A Finite-Difference Scheme for Two-Dimensional Incompressible Turbulent Flows Using Curvilinear Coordinates

Abstract

An implicit time-marching finite-difference method, which has been developed previously to solve the incompressible Navier-Stokes equations of contravariant velocities in curvilinear coordinates, is extended to a turbulent flow scheme employing a suitable low Reynolds number κ-ε model. The present method has second-order accuracy in time with application of the Crank-Nicholson scheme, and utilizes the QUICK (Quadratic Upstream Interpolation for Convective Kinematics) upwind-difference scheme in space. The elliptic equation of pressure is solved by means of the Tschebyscheff SLOR (Successive Line Over Relaxation) method with alteration of the computational directions. The present implicit turbulent flow scheme is stable under the proper boundary conditions, since spurious error and numerical instabilities can be suppressed by employing a staggered grid. Numerical calculations are performed for turbulent flows through a two-dimensional cascade. Computed results of the cascade turbulent boundary layers and the wake profiles are shown. The calculated surface pressure distribution is in good agreement with the experimental data.