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THE PENNSYLVANIA STATE UNIVERSITY
SCHREYER HONORS COLLEGE
DEPARTMENT OF AEROSPACE ENGINEERING
COMBUSTION OF SOLID FUELS IN A DIFFUSION FLAME ENVIRONMENT
CHRISTOPHER MICHAEL BURGER
SPRING 2017
A thesis
submitted in partial fulfillment
of the requirements
for baccalaureate degrees
in Aerospace Engineering and Physics
with honors in Aerospace Engineering
Reviewed and approved* by the following:
Richard Yetter
Professor of Mechanical Engineering
Thesis Supervisor
Phillip Morris
Professor of Aerospace Engineering
Honors Adviser
Michael Micci
Professor of Aerospace Engineering
Faculty Reader
* Signatures are on file in the Schreyer Honors College.
i
ABSTRACT
Fundamental combustion studies were performed in a pressurized counterflow burner
using Hydroxyl-Terminated Polybutadiene (HTPB) and gaseous oxygen. The goal of the study
was to explore whether or not diffusion flame combustion in a counterflow configuration
correlated well to diffusion flame combustion in the cross-flow configuration of hybrid rockets.
The oxidizer flow rate was varied throughout the study with mass flux values ranging from 7 to
112 kg/(m2s), while the chamber pressure was held at a target pressure of 200 psig. It was found
at low values of oxidizer mass flux that the experimental regression rates of the HTPB correlated
well to the predicted diffusion flame power law, commonly used for hybrid rocket motors. At
higher oxidizer mass fluxes, however, the regression rate plateaued to a near-constant value that
was independent of oxidizer mass flow rate. This plateau has not been encountered in lab-scale
hybrid rocket motors tests; however, a similar effect has been observed slab burner experiments.
A computational model created using CHEMKIN and GNU Octave was used to simulate the
combustion process in a counterflow configuration. The purpose was to achieve a better
understanding of the diffusion flame structure and chemistry. As oxidizer mass flux increases,
the model indicates that the diffusion flame moves closer to the fuel surface. The model
predicted the experimentally observed trends, with burning rate increasing with oxidizer flow
rate and achieving a plateau at the highest flow conditions. Flame structure results from the
model support the hypothesis that the location of the diffusion flame becomes increasingly
invariant with increasing oxidizer mass flux.
ii
TABLE OF CONTENTS
LIST OF FIGURES .................................................................................................... iii
NOMENCLATURE .................................................................................................... iv
ACKNOWLEDGEMENTS ......................................................................................... v
Introduction ................................................................................................. 1
1.1 Hybrid Rockets........................................................................................................... 1 1.2 Counterflow Experiments .......................................................................................... 2 1.3 Research Objectives ................................................................................................... 3
Background and Motivation ........................................................................ 4
2.1 Combustion Process in a Hybrid Motor ..................................................................... 4 2.1 Combustion Process in a Counterflow Burner ........................................................... 7 2.2 Experimental Setup .................................................................................................... 9
Experimental Results and Discussion ......................................................... 13
Theoretical Method ..................................................................................... 16
4.1 Condensed Phase Model ............................................................................................ 17 4.2 Gas Phase Solver ........................................................................................................ 20 4.3 Solution Coupling ...................................................................................................... 22
Theoretical Results ...................................................................................... 24
Burning Rate .................................................................................................................... 24 Flame Structure ................................................................................................................ 26
Summary and Conclusion ........................................................................... 28
BIBLIOGRAPHY ........................................................................................................ 29
iii
LIST OF FIGURES
Figure 1: Classical hybrid combustion schematic [4]. ............................................................. 4
Figure 2: Example hybrid rocket burn-profile ......................................................................... 6
Figure 3: Diagram of Opposed-flow flame [6] ........................................................................ 7
Figure 4: Opposed flow burner flame zone ............................................................................. 8
Figure 5: LVDT data from a pellet burning ............................................................................. 10
Figure 6: Block Diagram of Pressurized Counterflow System [4] .......................................... 11
Figure 7: Regression Rate vs. Oxidizer Mass Flux for HTPB & gaseous O2 at 200 psig........ 13
Figure 8: Averaged Regression Rate vs. Oxidizer Mass Flux ................................................. 14
Figure 9: Counterflow data compared with lab-scale hybrid rocket motor data ...................... 15
Figure 10: Temperature distribution zone of a hybrid fuel grain [12] ..................................... 17
Figure 11: Control Volume used in Model [7] ........................................................................ 18
Figure 12: OppDiff Block diagram [16] .................................................................................. 21
Figure 13: Octave Computational Model Block Diagram [7] ................................................. 23
Figure 14: 200 psia computational data compared to 200 psig experimental results............... 24
Figure 15: 200 psia computational data compared to 250 psia computational data................. 25
Figure 16: Flame Structure of Diffusion Flames at 200psia .................................................... 26
Figure 17: Flame Structure Close to Fuel Surface at 200psia .................................................. 27
iv
NOMENCLATURE
a Fuel Specific Regression Rate Coefficient
Ap Port area
GOx Oxidizer Mass Flux
HTPB Hydroxyl-terminated Polybutadiene
Isp Specific Impulse
𝑟 Regression Rate
LVDT Linear Variable Displacement Transducer.
