Effect of Initial and Boundary Conditions on Development of Three-Dimensional Wall Jets

Abstract

Detailed flow field measurements in the wall jets exiting a contoured nozzle and two long pipes with different boundary conditions are reported here. It was found that the growth rate of the jets, the mean velocity and turbulence stress profiles, and the mean velocity and vorticity contours were essentially unaffected by the changes in exit conditions or initial conditions in the intermediate region. There were differences in the half-widths of the jets, the local Reynolds number and the decay of the velocity field downstream. It was also found that the presence of a wall behind the nozzle and the change of the size of this back wall and the room did not affect the jet spread in the lateral direction, but did affect the vertical width and growth rate. Introduction The three-dimensional wall jet formed by a round jet exiting over a flat plate is an useful model for the wall jets that occur in many film cooling applications. One notable feature of these jets is the large anisotropy in the growth rate of the jet. The growth rate in the lateral direction is 'typically 4-6 times larger than that in the vertical direction. It is known that this large anisotropy in the growth rates is caused by the large-scale structures in the wall jet. Matsuda et al. 7 and Ewing and Pollard 5 recently proposed a model to explain how the vortex rings that develop in the jet shear layers deform to generate large-scale turbulent structures that cause the anisotropic growth rates. Abrahamsson et al. noted recently that there were significant differences in the reported growth rates for the three-dimensional wall jets. In particular, the lateral and vertical growth rates for the wall jet exiting a round contoured nozzle were approximately 15% and 20% larger than those of the jet exiting a round fully developed pipe. Eriksson et al. found that boundary conditions, such as the size or presence of a wall behind the jet exit could also affect the growth rate of the wall jet. Since different boundary conditions were used in many of previous measurements, it is not clear whether the differences of the growth rates observed by Abrahamsson et al. l are mainly Copyright© 2002 The American Institute of Aeronautics and Astronautics Inc. All rights reserved. caused by differences in initial conditions or boundary conditions. The objective of this investigation is to examine how changes in initial conditions and boundary conditions affect the development of three-dimensional wall jets. This was accomplished by performing a series of experiments where only one parameter was changed in each experiment. Initially, the effect of changes in initial conditions was investigated by examining the development of the flow exiting a contoured nozzle with top hat velocity profile and a long pipe with the fully developed velocity profile. Measurements were also performed for the wall jets with two different Reynolds numbers in the case of the fully developed pipe to examine if changes in Reynolds numbers affect the flow development. The effect of the wall behind the nozzle exit was then investigated by measuring the development of jets exiting fully developed pipe with and without this plate. Finally, the effect of changing the size of the back wall and in fact the room, was investigated by measuring the jet exiting a smaller fully developed pipe. In all cases, the development of the wall jet was characterized by measuring the profiles of the mean velocities and Reynolds stresses, and contours of the mean streamwise velocity and vorticity. The self-similar solutions for the three-dimensional wall jet outlined by Sun and Ewing 9 were used to scale the data. Initially the experimental facilities used in this experiment are described in detail. The key results of the similarity analysis outlined by Sun and Ewing 9 are summarized. Finally, the measurements for the different cases are presented and discussed. Experimental Facility and Procedures Measurements were performed in the wall jet exiting three different nozzles: a contoured nozzle, a large diameter long pipe, and a small diameter long pipe. In all cases, these jets exited tangentially to a horizontal plate with a length of 1.8 m and a width of 2.5 m shown in figure 1. The experimental apparatus was designed so a vertical wall could be positioned flush with the jet exit in order to block the entrainment from behind the jet. This wall had a width of 2.5 m and a height of 1.1 m. The first wall jet studied was formed from a jet exiting a contoured nozzle with an exit diameter of 38.1 mm. The contour on the inside nozzle was fifth order polynomial and the area contraction ratio was 28:1. The flow 1 American Institute of Aeronautics and Astronautics (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.