DNS and Reynolds Stress Transport Modeling of Adverse Pressure Gradient Flat Plate Flow*

A systematic study is carried out to study the Reynolds stress budgets in strongly adverse pressure gradient turbulent boundary layers. We perform Direct Numerical Simulations (DNS) of Re_τ = 500 boundary layers with Clauser pressure-gradient parameters of 0, 10 and 20. The focus of these simulations and their statistics is to obtain term-wise comparisons of the budget terms in the Reynolds stress transport equations for use in Reynolds Averaged Navier-Stokes (RANS) model assessments. Accordingly, we present the exact closure terms for material transport, production, turbulent and pressure diffusion, redistribution and dissipation. These are compared against DNS predictions for the sub-models (diffusion, redistribution, dissipation) that have been proposed for various sublayer resolved conventional Full Reynolds Stress Models (FRSM).  Additionally, we study the results returned by the RANS FRSM code itself for these mean statistics. Several severe shortcomings are observed in the submodel forms which conspire to compromise the FRSM accuracy in predicting even low order moments.