The objective of this work is the development of an implicit block-structured central-differencing scheme with implicit treatment of the boundary conditions for the calculation of three-dimensional inviscid compressible steady flow, primarily through transonic turbomachinery stages. The implicit boundary treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations. Steady-state non-reflecting boundary conditions at the inflow and outflow boundaries and at the stator/rotor interface based on Fourier analysis applied to the linearized Euler equations are also used. Getting a monotonous resolution of shocks, a non-linear additive viscosity term of 2nd and 4th order with pressure-controlled factors is implemented. The three-dimensional blade geometry consists of Bézier-surfaces which are determined by two-dimensional blade profiles based on Bézier-curves. The grid for the flow calculation is obtained by parameterizing special Bézier-surfaces, respectively Bézier-volumes. Finally, the aerodynamic design of the one-stage highly loaded transonic test turbine of Institute of Thermal Turbomachinery and Machine Dynamics - Graz University of Technology) with these tools described above is illustrated with detailed presentation of the specific aerodynamic features, the design technology and the computational results.

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