𝜌𝑓 Solid fuel density
∆𝐻 Effective heat of gasification of the solid fuel
�� 𝑎𝑣𝑔 Average flow velocity
O/F Oxidizer – Fuel Ratio
��𝑜𝑥 Oxidizer Mass Flow
��𝑁2 Nitrogen Mass Flow
𝜑 Equivalence ratio
v
ACKNOWLEDGEMENTS
I would like to thank my thesis supervisor Dr. Richard Yetter for his support and
guidance as I pursued undergraduate research work. Special thanks to Mr. Terry Connell for
guiding me through the operations of the counterflow burner, supporting me during every
counterflow test, and providing valuable knowledge on the subjects of hybrid rockets and
diffusion flames. I also thank Dr. Eric Boyer for his role as mentor and for helping me
understand the programming involved with Octave and CHEMKIN. I thank Dr. Andrew
Cortopassi for his initial role as a mentor and for providing knowledge on hybrid rocketry. In
addition, I thank Paige Nardozzo for teaching me to her method for computationally modeling
diffusion flames in a counterflow configuration.
1
Introduction
1.1 Hybrid Rockets
The most prevalent form of rocket propulsion today is chemical propulsion. Such systems
are generally divided into three categories: solid, liquid or bipropellant, and hybrid. Solid rockets
consist of a fuel and oxidizer mixed in a solid form. Liquid rockets consist of separately stored
fuel and oxidizer, both of which are typically stored in liquid phase. In the hybrid propulsive
system, fuel and oxidizer are stored both physically separated and in different phases. In the
classical hybrid system, an inert solid fuel is stored within the combustion chamber and a liquid
or gaseous oxidizer is pumped into the chamber at the time of ignition. Of these three propulsion
systems, hybrid rockets are the least established and much of their fundamental combustion
behaviors remain unknown [1].
Hybrid rockets provide potential advantages over solid and liquid systems. The physical
separation of reactants provides a measure of safety, while permitting throttling and shutoff
capabilities. This results in hybrid rockets having almost no explosion hazard [2]. Because one of
the reactants is stored within the combustion chamber, only one feed system is required.
Advantages that hybrids have over solid propellants is that solid propellants cannot be throttled
and generally have no shutoff capability. In addition, hybrid rockets require less plumbing than
their liquid counterparts do, as the fuel in a hybrid does not require plumbing [3].
2
Hybrid rocket systems are not without their disadvantages, however. A major factor in
their lack of utilization is due to low solid fuel regression rates. The regression rate of
fuel/binders in hybrid rockets such as hydroxyl-terminate polybutadiene (HTPB) is often an
order of magnitude lower than that of solid composite propellants. This results in a larger
burning surface area requirement for the hybrid propulsive systems to produce a similar level of
thrust as in solids [2]. Recent fundamental research on hybrid rocket combustion often involves
fuel additives that may increase the energy density and burning rate of the solid fuel. These
regression rate measurements are typically obtained by conducting motor firings, using the pre
and post-fired grain port dimensions to determine average values.
1.2 Counterflow Experiments
In a counterflow combustion system, fuel and oxidizer are diametrically opposed. The
fuel and oxidizer flows meet to form a stagnation plane near where the species react. This
counterflow configuration is often used in fundamental combustion research as it produces a flat
and stable diffusion flame that may be directly observed and analyzed as a one-dimension system
along the stagnation streamline.
The counterflow experiments can be used to directly measure the solid fuel regression
rate, and thus, provides a means to evaluate the performance of various fuels, oxidizers, and
additives. Hybrid rocket motors burn via diffusion-controlled combustion, and the counterflow
configuration can be thought of as a one-dimensional diffusion flame. A notable difference
between the counterflow burner and hybrid rocket systems is that in the counterflow systems, the
flows are diametrically opposed while a crossflow condition exists in the motor.
3
1.3 Research Objectives
Burning rate measurements of HTPB pellets in opposed-flow configurations have been
thoroughly investigated at low oxidizer mass flux conditions. The aim of the current study is to
explore regions of higher oxidizer mass flux both experimentally and computationally. Increased
understanding of combustion in the counterflow configuration may allow small-scale
counterflow experiments to predict a fuel’s regression rate in a larger scale hybrid rocket. The
specific goals of this project included:
Burning HTPB pellets in a pressurized counterflow burner with O2 at high
oxidizer mass flux conditions in the regime of laboratory-scale hybrid rocket
motors. Compare these results to those of low oxidizer mass flux conditions of
previous counterflow experiments, and high oxidizer mass flux conditions of
previous rocket motor experiments.
Determine whether HTPB regression rates from a counterflow configuration
behave similarly to HTPB regression rates from a crossflow configuration.
Determine whether a diffusion flame computational model can be used to
accurately replicate and explain experimental results.
4
Background and Motivation
2.1 Combustion Process in a Hybrid Motor
In a hybrid system, oxidizer is injected through porting within the grain. Following
ignition, a diffusion flame forms within the boundary layer. The flame occurs in the region
where fuel and oxidizer diffuse together in stoichiometric proportions. This diffusion flame is a
result of the cross-flow of oxidizer interacting with decomposition products from the solid fuel
surface. A diagram of the combustion process is provided in Figure 1. Heat feedback from the
flame results in fuel pyrolysis. The pyrolysis produces a sustained flow of decomposition
products from the fuel surface up towards the oxidizer flow.
