An Inverse (Design) Problem Solution Method for the Blade Cascade Flow on Streamsurface of Revolution

On the basis of the fundamental equations of aerothermodynamics a method for solving the inverse (design) problem of blade cascade flow on the blade-to-blade streamsurface of revolution is suggested in the present paper. For this kind of inverse problem the inlet and outlet flow angles, the aerothermodynamic parameters at the inlet, and the other constraint conditions are given. Two approaches are proposed in the present paper: the suction-pressure-surface alternative calculation method (SSAC) and the prescribed streamline method (PSLM). In the first method the metric tensor (blade channel width) is obtained by alternately fixing either the suction or pressure side and by revising the geometric form of the other side from one iteration to the next. The first step of the second method is to give the geometric form of one of the streamlines. The velocity distribution or the mass flow rate per unit area on that given streamline is estimated approximately by satisfying the blade thickness distribution requirement. The stream function in the blade cascade channel is calculated by assuming initial suction and pressure surfaces and solving the governing differential equations. Then, the distribution of metric tensor on the given streamline is specified by the stream function definition. It is evident that the square root of the metric tensor is a circumferential width of the blade cascade channel for the special nonorthogonal coordinate system adopted in the present paper. The iteration procedure for calculating the stream function is repeated until the convergence criterion of the metric tensor is reached. A comparison between the solutions with and without consideration of viscous effects is also made in the present paper.