Analytical Non-Newtonian Oldroyd-B Transient Model for Pretransient Turbulent Flow in Smooth Circular Lines

Abstract

A new approach for obtaining a normalized closed-form frequency domain analytical model for the non-Newtonian shear thinning effects on the pressure and shear stress transients in a pretransient turbulent flow of fluids in smooth circular lines is formulated. The Oldroyd-B model is utilized to analyze these shear thinning effects on these transients. The process of converting the analytical frequency domain model to the time domain using an inverse frequency algorithm commonly used in system identification is explained and demonstrated. The boundary conditions at the ends of the line are defined by the flow and pressure variables, which are in general functions of time or defined by causality relationships. Corresponding equations for the transient changes in the velocity profile and shear stress are also formulated. Two examples demonstrating the application versatility of the model and the sensitivity of the transients to the shear thinning parameters are included. For these specific examples, the sensitivity of the pressure and velocity transients is observed to be relatively low compared to the sensitivity of the wall shear stress. Insight into when the non-Newtonian complexities associated with shear thinning need to be included in a model for fluid transients considering the mode frequencies and/or the input frequencies is provided. The analytical model can easily be simplified for laminar flow and Newtonian fluids.