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CFD analysis of turbopump volutes

An effort is underway to develop a procedure for the regular use of CFD analysis in the design of turbopump volutes. Airflow data to be taken at NASA Marshall will be used to validate the CFD code and overall procedure. Initial focus has been on preprocessing (geometry creation, translation, and grid generation). Volute geometries have been acquired electronically and imported into the CATIA CAD system and RAGGS (Rockwell Automated Grid Generation System) via the IGES standard. An initial grid topology has been identified and grids have been constructed for turbine inlet and discharge volutes. For CFD analysis of volutes to be used regularly, a procedure must be defined to meet engineering design needs in a timely manner. Thus, a compromise must be established between making geometric approximations, the selection of grid topologies, and possible CFD code enhancements. While the initial grid developed approximated the volute tongue with a zero thickness, final computations should more accurately account for the geometry in this region. Additionally, grid topologies will be explored to minimize skewness and high aspect ratio cells that can affect solution accuracy and slow code convergence. Finally, as appropriate, code modifications will be made to allow for new grid topologies in an effort to expedite the overall CFD analysis process.

Ascoli, Edward P.↗

CFD Modeling of Turbulent Duct Flows for Coolant Channel Analysis

The design of modern liquid rocket engines requires the analysis of chamber coolant channels to maximize the heat transfer while minimizing the coolant flow. Coolant channels often do not remain at a constant cross section or at uniform curvature. New designs require higher aspect ratio coolant channels than previously used. To broaden the analysis capability and to complement standard analysis tools an investigation on the accuracy of CFD predictions for coolant channel flow has been initiated. Validation of CFD capabilities for coolant channel analysis will enhance the capabilities for optimizing design parameters without resorting to extensive experimental testing. The eventual goal is to use CFD to determine the flow fields of unique coolant channel designs and therefore determine critical heat transfer coefficients. In this presentation the accuracy of a particular CFD code is evaluated for turbulent flows. The first part of the presentation is a comparison of numerical results to existing cold flow data for square curved ducts (NASA CR-3367, 'Measurements of Laminar and Turbulent Flow in a Curved Duct with Thin Inlet Boundary Layers'). The results of this comparison show good agreement with the relatively coarse experimental data. The second part of the presentation compares two cases of higher aspect ratio channels (AR=2.5,10) to show changes in axial and secondary flow strength. These cases match experimental work presently in progress and will be used for future validation. The comparison shows increased secondary flow strength of the higher aspect ratio case due to the change in radius of curvature. The presentation includes a test case with a heated wall to demonstrate the program's capability. The presentation concludes with an outline of the procedure used to validate the CFD code for future design analysis.

Ungewitter, Ronald J.↗

CFD Study of Turbo-Ramjet Interactions in Hypersonic Airbreathing Propulsion System

Advanced airbreathing propulsion systems used in Mach 4-6 mission scenarios, usually involve turbo-ramjet configurations. As the engines transition from turbojet to ramjet, there is an operational envelope where both engines operate simultaneously. In the first phase of our study, an over/under nozzle configuration was analyzed. The two plumes from the turbojet and ramjet interact at the end of a common 2-D cowl, where they both reach an approximate Mach 3.0 condition and then jointly expand to Mach 3.6 at the common nozzle exit plane. For the problem analyzed, the turbojet engine operates at a higher nozzle pressure ratio than the ramjet, causes the turbojet plume overpowers the ramjet plume, deflecting it approximately 12 degrees downward and in turn the turbojet plume is deflected 6 degrees upward. In the process, shocks were formed at the deflections and a shear layer formed at the confluence of the two jets. This particular case was experimentally tested and the data were used to compare with a computational fluid dynamics (CFD) study using the PARC2D code. The CFD results were in good agreement with both static pressure distributions on the cowl separator and on nozzle walls. The thrust coefficients were also in reasonable agreement. In addition, inviscid relationships were developed around the confluence point, where the two exhaust jets meet, and these results compared favorably with the CFD results. In the second phase of our study, a 3-D CFD solution was generated to compare with the 2-D solution. The major difference between the 2-D and 3-D solutions was the interaction of the shock waves, generated by the plume interactions, on the sidewall. When a shock wave interacts with a sidewall and sidewall boundary layer, it is called a glancing shock sidewall interaction. These interactions entrain boundary layer flow down the shockline into a vortical flow pattern. The 3-D plots show the streamlines being entrained down the shockline. The pressure of the flow also decreases slightly as the sidewall is approached. Other difference between the 2-D and 3-D solutions were a lowering of the nozzle thrust coefficient value from 0.9850 (2-D) to 0.9807 (3-D), where the experimental value was 0.9790. In the third phase of our study, a different turbo-ramjet configuration was analyzed. The confluence of a supersonic turbojet and a subsonic ramjet in the turbine based combined-cycle (TBCC) propulsion system was studied by a 2-D CFD code. In the analysis, Mach 1.4 primary turbojet was mixed with the subsonic ramjet secondary flow in an ejector mode operation. Reasonable agreements were obtained with the supplied I-D TBCC solutions. For low downstream backpressure, the Fabri choke condition (Break-Point condition) was observed in the secondary flow within mixing zone. For sufficient high downstream backpressure, the Fabri choke no longer exist, the ramjet flow was reduced and the ejector flow became backpressure dependent. Highly non-uniform flow at ejector exit were observed, indicated that for smooth downstream combustion, the mixing of the two streams probably required some physical devices.

