Поток без осевой симметрии через вращающуюся решетку турбомашины на поверхности тока S₂

Abstract

Рассмотрено относительное установившееся течение идеального газа через вращающуюся решетку осевой турбомашины. Поверхности тока S₂ являются скрученными произвольным образом поверхностями. Используется цилиндрическая система координат, однако вектор скорости потока однозначно определен не тремя проекциями на координатные оси, а только двумя проекциями на направления, которые однозначно задаются геометрией поверхности тока. Для расчета течения без осевой симметрии в слое переменной толщины получено точное уравнение количества движения.As of today the development of the CFD-method that would allow us to find the accurate solution for the inverse problem of the cascade theory has no prospects in the nearest future. Therefore we propose the further development of the classic version of the Q3D- approach for which we assume the current motion in the layers on stream surfaces S1 and S2 and the use of the Euler equation and the solution search process will be iterative. The advanced method of the solution of the inverse problem for the stream on the surface S2 has no axial symmetry and the problem is solved for the layer of a variable thickness using new forms of discontinuity equations and the equations of the amount of motion. The surfaces S1 are arbitrary twisted, and the 3-D flow is reduced to the 2-D flow with no assumption that the radial component of the velocity and all the derivatives in the radial direction are homogeneous and retain their values that correspond to the solution of the problem for the surfaces S2. The inverse problem of the theory of cascades is solved step-by-step. At the first stage the geometry of two adjacent surfaces S2 that form the layer of a variable thickness, for example in the middle of the channel, is prescribed and the meridional contours of the root and the periphery of the interblade channel for this layer are defined. At the second stage the problems are solved for S1 surfaces that can be twisted. At the third stage we performed the volumetric profiling of the blade using determined geometric characteristics of the interblade channel.