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Film cooling is a typical three-dimensional fluid phenomenon, where the coolant with lower temperature is ejected from discrete holes to protect metal walls from being burnt by the hot mainstream. It is a great challenge for Reynolds-averaged Navier–Stokes (RANS) methods to accurately predict the coolant coverage on the wall because the turbulent thermal diffusion tends to be under-predicted due to inherent assumptions behind RANS models. In this paper, a framework of integrated field inversion and machine learning is built to enhance RANS prediction of turbulent thermal diffusion. A neural network (NN) is trained in this framework to predict the spatially varying turbulent Prandtl number ( Pr t ) and to improve the prediction of RANS models. The temperature distribution obtained from the large eddy simulation is used as the learning target, and the discrete adjoint method is used as the inverse model that helps calculate derivatives of mean square error of the temperature distribution to NN parameters. The training process of NN shows good convergence properties. The results show that the obtained NN effectively increases the insufficient turbulent thermal diffusion by predicting much lower Pr t than the commonly used value of 0.9. The NN-enhanced RANS provides significant improvements on predicting experimental temperature distributions compared with general RANS models not only on the training data but also on the unseen testing data. In addition, the obtained NN can be implemented into general-purpose software with minimal effort and no numerical stability problem. [ABSTRACT FROM AUTHOR]

The interaction between the film-cooling jet and vortex structures in the turbine passage plays an important role in the endwall cooling design. In this study, a simplified topology of a blunt body with a half-cylinder is introduced to simulate the formation of the leading-edge horseshoe vortex, where similarity compared with that in the turbine cascade is satisfied. The shaped cooling hole is located in the passage. With this specially designed model, the interaction mechanism between the cooling jet and the passage vortex can therefore be separated from the crossflow and the pressure gradient, which also affect the cooling jet. The loss-analysis method based on the entropy generation rate is introduced, which locates where losses of the cooling capacity occur and reveals the underlying mechanism during the mixing process. Results show that the cooling performance is sensitive to the hole location. The injection/passage vortex interaction can help enhance the coolant lateral coverage, thus improving the cooling performance when the hole is located at the downwash region. The coolant is able to conserve its structure in that, during the interaction process, the kidney vortex with the positive rotating direction can survive with the negative-rotating passage vortex, and the mixture is suppressed. However, the larger-scale passage vortex eats the negative leg of the kidney vortices when the cooling hole is at the upwash region. As a result, the coolant is fully entrained into the main flow. Changes in the blowing ratio alter the overall cooling effectiveness but have a negligible effect on the interaction mechanism. The optimum blowing ratio increases when the hole is located at the downwash region. [ABSTRACT FROM AUTHOR]