Development of an explicit algebraic turbulence model for buoyant flows – Part 1: DNS analysis

An analysis of DNS databases of vertical plane channel flow for forced, mixed and natural convection is proposed. This analysis aims to assess the main features needed to develop an algebraic model for buoyant flows. First, the weak equilibrium assumption, at the root of algebraic models, is investigated. This hypothesis is shown to fail near the velocity maximum and close to the walls but remains valid otherwise, whatever the convection regime. The models for the redistribution term and the pressure scrambling term are then analyzed on the same configurations. A linear form of the Speziale et al. (1991) model is retained for the redistribution term. No model for the pressure scrambling term is fully satisfactory; nevertheless some models are recommended. The buoyant contributions to the pressure term are investigated. Finally, the generalized gradient diffusion hypothesis, which could be used to model the turbulent heat fluxes in order to avoid the coupling with the Reynolds stresses, is shown to be inaccurate.