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High Fidelity System Simulation of Multiple Components in Support of the UEET Program

The High Fidelity System Simulation effort has addressed various important objectives to enable additional capability within the NPSS framework. The scope emphasized High Pressure Turbine and High Pressure Compressor components. Initial effort was directed at developing and validating intermediate fidelity NPSS model using PD geometry and extended to high-fidelity NPSS model by overlaying detailed geometry to validate CFD against rig data. Both "feedforward" and feedback" approaches of analysis zooming was employed to enable system simulation capability in NPSS. These approaches have certain benefits and applicability in terms of specific applications "feedback" zooming allows the flow-up of information from high-fidelity analysis to be used to update the NPSS model results by forcing the NPSS solver to converge to high-fidelity analysis predictions. This apporach is effective in improving the accuracy of the NPSS model; however, it can only be used in circumstances where there is a clear physics-based strategy to flow up the high-fidelity analysis results to update the NPSS system model. "Feed-forward" zooming approach is more broadly useful in terms of enabling detailed analysis at early stages of design for a specified set of critical operating points and using these analysis results to drive design decisions early in the development process.

Plybon, Ronald C.↗

Application of the CATNLF Design Method to a Transonic Transport Empennage Using CDISC

A novel Crossflow Attenuated Natural Laminar Flow (CATNLF) design method has been developed to achieve laminar flow on aircraft empennage at transonic flight conditions. This approach has been applied to the design of a nonlifting vertical tail using CDISC, a knowledgebased aerodynamic design tool developed at the NASA Langley Research Center. A horizontal tail was also designed using an enhanced CATNLF design approach for low-lift components. CDISC was coupled with USM3D-ME, a Navier-Stokes computational fluid dynamics solver. Stability and transition software was used to determine the laminar extent on the surfaces. Results indicate laminar flow can be sustained at midcruise conditions to about x/c=0.40 on the vertical tail and as much as x/c=0.65 on the horizontal tail lower surface. Transonic longitudinal off-design analysis indicates minimal change in the laminar extent. However, nonzero sideslip angles at transonic conditions can cause premature transition relative to the midcruise condition.

Brent W. Pomeroy↗

Numerical Study of Flow Past a Circular Cylinder Using RANS, Hybrid RANS/LES and PANS Formulations

Two multiscale type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k(sub epsilon)) model with a RANS/LES transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) model, where the unresolved kinetic energy parameter (f(sub k)) is allowed to vary as a function of grid spacing and the turbulence length scale. Solutions from these models are compared to RANS results and experimental data for a stationary and rotating cylinder. The parameter f(sub k) varies between zero and one and has the characteristic to be equal to one in the viscous sub layer, and when the RANS turbulent viscosity becomes smaller than the LES viscosity. The formulation, usage methodology, and validation example are presented to demonstrate the enhancement of PAB3D's time-accurate and turbulence modeling capabilities. The models are compared to RANS results and experimental data for turbulent separated flows (TS) and laminar separated flows (LS) around stationary and rotating cylinders. For a stationary cylinder, the TS case is accurately simulated using the general two-equation k(sub epsilon) turbulence model (eddy-viscosity model). PAB3D accurately predicts the drag coefficient (CD), lift coefficient (CL) and the Strouhal number (St). The LS case was a challenge for the RANS computation with an eddy-viscosity turbulence model. The RANS/LES and PANS performed well and showed marked improvements over the RANS solution. The modified PANS model was the most accurate. For the rotating cylinder, the spin ratio varied from zero to one, and the PANS results were in good agreement with published experimental data. RANS/LES and PANS capture both temporal and spatial fluctuations and produce large-scale structures that do not occur in the RANS simulation. The current results show promise for the capability of PANS in simulating unsteady and complex flow phenomena.

Elmiligui, Alaa A.↗

MinCostFlows.jl

MinCostFlows.jl is a utility package in the Julia programming language for efficiently solving min-cost network flow problems through an implementation of the relaxation dual ascent method (Bertsekas, 1985, https://link.springer.com/article/10.1007/BF01586087). The use of a dual ascent method allows for warm-starting the solver with a solution from a previously-solved problem that need not be feasible for the new problem, providing computational performance benefits when repeatedly solving similar network flow problems. This approach is particularly useful for Monte Carlo power system resource adequacy models.

