A THEORETICAL APPROXIMATION FOR LAMINAR FLOW BETWEEN ECCENTRIC CYLINDERS

Abstract

Taylor-Couette flow between two concentric cylinders has received much attention due to its use in various applications, including biomedical devices, micro electro-mechanical systems, polymer pumping and electric motor cooling. Due to the complex interaction of the viscosity and the involved geometry within the confined space, different flow regimes are dominant under different conditions, affecting the fluid dynamics and heat transfer. In analyzing the mentioned flow, besides the experimental and computational studies, analytical models have been developed with varying levels of complication. In the present study, using the homotopy of both the flow and the domain geometry between the concentric and eccentric cylinders, a practical formula for flow between eccentric cylinders is developed. In doing so, an appropriate transformation function for the geometry is developed and embedded into the velocity equation for the concentric cylinders. The resultant equation is tested against flow simulation results. A validity margin analysis is performed based on the variation of the mass flow rate between the cylinders. It is seen that the proposed model for eccentric cylinders is applicable for all gap distances, unlike the previous models that are restricted to narrow gaps. Finally, a separate formula to quantify the error in the estimates of the present method is also derived, which involves the ratio of the cylinders and the eccentricity.