Parametric analysis of fully developed turbulent Wall jets

Abstract

From an examination of all available data on wall jets, it is concluded that at distances sufficiently far downstream from the slot, a fully developed state of the flow can be identified, where the details of the initial conditions are not important, but rather only certain dynamically equivalent gross quantities. In particular, for the wall jet in still air, it is found that a fully developed state of the flow, depending only on the momentum flux and viscosity, can be identified at distances of more than about 30 slot heights. It is found that a measure of wall jet thickness grows roughly like the nine-tenths power of distance and involves a weak but unmistakable dependence on viscosity. The arguments used in this analysis also suggest a plausible explanation for some recent observations, in which a Reynolds number based on local velocity and length scales of the wall jet was found to settle down to values practically independent of distance from the slot. On the basis of a reasonably successful correlation of these results with the span of the tunnel used, it is suggested that the observed effect is due to flow contamination from the sidewalls. For the wall jet beneath a free stream, the relevant parameters characterizing the fully developed state of the flow (again at distances greater than about 30 slot heights from the slot) are suggested as the momentum flux and the free stream velocity; laws governing the development of the wall jet are proposed in terms of these variables. These laws (particularly the velocity decay) show a weak but definite dependence on viscosity. Somewhat surprisingly, the same laws are found to predict the development of a wall jet in an adverse pressure gradient, as comparisons with the measurements of Gartshore and Newman show. Based on a set of experiments conducted to study the effect of compressibility on the development of wall jets in still air, it is found that the kind of coordinates proposed for incompressible wall jets describe (after appropriate modification) the compressible wall jets also; further, from the limited results available, it seems that appreciable differences between the compressible and incompressible cases become noticeable only after the appearance of waves in the flow. It is concluded that the concept of a fully developed wall jet flow, depending only on the net momentum flux in the jet and not on the detailed initial conditions, is useful for correlating data as well as for isolating the dominant parameters under a variety of external conditions.