Dissipation Rate Estimation in a Highly Turbulent Isotropic Flow Using 2D-PIV

Abstract

In experimental turbulent flows, the estimation of the dissipation rate of turbulent kinetic energy, $\varepsilon$, is a challenge. The dimensional analysis approach is the simplest of the many available strategies, where $\varepsilon = C_{\varepsilon} k^{3/2}/L$. Although the proportionality constant, $C_{\varepsilon}$, is commonly stated to be on the order of unity, there is little experimental evidence to verify this claim for zero-mean stirred-chamber configurations in general, nor is there detailed information on how $C_{\varepsilon}$ might systematically vary with flow conditions. Given the importance of zero-mean chambers for both practical and fundamental studies on turbulent flows, reliable data on the magnitude of $C_{\varepsilon}$ would be an asset. The goal of the present investigation is to rigorously determine $\varepsilon$ in turbulent helium gas using medium-resolution particle image velocimetry (PIV) combined with the corrected spatial gradient method—these results lead directly to $C_{\varepsilon}$. Helium maintains relatively large Kolmogorov length scales, $\eta$, due to its high kinematic viscosity, making it possible to resolve spatial velocity gradients in strongly turbulent fields ($k \le {17.6}\,\hbox {m}^{2}\,\hbox{s}^{-2}$) with only modest magnification while avoiding many of the difficulties associated with micro-PIV. The results confirm that the vector spacing, $\varDelta x$, must be less than $\eta$ to properly calculate the spatial velocity gradients—a recommendation that has not been universally agreed upon. We provide comprehensive $C_{\varepsilon}$ results up to $Re_\lambda = 220$ by varying the fan speed, fan count, and chamber pressure. $C_{\varepsilon}$ eventually falls to a value of ${\sim }0.5$, although the true asymptotic value of $C_{\varepsilon}$—if it exists—remains elusive.