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NASA NTRS2024

LAURA Users Manual: 5.7

This users manual provides in-depth information concerning installation and execution of Laura, version 5. Laura is a structured, multi-block, compu- tational aerothermodynamic simulation code. Version 5 represents a major refactoring of the original Fortran 77 Laura code toward a modular structure afforded by Fortran 2003. The refactoring improved usability and maintain- ability by eliminating the requirement for problem-dependent re-compilations, providing more intuitive distribution of functionality, and simplifying inter- faces required for multi-physics coupling. As a result, Laura now shares gas-physics modules, MPI modules, and other low-level modules with the Fun3D unstructured-grid code. In addition to internal refactoring, several new features and capabilities have been added, e.g., a GNU-standard instal- lation process, parallel load balancing, automatic trajectory point sequencing, free-energy minimization, and coupled ablation and flowfield radiation.

CFD hypersonics reentry↗

NASA NTRS1983

Explanation of the hypersonic longitudinal stability problem: Lessons learned

Inviscid and viscous CFD codes have been applied to a modified Space Shuttle orbiter geometry to investigate differences between preflight aerodynamic predictions and aerodynamic data from hypersonic reentry flight. Flow field solutions were obtained for wind tunnel conditions and flight conditions to assess Mach number, real-gas, and viscous effects on the reentry aerodynamics of the orbiter. Based on the CFD studies, a methodology model has been developed to (1) extrapolate wind tunnel data to flight conditions and (2) calculate a DCM for use with the Aerodynamic Design Data Book. Comparisons are made with selected flight data. Results of the study indicate that the differences between flight and pre-STS-1 predictions of hypersonic pitching moment are primarily due the to Mach number and real-gas effects.

Griffith, B. J.↗

NASA NTRSDate not supplied

Implicit Thermochemical Nonequilibrium Compressible Flow Simulations on Unstructured Grids Using GPUs

As next-generation exascale-class systems arrive, existing software must be updated accordingly to effectively utilize these systems. For high concurrency and energy efficiency, many of these systems utilize GPU architectures. In this work, we present a CUDA C++ implementation of FUN3D's thermochemical nonequilibrium capability for turbulent flows. Efficiency is demonstrated at scale using the Summit system at the Oak Ridge Leadership Computing Facility which is representative of future exascale systems. This work enables faster, higher fidelity, and scale-resolving simulations of thermochemical nonequilibrium flows including reentry, hypersonics, and combustion.

CFD, GPU, HPC, Hypersonics, Chemistry↗

NASA NTRS2010

HYTHIRM Radiance Modeling and Image Analyses in Support of STS-119, STS-125 and STS-128 Space Shuttle Hypersonic Re-entries

We provide the first geometrically accurate (i.e., 3-D) temperature maps of the entire windward surface of the Space Shuttle during hypersonic reentry. To accomplish this task we began with estimated surface temperatures derived from CFD models at integral high Mach numbers and used them, the Shuttle's surface properties and reasonable estimates of the sensor-to-target geometry to predict the emitted spectral radiance from the surface (in units of W sr-1 m-2 nm-1). These data were converted to sensor counts using properties of the sensor (e.g. aperture, spectral band, and various efficiencies), the expected background, and the atmosphere transmission to inform the optimal settings for the near-infrared and midwave IR cameras on the Cast Glance aircraft. Once these data were collected, calibrated, edited, registered and co-added we formed both 2-D maps of the scene in the above units and 3-D maps of the bottom surface in temperature that could be compared with not only the initial inputs but also thermocouple data from the Shuttle itself. The 3-D temperature mapping process was based on the initial radiance modeling process. Here temperatures were guessed for each node in a well-resolved 3-D framework, a radiance model was produced and compared to the processed imagery, and corrections to the temperature were estimated until the iterative process converged. This process did very well in characterizing the temperature structure of the large asymmetric boundary layer transition the covered much of the starboard bottom surface of STS-119 Discovery. Both internally estimated accuracies and differences with CFD models and thermocouple measurements are at most a few percent. The technique did less well characterizing the temperature structure of the turbulent wedge behind the trip due to limitations in understanding the true sensor resolution. (Note: Those less inclined to read the entire paper are encouraged to read an Executive Summary provided at the end.)