Gordon, Stephen↗

Improvements in Iterative Convergence of FUN3D Solutions

This paper presents a hierarchical adaptive nonlinear iteration method (HANIM) implemented in the NASA computational fluid dynamics code, FUN3D, to improve robustness and computational efficiency. In contrast to the legacy FUN3D iterative solver that relies on an approximate Jacobian, a simple multicolor Gauss-Seidel point-implicit iteration scheme, and linear Courant-Friedrichs-Lewy number (CFL) ramping, HANIM is based upon a hierarchy of modules including preconditioner, generalized conjugate residual, realizability check, nonlinear control, and CFL adaption modules. HANIM performance is systematically compared with the performance of the legacy solver of FUN3D and a baseline solver based on a preconditioner alone. Iterative solutions are compared for three benchmark cases: a subsonic separated flow around a hemisphere cylinder, a supersonic flow through a long duct, and a subsonic flow over the NASA wing-fuselage juncture model. Two Reynolds-averaged Navier-Stokes turbulence models are used in these computations, namely, the negative variant of the linear one-equation Spalart-Allmaras model and its nonlinear extension based on quadratic constitutive relations.

CFD↗

Extension and Demonstration of NEAMS Multiphysics Tools to Lead-Cooled, Sodium-Cooled, and Molten Salt Fast Reactor Applications

The SHARP toolkit is a high-fidelity reactor simulation tool developed under the U.S. Department of Energy, Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Campaign. SHARP toolkit is comprised of the neutronics module PROTEUS thermal hydraulics module Nek5000, and structural mechanics module Diablo. During FY17 and FY18, the PROTEUS and Nek5000 components of SHARP were applied to solve challenging sodium-cooled fast reactor (SFR) problems. In particular, selected hot channel factors (HCF) for a prototype metal-fueled SFR design (the AFR-100) were analyzed in high fidelity, and the “SHARP zooming capability” for SFRs was developed and demonstrated to reduce computational expense for full core problems in cases where detailed data is needed in selected fuel assemblies. After the previous success applying SHARP to challenging SFR problems, the focus in FY19 expanded to additional fast reactor applications: lead cooled fast reactors (LFR), sodium cooled fast reactors (SFR), and fast molten salt reactors (MSR). The specific technical tasks were (1) assessment of hot channel factors for LFR, for which no data currently exists, (2) implementation of a gamma transport capability in the PROTEUS solvers to extend the zooming capability to non-fueled assemblies, (3) demonstration of zooming capability in assemblies of the Versatile Test Reactor (VTR), and (4) development of a new coupled capability for simulating fast MSRs, specifically modeling precursor transport inside and outside the core. The progress on tasks (1) and (3) are discussed primarily in this document. Tasks (2) and (4) are briefly mentioned in this document, and the interested reader is referred to separate reports for detailed information. First-of-a-kind hot channel factor (HCF) estimation for LFR with high fidelity codes (PROTEUS/Nek5000) was successfully demonstrated in this study. Selected HCF were computed and compared with SFR data (AFR-100, EBR-II). The findings confirm that different reactor types, design parameters and uncertainties lead to different HCFs. Careful estimation of HCF for a specific design is necessary to obtain appropriate HCFs. In addition to improvement in HCF accuracy, high fidelity tools generate data to help the designer better understand the mechanism of the impact from these uncertainties. For example, the impact of cladding thickness manufacturing tolerance resulted in non-intuitive effects in the corner pins of the LFR assembly. This procedure of computing HCF using high fidelity models shows promise and flexibility for being repeated for any arbitrary reactor of choice, since these tools are targeted to solve many reactor types and geometries. Progress was made towards extending the previously demonstrated SHARP zooming capability to non-fueled SFR assemblies. In particular, a gamma transport capability was implemented in both high fidelity PROTEUS solvers in order to accurately account for heat deposition caused by gamma particles, which accounts for ~10% of total core power. Neutronics verification cases were carried out for a candidate Versatile Test Reactor (VTR) design using the new gamma transport capability in PROTEUS. Comparisons were made with continuous energy MCNP calculations and shown to agree well. The models for the full core design with heterogeneous control and fuel assemblies is in progress and will be completed in FY20. In the fast molten salt reactor (MSR) domain, a new capability was developed to model the flow of neutron precursors both inside and outside of the core, which impacts the effective delayed neutron fraction of the system. The PROTEUS-SN and PROTEUS-NODAL solvers were coupled to Nek5000 in order to simulate precursor flow. The workflows were demonstrated on test problems. The fast MSR modeling capability was supported under two other work packages, and comprehensive details are included in a separate report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Presentation of the MERC work-flow for the computation of a 2D radial reflector in a PWR

