Abstract
Understanding the behavior of viscoelastic (VE) fluids in confined geometries is crucial for applications in biologic systems, heat transfer devices, enhanced oil recovery, and many others. Here, we perform a systematic steady-state simulation of a VE fluid at low Reynolds numbers through a channel with successive smooth contractions and expansions. We analyze the hydrodynamic performance of the fluid with particular attention to vortex patterns that develop downstream of the contractions. We show that elastic vortices form at higher contraction ratios and that there are critical Weissenberg numbers (Wic) unique to each contraction ratio where the flow shifts from non-vortical to vortical. This Wic increases with an increasing contraction length. The coexistence of elongational-, shear-, and rotational-flow is essential for vortex development and evolution. We also analyzed the effect of the Deborah number (De) on the vortex pattern in a multiple contraction system and observed that the vortex area significantly depends on the distance between the contractions. We show that there are three distinctly different regions in De, in which the flow characteristics change in successive contractions. For high De, the flow in the downstream contraction is significantly affected by the upstream contraction. Our results have implications for the use of VE fluids with various VE properties in different types of porous media.
Highlights
In this work, we numerically investigate the behavior of a VE fluid through a channel with single and multiple smooth contractions at low Reynolds numbers, which mimics flow in micro-scale systems
There are various hydrodynamic and geometric properties involved in the VE flow through contractions, but for the sake of brevity, we focus on the parameters that are of critical importance to govern the behavior of polymeric solutions in pores
We investigated the development of the rotational flow downstream of smooth contractions in systems with single and multiple contractions
Summary
The flow of non-Newtonian viscoelastic (VE) fluids has been investigated for over fifty years[1,2] due to a large number of applications in polymer processing,[3,4,5] biology and medicine,[6,7,8] enhanced oil recovery (EOR),[9,10,11,12,13,14] dampers,[15,16,17] and many others.[18,19] The prediction of the performance of polymer solutions when exposed to a high shear rate environment (e.g., flow in porous media) is complex as the VE behavior of the solution is highly dependent on the pore size and geometry.[20]. The existence of flow divergence was introduced as a purely elastic phenomenon that can be intensified by adding inertial effects to the model by increasing the Reynolds number This phenomenon is studied in the same manner for a 3D channel to investigate the so-called “cat’s ear” effect (nearwall velocity overshoots’ phenomenon) upstream of the smooth contraction using UCM and PTT models at the creeping flow.[54]. They showed that the dominant energy dissipation occurs in a purely shear flow regime, especially at high Deborah numbers.[26] Extensional viscosity is another factor that is experimentally and numerically investigated based on the first normal stress difference and strain rate by measuring the pressure drop as a function of flow rate[59–61] and elastic properties[62] in contraction/expansion geometries. We show that the contraction ratio and the distance between the contractions can significantly affect the distribution of local stresses and the flow characteristics throughout the channel, which, for instance, has implications for the use of polymer solutions in enhanced oil recovery
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