Eckert number application for scaling of heat-mass transfer analogy in transonic film cooling

Film cooling is energy mixing based on flow mixing. Using the mass transfer method to obtain the film cooling effectiveness is biased. In this paper, a corrected turbulence model with experimental verification is used. The difference between energy mixing and mass mixing is investigated, and a method is proposed to obtain a more accurate adiabatic wall temperature. The computational domain is set up in a convergent-divergent nozzle that can realise supersonic flow. A row of 20-degree film holes is set in the convergent and divergent sections. The density ratio and specific heat capacity are the main research parameters. The density ratio and specific heat capacity represent the scaling criteria of flow mixing and energy mixing from engine conditions to experimental conditions. Three definitions of film cooling are compared to determine the relatively appropriate heat-mass transfer analogy parameters. The results show that using the temperature and substance analogy shows deviations under engine conditions, while using the enthalpy and substance analogy reduces these deviations. The deviations are caused by viscous dissipation. The Eckert number, which is a key part of scaling from engine conditions to experimental conditions, is a measure of the deviations.