hardware used to mate each catalyst bed to the transverse
injector. All hardware downstream of and including the transverse injector is identical in
both cases. A schematic of the two assemblies is shown in Figure 4.4 and a photo of
each is shown in Figure 4.3. All hardware excluding the chamber and nozzles are
fabricated from stainless steel, SS 304. Copper is used for the combustion chamber and
nozzles because of its high thermal diffusivity, which means that heat travels through the
material very quickly. As a result, the temperature at the inner walls of the chamber and
nozzles rises slowly extending the time which they can be exposed to high temperatures.
However, even with copper the biprop test duration is limited to five seconds or less, at a
mixture ratio of five with 90% H2O2 and JP-8, to avoid thermal damage to the throat.
The chamber inner diameter is 2.56 inches and three nozzles were fabricated at
contraction ratios of 3.0, 5.0, and 6.5. This corresponds to throat diameters of 1.478,
1.145, and 1.000 inches respectively. These contractions ratios set the characteristic
length of the chamber, measured from the face of the rearward step to the throat, at 24.1,
40.4, and 52.7 inches respectively. The nozzles with contraction ratios of 3.0 and 6.5 are
shown in Figure 4.4. Viton o-rings are used to seal most of the interfaces between
engine hardware. This material is compatible with hydrogen peroxide and has a
maximum operating temperature of 600°F. Typically, for tests of between three and five
seconds, these o-rings will begin to deteriorate from exposure to high temperatures.
Pressure-filled stainless steel o-rings are used for sealing between the catalyst beds and
their mating pieces. These o-rings were specified by the catalyst bed manufacturers. A
water-cooled carbon steel deflection plate was used to direct the exhaust gases from the
engine outside of the test cell. The deflection plate can be seen at the bottom of the photo
in Figure 4.3a. Part drawings for the deflection plate are contained in Appendix A.
68
Figure 4.2: Simplified schematic of test stand with instrumentation locations.
a) b)
Figure 4.3: Photos of installed test article for: a) GK catalyst bed and b) PCI catalyst bed assemblies.
69
Figure 4.4: Comparison of engine assemblies for each catalyst bed design. Axial
locations of instrumentation are indicated in schematic.
The locations of pressure transducers and thermocouples on the test article are
shown in Figure 4.4. This can also be seen in the photos in Figure 4.3. General Kinetics,
LLC specifies that the catalyst be heated to approximately 350°F prior to firing. This
was accomplished using a 150 Watt, cloth- insulated electric wrap heater purchased from
Cole Palmer Instrument Company. The wrap heater was two inches wide and two feet
long and can be seen wrapped around the catalyst bed at the top of Figure 4.3a. A
thermocouple was surface welded to the outside wall of the of the GK catalyst bed to
monitor its temperature, Tskin. Immediately downstream of the catalyst bed in both
assemblies an exposed thermocouple is used to measure the decomposition temperature,
Td, of the hydrogen peroxide. This thermocouple is positioned such that the probe is at
the centerline of the duct. The pressure at the exit of the catalyst bed, Pcb_out, is also
70
measured by a transducer at the same position. Four grounded thermocouples were used
in the combustion chamber to measure the temperature profile along the chamber length,
Tc1-Tc4. These probes are positioned flush with the inner chamber wall and spaced
equally along the length of the chamber. Two pressure transducers are used in the
combustion chamber. The transducer at the first axial position in the chamber measures
the static pressure in the recirculation zone behind the rearward-facing step, Pc1. The
second measures the static pressure just upstream of the chamber contraction, Pc2. This
measurement is used to calculate the characteristic velocity. A typical list of
instrumentation used during autoignition testing is shown in Table 4.3.
Table 4.3: Typical instrumentation list for autoignition testing.
Description Instrument Designation Oxidizer Tank Ullage Pressure Druck 0-3000 psia Pox_ull
Oxidizer Venturi Inlet Pressure Druck 0-3000 psia Pox_cv Catalyst Bed Inlet Pressure Druck 0-3000 psia Pcb_in Fuel Tank Ullage Pressure Druck 0-3000 psia Pfu_ull Fuel Venturi Inlet Pressure Druck 0-3000 psia Pfu_cv Fuel Injector Inlet Pressure Druck 0-3000 psia Pfu_inj
Catalyst Bed Outlet Pressure Druck 0-3000 psia Pcb_out Chamber Pressure 1 Druck 0-3000 psia Pc_1 Chamber Pressure 2 Druck 0-3000 psia Pc_2
Oxidizer Tank Temperature Omega Type K Grounded Tox
Decomposition Temperature Omega Type K Exposed Td Chamber Temperature 1 Omega Type K Grounded Tc1
Chamber Temperature 2 Omega Type K Grounded Tc2
Chamber Temperature 3 Omega Type K Grounded Tc3
Chamber Temperature 4 Omega Type K Grounded Tc4
Catalyst Bed Skin Temperature Omega Type K Surface Welded Tskin
71
4.6 Hydrogen Peroxide Dilution
Propellant grade hydrogen peroxide from FMC Corporation was used during
autoignition testing. Hydrogen peroxide from FMC comes standard in 90 and 98%
concentrations. These standard concentrations were diluted using deionized water prior
to testing in order to create non-standard concentrations such as 85, 87.5, and 94%. The
amount of H2O2 needed at these lower concentrations is usually known prior to testing.
Therefore, one must calculate the amount of dilution water and hydrogen peroxide at
standard concentration that must be mixed to meet the new mass and concentration
requirements. The required water mass, mH2Oadd, is determined from the following
equation:
2@221
22 1 WOHOaddH m
WW
m
−= , (4.6)
Here W1 is the current or standard concentration (in weight percent), W2 is the
desired concentration, and mH2O2@W2 is the desired mass of hydrogen peroxide as the new
concentration. Note that the mass to be added becomes negative if the desired
concentration is greater than the current concentration, W2 > W1. The mass required at
the current concentration, mH2O2@W1 , is found from:
2@221
21@22 WOHWOH m
WW
m
= , (4.7)
Once these masses were determined the required amounts of water and hydrogen
peroxide were measured, poured into a plastic jug, sealed, and shaken by turning end
over end until the liquids were well mixed. The concentration was then measured to
verify that it matched the desired value. The hydrogen peroxide was then stored in the
jug at room temperature until it was loaded into the run tank during the test. Both the
hydrogen peroxide and JP-8 fuel were stored at room temperature, around 70°F, for these
autoignition tests.
The concentration of hydrogen peroxide is determined by measuring the refractive
index of the liquid. The refractive index can be used to determine the hydrogen peroxide
72
concentration since the density of H2O2 varies with concentration and the refractive index
of a fluid is dependent on its density. The density of hydrogen peroxide, ?H2O2, varies
with temperature and concentration according to the following curve-fit equation:3
?H2O2 = 66.166 + 1.577*10-1W + 1.112*10-3W 2 – 2.310*10-2T –
4.700*10-6T 2 - 1.380*10-4WT, (4.8)
Here density is in units of lbm/ft3, W is the weight percent of hydrogen peroxide,
and T is the H2O2 temperature in °F. At APCL a refractometer is used to measure the
refractive index of hydrogen peroxide. To determine concentration the measured
refractive index of the hydrogen peroxide is compared against previously recorded values
of refractive index for a range of H2O2 concentrations.3 This data was recorded at a fixed
temperature of 77°F therefore a heater/refrigerator system is used to maintain the
refractometer at this temperature as well.
4.7 Pressure Budget
Prior to beginning test procedures it is customary to calculate the expected
readings from each piece of instrumentation. Estimates of the pressure at each
measurement location in the system are especially important when using cavitating
venturis since the downstream pressure has a significant influence on cavitation. Since
only a certain range of back pressures are allowed based on venturi supply pressure and
flow rate the summary of system pressures is often termed a pressure budget. Calculation
of the pressure budget begins by calculating the chamber pressure, Pc2, during the
monoprop and biprop modes of operation. Equation 2.1 is used to calculate chamber
pressure based on known test parameters of throat diameter, mass flow rate, and C* and
an assumed C* efficiency. An efficiency of 98% is a good upper bound estimate for both
monoprop and biprop cases. The characteristic velocity is dependent on H2O2
concentration for the monoprop case and mixture ratio for the biprop case. Both of these
parameters are set for each test.
The pressure drop across the fuel injector can be calculated using equations 2.2
through 2.4 and added to the chamber pressure to determine the injector inlet pressure,
73
Pfu_inj. The cavitating venturi supply pressure, Pfu_cv, is calculated with equation 4.4
using the desired mass flow rate and selected cavitating venturi geometry, Table 4.1. To
verify cavitation the injector pressure is divided by the fuel venturi inlet pressure. If this
ratio is greater than 0.75 cavitation will not occur and a new venturi must be selected
which requires a higher supply pressure to meet the necessary flow rate. In some cases
none of the venturis available at APCL meet the mass flow and supply pressure
requirements. A new cavitating venturi may need to be ordered at that point
Calculations for the oxidizer line pressures work similarly to the fuel, but the
catalyst bed pressure drop is more difficult to calculate. Typically, the pressure drop is
estimated based on previous test data. A conservative assumption for pressure drop
across the GK bed is 400 psid and for the PCI bed is 500 psid for both operational modes.
The pressure drop will be lower during biprop operation than monoprop due to the
increased back pressure on the bed. This decreases the flow rate through the bed and as a
result the pressure loss. The pressure drop is added to the catalyst bed outlet pressure,
which can be assumed to be roughly equivalent to the chamber pressure, to determine the
catalyst bed inlet pressure, Pcb_in . The venturi calculations for the oxidizer line proceed in
the same manner as for the fuel line. Ullage pressures for both the oxidizer and fuel
system, Pox_ull and Pfu_ull, are typically anywhere from 0-150 psi greater than the venturi
inlet pressures. This is due to pressure losses associated with the valves and bends in the
lines between the tank and the venturi. These losses increase as the flow rate, or velocity
in the feed line, increases. A conservative estimate would be anywhere between 50 and
150 psid, but it is better to guess high than low to ensure cavitation. Deviations of actual
pressure drop from these estimates will affect the mass flow rate through the system.
The upstream chamber pressure, Pc1, is more difficult to estimate due to its
location in the recirculation zone behind the rearward-facing step. It is usually estimated
to be equal to the downstream chamber pressure. The decomposition temperature can be
estimated using a thermochemistry code4 and is dependent on concentration. The
chamber skin temperature should be roughly equal to 350°F and oxidizer temperature
should be around room temperature, 77°F. The chamber temperatures, Tc1-Tc4, are very
difficult to estimate and typically fail due to high temperatures in the chamber. They
74
roughly measured the wall temperature and a conservative estimate would be around
1500°F for biprop operation and around 800°F for monoprop. A table of estimated
conditions for the baseline design conditions, see Chapter 2, is shown in Table 4.4. The
baseline engine used the 0.111 inch throat diameter cavitating venturi for the oxidizer line
and the 0.058 inch venturi for the fuel line, see Table 4.1.
Table 4.4: Pressure budget for a test at baseline design conditions using the GK catalyst bed, see Chapter 2.
Designation Monoprop Biprop Pox_ull (psia) 1550 1550 Pox_cv (psia) 1400 1400 Pcb_in (psia) 667 920
Pcb_in/Pox_cv (--) 0.43 0.66 Pfu_ull (psia) -- 1750 Pfu_cv (psia) -- 1700 Pfu_inj (psia) -- 608
Pfu_inj/Pfu_cv (--) -- 0.36 Pcb_out, Pc_1, Pc_2 (psia) 267 520
Tox (°F) 77 77 Td (°F) 1390 1390
Tc1-Tc4 (°F) 800 1500 Tskin (°F) 350 350
4.8 Test Procedure
Four people are required to conduct a rocket test at APCL, and each of these
people has a specific set of responsibilities during the test. The test conductor is
responsible for all test operations, reads the test procedures, and maintains the list of test
conditions. The test operator loads propellants, operates manual valves and regulators,
and performs other functions related to propellant or pressurant as dictated by the test
conductor. The data system operator runs the LabVIEW program, monitors and records
test data, and maintains operability of all instrumentation and controls for each test. The
site safety director maintains functionality of safety equipment, keeps site clear of
unauthorized personnel, and ensures that test personnel follow safety procedures at all
times.
75
A typical test procedure can be split into four parts: test preparation, propellant
loading, test firing, and shutdown. Test preparation begins by measuring the
concentration of the hydrogen peroxide and, if required, diluting to a lower concentration.
Next, the catalyst bed heater is turned on when using the GK catalyst bed. Typically
one-half hour is required for the bed to heat up sufficiently, which is roughly the amount
of time it takes to complete the test procedures. Following this step the computer,
instrumentation, valves, relay board, and chassis are powered up. Next the LabVIEW
program file is opened and the file name, scan rate, and channel list are set. Once this
information has been verified by the test conductor the data system operator can begin
running the program. Next the communication between the computer and the
instrumentation is checked as well as the readings from each instrument to verify they are
functioning properly. Then the outside doors to the test cell are opened, and the cameras
are set up and checked for functionality. Then the VHS tapes used to record each camera
view are queued to the correct position and the test number is recorded on each tape.
Following this all of the manual regulators on the panel in the control room are fully
unloaded, the nitrogen and helium supplies are checked for adequacy, and if so the
helium regulator is loaded to 100 psia. For most tests a nitrogen supply of at least 2200
psia is required to maintain ullage pressure. Next, the remotely controlled valves are
cycled to make sure they are functioning properly. During the final step of test
preparation each of the manual and remote valves are verified to be in their power off
position.
The fuel is loaded first during the test procedure because it can safely sit in its
tank for a longer period of time than hydrogen peroxide. The loading procedure is
identical for both propellants, but extra care is required for handling hydrogen peroxide
and is described here. Following test preparation the oxidizer tank vent valve is closed
and the isolation valve is opened, this allows the propellant to fill the system all the way
down to the main valve. The vacuum isolation valve is opened, the vacuum line is
connected to the pump, and the pump is turned on. At this point the warning light is
turned on to alert anyone outside the building that a test is about to take place. The
pressure in the tank is monitored and when it reaches approximately 4 psia the vacuum
76
isolation valve is closed, the pump is turned off, and the vacuum line is disconnected
from the pump. Next, the test operator puts on the appropriate safety gear for handling
hydrogen peroxide and brings the propellant into the test cell. The jug of propellant is
placed on a scale and the initial mass is recorded, the fill valve is opened, and the
propellant is sucked into the tank. The data system operator must monitor the
temperature and pressure in the tank at all times while hydrogen peroxide is being loaded.
In the event that rapid decomposition begins in the tank these are the first signs of
problems. When the required amount of mass has been loaded into the tank the fill valve
is closed and the final mass is recorded. Then the vent valve is opened and the tank is
allowed to return to ambient pressure. Before returning the propellant jug to storage and
taking off safety gear the test operator must make a thorough review of the propellant
tank and feed lines to make sure there are no obvious propellant leaks. Since fuel loads
are usually small a graduated cylinder is used to load the propellant into the tank. This
requires volume-based loading rather than mass-based, which is the case for H2O2.
While all the pressure transducers are measuring ambient pressure the data system
operator acquires two seconds of data. This data is used to zero the pressure transducer
measurements in the data reduction code. This is explained in the next section. Next, the
door between the test cell and control room is bolted shut. Following this the oxidizer
and fuel purge regulators are loaded to the desired pressure. Typically, the oxidizer purge
is loaded to 100 psia while the fuel purge is load to 1.5 to 2.0 times the monoprop
chamber pressure. This is to ensure that hot decomposed gases do not enter the fuel
injector during the monoprop stage of the test. Then the tank vent valves are closed, the
pressurization valves are opened, and the ullage pressure regulators for both tanks are
loaded to the desired test pressures. As previously described, these regulators actually set
the pressure in the dome of the dome-loaded regulators located in the test cell. Once the
tanks have reached the desired ullage pressure the valve timing sequence is entered into
the LabVIEW code. The timing sequence is unique to each catalyst bed and will be
explained in more detail later. Next, the VCR’s are set to begin recording, data
acquisition is started, and then the fire button in LabVIEW is pressed to start the fire
sequence. Once the sequence is complete the VCR’s are stopped.
77
After the completion of the test the ullage pressure regulators are unloaded, the
tank vent valves are opened, and the tank pressure is allowed to return to ambient. While
the tank is venting the purge valves are opened to purge any remaining propellant from
the engine. The oxidizer purge valve is always opened before the fuel purge to prevent
fuel from being blown into the catalyst bed. This could potentially cause significant
internal damage to the catalyst bed. While the purge valves are still open the regulators
are unloaded, fuel first, and then the valves are closed. This guarantees that all the
pressure has been vented from the purge lines. At this point the tanks should be fully
vented and the pressurization and isolation valves are closed. In most cases, the
propellants are run to completion during a test. This means that there is no propellant left
in the tanks or lines following the test. If propellant is suspected to remain in the lines a
dump procedure, not described here, must be followed to completely drain the
appropriate tank or tanks. At this point the test is completed, the LabVIEW program can
be stopped, and all the power can be turned off. The nitrogen and helium bottles must be
closed and each line must be vented to ambient pressure.
4.9 Firing Sequence
Each catalyst bed required some form of warm-up prior to running an autoignition
test. This was done to make sure that the bed was fully decomposing the hydrogen
peroxide before any fuel was supplied to the engine. The decomposition efficiency of the
catalyst bed can be determined in a number of ways including monitoring the chamber
pressure, decomposition temperature, or by visual observation of the exhaust gases. A
clear exhaust plume indicates full decomposition while a cloudy plume indicates poor
decomposition. The GK catalyst bed, as previously mentioned, is pre-heated for
approximately one-half hour prior the actual test firing. In addition to this the catalyst
bed is fed a number of short pulses of hydrogen peroxide to warm it further. A typical
pulse sequence consists of two half second pulses followed by two one second pulses
with at least ten seconds in between. The ten second waiting period allows the heat
generated during the pulse to soak into the bed. A minimum of ten seconds wait period is
78
required before initiating the autoignition test as well. This pulse sequence is usually
sufficient to produce good decomposition. The PCI catalyst bed, on the other hand, is not
built to handle short duration, cyclic pulsing. For this reason the bed is warmed by
running it for five seconds and followed by at a least ten second wait before commencing
the autoignition test. By the end of the ten second warm-up period the catalyst bed
should be adequately decomposing the hydrogen peroxide. For both catalyst beds, the
mass flow rate of hydrogen peroxide used during the warm-up period should be the same
as required for the autoignition test. A benefit of the catalyst bed warm-up period is that
is offers the opportunity to evaluate the catalyst bed performance prior to the autoignition
test. If the catalyst beds are not functioning properly at the end of the warm-up period the
test can be aborted at that point. Whereas, if there were no pulse sequence there would
not be enough time recognize poor decomposition and then abort before the fuel flow was
turned on.
Typically before any pulsing has been performed the purge lines are opened in the
system. As previously mentioned, the oxidizer purge valve should always be opened
before the fuel purge to prevent fuel vapor from entering the catalyst bed. Fuel droplets
usually remain in the injector manifold from previous tests and can be blown into to the
engine when the nitrogen purge is turned on. Therefore, the oxidizer purge valve is
opened first followed by the fuel purge valve. Once it is visually verified that there is no
fuel vapor exiting the engine the oxidizer purge valve is turned off. This is to prevent the
nitrogen from cooling the catalyst bed and from contaminating the catalyst material. The
fuel purge usually remains on during the pulse sequence as well as the autoignition test.
There are check valves in both the oxidizer and fuel purge lines to prevent liquid
propellant or other gases from penetrating into the lines during the test. If at any point
during test operations the fuel purge valve is closed the oxidizer purge must be opened
before the fuel purge can be opened again. As soon as any fuel vapor has dissipated the
oxidizer purge is closed. Also, before the autoignition test the water flow to the
deflection plate is turned on. It takes approximately ten seconds for the water to fill the
manifold behind the plate at which point it begins to flow full. After the test the water
flow is turned off.
79
Following the pulse sequence the autoignition test is begun by starting the
hydrogen peroxide flow to the catalyst bed. After one-half second the fuel flow is turned
on and remains flowing for another second. Following fuel shutdown the hydrogen
peroxide flows for two more seconds and then is turned off. By lagging the fuel by
one-half of a second any transients involved with the start-up of the catalyst beds are
bypassed allowing the beds to reach steady-state decomposition. This lag is also short
enough that it does not allow the decomposed gases to heat the engine significantly,
which may affect autoignition behavior. If the conditions in the engine are sufficient
autoignition should occur almost instantaneously upon fuel injection. For this reason the
biprop test duration is limited to one second in length. Usually, after the fuel flow is
turned off, there is residual fuel remaining in the feed lines that trickles into the engine.
To burn off any residual fuel in the engine, injector, or feed lines the hydrogen peroxide
flow remains on for two additional seconds following fuel shut down. Typically the
oxidizer and fuel main valves remain open for one second following propellant depletion
to allow nitrogen in the tank to exhaust through the engine. This thoroughly purges the
entire feed system of any remaining drops of propellant. The typical valve sequencing
for each catalyst bed engine assembly is shown in Table 4.5.
80
Table 4.5: Typical valve firing sequence for each catalyst bed design.
Valve (ON/OFF)
GK (seconds)
PCI (seconds)
Oxidizer Purge ON t – 58.0 t – 30.0 Fuel Purge ON t – 56.0 t – 28.0 Oxidizer Purge OFF t – 51.0 t – 23.0 Oxidizer Main ON t – 48.0 -- Oxidizer Main OFF t – 47.5 -- Oxidizer Main ON t – 37.5 -- Oxidizer Main OFF t – 37.0 -- Oxidizer Main ON t – 27.0 -- Oxidizer Main OFF t – 26.0 -- Oxidizer Main ON t – 16.0 t – 20.0 Oxidizer Main OFF t – 15.0 t – 15.0 Deflection Plate Water ON t – 10.0 t – 10.0 Oxidizer Main ON t – 0.5 t – 0.5 Fuel Main ON t – 0.0 t – 0.0 Fuel Main OFF t + 1.0 (+1.0) t + 1.0 (+1.0) Oxidizer Main OFF t + 2.0 (+1.0) t + 2.0 (+1.0) Deflection Plate Water OFF t + 5.0 t + 5.0 Fuel Purge OFF t + 10.0 t + 10.0
81
CHAPTER 5: EXPERIMENTAL RESULTS
As discussed in Chapter 3 the primary objective of this study was to develop an
autoignition model that could be used to aid in the design of a H2O2/kerosene staged
rocket engine. Based on past data the decomposed gas temperature, equivalence ratio,
and gas velocity were reasoned to be the most influential to autoignition in these engines.
Testing was structured to investigate each of these factors through the hydrogen peroxide
concentration, mixture ratio of H2O2 to JP-8, and chamber contraction ratio respectively.
A secondary objective of this study was to develop a better understanding of the design
and operation of these staged-bipropellant engines. The data and experience accumulated
through each autoignition test builds toward this goal.
5.1 Test Plan Overview
In most kerosene autoignition studies the gas temperature is gradually increased
over the course of a test to the point of autoignition. Operating conditions such as
pressure, gas flow velocity, and equivalence ratio remain relatively constant during this
process. When air is used as the working gas it can be gradually heated to increase its
temperature, but modifying the temperature of decomposed hydrogen peroxide requires a
different approach. Since the decomposition temperature of hydrogen peroxide is
dependent on its concentration in liquid form the concentration must be varied to alter the
decomposition temperature. Walder8 mixed water with hydrogen peroxide prior to
entering a catalyst pack to continuously control its concentration. Unfortunately, the
setup of Test Cell A at APCL at the time of testing was not conducive to this type of
operation. In addition, if modifications were made to the stand there still would have
82
been a number of issues to consider regarding the mixing of water and hydrogen peroxide.
Some of these include: determining the time and method required to completely mix the
liquids, damaging the catalyst beds through water soaking, altering the control program
for active adjustment of water flow rate, and sizing new propellant tanks to meet total
expected run time during a test. To avoid these issues hydrogen peroxide of 90 and 98%
concentrations were diluted to lower concentrations, as described in Chapter 4, prior to
testing. The advantage of this approach is that the concentration can be measured very
precisely prior to loading. However, a disadvantage exists in that the decomposition
temperature is set for each test.
The test plan for this autoignition study was not predetermined, but instead
evolved based on the outcome of each test. Testing began by running the engine at
baseline conditions, Chapter 2, but using a nozzle with a contraction ratio of 3.0. If
autoignition were achieved at these conditions the equivalence ratio would be increased
for the following test. If autoignition occurred at these new conditions then the
equivalence ratio would be increased again for the next test and again until a value was
found at which no autoignition occurred. In event that autoignition was not achieved
during the initial test the equivalence ratio would be decreased for the next test.
Subsequent tests would follow a similar pattern as the first case but now the equivalence
ratio would continually be decreased until autoignition occurred. This procedure
determines the autoignition boundary in terms of equivalence ratio at a specific
decomposition temperature and contraction ratio. After defining the autoignition
boundary for 90% H2O2 at a contraction ratio of 3.0 this process could be extended to
other concentrations. In addition, the contraction ratio could be changed and the process
repeated at a constant concentration.
To modify the equivalence ratio the hydrogen peroxide mass flow rate was varied
while the fuel mass flow rate was kept at the baseline value. The reasoning behind this
was that if the hydrogen peroxide flow were kept constant the fuel flow would need to be
increased to increase equivalence ratio. Since pressure drop varies with the square of the
fuel flow rate the injector pressure drop would increase substantially with flow rate along
with the venturi back pressure as a result. If the fuel flow rate were increased past a
83
certain point cavitation would be impossible with any venturi because the back pressure
on the venturi would be too large. On the other hand, the fuel flow rate would need to be
decreased to decrease equivalence ratio. Thus, pressure drop would decrease as well,
which would ensure cavitation. However, the injection velocity would also decrease
lowering the fuel momentum and potentially causing poor fuel distribution. In addition,
if the injector pressure drop fell too low in relation to chamber pressure it could affect the
stability of the engine. New injectors could be fabricated with new geometry to correct
these problems, but the engine would need to be disassembled to insert the new hardware.
As a result, it was decided to vary the hydrogen peroxide flow rate. One benefit of
varying H2O2 flow rate over fuel flow rate is that the pressure drop across a catalyst bed
is typically much less sensitive to changes in mass flow rate than a fuel injector. In
addition, catalyst beds are usually more resistant to instability over a fairly large range of
flow rates.
