Estimation of effective eddy viscosity profile in Taylor-Couette flow by means of ultrasonic velocity profiler

Abstract

We propose a method termed eddy viscosity profiler to quantify momentum transport in turbulent shear flows for evaluating turbulent modulation by additives such as bubbles and polymers. In the present method, effective eddy viscosity \(\nu _t\) is estimated by substituting mean velocity profile to the equation of fluid motion for turbulent mean flows. Taylor-Couette flow in a fluid layer between rotating coaxial double cylinders was chosen as the measurement platform, and mean velocity profiles are obtained with ultrasonic technique. In the present paper, three classical regimes of Taylor-Couette flow of a Newtonian fluid were investigated to examine the applicability of the method. By analyzing the radial profiles of the spatiotemporal-mean angular velocity \(\langle \omega\rangle\), the radial profiles of \(\nu _t\) are obtained. The spatially averaged \(\nu _t\) shows non-monotonic behavior with respect to Reynolds number. Reynolds shear stress and turbulent production rate were also calculated from the estimated \(\nu _t\). Reorganization of the normalized \(\nu _t\) by the normalized spatiotemporal-mean shear rate, which is also calculated from experimental data, enables us to compare with previous studies and to verify the \(\nu _t\) profiles. To associate the idea of the effective eddy viscosity with the conventional concept in turbulent studies, Prandtl’s wall law was introduced to the \(\langle \omega \rangle\) profiles. This comparison finds the similarity as \(\nu _t/\nu \sim \kappa Re_\tau\), where \(\kappa\) and \(Re_\tau\) are von-Karman constant and Reynolds number defined by friction velocity, respectively, and rationalizes the non-monotonic behavior of the spatially averaged \(\nu _t\).

Graphical abstract