The paper is intended to describe a method for the calculation of 3D viscous compressible (subsonic or supersonic) flow in axial turbomachines described in the form of thin-layer Reynolds-averaged Navier-Stokes equations. The method draws on Godunov-type upwind differencing and ENO reconstruction suggested by Harten (1987), so as to assure monotonicity preservation and high accuracy of computational results. The computational efficiency is achieved thanks to the implementation of a simplified H-type multi-grid approach and delta -form implicit step. Turbulent effects are simulated with the help of a modified algebraic model of Baldwin-Lomax (1978). This method was at the foundation of a computer code-a complex software package to calculate 3D flow in multi-stage turbomachines that allows us to obtain local characteristics, like temperature, pressure, density or velocity distributions, as well as global characteristics, such as flow rates, stage reaction, flow efficiency for the considered turbine/compressor stage. The paper also gives selected results of computation of a number of turbomachinery cascades, showing that these results agree reasonably well with the available experimental data.
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