Generalised approach for transient computation of start-up pressure-driven viscoelastic flow

This article investigates a generalised solution approach for transient viscoelastic flows employing consistent dynamic boundary conditions. Such a procedure vaunts three key properties—independence of reference frame, problem dimension and constitutive equation type. Three different boundary condition protocols have been investigated, two transient and one steady, through a time-dependent incremental pressure-correction formulation with a hybrid finite element/finite volume scheme. These procedures are compared and contrasted through application to pressure-driven start-up flow in 4:1 planar rounded-corner contractions for two fluid models, Oldroyd and pom-pom. Some novel differences are highlighted in the dynamic evolution of flow structure and the impact upon stress generation, as a consequence of protocol, whether steady or transient, under flow-rate or force-driven control. Overshoot–undershoot kinematics observed under any particular flow protocol have been mutually linked to the precise boundary conditions imposed. Under flow-rate controlled protocols, large oscillations are stimulated in pressure, which may disturb computational tractability. Comparatively, the evolution of force-driven flow can provide considerably smoother development patterns in pressure, with largest attached vortices and strong oscillatory vortex structure features. Specifically under transient flow-rate control, some distinct complex flow features have emerged, including reversed flow, followed by vortex detachment and reattachment. For pom-pom SXPP-fluids and force-driven protocol, transient flow development is observed to be relatively smooth and non-oscillatory at a Weissenburg number of unity. At larger levels of Weissenburg number, transient overshoots have been detected in characteristic variables of stress and molecular backbone-stretch. In addition, Weissenburg number continuation to steady state, has been shown to disconnect the dynamics between velocity and stress, which prevents highly elastic localised regions from developing.