Уравнение неразрывности для течения в слое переменной толщины на поверхности S₂

Abstract

Рассмотрено относительное установившееся течение идеального газа через рабочую решетку осевой турбомашины. Для получения приближенного решения используется квазитрехмерный (Q3D) подход, который в своей классической постановке был всесторонне разработан Ч. Х. Ву. Поток разделен на слои поверхностями S₁ и S₂. Поверхности S₁ не имеют оси симметрии, которая совпадает с осью турбомашины. Трехмерное течение на поверхности S₂ сведено к двумерному течению без допущения о том, что течение является осесимметричным.

A constant flow of ideal gas through the cascade of axial turbomachine has been considered. To obtain the approximate solution we usedthe quasi-three-dimensional (Q3D) approach, which in its classical statement was comprehensively developed by Ch. Kh. Wu. The flow is separated into the layers by S₁ and S₂ surfaces. The S₁ surfaces have no symmetry axis that coincides with the turbomachine axis. Three –dimensional flow on the S₂ surface is reduced to the two-dimensional flow with no assumption that the flow is axially symmetric. It is assumed that the flow moves in the layers of a variable thickness on two surfaces S₁ and S₂. The Euler equation is used by the surface problems to describe the flows. The problem is solved individually for each surface taking into consideration mutual influence of two-dimensional (2D) flows. First the solution for axial symmetric problem is sought on arbitrary twisted surfaces S2 assuming that it gives satisfactory data with regard to the averaged parameters of the cascade flow and then flowparameters are determined on axial symmetric surfaces S₁ in the layers of variable thickness in the interbladechannel as the deviation from average parameters. To create new methods for the solution of direct and inverse problems of the theory of turbomachine cascades the following approach tothe development of Q3D technique is proposed, in particular an assumption of axial symmetry of the flow is eliminated for the problem on S₂ surfaces and the problem is solved for the layer of variable thickness.