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Research Papers: Fundamental Issues and Canonical Flows

# Numerical Study of the Laminar Flow Past a Rotating Square Cylinder at Low Spinning Rates

[+] Author and Article Information
Dipankar Chatterjee

Simulation and Modeling Laboratory,
CSIR—Central Mechanical Engineering
Research Institute,
Durgapur 713209, India
e-mail: d_chatterjee@cmeri.res.in

Satish Kumar Gupta

Department of Mechanical Engineering,
National Institute of Technology,
Durgapur 713209, India

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 21, 2014; final manuscript received August 22, 2014; published online September 26, 2014. Assoc. Editor: D. Keith Walters.

J. Fluids Eng 137(2), 021204 (Sep 26, 2014) (10 pages) Paper No: FE-14-1144; doi: 10.1115/1.4028500 History: Received March 21, 2014; Revised August 22, 2014

## Abstract

The fluid dynamic interaction between a uniform free stream flow and the rotation induced flow from a sharp edged body is numerically investigated. A two-dimensional (2D) finite volume based computation is performed in this regard to simulate the laminar fluid flow around a rotating square cylinder in an unconfined medium. Body fitted grid system along with moving boundaries is used to obtain the numerical solution of the incompressible Navier–Stokes equations. The Reynolds number based on the free stream flow is kept in the range $10≤Re≤200$ with a dimensionless rotational speed of the cylinder in the range $0≤Ω≤5$. At low $Re=10$, the flow field remains steady irrespective of the rotational speed. For $50≤Re≤200$, regular low frequency Kármán vortex shedding (VS) is observed up to a critical rate of rotation ($Ωcr$). Beyond $Ωcr$, the global flow shows steady nature, although high frequency oscillations in the aerodynamic coefficients are present. The rotating circular cylinder also shows likewise degeneration of Kármán VS at some critical rotational speed. However, significant differences can be seen at higher rotation. Such fluid dynamic transport around a spinning square in an unconfined free stream flow is reported for the first time.

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## Figures

Fig. 1

Schematic of the physical problem

Fig. 2

Typical grids used for simulation (a) full domain and (b) expanded view around the cylinder

Fig. 3

Variation of (a) overall drag coefficient and (b) Strouhal number with Reynolds number for free stream flow over a stationary square cylinder (Ω = 0). The parameters are time averaged for the unsteady periodic region.

Fig. 4

Instantaneous streamlines and vorticity contours around the cylinder at Re = 10 for different rotational speeds

Fig. 5

Time response of the lift coefficient signal at Re = 10 and for different rotational speeds

Fig. 6

Instantaneous streamlines around the cylinder at Re=100 for different rotational speeds

Fig. 7

Global vorticity contours for different rotational speeds and Reynolds numbers

Fig. 8

Streamlines and vorticity contours around the cylinder at Re = 100 for different positions and Ω = 1

Fig. 9

Lift coefficient signal at Re = 100 for different rotational speeds

Fig. 10

Phase diagram for various rotational speeds and at Re = 100

Fig. 11

(a) Time average and (b) rms drag coefficient as a function of rotational speed for various Reynolds numbers

Fig. 12

(a) Time average and (b) rms lift coefficient as a function of rotational speed for various Reynolds numbers

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