Application of Schwarz-Christoffel Transformation in Solving Two-Dimensional Turbulent Flow with Complex Geometries

In this paper, two-dimensional turbulent flows with complex geometries and variety of shapes are simulated using a new and accurate grid generation method. In order to obtain the flow properties, the numerical solution of Navier- Stokes equations with the equations governing the kinetic energy of turbulence and the dissipation rate are solved using CFD techniques. Considering the complexity of the physical geometry, conformal mapping is used to generate an orthogonal grid by means of the Schwarz-Christoffel transformation. The standard rd k -e turbulence model is employed to simulate the mean turbulent flow field. The governing equations are transformed in the computational domain and the discretized forms of the transformed equations are obtained by the control volume method. Finite different forms of the governing equations are solved in the computational plane and the SIMPLE algorithm is used for the pressure–velocity coupling. The important part of the present work is based on the numerical integration of the Schwraz-Christoffel transformation in grid generation for fluid flows with different complex geometries. To validate the computational results, comparison with the experimental data of other investigators is made, and reasonable agreement is found.