COMPLEX BOUNDARY INTEGRAL EQUATION METHOD FOR MODELING OF AVIATION GAS TURBINE COOLED ELEMENTS

摘要

At the present the heat protection of high-temperature gas turbine blades is mainly provided at the expense of efficient cooling systems development. The task of turbine cascades streamlining comes to boundary integral equation (BIE) Fredholm II with a peculiarity. Stationary and quasistationary temperature fields of blades are calculated with application of new mathematical models represented in BIE in multi connected fields of complex configuration. For solving proper equations discrete operators have been investigated, converging quadrature and cubature processes have been developed and values in terms of A. Zigmound′s modules of continuity have been received. Approximate BIE solutions are mathematically proved by appropriate theorems and lemmas. Methods of turbine profile approximation have been developed (method of least square with automatic joint, smoothing splines, smooth replenishment and neural nets have been used). In basis of potential flow theory, boundary integral equations had been received for components of flow complex potential-velocity potential and stream function differing from existence of the effectiveness of numerical realization (Complex Boundary Integral Equation Method). The corresponding algorithms and softwares in object-oriented programming language DELPHI 7 were created for the solution of equations. The reliability of the methods was proved by numerical and experimental investigations heat and hydraulic characteristics of the first stage of cooled nozzle blade of high pressure turbine. Geometric model, equivalent hydraulic schemes of cooling tracks have been obtained, cooler parameters and temperature field of gas turbine nozzle blade have been determined. Methods have demonstrated high efficiency at repeated and polivariant calculations, on the basis of which the way of blade cooling system modernization has been offered.