Chang, Ing↗

Computational Fluid Dynamics (CFD) Analysis for the Reduction of Impeller Discharge Flow Distortion

The use of Computational Fluid Dynamics (CFD) in the design and analysis of high performance rocket engine pumps has increased in recent years. This increase has been aided by the activities of the Marshall Space Flight Center (MSFC) Pump Stage Technology Team (PSTT). The team's goals include assessing the accuracy and efficiency of several methodologies and then applying the appropriate methodology(s) to understand and improve the flow inside a pump. The PSTT's objectives, team membership, and past activities are discussed in Garcia1 and Garcia2. The PSTT is one of three teams that form the NASA/MSFC CFD Consortium for Applications in Propulsion Technology (McConnaughey3). The PSTT first applied CFD in the design of the baseline consortium impeller. This impeller was designed for the Space Transportation Main Engine's (STME) fuel turbopump. The STME fuel pump was designed with three impeller stages because a two-stage design was deemed to pose a high developmental risk. The PSTT used CFD to design an impeller whose performance allowed for a two-stage STME fuel pump design. The availability of this design would have lead to a reduction in parts, weight, and cost had the STME reached production. One sample of the baseline consortium impeller was manufactured and tested in a water rig. The test data showed that the impeller performance was as predicted and that a two-stage design for the STME fuel pump was possible with minimal risk. The test data also verified another CFD predicted characteristic of the design that was not desirable. The classical 'jet-wake' pattern at the impeller discharge was strengthened by two aspects of the design: by the high head coefficient necessary for the required pressure rise and by the relatively few impeller exit blades, 12, necessary to reduce manufacturing cost. This 'jet-wake pattern produces an unsteady loading on the diffuser vanes and has, in past rocket engine programs, lead to diffuser structural failure. In industrial applications, this problem is typically avoided by increasing the space between the impeller and the diffuser to allow the dissipation of this pattern and, hence, the reduction of diffuser vane unsteady loading. This approach leads to small performance losses and, more importantly in rocket engine applications, to significant increases in the pump's size and weight. This latter consideration typically makes this approach unacceptable in high performance rocket engines.

Garcia, R.↗

Inlet-Compressor Analysis using Coupled CFD Codes

Propulsion performance and operability are key factors in the development of a successful aircraft. For high-speed supersonic aircraft, mixed-compression inlets offer high performance but are susceptible to an instability referred to as unstart. An unstart occurs when a disturbance originating in the atmosphere or the engine causes the shock system to be expelled from the inlet. This event can have adverse effects on control of the aircraft, which is unacceptable for a passenger plane such as the high speed civil transport (HSCT). The ability to predict the transient response of such inlets to flow perturbations is, therefore, important to the proper design of the inlet and the control measures used to prevent unstart. Computational fluid dynamics (CFD) is having an increasing role in the analysis of individual propulsion components. Isolated inlet studies are relatively easy to perform, but a major uncertainty is the boundary condition used at the inlet exit to represent the engine - the so-called compressor face boundary condition. A one-dimensional (1-D) Euler inlet simulation showed that the predicted inlet unstart tolerance to free-stream pressure perturbations can vary by as much as a factor of about six, depending on the boundary condition used. Obviously a thorough understanding of dynamic interactions between inlets and compressors/fans is required to provide the proper boundary condition. To aid in this understanding and to help evaluate possible boundary conditions, an inlet-engine experiment was conducted at the University of Cincinnati. The interaction of acoustic pulses, generated in the inlet, with the engine were investigated. Because of the availability of experimental data for validation, it was decided to simulate the experiment using CFD. The philosophy here is that the inlet-engine system is best simulated by coupling (existing) specialized CFD component-codes. The objectives of this work were to aid in a better understanding of inlet-compressor interaction physics and the formulation of a more realistic compressor-face boundary condition for time-accurate CFD simulations of inlets. Previous simulations have used 1-D Euler engine simulations in conjunction with 1-D Euler and axisymmetric Euler inlet simulations. This effort is a first step toward CFD simulation of an entire engine by coupling multidimensional component codes.

