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

## TL;DR

This study numerically investigates how shear-thickening power-law fluids behave around a confined circular cylinder, identifying critical flow parameters and transitions, with implications for engineering applications.

## Contribution

It provides new numerical insights into flow transitions of shear-thickening fluids around confined cylinders, including critical Reynolds numbers and their dependence on fluid and confinement properties.

## Key findings

- Critical Reynolds numbers increase with shear-thickening index n.
- Flow transition delays with increased confinement and n.
- Predictive correlations for critical Re as functions of n and b.

## Abstract

In this work, the critical parameters for an incompressible flow of shear-thickening power-law fluids across a channel confined circular cylinder have been investigated numerically. The governing equations have been solved by using finite volume method for wide range of power-law (n=1 - 1.8) fluids and for two blockage ratio (b = 2 and 4). Transitional insights of channel confined cylinder, in particular, critical parameters indicating 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 increasing values of the power-law index (n) and the wall confinement. The dependence of critical Re on n for the confined (finite b) flow are, however, completely opposite to that for unconfined flow, i.e., critical Re decreased with increasing n. The influence of power-law index on the onset of vortex is quite stronger than that on onset of wake formation. For instance, Re^c for b=(2, 4, \infty) altered from (12.5, 7.25, 6.25) to (30.5, 9.25, 0.75) and 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. Stokes paradox (i.e., no creeping flow even as Re ~ 0) apparent with unconfined flow of power-law fluids is non-relevant in confined flows. Finally, predictive correlations for critical Re as a function of dimensionless parameters (n and b) are presented for their easy use in engineering analysis.

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Source: https://tomesphere.com/paper/1901.07362