1 EFFECT OF FLIGHT AND MOTOR OPERATING CONDITIONS ON IR SIGNATURE PREDICTIONS OF ROCKET EXHAUST PLUMES Robert Stowe 1 , Sophie Ringuette 1 , Pierre Fournier 1 , Tracy Smithson 1 , Rogerio Pimentel 1 , Derrick Alexander 2 , Richard Link 2* 1 Defence Research and Development Canada 2 Martec 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
Transcript
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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
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.
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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.
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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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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
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
