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Computational Prediction of NASA Langley HYMETS
Arc Jet Flow with KATS
¨
Umran D¨uzel∗
, Olivia Schroeder†
, Huaibao Zhang‡
, and Alexandre Martin§
University of Kentucky, Lexington, KY, 40506
Atmospheric entry occurs at very high velocities which makes the physics of the flow
complicated to predict. Although high enthalpy flow facilities such as arc jets and plasma
wind tunnels are widely used to examine the entry flow conditions, they can involve as-
sumptions which make unrealistic predictions. High-fidelity modeling tools are essential for
accurate predictions of the physical phenomena that occur during planetary entry as well
as to better interpret ground testing. The Kentucky Aerothermodynamic and Thermal-
response System - Fluid Dynamics (KATS-FD) is a research tool developed mainly to pre-
dict planetary entry conditions. In order to better understand and interpret the physics of
an arc jet flow, KATS-FD is used and compared to a set of experimental data. The latter is
provided by NASA Langley Hypersonic Material Environment Testing System (HYMETS)
arc jet facility. From the array of experiments a test case was selected which consisted of a
6.5 MJ/kg enthalpy flow that discharged into a vacuum chamber at 0.228 kPa. The simu-
lation parameters are compared to radial and axial velocity profiles measured using Planar
Laser Induced Fluorescence (PLIF). Surface pressure and heat flux profiles are analyzed.
The species concentration along the centerline is computed and presented. A parametric
study of the nozzle wall boundary conditions and variation of bulk enthalpy is carried out
in order to better assess the ground testing and numerical results.
Nomenclature
F
F
FConvective flux matrix
F
F
FdDiffusive flux matrix
SVector of source terms
QVector of conservative variables
PVector of primitive variables
J
J
JConvective flux Jacobian
HBulk enthalpy, MJ/kg
˙mMass flow rate, slmp
ρDensity, kg/m3
PPressure, Pa
TTemperature, K
uFreestream velocity, m/s
qHeat flux, W/cm2
sArc-length coordinate, m
Subscript
cChamber
wWall
iVariable number
tr Translational-rotational
ve Vibrational-electronic
∗Ph.D. Candidate, Department of Mechanical Engineering.
†M.Sc. Student, Department of Mechanical Engineering.
‡Research Associate, currently at Computational Fluid Dynamics Research Center, Sun Yat-sen University.
§Associate Professor, Department of Mechanical Engineering, Associate Fellow AIAA.
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I. Introduction
One of the biggest challenges of space flight is the ability of safely enter an atmosphere. Although the
duration of that phase is usually no more than a few minutes, entry vehicles encounter extreme conditions
in this short period of time, which can be damaging to the integrity of the vehicle and the payload. This
is caused by the high velocities that the vehicle has at the beginning of the entry phase. Typical entry
velocities can vary between 7 km/s and 13 km/s in Earth atmosphere.1,2At these velocities, a strong bow
shock is formed in front of the spacecraft. Most of the kinetic energy from the free stream is transferred
into thermal energy as it goes through the formed shock wave. The vehicle has to overcome this thermal
load. The encountered flow becomes chemically reactive and more complex to characterize. The extreme
environment must be overcome through design parameters so that the spacecraft can preserve its integrity.
Thermal Protective Systems (TPS) are developed so that the harsh entry conditions can be withstood.
The characteristics such as size, thickness, material composition, etc., of the TPS are chosen based on the
expected heat load of the atmospheric entry. One important remark on TPS is that they are described as
Single-Point-of-Failure (SPOF)3which indicates that if it fails, the complete system fails. Hence, accurate
prediction of the entry conditions is vital in order to select and size the TPS.
Figure 1. Schematic view of HYMETS test section (Image from
Inman et al.4)
In order to better understand the physics be-
hind entry, an experimental approach – flight
and ground testing – is commonly used. The
flight tests are the best option to understand
and predict atmospheric entry with high accu-
racy but they are rare due to their high cost.
The ground testing facilities such as arc jets
and inductively coupled plasma (ICP) wind tun-
nels are build mainly to match the enthalpy of
entry flow conditions. Although these facilities
are widely used for reproducing the flight condi-
tions, they maintain drawbacks such as high un-
certainties, difficulties in achieving target condi-
tions, cost, and deviation from flight conditions.
