Slip viscosity and strain-rate viscosity in Taylor-Couette laminar flows: Experimental falsification and end-wall effects

TL;DR

This study experimentally and numerically investigates slip and strain-rate viscosities in Taylor-Couette flows, confirming the slip viscosity model's validity and revealing end-wall effects on flow patterns.

Contribution

It experimentally verifies the slip viscosity model's accuracy and demonstrates how end-wall effects influence flow structures in Taylor-Couette systems.

Findings

Maximum deviation from rigid-body rotation is about 0.86%.

End-walls affect flow only under the slip viscosity model.

Flow develops a 3D spiral pattern influenced by geometry and rotation.

Abstract

The viscous force should be shear force, the difference between the strain-rate viscosity and the slip viscosity is that the former has conjugate shear force, while the latter does not. The study in this paper verifies the physical authenticity of two viscosity models through Taylor Couette laminar flow experiments with inner and outer cylinders rotating at the same angular velocity, and numerically investigate the influence of relative cylinder spacing and rotational speed on the circumferential velocity under the slip model. The experimental results of LDV measurement with a relative cylinder spacing of 0.3 indicate that the maximum deviation from rigid-body rotation is about 0.86%, which is consistent with the theoretical prediction of slip viscosity model. The numerical simulations show that the end-walls have no effect under the strain-rate viscosity model; but when the slip viscosity model is introduced, the end-walls inevitably bring about the circumferential velocity profile changing along the axial direction, and result in a three-dimensional (3D) spiral streamline pattern influenced by the relative cylinder spacing and angular speed of cylinders.