A Three-Dimensional, Immersed Boundary, Finite Volume Method for the Simulation of Incompressible Heat Transfer Flows around Complex Geometries

Abstract

The currentwork focuses on the development and application of a newfinite volume immersed boundarymethod (IBM) to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers.The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS) of a turbulent flow around a surface-mounted matrix of cubes.The results computed with the present method compare very well with Laser Doppler Anemometry (LDA) measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.