effect of flight and motor operating conditions on ir … · 2015. 9. 28. · 1 effect of flight...
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EFFECT OF FLIGHT AND MOTOR OPERATING
CONDITIONS ON IR SIGNATURE PREDICTIONS OF ROCKET
EXHAUST PLUMES
Robert Stowe1, Sophie Ringuette1, Pierre Fournier1, Tracy Smithson1, Rogerio
Pimentel1, Derrick Alexander2, Richard Link2*
1Defence Research and Development Canada
2Martec Limited
*Address all correspondence to Robert Stowe, [email protected]
ABSTRACT
A computationally-efficient methodology based on Computational Fluid Dynamics (CFD) has
been developed to predict the flow field and infrared signatures of rocket motor plumes. Because
of the extreme environment in the plume and the difficulties in taking measurements of motors in
flight, it has been partially validated with temporally- and spatially-resolved imaging
spectrometer data from the static firings of small flight-weight motors using a non-aluminized
composite propellant. Axisymmetric simulations were carried out for a variety of motor burn
time, flight velocity, altitude, and modelling parameters to establish their effects on the results.
By extrapolating the axisymmetric CFD output into three dimensions, images of the rocket
plume as seen by an infrared sensor outside the computational domain were also created. The
CFD methodology correctly predicted the afterburning zone downstream of the nozzle, and good
agreement for its location was obtained with the imaging spectrometer data. It also showed that
flight velocity and altitude have substantial effects on the size, shape, and infrared emissions of
the plume. Smaller effects on plume properties were predicted for different motor burn times, but
DRDC-RDDC-2014-P112
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indicated that more experimental data of greater temporal and spatial resolution of single static
firings are required to better validate the CFD plume prediction methodology.
KEY WORDS: rocket, plume, infrared, signature, solid propellant, CFD, computational fluid
dynamics, imaging spectrometer
1. INTRODUCTION
Most rocket plume signature measurements are performed on static firings. Due to the close
proximity of the measurement equipment, and the fact that the rocket does not have to be tracked
in flight, these firings can produce the best quality data for signature prediction validation. They
also have the added benefit of allowing the collection of motor performance data such as motor
chamber pressure and thrust. For many applications requiring rocket plume signature data,
however, data from rockets in flight are of much more relevance than those from static firings.
Since flight experiments are much more costly and difficult to carry out than static firings, the
use of Computational Fluid Dynamics (CFD), coupled with the appropriate radiation and
atmospheric transmission submodels, provide a practical alternative to generate plume signature
predictions of rockets in flight.
The static firing of a solid propellant rocket motor is a very challenging problem for a CFD code.
Not only are there areas of low subsonic to high supersonic flow velocity, but the flow is highly
turbulent, and the exhaust is underexpanded as it exits the nozzle, resulting in a series of shock
waves. To generate maximum specific impulse, the propellant is formulated so that the exhaust is
fuel-rich, and contains significant quantities of hydrogen and carbon monoxide that afterburn
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once mixed with the surrounding air. The accompanying rise in temperature can increase the
intensity of radiation from the plume over many wavelength bands, including infrared (IR).
Figure 1 shows a photograph of the plume from the static firing of a small rocket motor using a
non-aluminized composite propellant. The shock pattern results in visible emissions, strongest
near the nozzle exit, with peaks present before fading out just before 2 m downstream. While this
propellant contains no aluminum fuel, there are still particles in the flow from small amounts of
solid additives and debris from inside the motor and the nozzle. These particles, along with the
high temperature gases, mask the background slightly, spreading outwards and downstream from
the nozzle at an angle close to the nozzle half-angle of 7.5 degrees. At the extremities of the
plume, the surrounding air mixes and provides oxygen for afterburning. Once mixed, however,
the high speeds present within the plume mean that the chemical reactions governing the
afterburning take a certain distance to occur, and the temperature peaks on the centerline well
downstream of the nozzle. Unfortunately, due to the extreme environment in the motor and
plume, experimental data on temperatures, velocities, and species are difficult to generate. Most
validation data come from non-intrusive infrared radiation measurements, so this implies
predicting both the flow field and the radiative emissions for comparison. The appropriate
corrections due to atmospheric effects such as molecular absorption must be taken into account
for direct comparison between the predictions and experimental data. These corrections depend
on how the molecular absorption database has been implemented. Even with experimental data
available for validation of the plume prediction, experimental measurements of the temperatures,
velocities, and species in the motor or at the nozzle exit are not available, so estimates, usually
from a thermochemical equilibrium code, must be made to establish the boundary conditions for
the CFD modelling.
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1.1 Previous Work
Unfortunately, there are few open literature publications available on rocket motor plume
predictions, particularly on small solid-propellant rocket motors. Quantitative experimental data
available to compare to the predictions was based on small ballistic test motors designed to burn
at constant chamber pressure, but with nozzles not optimized for flight so the plume may not be
representative of a flight-weight rocket motor. While they did not present any comparison with
experimental data, Jensen and Jones (1981) used a Reynolds-Averaged Navier-Stokes (RANS)
finite-difference axisymmetric solver to study afterburning in the exhaust of small double-base
propellant motors. They employed a 23-reaction finite-rate chemistry model, for which the
Arrhenius rate coefficients are given, a two-equation turbulence model, and estimated the nozzle
exit plane conditions by assuming thermochemical equilibrium in the motor chamber and some
non-equilibrium effects in the nozzle. With this model, they successfully predicted the
suppression of afterburning in the plume by adding small amounts of potassium to the propellant.