Figure 1: Classical hybrid combustion schematic [4].
As the grain regresses, the port area Ap increases with time. In solid rocket motors where
the fuel and oxidizer are thoroughly mixed or in liquid systems where the fuel and oxidizer flow
5
rate can be precisely controlled, the global equivalence ratio 𝜑 remains constant. This is not the
case for the hybrid rocket system. In hybrid motors, as the web regresses, the value of Ap
increases and the regression rate decrease. For a fixed oxidizer mass flow rate, 𝜑 varies
throughout the burn duration. This effect can be counteracted by proportionally varying the
oxidizer mass flow rate ��𝑜𝑥 with time to respond to the increased port area, but this complicates
the system.
For a fixed value of ��𝑜𝑥, the oxidizer mass flux GOx is defined as :
𝐺𝑂𝑥 = ��𝑜𝑥
𝐴𝑝⁄ (2.3)
and decreases with respect to time because of the increasing value of 𝐴𝑝. This change in GOx
with respect to time has a significant impact on the burning rate of the solid fuel grain. The
relationship between regression rate and oxidizer mass flux for a constant oxidizer flow
condition, as stated by Oiknine [5], is:
�� ∝ (𝐺𝑂𝑥)0.8 (2.2)
where �� is the linear regression rate. As a hybrid rocket motor with a constant ��𝑜𝑥 is fired,
��, 𝐺𝑂𝑥, and 𝜑 all decrease with time. An example of this behavior is shown in Figure 2, which is
an example burn of a small-scale hybrid rocket, predicted using a semi-empirical computational
model. It can be seen that the largest values of �� and GOx occur at the very start of the motor
firing, and the lowest values at the very end.
6
As 𝜑, ��, GOx, and pressure all vary with time, time-averaged values are often used to
describe the performance of the motor. These time-averaged values that are typically used to
evaluate and report the results of motors experiments. However, this may not be the best way to
present hybrid rocket data. A potential issue with only reporting the time-averaged values is that
the equations that satisfy the time-averaged value may not satisfy the large, instantaneous values
at the start of the motor firing. In fact, the instantaneous values of ��, and GOx at the start of the
burn can be multiple times larger than the average value over the duration of the burn.
Figure 2: Example hybrid rocket burn-profile
0
50
100
150
200
250
300
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 2000 4000
Ins
ten
tan
eo
us O
xid
izer
Mass F
lux
[kg
/m2
-s]
Ins
ten
tan
eo
us
Re
gre
ss
ion
Ra
te [
mm
/s]
or
Eq
uiv
ale
nc
e R
ati
o
Time [ms]
Regression Rate
Equivalence Ratio
Average Regression Rate
Gox
Average GOx
7
2.1 Combustion Process in a Counterflow Burner
The combustion process in a counterflow burner can be idealized as the combustion
process in a one-dimensional hybrid rocket system. The counterflow diffusion flame behaves
similarly to that of a hybrid motor, with the difference being that the cross-flow component is not
present. The flow configuration of the counterflow burner is presented in Figure 3, obtained from
[6]. Oxidizer is injected perpendicular to the surface of the fuel. Upon ignition, a melt layer
forms and pyrolyzing fuel species evolve from the fuel surface. A stagnation plane between the
flows of fuel and oxidizer forms. After reaching the stagnation plane the fuel, oxidizer, and
combustion products travel horizontally away along the flow streamlines of the stagnation plane.
Just below the stagnation plane sits the diffusion flame. The flame provides heat feedback to
sustain the pyrolysis process, and the rate of heat feedback is directly proportional to the
regression rate of the fuel:
Figure 3: Diagram of Opposed-flow flame [6]
Diffusion Heat Feedback
8
𝜌𝑓�� = ��𝑤/∆𝐻 (2.1)
with a solid fuel density 𝜌𝑓, linear regression rate ��, heat transfer per unit area to the wall ��𝑤,
and effective heat of gasification of the solid fuel ∆𝐻 [7]. The heat feedback to the surface
occurs through conduction, convection, and radiation heat transfer.
The location of the flame is near the stoichiometric condition, as that is where the mixture
ratio results in the temperature being highest and therefore produces the fastest reaction rates.
The stagnation plane, and as a result the diffusion flame location, can be moved closer to the fuel
surface by increasing the oxidizer mass flux. The increased momentum of the oxidizer moves the
flame closer to the fuel surface, increasing the surface temperature gradient. This results in an
increased rate of fuel pyrolysis. Figure 4 shows an image of an HTPB pellet burning under a
gaseous oxygen flow in the counterflow burner.
Oxidizer Supply nozzle
Solid-Fuel Pellet Stagnation Plane
Figure 4: Opposed flow burner flame zone
9
Unlike in center perforated motor experiments in which ��, GOx, and pressure all change
with time, these values can be maintained at steady state conditions using the counterflow
burner. The oxidizer mass flow rate value is fixed via choked flow through an orifice, and the
burn area of the fuel sample remains constant if it burns uniformly.
