Genetic algorithm for gas turbine blading design

Designing a gas turbine from scratch has always been an extremely laborious task in terms of obtaining the desired power output and efficiency. Theoretical prediction of the performances of a gas turbine has proven in time to be a compromise between accuracy and simplicity of the calculus. Methods such as the Smith chart are very easy to apply, but to make an exact prediction of the flow in a turbine would lead to an almost infinite number of variables to be considered. A quite precise method of determining total-loss coefficients for a gas turbine, based on a large number of turbine tests, was developed by D.G. Ainley and G.C.R. Mathieson, with an error of the calculated efficiency within 2%. The accuracy of the method has been validated by Computational Fluid Dynamics simulations, included in the paper. Even if it is not a novel approach, the method provides accurate numerical results, and thus it is still widely used in turbine blade design. Its difficulty consists of the large number of man-hours of work required for estimating the performances at each working regime due to the many interdependent variables involved. Since this calculus must be conducted only once the geometry of the turbine is determined, if the results are not satisfactory one must go back to the preliminary design and repeat the entire process. Taking into account all the above, this paper aims at optimizing the efficiency of a newly design turbine, while maintaining the required power output. Considering the gas-dynamic parameters used for determining the preliminary geometry of a turbine, and the influence of the geometry upon the turbine efficiency, according to the procedure stated above, a Monte Carlo optimizing method is proposed. The optimization method consists in a novel genetic algorithm, presented in the paper. The algorithm defines a population of turbine stage geometries using a binary description of their geometrical configuration as the chromosomes. The turbine efficiency is the fitness function and also acts as the mating probability criterion. The turbine energy output is verified for each member of the population in order to verify that the desired turbine power is still within acceptable limits. Random mutations carried on by chromosome string reversal are included to avoid local optima. Hard limits are imposed on optimization parameter variation in order to avoid ill defined candidate solutions. The approach presented here significantly reduces the time between design goal definition and the prototype.