The Prediction of Three-Dimensional Discrete-Hole Cooling Processes—Part 1: Laminar Flow

Abstract

The paper describes the application of a three-dimensional finite-difference procedure to the problem of predicting the flow and thermal fields arising from the injection of fluid in discrete jets through a wall past which an external stream is flowing. The numerical scheme is of the “partially parabolic” type originated by D. B. Spalding. Predictions of mean velocity and temperature for laminar flow are provided for the cases of a single row of holes inclined at 90, 45, and 35 deg to the plate surface and for a surface with multiple rows of holes in a staggered array. These specifications are for a uniform density flow and a uniform velocity external stream. A final example is presented, simulating typical operating conditions for a gas turbine blade cooled with a single row of holes aligned at 30 deg to the blade surface. Strong streamwise accelerations and density gradients are present. The results show, as has been observed experimentally, that due to the strong acceleration the lateral rate of spread is diminished. Moreover a counter-rotating vortex pair is created downstream from the hole which shifts the minimum effectiveness away from the mid-plane between the holes.