Theoretical understanding of unsteady flow separation for shear flow past three square cylinders in vee shape using stru
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Theoretical understanding of unsteady flow separation for shear flow past three square cylinders in vee shape using structural bifurcation analysis Atendra Kumar1,2 · Rajendra K. Ray2 Received: 1 July 2019 / Revised: 15 April 2020 / Accepted: 18 May 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract The unsteady flow separation of two-dimensional (2-D) incompressible shear flow past three identical square cylinders arranged in vee shape is studied in this paper, using theoretical structural bifurcation analysis based on topological equivalence. Through this analysis, the exact location and time of occurrence of bifurcation points (flow separation points) associated with secondary and tertiary vortices on all cylinders are studied. The existence of saddle points is also studied during primary flow separation. Different gap ratios between the downstream cylinders, s/d = 0.6–3.0 (where s is the gap between cylinders, d is the length of cylinder side) with fixed gap 2d between upstream and downstream cylinders for different shear parameter (K ) values ranging from K = 0.0 to 0.4 are considered at Reynolds number (Re) 100. In this process, the instantaneous vorticity contours and streakline patterns, centerline velocity fluctuation, phase diagram, lift and drag coefficients are studied to confirm the theoretical results. Computations are carried out by using higher order compact finite difference scheme. Present study mainly investigates the effect of K and gap ratio on unsteady flow separation and vortex-shedding phenomenon. All the computed results very efficiently and very accurately reproduce the complex flow phenomenon. Through this study, many noticeable and interesting results are reported for the first time for this problem. Keywords Unsteady shear flow · Square cylinders in vee shape · Vortex shedding · Flow separation · HOC scheme · Structural bifurcation Mathematics Subject Classification 65N06 · 65Z05 · 65Y99
Communicated by Corina Giurgea.
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Rajendra K. Ray [email protected] Atendra Kumar [email protected]
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Department of Computational and Data Science, Indian Institute of Science Bangalore, Bangalore, India
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School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, India 0123456789().: V,-vol
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A. Kumar, R. K. Ray
List of symbols d Side length of square cylinder s Vertical distance between downstream cylinders Xu Upstream distance Xd Downstream distance Yh Distance to upper and lower boundary from cylinder surface Uc Centerline velocity u, ˜ u Dimensional and dimensionless horizontal velocities v, ˜ v Dimensional and dimensionless vertical velocities τ Dimensional time t Dimensionless time (= τ Uc /d) Re Reynolds number ν Kinematic viscosity of the fluid K Non-dimensional shear rate (= Gd/Uc ) G Dimensional transverse velocity gradient x, y Cartesian coordinates ˜ ψ ψ, Dimensional and dimensionless stream functions ω, ˜ ω Dimensional and dimensionless vorticities p Dimensionless pressure CL Lift coefficient CD D
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