Heat transfer and turbulent heat flux budgets in cooling films

Statistics from large-eddy-simulation (LES) of cooling films with different cooling holes are used to evaluate budgets in the transport equation of turbulent heat flux. The capability of LES has been assessed by comparing simulated results with experimental data, while the correctness of the procedure generating turbulent heat flux budgets has been examined on a turbulent boundary layer. The mechanism of heat transfer has been preliminarily studied throughout the three-dimensional flow field at different blowing ratios using a general outer scaling, to recognize specific regions with corresponding heat transfer patterns. A compressible version of budget terms in the transport equation of turbulent heat flux is then explored to show the thermal behavior of flow downstream from the cooling film holes. Characteristics of each budget term are presented in a defect scaling consistent with the scaling suitable for Reynolds stresses and Reynolds stress budgets. Furthermore, these budget terms are compared among an array of different cooling hole shapes combined with different blowing ratios to explore self-similarity. Results show that the dynamic balance of all budget terms is significantly influenced by the cooling hole shape, while each turbulent heat flux budget term may scale with the velocity defect, temperature deficit, and the normalized streamwise distance to the power of an exponent dependent on the hole shape.