A Method for Constructing Empirical Correlation Equations for Film Cooling Based on Symbolic Regression and Undetermined Coefficient Optimisation

To address the problems in turbine design where the construction of empirical correlations relies heavily on expert experience, the semi-empirical and semi-fitting method exhibits significant uncertainties, and traditional polynomial fitting suffers from poor generalization and insufficient physical interpretability, a method for constructing film cooling empirical correlations based on symbolic regression and optimization of undetermined coefficients was proposed. Taking the laterally averaged effectiveness and surface effective heat transfer coefficient of film cooling as the research objects, the symbolic regression method was improved for industrial design scenarios. By selecting key feature variables, incorporating undetermined coefficients, and optimizing with the least square method, correlations applicable to various working conditions such as different hole types and turbulence intensities were constructed. Results show that the correlations established by the improved method demonstrate excellent fitting performance, with a maximum correlation coefficient of 0.997 2 and a maximum relative error of 8.47% for the surface heat transfer coefficient. The correlations comply with the physical laws of film cooling and can effectively extrapolate to predict parameter values under other working conditions.