Full velocity-scalar probability density function computation of heated channel flow with wall function approach

Abstract

A joint velocity-scalar probability density function (PDF) method is presented to model and simulate turbulent flows with passive inert scalars (here temperature). The full PDF approach is applied for wall-bounded flows. In the present work, the boundary conditions are imposed in the logarithmic region and the modeling is therefore performed in the wall-function spirit. The PDF equation is solved by a Monte Carlo method and the whole approach appears as a Lagrangian simulation using stochastic particles. The purpose of the work is to analyze the behavior of classical PDF models in the near-wall region and to develop new particle boundary conditions for the velocity and scalars attached to each particle. First of all, the logarithmic region is described as an equilibrium zone and resulting analytical formulas for second-order temperature–velocity statistics 〈θ2〉, 〈uθ〉, 〈vθ〉 are derived. Boundary conditions for scalars are then developed and formulated in terms of instantaneous particle variables. These results are useful to discuss consistency issues between the formulation of scalar mixing models and the statement of boundary conditions. Finally, heated channel flow is simulated with a stand-alone PDF code for two different heat-flux conditions and results are compared with available direct numerical simulation and experimental data.