These facilities also use significant assumptions
in order to simplify the flow field and be able
to measure the targeted parameters.5–8High
fidelity real gas computational fluid dynamics
(CFD) solvers have been developed recently not
only to predict the flight conditions but also to
better understand the physics behind atmospheric entry phenomena, to assist in ground testing and to better
interpret experimental results. Currently used numerical tools for entry and ground testing simulations are
presented in review study.9With the aid of these CFD tool, it is also possible to predicted parameters
such as boundary layer thickness, boundary layer edge enthalpy, edge Mach number, and shear stress which
are note quite captured during testing but are essential to characterizing TPS. Moreover, if needed, these
parameters would be main inputs for material response10 and thermal stress simulations.11
The purpose of this paper is to model the NASA Langley Hypersonic Material Environment Testing
System (HYMETS) arc jet flow and, at the same time, assess the capability of the Kentucky Aerothermo-
dynamic and Thermal-response System - Fluid Dynamics (KATS-FD)12,13 to model such flow. The study
includes the HYMETS Mach 5 nozzle simulation which discharge of the flow into a vacuum chamber at a
pressure of 228 Pa. Moreover, a test specimen will be placed downstream of the nozzle exit in order to
determine the heat flux and surface pressure.
II. HYMETS arc jet facility and test data
The experiment used to verify the KATS-FD code was published in Inman et al.,4and conducted at
HYMETS facility. The HYMETS facility was developed at NASA Langley Research Center in the late 60s.
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The facility was constructed to operate at 100 kW power. The plasma wind tunnel specifically was used
to conduct research for emissivity, catalycity, and dynamic oxidation testing of materials for hypersonic
vehicles.14 The facility was upgraded to operate up to 400 kW power in early 2000. Currently, the facility
is capable of heating a specimen surface up to 2800 K (4500 oF). Specimen stagnation pressure can vary
between 0.013 amd 0.079 atm, and the nominal free stream Mach number is 5. The bulk enthalpy of the
free stream can reach up to ≈27 MJ/kg (11500 Btu/lbm). Detailed information and historical development
of the facility is presented in Splinter et al.14
Figure 1 depicts the arc plasma generator, the nozzle, and the vacuum test chamber of the facility. The
laser sheet where the measurements are taken is illustrated by the dashed purple region. The mounted nozzle
is a Mach 5 converging/diverging nozzle, with a 12.7 mm throat diameter, and a 63.5 mm exit diameter. The
diverging section has 8ohalf angle. Depending on the atmosphere of the planet to replicate, the gases can
vary in content of Argon (Ar), Nitrogen (N2), Oxygen (O2) and Carbon Dioxide (CO2). The gas is heated in
the arc-plasma-generator section, accelerated through the nozzle and is discharged to 0.6 m diameter by 0.9
m diameter vacuum chamber. The facility is capable of using intrusive (pressure probes, heat flux probes,
etc.) and non-intrusive (flow visualization, spectroscopy, etc.) measurement instrument.
The provided test data4was obtained by Planar Laser-Induced Fluorescence (PLIF) which is a non-
intrusive measurement technique. PLIF was primarily used to visualize the arc jet flow, and the PLIF
molecular tagging velocimetry (MTV) was used to measure the axial velocity profile of the jet flow. Moreover,
Doppler-Shift based velocimetry was used to gather the radial velocity profiles. The provided test data is
intended to emulate Earth’s atmosphere, using a chemical composition of 75% N2, 20% O2and 5% Ar by
volume. Figure 2 illustrates the vacuum chamber before testing, the test specimen facing the plasma flow,
and the laser sheet for measuring the flow properties downstream of the nozzle exit.
