A control‐volume based finite element method for three‐dimensional incompressible turbulent fluid flow, heat transfer, and related phenomena

Abstract

AbstractA control‐volume based finite element method of equal‐order type for three‐dimensional incompressible turbulent fluid flow, heat transfer, and related phenomena is presented. The discretization equations are based mainly on the physics of the phenomena under consideration, more than on mathematical arguments. Special emphasis is devoted to the discretization of the convective terms and the continuity equation, and to the treatment of the boundary conditions imposed by the use of a high Reynolds k‐ϵ, type turbulence model. The pressure‐velocity coupling in the fluid flow calculation is made from a derivative of the original SIMPLER method, without pressure correction. The discretized equations are solved in a sequential, rather than a coupled, form with significant advantage in the required computer time and storage. The method is an extension of a former version proposed by us for two‐dimensional, laminar problems, and is here successfully applied to the following situations: three‐dimensional deflected turbulent jet, and flows in 90° and 45° junctions of ducts with rectangular cross sections. The calculated results are in very good agreement with the experimental and numerical (obtained with the well established finite difference method) data available in the literature.