Modal Analysis of Inclined Jet Film Cooling Flows With Density Variation

Abstract

Thermal and hydrodynamic flow field over a flat surface cooled with a single round inclined film cooling jet and fed by a plenum chamber is numerically investigated using Large Eddy Simulation (LES) and validated with published measurements. The calculations are done for a free stream Reynolds number Re = 16000, density ratio of coolant to free stream fluid ρj/ρ∞ = 2.0 and blowing ratio BR = ρjV/ρ∞V = 1.0. A short delivery tube with aspect ratio l/D = 1.75 and 35° inclination is considered. The evolution of the Kelvin-Helmholtz (K-H), hairpin and Counter-Rotating Vortex Pair (CVP) vortical structures are discussed to identify their origins. Modal analysis of the complete 3D flow and temperature field is carried out using a Dynamic Mode Decomposition (DMD) technique. The modal frequencies are identified, and the specific modal contribution towards the cooling wall temperature fluctuation is estimated on the film cooling wall. The low and intermediate frequency modes associated with streamwise and hairpin flow structures are found to have largest contribution (in-excess of 28%) towards wall temperature (or cooling effectiveness) fluctuations. The high frequency Kelvin-Helmholtz mode contributes towards initial mixing in the region of film cooling hole away from the wall. The individual modal temperature fluctuations on the wall and their corresponding hydrodynamic flow structures are presented and discussed.