Computation of Reynolds stresses in axisymmetric vortices and jets using a second order closure model

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Virginia Tech


Donaldson's single-point second-order model [13] is used to close the Reynolds stress transport equations in cylindrical coordinates. A reduced set of equations are then solved for the decay of axisymmetric vortices and jets. A self-similar solution to the axisymmetric vortices is obtained numerically. The characteristics of the mean flow variables as well as the Reynolds stresses in this solution are discussed. Comparisons of the current results with Donaldson[13J and Donaldson and Sullivan[16] are also presented.

The results show that the vortex core is free from turbulent shear stresses. The turbulent kinetic energy is also found to be relatively weak within the core region. The overshoot of the circulation is found to be 5% of the circulation at infinity over a wide range of Reynolds numbers.

The effects of Reynolds number on the decay of the vortices are computed and discussed. Some of the quantities, such as mean flow circulation and turbulent kinetic energy, are found to be sensitive to the Reynolds number. However, the overshoot is found to be insensitive to the Reynolds number but its location does.

A set of suitable model constants for the axisymmetric jets is also found and a self similar solution for the jet case is obtained. Comparisons of the computed results with some recent experimental data are presented.