On the hydrodynamic braking flow of a viscoelastic fluid

Abstract

This paper considers the flow of a viscoelastic fluid between two parallel plates. The bottom plate slides in its own plane and the top plate moves normal to its own plane. The flow is thus a combination of shearing and squeeze-film flow, and mimics a hydrodynamic braking action. The computation includes not only the flow between the plates but also the inlet and outlet regions which contribute to the load and greatly increase the difficulty of the problem. There does not seem to have been any previous attempt to include this feature. The fluid model adopted is a differential-type viscoelastic constitutive equation, which predicts a decreasing (Carreau-type) viscosity in steady state simple shear flow, and overshooting, oscillatory behaviour in the starting-up of a simple shear flow. The problem is solved by a decoupled boundary element method, adapted to solve non-linear transient flow problems. The program treats non-linear terms as pseudo-body forces in the repeated solving of a set of linear problems. The numerical results point to the existence of strong vortices at the inlet and outlet of the bearing in the viscoelastic case, and they show an increase in both the normal and the tangential forces as the product of the relaxation time and the squeeze rate (Weissenberg number) rises. There is also an increase as the sliding velocity increases. The frictional coefficient, however, is nearly the same as the newtonian value. The results form an explanation for the increased resistance to squeezing found in viscoelastic films.