Flow and heat transfer characteristics of a rotating cylinder in a FENE-P type viscoelastic fluid

Abstract

A detailed numerical study on the flow and heat transfer phenomena from a rotating cylinder submerged in a streaming viscoelastic FENE-P fluid has been carried out. The governing equations, along with the FENE-P viscoelastic constitutive equation, have been solved using OpenFOAM over the following ranges of conditions: Reynolds number, 10 ≤ Re ≤ 100; Weissenberg number, 0 ≤ Wi ≤ 10; non-dimensional rotational velocity or the Rossby number, 0 ≤ Ro ≤ 2; polymer extensibility parameter, 10 ≤ L2 ≤ 500 and for a fixed value of the Prandtl number of Pr = 50. For a stationary cylinder, the separation of the boundary layers is suppressed with the increasing values of the Weissenberg number and the polymer extensibility parameter (L2). Over the range of conditions encompassed in this study, the rotation of the cylinder tends to stabilize the flow for a Newtonian fluid, whereas for a viscoelastic FENE-P fluid, it first induces an inertio-elastic instability which thereby destabilizing the flow with further increase in the rotation rate, viscoelasticity tends to stabilize the flow. The tendency for the onset of this inertio-elastic instability increases with the increasing Weissenberg number, Reynolds number and polymer extensibility parameter. The average Nusselt number increases with the increasing Reynolds number whereas it decreases with the increasing values of the Weissenberg number, polymer extensibility parameter and cylinder rotation rate. On the other hand, the drag coefficient decreases and lift coefficient increases with the cylinder rotation rate irrespective of the fluid type, i.e., Newtonian or viscoelastic. Finally, a simple expression is presented for the average Nusselt number thereby enabling the interpolation of the present results for the intermediate values of the parameters.