This paper presents a work-flow for computing an equivalent 2D radial reflector in a pressurized water reactor (PWR) core, in adequacy with a reference power distribution, computed with the method of characteristics (MOC) of the lattice code APOLLO2. The Multi-modelling Equivalent Reflector Computation (MERC) work-flow is a coherent association of the lattice code APOLLO2 and the core code COCAGNE, structured around the ADAO (Assimilation de Donnees et Aide a l'Optimisation) module of the SALOME platform, based on the data assimilation theory. This study leads to the computation of equivalent few-groups reflectors, that can be spatially heterogeneous, which have been compared to those obtained with the OPTEX similar methodology developed with the core code DONJON, as a first validation step. Subsequently, the MERC work-flow is used to compute the most accurate reflector in consistency with all the R and D choices made at Electricite de France (EDF) for the core modelling, in terms of number of energy groups and simplified transport solvers. We observe important reductions of the power discrepancies distribution over the core when using equivalent reflectors obtained with the MERC work-flow. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Flow Characterization of the NASA Langley Unitary Plan WindTunnel, Test Section 2: Computational Results

Flow in the empty Unitary Planform Wind Tunnel at the NASA Langley Research Center issimulated with computational fluid dynamics methods. The objectives are to assess CFD’s truepredictive capability and to generate flow-field maps upstream of the tunnel’s test section foruse in associated vehicle tests. Multiple CFD solvers, grid adaption methods, and turbulencemodels are used by five teams doing the simulations. The simulation domain is as large aspractical: from the start of the settling chamber, just downstream of the last set of turningvanes, to well downstream of the test section. Simulations are done at three Mach numbers andseveral Reynolds numbers that cover most of the tunnel’s operating range. The sensitivity ofthe CFD solutions to simulation process details, including turbulence model, spatial resolutionand settling-chamber inflow velocity profile, is characterized. Significant sensitivities in somedetails of the predicted test section flow are described. CFD predicts that details of flow inthe settling chamber can affect the flow in the test section. Turning of the flow through thetunnel contraction and past nozzle-block hardware generates streamwise vortices, some ofwhich survive into the core of the test section, principally at low Mach number. Preliminarycomparisons to experimental measurements are given. The major flow characteristics andthe dynamical vortices predicted by CFD exist in the experiment. Several details in CFD andexperiment are observed to differ, including the effects of the vortices and features that appearto be Mach waves in the test section. Sensitivity to grid resolution and turbulence modelingis noted in the vortices; no potential cause for the differences in Mach waves has yet beenidentified in the CFD sensitivity studies.

wind tunnel↗

LES-Based Analysis of Film Cooling in a High-Pressure Turbine Rotor Including Effects of Purge and Tip Flow

