Optimization of cooling of gas turbine blades with channels filled with porous material

The following paper presents an iterative algorithm for the determination of porosity distributions in a porous material applied for the cooling of gas turbine blades. Numerical calculations with the use of this algorithm are performed to determine the temperature distributions on the boundaries of the blade. Further calculations verifying the correctness of algorithm's operation were performed. Based on the known distribution of material porosity in channels cooling the blade, the temperature distribution on the outer boundary of the blade was determined (direct problem). Numerical calculations for the blade with a single cooling channel showed a high level of numerical calculations consistence with the solution of the direct problem. Constant temperature on the outer boundary of the blade was assumed to be the optimization criterion; and based on this assumption the porosity distribution and temperature on the walls of cooling channels of the gas turbine blade were determined. Functional optimizing the solution to the inverse problem was extended with a term regularizing temperature gradient within the region of the blade and porous material. Conducted calculations showed that it was difficult to apply porous material to optimize the process of blades' cooling in the vicinity of the leading and trailing edges. Results of calculations indicated the possibility for applying this algorithm practically to optimize the process of gas-turbine blades cooling in those parts of the blade, where it is possible to remove the required amount of heat through the cooling channel.