The numerical solution of turbulent flow in three-dimensional curvilinear co-ordinates

Abstract

Many fluid flow applications that exist in engineering practice can be solved by means of numerical techniques. Most of these problems require complete three-dimensional modelling of flow in· complex curvilinear geometries. This motivated the development of a numerical model for the solution of three-dimensional turbulent flow based on a general curvilinear co-ordinate system. Three-dimensional turbulent flow is described by six highly non-linear partial differential equations. These include the three momentum equations, the continuity equation and the two equations of the k - £ turbulence model. In order to apply the conservation principles in the above equations to general curvilinear co-ordinates, transformation relations are used in formulating the equations in terms of general curvilinear form. A finite volume numerical approach is used to discretize the relevant equations into a linear form. The equations are then solved simultaneously by an iterative process. A segregated approach based on the SIMPLE algorithm is used for this purpose whereby pressures and velocities are calculated separately. Due to the application of the segregated approach, decoupling between pressures and velocities occurs. A specific interpolation scheme is implemented whereby strong pressure velocity coupling is ensured. Turbulence effects are included by calculating an additional turbulent viscosity, which has the effect of increasing the effective fluid viscosity. The computer program (3DFLO) is written in Fortran 77 and executed on an IBM f550 computer. After each stage of the development process, various test cases were solved to verify the accuracy of the code. It is shown that the numerical results compare favourably to analytical, experimental and previous numerical results. The code was then applied to the modelling of three dimensional atmospheric boundary layer flow over and around arbitrary shaped buildings. The use of non-orthogonal boundary fitted grids enabled the exact conformation of sharp ridge geometry and pitched roof inclines. The numerical predictions are in good agreement with full scale measurements and prove to be superior to previous numerical predictions. This can be mainly attributed to an improved representation of physical flow boundaries and to complete three-dimensional modelling.