Gibson, David M.↗

NASA NTRS1987

Retooling CFD for hypersonic aircraft

The CFD facility requirements of hypersonic aircraft configuration design development are different from those thus far employed for reentry vehicle design, because (1) the airframe and the propulsion system must be fully integrated to achieve the desired performance; (2) the vehicle must be reusable, with minimum refurbishment requirements between flights; and (3) vehicle performance must be optimized for a wide range of Mach numbers. An evaluation is presently made of flow resolution within shock waves, transition and turbulence phenomenon tractability, chemical reaction modeling, and hypersonic boundary layer transition, with state-of-the-art CFD.

Dwoyer, Douglas L.↗

NASA NTRS2010

Assessment of Turbulent CFD Against STS-128 Hypersonic Flight Data

Turbulent CFD simulations are compared against surface temperature measurements of the space shuttle orbiter windward tiles at reentry flight conditions. Algebraic turbulence models are used within both the LAURA and DPLR CFD codes. The flight data are from temperature measurements obtained by seven thermocouples during the STS-128 mission (September 2009). The flight data indicate boundary layer transition onset over the Mach number range 13.5{15.5, depending upon the location on the vehicle. But the boundary layer flow appeared to be transitional down through Mach 12, based upon the flight data and CFD trends. At Mach 9 the simulations match the flight data on average within 20 F/11 C, where typical surface temperatures were approximately 1600 F/870 C.

Wood, William A.↗

NASA NTRS2011

Comparison of DSMC and CFD Solutions of Fire II Including Radiative Heating

The ability to compute rarefied, ionized hypersonic flows is becoming more important as missions such as Earth reentry, landing high mass payloads on Mars, and the exploration of the outer planets and their satellites are being considered. These flows may also contain significant radiative heating. To prepare for these missions, NASA is developing the capability to simulate rarefied, ionized flows and to then calculate the resulting radiative heating to the vehicle's surface. In this study, the DSMC codes DAC and DS2V are used to obtain charge-neutral ionization solutions. NASA s direct simulation Monte Carlo code DAC is currently being updated to include the ability to simulate charge-neutral ionized flows, take advantage of the recently introduced Quantum-Kinetic chemistry model, and to include electronic energy levels as an additional internal energy mode. The Fire II flight test is used in this study to assess these new capabilities. The 1634 second data point was chosen for comparisons to be made in order to include comparisons to computational fluid dynamics solutions. The Knudsen number at this point in time is such that the DSMC simulations are still tractable and the CFD computations are at the edge of what is considered valid. It is shown that there can be quite a bit of variability in the vibrational temperature inferred from DSMC solutions and that, from how radiative heating is computed, the electronic temperature is much better suited for radiative calculations. To include the radiative portion of heating, the flow-field solutions are post-processed by the non-equilibrium radiation code HARA. Acceptable agreement between CFD and DSMC flow field solutions is demonstrated and the progress of the updates to DAC, along with an appropriate radiative heating solution, are discussed. In addition, future plans to generate more high fidelity radiative heat transfer solutions are discussed.

Liechty, Derek S.↗

NASA NTRS1987

Computational fluid dynamics for hypersonic airbreathing airplanes

Computational fluid dynamics (CFD) technology is discussed as it relates to the computation of flowfields associated with hypersonic air-breathing airplanes. It is shown that the unique aerodynamics of these vehicles places different demands on CFD than reentry bodies do. The major areas requiring the use of advanced CFD techniques are the prediction of airframe aerodynamics, propulsion/airframe flowfield interaction, and internal engine flows.

Dwoyer, Douglas L.↗

NASA NTRS2012

Improved Finite-Volume Method for Radiative Hydrodynamics

Fully coupled simulations of hydrodynamics and radiative transfer are essential to a number of fields ranging from astrophysics to engineering applications. Of particular interest in this work are hypersonic atmospheric entries and associated experimental apparatus, e.g., shock tubes and high enthalpy testing facilities. The radiative transfer calculations must supply to the CFD a heating term in the energy equation in the form of the divergence of the radiative heat flux and the radiative heat fluxes to bounding surfaces. It is most efficient to solve the radiative transfer equation on the same grid as the CFD solution, and this work presents an algorithm with improved accuracy for such simulations on structured and unstructured grids compared to more conventional approaches. Results will be shown for shock radiation during hypersonic reentry. Issues of parallelization within a radiation sweep will also be discussed.