Due to the diffusion controlled combustion process, the burning rate is relatively pressure
independent. Researchers have reportedly observed pressure dependence at higher mass flux
rates where fuel regression rates begin to plateau with increasing GOx values [8]. The reason for
this behavior is still relatively unknown.
2.2 Experimental Setup
The counterflow burner used in this study consists of an optically accessible pressurized
vessel in which oxidizer and co-flow gases can be injected. The fuel is a solid pellet that stored
within a pellet housing and undergoes pyrolysis/decomposition during combustion. Oxygen
enters the pressure vessel through the center of a co-axial tube diametrically opposed to the fuel
pellet. Through the outer tubing on both the oxidizer and fuel ends, a co-flow of nitrogen is used
to prevent shear-induced mixing of the center flows with the surrounding environment. .
The fuel pellet is seated on a Teflon follower. Both the pellet and follower sit on top of a
linear variable differential transformer (LVDT) that is compressed as the pellet surface is
maintained flush with the holder. A nichrome wire is placed across the surface of the pellet to fix
the surface location. During the experiment as the pellet regresses, the spring force from the
LVDT ensures that the surface of the pellet remains in the same location as it burns. It is in the
extension of the LVDT as the pellet regresses that provides the regression rate measurement.
10
Figure 5 shows a distance vs. time plot that was recorded using the LVDT during one of the
experiments. The slope of the line provides the rate at which the pellet was regressing. The plot
provided in Figure 5 shows LVDT data during the initial ignition and subsequent steady state
burning. The regression rate is measured during the steady-state portion of the curve.
The regression rate of the fuel is related to the oxidizer flow rate, thus control of
��𝑜𝑥 must be maintained over the course of the experiment. As the area of the oxidizer exhaust
nozzle on the counterflow burner is fixed, the value of GOx only depends on ��𝑜𝑥. The ��𝑜𝑥
value is controlled in the system by choking the flow of oxidizer through an orifice. In order to
r =𝑑𝑦
𝑑𝑡
Figure 5: LVDT data from a pellet burning
11
maintain the choked flow condition, the upstream pressure of the oxygen is well above twice that
of the chamber pressure. Choking the flow is also the method used to control ��𝑁2, the mass flow
rate of nitrogen in the co-flows. Variation in ��𝑜𝑥 or ��𝑁2 is achieved by changing the upstream
pressures or replacing the orifices. Figure 6 shows a block diagram of the schematic and a
depiction of the location of the fuel pellet relative to the oxidizer flow and N2 co-flows nozzles
[4].
Figure 6: Block Diagram of Pressurized Counterflow System [4]
12
Before an experiment was conducted, the HTPB fuel samples were prepared by coating
the sample’s top surface with nitrocellulose layers. The nitrocellulose coating ensures quick and
even ignition of the pellet. After being prepped, the pellet was then loaded into the pellet holder
and tied down with a nichrome wire. A second nichrome wire connected to a 10V power was
placed against the top surface of the pellet. This second wire was used to achieve ignition. The
left image in Figure 7 shows a pellet loaded in the pellet holder and held down with the nichrome
wire. The image on the right in Figure 7 shows the pellet holder without a pellet sample.
Prior to the conduction of the experiment, the chamber was pressurized with inert gas. In
order to maintain a steady pressure during the experiment, a continuous flow through the
chamber is maintained through use of an exhaust valve. Electro-pneumatic solenoid values
permit shutoff control for the oxygen and nitrogen flow systems. Once the chamber pressure has
reached steady-state conditions, the pellet is ignited and allowed to burn until the LVDT had
fully extended.
Figure 7: Images of pellet holder base for pressurized counterflow burner [4]
13
Experimental Results and Discussion
Experiments where conducted on 19 pellets on HTPB, tested in flow conditions that were
varied by changes in upstream gas pressure and orifice diameter. Of the 19 tests, a regression rate
was determined from 16 of the tests. In the 2 of the 3 tests not included, the nichrome wire that
holds in the pellet in place broke before the LVDT recorded steady state data. The 3rd unused test
was performed without the N2 co-flow that the other tests were conducted with, so it has been
exclude. The measured regression rate values obtained over an oxidizer mass flux range of
approximately 7 kg/(m2s) to 112 kg/(m2s) at a target chamber pressure of 200 psi are plotted in
Figure 7. The results show the dependence of regression rate on the oxidizer mass flux. For
oxidizer mass flux values below 57 kg/(m2s), the regression rate increases with oxidizer mass
0.1
1
1 10 100
Reg
ress
ion R
ate
(mm
/s)
Oxidizer Mass Flux (kg/(s*m^2))
�� ≈ 𝑐𝑜𝑛𝑠𝑡.
Figure 7: Regression Rate vs. Oxidizer Mass Flux for HTPB & gaseous O2 at 200 psig
14
flux. Under higher oxidizer mass flow conditions, the regression rate begins to plateau to a near
constant value.
The averaged oxidizer mass flux and regression rate values are plotted in Figure 8. A
17% error in regression rate and a 1.9% error in oxidizer mass flux was calculated locally for the
cluster of 7 points near an oxidizer mass flux of 57 kg/(m2s) in Figure 7. These percent error
values were then assumed as the global percent error values for the averaged data points. All of
the experiments had a target chamber pressure of 200 psig, however it was found that the
average pressure over all of the test runs was 213 psig with a 3% error.
