The effect of expansion ratio for creeping expansion flows of UCM fluids

Abstract

a b s t r a c tA systematic numerical investigation on creeping flows in planar sudden expansions of viscoelastic fluids obeying the upper-convected Maxwell model is carried out to assess the combined effects of viscoelasticity, through the Deborah number, and expansion ratio (ER), which was varied between 1.25 and 32. At large expansion ratios (ER ≥ 4) the flow becomes dominated by the downstream duct size and appropriately normalized quantities tend to be independent of ER. The recirculation size and strength become decreasing functions of De, whereas the Couette correction (the normalized entry pressure drop due to the presence of the expansion) increases. At small ER (ER ≤ 3), however, no simple scaling laws are found and there is a complex interaction between De and ER leading to non-monotonic variations, with an initial decrease in the recirculation length at low Deborah numbers, followed by an enhancement as De increases.

New contributions on laminar flow of inelastic non-Newtonian fluid in the two-dimensional symmetric expansion: Creeping and slowly moving flow conditions

“…For instance, in studies using viscoelastic fluids obeying the upper-convected Maxwell and Oldroyd-B model it is shown that, while in expansion flows Newtonian fluids generate significant vortex activity, viscoelastic effects reduce both the length and intensity of the recirculation region downstream of the expansion [18]. Finally, recent work of Poole et al [19] pointed out that elasticity affects the flow differently depending on the expansion ratio. For high expansion ratio (i.e.…”

Flow of a Blood Analogue Solution Through Microfabricated Hyperbolic Contractions

“…When the flow rate is increased even further, competing elastic and inertial effects are present and a lip vortex emerges downstream of the expansion plane as was observed for the Newtonian fluid flow when inertial effects become important. However, as a consequence of the relevance of elastic forces, in this case the inertiadriven downstream vortices are weaker than those observed for the Newtonian fluid at the same Re, since elasticity is responsible for the development of normal stresses in shear which are known to lead to jet swelling and consequently to a reduction of the size of downstream recirculations [12].…”

Modeling Asymmetric Flow of Viscoelastic Fluid in Symmetric Planar Sudden Expansion Geometry Based on User-Defined Function in FLUENT CFD Package

“…The results of numerical simulations with different constitutive models showed that the reduction of both the length and intensity of the vortex, which was caused by the effect of elasticity, is much lower than that reported in previous studies, and a significant region of recirculation still exists for all the models at high Deborah number [15]. The study of expansion ratio effect on the flow characteristics showed that both the length and intensity of the recirculation zone are increased with increasing expansion ratio at the same Deborah number, and for large expansion ratios the recirculation size and strength are decreased with increase of Deborah number, while for small expansion ratios the recirculation length is initially decreased at low Deborah numbers, followed by an increase as Deborah number increases [16]. Since the Reynolds number in above numerical researches is lower than a certain critical Reynolds number, the flow in sudden expansion geometry is symmetry.…”

“…Darwish et al [13] and Missirlis et al [14] applied upper-convected Maxwell (UCM) model and developed finite volume method to simulate the creeping flows of viscoelastic fluid in a 1 : 4 sudden expansion at Re = 0.1. Poole et al [15,16] numerically investigated the creeping flow of viscoelastic fluid with three different models (UCM, Oldroyd-B, and the linear form of PTT model) through a 1 : 3 planar sudden expansion and studied the effect of expansion ratio on the creeping flow of viscoelastic fluid obeying UCM model. The results of numerical simulations with different constitutive models showed that the reduction of both the length and intensity of the vortex, which was caused by the effect of elasticity, is much lower than that reported in previous studies, and a significant region of recirculation still exists for all the models at high Deborah number [15].…”