A FINITE-DIFFERENCE SCHEME FOR 2-DIMENSIONAL INCOMPRESSIBLE TURBULENTFLOWS USING CURVILINEAR COORDINATES

An implicit time-marching finite-difference method, which has been dev eloped 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 k-ep silon model. The present method has second-order accuracy in time with application of the Crank-Nicholson scheme, and utilizes the QUICK (Qu adratic Upstream Interpolation for Convective Kinematics) upwind-diffe rence scheme in space. The elliptic equation of pressure is solved by means of the Tschebyscheff SLOR (Successive Line Over Relaxation) meth od with alteration of the computational directions. The present implic it turbulent flow scheme is stable under the proper boundary condition s, since spurious error and numerical instabilities can be suppressed by employing a staggered grid. Numerical calculations are performed fo r turbulent flows through a two-dimensional cascade. Computed results of the cascade turbulent boundary layers and the wake profiles are sho wn. The calculated surface pressure distribution is in good agreement with the experimental data.