Probability density function computation of heated turbulent channel flow with the bounded Langevin model

Abstract

The paper addresses the modelling and computation of heated turbulent flowswith temperature treated as a dynamically passive scalar variable. The probability density function (PDF) method is appliedto wall-bounded turbulence. In a one-point PDF statistical approach with additional scalars, turbulent mixing models remain an open issue.The bounded Langevin model for scalar mixing is presentedin the form of a stochastic diffusion process in continuous time and is shown to successfully predict the turbulent mixing of initially bimodal scalar distribution. In the paper, two variants of the PDF approach are formulated and solved in the Lagrangian setting. First, the stand alone joint velocity-scalar PDF is considered with the assumptions of log-layer for both velocity and temperature that result in the Lagrangian wall-function approach. Corresponding formulae are derived for the equilibrium values of the second order temperature-velocity statistics. The Lagrangian stochastic evolution equations are solved for velocity, turbulent energy dissipation rate and temperature. Second, the scalar PDF closure proposal with down to the wall integration is formulated using externally provided turbulence statistics. For both formulations of the PDF approach,the heated channel flow is considered as the validation case. PDF computation results are presented and compared with available DNS data. Consistency issues are discussed regarding the formulation of the scalar mixing model. This article is a modified version of the original article from the Proceedings of the 5th International Symposium on Engineering Turbulence Modelling and Measurements, Mallorca, 16-18 September 2002, which appeared in ‘Engineering Turbulence Modelling Measurements 5’, Elsevier Science, ISBN 0-08-044114-9, ed W Rodi and N Fueyo.