Three methods were used to determine whether or not autoignition occurred
during each test. The first method of evaluation was through real-time visual observation
of the exhaust plume. This was accomplished by viewing two television monitors,
located in the control room, during the test. These views were provided by two cameras
located in the test cell, one on the north side and one on the south side of the cell. In
most cases it is difficult to observe the presence of a delay between the instant of fuel
injection and the appearance of a flame in real-time. For this reason, a second evaluation
of autoignition was achieved through frame-by-frame playback of the test. The cameras
used during testing recorded at approximately 30 frames per second or about one frame
every 30 milliseconds. Significant delays in autoignition or unstable combustion can be
identified at these slow playback speeds. Finally, autoignition could also be scrutinized
by viewing plots of chamber pressure data versus time. The rise in magnitude of
chamber pressure following fuel injection can be evaluated using this data as well as the
lag between the chamber pressure and fuel injector pressure rise.
84
5.2 Data Reduction
As shown in Table 4.3, there are sixteen different measurements that are made
during a typical autoignition test. The output from each of these pressure transducers and
thermocouples are connected to a specific terminal or channel in the SCXI chassis.
During a test LabVIEW is used to sample the reading from each channel and record it to
a data file 1000 times each second. Each successive sample of data is placed in a new
row in the data file and each channel of data is placed in its own column in the file. As a
result, sampling all sixteen channels for one second would create a data file with 1000
rows and 16 columns. Typically each column of data is referred to as an array.
5.2.1 Pressure Transducer Data
Since the thermocouple readings are converted to units of degrees Fahrenheit by
LabVIEW it is recorded in temperature units in the data file. Pressure data, on the other
hand, is recorded in units of volts and must be converted to pressure units, psia, using a
MATLAB data reduction file, shown in Appendix D. As described in Chapter 4, the
Druck pressure transducers have a linear calibration curve of pressure versus voltage.
For a transducer with a range of 0-3000 psia the slope of the calibration curve is 750
psi/volt. The first step in conversion to pressure units is to multiply the voltage data by
the slope of the calibration curve, mpt:
[ ] [ ]ipti Vmp = , (5.1)
Here [V]i is an array of voltage data and [p]i is the calculated array of pressure
data. Brackets, [], are used to denote that voltage and pressure are one-dimensional
arrays. The channel of pressure transducer data used in the calculation is denoted by the
subscript ‘i.’ As it currently stands this equation does not give the correct absolute
pressure reading, i.e. when an element of [V]i is equal to five volts the same element of
[p]i does not equal 3000 psia but 3750 psia. An adjustment factor must be used to correct
the pressure calculated in equation 5.1 to the actual pressure. Typically this is done by
85
taking two seconds of data, called zero data in Chapter 4, while the entire system is at
ambient pressure. At this point all pressure transducers should be reading approximately
14.7 psia. The voltage data taken during this initial two seconds is multiplied by the
slope of the calibration curve using equation 5.1 and then averaged. The adjustment
factor is calculated as follows:
avgzeroiptatmavgzeroiatmadji Vmpppp _____ −=−= , (5.2)
The constant adjustment factor is represented as pi_adj, the atmospheric pressure is
denoted by patm, and the average zero pressure and voltage data are represented as
pi_zero_avg and Vi_zero_avg respectively. The subscript ‘i’ is used in equation 5.2 because the
averaged zero values and adjustment factors are different for each transducer. The actual
pressure as measured by the transducers can now be calculated from:
[ ] [ ] adjiipti pVmp _+= , (5.3)
The data reduction code is also used to plot pressure and temperature data as a
function of time. Time is calculated by divided the sample number by the sample rate. A
typical plot of chamber pressure, pc2, versus time during a test in which autoignition
occurred is shown in Figure 5.1. The monoprop, biprop, and shutdown segments of the
test are clearly distinguished in the plot. A steady chamber pressure is achieved within
approximately 0.2 seconds of the start of both the monoprop and biprop sections of the
test.
Figure 5.1: Plot of pc2 from an autoignition test using PCI catalyst bed. Test conditions:
98% H2O2, φ = 1.84, CR = 3.0.
86
5.2.2 FFT and Filtering
A benefit of using MATLAB for data reduction is that it has built- in fast Fourier
transform, FFT, and filter design functions. The fast Fourier transform is an algorithm
used to speed up the computation of the discrete Fourier transform, DFT, of an array of
data. The DFT is used to convert data from the time domain to the frequency domain and
is used to determine which frequencies are most dominant in a set of noisy or oscillatory
data. Knowledge of the dominant frequency in chamber pressure data can help in
designing a filter to drown out the noise or to determine if an instability exists in the
chamber. A plot of a noisy chamber pressure signal during monoprop operation is shown
in Figure 5.2a).
A signal in the time domain is broken down into a sum of sine and cosine
functions with specific magnitudes and natural frequencies by the DFT. Resolution in the
frequency domain, or the resolution in the natural frequencies of the sine and cosine
functions, is dependent on the resolution in the time domain and the number of data
points used to compute the DFT. The time resolution for this study is equal to 0.001
seconds, or one over the scan rate. Most FFT algorithms require 2p points to compute the
FFT more efficiently, usually the number of points is set to 256, or p = 8. This would set
the frequency resolution at approximately 4 Hz based on the time resolution used in this
study. During data reduction the number of points used in the FFT was typically much
greater than 256, often nearer to 1024 points or p = 10, which dropped the frequency
resolution to less than 1 Hz. The ‘fft’ function in MATLAB performs a discrete Fourier
transform on an array of data and outputs the real and imaginary parts of the Fourier
coefficients corresponding to each frequency. The magnitude of the Fourier coefficients
is computed by taking the square root of the sum of the squares of the real and imaginary
parts. A plot of the magnitude of the Fourier coefficients versus frequency is called a
power spectrum. The power spectrum indicates which frequencies are most dominant in
a particular set of data. The power spectrum computed from the data in Figure 5.2a) is
shown in Figure 5.3a) and b). The high magnitude at a frequency of approximately 43
Hz indicates that this is the dominant frequency in the data.
87
A low-bypass filter is used to eliminate frequencies inherent in a set of data that
are greater than a critical value, called the cutoff frequency. Plotting the power spectrum
of a set of data is often helpful in determining the cutoff frequency. A function in
MATLAB, called ‘butter’, designs a low-bypass digital Butterworth filter of order n with
a specified cutoff frequency. The coefficients that are to be used in the numerator and
denominator of the nth order transfer function describing the filter are output as two
separate arrays by the ‘butter’ function. These arrays as well as the array of data to be
filtered are input to a second MATLAB function called ‘filter.’ This function outputs the
filtered form of the data which excludes all frequencies greater than the cutoff frequency.
The data plotted in Figure 5.2a) was filtered using a cutoff frequency of 15 Hz and the
result is shown in Figure 5.2b). This plot shows that nearly all the noise and oscillations
were removed from the signal.
a) b)
Figure 5.2: Plots of pc2 in a) unfiltered and b) filtered form. Test conditions: 87.5% H2O2, φ = 1.40, and CR = 3.0.
88
a) b)
Figure 5.3: a) Full and b) partial power spectrum of monoprop chamber pressure data shown boxed in Figure 5.2a).
5.2.3 Calculations using Measured Data
The temperature and pressure data collected during the steady state portions of
both the monoprop and biprop sections of each test are averaged using the data reduction
file. These average values of pressures and temperatures are used in subsequent
calculations. The oxidizer flow rate is calculated using equation 4.4 with the averaged
oxidizer cavitating venturi inlet pressure from each mode of test operation. The density
of the hydrogen peroxide is calculated using equation 4.8 based on the measured
concentration and the averaged temperature of the hydrogen peroxide in the tank. The
pressure drop across the catalyst bed, ?pcb, is calculated from the following equation:
outcbincbcb ppp __ −=∆ , (5.4)
The fuel flow rate is also calculated from equation 4.4 using the fuel cavitating
venturi inlet pressure during biprop mode. The density of JP-8 fuel varies with
temperature, but the fuel temperature was never measured during testing. Since the fuel
was stored at room temperature the density was calculated assuming an average
temperature of 72.5°F, the density varies by less than 1.0% with a ±5°F variance from
this average value. The mixture ratio, O/F, during biprop mode is calculated as follows:
89
f
ox
mm
FO&&
= , (5.5)
The equivalence ratio was calculated using equation 3.6. The pressure drop
across the fuel injector, ?pf, is calculated from:
1_ cinjff ppp −=∆ , (5.6)
The discharge coefficient of the fuel orifices cannot be directly calculated from
the pressure drop found in equation 5.6. This is due to the fact that pf_inj is measured at
the entrance to the injector manifold not at the entrance to the orifices. As a result, the
calculated pressure drop contains the pressure drop across the feed line and manifold as
well as the orifices. Calculating a discharge coefficient using the pressure drop found
from equation 5.6 would actua lly be the coefficient of the entire injector not just the
orifice. The static pressure behind the rearward step, pc1, is used in this calculation
because the velocity of the gas at that point is closest to what the velocity would be in the
gas port. The velocity at the end of the chamber is much lower than in the gas port and as
such using pc2 for this calculation would give erroneous results. Since the diameter at the
exit of the PCI catalyst bed is roughly equivalent to the diameter of the gas port the
catalyst bed exit pressure, pcb_out, could be used in place of pc1. The exit diameter of the
GK catalyst bed, on the other hand, is significantly larger than that of the gas port and, as
a result, the velocity is much lower there. This prevents the use of pcb_out in equation 5.6
when using the GK catalyst bed. The velocity of the fuel exiting the orifices was
calculated using equations 2.3 and 2.4 assuming a CD of 0.8.
Using the calculated mass flow rates the characteristic velocity can be calculated
from the following equation which is a modified version of equation 2.11:
tot
cttotc
m
gApC
&_2=∗ , (5.7)
Due to the small contraction ratios used during testing the Mach number at the
end of the chamber was too significant to ignore. As a result, the static pressure
measured at the end of the chamber, pc2, was adjusted to a total pressure, pc2_tot, and used
in equation 5.7. Table 5.1 below lists the Mach number and total-to-static pressure ratio
at the end of the chamber based on contraction ratio for both monoprop and biprop
90
conditions. The Mach number at the end of the chamber, Mc, was calculated iteratively
from the following equation:
( )121
2
21
11
21 −+
−
++
=γ
γ
γγ c
c
MM
CR , (5.8)
For the biprop case the specific heat ratio, ?, varies widely with mixture ratio and
chamber pressure. A value of 1.22 was used as an average based on the tested conditions.
In monoprop mode and average specific heat ratio was also used and set at 1.265, which
corresponds to that of decomposed 90% H2O2, since the Mach number and pressure ratio
vary by less than 0.1% over the range of hydrogen peroxide concentrations used during
testing. As Table 5.1 shows the Mach number varies by less than 0.1% between
monoprop and biprop specific heat ratios as well. The total pressure ratio is calculated
from the isentropic flow relation as follows:
12
2
_2
21
1−
−
+=γ
γγ
cc
totc Mp
p, (5.9)
For the monoprop case, as discussed in Chapter 2, the total mass flow rate from
equation 5.7 is equal to the oxidizer flow rate only. In biprop mode the total mass flow
rate is equal to the sum of the fuel and oxidizer flow rates. The efficiency of
decomposition in monoprop mode and the efficiency of combustion in biprop mode were
calculated using the following equation for C* efficiency, *Cη :
∗
∗
=th
C CC
*η , (5.10)
The theoretical C*, ∗thC , in monoprop mode is dependent on the concentration of
the hydrogen peroxide. Table 5.2 lists theoretical C* values along with other
decomposed gas properties based on concentration. For biprop mode the theoretical C* is
strongly dependent on the mixture ratio and hydrogen peroxide concentration and weakly
on the chamber pressure. The variation in theoretical C* with equivalence ratio for the
tested concentrations of H2O2 assuming a chamber pressure of 500 psia is shown in
Figure 5.4.
91
Table 5.1: Variation in chamber gas properties based on chamber contraction ratio. CR (--) 3.0 5.0 6.5
Conditions Monoprop Biprop Monoprop Biprop Monoprop Biprop ? (--) 1.265 1.220 1.265 1.220 1.265 1.220
Mc (--) 0.200 0.201 0.118 0.119 0.091 0.091
2
_2
c
totc
p
p 1.026 1.025 1.009 1.009 1.005 1.005
The trajectory of the liquid fuel jet is most important at the instant of fuel
injection prior to combustion. For this reason, the gas flow properties and momentum
ratio were calculated only for the monoprop chamber conditions. The decomposed gas
Mach number, velocity, and density were calculated assuming both compressible and
incompressible flow. In both cases the total pressure of the decomposed gas was
assumed to be equal to the monoprop total chamber pressure, pc2_tot_mono, and the total
temperature of the decomposed gas was calculated using the following equation:
thtoxmonoCtox TT _2
_*η= , (5.11)
Here the monoprop decomposition efficiency is denoted by ?C*_mono, and the
theoretical total temperature of the decomposed gas is represented by Ttox_th. The
theoretical decomposed gas temperature is shown in Table 5.2 as a function of
concentration. Equation 5.11 was due to unreliable decomposed gas temperature
measurement. For the case of compressible flow equations 2.7, 2.9, and 2.10 and the
method described in Chapter 2 were used to calculate gas Mach number, velocity, and
density. For the case of incompressible flow these values were calculated from modified
forms of equations 2.7, 2.9, and 2.10 as follows:
γox
toxu
oxtox
oxox MW
TRAp
mM
&= , (5.12)
ox
toxuoxoxoxox MW
TRMaMV
γ== , (5.13)
toxu
oxtoxox TR
MWp=ρ , (5.14)
92
The value of the specific heat ratio and molecular weight varies with the
concentration of hydrogen peroxide as shown in Table 5.2. The momentum ratio of the
liquid fuel to the decomposed hydrogen peroxide was calculated using equation 2.24 and
the shear layer characteristic time was calculated using equation 2.12.
Table 5.2: Decomposition properties of hydrogen peroxide as a function of concentration.
W (%) 85% 87.5% 90% 94% 98% Ttox_th (°F) 1173 1283 1393 1570 1746 C*th (ft/s) 2904 2996 3083 3217 3343
MWox (lbm/lbm-mol) 21.83 21.97 22.11 22.33 22.56 ? (--) 1.274 1.269 1.265 1.258 1.251
Mass Fraction O2 0.400 0.412 0.423 0.442 0.461 Mass Fraction H2O 0.600 0.588 0.577 0.558 0.539
O/Fs (--) 8.49 8.25 8.02 7.68 7.36
3500
3750
4000
4250
4500
4750
5000
5250
5500
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Equivalence Ratio, φ (--)
Ch
arac
teri
stic
Vel
oci
ty, C
* (f
t/s)
98% H2O294% H2O290% H2O287.5% H2O285% H2O2
Figure 5.4: Variation in C* with φ for H2O2 combusting with JP-8.
93
5.3 Uncertainty Analysis
An analysis was performed to determine the relative uncertainty in all calculated
parameters and the route by which error propagated through each calculation. The
method of uncertainty analysis presented in Fox and McDonald61 was used in this
autoignition study. The uncertainty analysis is based around the relative uncertainty, uxi,
of a measured quantity, xi, and is defined as the variation or random error in the value, dx i,
divided by the measured value itself. The variation in any measurement is the sum of
fixed and random error. Fixed error is repeatable and can be eliminated through proper
calibration of a measuring device. In this analysis the fixed error is assumed to be
negligible. The goal of any uncertainty analysis is to estimate the random error, which is
nonrepeatable, in each calculated value and to determine how random error propagates
through to each calculated value. Typically the random error in any measurement is
estimated as plus or minus one-half of the smallest measuring increment of the device.
For instance, the accuracy of a 3000 psia pressure transducer is stated at ±7.5 psia or
0.25% of full scale. This correlates to a random error estimate of ±3.25 psia or 0.125%
of full scale. In most cases sound engineering judgment based on experience is used to
estimate random error. Generally, a conservative approach is taken in order to avoid
underestimation of random error.
The relative uncertainty of a calculated variable, R, is found from the following
equation assuming R is a function of x1, x2, … xn:61
21
22
22
2
2
11
1 ...
∂∂
++
∂∂
+
∂∂
±= xnn
nxxR u
xR
Rx
uxR
Rx
uxR
Rx
u , (5.15)
This guideline for computing relative uncertainty was applied to all the calculated
values used in this study. A summary of the resulting equations for uncertainty of each
calculated variable is shown in Appendix E. As an example, the uncertainty in the
characteristic velocity can be determined as follows:
( ) ( ) ( )[ ] 21
222_2* 2 totmDthtotpcC uuuu &++±= , (5.16)
94
The estimated random error for each measured test parameter is shown in Table
5.3. All pressure measurements were assumed to have an error equal to the accuracy of
the pressure transducer, which may be a slight overestimation. Also, the error in the total
pressure ratio used to correct the static chamber pressure measurement was assumed to be
negligible since it does not vary significantly with the specific heat ratio. The error in the
measurement of the throat diameter of each cavitating venturi was set equal to zero.
Instead this error was lumped into the estimation of the error in the discharge coefficient.
This was also done in estimating the error of the fuel injector orifice diameter and
discharge coefficient. All other diameter and length measurements were assumed to have
an error of ±0.005 inches, which is based on machining tolerances and wear and tear on
the parts. Since the temperature of the fuel was not measured it was assumed to have a
fairly large error of ±5.0°F. The oxidizer temperature was measured by a thermocouple
and the error was likely overestimated at ±2.0°F. The measurement of the refractive
index of hydrogen peroxide was accurate to within ±0.0005, neglecting human error, and
puts the error in the measurement of concentration at approximately ±0.1%.
The error in the theoretical decomposition temperature and monoprop C* were
estimated very conservatively. The values of the decomposition temperature and C*
were calculated using a thermochemistry code assuming an exact hydrogen peroxide
concentration, pressure, and liquid temperature. In reality these theoretical values vary
based on the operating conditions of each test and for this reason the error in
decomposition temperature was estimated at ±10.0 °F and the error in C* at ±10.0 ft/s. A
similar logic was applied to estimating the error in the biprop theoretical C*. The
difference here is that the theoretical C* for biprop mode varies significantly with
equivalence ratio especially over the range of values used during autoignition testing,
shown boxed in Figure 5.4. The slope of the theoretical C* curves is very steep in this
region of equivalence ratios and small deviations in equivalence ratio have a large effect
on C*. In addition, small errors in hydrogen peroxide concentration and chamber
pressure can also result in large changes in C*. For these reasons the error in theoretical
C* for the biprop case was estimated at ±20.0 ft/s.
95
Table 5.3: Estimated random error for all measured variables.
Measurement Description Estimated Random Error Pressure ± 7.5 psia
Chamber Diameter, Chamber Throat Diameter,
Oxidizer Port Diameter, Rearward Step Height
± 0.005 in.
Oxidizer Temperature ± 2.0 °F Hydrogen Peroxide
Concentration ± 0.1 %
Theoretical Decomposition Temperature
±10.0 °F
Theoretical Monoprop C* ± 10.0 ft/s Theoretical Biprop C* ± 20.0 ft/s All Cavitating Venturi Discharge Coefficients ± 0.007
All Cavitating Venturi Throat Diameters
± 0.0 in.
Fuel Injector Orifice Discharge Coefficient ± 0.05
Fuel Injector Orifice Diameter
± 0.0 in.
Fuel Temperature ± 5.0 °F
96
5.4 Data Summary
A total of 24 tests were conducted to investigate the relative affects of
equivalence ratio, decomposed gas temperature, and contraction ratio on the autoignition
of JP-8 in decomposed hydrogen peroxide. Hydrogen peroxide concentration was varied
from 85 to 98%, equivalence ratios ranged from 1.4 to 4.0, and contraction ratio was set
to values of 3.0, 5.0 and 6.5. Autoignition was classified into three regimes: strong, weak,
and no ignition based on visual observations from real time and slow-motion video and
recorded chamber pressure data. Tables of measured and calculated test data are
contained in Appendix F.
5.4.1 Strong Autoignition
Tests which resulted in strong autoignition were characterized by bright, stable
red-orange flames and calculated bipropellant C* efficiencies of over 90%. The delay
between the initiation of fuel injection and autoignition was typically very small. A plot
of chamber pressure, pc2, and fuel injector pressure, pfu_inj, from a strong autoignition test
running 90% H2O2 through the GK catalyst bed at an equivalence ratio of 1.59 and a
contraction ratio of 3.0 is shown in Figure 5.5a). As the figure shows the chamber
pressure rises sharply, indicating autoignition, approximately 0.1 seconds following the
rise in the fuel injector pressure. This most likely corresponds to the time required to fill
the fuel manifold as the pressure drop across the injector reaches approximately 100 psid
at this instant as well. The small hump in the fuel injector pressure prior to the initiation
of fuel flow is a result of mechanical vibration caused when the fuel main valve is opened.
There is a slight oscillation in the chamber pressure following autoignition before it
steadies out. The chamber pressure for a strong autoignition test typically increases by
approximately 100% from monoprop to biprop modes. For this particular test the
monoprop decomposition efficiency was approximately 97% while the biprop C*
efficiency was about 94%.
97
A frame-by-frame view of the startup of the biprop portion of this test is shown in
Figure 5.6. Clear decomposed hydrogen peroxide gas is being exhausted from the
engine in frames a) and b) of Figure 5.6. The decomposed gas contacts the water
cooling the deflector plate and vaporizes some of it to produce the white cloud of vapor at
the bottom left of frames a) and b). In frame c) the white cloud of vapor seems to grow a
little bit denser possibly indicating the presence of fuel vapor in the exhaust. In the
following frame, frame d), a bright red-orange flame appears indicating that autoignition
has occurred. Following this in frames e) and f) the flame continues to burn with the
same intensity indicating that it is quite stable. The sequence of frames pictured in
Figure 5.6 agree very well with the conclusions drawn from the pressure data plotted in
Figure 5.5a). In fact, the 0.1 second delay between the fuel injector pressure rise and the
chamber pressure rise make present itself as the increase in vapor density seen in frame c)
in Figure 5.6 prior to autoignition.
A similar result was seen in the pressure data and frame-by-frame representation
of the startup transient running the PCI catalyst bed at nearly identical conditions. This
test was run using 90% H2O2 at a contraction ratio of 3.0 and a nearly identical
equivalence ratio of 1.58. Monoprop decomposition efficiency was calculated at 94%
while the biprop C* efficiency was approximately 96%. The pressure data plotted in
Figure 5.5b) for this test is almost identical to that of the GK bed, shown in Figure 5.5a).
The main differences between the two are that chamber pressure rises slightly earlier
following the rise in fuel injector pressure than for the GK bed and there are no large
chamber pressure oscillations present following autoignition in the PCI case. The
chamber pressure in the PCI takes about 0.1 seconds to reach the steady-state value while
for the GK case it is only about 0.05 seconds.
The frame-by-frame representation of the startup of the biprop portion of this test
is shown in Figure 5.7. A similar white water vapor cloud is seen during the monoprop
phase in frames a) and b) of Figure 5.7 and it also seems to thicken in frame c) possibly
indicating fuel injection. The flame appears in frame d) indicating autoignition and
seems to have more predominantly orange color than frame d) in Figure 5.6. This could
be due to the difference in ambient light settings between the two tests. The flame
98
remains stable and its color and luminosity are nearly identical in frames e) and f). Again
the frame-by-frame view of this test agrees very well with the pressure data in Figure
5.5b). The orange flame seen in frame c) of Figure 5.7 may be a result of the long delay
in reaching the steady state chamber pressure during biprop mode.
a) b)
Figure 5.5: Plots of pfu_inj and pc2 at the point of injection for a strong autoignition test using: a) the GK catalyst bed using 90% H2O2 at φ = 1.59 and CR = 3.0 and b) the PCI
catalyst bed using 90% H2O2 at φ = 1.58 and CR = 3.0.
99
a) b)
c) d)
e) f) Figure 5.6: Frame-by-frame view of a strong autoignition test using GK catalyst bed.
Test conditions: 90% H2O2, φ = 1.59, CR = 3.0.
100
a) b)
c) d)
e) f) Figure 5.7: Frame-by-frame view of a strong autoignition test using PCI catalyst bed.
Test conditions: 90% H2O2, φ = 1.58, CR = 3.0.
101
5.4.2 Weak Autoignition
Tests classified as resulting in weak autoignition typically produced flames that
were very unstable and varied in color, from red-orange to green, and intensity. These
tests were characterized by large chamber pressure instabilities, in most cases, and
resulted in biprop C* efficiencies ranging from 60 to 90%. A typical plot of fuel injector
and chamber pressure at the start of the biprop portion of a weak autoignition test is
shown in Figure 5.8a). As the plot shows, the chamber pressure data for this test
contained significant pressure oscillations, the amplitude of which is nearly equivalent to
the average chamber pressure. The data was fed through a low-pass Butterworth filter
with a cut-off frequency of 15 Hz to eliminate these fluctuations. The filtered data is
plotted in Figure 5.8b). This test was run using the GK catalyst bed using 87.5% H2O2 at
a contraction ratio of 3.0 and an equivalence ratio of 1.62. The delay between the time in
which the fuel was turned on and the sudden rise in chamber pressure was approximately
equivalent if not shorter than that presented in Figure 5.5a) and b). However, the rise is
not as sharp and does not reach as high of a magnitude as in the strong ignition cases.
The monoprop decomposition efficiency for this test was about 93% and the biprop C*
efficiency was approximately 69%.
a) b)
Figure 5.8: a) Unfiltered and b) filtered plots of pfu_inj and pc2 at the point of injection for a weak autoignition test using the GK catalyst bed. Test conditions: 87.5% H2O2,
φ = 1.62, and CR = 3.0.
102
a) b)
c) d)
e) f)
Figure 5.9: Frame-by-frame view of a weak autoignition test using GK catalyst bed. Test conditions: 87.5% H2O2, φ = 1.62, CR = 3.0.
103
g) h)
i) j)
k) l) Figure 1.5 (cont.): Frame-by-frame view of a weak autoignition test using GK
catalyst bed. Test conditions: 87.5% H2O2, φ = 1.62, CR = 3.0.
