Heat Transfer Predictions in a Laminar Hypersonic Viscous/Inviscid Interaction

Resultsaredocumentedofablindvalidationstudytocharacterizetheaccuracyofanupwind-biasede nitevolume methodinpredictingthesurfaceloadscaused byalaminarviscous/inviscidinteraction.Theeffortsupportsarecent Research and Technology Organization code validation initiative and considers a benchmark cone guration of the Working Group 10, consisting of Mach 9.5 e owpast a 25/55 deg sharp-tipped doubleconeat a Reynolds number of 1.39435 £ 10 6 /m. Roe’ s e ux-difference splitting scheme is employed with a nominally third-order reconstruction method and harmonic limiting. An extensive iterative- and grid-convergencestudy is performed to ensure solution accuracy. Comparison with experimental data shows that overall the numerical method reproduces the features of the interaction, including location and extent of separation to a degree that may be characterized as adequate for engineering purposes. However, upstream of separation and in the narrow peak heating region, discrepancies in heat transfer rates between computation and experiment range between 10 and 15% of maximum values. An exploration of the sensitivity of the solution to small variations (up to 10%) in several e ow and numerical parameters reveals only modest ine uence on the nondimensionalized quantities.

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

[2]  P. Roe Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[3]  D. Gaitonde,et al.  Accuracy of flux-split algorithms in high-speed viscous flows , 1993 .

[4]  Graham V. Candler,et al.  Navier-stokes predictions of hypersonic double-cone and cylinder-flare flow fields , 2001 .

[5]  Doyle Knight,et al.  Some insights in turbulence modeling for Crossing-Shock-Wave/Boundary-Layer Interactions , 2000 .

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

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

[8]  Meng-Sing Liou,et al.  Choice of implicit and explicit operators for the upwind differencing method , 1988 .

[9]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[10]  T. Kubota,et al.  Experimental investigation of supersonic laminar, two-dimensional boundary-layer separation in a compression corner with and without cooling. , 1967 .

[11]  F. White Viscous Fluid Flow , 1974 .

[12]  Robert W. Walters,et al.  Upwind relaxation algorithms for the Navier-Stokes equations , 1987 .

[13]  J. Stewart,et al.  Shock interference studies on a circular cylinder at Mach 16 , 1990 .

[14]  W. K. Anderson,et al.  Comparison of Finite Volume Flux Vector Splittings for the Euler Equations , 1985 .

[15]  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 .

[16]  R. Maccormack Current status of numerical solutions of the Navier-Stokes equations , 1985 .

[17]  B. Mueller,et al.  Simple improvements of an upwind TVD scheme for hypersonic flow , 1989 .

[18]  Numerical investigation of new topologies in strong crossing shock-wave/turbulent boundary-layer interactions , 2000 .

[19]  H. C. Yee Upwind and Symmetric Shock-Capturing Schemes , 1987 .

[20]  Skin-Friction Predictions in a Crossing-Shock Turbulent Interaction , 1997 .

[21]  D. Knight,et al.  Three-dimensional shock/boundary-layer interaction using reynolds stress equation turbulence model , 1996 .

[22]  Edney ANOMALOUS HEAT TRANSFER AND PRESSURE DISTRIBUTIONS ON BLUNT BODIES AT HYPERSONIC SPEEDS IN THE PRESENCE OF AN IMPINGING SHOCK. , 1968 .

[23]  A. F. Messiter,et al.  Analysis of Two-Dimensional Interactions Between Shock Waves and Boundary Layers , 1980 .

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

[25]  Graham V. Candler,et al.  Computational analysis of hypersonic laminar viscous-inviscid interactions , 2000 .

[26]  Peter Bradshaw,et al.  Turbulence: the chief outstanding difficulty of our subject , 1994 .

[27]  D. Gaitonde,et al.  Evaluation of an upwind-biased method in a laminar hypersonic viscous/inviscid interaction , 2001 .

[28]  Dean R. Chapman,et al.  Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition , 1958 .

[29]  A. I. Maksimov,et al.  Three-Dimensional Turbulent Interactions Caused by Asymmetric Crossing-Shock Configurations , 1999 .

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

[31]  B. Leer,et al.  Flux-vector splitting for the Euler equations , 1997 .

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

[33]  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 .

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