(a) Test chamber (b) Test specimen (c) Nozzle flow
Figure 2. Images of the HYMETS facility at NASA Langley Research Center (Image from Inman et al.4)
Table 1 presents the test conditions for the provided data. Axial velocity profiles and radial velocity
profiles are presented in Fig. 3. The axial velocity profiles are presented as averaged and single-measurement
results. As it was explained in Inman et al.,4the center of the given points correspond to the measured mean
velocities, and the widths correspond to twice the associated uncertainty of the mean velocities. Stagnation
pressure was measured with a pitot tube and the 47 mm (1.85 inch) long, 3.175 mm (0.125 inch) edge radius
test specimen was located 50.8 mm (2 inch) downstream of the nozzle exit.
Table 1. Experimental conditions for provided test case (Earth atmosphere)
Enthalpy Mass Flow Rate Arc-Pressure Chamber Pressure
6.5 MJ/kg 403 slmp 109 kPa 0.228 Pa
III. Numerical approach
III.A. Numerical framework
The HYMETS Mach 5 non-equilibrium nozzle flow is simulated using the Fluid Dynamics (FD) of the Ken-
tucky Aerothermodynamics and Thermal-response System (KATS). KATS-FD is a high-fidelity, aerother-
modynamic, CFD solver developed at the University of Kentucky, used for the study and computation of
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(a) Axial velocity – averaged (b) Axial velocity – single-
measurement
(c) Radial velocity
Figure 3. Velo city profiles measured in the HYMETS facility (Image from Inman et al.4)
high enthalpy flows. KATS-FD has been used for the study of non-equilibrium re-entry flows, such as in
Stardust2and Mars Science Laboratory, as well as arc jet flows over test samples, and pure nozzle flow.12
The framework of KATS-FD is detailed in Ref.,12 and examples of its capability are shown in Refs.15–17 The
code uses a second order finite-volume approach with implicit, first-order backward Euler time integration
scheme to solve the 3D, unsteady, compressible Navier-Stokes equations. In their conservative form, the
governing equations can be represented by
∂Q
∂t +∇ · (F
F
F − F
F
Fd) = S,(1)
In KATS, the conservative variables in the time derivative Qare changed to primitive variables Pthrough
the introduction of a flux Jacobian J
J
J=∂Q
∂t , making the solved system
J
J
J∂P
∂t +∇ · (F
F
F − F
F
Fd) = S,(2)
Here, Qis the vector of conservative variables, Pthe vector of primitive variables, Sis the source terms vector,
and F
F
Fand F
F
Fdare the convective and diffusive flux matrices, respectively. In this work, the convective flux
vector uses a Steger-Warming flux-splitting scheme for adding numerical dissipation to the shock in order
to stabilize the solution.18 While for equilibrium flows KATS-FD uses a single temperature to describe
the flow in the energy equation, for non-equilibrium problems, Park’s two temperature model is used. In
this model, the translational and rotational energy modes of the particles is described by one temperature
Ttr, while the vibrational and electronic energy modes are described by another Tve. The combination of
translational-rotational temperature and the vibrational-electronic temperature is also used to control the
dissociation reactions.
Finally, the transport properties of the gas are modeled using Wilke’s mixing rule,19 where viscosity is
calculated from Blottner’s curve fits.20 The species thermal conductivities are determined with Eucken’s
model.21
III.B. Mesh description
III.B.1. Nozzle
The computational prediction of the HYMETS arc jet flow first is assessed with the Mach 5 nozzle test
case. KATS-FD not only has been developed to compute external flow, but also to predict the internal flow
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behavior. Since the problem is 2-dimensional, symmetry was used to reduce computational time, which makes
all of the computational domains axisymmetric. The nozzle geometrical constraint and the computational
domain is illustrated in Fig. 4. The nozzle mesh includes 210 nodal points in the stream-wise and 64 in the
radial directions. In order to ensure accurate simulation of the flow field, the mesh was refined at the wall.
Figure 4. HYMETS Mach 5 nozzle dimensions and computational domain
III.B.2. Nozzle connected to the vacuum chamber
Figure 5. HYMETS Mach 5 nozzle flow discharged into vacuum chamber
The nozzle is attached to a vacuum
chamber and the domain is con-
structed assuming there is no test
specimen. The vacuum chamber
domain is assembled according to
the real geometry , which has di-
mension of 0.6 m diameter by 0.9
m length. The mesh generated is
presented in Fig. 5. Although it is
computationally expensive, the en-
tire chamber is modeler to verify the
flow development at the nozzle exit.