Accurate modeling of coolant airflows, which form protective films over turbine blades, is essential for designing fuel-efficient and environmentally sustainable gas turbine engines. Excessive coolant reduces thermal efficiency, while insufficient coolant leads to blade overheating and causes damage. Therefore, precise prediction of flow field interactions with cooling air is critical for optimizing turbine performance. This study numerically investigates the cooling effectiveness of purge and film cooling flows within a high-pressure turbine (HPT) rotor using Large Eddy Simulation (LES). The study utilizes NASA Glenn Research Center’s Glenn-HT solver. The simulation models ethe conditions of the Penn State University START rotating rig. A high-fidelity structured mesh comprising up to 800 million cells is employed to resolve high-Reynolds number flow (Re ≈ 350,000) and to capture intricate secondary flow structures, including tip leakage and purge-induced vortices. Film cooling effectiveness computations are highly sensitive to boundary conditions at the cooling holes and to grid resolution. Even with well-resolved grids and included plena, strong mixing challenges traditional eddy viscosity models. To address this, a simplified configuration is simulated: a truncated row of shaped holes on the suction side near the leading edge and a row on the pressure side, both fed from internal plena while the purge slot and tip clearance are also modeled. Two isothermal LES cases are conducted at two distinct wall temperatures, which yield the adiabatic wall temperature and the heat transfer coefficient. The definition and means of computation of the effectiveness is discussed in this paper. The simulations reveal detailed three-dimensional unsteady flow features, including coherent vortical structures and secondary flows originating from the purge cavity. Film cooling effectiveness and Nusselt number distributions are presented for both the blade surface and tip, highlighting regions of elevated heat transfer and complex thermal behavior. These findings underscore the importance of high-resolution LES and realistic boundary conditions in capturing the dynamics of purge and film cooling, offering valuable insights for improving turbine blade design and thermal management strategies.

Secondary Flows↗

A GPU-based Approach for Turbomachinery Application

Accurate modeling of coolant airflows, which form protective films over turbine blades, is essential for designing fuel-efficient and environmentally sustainable gas turbine engines. Excessive coolant reduces thermal efficiency, while insufficient coolant leads to blade overheating and causes damage. Therefore, precise prediction of flow field interactions with cooling air is critical for optimizing turbine performance. This study numerically investigates the cooling effectiveness of purge and film cooling flows within a high-pressure turbine (HPT) rotor using Large Eddy Simulation (LES). The study utilizes NASA Glenn Research Center’s Glenn-HT solver. The simulation models ethe conditions of the Penn State University START rotating rig. A high-fidelity structured mesh comprising up to 800 million cells is employed to resolve high-Reynolds number flow (Re ≈ 350,000) and to capture intricate secondary flow structures, including tip leakage and purge-induced vortices. Film cooling effectiveness computations are highly sensitive to boundary conditions at the cooling holes and to grid resolution. Even with well-resolved grids and included plena, strong mixing challenges traditional eddy viscosity models. To address this, a simplified configuration is simulated: a truncated row of shaped holes on the suction side near the leading edge and a row on the pressure side, both fed from internal plena while the purge slot and tip clearance are also modeled. Two isothermal LES cases are conducted at two distinct wall temperatures, which yield the adiabatic wall temperature and the heat transfer coefficient. The definition and means of computation of the effectiveness is discussed in this paper. The simulations reveal detailed three-dimensional unsteady flow features, including coherent vortical structures and secondary flows originating from the purge cavity. Film cooling effectiveness and Nusselt number distributions are presented for both the blade surface and tip, highlighting regions of elevated heat transfer and complex thermal behavior. These findings underscore the importance of high-resolution LES and realistic boundary conditions in capturing the dynamics of purge and film cooling, offering valuable insights for improving turbine blade design and thermal management strategies.

Gas Turbine↗

SimELIT: A Novel GUI-Based Comprehensive Ion Trajectory Simulation Software for Mass Spectrometry

Ion trajectory simulation in mass spectrometry systems from injection to detection is technically challenging but very important for better understanding the ion dynamics in instrument development. Here, in this work, we present SimELIT (Simulator of Eulerian and Lagrangian Ion Trajectories), a novel ion trajectory simulation platform. SimELIT is built upon a suite of multiphysics solvers compiled into OpenFOAM (an open-source numerical solver library particularly used for computational mechanics), with a simple web-based graphical user interface (GUI) allowing users to define the details of OpenFOAM cases and run simulations. SimELIT is a modular program and can provide extensions of physics (e.g., gas flows, electrodynamic fields) and thus enable ion trajectory simulations from the ion source to detector. The current version (SimELIT) provides two numerical solvers for ion trajectory simulations–(1) a Lagrangian particle tracker in vacuum and (2) a Eulerian ion density solver in background gas in the presence of electric fields. Here, we describe the architecture of SimELIT, including its use of Docker and the React Framework, and demonstrate the computation of ion trajectories of multiple m/z values in a static/linear voltage drop in vacuum (across a 1 m long flight tube). Further, the drift motion of ions under 1 Torr pressure conditions in a static background (N 2 ) gas through a 20 V/cm static electric field is shown. The results produced from SimELIT were compared with SIMION and theoretical estimates. In addition, we report the computation of ion trajectories in electrodynamic fields within a planar FAIMS device operating at atmospheric pressure.

