Kinetic description of the turbulence in the supersonic compressible flow over a backward/forward-facing step

Abstract In the present paper the Boltzmann kinetic equation is applied to investigate a supersonic turbulent compressible flow. For this purpose a numerical simulation of supersonic compressible two-dimensional flow in the vicinity of a backward/forward-facing step with leeward-face angle ranging from 8° to 90° and free-stream Mach number Ma ∞  ≈ 3 is carried out. An explicit–implicit numerical scheme in the framework of the direct approach for the solution of the full Boltzmann equation is used. Principal features of the kinetic approach for the description of compressible turbulence are discussed. The comparison with experimental and numerical results presented in the open literature is performed in terms of pressure, skin friction and heat-transfer coefficient distributions over the step surface. Kinetic computed flow field structures for different leeward-face angles are presented and discussed. A good agreement with the experimental results is observed.

[1]  Nikolaus A. Adams,et al.  Large-eddy simulation of shock-wave/turbulent-boundary-layer interaction , 2006, Journal of Fluid Mechanics.

[2]  Comparative analysis of the numerical solution of full Boltzmann and BGK model equations for the Poiseuille flow in a planar microchannel , 2013 .

[3]  Analysis of the evolution of an eddy system based on the Boltzmann equation , 2007 .

[4]  D. Wilcox.  Turbulence modeling for CFD , 1993 .

[5]  A. Sakurai,et al.  Molecular kinetic approach to the problem of compressible turbulence , 2003 .

[6]  A. A. Zheltovodov,et al.  Development of separation in the region where a shock interacts with a turbulent boundary layer perturbed by rarefaction waves , 1993 .

[7]  N. N. Fedorova,et al.  Computation of Gas–Dynamic Parameters and Heat Transfer in Supersonic Turbulent Separated Flows near Backward–Facing Steps , 2001 .

[8]  Jean Muylaert,et al.  Hypersonic Experimental and Computational Capability, Improvement and Validation. Volume 1 (l'Hypersonique experimentale et de calcul - capacite amelioration et validation). Volume 1, , 1996 .

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

[10]  E. M. Shakhov.  Approximate kinetic equations in rarefied gas theory , 1968 .

[11]  E. M. Shakhov.  Generalization of the Krook kinetic relaxation equation , 1968 .

[12]  Mikhail Naumovich Kogan,et al.  Rarefied Gas Dynamics , 1969 .

[13]  Kinetic model of the spatio-temporal turbulence , 2010 .

[14]  A. Zheltovodov,et al.  SOME ADVANCES IN RESEARCH OF SHOCK WAVE TURBULENT BOUNDARY LAYER INTERACTIONS , 2006 .

[15]  S. Tsuge.  Approach to the origin of turbulence on the basis of two‐point kinetic theory , 1974 .

[16]  V. Aristov.  Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows , 2001 .

[17]  Felix Tcheremissine,et al.  Direct Numerical Solution Of The Boltzmann Equation , 2005 .

[18]  V. V. Aristov,et al.  Application of the Boltzmann kinetic equation to the eddy problems , 2011 .

[19]  A. Zheltovodov,et al.  Shock waves/turbulent boundary-layer interactions - Fundamental studies and applications , 1996 .

[20]  Doyle Knight,et al.  RTO WG 10: CFD Validation for Shock Wave Turbulent Boundary Layer Interactions , 2002 .