Interrelationships of entropy production and turbulence kinetic energy associated with simple angle and compound angle full coverage film cooling

Abstract

The present paper compares experimentally-measured distributions of entropy generation with numerically-predicted distributions of streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy. These comparisons are provided for two full-coverage film cooling environments which are designed to model the thermal management arrangements employed for combustor liners within gas turbine engines. One of these arrangements includes alternating compound angle values of +30° in one row of holes, followed by −30° in the next row of holes. The other arrangement includes simple angle holes with a zero degree compound angle value. The associated full-coverage film cooled boundary layers are investigated within a double-wall cooling test facility wherein the air for each full-coverage film cooling arrangement is provided by an impingement jet array. Experimentally-measured entropy generation values are obtained from film cooled boundary layer measurements of local total pressure variations, obtained in isothermal flow, relative to the freestream values outside of the boundary layer. The resulting entropy generation values quantify second law losses, which are associated with aerodynamic gains. To obtain the associated numerical-prediction results for a steady-state, three-dimensional flow field, employed is the ANSYS FLUENT Version 2022 R2 computational code with a SST k–ω turbulence closure model. The resulting comparisons of entropy generation, streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy are provided for a blowing ratio BR of 2.9 for simple angle film cooling with a main flow Reynolds number Rems of 138,000, and for compound angle film cooling with a main flow Reynolds number Rems of 142,000. Overall, evidence is provided of strong relationships between local turbulence kinetic energy and local entropy production since the two quantities are highly correlated with each other over s substantial range of experimental conditions and configurations. For example, ratio of turbulence kinetic energy to entropy generation data collapse for Z/de values from 0 to 3.5 for Y/de = 0.5, Y/de = 1.5, and both film cooling arrangements. Here, the value of the TKE/Sgen ratio is approximately constant for these conditions, which evidences direct and simple dependences of local turbulence kinetic energy upon local entropy generation, even for lower magnitudes of Z/de. The direct and simple dependences of local turbulence kinetic energy upon local entropy generation are further illustrated by the simplicity of linear correlation equations, which represent physical behavior for different conditions and configurations. These correlation equations are developed for three arrangements, which are associated with X/de = 54.54.