Data from multiple lab-scale hybrid motor studies similarly using HTPB and gaseous
oxygen are plotted against the counterflow data from this study in Figure 9. The regression rates
values for the hybrid motors are the time-averaged values over the course of the firing. The
experimental data from the current study burned with higher regression rates than those found in
0.1
1
1 10 100
Reg
ress
ion R
ate
(mm
/s)
Oxidizer Mass Flux (kg/(s*m^2))
Figure 9: Averaged Regression Rate vs. Oxidizer Mass Flux Figure 8: Averaged Regression Rate vs. Oxidizer Mass Flux
15
the hybrid motors firings. In addition, the hybrids data obeys the diffusion flame power law
while at similar oxidizer mass fluxes the counterflow regression rates plateau to a constant value.
The deviation from the power law relationship at higher oxidizer mass flux values has
previously been observed by researchers investigating the burning rate of butyl rubber grains
combusted in a pressurized slab burner [8]. They observed that increasing the pressure within is
plateau region resulted in increased regression of the solid fuel. This high oxidizer mass flux
behavior remains relatively unexplained.
As the mass flux increases, the diffusion flame is pushed closer to the fuel surface. This,
in turn, increases the regression rate due to the increase heat feedback to the fuel surface.
However, there is a finite distance between the fuel surface and the diffusion flame. At the higher
mass flux, the diffusion flame may already be close enough to the fuel surface that increasing the
flux does not significantly increase the surface temperature gradient. This would result in the
regression rate eventually plateauing at higher mass flux as was observed. Smoot and Price [8]
saw in their cross-flow slab motor experiments a pressure dependency that started in the region
0.1
1
1 10 100
Reg
ress
ion R
ate
(mm
/s)
Oxidizer Mass Flux (kg/(s*m^2))
Current Study
Hybrid Rocket Data (Connell et al. 2009) [9]
Hybrid Rocket Data (Weismiller et al. 2010) [10]
Hybrid Rocket Data (Connell et al. 2017) [11]
Figure 9: Counterflow data compared with lab-scale hybrid rocket motor data
16
that deviated from the 0.8 power rule. They report that there is no pressure dependency in the
lower mass flux region. The deviation from the power law and the introduction of the pressure
dependency may be the result of finite rate kinetics.
Theoretical Method
The following section is based off the computational model created and developed by
Nardozzo (2016), which was used to study the combustion of solid fuels with nitrous oxide and
gaseous oxygen under lower oxidizer flow conditions [7]. The model is run through GNU
Octave, a free open-source alternative to MATLAB, and makes use of CHEMKIN 10141. Codes
from the original work have been slightly modified to properly match the conditions of the
current study.
The model is used for developing an understanding of the flame structure and location of
the diffusion flame under various pressures and flow conditions. It uses conservation of energy
and species for the counterflow configuration to solve for the regression rate of the solid fuel,
temperature, species, and others key combustion parameters [7]. From the input conditions of
oxidizer velocity and chamber pressure, the code models the fuel pellet in a ‘condensed phase
model’ and the decomposed gas just above the fuel surface in a ‘gas phase solver’. The boundary
between the two models is the surface of the fuel pellet. These two models are loosely coupled
and iterated until the energy and species leaving the condensed phase are equal to the energy and
species entering the gas phase, within a defined tolerance [7]. When convergence is achieved,
the regression rate of the fuel pellet is extracted from the condensed phase model.
17
4.1 Condensed Phase Model
During the combustion process, the rate of regression of the solid fuel is determined by
the heat feedback from the flame to the fuel pellet. The pyrolysis products that evolve from the
pellet surface react exothermically with the gaseous oxygen oxidizer. HTPB requires heat to
undergo pyrolysis; as a result, the rate of heat transfer into the HTPB pellet governs the rate at
which the fuel regresses. Pyrolysis mainly occurs in a melt layer at the surface of the fuel pellet.
Figure 10 shows the temperature distribution of the melt layer in a hybrid fuel grain.
Figure 10: Temperature distribution zone of a hybrid fuel grain [12]
18
The model defines that the interactions between the melt layer and fuel pyrolysis
products occur at the surface of the fuel. The control volume is shown in Figure 11. Solid fuel
enters the control volume and decomposition products exit. This set up allows the control
volume to be stationary during the burn [7].
