Direct numerical simulation and data analysis of a Mach 4.5 transitional boundary-layer flow

Abstract

This paper describes the creation by temporal direct numerical simulation and the analysis based on the Reynolds stress transport equations of a high quality data set that represents the laminar–turbulent transition of a high-speed boundary-layer flow. Following Pruett and Zang [Theoret. Comput. Fluid Dyn. 3, 345 (1992)], and with the help of algorithmic refinements, the evolution of an axial, Mach 4.5 boundary-layer flow along the exterior of a hollow cylinder is simulated numerically. From a perturbed laminar initial state, the well-resolved simulation proceeds through laminar breakdown to the beginning of a turbulent flow regime. Favre-averaged Reynolds stress transport equations are derived in generalized curvilinear coordinates and are then specialized to the cylindrical geometry at hand. Reynolds stresses and various turbulence quantities, such as turbulent kinetic energy and turbulent Mach number, are calculated from the numerical data at various stages of the transition process. The kinetic energy ‘‘budgets’’ are also constructed from the transport equations. Various contributing terms for the evolution of kinetic energy, like the rates of production, dissipation, transport, and diffusion, are presented. The compressible dissipation rate is small in comparison with the solenoidal dissipation rate for all times. The pressure–dilatation term is of the same order of magnitude as the compressible dissipation rate. The authors hope that both the data set and the analysis presented will benefit those who attempt to model high-speed transitional flow.