While they concluded their approach to the chemistry was adequate, more effort on correctly
modelling the turbulent flow field and its effects on combustion were required.
Devir et al. (2001) carried out an experimental and modelling study of the plume from a
statically-fired small ballistic test motor, designed to deliver constant chamber pressure, and
therefore flow-field properties, over its burn time. Their compressible flow RANS solver used a
two-equation (k-omega) turbulence model and a finite rate chemistry model (10 reactions) to
solve an axisymmetric computational grid (50000 cells). The propellant was reduced smoke and
contained approximately 87% ammonium perchlorate (AP) oxidizer and the remainder hydroxyl-
terminated polybutadiene (HTPB) binder and other ingredients. However, they did not model
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any of the reactions involving chlorine, and did not give the Arrhenius rate coefficients. They
state their assumed nozzle exit plane conditions. They also assumed purely axial flow out of the
nozzle despite a cone half-angle of 7.5 degrees. Due to difficulties in obtaining converged
solutions because of areas of low flow velocities with the CFD solver, they needed to use a high
free-stream velocity (68 m/s) which was not present during the experiments. Their calculated
temperature distribution along the plume axis showed a series of near-field shocks, but no
obvious afterburning after these shocks (downstream approximately 0.5 m). They post-processed
the CFD results with IR and ultraviolet (UV) codes to predict signatures. Despite the limitations
of their modelling, they predict a series of shocks which are shown in their IR and UV images,
and there is some correlation with IR radiance. They also achieve some agreement on the time-
averaged spectral radiance near main emission bands for water and carbon dioxide, but they were
unable to pick up the chlorine emissions. However, their IR radiance data in the 2212-2283 cm-1
band, indicative of carbon dioxide emissions, does show strong emissions downstream of where
they predicted the shocks and the highest temperatures, so in reality there may have been an
afterburning zone which was not correctly modelled.
Dennis and Sutton (2005) built on the work carried out in the United Kingdom that Jensen and
Jones (1981) supported. They stated that significant effort had gone into the earlier work to
determine the chemical reaction rates in a rocket plume environment, and that the use of a finite-
rate chemistry model was justified since thermochemical equilibrium could not be expected to be
reached in the faster regions of the flow field. Taking advantage of capabilities in more modern
CFD codes to improve their plume prediction methodology, they implemented the earlier
chemical reaction schemes in FLUENT®, a 3D finite-volume solver. Using a k-epsilon
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turbulence model and the compressible coupled implicit solver, they modelled a small tactical
motor of 6 kN thrust that used a non-aluminized HTPB/AP propellant. They showed they could
predict a similar number of temperature peaks as the emission peaks on a photograph, but the
positions were slightly different because the CFD modelling was done for a 10% higher thrust
level. Calculated temperatures compared well with the earlier axisymmetric plume code. The
effect of modelling the combustion was evident by comparing the non-reacting flow-field
temperatures with the reacting flow-field prediction; the highest temperatures were more than
1 m downstream of the nozzle exit, and just over 2000 K. They felt that FLUENT® better
reproduced the shape of the plume and shock structure than the earlier axisymmetric plume code.
The predicted and measured IR signatures also showed some similarities, but no details were
given on how the measurements or the predictions were carried out. However, their IR signature
plots show IR emissions peak well downstream from the nozzle for both the experimental and
modelling data.
Wang et al. (2010) reiterated the importance of modelling afterburning to get good signature
predictions. They modelled the same motor that Devir et al. (2001) studied, and their finite-rate
chemistry scheme used 10 reactions from the list by Jensen and Jones (1981). As in Devir et al.
(2001), they did not model the chlorine reactions. They used FLUENT® with the RNG k-epsilon
turbulence model to predict the flow field, and took into account radiation in the flow field so
that they were solved in a coupled way. The radiation model was the discrete ordinates method
(Modest 2003) and they used the HITRAN and HITEMP molecular spectroscopy for the
absorption and emission properties. They show a figure of their axisymmetric computational grid
near the nozzle exit, but details on the overall grid size are not given. By comparing the non-
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reacting and reacting flow fields, they showed that afterburning makes a 200-300 K difference in
the temperature of the plume downstream of the first few shocks. Their normalized spectral
radiance curve gave similar results as the predictions from Devir et al. (2001); once again,
contributions due to chlorine emissions were missing. The same research group (Wang et al.
2013) used a similar approach to model small double-base propellant motors using three
different propellant formulations. Unfortunately, very few details on the rocket motor are given
apart from the propellant formulation, but the nozzle expansion ratio (2.3) is typical of a small
ballistic test motor designed for constant chamber pressure. Rather than modelling the flow from
the nozzle exit, they modelled the flow from the chamber through the nozzle and the plume.