Wray, Alan↗

NASA NTRS2017

Computational Simulations of the NASA Langley HyMETS Arc-Jet Facility

The Hypersonic Materials Environmental Test System (HyMETS) arc-jet facility located at the NASA Langley Research Center in Hampton, Virginia, is primarily used for the research, development, and evaluation of high-temperature thermal protection systems for hypersonic vehicles and reentry systems. In order to improve testing capabilities and knowledge of the test article environment, an effort is underway to computationally simulate the flow-field using computational fluid dynamics (CFD). A detailed three-dimensional model of the arc-jet nozzle and free-jet portion of the flow-field has been developed and compared to calibration probe Pitot pressure and stagnation-point heat flux for three test conditions at low, medium, and high enthalpy. The CFD model takes into account uniform pressure and non-uniform enthalpy profiles at the nozzle inlet as well as catalytic recombination efficiency effects at the probe surface. Comparing the CFD results and test data indicates an effectively fully-catalytic copper surface on the heat flux probe of about 10% efficiency and a 2-3 kpa pressure drop from the arc heater bore, where the pressure is measured, to the plenum section, prior to the nozzle. With these assumptions, the CFD results are well within the uncertainty of the stagnation pressure and heat flux measurements. The conditions at the nozzle exit were also compared with radial and axial velocimetry. This simulation capability will be used to evaluate various three-dimensional models that are tested in the HyMETS facility. An end-to-end aerothermal and thermal simulation of HyMETS test articles will follow this work to provide a better understanding of the test environment, test results, and to aid in test planning. Additional flow-field diagnostic measurements will also be considered to improve the modeling capability.

Brune, A. J.↗

NASA NTRS2006

Understanding Columbia's Reentry Problems

Soon after the Space Shuttle Columbia accident occurred last year, a group of CFD analysts from NASA centers and private industry was organized to help determine the cause of the accident. This group was under the direction of the Applied Aeroscience and CFD Branch of the Aeroscience and Flight Mechanics Division at the Johnson Space Center. For external flow simulations, noncommercia2 CFD codes that specialize in hypersonic or high Mach number flows were used. These tools were used to determine heating rates, pressures, and temperatures for a large number of vehicle damage scenarios. Lockheed Martin Space Operations was called upon to provide CFD support in the area of internal flows within the shuttle wing cavity, and for these simulations, FLUENT 6.1 was chosen. Two large-scale, simplified models were m to understand the flow patterns once a breach of the internal wing cavity was initiated. The results were primarily used to visualize flow patterns within the wing cavity. The first CFD model included the entire lee wing without the wheel well cavity. The purpose of the first model, which did not include the reinforced carbon-carbon (RCC) cavity along the wing leading edge, was to visualize the flow field within the wing cavity immediately after the leading edge spar breach, This model assumed that the flow coming into the wing cavity was normal to the spar. It included all of the primary vents that allow for flow between the main cavities of the wing. A six-inch diameter hole was modeled in the spar at the approximate location where the spar breach was judged to have occurred, which was between RCC panels 8 and 9. The results of the modeling showed that at this location, the high temperature, high velocity gas stream entering the wing cavity impinged on the outboard wheel well cavity. Instrumentation in the Shuttle wheel well cavity registered abnormal temperatures during reentry, so the FLUENT results helped support the conclusion of the accident investigation team that the spar breach was in the RCC panel 8-9 area, and that the initial spar breach was likely entering the wing cavity normal to the spar. This model also showed that the flow entering the wing cavity tended to swirl within the cavity just outboard of the wheel well, and did not initially penetrate further into the rear cavities of the wing. The second CFD model was a 2-D simulation of the left wing cavity and the RCC cavity. It was used to visualize the flow through the RCC breach, through the wing spar breach, and into the wing cavity directly outboard of the wheel well. The purpose of this model was to verify whether or not it was possible for the flow to come into the wing cavity normal to the leading edge spar. The results from this 2-D model showed that the internal structure behind the RCC panels probably deflected the flow entering the RCC cavity so that it impinged normal to the spar. As in the 3-D model, this deflected flow stream was Found to impinge on the wheel well outer wall. This model again supported the conclusions regarding the location of the spar breach and how the flow behaved inside the wing cavity.