97 MATHEMATICS AND COMPUTING↗

Estimation of propulsion-induced effects on transonic flows over a hypersonic configuration

Boundary conditions are formulated for treating selected patches of a subject configuration as inlet or nozzle areas. For subsonic inflow, the mass flow through the inlet is controlled by the exhaust conditions and the effects of mass and heat addition. For supersonic inflow, the exhaust conditions are based on the inlet conditions and on combustion data. These formulations were included into an existing Euler/Navier-Stokes solver. Comparisons with experimental data demonstrate that the resulting software package efficiently permits the assessment of propulsion-induced effects on external flow fields, particularly around highly blended configurations.

Hartwich, Peter M.↗

A Study of Coaxial Rotor Performance and Flow Field Characteristics

As a precursor to studying the acoustics of a coaxial rotor system, the aerodynamics and flow field of a coaxial rotor were simulated to better understand the interaction between the two rotors. RotUNS, an unsteady Navier-Stokes solver that uses a simplified blade aerodynamics model, was used to predict coaxial rotor performance in hover and forward flight. RotUNS steady hover calculations showed improved performance compared to blade element momentum theory. Prior to examining the complex 3D flow field of a coaxial rotor in detail, two airfoils traveling in opposite directions with a vertical separation distance equivalent to the separation between the upper and lower rotor of the coaxial system were simulated. The pressure field generated by the two airfoils aided our interpretation of the more complex coaxial rotor system flow field. The pressure fields above, between, and below the coaxial rotor system were then examined for different azimuth positions of the upper and lower rotor blades.

Barbely, Natasha L.↗

Development of a 3-D upwind PNS code for chemically reacting hypersonic flowfields

Two new parabolized Navier-Stokes (PNS) codes were developed to compute the three-dimensional, viscous, chemically reacting flow of air around hypersonic vehicles such as the National Aero-Space Plane (NASP). The first code (TONIC) solves the gas dynamic and species conservation equations in a fully coupled manner using an implicit, approximately-factored, central-difference algorithm. This code was upgraded to include shock fitting and the capability of computing the flow around complex body shapes. The revised TONIC code was validated by computing the chemically-reacting (M(sub infinity) = 25.3) flow around a 10 deg half-angle cone at various angles of attack and the Ames All-Body model at 0 deg angle of attack. The results of these calculations were in good agreement with the results from the UPS code. One of the major drawbacks of the TONIC code is that the central-differencing of fluxes across interior flowfield discontinuities tends to introduce errors into the solution in the form of local flow property oscillations. The second code (UPS), originally developed for a perfect gas, has been extended to permit either perfect gas, equilibrium air, or nonequilibrium air computations. The code solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that was modified to account for real gas effects. The dissipation term associated with this algorithm is sufficiently adaptive to flow conditions that, even when attempting to capture very strong shock waves, no additional smoothing is required. For nonequilibrium calculations, the code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. This code was used to calculate the hypersonic, laminar flow of chemically reacting air over cones at various angles of attack. In addition, the flow around the McDonnel Douglas generic option blended-wing-body was computed and comparisons were made between the perfect gas, equilibrium air, and the nonequilibrium air results.

