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# Impact of inlet shear on unsteady boundary layer separation from two square cylinders in tandem arrangement

Kumar, A and Ray, RK and Raha, S (2021) Impact of inlet shear on unsteady boundary layer separation from two square cylinders in tandem arrangement. In: Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43 (12).

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Official URL: https://doi.org/10.1007/s40430-021-03252-6

## Abstract

We know that boundary layer separation is essentially the structural bifurcation of the velocity field of fluid flows (Ma and Wang in Geometric theory of incompressible flows with applications to fluid dynamics. No. 119, American Mathematical Soc, 2005; Wang and Ma in Revista de la Real Academia de Ciencias Exactas 96(3):447â��459, 2002; Ghil et al. in Phys D Nonlinear Phenom 197(1â��2):149â��173, 2004; Ghil et al. in SIAM J Appl Math 65(5):1576â��1596, 2005). In this paper, the unsteady separation of two-dimensional shear flow having constant fluid properties from the surfaces of a pair of square cylinders in a tandem arrangement is analyzed numerically. The mechanism of separation has been characterized using the structural bifurcation concept developed by Ma and Wang (Disc Contin Dyn Syst A 10(1&2):459, 2004). The investigation is carried out by analyzing the solutions of Navierâ��Stokes equations on uniform Cartesian grids using a higher-order compact finite difference scheme. The numerical scheme is validated by comparing the results with the previous results in the literature. The effect of shear rate K and gap ratio s/d (where s is the distance between two cylinders, d is the side length of the cylinder) on the initial flow separation and fully developed vortex shedding structure are discussed. The results are presented for initial flow development with time and fully developed flow for the parameter range 0.0 â�¤ Kâ�¤ 0.4 , 0.5 â�¤ s/ dâ�¤ 6.0 at Reynolds number (Re) 100. The details of the flow separation points (i.e., bifurcation points), time of their occurrences, saddle points, vorticity contours and streaklines pattern are presented. The centerline velocity profiles along x-axis and phase diagrams are also shown. The present study confirms the significant effect of the K value and s/d ratio on the exact location and time of flow separation and its connection to complex vortex shedding phenomena. It is observed that the downstream cylinder does not go through the process of structural bifurcation from its upper and lower surfaces at the present Re value. We say that the placement of the upstream cylinder suppresses the flow separation from the surface of the downstream cylinder. To the best of our knowledge, this is the first time, a topological aspect-based structural bifurcation analysis has been done to understand the vortex shedding phenomenon and flow separation for this problem. Â© 2021, The Brazilian Society of Mechanical Sciences and Engineering.

Item Type: Journal Article Journal of the Brazilian Society of Mechanical Sciences and Engineering Springer Science and Business Media Deutschland GmbH The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH Bifurcation (mathematics); Boundary layers; Cylinders (shapes); Finite difference method; Flow separation; Navier Stokes equations; Reynolds number; Velocity; Vortex flow; Vortex shedding; Vorticity; Wakes, Boundary-layer separation; Downstream cylinders; HOC scheme; Initial flow; Square cylinders; Structural bifurcation; Tandem arrangement; Two identical square cylinder in tandem arrangement; Unsteady separation; Vortex-shedding, Shear flow Division of Interdisciplinary Sciences > Computational and Data Sciences 03 Dec 2021 08:45 03 Dec 2021 08:45 http://eprints.iisc.ac.in/id/eprint/70607

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