Scaling and similarity laws in three-dimensional wall jets

Abstract

Wall jets appear in many situations of technological and scientific interest. In gas turbines, flows produced by the film as well as impingement cooling devices are three-dimensional wall jets. High-lift devices produce flows that can easily be represented by two-dimensional wall jets. It has been known for a long time that wall jets in both stagnant and moving environments display a layered structure and only partially obey similarity laws. In this paper, we derive scaling laws and obtain self-similar velocity defect and Reynolds stress profiles for the outer part of three-dimensional wall jets in the high-Reynolds-number limit. The scaling laws are derived from prime principles under realistic assumptions about the behavior of the flow. We show that the leading term in an expansion of the turbulent kinetic energy (TKE) as a series of powers of the distance from the source must scale like the transversal velocity causing the jet to spread laterally. Only the second term in the TKE expansion is shown to scale like the square of the velocity defect. The scaling laws are tested on numerical and experimental data representing two commonly used film cooling devices.