Mathematical model and software package of conjugate heat transfer between viscous gas-dynamic flows and cooled gas turbine blades


Kolesnik S. A.*, Formalev V. F.**, Selin I. A.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



Physical and mathematical model, algorithm and software package for solving the problem of conjugate heat transfer between a viscous gas-dynamic flows and cooled gas turbine blades produced by means of a compound permeable shells technology are expounded. The mathematical model includes the dynamical and heat boundary layers equations, equations of the flow and heat exchange of air, in flowed from a power machine compressor, in complex channels inside the compound permeable shells (CPS), space no steady heat conduction in CPS skeletons, cooler injection in the gas-dynamic boundary layer, conjugate heat transfer between hydraulic gas dynamic flows and CPS construction.
Flow and heat exchange of the cooler are expounded in detail in each of seven typical CPS zones, which are essentially differ in a heat exchange level and accordingly in heat pick up from hot walls. The effective method permitting to define temperature fields by means when coordinate lines go out from a computational area in gas cavities and again get into the cavities with extraction of complex boundaries and putting fractional space steps on it was suggested for numerical solving of conjugate heat exchange problems in multiply connected space areas. The software package SPO was developed on programming language FORTRAN using modular concept permitting to expand functional possibilities adding new modules. Huge number of results in heat flows and space temperature fields in the elements of CPS were obtained using SPO. Efficiency of SPO was tested in cases of different rates of cooler flux and different heat flows caused by high temperature gas-dynamic flow (up to 2000K).
It was revealed, CPS take middle place between porous and perforating refrigerating in cooling efficiency, however, it is too difficult technologically to make a porous skeleton. Researches showed the cooling efficiency with applying CPS is great deal higher in case of small heat flows caused by hot gas. Also it was determined, in case of big rate of cooler flux, starting from 0,1 g/s and higher, the efficiency does not rise, i.e. it is possible do not increase the rate of cooler flux. It was showed, in a case of minimum rate of cooler flux ~0,1 g/s the CPS skeleton temperature reaches 400C when the gas-dynamic flow temperature is 1600K, that decreases strength of CPS skeleton considerably.


compound permeable shells, gas-dynamic flow, conjugate heat transfer, conjugate heat transfer, heat flux, cooling efficiency, special software, boundary layer


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