Influence of elastic instability and elastic turbulence on mixed convection of viscoelastic fluids in a lid-driven cavity

Abstract

The addition of a minute amount of solid polymers into a Newtonian solvent like water can originate an elastic instability as the Weissenberg number (ratio of the elastic forces to that of the viscous forces) gradually increases. These instabilities further transit to elastic turbulence (ET) regime at high Weissenberg numbers. In this study, we investigate how these elastic instabilities and elastic turbulence would tend to influence the mixed convective heat transfer phenomena in a lid-driven cavity, which is one of the widely studied problems in the domain of transport phenomena. In doing so, extensive two-dimensional time-resolved numerical simulations have been conducted by using an open-source CFD code OpenFOAM. The Oldroyd-B viscoelastic constitutive model is used in this study to realize the rheological behaviour of a constant shear-viscosity viscoelastic fluid or the so-called Boger fluid. To investigate the effect of the shear-thinning behaviour of a viscoelastic fluid on the elastic instability and elastic turbulence phenomena, we have further conducted limited simulations using the FENE-P (finitely extensible non-linear elastic spring with the Peterlin's approximation) viscoelastic fluid model. A detailed discussion is presented on how the flow dynamics and heat transfer mechanism inside the cavity can be influenced by the Weissenberg number along with the Reynolds, Prandtl, and Richardson numbers. We show that the heat transfer rate inside the cavity can be increased by more than 100% under appropriate conditions if one uses a constant shear-viscosity Oldroyd-B fluid instead of a simple Newtonian fluid due to the presence of elastic instability and elastic turbulence in the former fluid. Furthermore, we have found that the shear-thinning behaviour of a FENE-P viscoelastic fluid tends to suppress these instabilities and turbulence and hence decreases the heat transfer rate inside the cavity. Therefore, one can use the present approach of using a constant shear-viscosity Oldroyd-B fluid as an efficient way to increase the rate of heat and mass transport processes in various systems. Our approach can be served as an alternative possibility to the existing approaches such as the application of an electric or a magnetic field or the use of a nanofluid. However, one needs to be careful in the selection of the polymer type and its degradation behaviour as well as its appropriate concentration in the solution when choosing this approach.