104
A frame-by-frame view of this test shows how the instability affects the
appearance of the flame exiting the combustor. Frames a) through c) in Figure 5.5 show
the clear decomposed peroxide steam and increase in vapor density prior to autoignition
which are typical based on the tests discussed so far. In Frame d) and e) a faint
red-orange flame appears exiting the nozzle. This flame is much smaller in size and less
intense than those seen in the strong autoignition cases. In frames f) through i) an intense
green flame appears, which is similar in size to the strong ignition cases. The flame
reverts to a small red-orange flame in frames j) and k) and then back to a green flame
again in frame l). The unstable, oscillatory nature in the color and intensity of the flame
exiting the combustor agrees with the large oscillations in the measured chamber pressure
data. Each color flame last for approximately three frames or about 0.1 seconds,
assuming 30 frames per second. The peaks and valleys in the chamber pressure appear at
a much shorter interval of about 0.02 seconds based on Figure 5.8a). The green flame
indicates that it is a cooler flame, which may correspond to the valleys in the chamber
pressure data. The smaller, red-orange are hotter flames and could correspond to the
peaks in the pressure data. If this is the case it may mean that the camera did not
completely record the changes in the flame since many of them could have occurred
between frames.
5.4.3 No Autoignition
During tests in which no autoignition occurred a thick cloud of vapor was
typically seen issuing from the nozzle following fuel injection. In some cases, the
difference in appearance between the exhaust during monoprop mode and following fuel
injection was almost unnoticeable. In general, flames were not seen exiting the engine
during tests classified as no ignition. However, sparks of flame were sometimes seen at
shutdown. A plot of fuel injector inlet pressure and chamber pressure for a no
autoignition test is shown in Figure 5.10. This test was run using 94% H2O2 at a
contraction ratio of 3.0 and an equivalence ratio of 2.15. Following fuel injection the
chamber pressure rises by only about 10 psi or 6% of the monoprop chamber pressure.
105
This small increase in pressure is a result of the fuel being vaporized in the chamber. A
sharp increase in pressure does not occur following fuel injection like that of the strong
and weak autoignition cases, which suggests that the decomposed gas had only enough
energy to vaporize the fuel and not enough to ignite the resulting mixture. The monoprop
decomposition efficiency for this test was approximately 82% while the biprop C*
efficiency was about 47%. Biprop C* efficiencies for all no ignition cases were less than
65%.
A frame-by-frame view of this test is shown in Figure 5.11. Again, frames a)
through c) of Figure 5.11 are similar to the corresponding frames for the strong and weak
autoignition cases. However, following fuel injection a flame is not visible exiting the
engine as shown in frames d) through f). In fact, the difference in the plume following
fuel injection is so small that the only way to tell fuel is actually in the plume is by
difference in the density of the water vapor cloud surrounding the deflector plate between
frames b) and d). This result agrees with the conclusions drawn based on the small
increase in the measured chamber pressure.
Figure 5.10: Plot of pfu_inj and pc2 at the point of injection for a test using PCI catalyst bed.
Test conditions: 94% H2O2, φ = 2.15, and CR = 3.0.
106
a) b)
c) d)
e) f)
Figure 5.11: Frame-by-frame view of a test with no autoignition using PCI catalyst bed. Test conditions: 94% H2O2, φ = 2.15, CR = 3.0.
107
5.4.4 Trends in Autoignition Data
One of the goals of this study was to determine the effect of equivalence ratio and
decomposition temperature on autoignition of JP-8. A total of 20 tests were conducted at
a contraction ratio of 3.0 to determine autoignition boundary in terms of equivalence ratio
at a constant H2O2 concentration. Hydrogen peroxide concentrations of 85, 87.5, 90, 94,
and 98% were used to vary the decomposition gas temperature. The GK catalyst bed was
used for concentrations of 90% and below while the PCI catalyst bed was used for
concentrations 90% and above. The data resulting from these tests is shown in Error!
Reference source not found.. The uncertainties in equivalence ratio and hydrogen
peroxide concentration were less than 1.5% for all test conditions.
As Figure 5.12 shows, the strong autoignition boundary in terms of equivalence
ratio widens with increasing hydrogen peroxide concentration. It stretches from a value
of less than 1.37 at a concentration of 85% to 2.06 at a concentration of 98%. However,
the autoignition boundary is not necessarily clearly defined especially at concentrations
of 85, 87.5, and 90%. At a concentration of 85% a strong or weak autoignition condition
was not found even at an equivalence ratio as low as 1.37. A test was not conducted at a
lower equivalence ratio because the oxidizer flow rate, 2.33 lbm/s, needed to reach a φ of
1.37 was close to the highest recommended flow rate for the GK catalyst bed. At
concentrations of 87.5 and 90% weak autoignition was observed over a wide range of
equivalence ratios before reaching a no autoignition condition. For instance, at 90%
H2O2 strong autoignition was observed at the baseline equivalence ratio of 1.59 using the
GK catalyst bed. However, a no ignition condition was not found up to an equivalence
ratio of 2.19. Similarly, at a concentration of 87.5% using the GK catalyst bed strong
autoignition was observed at an equivalence ratio of 1.40, but a no autoignition condition
was not achieved until a φ of 1.86.
The PCI catalyst bed was tested at three test conditions that were nearly identical
to those run with GK catalyst bed. At the baseline conditions the PCI bed produced a
strong autoignition result in agreement with that of the GK bed. Running the PCI catalyst
bed at equivalence ratios of 2.01 and 2.23 resulted in no autoignition rather than weak
108
autoignition in both cases. In fact, the PCI catalyst bed did not produce weak
autoignition results at any of the tested conditions. At concentrations of 94 and 98%
strong autoignition was observed at equivalence ratios of 1.70 and 2.06 respectively.
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
84.0 86.0 88.0 90.0 92.0 94.0 96.0 98.0 100.0
H2O2 Concentration, W (%)
Equ
ival
ence
Rat
io, φ
(--)
Strong, GKWeak, GKNo Ign., GKStrong, PCIWeak, PCINo Ign., PCI
Figure 5.12: Autoignition of JP-8 as a function of φ and H2O2 concentration at CR = 3.0.
Another goal of this study was to determine the effect of gas velocity on the
autoignition of JP-8 in decomposed peroxide. Four additional tests were performed at a
contraction ratio of 5.0 and a constant concentration of 85% using the GK catalyst bed to
determine the autoignition boundary in terms of equivalence ratio. The data resulting
from these tests along with those done at a contraction ratio of 3.0 with 85% H2O2 are
shown in Figure 5.13. Strong autoignition was achieved at an equivalence ratio of 1.36,
a point at which no autoignition was achieved at a contraction ratio of 3.0. Following this
test the equivalence ratio was increased in an attempt to find a point a no autoignition
point. Weak autoignition was observed at equivalence ratios of 1.70 and 2.31, and a no
autoignition point was found at a φ of 2.73. As with the lower contraction ratio the GK
catalyst bed produced two weak autoignition points at a contraction ratio of 5.0.
109
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Contraction Ratio, CR (--)
Eq
uiv
alen
ce R
atio
, φ (
--)
Strong, GKWeak, GKNo Ign., GK
Figure 5.13: Autoignition of JP-8 as a function of equivalence ratio and contraction ratio
at a constant H2O2 concentration of 85%.
5.4.5 Temperature Data
As described in Chapter 4, the temperature of the decomposed hydrogen
peroxide was measured using an exposed thermocouple. In addition, four grounded
thermocouples were located in the chamber to measure the temperature at the combustor
wall. During testing it was found that the thermocouples did not produce reliable
temperature readings. The response time of the exposed thermocouple was too slow to
achieve a steady state decomposition temperature reading in the one-half second of
monoprop lead in each autoignition test. Two plots of the decomposition temperature
measured during two separate tests are shown in Figure 5.14a) and b). The plot in
Figure 5.14a) shows that the measured decomposition temperature is still increasing at
the point at which autoignition occurs. Soon after autoignition there is a sudden increase
in the measured temperature from the previously measured value. This may indicate that
there is some heat soak-back to the thermocouple following autoignition. In Figure
5.14b) the measured decomposition temperature does not reach a steady value until the
end of the biprop section of the test. In both cases the monoprop chamber pressure is
110
very steady which indicates very steady decomposition. If the decomposition is steady
then the temperature of the gases should remain steady as well. Since this is not the case
it leads one to believe that the thermocouples are not responding quickly enough. This
casts some doubt as to the accuracy of the readings produced by the thermocouples at the
point of autoignition as well. For this reason, equation 5.11 was used to calculate the
decomposition temperature for each test. The only problem with this method is that the
uncertainty in the calculated temperature is quite large, up to 20.0%, due to the large error
in decomposition efficiency. The uncertainty in decomposition efficiency is discussed in
the following section.
The four grounded thermocouples in the combustion chamber behaved in a
similar manner. The response time of these thermocouples was slow as well and seldom
reached a steady state value at any time during the test. It was also unclear, due to the
flush mounted position in the wall, what the physical meaning was of each temperature
reading. It may have been reading the wall temperature, the temperature in the boundary
layer, or the free stream gas temperature. The thermocouple located behind the
rearward-facing step, Tc1, was somewhat useful in providing qualitative evidence of
autoignition. The temperature measured behind the step was lower in no autoignition and
weak autoignition cases than in strong autoignition. However, this temperature
measurement alone was not sufficient to classify the type of autoignition that occurred in
each test.
a) b)
Figure 5.14: Measured Td over the course of tests run at a) 90% H2O2 at φ = 1.59 and CR = 3.0 with GK bed and b) 98% H2O2 at φ = 1.84 and CR = 3.0 with PCI bed.
111
5.5 Catalyst Bed Performance
As described in the previous section there was a significant difference in the
performance of each catalyst bed during autoignition testing. This was especially evident
when the catalyst beds were run at nearly identical operating conditions. Remember,
from Chapter 4, that each catalyst bed is of a different internal design and should be
expected to behave differently. Each catalyst bed was subjected to similar operating
conditions in terms of concentration, mass flow rate, and monoprop chamber pressure
using 90% H2O2 and a contraction ratio of 3.0. The pressure drop and decomposition
efficiency of each catalyst bed as a function of mass flow rate at these conditions are
shown in Figure 5.15 and Figure 5.16. From Figure 5.15 it appears that the GK catalyst
bed produces higher average decomposition efficiency for each mass flow rate condition
than the PCI catalyst bed. However, the error bars shown in Figure 5.15 indicate that
there is substantial uncertainty in the calculated values of the decomposition efficiency.
In fact, the relative uncertainty in the decomposition efficiency ranges from 6.2 to 8.5%
at these conditions. The main reason for this large error is due to the fact that 3000 psia
transducers, with an estimated random error of 7.5 psia, are being used to measure the
monoprop chamber pressure which varies from 74 to 115 psia. Thus the relative
uncertainty in the pressure measurement itself is 6.5% to 8.8%.
Regardless of the error in the calculation, if the decomposition efficiency of the
PCI catalyst bed is lower than that of the GK bed then the decomposition temperature is
lower as well. Since autoignition is strongly dependent on the gas temperature this could
be one explanation for the inconsistent autoignition results. Using equation 5.11 the
2.5% difference in average decomposition efficiency at a flow rate of 1.80 lbm/s equates
to a 65°F difference in decomposition temperature. This is very significant seeing that
the theoretical decomposition temperature for 87.5 and 90% differs by only 110°F. At a
flow rate of approximately 1.60 lbm/s the decomposition efficiency differs by almost
10% which is a temperature difference of almost 200°F according to equation 5.11. This
indicates that it is not sufficient to plot these results in terms of concentration. Plotting in
terms of decomposition temperature may be more appropriate.
112
The pressure drop across the GK catalyst bed was consistently less than that of the
PCI bed under similar flow rate and chamber pressure conditions according to Figure
5.16. The uncertainty in the calculated pressure drop is less than 5% for each test
condition shown in Figure 5.16. The pressure drop across a catalyst bed does not
directly affect autoignition, but it does affect the range of operation of a cavitating venturi
and resistance of the catalyst bed to instability. Since the PCI bed has a higher pressure
drop it would seem to have an advantage in stability while the GK bed would seem to
have the advantage in operating range due to its lower pressure drop.
70.0%
75.0%
80.0%
85.0%
90.0%
95.0%
100.0%
105.0%
110.0%
1.40 1.60 1.80 2.00 2.20 2.40
H2O2 Mass Flow Rate, m H2O2 (lbm/s)
C*
Eff
icie
ncy
, ηC
* (%
)
GK, Monoprop
PCI, Monoprop
Figure 5.15: Comparison in decomposition efficiency produced by GK and PCI catalyst
beds using 90% H2O2 at approximately equivalent monoprop operating conditions.
113
0.0
100.0
200.0
300.0
400.0
500.0
600.0
1.40 1.60 1.80 2.00 2.20 2.40
H2O2 Mass Flow Rate, m H2O2 (lbm/s)
Cat
alys
t B
ed P
ress
ure
Dro
p, ∆
p cb
(p
sid
)
GK, Monoprop
PCI, Monoprop
Figure 5.16: Comparison in pressure drop across GK and PCI catalyst beds using 90%
H2O2 at approximately equivalent monoprop operating conditions.
During testing the GK catalyst bed consistently produced large pressure
oscillations in the chamber even in monoprop mode. In most cases, this instability could
be heard from the control room during the test. The effect was observed mainly during
tests classified as weak or no autoignition, but was sometimes present in strong
autoignition cases as well. A noise parameter, ?, was defined to quantify these pressure
oscillations. The standard deviation, s , in the chamber pressure, pc2, was calculated using
the same range of data used to calculate the average value of pc2 in each mode of
operation. Using the standard deviation the noise parameter is defined as:
2cpσ
ς = , (5.17)
The noise parameter is an indication of the relative magnitude of the pressure
oscillations in the chamber and can be expressed as a percentage. In addition, the
dominant frequency, fd, in the pressure data over this same averaging range was
determined using an FFT. The noise parameter is plotted against the dominant frequency
for the monoprop and biprop modes of each test in Figure 5.17 and Figure 5.18
respectively.
114
0.0
5.0
10.0
15.0
20.0
25.0
0.0 100.0 200.0 300.0 400.0 500.0
Dominant Frequency, f d (Hz)
Noi
se P
aram
eter
, ζ (
%)
GK, StrongGK, WeakGK, No Ign.PCI, StrongPCI, WeakPCI, No Ign.
Figure 5.17: Plot of the chamber pressure noise parameter against the dominant
frequency during the monoprop mode each autoignition test.
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.0 100.0 200.0 300.0 400.0 500.0Dominant Frequency, f d (Hz)
Noi
se P
aram
eter
, ζ (%
)
GK, StrongGK, WeakGK, No Ign.PCI, StrongPCI, WeakPCI, No Ign.
Figure 5.18: Plot of the chamber pressure noise parameter against the dominant
frequency during the biprop mode each autoignition test.
115
The type of autoignition that occurred for each test is also shown in Figure 5.17
and Figure 5.18. As the plots show the noise parameter calculated for eight out of the
fifteen tests using the GK catalyst bed exceeded 5% during monoprop mode. In some of
the tests the noise parameter was calculated as high as 20%. This indicates that the GK
catalyst bed is susceptible to instability. The instability may result from the low
monoprop chamber pressures used during testing. In biprop mode nine out of the fifteen
tests which used the GK bed had a noise parameter above 5% some reaching nearly 35%.
Many of these were classified as no or weak autoignition and some were not present at a
magnitude of greater than 5% during monoprop mode. This may suggest that the
addition of unburned fuel vapor to the chamber can enhance or trigger instability in the
engine. None of the tests run using the PCI bed had a noise parameter above 5%, in
monoprop or biprop mode. One must keep in mind that the standard deviation is only an
average deviation from the mean value, and the amplitude of the pressure oscillations
may be much greater than the noise parameter indicates in some cases. The dominant
frequency of each test with a noise parameter above 5% is between 27 and 47 Hz. It is
unclear as to why the large pressure oscillations exist within this particular range of
frequencies. However, all of the tests which were classified as weak autoignition have a
dominant frequency within this band during biprop mode even those with a noise
parameter of less than 5%.
All of this data suggests that the existence of a fluctuating pressure in the chamber
influenced the autoignition process. In more general terms this may mean that the
pressure of the decomposed gas very strongly influences autoignition. For an unstable
weak autoignition case, as discussed previously, the high end of the instability may
trigger an autoignition event. The heat produced by the combustion reaction may be
enough to sustain it as the pressure reaches the low point of the oscillation. This may be
why the color of the flame fluctuates during a weak autoignition test. When the pressure
is high the energy of the decomposed gas flow sustains the flame producing a red-orange
color. Whereas, at low pressure, the energy produced by the hot flame must sustain the
reaction and produces a cooler, green or light orange flame.
116
It is unclear why this instability was present for one catalyst bed and not the other,
but it may have to do with the internal design of each bed. However, it is interesting to
note the difference in the exit geometry of each catalyst bed. The bed with the instability
had an exit diameter 1.2 inches greater than that of the oxidizer port so it was contracted
down at an angle of 40° to match the port using an adapter piece, see Figure 4.5. That
means that the decomposed gas would exit the catalyst bed at a low velocity then be
accelerated through the contraction and then expanded again downstream of the
rearward-facing step. The exit diameter of the other catalyst bed was roughly the same
diameter as the oxidizer port and did not require a contraction. Therefore, the
decomposed gas was not accelerated after it exited the catalyst bed. No conclusions can
be drawn from this discussion, but the difference in geometry downstream of the catalyst
bed may have played a role in producing instability.
5.6 DMAZ Fuel
A total of six tests were run to compare the autoignition characteristics of DMAZ
fuel to those of JP-8. Tests were conducted using the GK catalyst bed at hydrogen
peroxide concentrations of 85 and 90% at a constant contraction ratio of 3.0. The same
transverse injector was used for these tests due to the similarity in density between JP-8
and DMAZ. As a result a similar, constant fuel flow rate was used as well. Strong
autoignition was achieved at equivalence ratios ranging from 2.02 to 2.60 using 90%
H2O2. The highest equivalence ratio at which strong autoignition was achieved using
JP-8 was only about 1.60 with weak autoignition up to an equivalence ratio of about 2.20
using the GK catalyst bed. A weak or no autoignition point was not found at 90% H2O2
using DMAZ. At 85% H2O2 the equivalence ratio was varied between 1.81 and 2.70.
Weak autoignition was achieved at each of these points, whereas no autoignition was
achieved at all using JP-8 down to an equivalence ratio of 1.37. The DMAZ autoignition
data points are compared those of JP-8 using the GK catalyst bed in Figure 5.19. The
data suggests that DMAZ is much easier to autoignite than JP-8.
117
Since the stoichiometric mixture ratio of DMAZ and hydrogen peroxide is about
half that of JP-8 lower mixture ratios were required to achieve similar equivalence ratios.
The lower mixture ratios required a low oxidizer flow rate and thus created a monoprop
chamber pressure of less than 50 psia for all of the DMAZ autoignition tests. Thus, the
calculated uncertainty in parameters based on chamber pressure was extremely high. In
addition the noise parameter calculated for the DMAZ tests was very high as well
particularly during tests conducted using 85% H2O2. During these tests the noise
parameter was calculated to be above 20% during both monoprop and biprop mode. The
dominant frequency was between 27 and 32 Hz as well. This is most likely the reason
why weak autoignition was observed for DMAZ during all of the tests conducted with
85% H2O2.
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
84.0 85.0 86.0 87.0 88.0 89.0 90.0 91.0 92.0
H2O2 Concentration, W (%)
Eq
uiv
alen
ce R
atio
, φ (-
-)
Strong, JP-8Weak, JP-8No Ign.,JP-8Strong,DMAZWeak, DMAZNo Ign., DMAZ
Figure 5.19: Comparison of DMAZ autoignition points to those of JP-8 using the GK catalyst bed at a CR = 3.0.
118
5.7 Data Analysis
5.7.1 Pressure Effects
As discussed in the previous section, it is more appropriate to plot autoignition
data in terms of decomposition temperature rather than concentration. This is due to the
fact that the efficiency of decomposition dictates the gas temperature. A plot of
equivalence ratio against the calculated decomposition temperature is shown in Figure
5.20 for JP-8 a contraction ratio of 3.0. Note the large error associated with the
decomposition temperature. This plot indicates, as did Figure 5.12, that at a constant
equivalence ratio the likelihood of strong autoignition increases as the decomposition
temperature increases. Again, this data indicates that equivalence ratio plays an
important role in determining the conditions for autoignition. However, because of the
fact that the oxidizer flow rate was varied to change the equivalence ratio for each test the
monoprop chamber pressure changed for each test as well.
As was discussed in Chapter 3, past data on the autoignition of kerosene
indicated that pressure strongly influences ignition delay. In addition, the unstable
chamber pressures encountered during all of the weak autoignition tests also suggest that
pressure is an important factor. The measured average monoprop chamber pressure for
tests conducted at a contraction ratio of 3.0 are shown in Figure 5.21 as a function of
calculated decomposition temperature. The figure shows that as the monoprop chamber
pressure falls at a particular temperature so does the likelihood of achieving strong
autoignition. There is one strong autoignition point that does not follow this trend. This
particular test was run using 94% H2O2 and achieved a monoprop efficiency of about
82%, which pushed the calculated decomposition temperature down. This may indicate
that there is another factor involved or that the measurement of chamber pressure and
thus the calculated decomposition temperature could be in error. The weak autoignition
points are all close enough to the strong autoignition points that small oscillations in
chamber pressure could push them into the strong autoignition regime.
119
Based on this discussion it is not conclusive that equivalence ratio is the factor
which most effected autoignition under the tested conditions. The monoprop chamber
pressure seems to be a very influential factor as well. There also has been mixed results
regarding these two factors from past studies as well. Nearly all autoignition correlations
include the effect of pressure in some way or another, but many neglect the effect of
equivalence ratio.55 However, several studies have shown that equivalence ratio as well
as pressure influence autoignition.8,58 In dump combustors, it has been shown that
equivalence ratio is influential as well.41-43 It is suspected that both factors exert a
combined influence on the autoignition process, but from the present data it is very
difficult to separate the two.
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
400.0 600.0 800.0 1000.0 1200.0 1400.0 1600.0 1800.0 2000.0
Decomposition Temperature, T tox (oF)
Eq
uiv
alen
ce R
atio
, φ (-
-)
Strong, GKWeak, GKNo Ign., GKStrong, PCIWeak, PCINo Ign., PCI
Figure 5.20: Autoignition of JP-8 as a function of equivalence ratio and decomposition
temperature at a contraction ratio of 3.0.
120
60.0
70.0
80.0
90.0
100.0
110.0
120.0
130.0
400.0 600.0 800.0 1000.0 1200.0 1400.0 1600.0 1800.0
Decomposition Temperature, T tox (oF)
Mon
opro
p C
ham
ber
Pre
ssur
e, p
c_to
t_m
ono
(p
sia) Strong, GK
Weak, GKNo Ign., GKStrong, PCIWeak, PCINo Ign., PCI
Figure 5.21: Autoignition of JP-8 as a function of pc2_tot_mono and decomposition
temperature at a contraction ratio of 3.0.
5.7.2 Jet Trajectory
Chapter 2 discussed the effect of the fuel jet trajectory on the distribution and
atomization of the fuel in the gas port. The jet trajectory is dependent on chamber
pressure and, as a result, engine operating condition. Once autoignition occurs in the
chamber the pressure increases altering the trajectory, as described in Chapter 2. Prior
to autoignition, even when vaporized fuel is present in the chamber, the pressure is
roughly equal to the monoprop value. Therefore, when investigating the affects of jet
trajectory on autoignition it is beneficial to consider the trajectory based on monoprop
conditions. With this in mind, the fuel jet trajectory should be affected by changes in the
oxidizer mass flow rate along with chamber pressure. As the oxidizer flow rate is
lowered to increase equivalence ratio the oxidizer momentum will decrease. Assuming
the fuel momentum is constant, the fuel jet penetration should increase as a result. In
general, fuel distribution improves with increasing jet penetration and one would expect
121
the likelihood for strong autoignition to increase as well. However, this is not the case
from the results presented to this point.
At a contraction ratio of 3.0 the calculated momentum ratio, assuming monoprop
conditions, ranged from 4.2 to 8.1. Since the momentum ratio was calculated based on
the decomposition temperature its uncertainty reached 50% in some cases. Using the
calculated uncertainty values the momentum ratio ranged from 2.8 to 14.0. The
difference in trajectory resulting from this range of momentum ratios is shown in Figure
5.22. In the case of Q = 2.8 the fuel only penetrates about a quarter of the distance to the
centerline of the chamber prior to breakup. For Q = 14.0 the fuel penetrates slightly more
than halfway to the centerline of the chamber. Both of these trajectories achieved a no
autoignition result even though the penetration differed significantly. Since the rest of
the fuel trajectories at a contraction ratio of 3.0 are contained somewhere between those
shown in Figure 5.22 it suggests that the trajectory does not play a significant role in
autoignition at a constant contraction ratio. The Mach number of the decomposed gas
was approximately 0.45, with a maximum uncertainty of 15%, for all tests at this
contraction ratio.
When the contraction ratio was increased to 5.0 the calculated momentum ratio
ranged from approximately 7.1 to 18.1, or 5.4 to 25.7 based on uncertainty. These
trajectories are plotted in Figure 5.23. The Mach number of the decomposed gas during
these tests was approximately equal to 0.28 with a 15% uncertainty. The test run at a
minimum Q of 5.4, based on uncertainty, achieved strong autoignition. According to
Figure 5.23 the fuel jet penetrated only about one-third of the way to the centerline. For
the maximum Q case of 25.7 no autoignition was achieved and the fuel penetrated very
closely to the centerline prior to breakup. When the fuel penetrates this closely to the
centerline it is possible that fuel droplets from multiple jets could collide following
breakup forming larger drops that take longer to vaporize. Also, when the fuel is
centralized in the oxidizer port it may have difficultly making its may to the recirculation
zone behind the rearward-facing step. This may be reasons as to why autoignition did not
occur at this condition, but it is not known for certain. As with the low contraction ratio
there is no evidence to suggest that the fuel trajectory had an affect on autoignition.
122
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Axial Direction, x (in.)
Tra
nsv
erse
Dir
ecti
on
, y (i
n.)
Q = 2.8Q = 14.0Axial Fracture Point
Chamber WallsChamber Centerline
Figure 5.22: Trajectory variations in tests run at a contraction ratio of 3.0.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Axial Direction, x (in.)
Tra
nsv
erse
Dir
ecti
on
, y (i
n.)
Q = 5.4Q = 25.7Axial Fracture Point
Chamber WallsChamber Centerline
Figure 5.23: Trajectory variations in tests run at a contraction ratio of 5.0.