The one-dimensional mass balance for this control volume is:
𝑚 = 𝜌𝑠𝑈𝑠𝐴𝑠 = 𝜌𝑔𝑈𝑔𝐴𝑔 (4.1)
Diffusion Heat Feedback
Control Volume
Figure 11: Control Volume used in Model [7]
19
The area into and exiting the control volume are assumed to be equivalent, thus, As = Ag = A. In
addition, the velocity of the solid fuel (Us) also is the regression rate, resulting in a reduced
continuity equation of:
��
𝐴= 𝜌𝑠�� = 𝑈𝑔𝜌𝑔 (4.2)
The energy balance for the control volume is based on the assumptions of inviscid, isobaric flow
with no body forces, resulting in:
��𝑟𝑒𝑎𝑐 + ��𝑟𝑎𝑑+ ��𝑐𝑜𝑛𝑑 + ��ℎ𝑖 − ��ℎ𝑔 = 0 (4.3)
��𝑐𝑜𝑛𝑑 is the heat conducted into the solid fuel, ��𝑟𝑎𝑑 is the heat transfer caused by radiation, and
��𝑟𝑒𝑎𝑐 is the energy is reused pyrolyze the HTPB. ��𝑟𝑎𝑑 has been estimated to contribute
approximately 5-10% of the heat transfer [13, 14]. As there is minimal soot in the counterflow
burner during experiments and the products are quickly removed from the pellet surface, ��𝑟𝑎𝑑 is
neglected. Thus, energy balance reduces to:
��𝑐𝑜𝑛𝑑 = ��ℎ𝑔 − ��ℎ𝑖 − ��𝑟𝑒𝑎𝑐 (4.4)
The primary HTPB pyrolysis product is 1,3-butadiene, and Chambreau et al states that 1,3-
butadiene decomposes to ethylene (C2H4) and acetylene (C2H2) [15], such that:
1,3-𝐶4𝐻6→𝐶2𝐻2+𝐶2𝐻4 (4.5)
This chemistry is integrated into the model through conservation of species and assuming that
HTPB decomposes into equal parts C2H2 and C2H4:
𝐶7.337 𝐻10.982 𝑂0.058→1.83425 𝐶2𝐻4+1.83425𝐶2H2 (4.6)
The heat of this reaction, or the heat of pyrolysis, was determined through:
𝑄𝑟𝑒𝑎𝑐=Δ𝐻𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠−Δ𝐻𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 (4.7)
20
4.2 Gas Phase Solver
The region above the HTPB pellet surface is modeled as a one-dimensional, steady state,
axisymmetric, isobaric flow of pyrolysis products [7]. The following equations are employed in
the OppDiff driver code for Chemkin. The conservation equations start with the conservation of
mass:
𝑑
𝑑𝑥(𝜌𝑢) =
1
𝑟
𝑑
𝑑𝑟(𝜌𝑣𝑟) = 0
with u being the axial velocity and v being the radial velocity. The conservation of species is
given as:
𝜌𝑢𝑑𝑌𝑖
𝑑𝑥+
𝑑
𝑑𝑥(𝜌𝑌𝑖𝑉𝑖) = ��𝑖
where 𝑌𝑖is the species mass fraction and 𝜔i is the species rate of production. The conservation of
energy is:
𝜌𝑐𝑝𝑢𝑑𝑇
𝑑𝑥=
𝑑
𝑑𝑥(λ
𝑑𝑇
𝑑𝑥) − Σ (ρY𝑖V𝑖c𝑝𝑖
𝑑𝑇
𝑑𝑥) − Σ��𝑖ℎ𝑖
with 𝑐𝑝 as the specific heat and 𝜆 is the thermal conductivity. Specific enthalpy (hi) combines
both the sensible enthalpy and the heat of formation of the given species:
ℎ𝑖 = ℎ𝑓𝑖 + ∫ 𝑐𝑝𝑖𝑑𝑇𝑇
𝑇𝑖𝑛𝑡
Finally, the diffusion velocity is given by the mixture average:
𝑉𝑁 =1
𝑋𝑁��𝐷𝑁𝑚
𝑑𝑋𝑁
𝑑𝑥−
𝐷𝑁𝑇
𝜌𝑌𝑘
1
𝑇
𝑑𝑇
𝑑𝑥
21
where 𝐷𝑁𝑇 is the thermal diffusion coefficient. A schematic for the OppDiff driver code that
demonstrates how these equations are applied is provided in Figure 12.
Figure 12: OppDiff Block diagram [16]
CHEMKIN requires the users to input parameters for the OppDiff code to run. These
parameters include the reaction mechanism, thermodynamic properties, and transport properties
22
that are all preprocessed for the OppDiff program. OppDiff reads in these inputs, reads the setup
of the problem, and returns a solution in a text file.
4.3 Solution Coupling
The condensed phase and gas solvers both produce values for mass, species, and energy
fluxes at the boundary of the control volume. These solutions are then compared, and the solvers
are iterated by updating the fuel flow velocity until the solutions converge within a set tolerance
[7]. When the solution values converge, the regression rate of the pellet is then calculated from
mass flux and density from the condensed phase model. For the solutions to converge, one
requirement is that the surface temperature of the fuel must equal the temperature of the gas
directly above it:
𝑇𝑠 = 𝑇𝑔
The heat transfer by conduction to the condensed phase that results from the temperature
gradient of the gas just above it is calculated by the gas phase solver using:
��𝑐𝑜𝑛𝑑
𝐴= 𝑘𝑔
𝑑𝑇
𝑑𝑥
The coupling occurs by equating the gas velocities at the boundary, within a tolerance. The
model iterates by changing the value of the fuel gas velocity until both the condensed phase and
gas solver converge on a regression rate solution. The tolerance specified for the difference
between the regression rates is 1E-5 m/s. Figure 13 shows a flow chart of the iterative loop used
to calculate regression rate.
