Application of the Schwarz-Christoffel Transformation in Solving Two-Dimensional Turbulent Flows in Complex Geometries

Abstract

In this paper, two-dimensional turbulent flows in different and complex geometries are simulated by using an accurate grid generation method. In order to analyze the fluid flow, numerical solution of the continuity and Navier-Stokes equations 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 k-ε turbulence model is employed to simulate the mean turbulent flow field, using a linear low-Re k-ε model for near wall region. The governing equations are transformed in the computational domain and the discretized forms of these equations are obtained by the control volume method. Finite difference 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 Schwraz-Christoffel transformation in grid generation for simulating fluid flow in different complex geometries. To validate the computational results, the theoareticil data is compared with that of theoretical results achieved by other investigators, which are in reasonable agreement