123
5.7.3 Shear Layer Residence Time
The most important feature of a dump combustor is its flameholding capability
which is provided by a rearward-facing step, a described in Chapters 2 and 3. In
Chapter 3 it was suggested that autoignition could be correlated with the residence time
of the shear layer eddies created by the rearward-step. For this combustor the height of
the rearward step was kept fixed, which meant that the primary means of varying the
shear layer time was through the gas velocity. The gas velocity in the engine was altered
through the contraction ratio. Since many of the autoignition tests were performed at a
single contraction ratio the affect of the shear layer residence time was not explored in
depth. However, a shown in Figure 5.13, at a hydrogen peroxide concentration of 85%
the contraction ratio did affect autoignition. At a contraction ratio of 3.0 the shear layer
residence time was on the order of 0.075 milliseconds, ms. At this contraction ratio no
autoignition occurred at any of the tested conditions. When the contraction ratio was
increased to 5.0 the residence time increase to about 0.130 ms. Strong autoignition
occurred at an equivalence ratio of 1.36 at this contraction ratio and weak autoignition
was found up to 2.31 due to pressure oscillations. However, it is important to point out
that the monoprop chamber pressure also increased with contraction ratio and could have
also contributed to autoignition in addition to residence time. Since the shear layer
residence time was dependent on gas temperature the uncertainty approached 25% in
some cases.
5.7.4 Autoignition Correlation
The proposed correlation for autoignition based on shear layer residence time,
Chapter 3, was not attempted for a number of reasons. For one, the contraction ratio
was only varied at one hydrogen peroxide concentration, therefore the effect of residence
time was not observed at other temperatures. Also, even at a concentration of 85%,
where the contraction ratio was varied, a strong autoignition point was not achieved at a
124
contraction ratio of 3.0. As a result, there is no data indicating the conditions required for
autoignition at this contraction ratio and there was no way to compare the results between
the two. The pressure also changed with contraction ratio and therefore it may have
influenced autoignition as well as the residence time. In addition to the lack residence
time data, it is not clear from the results as to whether pressure or equivalence ratio had
the most influence on autoignition at a constant contraction ratio. Both parameters varied
when switching between test conditions and neither effect was ever isolated from the
other. Also, unstable chamber pressures in monoprop and biprop modes seemed to skew
the autoignition data. These instabilities created conditions for weak autoignition which
may have been classified as no autoignition under stable chamber pressure conditions.
Unreliable temperature measurements and low chamber pressures measured with high
range pressure transducers contributed to high uncertainty in many calculated parameters,
such residence time and decomposition temperature. This large uncertainty would cast
significant doubt into any autoignition correlation.
125
CHAPTER 6: SUMMARY AND CONCLUSIONS
A total of 24 tests were conducted to investigate the autoignition characteristics of
kerosene-based JP-8 fuel in decomposed hydrogen peroxide. Testing was performed
using staged-bipropellant rocket engine in a dump combustor configuration. The engine
used a catalyst bed to decompose the hydrogen peroxide and a transverse injector to
inject the JP-8 into the decomposed gas stream. A fuel jet trajectory analysis was
performed during injector design to model jet breakup and fuel distribution in the
oxidizer port and to prevent jet impingement. Downstream of the injection point a
rearward-facing step was used to provide flame stabilization at the entrance to the
combustion chamber. This design is commonly referred to as a dump combustor
configuration. Testing was structured to study the affects of gas temperature, gas
velocity, and equivalence ratio on autoignition.
Each test was classified into one of three groups based on visual observations and
measured chamber pressure data. Tests classified as strong autoignition produced a
stable, red-orange flame at the nozzle exit and bipropellant C* efficiencies of greater than
90%. The chamber pressure in these tests rose sharply within one-tenth of a second
following the initiation of fuel flow. The second classification, weak autoignition, was
typified by highly unstable flames that varied in color from red-orange to green. The C*
efficiencies for these tests ranged from 65 to 90%. The delay between fuel initiation and
chamber pressure rise was on the same order as the strong autoignition case, but the rise
was not as sharp. The third test classification was no autoignition. During these tests the
fuel was vaporized in the chamber but did not autoignite producing either a thick, white
vapor cloud or a clear plume at the nozzle exit. The biprop C* efficiencies for these tests
were less than 65% in most cases and the chamber pressure rise was minimal resulting
from the vaporization of the fuel.
126
It was determined that severe chamber pressure instabilities present during weak
autoignition tests caused the unstable flame structure. The instability caused the pressure
in the chamber to oscillate, and in some cases the average amplitude of the oscillation
was almost 30% of the chamber pressure. It is believed that the fuel and decomposed gas
mixture was initially autoignited at a high pressure point in the oscillation producing a
bright, red-orange flame. As the chamber pressure fell to a low point in the oscillation it
most likely altered the path of the combustion reaction causing a change in the color and
possibly the temperature of the flame. In some cases the pressure may have fell far
enough to quench the flame completely. This was seen during some tests when a flame
was visible at one instant and then a vapor cloud the next instant. As the pressure
continued to oscillate after the initial point of autoignition so too did the flame.
The gas temperature, gas velocity, and equivalence ratio were controlled during
testing by varying the H2O2 concentration, chamber contraction ratio, and oxidizer mass
flow rate respectively. Each test series was set up such that the concentration and
contraction ratio remained constant while the equivalence ratio was varied to determine
the boundary between strong autoignition and no autoignition for fuel rich conditions.
Once the boundary was determined at a particular concentration it was increased for the
next test series and the process was repeated again. Results showed that as the
concentration, or decomposition temperature, was increased the equivalence ratio at the
boundary between strong and no autoignition increased as well. At a contraction ratio of
3.0 and a concentration of 85% H2O2 no autoignition was achieved down to an
equivalence ratio of 1.37 while at a concentration of 98% strong autoignition was
achieved up to an equivalence ratio of 2.06. This trend agrees with past data from Mestre
and Ducourneau58 for kerosene in air as well as Walder8 for kerosene in decomposed
hydrogen peroxide. Both show that higher temperatures are required for autoignition as
equivalence ratio increases, or as the mixture becomes more fuel rich, for a specified
mixture residence time. Other studies done with kerosene fuel in air at oxidizer rich
equivalence ratios suggest that equivalence ratio plays a negligible role in autoignition.
However, due to the fact that the oxidizer flow rate was varied to change
equivalence ratio the monoprop chamber pressure was altered as well. There is nearly
127
universal agreement from past autoignition studies that the autoignition temperature
decreases with increasing pressure at a fixed residence time or contraction ratio in this
case. Data from Mestre and Ducourneau suggests that a pressure increase from 100 to
115 psia can alter the autoignition temperature of kerosene fuel in air by approximately
90°F at an equivalence ratio of 2.0. Data from Walder suggests a temperature difference
of about 20°F for kerosene fuel in decomposed hydrogen peroxide at the same pressures
and a stoichiometric equivalence ratio. It is believed that the variations in both the
pressure and equivalence ratio combined to influence the autoignition temperature at a
constant contraction ratio not just one or the other. However, the test conditions were
such that the variations could not be isolated from one another.
The effect of gas velocity on autoignition was investigated by varying the
contraction ratio of the engine. Increasing the contraction ratio decreases the Mach
number of the gases in the chamber as well as the decomposed gas in the oxidizer port.
As previously discussed, at contraction ratio of 3.0 no autoignition was achieved at all the
tested conditions using 85% H2O2. At this contraction ratio the Mach number in the
chamber is about 0.20 and 0.45 in the oxidizer port. When the contraction ratio was
increased to 5.0, however, strong autoignition was achieved at an equivalence ratio of
1.36 and weak autoignition was achieved up to an equivalence ratio of 2.31. At this
contraction ratio the Mach number in the chamber is about 0.12 and 0.20 in the oxidizer
port. Therefore, as the contraction ratio is increased, or the gas velocity decreased, the
temperature required to achieve autoignition at a particular equivalence ratio decreases.
This result also agrees with past data from Mestre and Ducourneau with regards to
residence time of a kerosene/air mixture. Walder made a similar conclusion and chose to
correlate the temperature decrease with the characteristic length of a rocket combustion
chamber instead of residence time. Intuitively this result makes sense because as the
available reaction time of the mixture increases the probability of autoignition should
increase as well at a certain temperature. Both studies suggest that the affect of residence
time, characteristic length, or gas velocity on the autoignition temperature is only
significant up to a point after which the effects are negligible. Since the fuel flow rate
was kept constant during contraction ratio variations as well the chamber pressure
128
increased with increasing contraction ratio. Based on the previous discussion on pressure,
it is believed that pressure affects also contributed to the decrease in autoignition
temperature at a larger contraction ratio.
Changes in contraction ratio also affected the trajectory of the fuel jet in the
oxidizer port. Fuel trajectory analysis was performed using momentum ratios calculated
from measured test data. All of the calculated trajectories at a contraction ratio of 3.0
penetrated halfway to the centerline of the duct or less, which includes both strong
autoignition tests and no autoignition tests. This may suggest that the fuel trajectory and
atomization did not play a critical role in autoignition. However, the variations in
momentum ratio were accompanied by changes in the equivalence ratio and flow rate of
hydrogen peroxide. Therefore, the affect of varying jet trajectory at a constant
equivalence ratio and monoprop chamber pressure was not determined.
As the contraction ratio was increased the shear layer residence time created by
the rearward-facing step was increased as well. Past studies have shown that the shear
layer time can be correlated with ignition delay to predict the stability of a flame. In this
study, the initial intention was to deve lop a correlation or model for autoignition relating
the shear layer residence time to an ignition delay parameter, which was similar in form
to that of past studies. The ignition delay parameter included the effects of temperature
and equivalence ratio, while velocity effects were included in the residence time
parameter. However, the correlation was not attempted due to inconclusive data
separating the effects of pressure, equivalence ratio, and contraction ratio. Most likely a
term would need to be added to the ignition delay portion of the correlation to include
pressure effects. In addition, large uncertainties were present in some of the calculated
data, including shear layer residence time. The large uncertainty originated from the
chamber pressure measurements, which were made using 3000 psia range transducers
with an accuracy of ±7.5 psia. During testing the monoprop chamber pressure was on the
order of 100 psia making the measurement uncertainty about 7.5%. The uncertainty
increased from this point through the rest of the calculations.
Despite this, it is believed that the rearward-facing step did provide enough
residence time to improve the autoignition limits based on past data. Many flight-rated
129
staged-bipropellant engines that used hydrogen peroxide and kerosene have had
contraction ratios of seven of higher and ran at stoichiometric equivalence ratios. A
study by Walder on the autoignition of kerosene in hydrogen peroxide used contraction
ratios of six and higher at stoichiometric conditions. In addition, data from Wu et al22
using a similar engine design running 85% H2O2 at an equivalence ratio somewhere
between 0.8 and 1.4 did not achieve autoignition at contraction ratio of approximately 5.0
even at a monoprop chamber pressure of 340 psia. Data from this study proved that
autoignition was possible at an equivalence ratio of 1.4 using 85% H2O2 at a monoprop
chamber pressure of approximately 100 psia. The data from this study also proves that
stable autoignition is possible at contraction ratios as low as 3.0 and equivalence ratios
less than 1.4 using 90% H2O2.
Future work should be aimed at developing the correlation for flame stability
based on shear layer residence time and ignition delay. This would require a study of the
affects of monoprop chamber pressure and equivalence ratio individually. To study
equivalence ratio effects at constant monoprop chamber pressure and contraction ratio the
flow rate of hydrogen peroxide would need to be held constant. As a result the fuel flow
rate would need to be varied to alter the equivalence ratio, which may require the use of
multiple fuel injectors to more accurately control the trajectory and pressure drop.
Unfortunately, to change out injectors the entire engine would need to be disassembled
with the current design. To study the effects of monoprop chamber pressure while
maintaining constant equivalence ratio and contraction ratio would require a change in
both the oxidizer and fuel flow rates. Most likely this would also require new injector
designs. In addition, a wider range of contraction ratios would need to be studied to
understand the effects of shear layer residence time on autoignition. The monoprop
chamber pressure would need to be held constant between contraction ratios to truly
determine this effect. Again this would require multiple fuel injectors to be made and a
catalyst bed would be required that performs adequately over a wide range of mass flow
rates.
Other suggestions for improvement to this autoignition study included finding an
improved method for measuring the temperature of the decomposed hydrogen peroxide.
130
The lack of an accurate temperature reading affects the uncertainty in the calculation of
the decomposed gas velocity and thus residence time and momentum ratio. Also, the use
of a more accurate pressure transducer in the chamber would also reduce the uncertainty
in many of the calculated parameters. It would also be beneficial to determine operating
conditions that reduce the probability of chamber pressure instability and to run
autoignition tests around these conditions. It would be preferable to eliminate pressure
oscillations from the autoignition tests. Use of a high-speed camera would create a better
picture of what occurs at the point of fuel injection and autoignition at the nozzle exit.
This could possibly allow the calculation of ignition delay following fuel injection. The
chamber length could also be varied to investigate its effect on residence time and
autoignition boundaries.
Despite its short comings this study generated some valuable data regarding the
autoignition of kerosene in a stream of decomposed hydrogen peroxide in a dump
combustor. In addition, a transverse injector design approach was developed which
proved to be both simple and reliable. Experimental data showed that the autoignition
limits were dependent on hydrogen peroxide concentration and chamber contraction ratio.
Also, a model for autoignition and flame stability was outlined based on the residence
time created by a rearward-facing step and ignition delay. Data showed that by adding a
flameholding capability to the engine autoignition could be achieved at lower contraction
ratios than in previous designs. This result may help in making staged-bipropellant
engines us ing hydrogen peroxide and kerosene lighter in weight and more reliable in
performance in the future.
131
LIST OF REFERENCES
1. Ventura, M., Mullens, P., “The Use of Hydrogen Peroxide for Propulsion and
Power,” AIAA Paper 99-2880, June 1999.
2. Andrews, D., “Advantages of Hydrogen Peroxide as a Rocket Oxidant,” Journal of The British Interplanetary Society, Vol. 43, 1990, pp. 319-328.
3. AFRPL-TR-67-144, “Hydrogen Peroxide Handbook,” Rocketdyne, Inc., July 1967.
4. TEP Version 1.5, SEA Software, Inc., Carson City, Nevada, 1999.
5. Humble, R. W., Henry, G. N., Larson, W. J., Space Propulsion Analysis and Design, McGraw-Hill Companies Inc., New York, 1995.
6. Hurlbert et al, “Nontoxic Orbital Maneuvering and Reaction Control Systems for Reusable Spacecraft,” Journal of Propulsion and Power, Vol. 14, No. 5, Sept.-Oct. 1998, pp. 676-687.
7. Chen et al, “Testing Research on Nontoxic H2O2/Kerosine Liquid Propellant Engines,” IAF-01-S309, 52nd International Astronautical Congress, Paris, 2001.
8. Walder, H., “An Investigation into the Thermal Ignition of Hydrogen Peroxide and Kerosine,” Report Number RPD 7, Royal Aircraft Establishment, May 1950.
9. Walder, H., “Further Investigations into the Thermal Ignition of Hydrogen Peroxide and Kerosine,” Technical Note Number RPD 43, Royal Aircraft Establishment, December 1950.
10. Walder, H. and Purchase, L. J., “The Influence of Injector Design on the Thermal Ignition of Hydrogen Peroxide and Kerosene,” Technical Note Number RPD 80, Royal Aircraft Establishment, April 1953.
132
11. Harlow, J., “Hydrogen Peroxide Engines: Early Work on Thermal Ignition at Westcott,” 2nd International Symposium on Hydrogen Peroxide, November 7-10, 1999.
12. Austin, B. L., Heister, S. D., “Characterization of Pintle Engine Performance for Nontoxic Hypergolic Bipropellants,” AIAA Paper 2002-4026, July 2002.
13. Long, M. R., Anderson, W. E., Humble, R. W., “Bi-Centrifugal Swirl Injector Development for Hydrogen Peroxide and Non-Toxic Hypergolic Miscible Fuels,” AIAA Paper 2002-4026, July 2002.
14. Andrews, D. “Rocket Engines for Satellite Launchers,” Proceeding from the International Symposium on Space Technology and Science, Tokyo, 1966, pp 111-120.
15. Healey, G. T., “Possibilities for Future Versions of Black Arrow-1,” Journal of Spacecraft, Vol. 10, No. 11, November 1968, pp. 394-401.
16. Gibbon et al, “Engergetic Green Propulsion for Small Spacecraft,” AIAA Paper 2001-3247, July 2001.
17. Coxhill, I., Richardson, G., Sweeting, M., “An Investigation of a Low Cost HTP/Kerosene 40N Thruster for Small Satellites,” AIAA Paper 2002-4155, July 2002.
18. Ventura, M., Wernimont, E., “History of the Reaction Motors Super Performance 90% H2O2/Kerosene LR-40 Rocket Engine,” AIAA Paper 2001-3838, July 2001.
19. Frazier, S. R., Moser, D. J., “Low Cost First Stage for Small Launch Vehicles,” AIAA Paper 95-3088, July 1995.
20. Phillips, E. H. “Beal Aerospace Developing New Launch Vehicle,” Aviation Week & Space Technology, Vol. 148, No. 14, April 6, 1998, pp. 74-75.
21. Phillips, E. H. “Beal Tests Stage 2 Liquid Fuel Engine,” Aviation Week & Space Technology, Vol. 152, No. 11, March 13, 2000, pp. 36.
22. Wu et al, “Development of a Pressure-Fed Rocket Engine Using Hydrogen Peroxide and JP-8,” AIAA Paper 99-2877, June 1999.
133
23. Anderson et al, “Upper Stage Flight Experiment 10K Engine Design and Test Results,” AIAA Paper 2000-3558, July 2000.
24. Fitzpatrick, S., Prater, D., Anderson, W., “A Design, Build, Test Course in Rocket Combustors,” AIAA Paper 2002-4186, July 2002.
25. Walder, H., Broughton, L. W., “Thermal Ignition Tests of Hydrogen Peroxide and Kerosine in a 2200lb Thrust Rocket Motor,” Technical Note Number RPD 70, Royal Aircraft Establishment, August 1952.
26. Miller, K. J., Sisco, J. C., Austin Jr., B. L., Martin, T. N., Anderson, W. E., “Design and Ground Testing of a Hydrogen Peroxide/Kerosene Combustor for a RBCC Application,” AIAA Paper 2003-4477, July 2003.
27. McCormick, J., “Hydrogen Peroxide Rocket Manual,” FMC Corporation, 1965.
28. Ventura, M., Wernimont, E., “Advancements in High Concentration Hydrogen Peroxide Catalyst Beds,” AIAA Paper 2001-3250, July 2001.
29. Andrews, D., Sunley, H., “The Gamma Rocket Engines for Black Knight,” Journal of The British Interplanetary Society, Vol. 43, 1990, pp. 301-310.
30. Helms, W. J., Mok, J. S., Sisco, J. C., Anderson, W. E., “Decomposition and Vaporization Studies of Hydrogen Peroxide,” AIAA Paper 2002-4028, July 2002.
31. Lefebvre, Arthur H., Atomization and Sprays, Hemisphere, New York, 1989.
32. Bayvel, L., Orzechowski, Z., Liquid Atomization, Taylor & Francis, 1993.
33. Doumas, M., Laster, R., “Liquid-Film Properties for Centrifugal Spray Nozzles,” Chemical Engineering Progress, Vol. 49, No. 10, 1953, pp 518-526.
34. Lin, K. C., Kennedy, P.J., Jackson, T. A., “Penetration Heights of Liquid Jets in High-Speed Crossflows,” AIAA Paper 2002-0873, January 2002.
35. Wu, P. K., Kirkendall, K. A., Fuller, R. P., Nejad, A. S., “Breakup Processes of Liquid Jets in Subsonic Crossflows,” AIAA Paper 96-3024, July 1996.
134
36. Chen, T. H., Smith, C. R., Schommer, D. G., Nejad, A. S., “Multi-Zone Behavior of Transverse Liquid Jet in High-Speed Flow,” AIAA Paper 93-0453, January 1993.
37. Mazallon, J., Dai, Z., Faeth, G. M., “Aerodynamic Primary Breakup at the Surface of Nonturbulent Round Liquid Jet in Crossflow,” AIAA Paper 98-0716, January 1998.
38. Sallam, K. A., Aalburg, C., Faeth, G. M., “Primary Breakup of Round Nonturbulent Liquid Jets in Gaseous Crossflows,” 16th Annual Conference on Liquid Atomization and Spray Systems, Monterey, CA, May 2003.
39. Ingebo, R. D., “Capillary and Acceleration Wave Breakup of Liquid Jets in Axial-Flow Airstreams,” NASA TP-1791, 1981.
40. Hautman, D. J., Rosfjord, T. J., “Transverse Liquid Injection Studies,” AIAA Paper 90-1965, July 1990.
41. Prior, R. C., Fowler, D. K., Mellor, A. M., “Engineering Design Models for Ramjet Efficiency and Lean Blowoff,” Journal of Propulsion and Power, Vol. 11, No. 1, Jan-Feb 1995, pp 117-123.
42. Plee, S. L., Mellor, A. M., “Characteristic Time Correlation for Lean Blowoff of Bluff-Body-Stabilized Flames,” Combustion and Flame, Vol. 35, 1979, pp. 61-80.
43. Craig, R. R., Drewry, J. D., Stull, F. D., “Coaxial Dump Combustor Investigations,” AIAA 78-1107, July 1978.
44. NASA SP-8089, “Liquid Rocket Engine Injectors,” National Aeronautics and Space Administration, March 1976.
45. Pitz, R. W., Daily, J. W., “Combustion in a Turbulent Mixing Layer Formed at a Rearward-Facing Step,” AIAA Journal, Vol. 21, No. 11, November 1983, pp. 1565-1570.
46. Hsiao, C. C., Oppenheim, A. K., Ghoniem, A. F., Chorin, A. J., “Numberical Simulation of a Turbulent Flame Stabilized Behind a Rearward-Facing Step,” Twentieth Symposium (International) on Combustion, The Combustion Institute, 1984, pp 495-504.
135
47. CRC Report No. 530, “Handbook of Aviation Fuel Properties,” Coordinating Research Council, 1983.
48. Kihm, K. D., Lyn, G. M., Son, S. Y., “Atomization of Cross-Injecting Sprays into Convective Air Stream,” Atomization and Sprays, Vol. 5, 1995, pp. 417-433.
49. Edwards, T., Harrison III, W. E., Maurice, L. Q., “Properties and Usage of Air Force Fuel: JP-8,” AIAA Paper 2001-0498, January 2001.
50. Edwards, T., “Kerosene Fuels for Aerospace Propulsion – Composition and Properties,” AIAA Paper 2002-3874, July 2002.
51. Turns, S. R., An Introduction to Combustion: Concepts and Applications, 2nd Edition, McGraw-Hill Companies, Inc., Boston, 2000.
52. Bodner, G. M., Pardue, H. L., Chemistry: An Experimental Science, 2nd Edition, John Wiley & Sons, Inc., New York, 1995.
53. Maron, S. H., Lando, J. B., Fundamentals of Physical Chemistry, Macmillan Publishing Co. Inc., New York, 1974.
54. AFAPL-TR-75-70, “Summary of Ignition Properties of Jet Fuels and Other Aircraft Combustible Fluids,” U.S. Bureau of Mines, September 1975.
55. Spadaccini, L. J., TeVelde, J. A., “Autoignition Characteristics of Aircraft-Type Fuels,” NASA CR-159886, June 1980.
56. Freeman, G., Lefebvre, A. H., “Spontaneous Ignition Characteristics of Gaseous Hydrocarbon-Air Mixtures,” Combustion and Flame, Vol. 58, 1984, pp. 153-162.
57. Freeman, G., “The Spontaneous Ignition Characteristics of Gaseous Hydrocarbon Fuel-Air Mixtures at Atmospheric Pressure,” M.S. Thesis, Purdue University, 1984.
58. Mestre, A., Ducourneau, F., “Recent Studies on the Spontaneous Ignition of Rich Air-Kerosene Mixtures,” Combustion Institute European Symposium, Academic Press, London, 1973, pp 225-229.
59. Colket III, M. B., Spadaccini, L. J., “Scramjet Fuels Autoignition Study,” Journal of Propulsion and Power, Vol. 17, No. 2, March-April 2001, pp 315-323.
136
60. Austin Jr., B. L., “Characterization of Pintle Engine Performance for Non-Toxic Hypergolic Bipropellants,” M.S. Thesis, Purdue University, 2002.
61. Fox, R. W., McDonald, A. T., Introduction to Fluid Mechanics, 5th Edition, John Wiley and Sons, Inc., New York, 1998.
137
Appendix A: Part Drawings
138
Figure A.1: Engine assembly using GK catalyst bed, page one.
139
Figure A.2: Engine assembly using GK catalyst bed, page two.
140
Figure A.3: Extension piece for GK catalyst bed, allows temperature and pressure
measurement upstream of the fuel injector.
141
Figure A.4: Mounting plate for engine assembly using GK catalyst bed.
142
Figure A.5: Page one of transverse fuel injector drawing, indicates manifold dimensions.
143
Figure A.6: Page two of transverse fuel injector drawing, indicates orifice dimensions.
144
Figure A.7: Transverse fuel injector seat, the fuel feed line is attached to this piece.
145
Figure A.8: Drawing of fuel film cooling injector seat, fuel feed line was capped for
autoignition testing.
146
Figure A.9: Drawing of fuel film cooling injector, fuel was not flowed through this piece
during autoignition testing.
147
Figure A.10: Page one of combustion chamber part drawing.
148
Figure A.11: Page two of combustion chamber part drawing.
149
Figure A.12: Page three of combustion chamber part drawing.
150
Figure A.13: Page four of combustion chamber part drawing.
151
Figure A.14: Drawing of nozzle piece with a contraction ratio of 3.0.
152
Figure A.15: Drawing of nozzle piece with contraction ratio of 5.0.
153
Figure A.16: Drawing of nozzle piece with contraction ratio of 6.5.
154
Figure A.17: Assembly drawing of water cooled deflection plate, water cooling apparatus
not shown.
155
Figure A.18: Engine assembly using PCI catalyst bed.
156
Figure A.19: Mounting plate used for engine assembly using PCI catalyst bed, this piece
was attached to the top of the catalyst bed.
