A Calculation Method for Convective Heat and Mass Transfer in Multiply-Slotted Film-Cooling Appliations

摘要

A computer model to calculate the development of wall jet boundary layers downstream of multiple film-cooling slots is described. The differential equations for the conservation of mass, momentum and energy in an incompressible two-dimensional for axisymmetric flow are solved using a downstream-marching, iterative, implicit, finite-difference scheme. The turbulent transport of mass in a conventional wall boundary layer is described by means of inner-outer two-layer eddy-viscosity model based on the Prandtl mixing-length hypothesis with Van Driest's modification in the near-wall region. Further alterations to include the effects of pressure gradients, heat and mass transfer are due to Cebeci and Smith. This basic model is extended to include cases with tangential fluid injection. Computed velocity profiles indicate that the law of the wall is obeyed in the inner layer and that the outer wake-like layer strives to resume the velocity-defect relationship that existed upstream of the point of fluid injection in zero pressure-gradient flow with no heat or mass transfer. Comparison between computed and experimental adiabatic wall temperature distributions in flows with heat transfer shows that the eddy-viscosity model is deficient in the near-slot region and tends to overestimate film-cooling efficiency. The absence of an eddy term to account for turbulence due to finite slot lip thickness is partly responsible for this overestimation. Recommendations are made to validate the model in pressure-gradient flows and to improve the predictive capability in the near-slot region. (Author)