Chamber properties were calculated with a thermochemical equilibrium code. One of the
propellants showed a 600 K difference downstream of the near-field shocks due to modelling the
afterburning. Maximum temperatures in the afterburning region were just below 2000 K. They
showed how the predicted temperature and radiation intensity fields varied between the three
propellants, and also that higher radiation intensity correlated with higher temperature in the
afterburning regions, well downstream from the nozzles, for the two propellants that
demonstrated afterburning. With radiation intensity data from measurements at one small area in
the plume with a Fourier transform infrared (FTIR) spectrometer in 7 spectral bands from 1000
to 4500 cm-1 wavenumbers, they showed good agreement with their predictions. They also
showed the influence of including the radiation source term in the energy equation (coupled
approach); this shows a slight effect in the temperature field for the two afterburning propellants.
However, this effect did not appear consistent; for one of the propellants, the temperature peak
on the centerline shifted downstream, and the other upstream.
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1.2 Test Motors
The solid propellant rocket motors used in this study, identical to the one shown in Figure 1,
were all 70 mm in diameter, approximately 1 m in length, and used a non-aluminized composite
propellant of approximately 12% by mass hydroxyl-terminated polybutadiene (HTPB) binder
and 88% ammonium perchlorate (AP) oxidizer. The non-aluminized propellant was chosen to
minimize the presence of combustion particles in the plume so the CFD modelling could
concentrate on a flow with mainly gaseous products. The nozzle expansion ratio, nominally 6.65
and with a nozzle half-angle of 7.5 degrees, is designed for good thrust characteristics and avoid
separation in the nozzle over the burn time. The motor uses a centrally-perforated cylindrical
grain, and therefore has a progressive thrust-time profile. This is typical of many flight-weight
rocket motors to maximize propellant loading. This, along with any nozzle erosion, means that
the motor operating pressure will vary significantly during the burn time, as will the estimates of
nozzle exit conditions such as pressure, velocity, temperature, and species composition. These
estimates are carried out with direct measurements of motor chamber pressure, the nozzle
geometry, the propellant formulation, and the firing temperature as inputs to a thermochemical
equilibrium code (McBride and Gordon 1996). Thermochemical equilibrium is assumed within
the motor chamber and through the nozzle to the exit; after many firings of these test motors, the
repeatability and good agreement between the measured and predicted characteristic velocities
and specific impulses indicate that this a valid assumption. The motors were fired statically on an
elevated test stand to prevent ground effects on the plume within the field-of-view of the imaging
spectrometer.
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1.3 Validation Data
Defence Research and Development Canada (DRDC) has been using spatially resolved
spectroscopy to measure thermal emissions from a variety of sources, including static rocket
motors. Through the use of an 8x8 discrete element detector array coupled to a Fourier
Transform Spectrometer modulator, rocket emission variation as a function of distance from
nozzle and time into burn can be measured simultaneously. By approaching the test stand as
close as possible (21.8 m) and by taking advantage of the repeatability of the test motors between
firings, the spatial resolution was maximized (0.15 m per pixel). The resulting images, made up
from a mosaic of 4 firings, were 8 pixels high by 31 long, with three pairs of pixels overlapping
(Figure 2). This meant that the spectrometer imaged 4.2 m long by 1.2 m high of the plume. The
spectral band was 1852.75 to 5007.65 cm-1 with a spectral resolution of 4 cm-1 and a temporal
resolution of 125 ms (8 Hz). The calibrated data presented are in absolute apparent radiant
intensity units (W/sr·cm-1). These units are “apparent” because the atmospheric attenuations have
not been removed. Furthermore, all background radiation and sky radiance contributions have
been subtracted from the spectra presented here.
1.4 CFD Modelling
In this study, the CFD simulations were carried out with the finite-volume ChinookIMP code,
developed by Martec Ltd. under contract to DRDC (Link and Donahue 2008, Fureby et al.
2012). It uses the Favre-averaged Navier-Stokes equations1 for a reacting multi-species mixture
that include the conservation of mass, momentum, energy, species mass, turbulent kinetic
energy, and specific turbulent dissipation. They are closed by the ideal gas equation of state. The
inviscid fluxes are computed via the Harten, Lax, and Van Leer (HLLC) approximate Riemann
1 For the compressible Navier-Stokes equations, Favre averaging is a process to remove the density fluctuations from the RANS equations (Wilcox 1998)
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solver (Toro et al. 1994). The spatial gradients in the flux terms are evaluated using the Green-
Gauss approach. Second-order spatial accuracy is achieved using the Venkatakrishnan slope
limited scheme (Venkatakrishnan 1995). Implicit matrix free Lower-Upper Symmetric Gauss
Siedel (LU-SGS) temporal integration (Luo et al. 2001) was used in conjunction with fully
coupled finite-rate chemistry. The thermodynamic and viscous properties of multi-species
mixtures are determined from NASA polynomials and Lennard-Jones coefficients. A modified
form of the 1998 k-omega turbulence model (Wilcox 1998) used coefficients (Table 1) from a
transformed k-epsilon model (Menter 1993) because they were thought more suitable for free
shear flows. In the absence of a turbulence/chemistry interaction model, for the simulations
presented in this work, the turbulent Prandtl number was set to 0.9, and the turbulent Schmidt
number was set to 0.7.
