A large eddy PIV method for turbulence dissipation rate estimation

Abstract

Accurate estimation of the turbulence dissipation rate is important for the turbulent flows in the chemical process industry. Previous studies, limited by single-point velocity measurement techniques, mainly focus on measuring the single-point local dissipation rate or averaged dissipation rate over a finite volume. Various methods — turbulent kinetic energy balance, Taylors hypothesis, and dimensional analysis — have been proposed to estimate the dissipation rate of turbulent kinetic energy. These methods cannot provide the global distribution of the dissipation rate over a large flow region. Since particle image velocimetry (PIV) is capable of providing multi-point instantaneous measurements of a flow field, it is more suitable for examining the dissipation rate distribution. However, PIV measurements are limited to finite grid sizes, which often exceed the smallest eddy sizes that dominate the turbulence dissipation rate. In this paper, a large eddy PIV method for dissipation rate estimation is proposed. Based on a dynamic-equilibrium assumption for the sub-grid scale (SGS) flux between the resolved and the sub-grid scales, our method measures the SGS energy flux, and thus, estimates the turbulence dissipation rate. The SGS flux is obtained from the strain-rate tensors computed from velocity fields and the modeled SGS stress. When the PIV measurement resolves down to the Kolmogorov scale, the SGS stress is replaced with the viscous shear stress. In other words, the resolved velocity fields directly give the dissipation rate. This method is applied to estimate the dissipation rate along the center plane of a stirred vessel with an axial 45° pitched-blade turbine. The results obtained are compared with those calculated using the dimensional analysis method. The average dissipation rates over the impeller and flow discharge regions are also evaluated and compared using both methods.