Uncertainty Assessments of 2D and Axisymmetric Hypersonic Shock Wave - Turbulent Boundary Layer Interaction Simulations at Compression Corners

This paper is one of a series of five papers in a special session organized by the NASA Fundamental Aeronautics Program that addresses uncertainty assessments for CFD simulations in hypersonic flow. Simulations of a shock emanating from a compression corner and interacting with a fully developed turbulent boundary layer are evaluated herein. Mission relevant conditions at Mach 7 and Mach 14 are defined for a pre-compression ramp of a scramjet powered vehicle. Three compression angles are defined, the smallest to avoid separation losses and the largest to force a separated flow engaging more complicated flow physics. The Baldwin-Lomax and the Cebeci-Smith algebraic models, the one-equation Spalart-Allmaras model with the Catrix-Aupoix compressibility modification and two-equation models including Menter SST, Wilcox k-omega 98, and Wilcox k-omega 06 turbulence models are evaluated. Each model is fully defined herein to preclude any ambiguity regarding model implementation. Comparisons are made to existing experimental data and Van Driest theory to provide preliminary assessment of model form uncertainty. A set of coarse grained uncertainty metrics are defined to capture essential differences among turbulence models. Except for the inability of algebraic models to converge for some separated flows there is no clearly superior model as judged by these metrics. A preliminary metric for the numerical component of uncertainty in shock-turbulent-boundary-layer interactions at compression corners sufficiently steep to cause separation is defined as 55%. This value is a median of differences with experimental data averaged for peak pressure and heating and for extent of separation captured in new, grid-converged solutions presented here. This value is consistent with existing results in a literature review of hypersonic shock-turbulent-boundary-layer interactions by Roy and Blottner and with more recent computations of MacLean.

[1]  Minwei Wu,et al.  Direct numerical simulation of supersonic turbulent boundary layer over a compression ramp , 2007 .

[2]  G. Candler,et al.  Data-Parallel Line Relaxation Method for the Navier -Stokes Equations , 1998 .

[3]  C. C. Horstman,et al.  Hypersonic shock-wave turbulent-boundary-layer interaction flows - Experiment and computation , 1991 .

[4]  C. Horstman,et al.  Documentation of Two- and Three-Dimensional Hypersonic Shock Wave/Turbulent Boundary Layer Interaction Flows , 1992 .

[5]  Gary S. Settles,et al.  Hypersonic Shock/Boundary-Layer Interaction Database , 1991 .

[6]  Alireza Mazaheri,et al.  LAURA Users Manual: 5.3-48528 , 2010 .

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

[8]  E. Hopkins,et al.  An evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic Mach numbers , 1971 .

[9]  Wolfgang Rodi,et al.  Experience with two-layer models combining the k-epsilon model with a one-equation model near the wall , 1991 .

[10]  Christopher J. Roy,et al.  Verification and Validation in Scientific Computing , 2010 .

[11]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[12]  C. L. Rumsey,et al.  Compressibility Considerations for κ - ω Turbulence Models in Hypersonic Boundary Layer Applications , 2009 .

[13]  F. Billig.  Research on supersonic combustion , 1992 .

[14]  Christopher J. Roy,et al.  Verification and Validation in Scientific Computing: Design and execution of validation experiments , 2010 .

[15]  Chau-Lyan Chang.  LASTRAC.3d: Transition Prediction in 3D Boundary Layers , 2004 .

[16]  Allan Paull,et al.  Transducer for Direct Measurement of Skin Friction in Hypervelocity Impulse Facilities , 2002 .

[17]  D. Knight,et al.  Advances in CFD prediction of shock wave turbulent boundary layer interactions , 2003 .

[18]  Graham V. Candler,et al.  Detached Eddy simulation of hypersonic base flows during atmospheric entry , 2006 .

[19]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[20]  G. Candler,et al.  Hypersonic Boundary Layer Stability Analysis Using PSE-Chem , 2005 .