Paul, Thomas↗

NASA NTRS2004

Understanding Columbia's Reentry Problems

Soon after the Space Shuttle Columbia accident occurred last year, a group of CFD analysts from NASA centers and private industry was organized to help determine the cause of the accident. This group was under the direction of the Applied Aeroscience and CFD Branch of the Aeroscience and Flight Mechanics Division at the Johnson Space Center. For external flow simulations, noncommercial CFD codes that specialize in hypersonic or high Mach number flows were used. These tools were used to determine heating rates, pressures, and temperatures for a large number of vehicle damage scenarios. Lockheed Martin Space Operations was called upon to provide CFD support in the area of internal flows within the shuttle wing cavity, and or these simulations, FLUENT 6.1 was chosen. Two large-scale, simplified models were run to understand the flow patterns once a breach of the internal wing cavity was initiated. The results were primarily used to visualize flow patterns within the wing cavity. The first CFD model included the entire left wing without the wheel. well cavity. The purpose of the first model, which did not include the reinforced carbon-carbon (RCC) cavity along the wing leading edge, was to visualize the flow field within the wing cavity immediately after the leading edge spar breach, This model assumed that the flow coming into the wing cavity was nom1 to the spar. It included all o f the primary vents that allow for flow between the main cavities of the wing. A six-inch diameter hole was modeled in the spar at the approximate location where the spar breach was judged to have occurred, which was between RCC panels 8 and 9. The results of the modeling showed that at this location, the high temperature, high velocity gas stream entering the wing cavity impinged on the outboard wheel well cavity. Instrumentation in the Shuttle wheel well cavity registered abnormal temperatures during reentry, so the FLUENT results helped support the conclusion of the accident investigation team that the spar breach was in the RCC panel 8-9 area, and that the initial spar breach was likely entering the wing cavity normal to the spar. This model also showed that the flow entering the wing cavity tended to swirl within the cavity just outboard of the wheel well, and did not initially penetrate further into the rear cavities of the wing. The second CFD model was a 2-D simulation of the left wing cavity and the RCC cavity. It was used to visualize the flow through the RCC breach, through the wing spar breach, and into the wing cavity directly outboard of the wheel well. The purpose of this model was to verify whether or not it was possible for the flow to come into the wing cavity normal to the leading edge spar. The results from this 2-D model showed that the internal structure behind the RCC panels probably deflected the flow entering the RCC cavity so that it impinged normal to the spar. As in the 3-D model, this deflected flow stream was found to impinge on the wheel well outer wall. This model again supported the conclusions regarding the location of the spar breach and how the flow behaved inside the wing cavity.