23
Figure 13: Octave Computational Model Block Diagram [7]
24
Theoretical Results
Burning Rate
Experimental conditions were input into the computational diffusion flame model with
the pressure fixed at 200 psia. Figure 14 provides a comparison between experimental and
theoretical results. It is evident that the model quite accurately predicts the trends observed
experimentally, including the plateau effect at higher GOx values. The modeling results exhibit
slightly increased regression rates compared to experimentally measure results. This makes sense
as they were determined via energy conservation, and experimentally not all of the heat released
through the flame is transferred into the fuel pellet for pyrolysis. As a result, a lower
experimental regression rate is expected.
0.1
1
1 10 100
Reg
ress
ion R
ate
(mm
/s)
Oxidizer Mass Flux (kg/(s*m^2))
Experimental Data
CHEMKIN 200 PSIA Data
Figure 14: 200 psia computational data compared to 200 psig experimental results
25
The same flow conditions were modeled at 250 psia to observe the effects of increasing
chamber pressure. Figure 15 plots the 200 psia and 250 psia modeling results compared to the
average experiment results. The experimental results had an average pressure of 213 psig, or
roughly 228 psia. It can be seen that the predicted regression rates are lower for a chamber
pressure of 250 psia than they are for 200 psia. The gas density increases with chamber pressure,
thus, for a fixed GOx value, the higher density has a lower velocity. A lower oxidizer velocity
results in the diffusion flame shifting further away from the fuel surface. This should reduce the
heat feedback and thus reduce regression rate. However, this goes against experimental slab
burner data indicated that regression rate increased with pressure in the plateau region [8].
0.1
1
1 10 100
Reg
ress
ion R
ate
(mm
/s)
Oxidizer Mass Flux (kg/(s*m^2))
Averaged Experimental Data
CHEMKIN 200 PSIA Data
CHEMKIN 250 PSIA Data
Figure 15: 200 psia computational data compared to 250 psia computational data
26
Flame Structure
In an attempt to investigate the cause of the regression rate plateau at high values of GOx,
the temperature profiles from the calculations of various GOx values were determined. Figure 16
shows that the temperature profile produced are a function of oxidizer mass flux. The
temperature profile indicates the location of the diffusion flame. At low GOx values, the
temperature profile is broad. As the oxidizer flow increases, the profiles become narrower and
shifts closer to the fuel surface, as the stagnation plane is pushed by the high flow of oxygen.
Thus, the location of the flame moves closer to the surface of the fuel with increasing oxidizer
mass flux resulting in increased heat feedback and increased regression rate. It can be seen that
the at higher oxidizer mass flux values, significantly more amounts of additional mass flux are
required to move the location of the diffusion flame, as compared to those of lower oxidizer
Figure 16: Flame Structure of Diffusion Flames at 200psia
27
mass flux values. At those lower values, a relatively small increase in oxidizer mass flux
corresponds to a large movement in the diffusion flame location.
Figure 17 shows the temperature gradient of gas that is adjacent to the fuel surface, taken
from the same profile as in Figure 16. At any given distance close to the fuel surface, the
temperature was found to increase with oxidizer mass flux. High temperature gradients near the
fuel surface corresponds to increased heat feedback. This phenomenon may be used to partially
explain the regression rate plateau effect. Starting at low oxidizer mass fluxes, small increases in
oxidizer mass flux result in substantial increases in the temperature gradient near the fuel
surface. The heat feedback to the fuel surface from the increasing temperature of the nearby gas
drives the increases in regression rate. As the value of oxidizer mass flux continues to increase,
location of the diffusion flame becomes less responsive to changes in oxidizer mass flux. The
Figure 17: Flame Structure Close to Fuel Surface at 200psia
28
increasing invariance of the temperature gradient with oxidizer mass flux may in part be
responsible for the regression rate plateau encountered at high oxidizer mass flux values.
Summary and Conclusion
Pressurized counterflow burner experiments were performed on pellets of HTPB with
gaseous oxygen as the oxidizer at a target pressure of 200 psia. Oxidizer mass flux was varied,
ranging from 7 to 112 kg/(s*m^2). Regression rates of the pellets were both experimentally
determined and computationally calculated. It was observed that at lower oxidizer mass fluxes,
the regression rates matched the predicted diffusion flame power-rule. At higher oxidizer mass
fluxes, the regression rate plateaus. As a result of this plateau, the results do not match well with
comparable lab-scale hybrid rocket experiments at the same oxidizer mass flux values.
The deviation from the power law found in both the counterflow and cross-flow cases at
high oxidizer mass fluxes has not been observed in comparable lab-scale hybrid rocket motor
tests. However, the experimental data gathered from this study appears to correlate well to trends
observed by others researchers under lower pressure lab-scale cross-flow configurations. A
CHEMKIN and GNU Octave computational model based on species and energy conservation
was used to simulate counterflow diffusion flame experiments. The model predicts the
experimental trends, even as they diverged from the expected power-law. Flame structure models
support the hypothesis that the location of the diffusion flame becomes increasingly less
responsive to changes in the value of oxidizer mass flux as the value increases.
29
BIBLIOGRAPHY
[1] H. S. Committee, "Hybrid Rocket Propulsion: Report of an AIAA Workshop,"
Washington, D.C., 1995.
[2] D. Pastrone, "Approaches to Low Fuel Regression Rate in Hybrid Rocket Engines,"
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[3] G. P. Sutton, Rocket Propulsion Elements, New York: John Wiley and Sons,
2001.
