Calculation of three-dimensional viscous gas flow in a straight cascade

A numerical method for solving the problem of three-dimensional flow around a straight cascade is developed, and its accuracy is evaluated. For simulating the turbulence effects, a two-parameter differential (q-ω) model of turbulence is used. The computational algorithm of the present study is based on Godunov's implicit relaxation scheme of the second accuracy order previously proposed for numerical integration of the Navier-Stokes equations. The system of equations is written in an arbitrary system of coordinates with retention of its divergent form. The vectors of flows through the cell sides are calculated similar to Godunov's explicit scheme by means of the arbitrary discontinuity decay procedure. For enhancing the approximation order of the spatial derivatives, piecewise-parabolic distributions satisfying the condition of monotony (for the linear system) are used. The calculation is implemented on an H-type computational net. As a test example, the calculation of stationary flow in a low-pressure turbine cascade is carried out. The method's accuracy is evaluated by comparing the distributions calculated with the experimental results.