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Abstract: This paper is interested in the numerical approximation of the turbulent 3D incompressible flow. The turbulent flow is mathematically modeled using the Reynolds averaged Navier–Stokes (RANS) equations and two classes of the turbulent models are considered. RANS equations are approximated by two numerical techniques, the finite volume and the finite element methods. The finite element approximation on general 3D domains using general meshes consisting of hexahedrons as well as tetrahedrons, pyramids and prisms is described. The definition of the continuous piecewise trilinear/linear finite element space is given, and the stabilization based on the streamline-upwind/Petrov–Galerkin method together with the pressure stabilizing/Petrov–Galerkin techniques is used. The turbulence model is approximated on the finite element spaces, and the nonlinear stabilization technique is applied. Furthermore, the finite volume technique is used for the approximation of the RANS equations. The turbulent or the explicit algebraic Reynolds stress models are used. The numerical solution is carried out by the implicit finite volume method. The artificial compressibility method is used to solve the incompressibility constraint. The numerical results are shown. [Copyright &y& Elsevier]

Highlights: [•] 2D and 3D simulations of backward facing step flows. [•] Step perpendicular or inclined, top wall parallel or inclined. [•] Used finite element and finite volume method. [•] Used eddy viscosity and EARSM turbulence models. [•] All results compared with experimental data. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with numerical solution of laminar and turbulent flows of Newtonian and non-Newtonian fluids in branched channels with two outlets. Mathematical model of the flow is based on the Reynolds averaged Navier–Stokes equations for the incompressible fluid. In the turbulent case, the closure of the system of equations is achieved by the explicit algebraic Reynolds stress (EARSM) turbulence model. Generalized non-Newtonian fluids are described by the power-law model. The governing equations are solved by cell-centered finite volume schemes with the artificial compressibility method; dual time scheme is applied for unsteady simulations. Channels considered in presented calculations are of constant square or circular cross-sections. Numerical results for laminar flow of non-Newtonian fluid are presented. Further, turbulent flow through channels with perpendicular branch is simulated. Possible methods for setting the flow rate are discussed and numerical results presented for two flow rates in the branch. [Copyright &y& Elsevier]

Abstract: The work deals with the numerical simulation of turbulent flow through turbine cascades including heat exchange between fluid and blades. The numerical algorithm couples an implicit AUSM finite volume solver for fluid flow and a finite element solver for heat conduction inside the blade. Several k-ω turbulence models are applied. The eddy diffusivity assumption is used for turbulent heat flux computation. The influence of inlet boundary conditions for turbulence models is discussed. A case of failure of eddy diffusivity turbulent heat flux with common value of turbulent Prandtl number Pr t =0.91 is presented, where remedy is achieved by lowering the magnitude of Pr t . [Copyright &y& Elsevier]