Viscoelastic flow in an undulating tube. Part II. Effects of high elasticity, large amplitude of undulation and inertia

Abstract

A mixed pseudospectral/finite difference technique is used in the simulation of steady-state viscoelastic flow through an undulating tube. The viscoelastic fluid behavior is modelled by the Oldroyd-B constitutive equation. It is shown that for creeping flow, even at high values of elasticity and large amplitude values, the flow resistance does not differ substantially from the Newtonian value. However, when inertia is present, the flow resistance can increase appreciably. Moreover, it is shown that viscoelasticity can significantly affect the shape and the size of the recirculation vortex at large enough amplitude values. The mixed pseudospectral/finite difference numerical method has succeeded in providing accurate solutions (converged with mesh refinement), provided that the size of the numerical discretinization was fine enough, depending on the flow parameters investigated. Even when inertia was present, under conditions when the steady-state equations change type, oscillation-free solutions were obtained. These calculations have confirmed the presence of standing waves of the vorticity in the radial direction predicted by Ahrens, Yoo and Joseph, J. Non-Newtonian Fluid Mech., 24 (1987) 67.