157
Figure A.20: Page one of drawing of transition piece between PCI catalyst bed and transverse fuel injector. This piece also allowed the measurement of pressure and
temperature at the exit of the catalyst bed.
158
Figure A.21: Page two of drawing of PCI transition piece, indicates dimension of
V-shaped groove for metal o-ring.
159
Appendix B: DMAZ Material Safety Data Sheet
160
MATERIAL SAFETY 3M DATA SHEET 3M Center (Experimental) St. Paul, Minnesota 55144-1000 1-800-364-3577 or (651) 737-6501 (24 hours) Copyright, 2001, Minnesota Mining and Manufacturing Company. All rights reserved. Copying and/or downloading of this information for the purpose of properly utilizing 3M products is allowed provided that: 1) the information is copied in full with no changes unless prior agreement is obtained from 3M, and 2) neither the copy nor the original is resold or otherwise distributed with the intention of earning a profit thereon. DIVISION: 3M SPECIALTY MATERIALS MATERIAL: L-15686 DEVELOPMENTAL MATERIAL ISSUED: February 14, 2001 SUPERSEDES: February 13, 2001 DOCUMENT: 09-0400-3 ---------------------------------------------------------------------------- 1. INGREDIENT C.A.S. NO. PERCENT ---------------------------------------------------------------------------- DIMETHYL-2-AZIDOETHYLAMINE.............. 86147-04-8 100 This material is not listed on the TSCA inventory and should be used for research and development purposes only under the direct supervision of a technically qualified individual. This material is not on EINECS and should be used in Europe only for research purposes in order to establish its properties. ---------------------------------------------------------------------------- 2. PHYSICAL DATA ---------------------------------------------------------------------------- BOILING POINT:................. 135 C VAPOR PRESSURE:................ 11 - 50 mmHg @ 20C VAPOR DENSITY:................. N/D EVAPORATION RATE:.............. N/D SOLUBILITY IN WATER:........... slight SPECIFIC GRAVITY:.............. 0.93 Water=1 PERCENT VOLATILE:.............. 100 % pH:............................ N/A VISCOSITY:..................... < 10 centipoise MELTING POINT:................. N/A APPEARANCE AND ODOR: Clear mobile liquid. Strong amine-type odor. ---------------------------------------------------------------------------- Abbreviations: N/D - Not Determined N/A - Not Applicable CA - Approximately
161
MSDS: L-15686 DEVELOPMENTAL MATERIAL February 14, 2001 PAGE 2 ---------------------------------------------------------------------------- 3. FIRE AND EXPLOSION HAZARD DATA ---------------------------------------------------------------------------- FLASH POINT:................... 30 C CC FLAMMABLE LIMITS - LEL:........ N/A FLAMMABLE LIMITS - UEL:........ N/A AUTOIGNITION TEMPERATURE:...... N/D EXTINGUISHING MEDIA: Water, Carbon dioxide, Dry chemical, Foam SPECIAL FIRE FIGHTING PROCEDURES: Wear full protective clothing, including helmet, self-contained, positive pressure or pressure demand breathing apparatus, bunker coat and pants, bands around arms, waist and legs, face mask, and protective covering for exposed areas of the head. UNUSUAL FIRE AND EXPLOSION HAZARDS: See Hazardous Decomposition section for products of combustion. ---------------------------------------------------------------------------- 4. REACTIVITY DATA ---------------------------------------------------------------------------- STABILITY: Stable INCOMPATIBILITY - MATERIALS/CONDITIONS TO AVOID: Strong Acids, Strong Oxidizing Agents May react with acrylic monomers or oxirane compounds. Reacts violently with fuming nitric acid or nitrogen tetroxide. HAZARDOUS POLYMERIZATION: Hazardous polymerization will not occur. HAZARDOUS DECOMPOSITION PRODUCTS: Carbon Monoxide and Carbon Dioxide, Toxic Vapors, Gases or Particulates. ---------------------------------------------------------------------------- 5. ENVIRONMENTAL INFORMATION ---------------------------------------------------------------------------- SPILL RESPONSE: Refer to other sections of this MSDS for information regarding physical and health hazards, respiratory protection, ventilation, and personal protective equipment. Ventilate area. Extinguish all ignition sources. Contain spill. Evacuate unprotected personnel from hazard area. Cover with absorbent material. Cover spill area with Light Water Brand or other ATC foam. (For further information on ATC foam usage, contact 3M Fire Protection Systems.) Collect using non-sparking tools. Clean up residue. Place in an approved metal container. Seal the container. ---------------------------------------------------------------------------- Abbreviations: N/D - Not Determined N/A - Not Applicable CA - Approximately
162
MSDS: L-15686 DEVELOPMENTAL MATERIAL February 14, 2001 PAGE 3 ---------------------------------------------------------------------------- 5. ENVIRONMENTAL INFORMATION (continued) ---------------------------------------------------------------------------- RECOMMENDED DISPOSAL: Incinerate in a permitted hazardous waste incinerator. ENVIRONMENTAL DATA: Not determined. REGULATORY INFORMATION: Volatile Organic Compounds: N/D. VOC Less H2O & Exempt Solvents: N/A. Since regulations vary, consult applicable regulations or authorities before disposal. In the event of an uncontrolled release of this material, the user should determine if the release qualifies as a reportable quantity. U.S. EPA Hazardous Waste Number = D001 (Ignitable) ---------------------------------------------------------------------------- 6. SUGGESTED FIRST AID ---------------------------------------------------------------------------- EYE CONTACT: Immediately flush eyes with large amounts of water for at least 15 minutes. Get immediate medical attention. SKIN CONTACT: Immediately flush skin with large amounts of water for at least 15 minutes in a chemical safety shower while removing contaminated clothing and shoes. Get immediate medical attention. Wash contaminated clothing before reuse. INHALATION: If signs/symptoms occur, remove person to fresh air. If signs/symptoms continue, call a physician. IF SWALLOWED: If swallowed, do NOT induce vomiting. Give victim two glasses of water. Call a physician immediately. Never give anything by mouth to an unconscious person. ---------------------------------------------------------------------------- 7. PRECAUTIONARY INFORMATION ---------------------------------------------------------------------------- EYE PROTECTION: Avoid eye contact. Wear vented goggles. ---------------------------------------------------------------------------- Abbreviations: N/D - Not Determined N/A - Not Applicable CA - Approximately
163
MSDS: L-15686 DEVELOPMENTAL MATERIAL February 14, 2001 PAGE 4 ---------------------------------------------------------------------------- 7. PRECAUTIONARY INFORMATION (continued) ---------------------------------------------------------------------------- SKIN PROTECTION: Avoid skin contact. Wear appropriate gloves when handling this material. Use one or more of the following personal protection items as necessary to prevent skin contact: apron. RECOMMENDED VENTILATION: Provide appropriate local exhaust ventilation at transfer points. Provide appropriate local exhaust ventilation on open containers. If exhaust ventilation is not adequate, use appropriate respiratory protection. RESPIRATORY PROTECTION: Avoid breathing of vapors, mists or spray. Select one of the following NIOSH approved respirators based on airborne concentration of contaminants and in accordance with OSHA regulations: Half-mask organic vapor respirator with dust/mist prefilter, full-face supplied air respirator. PREVENTION OF ACCIDENTAL INGESTION: Wash hands after handling and before eating. RECOMMENDED STORAGE: Keep container closed when not in use. Keep container in well- ventilated area. FIRE AND EXPLOSION AVOIDANCE: Keep container tightly closed. Flammable liquid and vapor. Keep away from heat, sparks, open flame, and other sources of ignition. Ground containers securely when transferring contents. Wear low static or properly grounded shoes. No smoking while handling this material. Vapors may ignite explosively. EXPOSURE LIMITS INGREDIENT VALUE UNIT TYPE AUTH SKIN* ---------------------------------------------------------------------------- DIMETHYL-2-AZIDOETHYLAMINE........... NONE NONE NONE NONE * SKIN NOTATION: Listed substances indicated with 'Y' under SKIN refer to the potential contribution to the overall exposure by the cutaneous route including mucous membrane and eye, either by airborne or, more particularly, by direct contact with the substance. Vehicles can alter skin absorption. SOURCE OF EXPOSURE LIMIT DATA: - NONE: None Established ---------------------------------------------------------------------------- Abbreviations: N/D - Not Determined N/A - Not Applicable CA - Approximately
164
MSDS: L-15686 DEVELOPMENTAL MATERIAL February 14, 2001 PAGE 5 ---------------------------------------------------------------------------- 8. HEALTH HAZARD DATA ---------------------------------------------------------------------------- EYE CONTACT: Chemical Related Eye Burns (chemical corrosivity): signs/symptoms can include cloudy appearance of the cornea, chemical burns, pain, tearing, ulcers, impaired vision or loss of vision. SKIN CONTACT: Skin Burns (chemical corrosivity): signs/symptoms can include redness, swelling, itching, pain, blistering, ulceration, sloughing, and scar formation. INHALATION: No information was found regarding effects from inhalation exposure. IF SWALLOWED: No information was found regarding effects from swallowing. Ingestion may cause: Irritation of Gastrointestinal Tissues: signs/symptoms can include pain, vomiting, abdominal tenderness, nausea, blood in vomitus, and blood in feces. ---------------------------------------------------------------------------- SECTION CHANGE DATES ---------------------------------------------------------------------------- PHYSICAL DATA SECTION CHANGED SINCE February 13, 2001 ISSUE ---------------------------------------------------------------------------- Abbreviations: N/D - Not Determined N/A - Not Applicable CA - Approximately ---------------------------------------------------------------------------- The information in this Material Safety Data Sheet (MSDS) is believed to be correct as of the date issued. 3M MAKES NO WARRANTIES, EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, ANY IMPLIED WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE OR COURSE OF PERFORMANCE OR USAGE OF TRADE. User is responsible for determining whether the 3M product is fit for a particular purpose and suitable for user's method of use or application. Given the variety of factors that can affect the use and application of a 3M product, some of which are uniquely within the user's knowledge and control, it is essential that the user evaluate the 3M product to determine whether it is fit for a particular purpose and suitable for user's method of use or application. 3M provides information in electronic form as a service to its customers. Due to the remote possibility that electronic transfer may have resulted in errors, omissions or alterations in this information, 3M makes no representations as to its completeness or accuracy. In addition, information obtained from a database may not be as current as the information in the MSDS available directly from 3M.
165
Appendix C: Test Cell P&ID
166
Figure C.1: Plumbing & Instrumentation Diagram of Test Cell A at APCL.
167
Appendix D: Data Reduction
The following are examples of the MATLAB scripts which were used to reduce
the data collected during each test. The first file called ‘DataReduction.m’ was used to
read the data file, convert voltage readings to pressure, calculate mass flow rate, mixture
ratio, and C*, as well as filter and plot the data. The second file called ‘Bipropavg.m’
was used to average the measured and calculated data over a set period in time during the
biprop portion of each test. This file also performed an FFT on the pressure data during
this period of time and calculated the standard deviation in the chamber pressure data.
The averaged results were written to a text file. A similar file was used to perform the
same functions for the monoprop section of each test and was called ‘Monoavg.m.’ The
mass flow rates, C*’s, efficiencies, and other parameters were recalculated for monoprop
and biprop mode in a spreadsheet using the mean pressures determined in the averaging
files. This was done so that all the calculations for each test were contained in one file
and to facilitate using the uncertainty analysis.
DataReduction.m
%============================== %FILENAME: DataReduction.m %BY: B.J. Austin %Modified By: Jim Sisco %============================== clear all; close all; %Setting Plot Titles PlotTitle1='Autoignition Testing: Test #90305002, 01/21/03 Unfiltered'; PlotTitle2='Autoignition Testing: Test #90305002, 01/21/03 15Hz Filter';
168
%Loading Data File NameIn = input('Input File Name: ','s'); datafile = load(NameIn); %------ %Inputs %------ % Scan rate used by LabVIEW code ScanRate = 1000; %[samples/sec] % Assumed atmospheric pressure Patm = 14.7; %[psia] % Set H2O2 concentration Percent_HP = 90.5; %[%] % Assumed fuel temperature T_Fu = 72.5; %[F] % Set gravitational constant g = 32.174; %[lbm-ft/lbf-s] %Cavitating venturi characteristics % Oxidizer Cd_CV_ox = 0.989; %C_D for 0.111" cavitating venturi D_CV_ox = 0.111; %in % Fuel Cd_CV_fu = 0.844; %Cd for the 0.058" Dt cavitating venturi D_CV_fu = 0.058; %in % Chamber throat diameter Throat_Diam = 1.478; %in % Monoprop theoretical C*, based on concentration cstarthmono = 3086; %ft/s %--------------------------- %Calculating Time Parameters %--------------------------- % Total number of scans scans = length(datafile(:,1)); % Time resolution based on scan rate dt = 1/ScanRate; %[sec] % Time array from number of scans and time resolution Time = (1:scans)*dt; %[sec]
169
%--------------------------------------------- %Assigning Variables from Columns of Test File %--------------------------------------------- % Load Cell F_LoadCell_raw = datafile(:,1); %Thrust (not used for autoignition testing) % Pressure Transducers P_OxUllage_raw = datafile(:,2); %Primary Oxidizer Tank Ullage Pressure P_FuUllage_raw = datafile(:,3); %Primary Fuel Tank Ullage Pressure P_Fu2Ullage_raw = datafile(:,5); %Secondary Fuel Tank Ullage Pressure P_OxCav_raw = datafile(:,8); %Oxidizer Cavitating Venturi Inlet Pressure P_Catbed_raw = datafile(:,9); %Catalyst Bed Inlet Pressure P_FuCav_raw = datafile(:,10); %Fuel Cavitating Venturi Inlet Pressure P_FuInj_raw = datafile(:,11); %Fuel Injector Inlet Pressure P_CatbedOut_raw = datafile(:,12); %Catalyst Bed Outlet Pressure P_Chamber1_raw = datafile(:,13); %Chamber Pressure 1 P_Chamber2_raw = datafile(:,14); %Chamber Pressure 2 % Thermocouples T_OxLiquid = datafile(:,6); %Oxidizer Tank Liquid Temperature T_CatbedOut = datafile(:,15); %Catalyst Bed Outlet Temperature T_Chamber1 = datafile(:,16); %Chamber Temperature 1 T_Chamber2 = datafile(:,17); %Chamber Temperature 2 T_Chamber3 = datafile(:,18); %Chamber Temperature 3 T_Chamber4 = datafile(:,19); %Chamber Temperature 4 T_ChamberSkin1 = datafile(:,20); %Chamber Skin Temperature %Clear raw data variables to empty memory storage clear datafile; %---------------------------------------------- %Converting Transducer Voltage Data to Pressure %---------------------------------------------- % Setting slope of the calibration curve for each transducer Slope_P_OxUllage = 750; %Primary Oxidizer Ullage Pressure Slope_P_FuUllage = 750; %Fuel Ullage Pressure Slope_P_Fu2Ullage = 750; %Secondary Fuel Ullage Pressure Slope_P_OxCav = 750; %Oxidizer Cavitating Venturi Pressure Slope_P_Catbed = 750; %Catalyst Bed Inlet Pressure Slope_P_FuCav = 750; %Fuel Cavitating Venturi Pressure Slope_P_FuInj = 750; %Fuel Injector Inlet Pressure Slope_P_CatbedOut = 750; %Catalyst Bed Outlet Pressure Slope_P_Chamber1 = 750; %Chamber Pressure 1 Slope_P_Chamber2 = 750; %Chamber Pressure 2
170
%Creating Filter Design % Low-bypass digital Butterworth filter of 2nd order with 15Hz cutoff frequency % Cutoff frequency expressed as fraction of the Nyquist frequency (= ScanRate/2) [b,a] = butter(2,15*2/ScanRate); %Setting zeroing range in terms of scans (500 scans = 0.5 seconds) % Zero data is collected within the first 2000 scans (2 seconds) m = 500; n = 1500; %Calculating zero offset, absolute pressure, and filtered pressure P_OxUllage = P_OxUllage_raw * Slope_P_OxUllage; P_OxUllage_zero = mean(P_OxUllage(m:n)); P_OxUllage = P_OxUllage - P_OxUllage_zero + Patm; P_OxUllage_filt = filter(b,a,P_OxUllage); P_FuUllage = P_FuUllage_raw * Slope_P_FuUllage; P_FuUllage_zero = mean(P_FuUllage(m:n)); P_FuUllage = P_FuUllage - P_FuUllage_zero + Patm; P_FuUllage_filt = filter(b,a,P_FuUllage); P_Fu2Ullage = P_Fu2Ullage_raw * Slope_P_Fu2Ullage; P_Fu2Ullage_zero = mean(P_Fu2Ullage(m:n)); P_Fu2Ullage = P_Fu2Ullage - P_Fu2Ullage_zero + Patm; P_Fu2Ullage_filt = filter(b,a,P_Fu2Ullage); P_OxCav = P_OxCav_raw * Slope_P_OxCav; P_OxCav_zero = mean(P_OxCav(m:n)); P_OxCav = P_OxCav - P_OxCav_zero + Patm; P_OxCav_filt = filter(b,a,P_OxCav); P_Catbed = P_Catbed_raw * Slope_P_Catbed; P_Catbed_zero = mean(P_Catbed(m:n)); P_Catbed = P_Catbed - P_Catbed_zero + Patm; P_Catbed_filt = filter(b,a,P_Catbed); P_FuCav = P_FuCav_raw * Slope_P_FuCav; P_FuCav_zero = mean(P_FuCav(m:n)); P_FuCav = P_FuCav - P_FuCav_zero + Patm; P_FuCav_filt = filter(b,a,P_FuCav); P_FuInj = P_FuInj_raw * Slope_P_FuInj; P_FuInj_zero = mean(P_FuInj(m:n)); P_FuInj = P_FuInj - P_FuInj_zero + Patm; P_FuInj_filt = filter(b,a,P_FuInj);
171
P_CatbedOut = P_CatbedOut_raw * Slope_P_CatbedOut; P_CatbedOut_zero = mean(P_CatbedOut(m:n)); P_CatbedOut = P_CatbedOut - P_CatbedOut_zero + Patm; P_CatbedOut_filt = filter(b,a,P_CatbedOut); P_Chamber1 = P_Chamber1_raw * Slope_P_Chamber1; P_Chamber1_zero = mean(P_Chamber1(m:n)); P_Chamber1 = P_Chamber1 - P_Chamber1_zero + Patm; P_Chamber1_filt = filter(b,a,P_Chamber1); P_Chamber2 = P_Chamber2_raw * Slope_P_Chamber2; P_Chamber2_zero = mean(P_Chamber2(m:n)); P_Chamber2 = P_Chamber2 - P_Chamber2_zero + Patm; P_Chamber2_filt = filter(b,a,P_Chamber2); %Calculating Differential Pressures % Catalyst bed pressure drop DP_Catbed = P_Catbed - P_CatbedOut; DP_Catbed_filt = filter(b,a,DP_Catbed); % Fuel injector pressure drop DP_FuInj = P_FuInj - P_Chamber_avg; DP_FuInj_filt = filter(b,a,DP_FuInj); %--------------------------- %Calculating Mass Flow Rates %--------------------------- %Calculating densities % Average H2O2 temperature T_Ox = mean(T_OxLiquid(1:scans)); %[F] % Calculate density of H2O2 rho_Ox = 66.166 + ; %[lbm/ft^3] % Calculate fuel temperature using user-defined function rho_Fu = jp8density(T_Fu); %[lbm/ft^3] %Oxidizer flow rate A_CV_ox = pi*(D_CV_ox/2)^2; %[in^2] Mdot_Ox_CV = Cd_CV_ox*A_CV_ox*sqrt(2*g*rho_Ox*P_OxCav./144);%[lbm/s] % Set oxidizer flow rate to zero when it is not flowing for i = 1:scans, if P_Catbed(i) < 50 Mdot_Ox_CV(i) = 0.0; end end
172
%Fuel flow rate A_CV_fu = pi*(D_CV_fu/2)^2; %[in^2] Mdot_Fu_CV = Cd_CV_fu*A_CV_fu*sqrt(2*g*rho_Fu*P_FuCav./144);%[lbm/s] % Set fuel flow rate to zero when it is not flowing for i = 1:scans, if P_FuInj(i) < 200 Mdot_Fu_CV(i) = 0.0; end end %------------------------ %Performance Calculations %------------------------ %Calculate mixture ratio Mix_Rat = Mdot_Ox_CV./Mdot_Fu_CV; %Set dummy array for theoretical C* for biprop and monoprop cstarth = Mix_Rat; %Read data file containing theoretical C* for biprop mode as function of % mixture ratio for H2O2/JP8 at 500 psia A = dlmread('cstarpc500.txt','\t',6,0); %Create arrays of theoretical data of1 = A(:,1); cstar1 = A(:,3); %Calculate Theoretical C* %Set theoretical C* based on mixture ratio % If Mix_Ratio > 0, interpolate from data file % If Mix_Ratio = 0, set to monoprop theoretical C* for i = 1:scans, if Mdot_Fu_CV(i) > 0.0; Mix_Rat(i) = Mix_Rat(i); cstarth(i) = interp1(of1,cstar1,Mix_Rat(i)); %[ft/s] else Mix_Rat(i) = 0; cstarth(i) = cstarthmono; %[ft/s] end end
173
%Calculate C* and Efficiency %Calculation for C* cstar = P_Chamber2.*((Throat_Diam)^2*pi/4)*g./(Mdot_Ox_CV+Mdot_Fu_CV);%[ft/s] %Create dummy array for efficiency cstareff = (cstar./cstarthmono)*100; %[%] %Create final array for C* and efficiency % This if statement sets C* and efficiency to zero % when the oxidizer flow rate is zero for i = 1:scans if Mdot_Ox_CV(i) > 0 cstar(i) = cstar(i); %[ft/s] cstareff(i) = (cstar(i)/cstarth(i))*100; %[%] else cstar(i) = 0; cstareff(i) = 0; end end %------------- %Plotting Data %------------- figure(1) plot (Time, P_OxUllage_raw, Time, P_Fu2Ullage_raw, Time, P_OxCav_raw, Time, P_Catbed_raw, Time, P_FuCav_raw, Time, P_FuInj_raw, Time, P_CatbedOut_raw, Time, P_Chamber1_raw, Time, P_Chamber2_raw) xlabel ('Time [sec]') ylabel ('Volts [VDC]') title (['Raw Data, ' PlotTitle1]) legend ('POxUlg','PFu2Ulg', 'POxCav','PCatbed','PFuCav','PFuInj','PCatbedOut','Pc1','Pc2',3) grid on figure(2) plot (Time, P_OxUllage, Time, P_Fu2Ullage, Time, P_OxCav, Time, P_Catbed, Time, P_FuCav, Time, P_FuInj, Time, P_CatbedOut, Time, P_Chamber1, Time, P_Chamber2) xlabel ('Time [sec]') ylabel ('Pressure [psia]') title (['System Pressures, ' PlotTitle1]) legend ('POxUlg','PFu2Ulg','POxCav','PCatbed','PFuCav','PFuInj','PCatbedOut','Pc1','Pc2',3) grid on
