Near Field of Film Cooling Jet Issued into a Flat Plate Boundary Layer: Les Study

We report results from a computational study of film cooling from cylindrical holes inclined at 35 degrees with respect to a flat surface using Large Eddy Simulations (LES). The hole length is L/d = 3.5, distance between the holes is P/d = 3, boundary layer above the flat surface is turbulent with Reθ = 938, density ratio = 0.95, velocity ratio = 0.5. All pertinent components of geometry, namely, supply plenum, film hole and crossflow region above the test surface, are simulated. The simulations are performed using a multicode approach, where a low Mach number code is employed inside the plenum and in the film hole, and a compressible code is used for the flow above the test surface. Flow inside the plenum, film hole and above the test surface is analyzed. Mean velocity and turbulence characteristics in the near field of the jet injection obtained in the simulations are compared to experimental data of Pietrzyk et al. [1]. Adiabatic film cooling effectiveness is estimated and compared with experiments of Sinha et al. [2]. Relation of the coherent vortical structures observed in the flow to film cooling performance is discussed. Advantage of LES over RANS methods for this type of flow is confirmed by showing that spanwise u′w′ shear stress and lateral growth of the jet are predicted correctly in the current LES as opposed to typical RANS computations. NOMENCLATURE B blowing ratio = (ρ jU j)/(ρ∞U∞) d film hole diameter DR density ratio = ρ j/ρ∞ I momentum ratio = (ρ jU j )/(ρ∞U ∞) L/d film hole length-to-diameter ratio M Mach number P/d holes pitch-to-diameter ratio Red Reynolds number based on d, ρ∞ and U∞ Reθ Reynolds number based on θ, ρ∞ and U∞ t time T static temperature T0 total temperature Taw adiabatic wall temperature T KE turbulent kinetic energy = √ 1/2(u′2 + v′2 +w′2)/U∞ u,v,w mean velocity components u′,v′,w′ fluctuating velocity components u′v′,u′w′ normal and spanwise Reynolds shear stresses U j coolant jet axial bulk velocity U∞ free-stream velocity V R velocity ratio = U j/U∞ x,y,z streamwise, wall-normal and lateral coordinates δ,δ? boundary layer 99% and displacement thickness ∆t time step size η film cooling effectiveness ηav laterally-averaged film cooling effectiveness ηc centerline film cooling effectiveness ρ density θ boundary layer momentum thickness 1 Copyright c © 2008 by ASME Θ normalized temperature