III.B.3. Test specimen at the vac-
uum chamber
Having created the nozzle flow with
and without the vacuum chamber, the test specimen was then placed at the testing location. Fig. 6 represents
the HYMETS Mach 5 nozzle mounted to a vacuum chamber where a test specimen is located 1.5 inches
downstream of the nozzle exit. The domain is cut-off in the vertical direction in order to decrease the
computational time. The mesh domain includes 400 points in the stream-wise and 200 in the radial direction.
Figure 6. Test specimen located ≈51 mm downstream of the nozzle exit
III.B.4. Shock alignment and boundary layer refinement
Once a converged solution is achieved with a coarse grid, the shock in front of the sample can be traced.
The trace is used to generate a more refined mesh in the aft-shock region. The new mesh contains cells
that are re-oriented to follow the tangential direction of the the shock, so that the latter can be accurately
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captured. A new spacing of 1 ×10−5m is also applied near the wall of the sample for better resolution in
the boundary layer and, ultimately, more accurate heat flux computation on the surface of the sample. The
mesh alignment process is manually repeated several time, until the shock is accurately captured. Figure 7
illustrates the process by showing one of the intermediate meshes obtained.
(a) Refined mesh near the shock (b) Shock capturing after refinement
Figure 7. Mesh alignment for accurate shock capturing
III.C. Initial and boundary conditions
In order to initialized the problem, the domain is split into two regions: upstream and downstream of the
nozzle throat. The downstream of the nozzle throat is initialized by applying a shrink factor to the pressure
and density. This helps the solution to converge. A shrink factor of 2.1×10−3is used. On the other hand,
the upstream of the nozzle is set to match inlet conditions. The nozzle inlet conditions are assigned based
on experimental data for the test case in conjunction with an equilibrium solver for computing mixture
and species properties. The parameters used from the experiment are presented in Table 1. The chemical
composition of an Earth’s atmosphere is used, which consists of a six species mixture (N2, O2, NO, N, O, and
Ar). Using the molar concentrations of N2, O2, and Ar, and mixture enthalpy of 6.5 MJ/kg, Mutation++22
is used to calculate the partial densities of the species at equilibrium. The translational-rotational as well
as vibrational-electronic temperature are determined by iteratively solving the equilibrium state until the
enthalpy is matched for the given arc-pressure. The same is done to determine the mixture density. Once
the mixture density is known, the inlet velocity is determined from the mass flow rate. The prescribed inlet
conditions are presented in Table 2.
Table 2. Inlet Conditions
T Tve u ρN2ρO2ρNO ρNρOρAr
3832 K 3832 K 208 m/s 61.7 g/m34.84 g/m34.50 g/m335.4 g/m31.22 ×10−2g/m36.06 g/m3
The outlet condition is set based on the pressure of the vacuum chamber, pc= 228 Pa. Finally, the
simulation uses a cold wall assumption of Tw= 350 K, and a non-catalytic, no-slip wall boundary condition.
IV. Numerical results and comparisons
IV.A. Nominal results
The experimental measurements were conducted at different locations for axial and radial velocity profiles.
The measurement window is represented in a sketch in Fig. 8 and the locations of each profile is stated
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in Table 3. The locations are defined from the exit of the arc jet nozzle. Mach 5 nozzle configuration is
simulated first in order to asses the internal flow results. Figures 9(a) and 9(b) illustrate the nozzle flow
contour of pressure and Mach number, respectively. By design and according to quasi-1D inviscid flow
theory, the nozzle should generate a Mach 5 flow. The nozzle simulation resulted in a Mach number of ≈4.9
which is in good agreement with the nozzle design specification.
Figure 8. Graphical representation of the laser measurement sheet and profile locations
Table 3. Laser measurement profile locations
LiL1L2L3L4
LAxial 0.57 cm 1.97 cm 2.97 cm –
LRadial 1 cm 2 cm 3 cm 4 cm
The species mass concentration along the nozzle centerline is given in Fig. 9(c). In arc jet nozzles, non-
equilibrium processes take place and species dissociate and recombine. Figure 10 illustrates the nozzle flow
discharged into the vacuum chamber which is at 0.228 kPa. It can be seen that the flow is under expansion.