174
figure(3) plot (Time, P_OxUllage_filt, Time, P_Fu2Ullage_filt, Time, P_OxCav_filt, Time, P_Catbed_filt, Time, P_FuCav_filt, Time, P_FuInj_filt, Time, P_CatbedOut_filt, Time, P_Chamber1_filt, Time, P_Chamber2_filt) xlabel ('Time [sec]') ylabel ('Pressure [psia]') title (['System Pressures, ' PlotTitle2]) legend ('POxUlg','PFu2Ulg','POxCav','Pcb','PFuCav','PFuInj','PCatbedOut','Pc1','Pc2',3) grid on figure(4) plot ( Time, Mdot_Ox_CV, Time, Mdot_Fu_CV) xlabel ('Time [sec]') ylabel ('Mass Flow [lbm/sec]') title (['Mass Flow Rate, ' PlotTitle1]) legend('Oxidizer','Fuel'); grid on; figure(5 plot ( Time, Mix_Rat) xlabel ('Time [sec]') ylabel ('Mixture Ratio') title (['Mixture Ratio, ' PlotTitle1]) grid on figure(6) plot(Time, cstar) xlabel ('Time [sec]') ylabel ('Cstar [ft/sec]') title (['Characteristic Velocity, ' PlotTitle2]) grid on figure(7) plot(Time, cstareff) xlabel ('Time [sec]') ylabel ('Cstar Efficiency [%]') title (['Cstar Efficiency, ' PlotTitle1]) grid on figure(8) plot (Time, T_OxLiquid) xlabel ('Time [sec]') ylabel ('Temperature [deg F]') title (['Oxidizer Liquid Temperature, ' PlotTitle2]) grid on
175
figure(9) plot(Time,P_Chamber_avg) xlabel ('Time [sec]') ylabel ('Pressure [psia]') title(['Average Chamber Pressure ' PlotTitle1]) grid on figure(10) plot(Time, DP_Catbed) xlabel ('Time [sec]') ylabel ('Pressure [psid]') title(['CatBed Pressure Drop ' PlotTitle1]) grid on figure(11) plot(Time, DP_Catbed_filt) xlabel ('Time [sec]') ylabel ('Pressure [psid]') title(['CatBed Pressure Drop ' PlotTitle2]) grid on figure(12) plot(Time, DP_FuInj) xlabel ('Time [sec]') ylabel ('Pressure [psid]') title(['Fuel Injector Pressure Drop ' PlotTitle1]) grid on figure(13) plot(Time, DP_FuInj_filt) xlabel ('Time [sec]') ylabel ('Pressure [psid]') title(['Fuel Injector Pressure Drop ' PlotTitle2]) legend('Transverse') grid on figure(14) plot(Time,P_OxCav ) xlabel ('Time [sec]') ylabel ('Pressure [psi]') title(['Oxidizer Venturi Inlet Pressure ' PlotTitle1]) grid on
176
figure(15) plot(Time,P_Catbed) xlabel ('Time [sec]') ylabel ('Pressure [psi]') title(['Catalyst Bed Inlet Pressure ' PlotTitle1]) grid on figure(16) plot(Time,P_FuCav ) xlabel ('Time [sec]') ylabel ('Pressure [psi]') title(['Fuel Venturi Inlet Pressure ' PlotTitle1]) grid on figure(17) plot(Time,P_FuInj) xlabel ('Time [sec]') ylabel ('Pressure [psi]') title(['Fuel Injector Inlet Pressure ' PlotTitle1]) grid on figure(18) plot(Time,P_CatbedOut ) xlabel ('Time [sec]') ylabel ('Pressure [psi]') title(['CatBed Outlet Pressure ' PlotTitle1]) grid on figure(19) plot(Time,P_Chamber1,Time,P_Chamber2) xlabel ('Time [sec]') ylabel ('Pressure [psi]') title(['Chamber Pressure' PlotTitle1]) legend('Pc1','Pc2'); grid on figure(20) plot (Time, T_CatbedOut) xlabel ('Time [sec]') ylabel ('Temperature [deg F]') title (['Catbed Outlet Temperature, ' PlotTitle2]) grid on
177
figure(21) plot (Time,T_Chamber1,Time,T_Chamber2,Time,T_Chamber3,Time,T_Chamber4 ) xlabel ('Time [sec]') ylabel ('Temperature [deg F]') title (['Chamber NFFC Temperatures, ' PlotTitle2]) legend('Tc1','Tc2','Tc3','Tc4',2) grid on figure(22) plot (Time,T_ChamberSkin1) xlabel ('Time [sec]') ylabel ('Temperature [deg F]') title (['Chamber Skin Temperatures, ' PlotTitle2]) grid on
178
Bipropavg.m
%========================== %FILENAME: Bipropavg.m %BY: Jim Sisco %========================== %Create output file fid = fopen('ign90305002out.txt','w'); %Set times which bound the averaging range t1 = 21.8; t2 = 22.5; %Convert the times to scans t1 = round(t1*1000); t2 = round(t2*1000); %----------------------- %Calculating Mean Values %----------------------- %Pressure data P_OxUllage2 = mean(P_OxUllage(t1:t2)); %Primary Oxidizer Tank Ullage Pressure P_OxCav2 = mean(P_OxCav(t1:t2)); %Oxidizer Cavitating Venturi Inlet Pressure P_Catbed2 = mean(P_Catbed(t1:t2)); %Catalyst Bed Inlet Pressure P_Fu2Ullage2 = mean(P_Fu2Ullage(t1:t2)); %Secondary Fuel Tank Ullage Pressure P_FuCav2 = mean(P_FuCav(t1:t2)); %Fuel Cavitating Venturi Inlet Pressure P_FuInj2 = mean(P_FuInj(t1:t2)); %Fuel Injector Inlet Pressure P_CatbedOut2 = mean(P_CatbedOut(t1:t2));%Catalyst Bed Outlet Pressure P_Chamber12 = mean(P_Chamber1(t1:t2)); %Chamber 1 Pressure P_Chamber22 = mean(P_Chamber2(t1:t2)); %Chmaber 2 Pressure %Temperature Data T_CatbedOut2 = mean(T_CatbedOut(t1:t2)); %Catalyst Bed Outlet Temperature %Calculated Data Mdot_Ox_CV2 = mean(Mdot_Ox_CV(t1:t2)); %Oxidizer Flow Rate Mdot_Fu_CV2 = mean(Mdot_Fu_CV(t1:t2)); %Fuel Flow Rate Mixture_Ratio = Mdot_Ox_CV2/Mdot_Fu_CV2; %Mixture Ratio cstar2 = mean(cstar(t1:t2)); %C* cstareff2 = mean(cstareff(t1:t2)); %C* Efficiency %Calculate differential pressures from average data dp_catbed = P_Catbed2 - P_CatbedOut2; %Catalyst Bed Pressure Drop dp_fuel_injector = P_FuInj2 - P_Chamber12; %Fuel Injector Pressure Drop %--------------
179
%Performing FFT %-------------- %Determine n, such that FFT uses 2^n points % (if 2^n is less than t1-t2 zero values are used to fill vector) p = ceil(log10(t2-t1)/log10(2)); N = 2^p; %Determine average value of important pressure parameters over time period P_Catbed_avg = mean(P_Catbed(t1:t2)); P_FuInj_avg = mean(P_FuInj(t1:t2)); P_CatbedOut_avg = mean(P_CatbedOut(t1:t2)); P_Chamber1_avg = mean(P_Chamber1(t1:t2)); P_Chamber2_avg = mean(P_Chamber2(t1:t2)); %Subtract out average value such that only noise remains P_Catbed_noise = P_Catbed - P_Catbed_avg; P_FuInj_noise = P_FuInj - P_FuInj_avg; P_CatbedOut_noise = P_CatbedOut - P_CatbedOut_avg; P_Chamber1_noise = P_Chamber1 - P_Chamber1_avg; P_Chamber2_noise = P_Chamber2 - P_Chamber2_avg; %Perform FFT on pressure noise [P_Catbed_FFT] = fft(P_Catbed_noise(t1:t2), N); [P_FuInj_FFT] = fft(P_FuInj_noise(t1:t2), N); [P_CatbedOut_FFT] = fft(P_CatbedOut_noise(t1:t2), N); [P_Chamber1_FFT] = fft(P_Chamber1_noise(t1:t2), N); [P_Chamber2_FFT] = fft(P_Chamber2_noise(t1:t2), N); %Calculate magnitude of FFT amplitude Mag_P_Catbed_FFT = sqrt(P_Catbed_FFT.*conj(P_Catbed_FFT)); Mag_P_FuInj_FFT = sqrt(P_FuInj_FFT.*conj(P_FuInj_FFT)); Mag_P_CatbedOut_FFT = sqrt(P_CatbedOut_FFT.*conj(P_CatbedOut_FFT)); Mag_P_Chamber1_FFT = sqrt(P_Chamber1_FFT.*conj(P_Chamber1_FFT)); Mag_P_Chamber2_FFT = sqrt(P_Chamber2_FFT.*conj(P_Chamber2_FFT)); %Calculate power spectrum Spectrum_P_Catbed = Mag_P_Catbed_FFT.^2./N; Spectrum_P_FuInj = Mag_P_FuInj_FFT.^2./N; Spectrum_P_CatbedOut = Mag_P_CatbedOut_FFT.^2./N; Spectrum_P_Chamber1 = Mag_P_Chamber1_FFT.^2./N; Spectrum_P_Chamber2 = Mag_P_Chamber2_FFT.^2./N;
180
%Calculate step in time and frequency del_t = 1/ScanRate; del_freq = 1/(N*del_t); %Calculate frequency vector (0-->Nyquist Frequency) freq = del_freq.*(0:N/2); %Calculate Max & Min of pressure noise as well as peak-to-peak amplitude Max_P_Catbed_noise = max(P_Catbed_noise(t1:t2)); Min_P_Catbed_noise = min(P_Catbed_noise(t1:t2)); Max_P_FuInj_noise = max(P_FuInj_noise(t1:t2)); Min_P_FuInj_noise = min(P_FuInj_noise(t1:t2)); Max_P_CatbedOut_noise = max(P_CatbedOut_noise(t1:t2)); Min_P_CatbedOut_noise = min(P_CatbedOut_noise(t1:t2)); Max_P_Chamber1_noise = max(P_Chamber1_noise(t1:t2)); Min_P_Chamber1_noise = min(P_Chamber1_noise(t1:t2)); Max_P_Chamber2_noise = max(P_Chamber2_noise(t1:t2)); Min_P_Chamber2_noise = min(P_Chamber2_noise(t1:t2)); PTP_P_Catbed_noise = Max_P_Catbed_noise - Min_P_Catbed_noise; PTP_P_FuInj_noise = Max_P_FuInj_noise - Min_P_FuInj_noise; PTP_P_CatbedOut_noise = Max_P_CatbedOut_noise - Min_P_CatbedOut_noise; PTP_P_Chamber1_noise = Max_P_Chamber1_noise - Min_P_Chamber1_noise; PTP_P_Chamber2_noise = Max_P_Chamber2_noise - Min_P_Chamber2_noise; %Find magnitude and frequency of highest peak in power spectrum [Max_Catbed, I_Catbed] = max(Spectrum_P_Catbed(1:(N/2)+1)); [Max_FuInj, I_FuInj] = max(Spectrum_P_FuInj(1:(N/2)+1)); [Max_CatbedOut, I_CatbedOut] = max(Spectrum_P_CatbedOut(1:(N/2)+1)); [Max_Chamber1, I_Chamber1] = max(Spectrum_P_Chamber1(1:(N/2)+1)); [Max_Chamber2, I_Chamber2] = max(Spectrum_P_Chamber2(1:(N/2)+1)); dom_freq_Catbed = freq(I_Catbed); dom_freq_FuInj = freq(I_FuInj); dom_freq_CatbedOut = freq(I_CatbedOut); dom_freq_Chamber1 = freq(I_Chamber1); dom_freq_Chamber2 = freq(I_Chamber2); %Calculate standard deviation of chamber pressure data std_Chamber2 = std(P_Chamber2(t1:t2));
181
%-------------------- %Plot Power Spectrums %-------------------- figure(80) plot(freq, Spectrum_P_Catbed(1:(N/2)+1), freq, Spectrum_P_FuInj(1:(N/2)+1)); legend('Catbed','FuInj'); grid; xlabel('Frequency (Hz)'); ylabel('Power (psi^2/Hz ???)'); title (['Power Spectrum, 'PlotTitle1]) figure(81) plot(freq, Spectrum_P_CatbedOut(1:(N/2)+1), freq, Spectrum_P_Chamber1(1:(N/2)+1), freq, Spectrum_P_Chamber2(1:(N/2)+1)); legend('CatbedOut','Chamber1','Chamber2'); grid; xlabel('Frequency (Hz)'); ylabel('Power (psi^2/Hz ???)'); title (['Power Spectrum, 'PlotTitle1]) %------------------ %Write Data to File %------------------ fprintf(fid,'Ignition Testing - Test 90-30-50-02 (PCI Catbed)\n\n'); fprintf(fid,'Oxidizer Ullage Pressure (psi) = \t\t\t\t\t\t\t%8.2f\n',P_OxUllage2); fprintf(fid,'Oxidizer Cavitating Venturi Inlet Pressure (psi) = \t\t\t%8.2f\n',P_OxCav2); fprintf(fid,'Catalyst Bed Inlet Pressure (psi) = \t\t\t\t\t\t%8.2f\n',P_Catbed2); fprintf(fid,'Catalyst Bed Outlet Pressure (psi) = \t\t\t\t\t\t%8.2f\n',P_CatbedOut2); fprintf(fid,'Catalyst Bed Pressure Drop (psi) = \t\t\t\t\t\t\t%8.2f\n',dp_catbed); fprintf(fid,'Oxidizer Flow Rate (lbm/s) = \t\t\t\t\t\t\t\t%8.3f\n\n',Mdot_Ox_CV2); fprintf(fid,'Fuel Ullage Pressure (psi) = \t\t\t\t\t\t\t\t%8.2f\n',P_Fu2Ullage2); fprintf(fid,'Fuel Cavitating Venturi Inlet Pressure (psi) = \t\t\t\t%8.2f\n',P_FuCav2); fprintf(fid,'Fuel Injector Supply Pressure (psi) = \t\t\t\t\t\t%8.2f\n',P_FuInj2); fprintf(fid,'Fuel Injector Pressure Drop (psi) = \t\t\t\t\t\t%8.2f\n',dp_fuel_injector); fprintf(fid,'Fuel Flow Rate (lbm/s) = \t\t\t\t\t\t\t\t\t%8.3f\n\n',Mdot_Fu_CV2); fprintf(fid,'Mixture Ratio = \t\t\t\t\t\t\t\t\t\t\t%8.2f\n',Mixture_Ratio); fprintf(fid,'Chamber Pressure 1 (psi) = \t\t\t\t\t\t\t\t\t%8.2f\n',P_Chamber12); fprintf(fid,'Chamber Pressure 2 (psi) = \t\t\t\t\t\t\t\t\t%8.2f\n',P_Chamber22); fprintf(fid,'Characteristic Velocity (ft/s) = \t\t\t\t\t\t\t%8.2f\n',cstar2); fprintf(fid,'C* Efficiency (percent) = \t\t\t\t\t\t\t\t\t%8.2f\n\n',cstareff2); fprintf(fid,'Catbed Outlet Temperature (F) = \t\t\t\t\t\t\t%8.2f\n\n\n',T_CatbedOut2); fprintf(fid,'Biprop Pressure Oscillations:\n\n'); fprintf(fid,'Catalyst Bed Inlet Pressure Frequency (Hz) =\t\t\t\t%8.2f\n',dom_freq_Catbed);
182
fprintf(fid,'Catalyst Bed Inlet Pressure Peak-to-Peak (psid) =\t\t\t%8.2f\n\n',PTP_P_Catbed_noise); fprintf(fid,'Fuel Injector Inlet Pressure Frequency (Hz) =\t\t\t\t%8.2f\n',dom_freq_FuInj); fprintf(fid,'Fuel Injector Inlet Pressure Peak-to-Peak (psid) =\t\t\t%8.2f\n\n',PTP_P_FuInj_noise); fprintf(fid,'Catalyst Bed Outlet Pressure Frequency (Hz) =\t\t\t\t%8.2f\n',dom_freq_CatbedOut); fprintf(fid,'Catalyst Bed Outlet Pressure Peak-to-Peak (psid) =\t\t\t%8.2f\n\n',PTP_P_CatbedOut_noise); fprintf(fid,'Chamber 1 Pressure Frequency (Hz) =\t\t\t\t\t\t\t%8.2f\n',dom_freq_Chamber1); fprintf(fid,'Chamber 1 Pressure Peak-to-Peak (psid) =\t\t\t\t\t%8.2f\n\n',PTP_P_Chamber1_noise); fprintf(fid,'Chamber 2 Pressure Frequency (Hz) =\t\t\t\t\t\t\t%8.2f\n',dom_freq_Chamber2); fprintf(fid,'Chamber 2 Pressure Peak-to-Peak (psid) =\t\t\t\t\t%8.2f\n\n',PTP_P_Chamber2_noise); fclose(fid);
183
Appendix E: Uncertainty Analysis
The following equations for uncertainty in each calculated variable were derived
by the method outlined in Fox and McDonald.61
Propellant Density
The density of hydrogen peroxide, ?ox, is calculated from its temperature, Tox, and
concentration, W, using equation 4.8, which has the following form:
oxoxoxox FWTETDTCWBWA +++++= 22ρ , (E.1)
Therefore, the uncertainty in the hydrogen peroxide density can be calculated
from the following equation:
21
22
∂∂
+
∂∂
= Toxox
ox
ox
oxW
ox
oxox u
TT
uW
Wu
ρρ
ρρρ , (E.2)
Taking the derivative of the hydrogen peroxide density with respect to
concentration and temperature gives the following:
oxox FTCWB
W++=
∂∂
2ρ
, (E.3)
FWETDT ox
ox
ox ++=∂∂
2ρ
, (E.4)
For JP-8, the density, ?f, is a linear function of temperature, Tf, and can be written
as follows:
ff QTP +=ρ , (E.5)
184
The derivative of this equation with respect to fuel temperature is equal to the
constant P. Then, the uncertainty in the density of JP-8 can be written as:
21
2
= Tf
f
ff u
TPu
ρρ , (E.6)
Data regarding the variation in the density of DMAZ with its temperature is not
currently known. As a result, the uncertainty in the DMAZ density was assumed to be
equal to zero.
Mass Flow Rate and Equivalence Ratio
Using equation 4.4 the uncertainty in the mass flow rate of hydrogen peroxide,
JP-8, or DMAZ can be determined from the following equation:
21
2222
∂∂
+
∂∂
+
∂∂
+
∂∂
= pdtt
tCD
D
Dm u
pm
mp
um
mu
dm
md
uCm
mC
u&
&&
&&
&&
&& ρρρ
, (E.7)
This equation can be simplified substantially, after substituting the appropriate
derivatives, to express the uncertainty in flow rate as:
( ) ( )2
122
22
222
+
++= p
dtCDm
uuuuu ρ
& , (E.8)
Starting from equations 3.6 and 5.5 the uncertainty in equivalence ratio can be
expressed as:
21
222
∂
∂+
∂∂
+
∂∂
= FsOs
sfm
f
foxm
ox
ox uFO
FOu
m
mu
mm
uφ
φφ
φφ
φφ && &
&
&&
, (E.9)
The equation for uncertainty in equivalence ratio can be simplified a great deal as
well to give:
( ) ( ) ( )[ ] 21
222FsOfmoxm uuuu ++−= &&φ , (E.10)
The uncertainty in the total mass flow rate, which is used to calculate C*, can be
determined from the following equation:
185
21
22
∂∂
+
∂∂
= fmf
tot
tot
foxm
ox
tot
tot
oxtotm u
mm
m
mu
mm
mm
u &&& &&
&
&
&&
&&
, (E.11)
Since the derivatives of the total mass flow rate with respect to the fuel and
oxidizer flow rate are equal to one this equation can be simplified to:
21
22
+
= fm
tot
foxm
tot
oxtotm u
m
mu
mm
u &&& &
&
&&
, (E.12)
Performance Parameters
The uncertainty in the characteristic velocity, equation 5.7, in both monoprop and
biprop modes can be calculated from the following equation:
21
222
*
∂∂
+
∂∂
+
∂∂
=∗
∗
∗
∗
∗
∗ totmtot
totDth
th
thpc
c
cC u
mC
Cm
uDC
CD
upC
Cp
u &&&
, (E.13)
Upon simplification the equation reduces to:
( ) ( ) ( )[ ] 21
222* 2 totmDthpcC uuuu &−++= , (E.14)
The C* or decomposition efficiency, equation 5.10, can be found from the
following:
21
2
**
*
2
**
**
∂∂
+
∂∂
=∗
∗
∗
∗
thCth
C
C
thC
C
CC u
CC
uC
Cu
ηη
ηηη , (E.15)
This equation reduces to:
( ) ( )[ ] 21
2*
2** thCCC uuu −+=η , (E.16)
186
Momentum Ratio and Residence Time
There are a number of uncertainty parameters which must be determined to
calculate the uncertainty in the momentum ratio. One of these parameters is the
uncertainty in the fuel velocity exiting the injector, calculated from equations 2.3 and
2.4. The uncertainty in fuel velocity can be found from the following equation:
21
22
22
∂
∂+
∂
∂+
∂
∂+
∂
∂
=
doo
f
f
oCD
D
f
f
D
ff
f
f
ffm
f
f
f
f
Vf
ud
V
Vd
uC
V
VC
uV
Vu
m
V
V
m
uρρ
ρ&&
&
, (E.17)
Upon simplification this equation becomes:
( ) ( ) ( ) ( )[ ] 21
2222 2 doCDffmVf uuuuu −+−+−+= ρ& , (E.18)
To calculate the uncertainty in the properties of the decomposed gases the
uncertainty in the temperature of the gas must be determined first. The uncertainty in the
decomposition temperature, equation 5.11, is calculated from the following:
21
2
__
_2
_**
_*
∂∂
+
∂∂
= thTtoxthtox
tox
tox
thtoxmonoC
C
tox
tox
monoCTtox u
TT
T
Tu
TT
u ηη
η, (E.19)
Simplifying this equation gives:
( ) ( )[ ] 21
2_
2_*2 thTtoxmonoCTtox uuu += η , (E.20)
Using the uncertainty in temperature the uncertainty in the density of the
decomposed gas, equation 5.14, is determined from the following equation assuming an
incompressible fluid:
21
2
22
∂
∂+
∂
∂+
∂
∂
=
Ttoxtox
oxg
oxg
tox
MWoxgoxg
oxg
oxg
oxgptox
tox
oxg
oxg
tox
oxg
uT
T
uMW
MWu
pp
uρ
ρ
ρ
ρ
ρ
ρρ , (E.21)
This equation can be simplified to:
187
( ) ( ) ( )[ ] 21
222TtoxMWoxgptoxoxg uuuu −++=ρ , (E.22)
With the uncertainty in the density known the uncertainty in the velocity of the
decomposed gas, equation 5.13 which assumes incompressible flow, can be found from:
21
222
∂∂
+
∂∂
+
∂∂
= Doxox
ox
ox
oxoxg
oxg
ox
ox
oxgoxm
ox
ox
ox
oxVox u
DV
VD
uV
Vu
mV
Vm
u ρρ
ρ&&
&, (E.23)
After simplification this equation becomes:
( ) ( ) ( )[ ] 21
222 2 DoxoxgoxmVox uuuu −+−+= ρ& , (E.24)
The uncertainty in momentum ratio, equation 2.24, can now be determined from
the following:
21
22
22
∂∂
+
∂∂
+
∂∂
+
∂∂
=
Voxox
oxoxg
oxg
oxg
Vff
ff
f
f
Q
uVQ
QV
uQ
Q
uVQ
Q
Vu
u
ρ
ρ
ρ
ρ
ρ
ρ
, (E.25)
This expression simplifies to:
( ) ( ) ( ) ( )[ ] 21
2222 22 VoxoxgVffQ uuuuu −+−++= ρρ , (E.26)
The uncertainty in the shear layer residence time, equation 2.12, is determined
from the following equation:
21
22
∂
∂+
∂∂
= hsl
slVox
ox
sl
sl
oxsl u
hh
uV
Vu
ττ
τττ , (E.27)
After simplification this equation becomes:
( ) ( )[ ] 21
22hVoxsl uuu +−=τ , (E.28)
Finally, the uncertainty in Mach number, equation 5.12, neglecting uncertainty in
the molecular weight and specific heat ratio of the decomposed gas is determined from:
188
21
22
22
∂∂
+
∂∂
+
∂∂
+
∂∂
=
Ttoxtox
ox
ox
toxDox
ox
ox
ox
ox
ptoxtox
ox
ox
toxoxm
ox
ox
ox
ox
Mox
uTM
MT
uDM
MD
upM
Mp
umM
Mm
u&&
&
, (E.29)
Following simplification this equation becomes:
( ) ( ) ( )2
12
222
22
+−+−+= Ttox
DoxptoxoxmMoxu
uuuu & , (E.30)
Other Uncertainty Parameters
The uncertainty in the pressure drop across the catalyst bed, equation 5.4, can be
calculated from the following equation:
21
2
__
_
2
__
_
∂∆∂
∆+
∂∆∂
∆=∆ outpcb
outcb
cb
cb
outcbinpcb
incb
cb
cb
incbpcb u
pp
p
pu
pp
p
pu , (E.31)
The uncertainty in the contraction ratio is calculated from:
21
22
∂∂
+
∂∂
= Dthth
thDc
c
cCR u
DCR
CRD
uDCR
CRD
u , (E.32)
This equation simplifies to the following:
( ) ( )[ ] 21
22 22 DthDcCR uuu −+= , (E.33)
189
Appendix F: Test Data
190
Table F.1: Measured and calculated test data during bipropellant operation.
Test Number Injector W Fuel CR Dth L* p_ox_cv dth_ox_cv CD_ox_cv T_ox rho_ox mdot_ox p_fu_cv dth_f_cv CD_f_cv rho_f mdot_f(xx-xx-xx-xx) (Catbed) (%) (--) (in.) (in.) (psia) (in.) (--) (F) (lbm/ft^3) (lbm/s) (psia) (in.) (--) (lbm/ft^3) (lbm/s)90-30-17-01 B (GK) 90.6 DMAZ 3.0 1.478 24.1 959.9 0.078 0.839 79.6 86.72 0.774 1682.1 0.058 0.844 57.98 0.46690-30-18-01 B (GK) 89.5 DMAZ 3.0 1.478 24.1 1160.7 0.078 0.839 73.2 86.57 0.850 1697.9 0.058 0.844 57.98 0.46890-30-22-01 B (GK) 89.5 DMAZ 3.0 1.478 24.1 1610.8 0.078 0.839 72.2 86.60 1.001 1704.5 0.058 0.844 57.98 0.46985-30-17-01 B (GK) 85.0 DMAZ 3.0 1.478 24.1 1026.6 0.078 0.839 73.9 85.00 0.792 1692.2 0.058 0.844 57.98 0.46785-30-21-01 B (GK) 84.7 DMAZ 3.0 1.478 24.1 1530.7 0.078 0.839 72.0 84.97 0.967 1686.6 0.058 0.844 57.98 0.46685-30-25-01 B (GK) 84.7 DMAZ 3.0 1.478 24.1 1640.9 0.078 0.839 73.3 84.93 1.001 1221.8 0.058 0.844 57.98 0.39785-30-50-01 B (GK) 85.4 JP-8 3.0 1.478 24.1 1374.7 0.111 0.989 82.8 84.82 2.186 1651.0 0.058 0.844 50.68 0.43185-30-64-01 B (GK) 85.4 JP-8 3.0 1.478 24.1 1446.4 0.111 0.989 79.6 84.94 2.243 1201.1 0.058 0.844 50.68 0.36885-30-64-03 B (GK) 85.4 JP-8 3.0 1.478 24.1 1558.6 0.111 0.989 73.9 85.14 2.331 1251.1 0.058 0.844 50.68 0.37687-30-44-01 B (GK) 87.7 JP-8 3.0 1.478 24.1 1073.5 0.111 0.989 72.3 85.98 1.944 1697.1 0.058 0.844 50.68 0.43790-30-40-02 B (PCI) 89.4 JP-8 3.0 1.478 24.1 1633.3 0.094 0.994 77.5 86.38 1.733 1666.8 0.058 0.844 50.68 0.43390-30-35-02 B (PCI) 90.5 JP-8 3.0 1.478 24.1 1318.1 0.094 0.994 78.8 86.71 1.560 1663.0 0.058 0.844 50.68 0.43394-30-35-01 B (PCI) 94.1 JP-8 3.0 1.478 24.1 1258.8 0.094 0.994 68.0 88.38 1.539 1652.4 0.058 0.844 50.68 0.43294-30-40-01 B (PCI) 94.1 JP-8 3.0 1.478 24.1 1666.2 0.094 0.994 80.9 87.90 1.765 1668.2 0.058 0.844 50.68 0.43498-30-30-01 B (PCI) 98.1 JP-8 3.0 1.478 24.1 938.4 0.094 0.994 56.8 90.24 1.342 1666.9 0.058 0.844 50.68 0.43385-50-31-01 B (GK) 85.2 JP-8 5.0 1.145 40.4 1033.2 0.094 0.994 72.3 85.13 1.368 1715.7 0.058 0.844 50.68 0.44087-30-60-01 B (GK) 87.3 JP-8 3.0 1.478 24.1 1562.3 0.111 0.989 72.8 85.83 2.344 1399.4 0.058 0.844 50.68 0.39790-30-50-01 B (GK) 90.0 JP-8 3.0 1.478 24.1 1342.4 0.111 0.989 75.1 86.67 2.183 1666.2 0.058 0.844 50.68 0.43390-30-50-02 B (PCI) 90.5 JP-8 3.0 1.478 24.1 1342.1 0.111 0.989 67.8 87.11 2.188 1657.5 0.058 0.844 50.68 0.43294-30-45-01 B (PCI) 93.5 JP-8 3.0 1.478 24.1 1068.6 0.111 0.989 81.9 87.65 1.959 1662.3 0.058 0.844 50.68 0.43398-30-35-01 B (PCI) 98.1 JP-8 3.0 1.478 24.1 1240.1 0.094 0.994 76.3 89.51 1.537 1648.4 0.058 0.844 50.68 0.43198-30-40-01 B (PCI) 98.1 JP-8 3.0 1.478 24.1 1585.2 0.094 0.994 80.7 89.35 1.736 1675.0 0.058 0.844 50.68 0.43485-50-64-01 B (GK) 86.0 JP-8 5.0 1.145 40.4 1511.0 0.111 0.989 79.5 85.14 2.296 1201.4 0.058 0.844 50.68 0.36887-30-52-01 B (GK) 87.4 JP-8 3.0 1.478 24.1 1425.9 0.111 0.989 72.6 85.87 2.239 1716.7 0.058 0.844 50.68 0.44087-30-49-01 B (GK) 87.7 JP-8 3.0 1.478 24.1 1265.2 0.111 0.989 74.3 85.91 2.110 1685.4 0.058 0.844 50.68 0.43690-30-35-01 B (GK) 89.5 JP-8 3.0 1.478 24.1 710.7 0.111 0.989 74.9 86.51 1.587 1668.6 0.058 0.844 50.68 0.43490-30-40-01 B (GK) 89.8 JP-8 3.0 1.478 24.1 933.4 0.111 0.989 64.0 87.00 1.824 1676.7 0.058 0.844 50.68 0.43590-30-44-01 B (GK) 89.8 JP-8 3.0 1.478 24.1 1071.4 0.111 0.989 68.4 86.85 1.952 1681.5 0.058 0.844 50.68 0.43585-50-37-01 B (GK) 84.8 JP-8 5.0 1.145 40.4 1442.7 0.094 0.994 77.2 84.82 1.614 1705.0 0.058 0.844 50.68 0.43885-50-50-01 B (GK) 86.0 JP-8 5.0 1.145 40.4 1334.2 0.111 0.989 79.5 85.14 2.157 1649.3 0.058 0.844 50.68 0.431
191
Table F.2: Measured and calculated bipropellant test data (cont.)
