Scaling of the turbulent boundary layer along a flat plate according to different turbulence models

Abstract

Abstract At sufficiently large Reynolds number the turbulent boundary layer along a flat plate under zero pressure gradient can be split up in an inner and outer layer. The classical theory says that a law-of-the-wall holds in the inner layer, and a defect law in the outer layer. It is shown that four different types of commonly used turbulence models (an algebraic, k – ϵ , k – ω and a differential Reynolds-stress model) all reproduce the classical similarity scalings for Re θ above about 10 4 . This was verified by numerically solving the turbulent boundary-layer equations for Reynolds numbers (based on the momentum-loss thickness) in between 300 and 5×10 7 . The boundary-layer solution in the outer layer is shown to converge to the similarity solution of a defect-layer equation. All turbulence models considered give a wall function and defect law that is close to Direct Numerical Simulations of Spalart (1988) and new high-Reynolds-number experiments by Fernholz et al. (1995) . An exception is the algebraic model that gives a too thin boundary layer.