Critical parameters for non-Newtonian shear-thickening power-law fluids flow across a channel confined circular cylinder

In this work, the critical parameters for an incompressible flow of non-Newtonian shear-thickening power-law fluids across a channel confined circular cylinder have been investigated numerically. The governing equations have been solved by using the finite volume method for the wide range of power-law (1 <= n <= 1.8) fluids and for two values of wall blockage ratio (beta = 2 and 4). The present methodology has extensively been validated with numerical and experimental results available for limited conditions. Transitional insights of channel confined cylinder, in particular, critical parameters indicating the transitions from creeping to separating flows (i.e., onset of steady symmetric wake formation), and from steady symmetric wake to unsteady asymmetric wake formation (i.e., onset of vortex formation) are investigated and presented in terms of the critical Reynolds numbers (Re-c and Re-c). The relative impacts of unconfined and confined flows on these critical parameters have also been explored. In general, both onsets of the flow separation and wake asymmetry delayed with an increasing values of the power-law index (n) and the wall confinement (lambda). The dependence of critical Re on n for the confined (finite beta) flow are, however, completely opposite to that for unconfined (beta = infinity) flow, i.e., critical Re decreased with increasing n. The influence of power-law index on the onset of vortex is quite stronger to that on the onset of wake formation. For instance, Re-c for beta=(2,4, infinity) altered from (12.5, 7.25, 6.25) to (30.5, 9.25, 0.75) and the corresponding changes with Re-c are noted from (84.5, 70.25, 46.5) to (449.5, 179.5, 33.5) as n varied from 1 to 1.8, respectively. The Stokes paradox (i.e., no creeping flow even as Re -> 0) apparent with unconfined flow of power-law fluids is irrelevant in confined flows, under otherwise identical conditions. Finally, the predictive correlations for critical Re as a function of dimensionless parameters (n and beta) are presented for their easy use in engineering analysis. (c) 2021 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.