IgnitionStrong,
Test Number mdot_tot O/F φ p_cb_in p_cb_out ∆p_cb p_c1 p_c2 p_c2/ P_c2_tot C* C*_th η_C* Weak, p_fu_inj ∆p_f CD_inj(xx-xx-xx-xx) (lbm/s) (--) (--) (psia) (psia) (psid) (psia) (psia) p_c2_tot (psia) (ft/s) (ft/s) (%) No Ign. (psia) (psid) (--)90-30-17-01 1.239 1.66 2.60 -- 115.7 -- 93.4 98.9 0.9753 101.4 4522.6 4636.2 97.6% Strong 211.7 118.3 0.6990-30-18-01 1.318 1.82 2.38 -- 123.5 -- 102.6 107.6 0.9756 110.3 4622.7 4704.0 98.3% Strong 217.9 115.3 0.7090-30-22-01 1.470 2.14 2.02 -- 138.1 -- 116.8 119.7 0.9756 122.7 4610.7 4817.6 95.7% Strong 236.5 119.7 0.6985-30-17-01 1.259 1.70 2.70 -- 107.5 -- 98.8 97.5 0.9753 99.9 4384.2 4454.2 98.4% Weak 206.3 107.5 0.7285-30-21-01 1.433 2.07 2.20 -- 120.4 -- 110.4 107.5 0.9756 110.2 4246.2 4691.5 90.5% Weak 219.5 109.1 0.7285-30-25-01 1.398 2.52 1.81 -- 113.3 -- 108.0 104.2 0.9756 106.8 4222.4 4846.5 87.1% Weak 185.2 77.2 0.7385-30-50-01 2.617 5.07 1.68 470.1 145.1 325.0 114.6 130.6 0.9757 133.8 2825.0 4982.8 56.7% No Ign. 225.2 110.6 0.7185-30-64-01 2.611 6.10 1.39 483.4 138.0 345.4 114.1 130.6 0.9757 133.9 2832.6 5102.0 55.5% No Ign. 205.2 91.1 0.6685-30-64-03 2.707 6.21 1.37 537.2 131.3 405.9 110.2 116.7 0.9757 119.6 2441.3 5116.8 47.7% No Ign. 198.3 88.0 0.6987-30-44-01 2.382 4.45 1.86 476.9 118.6 358.3 109.6 105.2 0.9757 107.9 2501.7 5002.4 50.0% No Ign. 235.9 126.3 0.6790-30-40-02 2.166 4.00 2.01 521.2 88.8 432.4 86.7 93.1 0.9757 95.4 2432.6 5003.9 48.6% No Ign. 185.1 98.4 0.7590-30-35-02 1.992 3.60 2.23 462.8 76.1 386.7 75.4 78.8 0.9757 80.7 2238.8 4898.4 45.7% No Ign. 179.9 104.4 0.7394-30-35-01 1.970 3.57 2.15 527.0 82.2 444.8 83.1 83.1 0.9757 85.2 2387.9 5049.3 47.3% No Ign. 181.3 98.2 0.7594-30-40-01 2.199 4.07 1.89 626.2 98.3 528.0 98.0 102.4 0.9757 105.0 2637.7 5168.3 51.0% No Ign. 196.1 98.1 0.7598-30-30-01 1.776 3.10 2.38 637.8 77.6 560.2 78.1 83.0 0.9757 85.1 2646.7 5027.4 52.6% No Ign. 175.5 97.3 0.7685-50-31-01 1.808 3.11 2.73 379.8 156.5 223.3 157.3 151.5 0.9915 152.8 2801.8 4502.1 62.2% No Ign. 281.9 124.6 0.6887-30-60-01 2.741 5.90 1.40 653.9 250.6 403.4 232.4 236.5 0.9757 242.4 4886.2 5175.5 94.4% Strong 320.6 88.2 0.7390-30-50-01 2.616 5.04 1.59 512.2 243.3 268.9 222.8 224.9 0.9757 230.5 4866.1 5159.2 94.3% Strong 323.9 101.1 0.7490-30-50-02 2.621 5.06 1.58 636.8 226.1 410.7 227.7 229.7 0.9757 235.4 4963.1 5183.1 95.8% Strong 330.6 102.9 0.7394-30-45-01 2.392 4.53 1.70 865.9 194.6 671.3 195.5 200.3 0.9757 205.3 4741.5 5236.8 90.5% Strong 301.3 105.8 0.7298-30-35-01 1.968 3.57 2.06 709.8 168.7 541.1 161.7 170.2 0.9757 174.4 4896.9 5191.7 94.3% Strong 265.0 103.3 0.7398-30-40-01 2.171 4.00 1.84 743.9 185.3 558.6 182.6 190.6 0.9757 195.3 4971.5 5282.5 94.1% Strong 286.1 103.5 0.7385-50-64-01 2.664 6.24 1.36 678.8 397.0 281.8 380.6 392.1 0.9915 395.5 4921.9 5109.6 96.3% Strong 457.0 76.4 0.7287-30-52-01 2.679 5.09 1.62 597.7 182.7 415.0 164.0 166.2 0.9757 170.3 3512.3 5098.8 68.9% Weak 284.8 120.8 0.6987-30-49-01 2.546 4.84 1.70 571.9 170.3 401.6 150.6 153.3 0.9757 157.1 3408.4 5066.0 67.3% Weak 282.4 131.8 0.6590-30-35-01 2.021 3.66 2.19 329.5 107.2 222.3 91.7 97.2 0.9757 99.6 2722.4 4898.4 55.6% Weak 188.2 96.5 0.7690-30-40-01 2.259 4.20 1.91 402.7 141.0 261.6 128.1 136.2 0.9757 139.6 3414.0 5026.1 67.9% Weak 244.3 116.2 0.6990-30-44-01 2.388 4.48 1.79 578.3 215.0 363.3 198.4 200.7 0.9757 205.7 4760.1 5092.7 93.5% Weak 304.3 105.9 0.7385-50-37-01 2.052 3.68 2.31 496.9 269.4 227.5 273.6 264.8 0.9915 267.1 4314.0 4729.1 91.2% Weak 371.1 97.5 0.7685-50-50-01 2.588 5.00 1.70 629.0 379.6 249.4 362.3 371.0 0.9915 374.1 4791.5 4982.8 96.2% Weak 464.0 101.7 0.74
Assume γ = 1.22Pc Correction Biprop Performance
C*_th @ 500 psiFuel Injector Performance
192
Table F.3: Measured and calculated monopropellant test data.
Test Number p_ox_cv mdot_ox G p_cb_in p_cb_out ∆p_cb p_c1 p_c2 p_c2/ P_c2_tot C* C*_th η_C* Ttox_th Ttox(xx-xx-xx-xx) (psia) (lbm/s) (lbm/s/in^2) (psia) (psia) (psid) (psia) (psia) p_c2_tot (psia) (ft/s) (ft/s) (%) (F) (F)90-30-17-01 956.4 0.772 0.12 -- 42.1 -- 32.2 36.0 0.9751 36.9 2638.7 3083 85.6% 1393 102090-30-18-01 1080.0 0.820 0.12 -- 49.1 -- 40.7 43.9 0.9751 45.1 3036.8 3083 98.5% 1393 135290-30-22-01 1608.8 1.001 0.15 -- 59.3 -- 50.0 52.8 0.9751 54.2 2990.5 3083 97.0% 1393 131185-30-17-01 1023.1 0.791 0.12 -- 41.3 -- 34.5 36.9 0.9750 37.9 2646.6 2904 91.1% 1173 97485-30-21-01 1528.4 0.966 0.15 -- 46.9 -- 38.1 38.2 0.9750 39.2 2240.3 2904 77.1% 1173 69885-30-25-01 1639.2 1.000 0.15 -- 48.7 -- 40.2 40.5 0.9750 41.6 2295.8 2904 79.1% 1173 73385-30-50-01 1375.0 2.186 0.33 451.7 122.3 329.4 95.0 106.8 0.9750 109.5 2768.1 2904 95.3% 1173 106685-30-64-01 1501.0 2.285 0.35 515.9 129.0 386.9 103.8 114.1 0.9750 117.0 2828.2 2904 97.4% 1173 111385-30-64-03 1562.6 2.334 0.35 508.0 106.4 401.6 84.0 91.3 0.9751 93.7 2216.4 2904 76.3% 1173 68387-30-44-01 1072.3 1.943 0.29 461.6 96.9 364.7 85.7 83.8 0.9750 85.9 2443.4 2996 81.6% 1283 85390-30-40-02 1631.6 1.732 0.55 519.0 81.3 437.7 80.9 87.4 0.9751 89.6 2858.4 3083 92.7% 1393 119790-30-35-02 1317.3 1.559 0.50 462.9 69.7 393.3 70.5 74.1 0.9751 76.0 2693.5 3083 87.4% 1393 106394-30-35-01 1262.1 1.541 0.49 519.7 68.8 450.9 70.6 71.7 0.9752 73.6 2637.9 3217 82.0% 1570 105694-30-40-01 1626.5 1.744 0.56 616.4 84.3 532.1 84.9 90.4 0.9752 92.7 2936.4 3217 91.3% 1570 130898-30-30-01 936.6 1.341 0.43 623.6 66.4 557.3 67.1 72.7 0.9753 74.5 3070.3 3343 91.8% 1746 147385-50-31-01 1031.8 1.367 0.21 326.6 102.8 223.8 98.0 94.0 0.9912 94.8 2299.1 2904 79.2% 1173 73587-30-60-01 1561.9 2.343 0.35 612.6 132.2 480.5 109.2 118.3 0.9750 121.4 2861.3 2996 95.5% 1283 117090-30-50-01 1337.2 2.179 0.33 461.9 127.6 334.4 106.6 114.9 0.9751 117.8 2987.5 3083 96.9% 1393 130890-30-50-02 1345.0 2.191 0.70 622.0 104.1 517.9 104.2 112.2 0.9751 115.0 2900.7 3083 94.1% 1393 123394-30-45-01 1070.8 1.961 0.62 867.6 85.7 781.9 90.3 93.9 0.9752 96.2 2711.5 3217 84.3% 1570 111598-30-35-01 1238.5 1.536 0.49 691.5 78.3 613.2 78.5 84.7 0.9753 86.8 3122.6 3343 93.4% 1746 152398-30-40-01 1584.4 1.736 0.55 721.6 85.9 635.7 88.0 95.1 0.9753 97.5 3104.0 3343 92.8% 1746 150585-50-64-01 1510.5 2.295 0.35 549.3 196.0 353.3 184.2 188.7 0.9912 190.4 2749.3 2904 94.7% 1173 105187-30-52-01 1433.9 2.246 0.34 569.2 124.3 444.9 102.4 110.7 0.9750 113.5 2792.8 2996 93.2% 1283 111587-30-49-01 1265.4 2.110 0.32 538.1 111.6 426.5 91.0 96.6 0.9750 99.1 2595.0 2996 86.6% 1283 96390-30-35-01 709.3 1.585 0.24 325.6 92.3 233.3 77.1 83.0 0.9751 85.1 2965.9 3083 96.2% 1393 128990-30-40-01 929.1 1.820 0.28 374.7 103.7 271.0 85.6 94.2 0.9751 96.6 2934.0 3083 95.2% 1393 126290-30-44-01 1072.6 1.953 0.30 546.4 112.8 433.6 92.6 102.8 0.9751 105.5 2982.8 3083 96.8% 1393 130485-50-37-01 1449.9 1.618 0.24 412.0 127.3 284.7 124.7 115.8 0.9912 116.8 2393.6 2904 82.4% 1173 79785-50-50-01 1375.7 2.190 0.33 498.4 179.4 319.0 166.5 169.9 0.9912 171.4 2594.3 2904 89.3% 1173 936
193
Table F.4: Calculated decomposed gas and fue l flow conditions.
Fuel Orifice
Test Number γ MW_ox D_ox M_ox V_ox rho_ox M Vox rho_ox CD V_f Q tsl(xx-xx-xx-xx) (--) (lbm/lbm-mol) (in) (--) (ft/s) (lbm/ft^3) (--) (ft/s) (lbm/ft^3) (--) (ft/s) (--) (ms)90-30-17-01 1.265 22.11 1.71 0.461 946.4 0.051 0.465 941.1 0.052 0.800 118.4 17.7 0.07590-30-18-01 1.265 22.11 1.71 0.443 1006.3 0.051 0.447 1001.1 0.052 0.800 118.9 15.8 0.07190-30-22-01 1.265 22.11 1.71 0.445 998.8 0.063 0.448 993.6 0.063 0.800 119.2 13.1 0.07185-30-17-01 1.274 21.83 1.71 0.454 925.7 0.054 0.458 920.8 0.054 0.800 118.7 17.7 0.07785-30-21-01 1.274 21.83 1.71 0.482 883.0 0.069 0.486 877.7 0.069 0.800 118.5 15.2 0.08185-30-25-01 1.274 21.83 1.71 0.477 887.7 0.071 0.482 882.5 0.071 0.800 100.9 10.6 0.08085-30-50-01 1.274 21.83 1.71 0.447 941.6 0.146 0.451 936.7 0.147 0.800 125.4 6.2 0.07685-30-64-01 1.274 21.83 1.71 0.445 949.8 0.151 0.448 945.0 0.152 0.800 107.0 4.2 0.07585-30-64-03 1.274 21.83 1.71 0.484 881.1 0.167 0.489 875.8 0.168 0.800 109.2 4.7 0.08187-30-44-01 1.269 21.97 1.71 0.470 912.4 0.134 0.474 907.2 0.135 0.800 127.2 7.3 0.07890-30-40-02 1.265 22.11 1.71 0.450 978.2 0.111 0.454 972.9 0.112 0.800 126.0 7.6 0.07390-30-35-02 1.265 22.11 1.71 0.458 954.0 0.103 0.462 948.7 0.103 0.800 125.9 8.6 0.07594-30-35-01 1.258 22.33 1.71 0.466 959.5 0.101 0.469 953.9 0.102 0.800 125.5 8.6 0.07494-30-40-01 1.258 22.33 1.71 0.452 1005.5 0.109 0.455 1000.0 0.110 0.800 126.1 7.3 0.07198-30-30-01 1.251 22.56 1.71 0.451 1040.5 0.081 0.454 1034.8 0.082 0.800 126.0 9.2 0.06885-50-31-01 1.274 21.83 1.71 0.286 532.8 0.161 0.287 531.7 0.162 0.800 127.9 18.1 0.13487-30-60-01 1.269 21.97 1.71 0.447 967.2 0.152 0.451 962.2 0.153 0.800 115.5 4.7 0.07490-30-50-01 1.265 22.11 1.71 0.445 998.4 0.137 0.449 993.1 0.138 0.800 126.0 5.9 0.07190-30-50-02 1.265 22.11 1.71 0.449 984.7 0.140 0.452 979.4 0.141 0.800 125.7 5.9 0.07294-30-45-01 1.258 22.33 1.71 0.462 970.2 0.127 0.466 964.7 0.128 0.800 125.9 6.7 0.07398-30-35-01 1.251 22.56 1.71 0.449 1049.9 0.092 0.452 1044.1 0.093 0.800 125.3 7.8 0.06898-30-40-01 1.251 22.56 1.71 0.450 1046.6 0.104 0.453 1040.8 0.105 0.800 126.3 7.1 0.06885-50-64-01 1.274 21.83 1.71 0.269 563.4 0.256 0.270 562.4 0.257 0.800 107.0 7.1 0.12687-30-52-01 1.269 21.97 1.71 0.450 957.3 0.148 0.454 952.2 0.148 0.800 127.9 6.1 0.07487-30-49-01 1.269 21.97 1.71 0.460 930.6 0.143 0.464 925.4 0.143 0.800 126.7 6.6 0.07690-30-35-01 1.265 22.11 1.71 0.446 994.9 0.100 0.449 989.7 0.101 0.800 126.1 8.1 0.07290-30-40-01 1.265 22.11 1.71 0.447 989.9 0.116 0.451 984.6 0.116 0.800 126.4 7.1 0.07290-30-44-01 1.265 22.11 1.71 0.445 997.6 0.123 0.449 992.4 0.124 0.800 126.6 6.6 0.07185-50-37-01 1.274 21.83 1.71 0.282 538.2 0.189 0.283 537.1 0.190 0.800 127.5 15.0 0.13285-50-50-01 1.274 21.83 1.71 0.274 551.6 0.250 0.275 550.5 0.250 0.800 125.4 10.5 0.129
Incompressible Calculations Compressible Calculations
194
Table F.5: FFT results for bipropellant portion of each test including maximum range of pressure oscillations.
Test Number Frequency Peak-to-Peak Frequency Peak-to-Peak Frequency Peak-to-Peak Frequency Peak-to-Peak Frequency Peak-to-Peak Standard Dev. ζ(xx-xx-xx-xx) (Hz) (psid) (Hz) (psid) (Hz) (psid) (Hz) (psid) (Hz) (psid) (psid) (%)90-30-17-01 2.0 200.9 2.0 24.2 2.0 22.7 21.5 14.4 2.0 13.5 2.2 1.1%90-30-18-01 2.0 0.8 2.0 26.8 31.3 17.1 31.3 13.2 31.3 12.2 2.7 1.3%90-30-22-01 29.3 3016.1 29.3 118.0 29.3 140.7 29.3 121.1 29.3 117.9 38.7 16.2%85-30-17-01 2.0 17.3 25.4 113.8 25.4 154.5 25.4 137.0 25.4 134.5 41.6 21.3%85-30-21-01 2.0 20.4 29.3 164.2 29.3 186.2 29.3 175.7 29.3 165.2 46.7 21.7%85-30-25-01 2.0 28.2 31.3 184.3 31.3 165.4 31.3 165.4 31.3 146.1 42.4 20.3%85-30-50-01 33.2 1321.5 33.2 455.3 33.2 297.8 33.2 331.5 33.2 356.3 79.4 30.4%85-30-64-01 34.2 1734.8 34.2 492.8 34.2 307.5 34.2 330.0 34.2 438.0 77.2 29.6%85-30-64-03 39.1 1892.4 39.1 437.6 39.1 280.1 39.1 255.2 39.1 303.2 56.9 24.4%87-30-44-01 37.1 1887.0 37.1 438.8 37.1 247.8 37.1 243.3 37.1 193.7 59.2 28.1%90-30-40-02 123.1 38.3 1.0 6.8 1.0 4.5 350.6 5.3 350.6 9.8 1.9 1.0%90-30-35-02 147.5 54.8 1.0 10.5 1.0 3.0 1.0 3.8 406.3 7.5 1.2 0.8%94-30-35-01 82.0 82.5 1.0 15.0 1.0 4.5 82.0 6.8 348.6 7.5 1.5 0.9%94-30-40-01 146.5 67.5 1.0 14.3 1.0 7.5 1.0 8.3 1.0 9.8 1.7 0.8%98-30-30-01 93.8 64.5 1.0 11.3 1.0 5.3 1.0 8.3 1.0 7.5 1.1 0.6%85-50-31-01 27.3 2139.7 27.3 768.0 27.3 313.1 27.3 324.3 27.3 292.5 92.4 30.5%87-30-60-01 365.2 239.0 230.5 18.0 230.5 71.5 230.5 22.0 230.5 25.5 6.1 1.3%90-30-50-01 294.4 453.8 0.5 29.3 221.2 48.8 221.2 61.5 221.2 94.5 14.1 3.1%90-30-50-02 1.0 27.8 1.0 105.0 1.0 18.8 1.0 22.5 1.0 26.3 3.8 0.8%94-30-45-01 245.2 97.5 1.0 9.8 1.0 11.3 1.0 21.8 245.1 26.3 0.2 0.1%98-30-35-01 160.2 78.8 1.9 9.8 1.0 10.5 1.0 13.5 489.3 25.5 5.1 1.5%98-30-40-01 211.9 81.8 1.0 12.8 1.0 12.8 2.9 18.0 398.4 57.8 5.6 1.5%85-50-64-01 308.6 270.8 2.0 44.3 2.0 77.3 2.0 51.0 2.0 62.3 9.5 1.2%87-30-52-01 35.2 1023.7 35.2 260.5 35.2 250.4 35.2 242.4 35.2 286.8 78.3 23.6%87-30-49-01 35.2 949.7 35.2 352.0 35.2 299.4 35.2 297.4 35.2 271.9 75.7 24.7%90-30-35-01 233.4 108.8 30.3 7.5 31.3 6.0 31.3 3.0 31.3 4.5 0.7 0.3%90-30-40-01 30.8 936.0 30.8 273.0 30.8 310.5 30.8 633.0 30.8 311.3 89.6 32.9%90-30-44-01 335.9 165.4 1.0 37.4 257.8 59.2 257.8 62.1 36.1 37.8 5.9 1.5%85-50-37-01 43.0 612.5 43.0 290.3 43.0 262.2 43.0 250.6 43.0 246.1 74.6 14.1%85-50-50-01 31.3 369.8 31.3 209.3 31.3 225.8 31.3 181.5 31.3 214.5 29.3 3.9%
p_c2p_c1p_fu_inj p_cb_outp_cb_in
195
Table F.6: FFT result for monopropellant section of each test including maximum range of pressure oscillations.
Test Number Frequency Peak-to-Peak Frequency Peak-to-Peak Frequency Peak-to-Peak Frequency Peak-to-Peak Frequency Peak-to-Peak Standard Dev. ζ(xx-xx-xx-xx) (Hz) (psid) (Hz) (psid) (Hz) (psid) (Hz) (psid) (Hz) (psid) (psid) (%)90-30-17-01 3.9 0.9 3.9 1.7 3.9 2.1 3.9 1.7 3.9 1.8 0.4 0.6%90-30-18-01 2.0 9.5 25.4 5.0 23.4 7.8 25.4 6.5 23.4 7.3 1.7 2.0%90-30-22-01 2.0 1.1 27.3 28.2 27.3 50.4 27.3 41.6 27.3 43.0 6.4 6.1%85-30-17-01 3.9 0.9 27.3 9.8 27.3 17.1 27.3 13.1 27.3 14.7 2.3 3.2%85-30-21-01 3.9 3.6 31.3 37.8 31.3 82.7 31.3 65.4 31.3 63.6 19.1 24.9%85-30-25-01 3.9 5.5 31.3 37.4 31.3 81.8 31.3 62.0 31.3 60.5 18.4 22.7%85-30-50-01 3.9 192.0 3.9 14.3 3.9 20.3 3.9 18.0 3.9 21.0 3.7 1.7%85-30-64-01 332.0 210.8 2.0 6.8 2.0 6.8 2.0 7.5 2.0 9.8 2.0 0.9%85-30-64-03 43.0 1694.9 43.0 67.5 43.0 152.3 43.0 109.6 43.0 133.2 41.8 22.9%87-30-44-01 39.1 1581.2 39.1 117.0 39.1 187.4 39.1 131.4 39.1 126.7 37.1 22.2%90-30-40-02 85.9 63.8 2.0 5.3 2.0 6.0 85.9 6.8 85.9 9.0 1.8 1.0%90-30-35-02 148.4 46.5 2.0 3.0 2.0 4.5 2.0 3.8 2.0 6.0 1.1 0.7%94-30-35-01 2.0 81.8 2.0 10.5 2.0 10.5 2.0 11.3 2.0 13.5 2.5 1.7%94-30-40-01 148.4 75.8 2.0 6.8 2.0 6.0 2.0 6.0 2.0 8.3 1.5 0.9%98-30-30-01 3.9 63.8 3.9 7.5 3.9 7.5 3.9 8.3 3.9 9.0 1.8 1.3%85-50-31-01 37.1 2203.4 37.1 93.2 37.1 174.0 37.1 151.0 37.1 136.4 39.6 21.1%87-30-60-01 43.0 413.1 43.0 39.9 43.0 64.2 43.0 51.8 43.0 56.9 13.7 5.8%90-30-50-01 367.2 320.3 2.0 22.5 2.0 5.3 2.0 5.3 2.0 5.3 1.2 0.5%90-30-50-02 191.4 24.0 2.0 3.0 2.0 3.8 2.0 5.3 418.0 7.5 1.4 0.6%94-30-45-01 255.9 92.3 2.0 6.0 2.0 7.5 2.0 8.3 2.0 8.3 0.3 0.1%98-30-35-01 3.9 86.3 3.9 6.8 3.9 7.5 3.9 7.5 3.9 8.3 1.5 0.9%98-30-40-01 2.0 82.5 2.0 9.8 2.0 9.8 2.0 9.8 2.0 11.3 2.0 1.1%85-50-64-01 345.7 248.3 2.0 14.3 2.0 13.5 2.0 13.5 2.0 15.8 3.9 1.0%87-30-52-01 39.1 659.6 39.1 74.9 39.1 134.4 39.1 105.9 39.1 116.6 31.9 14.4%87-30-49-01 37.1 900.6 37.1 85.4 37.1 164.8 37.1 138.2 37.1 131.7 39.6 20.5%90-30-35-01 238.3 87.8 2.0 17.3 2.0 4.5 2.0 5.3 2.0 6.0 1.1 0.7%90-30-40-01 343.8 226.5 2.0 8.3 2.0 10.5 2.0 10.5 2.0 10.5 2.4 1.3%90-30-44-01 37.1 115.3 37.1 7.4 37.1 11.1 37.1 10.2 37.1 12.0 2.7 1.3%85-50-37-01 46.9 2881.4 46.9 90.8 46.9 184.1 46.9 160.2 46.9 138.9 42.2 18.2%85-50-50-01 37.1 498.0 37.1 77.3 37.1 102.0 37.1 96.0 37.1 100.5 18.7 5.5%
p_cb_in p_fu_inj p_cb_out p_c1 p_c2
196
Table F.7: Calculated uncertainty in densities and mass flow rates.
