Study of non-linear k-epsilon model for turbulent swirling flows

Abstract

Computations on the axisymmetric turbulent flows were conducted to investigate the applicability of the non-linear models. Three kinds of the turbulence models of the standard k-s model, quadratic Reyno Ids stress-strain model, and cubic Reynolds stress-strain model were applied and computations were compared with data. The effects of inlet dissipation rate on predicted mean and turbulence quantities are investigated. The results show that, the cubic model can improve the prediction of the axial velocity component as compared with the standard k-e and quadratic models. Furthermore, the conventional k-e model and quadratic model fail to predict the parabolic profiles of the tangential velocity component. On the other hand, the cubic model can predict the experimental tendency of the parabolic profiles of tangential velocity component. Introduction Swirling flows are commonly encountered in gas turbine combustors to aid stabilizing the flame and create a region of strong shear to enhance mixing process. In these flow fields, the interaction between turbulence and the centrifugal force induced by the swirl has influence on the characteristics of the turbulent transfer of momentum, mass and energy. Numerous studies have been conducted to obtain a better understanding of these phenomena and to establish the prediction procedures for the swirling flows [1-3]. So far, the k-e model has been extensively used in engineering calculations, hi direct comparison of the k-e model predictions with experimental data, the model is successful in predicting the basic features of turbulent flows. When significant streamline curvatures are introduced into the flow field, the model does not adequately account for the enhanced turbulence diffusion caused by the extra strain rate associated with streamline curvature. Copyright © 1998 by authors. Published by AIAA Inc. with permission. The experimental data on the turbulent swirling flows in pipes indicate that there are two distinct rotational motions [4-5]. The one hi the inner region, near the centerline, where the swirl velocity is close to solidbody rotation, and the other is at the outer region and is dominated by the free-vortex motion. Forced vortex has a stabilizing effect, which provokes a reduction in the stresses and promotes the retardation of mixing and combustion in swirling flames [6]. On the contrary, the swirl of the free vortex results in destabilizing the flow and enhances the turbulent exchange of momentum, mass and energy. These phenomena seem to have concern with the increase of the wall friction and heat transfer rate in the swirling flow [7]. The two-equation k-e type model has failed to predict the observed combined forced-free vortex motion [2]. The standard k-e model has been subjected to a number of modifications in an effort to enhance its responsiveness to the extra strain rates imposed by rotation and streamline curvature [8-9]. The manner in which these corrections are implemented depends on the suppression or augmentation of turbulence occurs as a result of swirl motion. These approaches have been designed to ultimately increase or decrease the effective viscosity. Although the source terms of the ke model may require optimization with respect to strongly swirling flows, adjustment of the eddy viscosity level through stabilization or destabilization procedure is not sufficient. Perhaps the biggest limitation of the applicability of the k-e model is due to the assumption of isotropic eddy viscosity. One obvious choice of method for overcoming some of the limitations inherent in the k-e model is provided by Reynolds stress models. These models have been applied with considerable success to many complex swirling flows [10-11]. However, they are computationally complex and expensive and have not reached the state of practical application. Therefore, there is a real engineering need to develop a turbulent closure model for the flow equations that would give realistic results and yet is fast and reliable computationally. 1 American Institute of aeronautics and Astronautics