Cole, Gary↗

CFD Simulation of Liquid Rocket Engine Injectors

Detailed design issues associated with liquid rocket engine injectors and combustion chamber operation require CFD methodology which simulates highly three-dimensional, turbulent, vaporizing, and combusting flows. The primary utility of such simulations involves predicting multi-dimensional effects caused by specific injector configurations. SECA, Inc. and Engineering Sciences, Inc. have been developing appropriate computational methodology for NASA/MSFC for the past decade. CFD tools and computers have improved dramatically during this time period; however, the physical submodels used in these analyses must still remain relatively simple in order to produce useful results. Simulations of clustered coaxial and impinger injector elements for hydrogen and hydrocarbon fuels, which account for real fluid properties, is the immediate goal of this research. The spray combustion codes are based on the FDNS CFD code' and are structured to represent homogeneous and heterogeneous spray combustion. The homogeneous spray model treats the flow as a continuum of multi-phase, multicomponent fluids which move without thermal or velocity lags between the phases. Two heterogeneous models were developed: (1) a volume-of-fluid (VOF) model which represents the liquid core of coaxial or impinger jets and their atomization and vaporization, and (2) a Blob model which represents the injected streams as a cloud of droplets the size of the injector orifice which subsequently exhibit particle interaction, vaporization, and combustion. All of these spray models are computationally intensive, but this is unavoidable to accurately account for the complex physics and combustion which is to be predicted, Work is currently in progress to parallelize these codes to improve their computational efficiency. These spray combustion codes were used to simulate the three test cases which are the subject of the 2nd International Workshop on-Rocket Combustion Modeling. Such test cases are considered by these investigators to be very valuable for code validation because combustion kinetics, turbulence models and atomization models based on low pressure experiments of hydrogen air combustion do not adequately verify analytical or CFD submodels which are necessary to simulate rocket engine combustion. We wish to emphasize that the simulations which we prepared for this meeting are meant to test the accuracy of the approximations used in our general purpose spray combustion models, rather than represent a definitive analysis of each of the experiments which were conducted. Our goal is to accurately predict local temperatures and mixture ratios in rocket engines; hence predicting individual experiments is used only for code validation. To replace the conventional JANNAF standard axisymmetric finite-rate (TDK) computer code 2 for performance prediction with CFD cases, such codes must posses two features. Firstly, they must be as easy to use and of comparable run times for conventional performance predictions. Secondly, they must provide more detailed predictions of the flowfields near the injector face. Specifically, they must accurately predict the convective mixing of injected liquid propellants in terms of the injector element configurations.

Farmer, Richard↗

Emerging CFD Capabilities and Outlook: A NASA Langley Perspective

COMSAC goals include increasing the acceptance of CFD as a viable tool for S&C predictions, as well as to focus CFD development and improvement towards the needs of the S&C community. We view this as a symbiotic relationship, with increasing improvement of CFD promoting increasing acceptance by the S&C community, and increasing acceptance spurring further improvements. In this presentation we want to provide an overview for the non CFD expert of current CFD strengths and weaknesses, as well as to highlight a few emerging capabilities that we feel will lead toward increased usefulness in S&C applications.

Biedron, Robert T.↗

Analytic Corrections to CFD Heating Predictions Accounting for Changes in Surface Catalysis

A new approach for combining the insight afforded by integral boundary-layer analysis with comprehensive (but time intensive) computational fluid dynamic (CFD) flowfield solutions of the thin-layer Navier-Stokes equations is described. The approach extracts CFD derived quantities at the wall and at the boundary layer edge for inclusion in a post-processing boundary-layer analysis. It allows a designer at a work-station to address two questions, given a single CFD solution. (1) How much does the heating change for a thermal protection system (TPS) with different catalytic properties than was used in the original CFD solution? (2) How does the heating change at the interface of two different TPS materials with an abrupt change in catalytic efficiency? The answer to the second question is particularly important, because abrupt changes from low to high catalytic efficiency can lead to localized increase in heating which exceeds the usually conservative estimate provided by a fully catalytic wall assumption. Capabilities of this approach for application to Reusable Launch Vehicle (RLV) design are demonstrated. If the definition of surface catalysis is uncertain early in the design process, results show that fully catalytic wall boundary conditions provide the best baseline for CFD design points.

