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Research Papers: Forced Convection

# Influence of Thermal Buoyancy on Vortex Shedding Behind a Rotating Circular Cylinder in Cross Flow at Subcritical Reynolds Numbers

[+] Author and Article Information
Dipankar Chatterjee

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

Chiranjit Sinha

Simulation & Modeling Laboratory,
CSIR—Central Mechanical Engineering
Research Institute,
Durgapur 713209, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 27, 2013; final manuscript received November 4, 2013; published online xx xx, xxxx. Assoc. Editor: James A. Liburdy.

J. Heat Transfer 136(5), 051704 (Feb 26, 2014) (10 pages) Paper No: HT-13-1103; doi: 10.1115/1.4026007 History: Received February 27, 2013; Revised November 04, 2013

## Abstract

The vortex shedding (VS) behind stationary bluff obstacles in cross-flow can be initiated by imposing thermal instability at subcritical Reynolds numbers (Re). We demonstrate here that additional thermal instability is required to be imparted in the form of heating for destabilizing the flow around a rotating bluff obstacle. A two-dimensional numerical simulation is performed in this regard to investigate the influences of cross buoyancy on the VS process behind a heated and rotating circular cylinder at subcritical Re. The flow is considered in an unbounded medium. The range of Re is chosen to be 5–45 with a dimensionless rotational speed ($Ω$) ranging between 0 and 4. At this subcritical range of Reynolds number the flow and thermal fields are found to be steady without the superimposed thermal buoyancy (i.e., for pure forced flow). However, as the buoyancy parameter (Richardson number, Ri) increases flow becomes unstable and subsequently, at some critical value of Ri, periodic VS is observed to characterize the flow and thermal fields. The rotation of the cylinder is found to have a stabilizing effect and as $Ω$ increases more heating is observed to be required to destabilize the flow.

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## Figures

Fig. 2

Streamlines (left) and isotherms (right) around the cylinder at Re = 20 and without thermal buoyancy effect (Ri = 0) for different Ω

Fig. 3

Local Nu distribution for different Ω at Re = 20 and Ri = 0

Fig. 4

Stability diagram at different Ω, (a) Ω=0, (b) Ω=1, (c) Ω=2, and (d) Ω=4

Fig. 1

Schematic of the physical problem

Fig. 7

Variation of total positive and negative surface vorticity with Ω for Re = 40 and Ri = 0 and 1

Fig. 6

Variation of (a, c, and d) local surface vorticity and (b) baroclinic vorticity production along the surface of the cylinder at Re = 40 and for different Ω and Ri

Fig. 5

Contours of instantaneous vorticity magnitude at Re = 40 (a) Ri = 0.55 (left), and Ri = 0.60 (right) for Ω=0, (b) Ri = 0.65 (left) and Ri = 0.70 (right) for Ω=1, (c) Ri = 0.85 (left) and Ri = 0.90 (right) for Ω=2, and (d) Ri = 1.6 (left) and Ri = 1.65 (right) for Ω=4

Fig. 8

Variation of St with (a) Ri at Re = 40 and (b) Re at Ri = 1.5 and for different Ω

Fig. 9

Variation of time average (a, b) CD and (c, d) CL with Ri for different Re and Ω=0 and 4

Fig. 10

Variation of time and surface average Nu with Ri for different (a) Re at Ω=0 and (b) Ω at Re = 40

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