Use of turbulent kinetic energy in free mixing studies

The concept that the turbulent kinetic energy equation can be used to determine the shear in a turbulent flowfield through the use of a suitable relation between turbulent shear and turbulent kinetic energy has proved successful in the analysis of turbulent boundary-layer flows. In this paper, the application of a similar approach to the problem of turbulent free mixing of constant-density streams is described. By correlating measurements of turbulent shear and turbulent kinetic energy in a number of constant density free mixing flows, a linear relation between turbulent shear and turbulent kinetic energy is shown to exist. The combination of this relationship and a new rapid technique for the simultaneous solution of an arbitrary number of parabolic partial differential equations allows detailed calculation to be carried out for two-steam mixing systems of interest, one a plane mixing region and the other axisymmetric. Both mixing regions are constant density. Generally satisfactory agreement is achieved for both velocity and turbulent shear distribution. More important than the level of agreement reached, however, is the fact that the method used is more perceptive than previous phenomenological approaches and, thus, offers the promise of eventually leading to greater understanding of turbulent shear flow.