Diffusion mixing in grid turbulence without mean shear

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Abstract
An experimental examination of the fundamental properties of free turbulent interactions in a mixing flow has been conducted. A turbulent, two-dimensional, incompressible, uniform-density mixing layer was produced by using a parallel bar grid of different bar spacings but the same space to bar diameter ratio M/D = 2. In this unique mixing-flow geometry, two initially parallel flowing streams of air were formed in such a way as to possess the same mean structure but different turbulent kinetic energy. The mixing phenomenon was driven solely by the turbulent kinetic-energy self-diffusion process.The data showed the development of the turbulent properties without the interference caused by turbulence generated by a mean shear flow. A simple diffusion model was constructed by assuming an analogy between the unsteady gradient diffusion process and the transport of turbulent kinetic energy by the fluctuations. An empirical error function least squares curve fit, a diffusional power law and diffusion coefficients were derived. The empirical coefficients of self-diffusion were found to be 10.4 and 68.6 cm2 s−1 for the longitudinal and transverse turbulent energy components, or about a hundred and five hundred times faster than molecular viscous shear diffusion, respectively. This self-diffusion mechanism by microscale size eddies may account for some of the error found by other investigators in balancing the measured terms of the turbulent kinetic-energy equation.

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