Varying the pressure can reduce the expansion.23 The flow behavior is consistent with the nozzle flow studies
available in the open literature.23–25 Nozzle discharge into the vacuum chamber simulation (without a test
sample placement) is carried out in order to observe the flow development.
The test sample described above is a 25 mm diameter SiC probe placed ≈51 mm away from the nozzle
exit. The SiC probe is represented in Figure 11(a) and the placement of the probe is shown in Figure 11(b).
Unfortunately, Inman et al.4– from which the vleocity measurements were taken – does not report the
stagnation heat flux values. However, Splinter et al.14 contains a wide range of measurement obtained with
different sets of probes, one of which is very close to the values used here (Earth’s atmosphere, 6.5 MJ, 400
slpm). This measured heat flus was obtained with a TeflonR
Slug Calorimeter. Although it is not the same
probe and exact test, the TeflonR
Slug Calorimeter can provide an estimated non-catalytic cold-wall heat
flux to be compared with the KATS-FD predictions.
In high enthalpy arc jet testing, the flow directly hits the sample and a bow shock is formed. Figures 12(a)
and 12(b) illustrate the Mach and velocity contours over the sample. The shock is accurately captured by
aligning the grid to the shock,26 as shown in Sec. III.B.4. The test specimen wall is assumed to be cold
(350 K) and non-catalytic. This is a strong assumption but it is sufficient for the heat flux evaluation and
comparison to the results obtained with the Teflon R
Slug Calorimeter.14 The nozzle wall is also assumed to
be cold (350 K) and non-catalytic.
Figures 13(a) and 13(b) represent the computed surface pressure and heat flux of the corresponding
test case with respect to arc length. Although the behavior of the profiles are consistent with previous
studies, the measured values have not yet been obtained for a comparison with a SiC probe configuration.
Thus, the profiles are compared to a Teflon R
Slug Calorimeter14 heat flux measurement under similar testing
conditions. Stagnation heat flux predictions are approximately 20% different from measured values. This can
be due to the use of two different probes which may have different geometries and diameters, or differences
in testing conditions. Also, it is stated that the uncertainty in non-catalytic cold wall heat flux can be up to
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(a) SiC probe as a test sample (Image from Splin-
ter et al.14
(b) Location and configuration of test sample
Figure 11. Geometry and location of the test sample used for the simulation of the HYMETS facility
(a) Mach contours (b) Velocity contours
Figure 12. Simulation of the HYMETS nozzle and test-chamber, with specimen, using KATS-FD
(a) Pressure along the surface (b) Heat flux along the surface
Figure 13. Surface properties of a test specimen inside the HYMETS facility obtained using KATS-FD
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64.5%.14 Hence, the results indicate that the simulations have a good agreement for heat flux and surface
pressure. Axial velocity and radial velocity profiles are presented in Figs. 14(a)-14(b). The experimental
profiles are measured as presented in Fig. 8. The shaded area indicates the minimum and maximum value
of single shot images taken with PLIF.4The profiles and the shaded area show that KATS results are
approaching the measured minimum axial velocity profiles. Also, the radial velocity profiles are in good
agreement with the measurements. Although the radial velocity profile follows the same flow behaviour as
the experimental one, including the uncertainty analysis to the plots can show perfect approximation with
the experiments.
(a) Axial velocity profile at location L1(b) Axial velocity profile at location L2
(c) Axial velocity profile at location L3(d) Radial velocity profiles
Figure 14. Comparison of the experimental velocity profiles and the numerical results obtained using KATS-FD for
the HYMETS facility
IV.B. Nozzle wall boundary conditions and enthalpy variations
The nozzle exit is assumed to have sharp edge in the simulations however in reality the edge can be trimmed
or rounded so that the expansion can be different from the simulations. In order to answer the effect of
nozzle exit edge being sharp or curved, a set of simulations under 6.5 MJ enthalpy were conducted, with the
mesh shown in Fig 15. The nozzle exiting area, for both sharp and rounded edge, was kept constant. The
results of the simulations are presented in Fig. 16(a). The profiles indicates that the effect is taking place in
radial position which indicates that it affects the flow expansion. The change in axial velocity is recorded to
be between 1% and 2%.