Two different axisymmetric meshes were used to describe the calculation domain. The first
contained 509 cells in the streamwise x direction by 100 cells in radial y direction, (Figure 3),
clustered near the nozzle. Total domain length was 10 m. The rocket exhaust has 21 cells in the
radial direction. Slip wall conditions are used on the rocket surfaces and axis-of-symmetry. Air
flowed into the domain from the left and above using subsonic or supersonic inflow boundary
conditions, and the outflow to the right was a general outflow boundary condition (subsonic and
supersonic). To check dependence of the results on mesh size, the number of cells was doubled
in each direction for the refined mesh, and clustered even more closely around the nozzle.
The chemistry model uses a selection of 25 reversible reactions (Table 2) from Jensen and Jones
(1978) involving the CHONCl elements. The reactions in this reference, subsets of which were
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used by Jensen and Jones (1981), Dennis and Sutton (2005), and Wang et al. (2010, 2013) seem
to have correctly predicted the presence of afterburning in the plume. Third-body coefficients are
from Warnatz et al. (1999). The available elementary reactions involving these elements consist
of bimolecular or second order reactions, of the form A + B → C + D, or trimolecular reactions
which require a general third body, M: form A + B + M → C + D + M. The reaction rate of these
elementary reactions is given by the Arrhenius equation:
−= RTEAk Aexp
Eqn. 1
where k is the reaction rate, A the pre-exponential factor, EA the activation energy in kJ/mol, R
the universal gas constant in kJ/mol/K and T the temperature in K. The units for k are:
• cm3-mol-1-s-1 for the second order reactions
• cm6-mol-2-s-1for the third body reactions
The chemical reaction source term for species s is given by:
( ) [ ] [ ]∏∏= ==
−−=reactions
r
rspecies
mmrb
rspecies
mmrfrrd
treacrs
productrsssY
productrm
treacrm XkXkMS
1
,
1,
,
1,,3
tan,,,
,tan
, ννρ ννM
Eqn. 2
where:
Ms = molecular weight of species s
νs,rproduct = stoichiometric mole number of species s as a product in reaction r
νs,rreactant = stoichiometric mole number of species s as a reactant in reaction r
M3rd,r = third body efficiency factor in reaction (1 for no third bodies)
kf,r = forward reaction rate for reaction r
kb,r = backward reaction rate for reaction r
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[Xs] = concentration of species s = ρgYs/Ms
To allow the effects of radiation on the plume properties to be included in the flow-field
calculation in a coupled way, as was done by Wang et al. (2010, 2013), the energy equation in
ChinookIMP was modified to include radiation. If the contribution of radiation to the internal
energy and the pressure tensor can be considered negligible (Modest 2003), the conservation of
energy can be written as:
( ) ( ) 01
=+∇−∇−⋅∇+⋅⋅∇−+⋅∇+∂
∂rss
ns
s qYDhTuupuEtE κτρρ Eqn. 3
where:
ρ = density
E = specific energy
t = time
u = velocity
τ = stress matrix
κ = thermal conductivity
T = temperature
hs = specific enthalpy of species s
Ds = diffusion coefficient of species s
Ys = mass fraction of species s
qr = radiative heat flux
ns = number of species
The radiance energy transfer equation over a wavenumber band, Δη, (Modest 2003) is given by:
( ) Ω′∂Φ++−=∇⋅ ΔΔΔΔ'
44ˆ η
πηηηη π
κκκκ IIIIs ssaba Eqn. 4
= unit vector (ray) along which the radiance acts
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IΔη = spectral radiance at a mean band wavenumber of η (W/(m3 · sr)) in direction
κa = absorption coefficient (1/m)
Ibη = spectral blackbody radiance of wavenumber band (W/(m3 · sr))
κs = scattering coefficient (1/m)
IΔη’ = spectral radiance at a mean band wavenumber of η (W/(m3 · sr)) in direction ’
’ = unit vector (ray) from which scattering occurs
ΦΔη = scattering phase function between directions and ’
'Ω = solid angle, sr, in direction ’
To estimate the radiative heat flux qr, the following finite-volume methodology is used.
Equation 4 is integrated over all the solid angles. Since all the flux directions and spatial
coordinates are independent and black body radiation is assumed constant over all solid angles,
an equation for the spectral radiative heat flux, being the difference between the emitted and
absorbed radiation, can be derived. If the radiance can be assumed to be constant over all the cell
faces, this equation is integrated over all wavelengths to get the total radiative heat flux:
∞
=
Δ ∂−=⋅∇0
_
1 _4 λκπ η
η
fluxesn
ibar fluxesn
IIq Eqn. 5
Note that the radiation/turbulence interaction has been ignored in this formulation. If the
radiative heat flux term in the energy equation is Favre-averaged similar to the other terms in the
Navier-Stokes equations, additional turbulent correlations arise due to the dependence on
temperature and gas composition (Modest 2003). In general, 6 fluxes were used in this work to
calculate the radiative heat transfer. However, ChinookIMP is able to calculate up to 26 flux
directions to improve accuracy and minimize ray-effect (Modest 2003), but with increased
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computational time. Absorption coefficients for the molecular species are from a database based
on MODTRAN (Berk 1989).
