PROBING HIGH-SPEED WALL-BOUNDED FLOWS USING DNS M. F. Shahab (1) , G. Lehnasch (1) , T. B. Gatski, (1,2) and P. Comte (1) (1) Institute Pprime, BP 30179, F86962 Futuroscope Chasseneuil Cedex, France Email: thomas.gatski@lea.univ-poitiers.fr (2) Center for Coastal Physical Oceanography and Ocean, Earth and Atmospheric Sciences Old Dominion University, Norfolk, Virginia 23529 USA ABSTRACT Direct numerical simulations (DNS) of turbulent high-speed channel and boundary layer flows have been the subject of numerous numerical investigations for well over a decade. These simulations have included adiabatic and iso- thermal wall conditions as well as cases with shocks. While still at relatively low Reynolds numbers, these simulations have provided a large measure of detailed information that has further confirmed and augmented results from physical experiments. Some additional results from recent DNS of high speed boundary layer flows under adiabatic and isothermal wall con- ditions, and with and without an impinging shock are presented. 1. INTRODUCTION There have been significant advances in the numerical simulation of compressible turbu- lence and turbulent flows since the first simula- tion almost three decades ago [1]. For the first decade, the simulations were primarily limited to homogeneous turbulence and were focused on assessing the role of dilatational effects and the existence of eddy shocklets. For the last decade and a half, direct (and large eddy) simulations (LES) have been applied to in- creasing complex inhomogeneous flow fields. Such flows have been simulated in both the supersonic regime as well as in the low hyper- sonic [2,3] range. In the supersonic range, both adiabatic and isothermal wall conditions have been explored, with and without shocks. Unfor- tunately, as with all methodologies that be- come more readily accessible, there now cur- rently exists a multitude of numerical simula- tion studies. It, thus, becomes more difficult to be all inclusive of these more recent studies, so at the outset, this disclaimer, and an apol- ogy for any such omissions. 2. PROBLEM FORMULATION The compressible Navier-Stokes equations comprising the density ! , momentum !u j = !u, ( !v , !w ) , and total energy !E conservation equations, and coupled with the equation of state for a perfect gas, p = ! T are the differential starting point. In a non- dimensional form, these equations can be written as !" !t + ! !x j ("u j ) = 0 !("u i ) !t + !(u i "u j ) !x j = # !p !x i + M $ % Re $ !& ij !x j !("E ) !t + !(u j "H ) !x j = M $ % Re $ ’ ! !x j u i & ij # % % # 1 ( ) * + , - q j . / 0 1 2 3 4 5 6 7 6 8 9 6 : 6 (1) where ! ij = 2 μ S ij " # ij 3 S kk $ % & ’ ( ) , S ij = 1 2 *u i *x j + *u j *x i $ % & ’ ( ) E = T + " 1 + u i u i 2 , q j = " μ Pr *T *x j H = + + " 1 T t = + T + " 1 + u i u i 2 (2) with the molecular Prandtl number Pr and T t the total temperature. The non-dimensional scaling used in the above is based on a char- acteristic unit length scale and a velocity scale that is the free stream speed of sound, c ! , divided by ! ( ! = 1.4 is the constant ratio of specific heats for a perfect gas), and free stream thermodynamic variables. The Mach number M ! and Reynolds number Re ! are based on free stream values. Other related scalings can be used, but with the one shown here both the Mach number and Reynolds number parameters appear explicitly. Even though the Reynolds number range has been somewhat constrained, the numerous boundary layer simulations have generally