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With the advancements of numerical upstream and central difference methods in modeling the subsonic and supersonic flows in different paths including the flow inside turbine blades, employing the numerical CUSP technique in the Jameson’s finite volume method can simultaneously benefit from the positive features of both mentioned methods. The novelty of this paper is first, improving Jameson’s finite volume method in modeling a 2D supersonic flow between the blades of a steam turbine using the CUSP method, and second, defining the most optimum control function mode using the Marquardt-Levenberg inverse method and by accounting for the mass conservation equation. By considering the importance of the shock regions in the blade’s surface suction side, the focus of the mentioned method is on this part which results in the significant improvement of the pressure ratio in Jameson’s finite volume method. The results of the first combined method (Jameson and CUSP) at the shock region of the blade’s suction surface desirably agree with the experimental data, and a decrease of numerical errors at this region is resulted. Furthermore, the results of the second combined method (Jameson, CUSP and inverse method) shows that in comparison with original Jameson’s method and the first combined method, by average, the conservation of mass condition is improved 15% at the shock region of the blade’s suction surface.

Keywords: Stator turbine blade, Jameson’s method, CUSP method, Marquardt-Levenberg inverse method

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