2. PRELIMINARY RESULTS
The goal of this work was to produce a validated, efficient CFD methodology to predict plume
signatures for a multitude of flight conditions. To be a practical methodology, a single simulation
would need to run in a few hours rather than a few days on the currently-available computer
resources (50-node cluster of 2.4 GHz machines). It will be eventually expanded to 3 dimensions
to include effects such as flight-angle-of-attack, but to develop the methodology, all simulations
presented here are axisymmetric.
2.1 Effect of Flight Velocity
A nominal set of boundary conditions (Table 3) was used to generate a preliminary series of
predictions in order to identify some of the important parameters that could affect the results,
such as non-axial nozzle velocities, the importance of including radiation and discretization
method. To simulate the static firing, a small axial freestream velocity (10 m/s) in the same
direction as the rocket flow was imposed to speed convergence. It used the standard mesh of
approximately 50000 cells, and first order spatial discretization. A six flux radiation model was
employed with 10 axisymmetric divisions per quadrant. A “broadband” model that assumes a
single absorption coefficient over the entire infrared spectrum from 400 – 5000 cm-1 was used
for the carbon dioxide, water, and hard-body radiation. The rocket walls were considered to be
diffuse walls with an emissivity of 1.0 and all open boundaries were considered as black body
gas. As shown in Fig. 4, the centreline temperature dips immediately after the nozzle exit,
oscillates a couple of times, and then peaks at about 2000 K approximately 1.4 m downstream
from the nozzle. This compares favourably with simulations on the similar motor carried out by
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Dennis and Sutton (2005). The same methodology was used to investigate the effect of higher
flight velocities; Fig. 4 shows that they cause a decrease in peak afterburning temperature, and
that the peak occurs closer to nozzle. Figure 5 shows how the plume shape, as described by the
temperature field, changes with flight velocity, becoming narrower, cooler, and somewhat
longer. This is also reflected in the radiance plots of Fig. 6, derived from the radiant flux in the
out of page z-direction; flight velocity has a dramatic effect on the infrared emissions from the
rocket in flight.
2.2 Effect of Nozzle Exit Velocity
Given the profound effect of flight velocity on the plume properties, the consequence of
assuming purely axial flow out of the nozzle exit was determined. The actual rocket motor has a
7.5 degree nozzle half-angle. A new boundary condition was implemented in ChinookIMP to
allow for the linear variation of the ratio of axial and radial momentum over the nozzle exit
diameter. The decreased axial velocity and increased radial velocity cause the centreline
temperature to peak slightly earlier (Fig. 7).
2.3 Effect of Spatial Discretization
Figure 8 presents the effect of spatial discretization method on the amplitude of the temperature
oscillations near the nozzle and just past the afterburning zone. The visible emissions in the
accompanying photograph, due to grey-body emissions from the small amount of particles
present as well as molecular emissions, indicate seven shock positions. For each of these shocks,
a fluctuation in centreline temperature with axial distance should be expected. With the original
mesh and first order discretization, only the first three oscillations are predicted. The second
order discretization results in much more detail close to the nozzle, and can reproduce six, and
possibly seven oscillations. However, in both instances, the peak temperature in the afterburning
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region peaks at the same location. While the nominal boundary conditions may not exactly
correspond to the burn time at which the photograph was taken, there is good correspondence
between the shock positions and the predicted temperature fluctuations.
2.4 Effect of Coupled Radiation
Simulations fully coupling the radiation model with flow-field prediction were also carried out.
Compared with simulations without the fully coupled radiation model, the effect on the
centreline temperature was small. It reduced the peak temperature slightly and radiated some
energy heat downstream, raising the temperature there (Fig. 9). Because of the minor effect, most
of the following simulations neglected the contribution of radiation to the flow-field properties.
3. IMPROVED METHODOLOGY
Improvements to the methodology used for the preliminary predictions first looked at the effect
of using a refined mesh to better resolve the temperature fluctuations near the nozzle exit. While
it did not have a big effect on the results, the new boundary condition to allow for radial as well
as axial velocities at the nozzle exit plane was kept. The improved methodology was then used to
investigate the effect of motor burn time on static firing predictions, and also the effect of flight
altitude for a rocket cruising at 600 m/s.
3.1 Refined Mesh
The refined mesh contained twice as many cells in the axial and radial directions as the original
mesh for a total of approximately 200000 cells. As with the original mesh, cells were also
clustered at greater density near the nozzle exit, and the mesh size was coarsened toward the
downstream and upper edges of the CFD domain. For the set of boundary conditions in Table 4
for the 890 ms burn time, simulations were carried out on this new mesh for both first order and
second order spatial discretization. Figure 10 compares these results with those from the original
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mesh with second order discretization. There are slight differences in temperatures between the
second order original mesh and the first order refined mesh results, but the location of the
oscillations is the same, as is the maximum temperature. The second order refined mesh results
demonstrate similar locations for the first four oscillations, but with lower minimum
temperatures. The sixth peak is downstream of the others, and there is a seventh peak, possibly
corresponding to the seventh shock in Fig. 8. The afterburning zone also appears to be slightly
further downstream; this may be due to the lower minimum temperatures in the oscillations
slowing down the chemical reactions with respect to the other predictions. However, especially
in the absence of high spatial resolution validation data, the original mesh, combined with second
order spatial discretization, will likely give acceptable results.
