Applicability of Mixing Length Theory to a Turbulent Vortex System

The ability of mixing length theory to correlate vortex data is evaluated. Expressions are derived for eddy diffusivity by applying the techniques of von Karman and Prandtl which have been established for pipe flow. Total and static pressures were measured from the outer radius to the exhaust-nozzle radius of a vortex generator for a range of mass flows. These data are combined with Navier-Stokes solutions for this region of a compressible vortex to determine turbulent Reynolds numbers. The Reynolds number is related to Prandtl and Karman functions for various assumed boundary conditions, and the experimental data are used to determine the usefulness of these expressions. The following conclusions were reached: (1) Mixing length functions developed by applying von Karman's similarity hypothesis to vortex motion correlate the data better than do Prandtl functions obtained with the assumption that mixing length is proportional to radius. (2) Some of the expressions developed do not adequately represent the experimental data. (3) The data are correlated with acceptable scatter by evaluating the fluid radial inertia at the outer boundary and the shear stress at the inner boundary. The universal constant K was found to be 0.04 to 0.08, rather than the value of 0.4 which is accepted for rectilinear flow. (4) The data are best correlated by a modified Karman expression which includes an effect of radial inertia, as well as shear stress, on eddy diffusivity