Prediction of Film Cooling by a Row of Holes With a Two-Dimensional Boundary-Layer Procedure

Abstract

The present paper describes predictions of film cooling by a row of holes. The calculations have been performed by a two-dimensional boundary-layer code with special modifications that account for the basically three-dimensional, elliptic nature of the flow after injection. The elliptic reverse-flow region near the injection is leapt over and new boundary-layer profiles are set up after the blowing region. They take into account the oncoming boundary layer as well as the characteristics of the injected jets. The three dimensionality of the flow, which is very strong near the injection and decreases further downstream, is modeled by so-called dispersion terms, which are added to the two-dimensional boundary-layer equations. These terms describe additional mixing by the laterally nonuniform flow. Information on the modeling of the profiles after injection and of the dispersion terms has been extracted from three-dimensional fully elliptic calculations for specific flow configurations. The modified two-dimensional boundary-layer equations are solved by a forward-marching finite-volume method. A coordinate system is used that stretches with the growth of the boundary layer. The turbulent stresses and heat fluxes are obtained from the k -ε turbulence model. Results are given for flows over flat plates as well as for flows over gas turbine blades for different injection angles, relative spacings, blowing rates, and injection temperatures. The predicted cooling effectiveness and heat transfer coefficients are compared with experimental data and show generally fairly good agreement.