[4] R. H. Johansson, "Investigation of Solid Oxidizer and Gaseous Fuel Combustion
Performance Using an Elevated Pressure Counterflow Experiment and Reverse Hybrid
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Propulsion Conference and Exhibit, 2006.
[6] S. Shark, C.R. Zaseck, T.L. PourPoint, and S.F. Son "Solid-Fuel Regression Rates and
Flame Characteristics in an Opposed Flow Burner," Journal of Propulsion and Power,
pp. 1-10, 2014.
[7] P. Nardozzo, “Diffusion Flame Studies of Fuels with Nitrous Oxide,” Pennsylvania
State University, 2016.
[8] C.F. Price and L.D. Smoot, “Regression rates of nonmetalized hybrid fuel systems,”
AIAA Journal, Vol. 3, No 8 (1965), pp. 1
[9] Connell, T.L., et al., “Experiment and Semi-Emperical Modeling of Lab-scale Hybrid
Rocket Performance,” 2009
[10] M Weismiller et al., “Characterization of Ammonia Boran (NH3BH3) Enhancement to
a Parafiin Fueled Hybrid Rocket System,” 2010.
[11] Connell, T.L., et al. "Enhancement of HTPB Combustion in a Hybrid Rocket Motor
Using Amorphous Ti-Al-B Nanopowder Additives," Submitted to the 10th U.S.
National Combustion Meeting, Eastern States Section of the Combustion Institute,
April 23-26, 2017.
[12] Y. K, "Thermal Decomposition Study of HPTB Solid Fuel in the Presence of Activated
Charcoal and Paraffin," Journal of Thermal Analysis and Calorimetry, vol. 119, no. 1,
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pp. 557-565, 2015.
[13] G. A. Marxman, C. E. Wooldridge and R. J. Muzzy, "Fundamentals of Hybrid
Boundary Layer Combustion," Heterogeneous Combustion, Progress in Astronautics
and Aeronautics, vol. 15, pp. 485-521, 1964.
[14] L. Galfetti, "Innovative Solid Fuels," [Online]. Available:
https://www.politesi.polimi.it/bitstream/10589/28081/1/KHATTAB.pdf .
[15] S. D. Chambreau, J. Lemieux, L. Wang and J. Zhang, "Mechanistic Studies of the
Pyrolysis of 1,3-Butadiene-1,1,4,4,-d4 1,2-Butdadiene, and 2-Butyne by Supersonic
Jet/Photoionization Mass Spectrometry," J. Phys. Chem., pp. 2190-2196, 2005.
[16] A. Lutz, R. J. Kee, J. F. Grcar and F. M. Rupley, "OPPDIFF: A Fortran program for
computing opposed-flow diffusion flames," May 1997. [Online]. Available:
http://www.osti.gov/scitech/servlets/purl/568983/. [Accessed 24 December 2015].
31
CHRISTOPHER M. BURGER
(484) 639-2935 [email protected]
EDUCATION Pennsylvania State University, Schreyer Honors College Candidate for B.S. in Aerospace Engineering and B.S. in Physics, May 2017 Pursuing a minor in Mathematics
Schreyer Honors Scholar Vice President of Sigma Gamma Tau
WORK EXPERIENCE High Pressure Combustion Lab, State College, PA 2016 – Present Research Assistant
Fired 20+ hybrid rocket motors using gaseous and liquid oxidizers. Assembled the hybrid rocket motor testing stand, calibrated and installed the pressure transducers, installed the data
collection system, and wrote the Labview code to control actuators during motor firing. Created 20+ CAD models and drawings for hybrid rocket nozzles and components used in testing. Ran Chemical Equilibrium Analysis for 10+ hybrid rocket motors that had been tested. Working towards an undergraduate thesis on hybrid rockets.
NASA Glenn Research Center. Cleveland, OH 2016
Cryogenic Propellant Storage and Transportation Internship Performed a heat leak analysis for United Launch Alliance (ULA) on their conceptual upper stage vehicle ACES,
which is designed to replace the current CENTAUR upper stage. Created a tool to determine how long it takes the conceptual Mars Ascent Vehicle (MAV) to fill its propellant tanks
with liquid oxygen from gaseous oxygen that is produced on the surface of Mars. Spent 100+ hours in Thermal Desktop modeling the heat transfer involved in optical experiments.
Philmont Scout Ranch, Cimarron, NM 2014 - 2015 Summer Ranger
Facilitated team development and leadership skills to crews composed of 10-12 hikers Coached crews in camping and backpacking techniques to ensure a safe experience
ACTIVITIES Lunar Lion Team – Mission to the Moon 2014 - Present
Member of the student team developing a rocket system to be sent to the moon.
Researched and purchased the personal protective equipment used in the testing of the hydrogen peroxide engines.
Assists in transferring and filling the craft with hydrogen peroxide on testing days.
Sigma Gamma Tau – Aerospace Engineering Honor Society 2016 – Present Elected Vice President for 2016-2017
ADDITIONAL QUALIFICATIONS
Eagle Scout – Boy Scouts of America Computer Skills: AutoCAD, Thermal Desktop, Solidworks, Microsoft Office, Labview, and Matlab