Tannehill, J. C.↗

Summary of the 5th Propulsion Aerodynamics Workshop Nozzle Test Case: Heated Nozzle Exhaust Passing Over A Film-Cooled Plate

This paper summarizes findings from the fifth AIAA Propulsion Aerodynamics Workshop nozzle test case. The experimental configuration examined by workshop participants was a subsonic nozzle with a square exit blowing a heated exhaust over a film-cooled plate. Computational fluid dynamics solutions were obtained and compared to experimental measurements of flow velocities and temperatures, as well as plate surface temperatures. The heated nozzle operated with a Mach 0.3 exit flow at a static temperature ratio of 2.7. Cooling air blowing ratios of 0, 1, and 2 were considered. Computational meshes for the flow domain were provided for participants. Workshop participants from eight separate organizations represented government, industry, and academia. A variety of flow solutions were obtained: Most of the flow solutions employed a Reynolds-averaged Navier-Stokes (RANS) approach, but scale-resolving simulations were used in some cases, including wall-modeled large-eddy simulation (LES), and a few hybrid RANS-LES approaches. One Lattice-Boltzmann solver was employed. For heat transfer to the test article, many participants used a conjugate heat transfer approach. Effects of mesh sensitivity, flow solution approach, and wall heat transfer approach are considered. In general, a fully three-dimensional conjugate heat transfer approach enabled better prediction of surface temperatures than simpler wall temperature boundary treatments. Also, the scale resolving approaches provided better prediction of static temperatures in the flow immediately above the plate consisting of the hot jet exhaust boundary layer interacting with the cooling film. Comparisons of plate surface friction drag and heat transfer obtained from the computations are also presented.

nozzle↗

Summary of the 5th Propulsion Aerodynamics Workshop Nozzle Test Case: Heated Nozzle Exhaust Passing Over A Film-Cooled Plate

This paper summarizes findings from the fifth AIAA Propulsion Aerodynamics Workshop nozzle test case. The experimental configuration examined by workshop participants was a subsonic nozzle with a square exit blowing a heated exhaust over a film-cooled plate. Computational fluid dynamics solutions were obtained and compared to experimental measurements of flow velocities and temperatures, as well as plate surface temperatures. The heated nozzle operated with a Mach 0.3 exit flow at a static temperature ratio of 2.7. Cooling air blowing ratios of 0, 1, and 2 were considered. Computational meshes for the flow domain were provided for participants. Workshop participants from eight separate organizations represented government, industry, and academia. A variety of flow solutions were obtained: Most of the flow solutions employed a Reynolds-averaged Navier-Stokes (RANS) approach, but scale-resolving simulations were used in some cases, including wall-modeled large-eddy simulation (LES), and a few hybrid RANS-LES approaches. One Lattice-Boltzmann solver was employed. For heat transfer to the test article, many participants used a conjugate heat transfer approach. Effects of mesh sensitivity, flow solution approach, and wall heat transfer approach are considered. In general, a fully three-dimensional conjugate heat transfer approach enabled better prediction of surface temperatures than simpler wall temperature boundary treatments. Also, the scale resolving approaches provided better prediction of static temperatures in the flow immediately above the plate consisting of the hot jet exhaust boundary layer interacting with the cooling film. Comparisons of plate surface friction drag and heat transfer obtained from the computations are also presented.

nozzle↗

Preparing an Incompressible-Flow Fluid Dynamics Code for Exascale-Class Wind Energy Simulations: Preprint

The US Department of Energy has identified Exascale-Class wind farm simulation tools as critical to wind energy scientific discovery. A primary objective of the Exawind project is to build high-performance, predictive Computational Fluid Dynamics tools that satisfy these modeling needs. GPU accelerators will serve as the computational thoroughbreds of next generation, Exascale-Class, platforms. Here, we report on our efforts for preparing the Exawind unstructured mesh solver, Nalu-Wind, for Exascale-Class machines. For computing at this scale, a simple port of the incompressible-flow algorithms to GPUs is not sufficient. One needs novel algorithms that are application aware, memory efficient, and optimized for latest generation GPU devices to get high-performance. The result of our efforts are unstructured mesh simulations of wind turbines that use 1/6 the compute resources of Summit supercomputer at Oak Ridge National Lab. In particular, we demonstrate a first-of-its-kind, simulation using Algebraic Multigrid solvers on over 4000 GPUs.

algebraic multigrid↗

Hypersonic blunt body wake computations using DSMC and Navier-Stokes solvers

Numerical results obtained with direct simulation Monte Carlo (DSMC) and Navier-Stokes methods are presented for Mach 20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how does the wake structure change as a function of rarefaction, what are the afterbody levels of heating, and to what limits are continuum models realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Moss, James N.↗