Abstract
The lid-driven cavity flow is a well-known benchmark problem for the validation of new numerical methods and techniques. In experimental and numerical studies with viscoelastic fluids in such lid-driven flows, purely-elastic instabilities have been shown to appear even at very low Reynolds numbers. A finite-volume viscoelastic code, using the log-conformation formulation, is used in this work to probe the effect of viscoelasticity on the appearance of such instabilities in two-dimensional lid-driven cavities for a wide range of aspect ratios (0.125≤Λ=height/length≤4.0), at different Deborah numbers under creeping-flow conditions and to understand the effects of regularization of the lid velocity. The effect of the viscoelasticity on the steady-state results and on the critical conditions for the onset of the elastic instabilities are described and compared to experimental results.
Highlights
The fluid motion in a box induced by the translation of one wall – the so-called “lid-driven cavity flow” – is a classic problem in fluid mechanics [1]
We are concerned with the isothermal, incompressible flow of a viscoelastic fluid flow, and the equations we need to solve are those of conservation of mass
The critical conditions for the onset of a purely-elastic instability are presented in Fig. 9, both in terms of a critical reciprocal Weissenberg number (1/Wicr) and a Deborah number (Decr) as a function of aspect ratio, using three different lid regularizations (R1–R3), computed using mesh M3
Summary
The fluid motion in a box induced by the translation of one wall – the so-called “lid-driven cavity flow” – is a classic problem in fluid mechanics [1]. In addition to this main recirculation, smaller Moffatt [3] or corner eddies are induced at the bottom corners (labelled “C” and “D” in Fig. 1): at the bottom corners there is an infinite series of these vortices of diminishing size and strength as the corner is approached [3].
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