Gnoffo, Peter A.↗

Recent Enhancements to the Development of CFD-Based Aeroelastic Reduced-Order Models

Recent enhancements to the development of CFD-based unsteady aerodynamic and aeroelastic reduced-order models (ROMs) are presented. These enhancements include the simultaneous application of structural modes as CFD input, static aeroelastic analysis using a ROM, and matched-point solutions using a ROM. The simultaneous application of structural modes as CFD input enables the computation of the unsteady aerodynamic state-space matrices with a single CFD execution, independent of the number of structural modes. The responses obtained from a simultaneous excitation of the CFD-based unsteady aerodynamic system are processed using system identification techniques in order to generate an unsteady aerodynamic state-space ROM. Once the unsteady aerodynamic state-space ROM is generated, a method for computing the static aeroelastic response using this unsteady aerodynamic ROM and a state-space model of the structure, is presented. Finally, a method is presented that enables the computation of matchedpoint solutions using a single ROM that is applicable over a range of dynamic pressures and velocities for a given Mach number. These enhancements represent a significant advancement of unsteady aerodynamic and aeroelastic ROM technology.

Silva, Walter A.↗

Use of HART-II Measured Motion in CFD

This presentation examines the use of HART-II measured rotor blade motion in computational fluid dynamics (CFD). Historically, comprehensive analyses were used for input to acoustic calculations. These analyses focused on lifting line aerodynamics and beam models. However, there is a a need to evolve lifting line aerodynamics to first principles, notably the use of CFD instead of lifting line. The current analysis focuses on CFD and computational structural dynamics (CSD) coupling. Beam models are still very good (CSD is typically from comprehensive analysis), but generally CFD replaced aerodynamics in comprehensive analysis. This presentation examines both CFD and CSD individually and includes predictions using measured motion as well as predictions using measured motion versus coupled motion and calculations of "correct" airloads, noise and vibration.

Boyd, D. Douglas, Jr.↗

Integration of Engine, Plume, and CFD Analyses in Conceptual Design of Low-Boom Supersonic Aircraft

This paper documents an integration of engine, plume, and computational fluid dynamics (CFD) analyses in the conceptual design of low-boom supersonic aircraft, using a variable fidelity approach. In particular, the Numerical Propulsion Simulation System (NPSS) is used for propulsion system cycle analysis and nacelle outer mold line definition, and a low-fidelity plume model is developed for plume shape prediction based on NPSS engine data and nacelle geometry. This model provides a capability for the conceptual design of low-boom supersonic aircraft that accounts for plume effects. Then a newly developed process for automated CFD analysis is presented for CFD-based plume and boom analyses of the conceptual geometry. Five test cases are used to demonstrate the integrated engine, plume, and CFD analysis process based on a variable fidelity approach, as well as the feasibility of the automated CFD plume and boom analysis capability.

Li, Wu↗

Assessment of Computational Fluid Dynamics (CFD) Models for Shock Boundary-Layer Interaction

A workshop on the computational fluid dynamics (CFD) prediction of shock boundary-layer interactions (SBLIs) was held at the 48th AIAA Aerospace Sciences Meeting. As part of the workshop numerous CFD analysts submitted solutions to four experimentally measured SBLIs. This paper describes the assessment of the CFD predictions. The assessment includes an uncertainty analysis of the experimental data, the definition of an error metric and the application of that metric to the CFD solutions. The CFD solutions provided very similar levels of error and in general it was difficult to discern clear trends in the data. For the Reynolds Averaged Navier-Stokes methods the choice of turbulence model appeared to be the largest factor in solution accuracy. Large-eddy simulation methods produced error levels similar to RANS methods but provided superior predictions of normal stresses.

