Direct Numerical Simulation of Transition and Turbulence in a Spatially Evolving Boundary Layer

Abstract

A high-order-accurate finite-difference approach to direct simulations of transition and turbulence in compressible flows is described. The technique involves using a zonal grid system, upwind-biased differences for the convective terms, central differences for the viscous terms, and an iterative-implicit time-integration scheme. The integration method is used to compute transition and turbulence on a flat plate. The main objective is to determine the computability of such a flow with currently available computer speeds and storage and to address some of the algorithmic issues such as accuracy, inlet and exit boundary conditions, and grid-point requirements. A novel feature of the present study is the presence of high levels of broad band freestream fluctuations. The computed data are in qualitative agreement with experimental data (from experiments on which the computation is modeled). The computational results indicate that the essential features of the transition process have been captured. Additionally, the finite-difference method presented in this study can, in a straightforward manner, be used for complex geometries.