On the use of time-dependent fluids for delaying onset of transition to turbulence in the flat plate boundary-layer flow: A passive control of flow

Abstract

Inelastic time-dependent fluids display continuous and reversible changes in viscosity when subjected to a constant shear-rate. These alterations arise from the gradual modification of the material’s microstructure due to shear-induced effects, known as shear rejuvenation. When this process generates smaller structural units, it is termed thixotropy; conversely, if it produces larger units, it is labeled anti-thixotropy. Aging is another characteristic of such fluids, denoting the capacity of the material to regain its original structure in the absence of shear, thus reversing the initial time-dependent change. This phenomenon often results from thermally activated Brownian motion prompting the reorganization of the material’s microconstituents. Consequently, attractive forces between these components can instigate the reconstruction of a network-like structure within the material. This study centers on investigating how variations in fluid microstructure impact the onset of transition to turbulence in a flat plate boundary-layer flow. Specifically, the focus is on cases where larger structural units emerge during the breakdown process (anti-thixotropy). To represent such fluids, the Quemada model, an inelastic structural-kinetic model, is employed. This model effectively captures thixotropy and anti-thixotropy by appropriately configuring model parameters. The analysis begins with obtaining a local similarity solution for the generalized Blasius equation, representing the base flow. Subsequently, the stability of this flow is assessed using linear temporal stability theory. This involves introducing infinitesimally-small normal-mode perturbations to the base flow, yielding the generalized Orr–Sommerfeld equation. Solving this equation using the spectral method provides insights into stability. Results from this study indicate that for low Deborah numbers, the shear-thickening behavior prevails, causing destabilization. In contrast, higher Deborah numbers lead to stability. This implies that anti-thixotropy effectively delays the onset of transition to turbulence and could hold practical applications for flow control.