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.