DeBonis, James R.↗

Assessment of CFD Hypersonic Turbulent Heating Rates for Space Shuttle Orbiter

Turbulent CFD codes are assessed for the prediction of convective heat transfer rates at turbulent, hypersonic conditions. Algebraic turbulence models are used within the DPLR and LAURA CFD codes. The benchmark heat transfer rates are derived from thermocouple measurements of the Space Shuttle orbiter Discovery windward tiles during the STS-119 and STS-128 entries. The thermocouples were located underneath the reaction-cured glass coating on the thermal protection tiles. Boundary layer transition flight experiments conducted during both of those entries promoted turbulent flow at unusually high Mach numbers, with the present analysis considering Mach 10{15. Similar prior comparisons of CFD predictions directly to the flight temperature measurements were unsatisfactory, showing diverging trends between prediction and measurement for Mach numbers greater than 11. In the prior work, surface temperatures and convective heat transfer rates had been assumed to be in radiative equilibrium. The present work employs a one-dimensional time-accurate conduction analysis to relate measured temperatures to surface heat transfer rates, removing heat soak lag from the flight data, in order to better assess the predictive accuracy of the numerical models. The turbulent CFD shows good agreement for turbulent fuselage flow up to Mach 13. But on the wing in the wake of the boundary layer trip, the inclusion of tile conduction effects does not explain the prior observed discrepancy in trends between simulation and experiment; the flight heat transfer measurements are roughly constant over Mach 11-15, versus an increasing trend with Mach number from the CFD.

Wood, William A.↗

Pre-Test CFD for the Design and Execution of the Enhanced Injection and Mixing Project at NASA Langley Research Center

With the increasing costs of physics experiments and simultaneous increase in availability and maturity of computational tools it is not surprising that computational fluid dynamics (CFD) is playing an increasingly important role, not only in post-test investigations, but also in the early stages of experimental planning. This paper describes a CFD-based effort executed in close collaboration between computational fluid dynamicists and experimentalists to develop a virtual experiment during the early planning stages of the Enhanced Injection and Mixing project at NASA Langley Research Center. This projects aims to investigate supersonic combustion ramjet (scramjet) fuel injection and mixing physics, improve the understanding of underlying physical processes, and develop enhancement strategies and functional relationships relevant to flight Mach numbers greater than 8. The purpose of the virtual experiment was to provide flow field data to aid in the design of the experimental apparatus and the in-stream rake probes, to verify the nonintrusive measurements based on NO-PLIF, and to perform pre-test analysis of quantities obtainable from the experiment and CFD. The approach also allowed for the joint team to develop common data processing and analysis tools, and to test research ideas. The virtual experiment consisted of a series of Reynolds-averaged simulations (RAS). These simulations included the facility nozzle, the experimental apparatus with a baseline strut injector, and the test cabin. Pure helium and helium-air mixtures were used to determine the efficacy of different inert gases to model hydrogen injection. The results of the simulations were analyzed by computing mixing efficiency, total pressure recovery, and stream thrust potential. As the experimental effort progresses, the simulation results will be compared with the experimental data to calibrate the modeling constants present in the CFD and validate simulation fidelity. CFD will also be used to investigate different injector concepts, improve understanding of the flow structure and flow physics, and develop functional relationships. Both RAS and large eddy simulations (LES) are planned for post-test analysis of the experimental data.

Drozda, Tomasz G.↗

Variability in the Propagation Phase of CFD-Based Noise Prediction: Summary of Results From Category 8 of the BANC-III Workshop

The usage of Computational Fluid Dynamics (CFD) in noise prediction typically has been a two part process: accurately predicting the flow conditions in the near-field and then propagating the noise from the near-field to the observer. Due to the increase in computing power and the cost benefit when weighed against wind tunnel testing, the usage of CFD to estimate the local flow field of complex geometrical structures has become more routine. Recently, the Benchmark problems in Airframe Noise Computation (BANC) workshops have provided a community focus on accurately simulating the local flow field near the body with various CFD approaches. However, to date, little effort has been given into assessing the impact of the propagation phase of noise prediction. This paper includes results from the BANC-III workshop which explores variability in the propagation phase of CFD-based noise prediction. This includes two test cases: an analytical solution of a quadrupole source near a sphere and a computational solution around a nose landing gear. Agreement between three codes was very good for the analytic test case, but CFD-based noise predictions indicate that the propagation phase can introduce 3dB or more of variability in noise predictions.