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Figure 15. Rounded nozzle exit geometry
Another consideration was nozzle wall boundary
condition. In the results presented in the previous
section, KATS-FD under-predicts the axial velocity.
It was therefore hypothesized that the flow was los-
ing energy through the nozzle before reaching the
measurement location. To address this issue, a set
of simulations, also at 6.5 MJ, was performed where
the nozzle wall was adiabatic rather than set to a
cold-wall temperature. The results of this test are
shown in Fig. 16(a). It can be noted that while
the change in magnitude of the axial velocity at the
centerline is very small, the velocity profile is altered
significantly, making this a parameter worth considering in future works.
Lastly, uncertainty in the bulk enthalpy is an important concern both for ground testing and computa-
tional prediction. The measured bulk enthalpy uncertainty can be up to 14%.14 Therefore, it was of interest
to understand the degree to which the axial velocity profile changed by varying the enthalpy. A new set
of simulations were run at 9 MJ, and the comparison with the results of the previous section is shown in
Fig. 16(b). As expected, in the high enthalpy case, the magnitude of the velocity increases. Furthermore,
the profile of the velocity is practically unchanged, since only close to the centerline do the velocities differ
from each other. The centerline velocity gains 13% with increase of 2.5 MJ. Thus, the uncertainty in the
bulk enthalpy is an important aspect to consider when performing numerical predictions.
(a) Various nozzle wall boundary conditions (b) Enthalpy variation
Figure 16. Simulation results of the axial velocity profiles at L1for different configurations
V. Conclusion and remarks
High enthalpy flow facilities are commonly used for simulating conditions experienced during planetary
entries. However, these tests carry a high degree of uncertainty and are not fully capable of replicating
entry environments. Thus, there is a need for high fidelity modeling tools which can be applied to ground
testing as well as flight conditions. The scope of the current research is to asses the capability of KATS-FD
as a computational prediction tool by comparing results with a set of experiments conducted at HYMETS
facility at NASA Langley. In the future, KATS-FD can assist in ground testing by predicting unmeasured
parameters such as edge enthalpy, which is needed for surface recession investigation.
The current simulations show good agreement with the measurements. The solutions showed that the
axial and radial velocity profiles can be improved by correcting the bulk enthalpy, re-configuring the nozzle
exit edge and taking the nozzle wall boundary condition into consideration. The simulations with a cold-wall
nozzle, and sharp exit corner, at 6.5 MJ bulk enthalpy approaches the lower velocity limit of experiment
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single shot. Increasing the enthalpy by 40%, results in an increase of centerline velocity by ≈13%.It is
therefore concluded that uncertainties associated with bulk enthalpy are a non-negligible consideration when
conducting simulations of arc jet flows, specifically concerning centerline velocity.
Changing the geometry of the exit of the nozzle can also influence the velocity profile as it can change the
flow expansion. However the change in magnitude of the velocity is not very significant. Another important
note from these simulations is that using the cold-wall assumption in the nozzle is conservative and it affects
the velocity profiles both in magnitude and shape. A more accurate option may be to use a temperature
profile instead.
The specimen is assumed to have a cold wall, non-catalytic surface. The resulting stagnation heat flux is
compared with Teflon R
Slug Calorimeter measurements whose testing conditions were assumed to be similar
to testing conditions. Even though two different probes were compared and knowing the fact that cold-wall
non-catalytic heat flux measurements can have up to 64.5% uncertainty, the results are in good agreement
with the experiment.
Acknowledgments
Financial support for this work was provided by SpaceTech-REDDI ESI Award NNX16AD18G, and
NASA Kentucky Space Grant Graduate Fellowship NNX15AR69H. The authors greatly appreciate the help
of R.S.C. Davuluri from Gas Surface Interaction Laboratory with the KATS framework. Many thanks to S.
Splinter from NASA Langley for providing details of the nozzle geometry. Special thanks to T. Gok¸cen from
NASA Ames Research Center for his guidance with the nozzle flow conditioning.
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