Paul, Thomas H.↗

NASA NTRS2022

Design of Hypervelocity Flow Generator (HFG) and Its Diagnostics

Ground facilities for hypersonic research are a key element for successful development of aerodynamically proven hypervelocity vehicles. Design concepts and diagnostics of a hypervelocity flow generator (HFG) were made as a test platform for hypersonic/hypervelocity spacecraft models at the NASA Langley Research Center. The HFG is a hypersonic flow field generator using optically heated gas which is blown into an 80 cu m vacuum chamber. The vacuum chamber is kept at a stable vacuum pressure with a combination of three large vacuum pumps, while the HFG is in the test mode. The HFG provides a relatively small test section with approximately a 20 cm window. This facility was designed to generate 2.45 km/sec of flow speed, and potentially generate a continuous flow with the nozzle and vacuum system. The window in test section provides a direct view of the shock wave around a model in order to measure temperature, pressure, and density profile within the shock layer. One of the key test goals under this project is to understand why the emission spectra from the standing shockwave plasma predicted by Lora-Loran codes are significantly different from the measured emission spectra from the Flight Investigation Reentry Environment (FIRE II) Flight. The correct estimate of the thermal loading on the leading edge of hypersonic vehicles greatly affects the aerodynamic design, the material selection for the vehicle, and the cooling requirement and can be obtained by the precise modeling of emission spectra from shockwave plasma. However, the estimation of thermal loading is not an easy task due to complex non-equilibrium radiative process within high temperature shock layers that still falls into a category of cold plasma. Direct flight experiments are the most desirable, but not a cost-effective approach. Analysis by computational fluid dynamics (CFD) offers many test flexibilities. However, the CFD codes must be fully tested and validated with experimental data before the codes are effectively used for practical design. Large discrepancies between experiments and codes appear in hypersonic/hypervelocity flow regimes at high altitudes of 60 km ~ 90 km. This HFG facility offers some important parameters for CFD code validation, such as collision cross-sections, relaxation times, reaction rate coefficients and transportation coefficients. The HFG test facility is based on the ejection flow of high temperature gas heated over to 3500 K through a nozzle. The tungsten gas chamber of the HFG is heated up to a desired temperature by a 60 kW optical power beam source. This system consists of an optical power source, a thermal chamber, an expansion nozzle, a test section, and an 80 cu m vacuum tank. 60 kW optical input power is obtained from the 150 kW Vortek arc lamp system (by Vortek Industries, Vancouver, Canada). This optical beam is focused to heat the gas chamber within which a flow media is heated. The maximum achievable temperature of the flow medium reached approximately 3500 K or even higher but is limited by the melting point of the chamber material used. The exhaust velocity through the nozzle was determined by the stagnation temperature and the molecular weight of the working medium at the test section. To provide design parameters, a NASA Chemical Equilibrium with Application (CEA) computer program is used for the simulation of aerothermal data. This CEA program can calculate chemical equilibrium and properties of complex mixtures using shock tube parameters. For nitrogen gas at 2666 K stagnation temperature, the maximum achievable velocity at the test section is approximately 2.45 km/sec which is within the range of the thermal velocity of 8000 K shock layer. Based on the calculation through the CEA program, the design parameters of a HFG were determined and implemented for the test section that includes an expansion nozzle. The installed test section of the experimental facility can sustain a condition of a re-entry vehicle from the Space at an altitude of 60-90 km. After installation of the HFG, the system was fully tested and its operational parameters were measured. An 80 cu m vacuum chamber of HFG was set at 1 torr level to keep a stable downstream condition. The pumping time to reach the minimum vacuum pressure (~ 1 torr) at the test chamber from atmospheric pressure was approximately an hour using Kinney (MBV-14000/MB -1600/KT-300) and Stokes (Model 1772 and 412) pumps. Such a setup condition allowed a continued stable operation of the HFG experiment with flowrates through 1-, 3-, or 5-mm diameters of nozzle throat. The flow characteristics of the HFG for various operating conditions were performed using a focused Schlieren method. At 0.8 torr chamber pressure, a barrel shock was observed at the test section. With a sphere obstacle of 12 mm diameter in the flow, a bow shock (~ 2-mm thickness) was observed by a focused Schlieren visualization method.

Hypervelocity flow↗

NASA NTRSDate not supplied

Pterodactyl: Aerodynamic and Aerothermal Modeling for a Symmetric Deployable Earth Entry Vehicle with Flaps

NASA’s Pterodactyl project has investigated a deployable atmospheric entry vehicle integrated with a flap control system that provides precision targeting during reentry. The control system consists of eight flaps mounted at the edge of a heatshield that can deflect in and out of the flow. An aerodynamic and aerothermodynamic analysis process was developed for preliminary vehicle design and aerodynamic database generation using engineering and CFD tools with varying levels of fidelity. The objective of this analysis was to: 1) understand the inherent aerodynamics, 2) provide an aerodynamics database for stability and control analysis, and 3) provide qualitative and quantitative aeroheating analysis for Thermal Protection System modeling of the flaps. A high fidelity Euler code, Cart3D, was used to resolve complex flow features such as secondary shocks and shock impingement. A wide range of supersonic (Mach 2) and hypersonic Mach numbers (up to Mach 40) were tested with an Earth atmosphere model. A process was developed to utilize the adaptive volume mesh generator utility of the perfect gas model of Cart3D to create meshes with high cell efficiency and numerical stability prior to running a 2nd order accurate solution with a real gas model. High-fidelity aerothermal CFD simulations were performed using US3D to further improve the aerothermal analysis on hypersonic flow around a complex entry vehicle shape including viscosity, chemical reactions of air species, vibrational energy, and catalytic surface reactions. In this process, it was found that the flap control system provided multi-axis control that can be utilized for entry precision targeting. Additionally, the Pterodactyl vehicle can achieve up to a trim L/D of 0.2. Finally, the increased fidelity of the aerothermal heating environments revealed that the shear stress contributes to increasing the heating on the flaps.