Lopes, Leonard↗

Validation of High-Resolution CFD Method for Slosh Damping Extraction of Baffled Tanks

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involve the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations and knowledge were mainly carried out by extensive experimental studies. A Volume-Of-Fluid (VOF) based CFD program developed at NASA MSFC was applied to extract slosh damping in a baffled tank from the first principle. First, experimental data using water with subscale smooth wall tank were used as the baseline validation. CFD simulation was demonstrated to be capable of accurately predicting natural frequency and very low damping value from the smooth wall tank at different fill levels. The damping due to a ring baffle at different liquid fill levels from barrel section and into the upper dome was then investigated to understand the slosh damping physics due to the presence of a ring baffle. Based on this study, the Root-Mean-Square error of our CFD simulation in estimating slosh damping was less than 4.8%, and the maximum error was less than 8.5%. Scalability of subscale baffled tank test using water was investigated using the validated CFD tool, and it was found that unlike the smooth wall case, slosh damping with baffle is almost independent of the working fluid and it is reasonable to apply water test data to the full scale LOX tank when the damping from baffle is dominant. On the other hand, for the smooth wall, the damping value must be scaled according to the Reynolds number. Comparison of experimental data, CFD, with the classical and modified Miles equations for upper dome was made, and the limitations of these semi-empirical equations were identified.

Yang, H. Q.↗

Predictive Evaluations of Oxygen-Rich Hydrocarbon Combustion Gas-Centered Swirl Coaxial Injectors using a Flamelet-Based 3-D CFD Simulation Approach

NASA Marshall Space Flight Center (MSFC) has embarked upon a joint project with the Air Force to improve the state-of-the-art of space application combustion device design and operational understanding. One goal of the project is to design, build and hot-fire test a 40,000 pound-thrust Oxygen/Rocket Propellant-2 (RP-2) Oxygen-Rich staged engine at MSFC. The overall project goals afford the opportunity to test multiple different injector designs and experimentally evaluate the any effect on the engine performance and combustion dynamics. To maximize the available test resources and benefits, pre-test, combusting flow, Computational Fluid Dynamics (CFD) analysis was performed on the individual injectors to guide the design. The results of the CFD analysis were used to design the injectors for specific, targeted fluid dynamic features and the analysis results also provided some predictive input for acoustic and thermal analysis of the main Thrust Chamber Assembly (TCA). MSFC has developed and demonstrated the ability to utilize a computationally efficient, flamelet-based combustion model to guide the pre-test design of single-element Gas Centered Swirl Coaxial (GCSC) injectors. Previous, Oxygen/RP-2 simulation models utilizing the Loci-STREAM flow solver, were validated using single injector test data from the EC-1 Air Force test facility. The simulation effort herein is an extension of the validated, CFD driven, single-injector design approach applied to single injectors which will be part of a larger engine array. Time-accurate, Three-Dimensional, CFD simulations were performed for five different classes of injector geometries. Simulations were performed to guide the design of the injector to achieve a variety of intended performance goals. For example, two GCSC injectors were designed to achieve stable hydrodynamic behavior of the propellant circuits while providing the largest thermal margin possible within the design envelope. While another injector was designed to purposefully create a hydrodynamic instability in the fuel supply circuit as predicted by the CFD analysis. Future multi-injector analysis and testing will indicate what if any changes occur in the predicted behavior for the single-element injector when the same injector geometry is placed in a multi-element array.

Richardson, Brian R.↗

Comparison of CFD and DSMC Using Calibrated Transport Parameters

Hypersonic re-entry flows span a wide range of length scales where regions of both rarefied and continuum flow exist. Traditional computational fluid dynamics (CFD) techniques do not provide an accurate solution for the rarefied regions of such ‘mixed’ flow fields. Although direct simulation Monte Carlo (DSMC) can be used to accurately capture both the continuum and rarefied features of ‘mixed’ flow fields, they are computationally expensive when employed to simulate the low Knudsen number continuum regimes. Thus, a hybrid framework for seamlessly combining the two methodologies, CFD and DSMC, continues to be a topic of significant research effort. Ensuring consistency in the reaction kinetics and transport models employed within CFD and DSMC is a crucial requirement for obtaining a reliable solution from a hybrid framework for combined continuum/rarefied high speed flows. This paper represents one of the first studies to utilize the calibrated transport parameters developed to ensure consistency between CFD and DSMC solvers. The new variable soft sphere (VSS) parameters are compared to both previous “standard” variable hard sphere (VHS) parameters and also to solutions from the CFD transport properties that the new parameters were developed to reproduce.

Liechty, D. S.↗