3.2 Effect of Motor Burn Time
The flight-weight rocket motors used in this study have a progressive grain profile and an
eroding nozzle throat that results in nozzle exit plane conditions that vary with time. Five
specific burn times were chosen to establish the boundary conditions for modelling (Table 4).
Nozzle exit pressures, temperatures, velocities and species composition were estimated from the
propellant formulation, firing temperature, measured chamber pressure, and nozzle expansion
ratio at the various burn times. Since the nozzle throat continually erodes, the resulting decrease
in expansion ratio means that the nozzle exit temperature increases with burn time. All
predictions used the original mesh with second order spatial discretization.
Figure 11 presents the centreline temperatures versus burn time. The effect of nozzle exit
pressure results in a shifting of the temperature oscillations downstream, and also determines
where the maximum temperature occurs in the afterburning zone. An increase in nozzle exit
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temperature has the effect of raising the maximum temperature in the afterburning zone, but the
effect is not as large as the change in the estimated nozzle exit temperature. Figure 12 presents
the temperature fields at each of the burn times. As demonstrated in Fig. 11, the shock structure
moves downstream with an increase in pressure, and there is also a noticeable change in the
overall length of the plume. Any validation data, especially close to the nozzle up to the
afterburning zone, should be referenced to a particular burn time.
3.3 Effect of Altitude
In addition to flight velocity as shown in Fig. 5, altitude can have a profound effect on the shape
of a rocket plume (Sutton and Biblarz 2001). For a flight speed of 200 m/s and a burn time of
890 ms, simulations were done at flight altitudes of sea level, 5 km, and 10 km. Figure 13 shows
the significant change in shape of the plume for the three different altitudes. As the altitude
increases, the plume becomes longer and wider; the area of high temperatures increases and the
shock structure moves downstream.
4. VALIDATION AND PREDICTION OF SENSOR INPUT
As previously explained, the extreme environment of the plume makes direct measurements of
temperature, pressure, velocity, and species very difficult, and any data that exists is largely
based on non-intrusive techniques. The imaging spectrometer can provide some provide
temporal and spatial information on IR emissions and the presence of certain species. However,
such instruments must be treated as sensors, and direct comparison with the predicted properties
in the plume requires the appropriate corrections be made with respect to atmospheric
attenuation. This same process can be used to predict the IR signature of the plume as seen by a
sensor at a given standoff distance.
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4.1 Comparison with Imaging Spectrometer Data
Figure 14 shows the mosaic of imaging spectrometer data at a burn time of 1375 +/- 62 ms, to
correspond with the predictions at 1430 ms. Figure 15 is the summation of all the pixels together,
giving the total apparent radiant intensity captured by the imaging spectrometer in the 1900 to
5000 cm-1 wavenumber band. Each individual pixel captures spectral information much like
Fig. 15. This spectrum confirms the presence of carbon monoxide, carbon dioxide, hydrogen
chloride, and water. As presented in the plume predictions (Fig. 16), all of these species are
present in significant quantities.
Most of the IR emitting parts of the plume are captured by the rows beginning with pixels 63, 94,
and 125. The row beginning with pixel 94 is not aligned perfectly vertically with the centerline
of the nozzle, or adjacent rows would be expected to have spectra of similar magnitudes,
assuming an axisymmetric plume. For comparison with predicted centerline temperatures, all of
the pixels in each individual column were summed together to get the total apparent radiant
intensity versus axial distance from the nozzle. The same exercise was carried out for a burn time
of 875 +/- 62 ms, corresponding to the 890 ms burn time predictions.
Figure 17 compares the total apparent radiant intensity and predicted temperatures versus axial
distance from the nozzle. The oscillation at the beginning of the intensity curves may be due to
the predicted temperature oscillations just downstream of the nozzle, though the imaging
spectrometer does not have enough spatial resolution to follow all of the oscillations. There are
also uncertainties of 7.5 cm and 62 ms in the spatial and temporal resolutions of the spectrometer
data, as well as an additional uncertainty of using four different rocket motor firings to build the
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spectrometer mosaic. However, there is a good agreement between the peaks of the apparent
radiant intensity and the predicted temperatures. If the IR emissions in the 1900 to 5000 cm-1
wavenumber band captured by the imaging spectrometer are expected to correlate with
temperature, then the models and parameters governing the mixing and combustion in the plume
prediction methodology have been properly chosen to correctly reproduce the location of the
afterburning in the rocket exhaust plume.
4.2 IR Sensor Modelling
With radiation included in the energy equation, the CFD output includes spectral radiance in
each of the flux directions. However, this only gives the radiance at the edge of the CFD domain.
