The development of effective cooling systems is one of the most actual and difficult problems of development of gas-turbine engines. Significant amount of works is devoted to the research of characteristics and optimization of the film cooling holes shape. Different shapes of holes are investigated at various working conditions. However, the development of optimization methods of film cooling holes shape is covered insufficiently.
Optimization methods are widely applied for solving modern optimization problems on the basis of surrogate models. The most famous one is the method of response surface. The aim of this method is to construct an approximation response surface of the objective function. It is also necessary to create and evaluate many variants of the investigation object design and therefore to conduct the same amount of CFD calculations or experiments in order to provide the acceptable design of an experiment (DOE). Such number of points on the response surface results in extreme computational costs increasing, i.e. so called “Curse of Dimension”.
The main objective of the current paper is to develop the method to improve film-cooling holes shape along with minimum time and computational costs and acceptable accuracy of the surrogate model. Besides, the analysis of optimization results is considered.
In the structural-parametrical analysis, methods of transformation of multidimensional information are used to generalize geometrical parameters of film cooling holes shape. The optimization process is carried out by means of random search methods. As a result, the “fast” surrogate model featuring acceptable accuracy was obtained. Then by regression analysis methods the structural coupling equation (SCE) between the principal components of holes shape and its cooling effectiveness was obtained. The authors carried out the study of the optimum variant of a film cooling holes shape in the space of the principal components. Geometrical information of the optimized variant has been obtained and further calculation of its characteristics was carried out by means of the “reverse recovery” technology developed.
Finally, the offered method enables us to get the film-cooling holes geometry variant with a higher level of cooling effectiveness compared to the considered classical variants. Thus, the offered way of optimization provides eightfold decrease in necessary number of CFD calculations compared to the classical approach (DOE and the response-surface methods).
