Influence of Hydrodynamic Slip on the Wake Dynamics and Convective Transport in Flow Past a Circular Cylinder

Abstract

Hydrodynamic slip is known to suppress vorticity production at the solid-fluid boundary in bluff body flows. This suppression combined with the enhanced vorticity convection results in a substantial reduction in the unsteady vortex shedding and the hydrodynamic loads experienced by the bluff body. Here, using combined theoretical and computational techniques, we investigate the effect of slip on three-dimensional wake dynamics and convective scalar transport from a circular cylinder placed in the uniform cross-flow of a Newtonian incompressible fluid over Reynolds numbers ranging from 0.1 to 1000. We find the wake patterns to be strongly influenced by the degree of the slip, quantified through the non-dimensional slip length in the Naiver slip model, with the asymptotic slip lengths of zero and infinity characterizing no-slip and no-shear boundaries, respectively. With increasing slip length, the wake three-dimensionality, that is observed in the case of a no-slip surface for Re > 190, is gradually suppressed and eventually eliminated completely. For each Reynolds number, we identify the critical slip length beyond which the three-dimensionality is completely suppressed and the wake becomes two-dimensional, on the basis of the total transverse entropy present in the flow field. Over the Reynolds number range considered in this work, we find the critical slip length to be an increasing function of Reynolds number. For sufficiently large slip lengths, we observe suppression of two-dimensional vortex shedding leading to formation of a steady separated wake. Further increments in slip length lead to reduction in the intensity and size of the recirculating eddy pair eventually resulting in its complete disappearance for a no-shear surface for which the flow remains attached all along the cylinder boundary. Next, we quantify the effect of hydrodynamic slip on convective transport from an isothermal circular cylinder placed in the uniform cross flow of an incompressible fluid at a lower temperature. For low Reynolds and high P´eclet numbers, theoretical analysis based on Oseen and thermal boundary layer equations allows us to obtain explicit relationships for the dependence of transport rate on the prescribed slip length. We observe that the non-dimensional transport coefficients follow a power law scaling with respect to the P´eclet number, with the scaling exponent increasing gradually from the lower asymptotic limit of 1/3 for the no-slip surface to 1/2 for a no-shear boundary. Results from our simulations at finite Reynolds number indicate that the local time-averaged transport rates for a no-shear surface exceed the one for the no-slip surface all along the cylinder except in the neighbourhood of the rear stagnation region, where flow separation and reversal augment the transport rates substantially.