Test Number uT_ox uW urho_ox drho_ox uT_f urho_f drho_f uCD_ox_cv udt_ox_cv up_ox_cv umdot_ox dmdot_ox uCD_f_cv udt_f_cv up_fu_cv umdot_f dmdot_f(xx-xx-xx-xx) (--) (--) (%) (lbm/ft^3) (--) (%) (lbm/ft^3) (--) (--) (--) (%) (lbm/s) (--) (--) (--) (%) (lbm/s)90-30-17-01 2.51E-02 1.10E-03 0.1% 0.081 -- 0.0% -- 8.34E-03 0.00E+00 7.81E-03 0.9% 0.007 8.29E-03 0.00E+00 4.46E-03 0.9% 0.00490-30-18-01 2.73E-02 1.12E-03 0.1% 0.080 -- 0.0% -- 8.34E-03 0.00E+00 6.46E-03 0.9% 0.008 8.29E-03 0.00E+00 4.42E-03 0.9% 0.00490-30-22-01 2.77E-02 1.12E-03 0.1% 0.080 -- 0.0% -- 8.34E-03 0.00E+00 4.66E-03 0.9% 0.009 8.29E-03 0.00E+00 4.40E-03 0.9% 0.00485-30-17-01 2.71E-02 1.18E-03 0.1% 0.079 -- 0.0% -- 8.34E-03 0.00E+00 7.31E-03 0.9% 0.007 8.29E-03 0.00E+00 4.43E-03 0.9% 0.00485-30-21-01 2.78E-02 1.18E-03 0.1% 0.078 -- 0.0% -- 8.34E-03 0.00E+00 4.90E-03 0.9% 0.008 8.29E-03 0.00E+00 4.45E-03 0.9% 0.00485-30-25-01 2.73E-02 1.18E-03 0.1% 0.079 -- 0.0% -- 8.34E-03 0.00E+00 4.57E-03 0.9% 0.009 8.29E-03 0.00E+00 6.14E-03 0.9% 0.00485-30-50-01 2.42E-02 1.17E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 5.46E-03 0.8% 0.017 8.29E-03 0.00E+00 4.54E-03 0.9% 0.00485-30-64-01 2.51E-02 1.17E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 5.19E-03 0.8% 0.017 8.29E-03 0.00E+00 6.24E-03 0.9% 0.00385-30-64-03 2.71E-02 1.17E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 4.81E-03 0.7% 0.017 8.29E-03 0.00E+00 5.99E-03 0.9% 0.00387-30-44-01 2.77E-02 1.14E-03 0.1% 0.080 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 6.99E-03 0.8% 0.015 8.29E-03 0.00E+00 4.42E-03 0.9% 0.00490-30-40-02 2.58E-02 1.12E-03 0.1% 0.080 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 4.59E-03 0.7% 0.013 8.29E-03 0.00E+00 4.50E-03 0.9% 0.00490-30-35-02 2.54E-02 1.10E-03 0.1% 0.081 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 5.69E-03 0.8% 0.012 8.29E-03 0.00E+00 4.51E-03 0.9% 0.00494-30-35-01 2.94E-02 1.06E-03 0.1% 0.082 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 5.96E-03 0.8% 0.012 8.29E-03 0.00E+00 4.54E-03 0.9% 0.00494-30-40-01 2.47E-02 1.06E-03 0.1% 0.082 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 4.50E-03 0.7% 0.013 8.29E-03 0.00E+00 4.50E-03 0.9% 0.00498-30-30-01 3.52E-02 1.02E-03 0.1% 0.083 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 7.99E-03 0.8% 0.011 8.29E-03 0.00E+00 4.50E-03 0.9% 0.00485-50-31-01 2.77E-02 1.17E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 7.26E-03 0.8% 0.011 8.29E-03 0.00E+00 4.37E-03 0.9% 0.00487-30-60-01 2.75E-02 1.15E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 4.80E-03 0.7% 0.018 8.29E-03 0.00E+00 5.36E-03 0.9% 0.00490-30-50-01 2.66E-02 1.11E-03 0.1% 0.080 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 5.59E-03 0.8% 0.017 8.29E-03 0.00E+00 4.50E-03 0.9% 0.00490-30-50-02 2.95E-02 1.10E-03 0.1% 0.080 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 5.59E-03 0.8% 0.017 8.29E-03 0.00E+00 4.53E-03 0.9% 0.00494-30-45-01 2.44E-02 1.07E-03 0.1% 0.082 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 7.02E-03 0.8% 0.016 8.29E-03 0.00E+00 4.51E-03 0.9% 0.00498-30-35-01 2.62E-02 1.02E-03 0.1% 0.083 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 6.05E-03 0.8% 0.012 8.29E-03 0.00E+00 4.55E-03 0.9% 0.00498-30-40-01 2.48E-02 1.02E-03 0.1% 0.083 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 4.73E-03 0.7% 0.013 8.29E-03 0.00E+00 4.48E-03 0.9% 0.00485-50-64-01 2.51E-02 1.16E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 4.96E-03 0.8% 0.017 8.29E-03 0.00E+00 6.24E-03 0.9% 0.00387-30-52-01 2.75E-02 1.14E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 5.26E-03 0.8% 0.017 8.29E-03 0.00E+00 4.37E-03 0.9% 0.00487-30-49-01 2.69E-02 1.14E-03 0.1% 0.080 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 5.93E-03 0.8% 0.016 8.29E-03 0.00E+00 4.45E-03 0.9% 0.00490-30-35-01 2.67E-02 1.12E-03 0.1% 0.080 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 1.06E-02 0.9% 0.014 8.29E-03 0.00E+00 4.49E-03 0.9% 0.00490-30-40-01 3.13E-02 1.11E-03 0.1% 0.080 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 8.04E-03 0.8% 0.015 8.29E-03 0.00E+00 4.47E-03 0.9% 0.00490-30-44-01 2.92E-02 1.11E-03 0.1% 0.080 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 7.00E-03 0.8% 0.015 8.29E-03 0.00E+00 4.46E-03 0.9% 0.00485-50-37-01 2.590E-02 1.179E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.04E-03 0.00E+00 5.20E-03 0.8% 0.012 8.29E-03 0.00E+00 4.40E-03 0.9% 0.00485-50-50-01 2.514E-02 1.163E-03 0.1% 0.079 6.90E-02 0.3% 0.139 7.08E-03 0.00E+00 5.62E-03 0.8% 0.016 8.29E-03 0.00E+00 4.55E-03 0.9% 0.004
197
Table F.8: Calculated uncertainty in equivalence ratio and bipropellant performance parameters.
Test Number uφ dφ umdot_tot up_c2_tot uD_th uC* dC* dC*_th uC*_th uη_C* dη_C*(xx-xx-xx-xx) (%) (--) (--) (--) (--) (%) (ft/s) (ft/s) (--) (%) (%)90-30-17-01 1.3% 0.033 6.601E-03 7.393E-02 3.383E-03 7.5% 337.1 20.0 4.314E-03 7.47% 7.28%90-30-18-01 1.2% 0.030 6.532E-03 6.972E-02 3.383E-03 7.0% 325.2 20.0 4.252E-03 7.05% 6.93%90-30-22-01 1.2% 0.025 6.511E-03 6.266E-02 3.383E-03 6.3% 292.1 20.0 4.151E-03 6.35% 6.08%85-30-17-01 1.3% 0.034 6.561E-03 7.696E-02 3.383E-03 7.8% 339.9 20.0 4.490E-03 7.77% 7.64%85-30-21-01 1.2% 0.027 6.505E-03 6.979E-02 3.383E-03 7.0% 299.0 20.0 4.263E-03 7.05% 6.38%85-30-25-01 1.2% 0.022 6.692E-03 7.196E-02 3.383E-03 7.3% 306.5 20.0 4.127E-03 7.27% 6.33%85-30-50-01 1.2% 0.019 6.507E-03 5.744E-02 3.383E-03 5.8% 164.4 20.0 4.014E-03 5.83% 3.31%85-30-64-01 1.2% 0.016 6.610E-03 5.741E-02 3.383E-03 5.8% 164.8 20.0 3.920E-03 5.83% 3.24%85-30-64-03 1.2% 0.016 6.569E-03 6.426E-02 3.383E-03 6.5% 158.6 20.0 3.909E-03 6.51% 3.10%87-30-44-01 1.2% 0.022 6.649E-03 7.127E-02 3.383E-03 7.2% 179.9 20.0 3.998E-03 7.20% 3.60%90-30-40-02 1.1% 0.023 6.187E-03 8.059E-02 3.383E-03 8.1% 197.3 20.0 3.997E-03 8.12% 3.95%90-30-35-02 1.2% 0.026 6.249E-03 9.520E-02 3.383E-03 9.6% 214.1 20.0 4.083E-03 9.57% 4.38%94-30-35-01 1.2% 0.025 6.279E-03 9.026E-02 3.383E-03 9.1% 216.7 20.0 3.961E-03 9.08% 4.30%94-30-40-01 1.1% 0.022 6.190E-03 7.321E-02 3.383E-03 7.4% 194.6 20.0 3.870E-03 7.39% 3.77%98-30-30-01 1.2% 0.028 6.488E-03 9.035E-02 3.383E-03 9.1% 240.4 20.0 3.978E-03 9.09% 4.79%85-50-31-01 1.2% 0.032 6.366E-03 4.950E-02 4.367E-03 5.1% 142.0 20.0 4.442E-03 5.09% 3.17%87-30-60-01 1.2% 0.016 6.529E-03 3.171E-02 3.383E-03 3.3% 161.6 20.0 3.864E-03 3.33% 3.14%90-30-50-01 1.2% 0.018 6.522E-03 3.335E-02 3.383E-03 3.5% 168.6 20.0 3.877E-03 3.49% 3.29%90-30-50-02 1.2% 0.018 6.526E-03 3.265E-02 3.383E-03 3.4% 168.6 20.0 3.859E-03 3.42% 3.27%94-30-45-01 1.2% 0.020 6.670E-03 3.745E-02 3.383E-03 3.9% 183.2 20.0 3.819E-03 3.88% 3.52%98-30-35-01 1.2% 0.024 6.293E-03 4.407E-02 3.383E-03 4.5% 220.5 20.0 3.852E-03 4.52% 4.26%98-30-40-01 1.1% 0.021 6.203E-03 3.935E-02 3.383E-03 4.0% 200.9 20.0 3.786E-03 4.06% 3.82%85-50-64-01 1.2% 0.016 6.594E-03 1.913E-02 4.367E-03 2.2% 108.5 20.0 3.914E-03 2.24% 2.16%87-30-52-01 1.2% 0.019 6.482E-03 4.513E-02 3.383E-03 4.6% 161.9 20.0 3.922E-03 4.63% 3.19%87-30-49-01 1.2% 0.020 6.543E-03 4.894E-02 3.383E-03 5.0% 169.9 20.0 3.948E-03 5.00% 3.36%90-30-35-01 1.2% 0.027 7.190E-03 7.720E-02 3.383E-03 7.8% 211.9 20.0 4.083E-03 7.79% 4.33%90-30-40-01 1.2% 0.023 6.792E-03 5.507E-02 3.383E-03 5.6% 190.8 20.0 3.979E-03 5.60% 3.81%90-30-44-01 1.2% 0.021 6.659E-03 3.737E-02 3.383E-03 3.9% 183.5 20.0 3.927E-03 3.88% 3.62%85-50-37-01 1.1% 0.027 6.199E-03 2.832E-02 4.367E-03 3.0% 130.6 20.0 4.229E-03 3.06% 2.79%85-50-50-01 1.2% 0.020 6.522E-03 2.022E-02 4.367E-03 2.3% 110.1 20.0 4.014E-03 2.33% 2.24%
198
Table F.9: Calculated uncertainty in monopropellant performance parameters.
Test Number up_cb_in up_cb_out u∆p_cb d∆p_cb up_c2_tot uC* dC* dC*_th uC*_th uη_C* dη_C* uTtox_th uTtox dTtox(xx-xx-xx-xx) (--) (--) (%) (psid) (--) (%) (ft/s) (ft/s) (--) (%) (%) (--) (%) (°F)90-30-17-01 -- 1.784E-01 -- -- 20.34% 20.4% 537.5 5.0 1.622E-03 20.4% 17.4% 7.179E-03 40.7% 415.890-30-18-01 -- 1.526E-01 -- -- 16.64% 16.7% 506.6 5.0 1.622E-03 16.7% 16.4% 7.179E-03 33.4% 451.090-30-22-01 -- 1.265E-01 -- -- 13.85% 13.9% 415.4 5.0 1.622E-03 13.9% 13.5% 7.179E-03 27.8% 364.285-30-17-01 -- 1.816E-01 -- -- 19.80% 19.8% 524.9 5.0 1.722E-03 19.8% 18.1% 8.525E-03 39.7% 386.685-30-21-01 -- 1.601E-01 -- -- 19.14% 19.2% 429.6 5.0 1.722E-03 19.2% 14.8% 8.525E-03 38.4% 267.885-30-25-01 -- 1.540E-01 -- -- 18.04% 18.1% 415.0 5.0 1.722E-03 18.1% 14.3% 8.525E-03 36.2% 265.185-30-50-01 1.661E-02 6.134E-02 3.22% 10.6 6.85% 6.9% 191.6 5.0 1.722E-03 6.9% 6.6% 8.525E-03 13.9% 147.985-30-64-01 1.454E-02 5.814E-02 2.74% 10.6 6.41% 6.5% 183.6 5.0 1.722E-03 6.5% 6.3% 8.525E-03 13.0% 144.885-30-64-03 1.476E-02 7.052E-02 2.64% 10.6 8.01% 8.1% 178.9 5.0 1.722E-03 8.1% 6.2% 8.525E-03 16.2% 110.587-30-44-01 1.625E-02 7.742E-02 2.91% 10.6 8.73% 8.8% 214.7 5.0 1.669E-03 8.8% 7.2% 7.794E-03 17.6% 150.290-30-40-02 1.445E-02 9.222E-02 2.42% 10.6 8.37% 8.4% 241.0 5.0 1.622E-03 8.4% 7.8% 7.179E-03 16.9% 202.190-30-35-02 1.620E-02 1.077E-01 2.70% 10.6 9.87% 9.9% 267.2 5.0 1.622E-03 9.9% 8.7% 7.179E-03 19.9% 211.194-30-35-01 1.443E-02 1.091E-01 2.35% 10.6 10.20% 10.2% 270.3 5.0 1.554E-03 10.2% 8.4% 6.369E-03 20.5% 216.594-30-40-01 1.217E-02 8.900E-02 1.99% 10.6 8.09% 8.2% 239.4 5.0 1.554E-03 8.2% 7.4% 6.369E-03 16.3% 213.598-30-30-01 1.203E-02 1.130E-01 1.90% 10.6 10.06% 10.1% 310.7 5.0 1.496E-03 10.1% 9.3% 5.727E-03 20.2% 298.285-50-31-01 2.297E-02 7.299E-02 4.74% 10.6 7.91% 8.0% 183.9 5.0 1.722E-03 8.0% 6.3% 8.525E-03 16.0% 117.887-30-60-01 1.224E-02 5.675E-02 2.21% 10.6 6.18% 6.3% 179.2 5.0 1.669E-03 6.3% 6.0% 7.794E-03 12.6% 146.990-30-50-01 1.624E-02 5.879E-02 3.17% 10.6 6.37% 6.4% 192.6 5.0 1.622E-03 6.4% 6.2% 7.179E-03 12.9% 169.090-30-50-02 1.206E-02 7.206E-02 2.05% 10.6 6.52% 6.6% 191.4 5.0 1.622E-03 6.6% 6.2% 7.179E-03 13.2% 163.194-30-45-01 8.644E-03 8.752E-02 1.36% 10.6 7.79% 7.9% 213.2 5.0 1.554E-03 7.9% 6.6% 6.369E-03 15.7% 175.698-30-35-01 1.085E-02 9.575E-02 1.73% 10.6 8.64% 8.7% 271.7 5.0 1.496E-03 8.7% 8.1% 5.727E-03 17.4% 265.298-30-40-01 1.039E-02 8.727E-02 1.67% 10.6 7.69% 7.8% 240.8 5.0 1.496E-03 7.8% 7.2% 5.727E-03 15.5% 233.785-50-64-01 1.365E-02 3.827E-02 3.00% 10.6 3.94% 4.1% 112.9 5.0 1.722E-03 4.1% 3.9% 8.525E-03 8.3% 86.887-30-52-01 1.318E-02 6.033E-02 2.38% 10.6 6.61% 6.7% 186.7 5.0 1.669E-03 6.7% 6.2% 7.794E-03 13.4% 149.387-30-49-01 1.394E-02 6.723E-02 2.49% 10.6 7.57% 7.6% 198.1 5.0 1.669E-03 7.6% 6.6% 7.794E-03 15.3% 147.290-30-35-01 2.304E-02 8.124E-02 4.55% 10.6 8.81% 8.9% 263.4 5.0 1.622E-03 8.9% 8.5% 7.179E-03 17.8% 229.290-30-40-01 2.002E-02 7.232E-02 3.91% 10.6 7.76% 7.8% 229.8 5.0 1.622E-03 7.8% 7.5% 7.179E-03 15.7% 197.990-30-44-01 1.373E-02 6.648E-02 2.45% 10.6 7.11% 7.2% 214.4 5.0 1.622E-03 7.2% 7.0% 7.179E-03 14.4% 187.785-50-37-01 1.820E-02 5.892E-02 3.73% 10.6 6.42% 6.5% 156.1 5.0 1.722E-03 6.5% 5.4% 8.525E-03 13.1% 104.285-50-50-01 1.505E-02 4.181E-02 3.32% 10.6 4.38% 4.5% 117.4 5.0 1.722E-03 4.5% 4.0% 8.525E-03 9.1% 85.2
199
Table F.10: Calculated uncertainties in fuel and oxidizer flow parameter as well as momentum ratio and residence time.
Test Number uCD ud_o uV_f dV_f urho_ox_g drho_ox_g uD_ox uV_ox dV_ox uM_ox dM_ox uQ dQ utau_sl dtau_sl uCR dCR(xx-xx-xx-xx) (--) (--) (%) (--) (%) (lbm/ft^3) (--) (%) (ft/s) (%) (--) (%) (--) (%) (sec) (%) (--)90-30-17-01 6.25E-02 0.0 6.31% 7.47 45.5% 0.023 2.929E-03 45.6% 431.1 28.8% 0.133 102.6% 18.13 45.6% 0.034 0.8% 0.02390-30-18-01 6.25E-02 0.0 6.31% 7.50 37.3% 0.019 2.929E-03 37.3% 375.4 23.6% 0.105 84.4% 13.33 37.3% 0.026 0.8% 0.02390-30-22-01 6.25E-02 0.0 6.31% 7.52 31.0% 0.020 2.929E-03 31.1% 310.3 19.6% 0.087 70.6% 9.24 31.1% 0.022 0.8% 0.02385-30-17-01 6.25E-02 0.0 6.31% 7.49 44.3% 0.024 2.929E-03 44.4% 410.6 28.1% 0.127 100.0% 17.74 44.4% 0.034 0.8% 0.02385-30-21-01 6.25E-02 0.0 6.31% 7.48 42.9% 0.030 2.929E-03 42.9% 378.7 27.1% 0.131 96.7% 14.67 42.9% 0.035 0.8% 0.02385-30-25-01 6.25E-02 0.0 6.31% 6.37 40.4% 0.029 2.929E-03 40.4% 358.9 25.6% 0.122 91.3% 9.64 40.4% 0.032 0.8% 0.02385-30-50-01 6.25E-02 0.0 6.32% 7.92 15.5% 0.023 2.929E-03 15.5% 146.0 9.8% 0.044 36.9% 2.27 15.5% 0.012 0.8% 0.02385-30-64-01 6.25E-02 0.0 6.32% 6.76 14.5% 0.022 2.929E-03 14.5% 138.1 9.2% 0.041 34.9% 1.48 14.6% 0.011 0.8% 0.02385-30-64-03 6.25E-02 0.0 6.32% 6.90 18.0% 0.030 2.929E-03 18.1% 159.2 11.4% 0.055 42.3% 1.98 18.1% 0.015 0.8% 0.02387-30-44-01 6.25E-02 0.0 6.32% 8.03 19.6% 0.026 2.929E-03 19.7% 179.4 12.4% 0.058 45.7% 3.36 19.7% 0.015 0.8% 0.02390-30-40-02 6.25E-02 0.0 6.32% 7.96 18.8% 0.021 2.929E-03 18.9% 184.5 11.9% 0.054 44.0% 3.32 18.9% 0.014 0.8% 0.02390-30-35-02 6.25E-02 0.0 6.32% 7.95 22.2% 0.023 2.929E-03 22.2% 211.7 14.0% 0.064 51.2% 4.39 22.2% 0.017 0.8% 0.02394-30-35-01 6.25E-02 0.0 6.32% 7.93 22.9% 0.023 2.929E-03 22.9% 219.9 14.5% 0.067 52.8% 4.53 22.9% 0.017 0.8% 0.02394-30-40-01 6.25E-02 0.0 6.32% 7.96 18.2% 0.020 2.929E-03 18.2% 183.4 11.5% 0.052 42.7% 3.12 18.3% 0.013 0.8% 0.02398-30-30-01 6.25E-02 0.0 6.32% 7.96 22.6% 0.018 2.929E-03 22.6% 235.5 14.3% 0.064 52.2% 4.78 22.7% 0.015 0.8% 0.02385-50-31-01 6.25E-02 0.0 6.32% 8.08 17.9% 0.029 2.929E-03 17.9% 95.3 11.3% 0.032 41.9% 7.58 17.9% 0.024 1.0% 0.04887-30-60-01 6.25E-02 0.0 6.32% 7.30 14.0% 0.021 2.929E-03 14.0% 135.6 8.9% 0.040 33.8% 1.60 14.1% 0.010 0.8% 0.02390-30-50-01 6.25E-02 0.0 6.32% 7.96 14.4% 0.020 2.929E-03 14.4% 144.1 9.1% 0.041 34.6% 2.04 14.5% 0.010 0.8% 0.02390-30-50-02 6.25E-02 0.0 6.32% 7.94 14.7% 0.021 2.929E-03 14.8% 145.5 9.3% 0.042 35.4% 2.09 14.8% 0.011 0.8% 0.02394-30-45-01 6.25E-02 0.0 6.32% 7.95 17.6% 0.022 2.929E-03 17.6% 170.7 11.1% 0.051 41.3% 2.77 17.6% 0.013 0.8% 0.02398-30-35-01 6.25E-02 0.0 6.32% 7.92 19.4% 0.018 2.929E-03 19.5% 204.3 12.3% 0.055 45.3% 3.55 19.5% 0.013 0.8% 0.02398-30-40-01 6.25E-02 0.0 6.32% 7.98 17.3% 0.018 2.929E-03 17.4% 181.6 11.0% 0.049 40.8% 2.89 17.4% 0.012 0.8% 0.02385-50-64-01 6.25E-02 0.0 6.32% 6.76 9.2% 0.023 2.929E-03 9.2% 51.8 5.8% 0.016 24.1% 1.72 9.3% 0.012 1.0% 0.04887-30-52-01 6.25E-02 0.0 6.32% 8.08 14.9% 0.022 2.929E-03 15.0% 143.3 9.5% 0.043 35.8% 2.19 15.0% 0.011 0.8% 0.02387-30-49-01 6.25E-02 0.0 6.32% 8.00 17.1% 0.024 2.929E-03 17.1% 159.1 10.8% 0.050 40.2% 2.65 17.1% 0.013 0.8% 0.02390-30-35-01 6.25E-02 0.0 6.32% 7.96 19.8% 0.020 2.929E-03 19.9% 197.7 12.6% 0.056 46.2% 3.75 19.9% 0.014 0.8% 0.02390-30-40-01 6.25E-02 0.0 6.32% 7.98 17.5% 0.020 2.929E-03 17.5% 173.5 11.1% 0.050 41.2% 2.94 17.6% 0.013 0.8% 0.02390-30-44-01 6.25E-02 0.0 6.32% 8.00 16.1% 0.020 2.929E-03 16.1% 160.5 10.2% 0.045 38.1% 2.52 16.1% 0.012 0.8% 0.02385-50-37-01 6.25E-02 0.0 6.32% 8.05 14.6% 0.028 2.929E-03 14.6% 78.6 9.2% 0.026 35.0% 5.26 14.6% 0.019 1.0% 0.04885-50-50-01 6.25E-02 0.0 6.32% 7.92 10.1% 0.025 2.929E-03 10.1% 55.9 6.4% 0.017 25.9% 2.72 10.2% 0.013 1.0% 0.048
Fuel Orifice Using Incompressible Flow Equations