Boundary treatment and an efficient pressure algorithm for internal turbulent flows using the PDF method

Abstract

SUMMARY The generalized Langevin model, which is used to model the motion of stochastic particles in the velocity‐ composition joint probability density function (PDF) method for reacting turbulent flows, has been extended to incorporate solid wall effects. Anisotropy of Reynolds stresses in the near-wall region has been addressed. Numerical experiments have been performed to demonstrate that the forces in the near-wall region of a turbulent flow cause the stochastic particles approaching a solid wall to reverse their direction of motion normal to the wall and thereby, leave the near-wall layer. This new boundary treatment has subsequently been implemented in a full-scale problem to prove its validity. The test problem considered here is that of an isothermal, non-reacting turbulent flow in a two-dimensional channel with plug inflow and a fixed back-pressure. An efficient pressure correction method, developed in the spirit of the PISO algorithm, has been implemented. The pressure correction strategy is easy to implement and is completely consistent with the time-marching scheme used for the solution of the Lagrangian momentum equations. The results show remarkable agreement with both k‐ and algebraic Reynolds stress model calculations for the primary velocity. The secondary flow velocity and the turbulent moments are in better agreement with the algebraic Reynolds stress model predictions than the k‐ predictions. The velocity‐composition joint PDF method 1 is an important tool for the computation of reacting turbulent flows. Starting with the conservation equations for mass, momentum and compositions of various species (for a chemically reactive flow), a single transport equation can be derived for the joint probability density function of velocity and composition, fu V x t , as described in Reference 1. The quantity fu dV d represents the probability that V U V dV and d occurs simultaneously, where U is the velocity vector, is the set of all scalars (temperature or enthalpy and concentrations) and V and are independent sample space variables corresponding to U and respectively. The transport equation for the joint PDF is a multidimensional partial differential equation and cannot be solved efficiently by traditional finite difference or finite volume techniques. The Monte Carlo method is used instead. In this method the fluid within the whole computational domain is discretized into representative ‘particles’ (or samples). These ‘particles’ then move with time and their motion is governed by their Lagrangian