External Heat Transfer Predictions in Supersonic Turbines Using the Reynolds Averaged Navier-stokes Equations

External heat transfer predictions are performed for two-dimensional turbine blade cascades. The Reynolds averaged Navier-Stokes equations with algebraic (Baldwin-Lomax) and two-equation (low-Re k ?) turbulence closures are solved with an explicit Runge-Kutta time-marching nite volume method. Comparisons with measurement for subsonic and transonic cascades show good agreement in some cases, but also reveals problems with transition prediction and turbulence modeling. Stability, grid independence and problems in the stagnation point region are investigated. Blind simulations of a supersonic cascade are included to demonstrate the methods capability in handling this type of ows. Nomenclature cp Speciic heat J=kgK] C 1 , C 2 , C, k , Turbulence model constants ] D Turbulence model term J=kgs] E Turbulence model term J=kgs 2 ] e0 Total energy J=kg] f1, f2, f Damping functions ] k Turbulent kinetic energy J=kg] le Local equilibrium length scale m] p Static pressure Pa] P Production of k W=m 3 ] Pr Prandtl number ] qi Heat ux W=m 2 ] S Strain parameter ] T Static temperature K] ui Velocity m=s] yn Normal distance from the wall m] Dissipation of k J=kgs] ij Kronecker's delta function ] Speciic heat ratio ] Dynamic viscosity Ns=m 2 ] Density kg=m 3 ] S Extra Source Term, equation J=m 3 s 2 ] ij Shear stress tensor N=m 2 ] Vorticity parameter ] Subscript: t Turbulent contribution Superscript: lam Laminar part turb Turbulent part 0 Not an averaged quantity