Development of eddy viscosity measurement system utilizing velocity profiler

Abstract

We propose a novel turbulent eddy viscosity profiler to evaluate the influence of interactions between turbulent eddies and dispersed materials as an effective eddy viscosity in Taylor-Couette geometry for frictional drag reduction studies. This method was conceived from the ultrasonic spinning rheometry which evaluates rheological properties by substituting experimentally obtained velocity profiles into the equation of motion. The eddy viscosity is calculated using a model derived from Reynolds-averaged Navier-Stokes equation. By modeling the Reynolds shear stress using the concept of the eddy viscosity, only the spatial distribution of the eddy viscosity remains to be estimated from the mean velocity distribution. We can extract the contributions of eddies with different time and spatial scales depending on the definition of the averaging operation, since mean velocity profiles include the information of momentum transfer by eddies which have the specific time and spatial scales. In this paper we derive the analytical model equation where velocity profile is averaged in temporal and axial directions and the molecular viscosity term balances with the eddy viscosity term. In this case, we can separate the original flow field into Couette-like mean velocity and fluctuation components corresponding to Taylor vortices and smaller fluctuations. Additionally, we show the experimental apparatus and the result for a glycerin aqueous solution using the equation with the above averaging operation. The distribution of eddy viscosity is obtained as a function of radial position.