Navier-Stokes and Direct Simulation Monte Carlo Predictions for Laminar Hypersonic Separation

Axisymmetric direct simulation Monte Carlo (DSMC) and Navier‐Stokes simulations are performed as part of a code validation effort for hypersonice ows. The e owe eld examined herein is the Mach 11 laminar e ow over a 25 ‐ 55-deg blunted biconic. Experimental data are available for surface pressure and heat e ux at a Knudsen number Kn=0.019 based on the nose radius. Simulations at a reduced freestream density (Kn=0.057) are performed to explore the region of viability of the numerical methods for hypersonic separated e ows. A detailed and careful effort is made to address the numerical accuracy of these simulations, including iterative and grid convergence studiesforNavier ‐Stokesandtemporal,grid,andparticleconvergencestudiesforDSMC.Goodagreementisfound between the DSMC and Navier ‐Stokes simulation approaches for surface properties as well as velocity proe les within the recirculation zone for the reduced density case. The results obtained indicate that the failure of earlier DSMC simulations at Kn=0.019 is due to insufe cient grid ree nement within the recirculation zone. Furthermore, it is shown that accurate simulations of the biconic at the experimental conditions with the DSMC method are not yet possible due to the extreme computational cost. Nomenclature d = molecular diameter, m f = general solution variable Kn = Knudsen number based on nose radius, ¸=RN L = characteristic length scale, m n = number density, particles/m 3 p = pressure, N/m 2 , order of accuracy q = heat e ux, W/m 2

[1]  Doyle Knight,et al.  RTO WG 10: Test cases for CFD validation of hypersonic flight , 2002 .

[2]  Alexander J. Smits,et al.  Numerical and experimental investigation of double-cone shock interactions , 2000 .

[3]  M. Carpenter,et al.  Accuracy of Shock Capturing in Two Spatial Dimensions , 1999 .

[4]  Seokkwan Yoon,et al.  An LU-SSOR scheme for the Euler and Navier-Stokes equations , 1987 .

[5]  Eckart Meiburg,et al.  Comparison of the molecular dynamics method and the direct simulation Monte Carlo technique for flows around simple geometries , 1986 .

[6]  K. Ghia,et al.  Editorial Policy Statement on the Control of Numerical Accuracy , 1986 .

[7]  Christopher J. Roy,et al.  DSMC and Navier-Stokes Predictions for Hypersonic Laminar Interacting Flows , 2001 .

[8]  Christopher J. Roy,et al.  Verification and Validation for Laminar Hypersonic Flowfields, Part 1: Verification , 2003 .

[9]  Timothy Wadhams,et al.  CODE VALIDATION STUDY OF LAMINAR SHOCKIBOUNDARY LAYER AND SHOCK/SHOCK INTERACTIONS IN HYPERSONIC FLOW Part B: Comparison \\ith Navier-Stokes and DSMC Solutions , 2001 .

[10]  William L. Oberkampf,et al.  Issues in computational fluid dynamics code verification and validation , 1997 .

[11]  Christopher J. Roy,et al.  Verification and Validation for Laminar Hypersonic Flowfields , 2000 .

[12]  J. Torczynski,et al.  The Application of the BGK Model in Particle Simulations , 2000 .

[13]  Christopher J. Roy,et al.  Further Assessment of One-and Two-Equation Turbulence Models for Hypersonic Transitional Flows , 1998 .

[14]  S. Imlay,et al.  An efficient implicit method for solving viscous multi-stream nozzle/afterbody flow fields , 1986 .

[15]  Graham V. Candler,et al.  CFD Validation for Hypersonic Flight: Hypersonic Double-Cone Flow Simulations , 2002 .

[16]  Graeme A. Bird,et al.  Direct simulation of high-vorticity gas flows , 1987 .

[17]  P. Roache.  Perspective: A Method for Uniform Reporting of Grid Refinement Studies , 1994 .

[18]  Iain D. Boyd,et al.  Monte Carlo computations of hypersonic interacting flows , 2001 .

[19]  Graham V. Candler,et al.  Effect of Vibrational Nonequilibrium on Hypersonic Double-Cone Experiments , 2003 .

[20]  J. L. Payne,et al.  Massively parallel computational fluid dynamics calculations for aerodynamics and aerothermodynamics applications , 1998 .

[21]  Patrick J. Roache,et al.  Verification and Validation in Computational Science and Engineering , 1998 .

[22]  Francis J. Alexander,et al.  Cell size dependence of transport coefficients in stochastic particle algorithms , 1998 .

[23]  B. V. Leer,et al.  Towards the Ultimate Conservative Difference Scheme , 1997 .

[24]  Peter A. Gnoffo,et al.  Paper 2001-1025 CFD Validation Studies for Hypersonic Flow Prediction , 2022 .

[25]  M. Holden.  Experimental Studies of Laminar Separated Flows Induced by Shock Wave/Boundary Layer and Shock/Shock Interaction in in Hypersonic Flows for CFD Validation , 2000 .

[26]  C. J. Roy,et al.  Veri cation and Validation for Laminar Hypersonic Flow elds , Part 1 : Veri cation , 2003 .

[27]  H. Schlichting.  Boundary Layer Theory , 1955 .

[28]  Christopher J. Roy,et al.  Navier-Stokes and DSMC simulations for hypersonic laminar shock-shock interaction flows , 2002 .

[29]  John C. Tannehill,et al.  Computation of Hypersonic Laminar Separated Flows using an Iterated PNS Algorithm , 2001 .

[30]  Timothy J. Bartel,et al.  Icarus: A 2-D Direct Simulation Monte Carlo (DSMC) Code for Multi-Processor Computers , 2001 .

[31]  Mikhail S. Ivanov,et al.  Statistical simulation of laminar separation in hypersonic flows: Numerical challenges , 2002 .

[32]  Jeffrey L. Payne,et al.  PINCA: A scalable parallel program for compressible gas dynamics with nonequilibrium chemistry , 1995 .

[33]  Walker,et al.  Verification of computational aerodynamic predictions for complex hypersonic vehicles using the INCA{trademark} code , 1995 .

[34]  J. Torczynski,et al.  An approach for simulating the transport of spherical particles in a rarefied gas flow via the direct simulation Monte Carlo method , 2001 .

[35]  Jeffrey L. Payne,et al.  Implementation of a parallel algorithm for thermo-chemical nonequilibrium flow simulations , 1995 .

[36]  James N. Moss,et al.  DSMC Computations for Regions of Shock/Shock and Shock/Boundary Layer Interaction , 2001 .

[37]  J. Steger,et al.  Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods , 1981 .