Vortex Structure and Instability Characteristics of Dean–Taylor Flow through a Rotating Bent Square-Shaped Enclosure

The present paper investigates solution structure, instability characteristics, and chaotic nature of the Dean-Taylor flow with energy distribution through a rotating bent square-shaped enclosure adopting a spectral-based numerical approach. The channel is rotated about the vertical axis in the positive direction for the Taylor number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 \leqslant {\text{Tr}} \leqslant 2000$$\end{document}. A temperature difference is applied across the vertical walls while a room temperature is maintained on the horizontal walls. Numerical calculations are carried out for the Dean number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Dn}} = 1000$$\end{document} over a wide of curvature ranging from 0.001 to 0.5, and the combined effects of centrifugal, Coriolis, and buoyancy forces are examined. As a result, three branches of asymmetric steady solutions (SS), composed of 2- to 4-vortex solutions, are obtained by using arc-length path continuation technique. To understand the unsteady nature, the transient solution is then inspected by time series analysis, and flow transition is precisely identified by determining the phase trajectory of the temporal development and assessing the power spectrum density. The study shows that, as Tr increases, the flow progresses through various instabilities namely multi-periodic, chaotic, steady-state, periodic, and then chaotic-state again, demonstrating a transition that features asymmetric 2- to 8-vortex solutions. Nusselt numbers are calculated as a measure of convective heat transfer (HT) between the heating wall and the fluid, and it is discovered that chaotic flow (SF) considerably improves convective heat transfer (CHT). Finally, our computational findings are assessed against previously reported experimental data, and an adequate consistency is observed.