Reynolds stress description of opposed and impinging turbulent jets. Part I: Closely spaced opposed jets

Abstract

The flow arising from two, closely spaced turbulent jets flowing counter to one another is analyzed for both two-dimensional and axisymmetric configurations. By closely spaced it is indicated that the diameter of the jets is large compared to their separation distance. Two parameters, one a measure of the integral scale of the turbulence compared with half the separation distance of the jets, and a second, a measure of the intensity of the turbulence issuing from the jets, are assumed small and form the basis of an asymptotic analysis. As a consequence, the mean velocity components are given by the mean Euler equations, except in a thin layer that is centered about the plane containing either the stagnation line or point and within which discontinuities in the flow from each jet are adjusted. Thus, outside of this layer, the turbulence characteristics in a known mean velocity field are determined, in the present study, in terms of a Reynolds stress description. The rate of strain field associated with the stagnating flow results in anisotropy of the turbulence as the plane containing the stagnation line or point is approached. Differences in the mean velocities in two-dimensional and axisymmetric configurations result in significant differences in the evolution of the gradient of the Reynolds shear stress from the exit planes of the jets and thus in the thin layer at the stagnation plane. For two-dimensional flows, the velocity characteristics in the thin layer satisfy to lowest order in an expansion parameter the requisite symmetry conditions, whereas this is not the case for axisymmetric flows. The temperature in the two streams is assumed to be slightly different but uniform so that there is also a thermal layer at the stagnation plane. Comparison is made with the applicable experimental data for the mean velocity and the turbulence intensities with good and reasonable agreement, respectively.