A general non-orthogonal collocated finite volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence-transport closure, Part 1: Computational implementation

Abstract

A computational procedure has been developed for predicting separated turbulent flows in complex two-dimensional and three-dimensional geometries. The procedure is based on the fully conservative, structured finite volume framework within which the volumes are non-orthogonal and collocated such that all flow variables are stored at one and the same set of nodes. To ease the task of discretization and to enhance the conservative property of the scheme, a Cartesian or datum-line-adapted decomposition of the velocity field has been used. The solution algorithm is iterative in nature, approaching the steady solution with the aid of a pressure-correction scheme. Convection is approximated with a range of schemes, among them higher-order upstream-weighted approximations and a TVD-type MUSCL form, the last applied principally to the transport equations governing turbulence properties. Effects of turbulence are represented either by two-equation eddy-viscosity models or by a full Reynolds-stress-transport closure. The former category includes both high- and low-Reynolds-number variants in two- as well as three-dimensional conditions. To achieve a stable implementation of the Reynolds-stress equations, a special interpolation practice, analogous to that of Rhie and Chow for momentum [1], has been introduced within the general framework. The procedure has been formulated so as to apply to both incompressible and compressible flows. The latter may contain shocks and highly supersonic regions. To achieve this range of applicability, the retarded-density concept has been combined with the basic pressure-based algorithm to capture shock waves. A ‘Full Approximation Multigrid’ scheme for convergence acceleration has been incorporated and applied in conjunction with all turbulence models including second-moment closure. The present first part of a twin paper focuses on numerical and turbulence-modelling issues. In Part 2, computational results are presented for six representative applications out of fifteen recently predicted with the algorithm within an extensive validation exercise.