Comparison Between Prandtl’s Mixing Length Model and DNS Data for a Channel Flow Up to Reτ ≈ 5200

Abstract

Abstract This paper presents a theoretical study of fully developed turbulent flow in a channel at friction Reynolds numbers of 1000, 2000 and 5200. For the momentum equation, Reynolds Averaged Navier-Stokes (RANS) approach was used, where the Reynolds stress was modeled using Prandtl’s mixing length model with Van Driest’s modification to capture the damping effect near wall. The velocity profile was computed by solving the non-linear ODE for momentum using Euler’s method. The results were compared with the latest available DNS data.