In general, sensors to measure the radiation would be outside the CFD domain, and atmospheric
attenuation would influence the spectral and total signature they would see. To predict these
signatures, once the CFD solution has been generated with or without the influence of radiation
on the flow field, the plume properties can be post-processed to extract the IR signatures at any
point outside the CFD domain.
To do this post-processing, the axisymmetric mesh (x-y plane) is rotated about the x-axis to
create a three-dimensional surface with boundary cell normals that point toward a sensor placed
outside (Fig. 18). In this case, the sensor is located at x = 4 m and y = 20 m and looks in the
negative y-direction at the computational domain. The field-of-view of the sensor is 45 degrees
in the horizontal and vertical directions to include the entire boundary surface. It is 320 (i) by
240 (j) pixels and captured the total irradiance for wavenumbers from 1900 to 5000 cm-1.
21
Sensor images were created for the 200 m/s flight velocity and for sea level, 5 km, and 10 km
altitudes (Fig. 19). The nozzle exit is located at pixel 68 in the ith-direction. The extent of the
boundary surface can be seen faintly as all boundary cells are radiating some energy. As
expected, the size of the image increases with altitude, as did the size of the plume as shown in
Fig. 13. The sea level case has much lower overall intensity due to increased absorption in the
atmosphere from higher air density and the greater presence of water vapour (60% relative
humidity); dry air was assumed at the higher altitudes. This confirms the importance of correctly
modelling atmospheric effects between the plume and the sensor for accurate predictions.
5. CONCLUSIONS
An efficient CFD methodology was developed to model the exhaust plume of a flight-weight
rocket motor, and predict the presence of an afterburning zone downstream of the nozzle. Good
agreement for the location of this afterburning zone was obtained with imaging spectrometer
data for a static firing. To date, the methodology has been applied to only axisymmetric meshes,
but could also be extended to three dimensions to investigate, for example, the effect of flight
angle-of-attack on the plume.
The CFD predictions showed that an increase in flight velocity causes a decrease in peak
afterburning temperature, and overall the plume becomes narrower, cooler, and somewhat
longer. Radiance plots demonstrated that flight velocity has a dramatic effect on the infrared
signatures of the rocket in flight.
Simulations with and without the fully coupled radiation model had little effect on these results
for this non-aluminized composite propellant rocket motor.
22
For this progressive burn rocket motor, changes in nozzle exit boundary conditions with burn
time affected the properties and shape of the plume. The temperature oscillations near the nozzle
shifted downstream with an increase in pressure, and also determined where the peak
temperature occurs. There is a noticeable change in the overall length of the plume with nozzle
exit pressure. Any validation data, especially close to the nozzle up to the afterburning zone,
should be referenced to a particular burn time.
Flight altitude caused a significant change in shape of the plume. As the altitude increases, the
plume becomes longer and wider; the area of high temperatures increases and the shock structure
moves downstream. By extrapolating the axisymmetric CFD output into three dimensions,
images of the rocket plume as seen by an infrared sensor outside the computational domain were
also created. The size, shape, and intensity of these IR signature images were significantly
affected by changes in flight altitude.
The imaging spectrometer data agrees, within the experimental limitations, with the CFD plume
predictions for sea level static firings. However, experimental data of greater temporal and
spatial resolution of a single static firing is required to better validate the CFD plume prediction
methodology.
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25
Wang, W., Wei, W., Zhang, Q., Tang, J., and Wang, N., (2010) Study on infrared signature of
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26
Table 1: Turbulence model coefficients
Coefficient Value α 0.44 β 0.0828
*β 0.09
σ 0.769 *σ 1.0
Table 2: Reaction mechanism
Reactions Reaction rates Non-Unity Third Body EfficienciesO + O + M → O2 + M k = 1.09 X 1014 exp(7.48/RT) H2O = 6.5, N2 = 0.4 O + H + M → OH + M k = 3.63 X 1018 T-1 O2 = 0.4, H2O = 6.5, N2 = 0.4 H + H + M → H2 + M k = 1.09 X 1018 T-1 O2 = 0.4, H2O = 6.5, N2 = 0.4