[21]  G. N. Coleman,et al.  Van Driest transformation and compressible wall-bounded flows , 1994 .

[22]  Kathryn E. Wurster,et al.  Boundary-Layer Transition on X-43A , 2010 .

[23]  T. J. Coakley,et al.  Turbulence modeling for complex hypersonic flows , 1993 .

[24]  Christopher J. Roy,et al.  Review and assessment of turbulence models for hypersonic flows , 2006 .

[25]  Graham V. Candler,et al.  SUBGRID-SCALE MODEL FOR THE TEMPERATURE FLUCTUATIONS IN REACTING HYPERSONIC TURBULENT FLOWS , 1999 .

[26]  Peter A. Gnoffo,et al.  Uncertainty Assessment of Hypersonic Aerothermodynamics Prediction Capability , 2011 .

[27]  J. A. White,et al.  A Psuedo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations , 1999 .

[28]  Stephane Catris,et al.  Density corrections for turbulence models , 2000 .

[29]  Tuncer Cebeci,et al.  A Finite-Difference Method for Calculating Compressible Laminar and Turbulent Boundary Layers , 1970 .

[30]  J. L. Stollery,et al.  Heat transfer from hypersonic turbulent flow at a wedge compression corner , 1972, Journal of Fluid Mechanics.

[31]  T. Kármán,et al.  Turbulence and Skin Friction , 1934 .

[32]  M. Holden,et al.  Studies of the mean and unsteady structure of turbulent boundary layer separation in hypersonic flow , 1991 .

[33]  Shizhao Wang,et al.  Study of the shock motion in a hypersonic shock system/turbulent boundary layer interaction , 1995 .

[34]  James Brown,et al.  Turbulence Model Validation for Hypersonic Flows , 2002 .

[35]  P. Gnoffo.  An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows , 1990 .

[36]  Josef Ballmann,et al.  Performance of Upwind Schemes and Turbulence Models in Hypersonic Flows , 2004 .

[37]  Kam-Pui Lee,et al.  Viscous shock-layer analysis of hypersonic flows over long slender bodies , 1987 .

[38]  Matthew William Orr,et al.  Design, Analysis, and Initial Testing of a Fiber-Optic Shear Gage for 3D, High-Temperature Flows , 2004 .

[39]  Timothy Wadhams,et al.  EXPERIMENTAL STUDIES OF SHOCK WAVE/TURBULENT BOUNDARY LAYER INTERACTION IN HIGH REYNOLDS NUMBER SUPERSONIC AND HYPERSONIC FLOWS TO EVALUATE THE PERFORMANCE OF CFD CODES , 2010 .

[40]  Gordon Erlebacher,et al.  The analysis and modelling of dilatational terms in compressible turbulence , 1989, Journal of Fluid Mechanics.

[41]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

[42]  E. R. V. Driest,et al.  Turbulent Boundary Layer in Compressible Fluids , 2003 .

[43]  Alexander J. Smits,et al.  Current status of basic research in hypersonic turbulence , 2009 .

[44]  Holger Babinsky,et al.  Shock Wave-Boundary-Layer Interactions , 2014 .

[45]  T. Lundh,et al.  On boundary layers , 1996 .

[46]  Christopher L. Rumsey,et al.  Compressibility Considerations for Kappa-Omega Turbulence Models in Hypersonic Boundary Layer Applications , 2013 .

[47]  G. M. Elfstrom.  Turbulent hypersonic flow at a wedge-compression corner , 1972 .

[48]  P. G. Huang,et al.  Errata Van Driest transformation and compressible wall-bounded flows , 1995 .

[49]  Otto Zeman,et al.  Dilatation dissipation: The concept and application in modeling compressible mixing layers , 1990 .

[50]  Tuncer Cebeci,et al.  Behavior of turbulent flow near a porous wall with pressure gradient , 1970 .

[51]  Gary S. Settles,et al.  Supersonic and hypersonic shock/boundary-layer interaction database , 1994 .