Estimating the local effective eddy viscosity in non-Newtonian Taylor-Couette flow

Recently, we have developed a novel method to quantify the momentum transport by eddies in turbulent flows for drag reduction studies using non-Newtonian fluid such as a bubble suspension and a polymer solution. The present method, termed eddy viscosity profiler, captures the effective eddy viscosity as a profile from the mean velocity profile. In the present method, we firstly measure the mean velocity profile obtained in the Taylor-Couette flow, then the obtained mean velocity profile is substituted to the equation of motion of mean flow, namely Raynolds averaged Navier-Stokes (RANS) equation.

As a first step of the application to non-Newtonian fluids, we demonstrated this method with a surfactant solution. The RANS equation utilized to the analytical method has the kinematic viscosity as a function of the shear rate since the test fluid is non-Newtonian. To separate the momentum transport by the non-Newtonian viscosity from that by eddies, the shear rate dependent kinematic viscosity is required as an input data as well as the mean velocity profile in RANS equation. We measured the kinematic viscosity by an inhouse rheometer, then the eddy viscosity profile was obtained. We confirmed that the eddy viscosity of the surfactant solution reasonably decreased comparing to that of the Newtonian fluid. In the presentation, we will present the theoretical basis of this method and discuss the results and the applicability of the present method to the non-Newtonian fluid.