Deployable Entry Vehicle↗

NASA NTRSDate not supplied

Pterodactyl: Aerodynamic and Aerothermal Modeling for a Symmetric Deployable Earth Entry Vehicle with Flaps

Deployable Entry Vehicle↗

NASA NTRS1993

Two-layer convective heating prediction procedures and sensitivities for blunt body reentry vehicles

This paper provides a description of procedures typically used to predict convective heating rates to hypersonic reentry vehicles using the two-layer method. These procedures were used to compute the pitch-plane heating distributions to the Apollo geometry for a wind tunnel test case and for three flight cases. Both simple engineering methods and coupled inviscid/boundary layer solutions were used to predict the heating rates. The sensitivity of the heating results in the choice of metrics, pressure distributions, boundary layer edge conditions, and wall catalycity used in the heating analysis were evaluated. Streamline metrics, pressure distributions, and boundary layer edge properties were defined from perfect gas (wind tunnel case) and chemical equilibrium and nonequilibrium (flight cases) inviscid flow-field solutions. The results of this study indicated that the use of CFD-derived metrics and pressures provided better predictions of heating when compared to wind tunnel test data. The study also showed that modeling entropy layer swallowing and ionization had little effect on the heating predictions.

Bouslog, Stanley A.↗

NASA NTRS2013

Extension of a Kinetic Approach to Chemical Reactions to Electronic Energy Levels and Reactions Involving Charged Species With Application to DSMC Simulations

The ability to compute rarefied, ionized hypersonic flows is becoming more important as missions such as Earth reentry, landing high mass payloads on Mars, and the exploration of the outer planets and their satellites are being considered. Recently introduced molecular-level chemistry models that predict equilibrium and nonequilibrium reaction rates using only kinetic theory and fundamental molecular properties are extended in the current work to include electronic energy level transitions and reactions involving charged particles. These extensions are shown to agree favorably with reported transition and reaction rates from the literature for nearequilibrium conditions. Also, the extensions are applied to the second flight of the Project FIRE flight experiment at 1634 seconds with a Knudsen number of 0.001 at an altitude of 76.4 km. In order to accomplish this, NASA's direct simulation Monte Carlo code DAC was rewritten to include the ability to simulate charge-neutral ionized flows, take advantage of the recently introduced chemistry model, and to include the extensions presented in this work. The 1634 second data point was chosen for comparisons to be made in order to include a CFD solution. The Knudsen number at this point in time is such that the DSMC simulations are still tractable and the CFD computations are at the edge of what is considered valid because, although near-transitional, the flow is still considered to be continuum. It is shown that the inclusion of electronic energy levels in the DSMC simulation is necessary for flows of this nature and is required for comparison to the CFD solution. The flow field solutions are also post-processed by the nonequilibrium radiation code HARA to compute the radiative portion of the heating and is then compared to the total heating measured in flight.

Liechty, Derek S.↗

NASA NTRS2014

Extension of a Kinetic Approach to Chemical Reactions to Electronic Energy Levels and Reactions Involving Charged Species with Application to DSMC Simulations

The ability to compute rarefied, ionized hypersonic flows is becoming more important as missions such as Earth reentry, landing high mass payloads on Mars, and the exploration of the outer planets and their satellites are being considered. Recently introduced molecular-level chemistry models that predict equilibrium and nonequilibrium reaction rates using only kinetic theory and fundamental molecular properties are extended in the current work to include electronic energy level transitions and reactions involving charged particles. These extensions are shown to agree favorably with reported transition and reaction rates from the literature for near-equilibrium conditions. Also, the extensions are applied to the second flight of the Project FIRE flight experiment at 1634 seconds with a Knudsen number of 0.001 at an altitude of 76.4 km. In order to accomplish this, NASA's direct simulation Monte Carlo code DAC was rewritten to include the ability to simulate charge-neutral ionized flows, take advantage of the recently introduced chemistry model, and to include the extensions presented in this work. The 1634 second data point was chosen for comparisons to be made in order to include a CFD solution. The Knudsen number at this point in time is such that the DSMC simulations are still tractable and the CFD computations are at the edge of what is considered valid because, although near-transitional, the flow is still considered to be continuum. It is shown that the inclusion of electronic energy levels in the DSMC simulation is necessary for flows of this nature and is required for comparison to the CFD solution. The flow field solutions are also post-processed by the nonequilibrium radiation code HARA to compute the radiative portion.

Liechty, Derek S.↗