Numerical Analysis of Secondary Flow for Viscoelastic Fluid Through Elliptical Duct.

Abstract

The flow behavior of viscoelastic non-Newtonian fluid in circular and non-circular ducts is of special engineering interest. Therefore a numerical analysis has been performed for viscoelastic non-Newtonian fluid in elliptical duct. Special attention is paid for the generation of secondary flow for laminar flow by using two kinds of constitutive equation, i.e., Maxwell and Reiner-Rivlin models. As for Maxwell model, body force caused by the elastic stress is approximated by linear source term. In calculation, viscosity was represented by adopting power-law fluid and boundary-fitted coordinate system was introduced as the method of coordinate transformation. The calculated results of two models show the secondary flow in elliptical duct as the same as theoretically analyzed by Green and Rivlin. Adding to the prediction of secondary flow, the generation mechanism of secondary flow has been argued by evaluating the production terms of the transport equation for streamwise vorticity. As a result of this examination, it was found that the term of viscous diffusion and the term containing second normal stress difference played an important role in producing the secondary flow near the wall. At the same time, it is interested phenomenon that the circular direction of secondary flow for viscoelastic fluid is opposite sigh to that of secondary flow for Newtonian turbulent flow. As its cause, the present study clarified that the term containing second normal stress difference of viscoelastic fluid is the same type equation for that of turbulence, while the sign of its term for viscoelastic fluid is opposite to that for turbulent flow.