Development of a Two-Scale Turbulence Model and Its Applications

Abstract

The use of second order closure turbulence model in predicting turbulent flows is known to be more successful than the classical mixing length model. However, it is found that if the turbulence constants are not altered or modified, the second order closure turbulence model is unable to predict satisfactorily f or some flows such as round jet and wake flows. In order to improve the predictability of the second order closure model, the present work proposes to consider two turbulent scales in the modelling of turbulent flows. One of these scales is based on using the turbulent kinetic energy, k, and its dissipation rate, epsilon, to characterize the large energy containing eddies. The other scale is based on the dissipation rate and the kinematic viscosity, nie, to characterize the small energy dissipating eddies. The second scale is based on the well known Kolmogorov hypothesis that dissipation of turbulent kinetic energy occurs primarily at small eddies. The turbulence model derived based on the concept of two different scales is called the two-scale turbulence model. The existing turbulence model which is modelled based on the one-scale concept of k and epsilon is called the one-scale turbulence model. The two-scale turbulence model is then applied to predict turbulent free shear flows and recirculating flows. The calculations were done in three parts. The first test case was nonbuoyant free shear flows which included round and plane jets in stagnant and moving streams, plane wakes and mixing layer. In the second part, the model was tested for plane and round buoyant jets having different Froude numbers. Finally, some results were obtained for recirculating flows, namely, backward facing step and flow past an obstruction. It is shown in the present study that the two-scale turbulence model performs significantly better than the one-scale turbulence model in all the cases concerned. The prediction capability of the two-scale turbulence model is shown since one does not need to alter or modify the turbulence constants as in the case of the one-scale turbulence model