H + OH + M → H2O + M k = 3.63 X 1022 T-2 O2 = 0.4, H2O = 6.5, N2 = 0.4 CO + O + M → CO2 + M k = 2.54 X 1015 exp(-18.29/RT) CO2 = 1.5, CO = 0.75
OH + H2 → H2O + H k = 1.14 X 109 T1.3exp(-15.17/RT) O + H2 → OH + H k = 1.81 X 1010 T exp(-37.25/RT) H + O2 → OH + O k = 1.45 X 1014 exp(-68.59/RT)
CO + OH → CO2 + H k = 1.69 X 107 T1.3exp(2.74/RT) OH + OH → H2O + O k = 6.02 X 1012 exp(-4.57/RT) CO + O2 → CO2 + O k = 2.53 X 1012 exp(-199.54/RT) H + Cl2 → HCl +Cl k = 8.43 X 1013 exp(-4.82/RT) Cl + H2 → HCl + H k = 8.43 X 1012 exp(-17.71/RT)
H2O + Cl → HCl + OH k = 9.64 X 1013 exp(-75.66/RT) OH + Cl → HCl + O k = 2.41 X 1012 exp(-20.79/RT)
H + Cl + M → HCl + M k = 1.45 X 1022 T-2 Cl + Cl + M → Cl2 + M k = 7.26 X 1014 exp(7.48/RT) H + O2 + M → HO2 + M k = 7.25 X 1015 exp(4.16/RT) O2 = 0.4, H2O = 6.5, N2 = 0.4 Cl + HO2 → HCl + O2 k = 7.23 X 1013 exp(-3.99/RT) H + HO2 → OH + OH k = 2.41 X 1014 exp(-7.9/RT) H + HO2 → H2 + O2 k = 2.41 X 1013 exp(-2.91/RT)
H2 + HO2 → H2O + OH k = 6.02 X 1011 exp(-78.15/RT) CO + HO2 → CO2 + OH k = 1.54 X 1014 exp(-98.94/RT)
O + HO2 → OH + O2 k = 4.82 X 1013 exp(-4.16/RT) OH + HO2 → O2 + H2O k = 3.01 X 1013
27
Table 3: Nominal boundary conditions
Parameter Rocket Exit Plane Freefield Pressure [Pa] 227 510 101 325
Axial velocity [m/s] 2392.533 10.0 Radial velocity [m/s] 0.0 0.0
Temperature [K] 1605.0 300.0 Nozzle exit radius [m] 0.026206
N2 mass fraction 0.106 0.77 CO mass fraction 7.37×10-2 0.0 H2O mass fraction 0.291 0.0 CO2 mass fraction 0.256 0.0 H2 mass fraction 4.86×10-3 0.0 H mass fraction 3.85×10-7 0.0
OH mass fraction 6.49×10-9 0.0 O2 mass fraction 1.22×10-8 0.23 O mass fraction 6.11×10-9 0.0
HO2 mass fraction 1.26×10-8 0.0 Cl mass fraction 2.71×10-5 0.0 Cl2 mass fraction 2.71×10-8 0.0 HCl mass fraction 0.268 0.0 Turbulent intensity 0.1 0.1
Turbulent viscosity ratio 5840.8 10.0
Table 4: Rocket exit plane boundary conditions for various burn times
Burn time 50 ms 640 ms 890 ms 1150 ms 1430 ms Pressure [Pa] 188500 285610 347480 461880 275850
Exit velocity [m/s] 2362.2312 2307.5392 2282.0886 2225.9265 2220.7 Temperature [K] 1637.33 1710.59 1745 1816.41 1823.67 N2 mass fraction 1.06E-01 1.06E-01 1.06E-01 1.06E-01 1.06E-01
Nozzle exit radius [m] 0.026206 0.026206 0.026206 0.026206 0.026206CO mass fraction 7.27E-02 7.51E-02 7.62E-02 7.82E-02 7.84E-02 H2O mass fraction 2.90E-01 2.91E-01 2.92E-01 2.93E-01 2.93E-01 CO2 mass fraction 2.54E-01 2.50E-01 2.49E-01 2.46E-01 2.45E-01 H2 mass fraction 4.61E-03 4.44E-03 4.36E-03 4.22E-03 4.21E-03 H mass fraction 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
OH mass fraction 0.00E+00 1.00E-05 1.00E-05 2.00E-05 2.00E-05 O2 mass fraction 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 O mass fraction 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
HO2 mass fraction 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 Cl mass fraction 5.00E-05 8.00E-05 1.00E-04 1.60E-04 2.30E-04 Cl2 mass fraction 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 HCl mass fraction 2.73E-01 2.73E-01 2.73E-01 2.73E-01 2.73E-01 Turbulent intensity 0.1 0.1 0.1 0.1 0.1
Turbulent viscosity ratio 5840.8 5840.8 5840.8 5840.8 5840.8
28
Figure 1 – Static firing of a 70 mm diameter rocket motor
Figure 2 – Imaging spectrometer pixel positioning
Figure 3: Computational mesh, approximately 50000 cells
29
Figure 4: Effect of flight velocity on centerline temperature distribution (x=0 is the nozzle exit plane)
Figure 5: Temperature field versus flight velocity
30
Figure 6: Radiance field versus flight velocity
Figure 7: Effect of modelling the nozzle exit velocities on centerline temperature distribution
31
Figure 8: Location of visible emissions versus predicted temperature peaks, effect of spatial discretization
Figure 9: Effect of including radiation modelling on the centerline temperature distribution
32
Figure 10: Effect of mesh and spatial discretization on centerline temperatures
Figure 11: Centerline temperatures for various burn times
33
Figure 12: Temperature contours versus burn time
Figure 13: Temperature contours versus altitude, 200 m/s flight velocity
34
Figure 14: Mosaic of spectra at a burn time of 1375 +/- 62 ms
Figure 15: Apparent radiant intensity versus wavenumber, burn time 1375 +/- 62 ms
35
Figure 16: Species in the plume at 1430 ms burn time, sea level
Figure 17: Comparison of experimental apparent radiant intensity with predicted centerline temperature distribution
36
Figure 18: CFD domain boundary seen by the IR sensor
Figure 19: Sensor images for various altitudes, 200 m/s flight velocity