Suitability of the k–ω turbulence model for scramjet flowfield simulations

The suitability of Wilcox's 2006 k ? turbulence model for scramjet flowfield simulations is demonstrated by validation against five test cases that have flowfields representative of those to be expected in scramjets. The five test cases include a 2D flat plate, an axisymmetric cylinder, a backward-facing step, the mixing of a pair of coaxial jets and the interaction between a shock wave and turbulent boundary layer. A generally good agreement between the numerical and experimental results is obtained for all test cases. These tests reveal that despite the turbulence model's sensitivity to freestream turbulence properties, the numerically predicted skin friction agrees with experimental data and theoretical correlations to their degree of uncertainty. The tests also confirm the importance of using a y+ value of less than 1 in getting accurate surface heat transfer distributions. In the coaxial jets case, the importance of matching the turbulence intensities at the inflow plane in improving the predictions of the turbulent mixing phenomena is also shown. A review of guidelines with regard to the setting up of grids and specification of freestream turbulence properties for turbulent Reynolds-averaged NavierStokes CFD simulations is also included in this paper. Copyright (C) 2011 John Wiley & Sons, Ltd.

[1]  Russell R. Boyce,et al.  Shock-induced three-dimensional separation of an axisymmetric hypersonic turbulent boundary layer , 2000 .

[2]  Doyle Knight,et al.  Insights in Turbulence Modeling for Crossing-Shock-Wave/Boundary-Layer Interactions , 2001 .

[3]  James C. McDaniel,et al.  Transverse injection into Mach 2 flow behind a rearward-facing step - A 3-D, compressible flow test case for hypersonic combustor CFD validation , 1991 .

[4]  Mark J. Lewis,et al.  Experimentation, Test, and Evaluation Requirements for Future Airbreathing Hypersonic Systems , 2001 .

[5]  Meng-Sing Liou,et al.  A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics) , 1994 .

[6]  G. B. Northam,et al.  A comparative computational/experimental investigation of Mach 2 flow over a rearward-facing step , 1995 .

[7]  Frederic Thivet,et al.  Lessons Learned from RANS Simulations of Shock-Wave/Boundary-Layer Interactions , 2002 .

[8]  Peter A. Jacobs,et al.  Helmholtz Resonance of Pitot Pressure Measurements in Impulsive Hypersonic Test Facilities , 2009 .

[9]  P. Durbin.  On the k-3 stagnation point anomaly , 1996 .

[10]  T. Coakley,et al.  TURBULENCE MODELING VALIDATION , 1997 .

[11]  Peter A. Jacobs,et al.  Rarefied, superorbital flows in an expansion tube , 2004 .

[12]  Stephen B. Pope,et al.  An explanation of the turbulent round-jet/plane-jet anomaly , 1978 .

[13]  Glenn S. Diskin,et al.  Supersonic coaxial jet experiment for computational fluid dynamics code validation , 2006 .

[14]  Peter A. Jacobs,et al.  Supersonic Boundary-Layer Combustion: Effects of Upstream Entropy and Shear-Layer Thickness , 2010 .

[15]  Peter A. Jacobs,et al.  Diagnostic modelling of an expansion tube operating condition , 2009 .

[16]  L. C. Squire.  The accuracy of flat plate, turbulent skin friction at supersonic speeds , 2000, The Aeronautical Journal (1968).

[17]  Joan G. Moore,et al.  Realizability in two-equation turbulence models , 1999 .

[18]  Jean P. Sislian,et al.  Validation of the Wilcox k-omega Model for Flows Characteristic to Hypersonic Airbreathing Propulsion , 2004 .

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

[20]  Ronald S. Fry,et al.  A Century of Ramjet Propulsion Technology Evolution , 2004 .

[21]  H H Fernholz,et al.  A Critical Compilation of Compressible Turbulent Boundary Layer Data , 1977 .

[22]  Vinayak Kulkarni,et al.  Drag reduction by a forward facing aerospike for a large angle blunt cone in high enthalpy flows , 2009 .

[23]  Foluso Ladeinde.  Advanced Computational-Fluid-Dynamics Techniques for Scramjet Combustion Simulation , 2010 .

[24]  D. Wilcox.  Reassessment of the scale-determining equation for advanced turbulence models , 1988 .

[25]  Peter A. Jacobs,et al.  Drag force on quasi-axisymmetric scramjets at various flight Mach numbers: theory and experiment , 2009 .

[26]  Peter A. Jacobs,et al.  Scramjet Experiments in an Expansion Tunnel: Evaluated Using a Quasi-Steady Analysis Technique , 2010 .

[27]  Michael N. Macrossan,et al.  The equilibrium flux method for the calculation of flows with non-equilibrium chemical reactions , 1989 .

[28]  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 .

[29]  C. J. Roy,et al.  Methodology for Turbulence Model Validation: Application to Hypersonic Flows , 2003 .

[30]  S. G. Mallinson,et al.  Gun tunnel flow calibration: defining input conditions for hypersonic flow computations , 2000 .

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

[32]  Andrew D. Cutler,et al.  An Experimental and CFD Study of a Supersonic Coaxial Jet , 2001 .

[33]  Kwang-Soo Kim,et al.  Skin-friction measurements and computational comparison of swept shock/boundary-layer interactions , 1991 .