Navier-Stokes analysis of turbomachinery blade external heat transfe

The two-dimensional compressible, thin layer Navier-Stokes and energy equations were solved numerically to obtain heat transfer rates on turbomachinary blades. The Baldwin-Lomax algebraic model and the q-$omega$ Low Reynolds Number Two-Equation model were used for modeling of turbulence. For the numerical solution of the governing equations a four stage Runge-Kutta solver was employed. The turbulence model equations were solved using an implicit scheme. Numerical solutions are presented for two-dimensional flow over a flat plate cascade and three vane cascades. The heat transfer results and the pressure distributions were compared with published theoretical results and experimental data. The agreement between the numerical calculations and the experimental values were found to be generally favorable. The position of transition from laminar to turbulent flow was also predicted fairly accurately.;It was discovered that with a Navier-Stokes solver the numerical diffusion present as a result of the smoothing operation is detrimental to the evaluation of heat transfer results. A correction was suggested and this was implemented in the numerical procedure. The results show the potential of this method in prediction of heat transfer on blades without the need for zoning and patching of the flow field as is done in the boundary layer methods presently employed for the estimation of heat transfer coefficients.