Computation of unsteady transonic cascade flow using the Euler and Navier-Stokes equations of contravariant velocities

The purpose of the present paper is to investigate the steady and unsteady flows through subsonic and transonic turbine cascades using the Euler and Navier-Stokes (N-S) solvers developed by the authors. Use of the fundamental equations of contravariant velocity components also proposed by the authors is very convenient for treating several kinds of boundary conditions. Some efficient numerical schemes for the unsteady calculation, shock capturing and turbulent quantities are also developed. As numerical examples, we show the numerical results of some turbine cascade flows by assuming the flows to be inviscid or viscous (turbulent) and steady or unsteady. The results are compared with each other and with the experimental data. Finally, the reliability and the limitation of the present numerical solvers for the turbine cascade cases are discussed.