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Research Papers: Natural and Mixed Convection

# Turbulent Rotating Rayleigh–Benard Convection: Spatiotemporal and Statistical Study

[+] Author and Article Information
A. Husain, H. Varshney

Department of Mechanical Engineering, Aligarh Muslim University, Aligarh 202002, India

M. F. Baig1

Department of Mechanical Engineering, Aligarh Muslim University, Aligarh 202002, Indiadrmfbaig@yahoo.co.uk

1

Corresponding author.

J. Heat Transfer 131(2), 022501 (Dec 12, 2008) (10 pages) doi:10.1115/1.2993545 History: Received December 03, 2007; Revised August 07, 2008; Published December 12, 2008

## Abstract

The present study involves a 3D numerical investigation of rotating Rayleigh–Benard convection in a large aspect-ratio (8:8:1) rectangular enclosure. The rectangular cavity is rotated about a vertical axis passing through the center of the cavity. The governing equations of mass, momentum, and energy for a frame rotating with the enclosure, subject to generalized Boussinesq approximation applied to the body and centrifugal force terms, have been solved on a collocated grid using a semi-implicit finite difference technique. The simulations have been carried out for liquid metal flows having a fixed Prandtl number $Pr=0.01$ and fixed Rayleigh number $Ra=107$ while rotational Rayleigh number $Raw$ and Taylor number Ta are varied through nondimensional rotation rate $(Ω)$ ranging from 0 to $104$. Generation of large-scale structures is observed at low-rotation $(Ω=10)$ rates though at higher-rotation rates $(Ω=104)$ the increase in magnitude of Coriolis forces leads to redistribution of buoyancy-induced vertical kinetic energy to horizontal kinetic energy. This brings about inhibition of vertical fluid transport, thereby leading to reduced vertical heat transfer. The magnitude of rms velocities remains unaffected with an increase in Coriolis forces from $Ω=0$ to $104$. An increase in rotational buoyancy $(Raw)$, at constant rotation rate $(Ω=104)$, on variation in $Raw/Ta$ from $10−3$ to $10−2$ results in enhanced breakup of large-scale structures with a consequent decrease in rms velocities but with negligible reduction in vertical heat transport.

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## Figures

Figure 8

Variation in the root mean square velocities urms, vrms, and wrms at Ra=107: (a) Ta=0 and Raw=0, (b) Ta=102 and Raw=10−1, (c) Ta=106 and Raw=103, (d) Ta=108 and Raw=105, (e) Ta=108 and Raw=2×105, and (f) Ta=108 and Raw=106

Figure 7

Time history of the average Nusselt number on the hot and cold walls at Ra=107: (a) Ta=0 and Raw=0, (b) Ta=102 and Raw=10−1, (c) Ta=106 and Raw=103, (d) Ta=108 and Raw=105, (e) Ta=108 and Raw=2×105, and (f) Ta=108 and Raw=106

Figure 6

(a) 3D streamtraces, (b) streamlines at the central x-z plane, (c) streamlines at the central y-z plane, (d) 3D isotherms, and (e) isotherms in the central x-z plane at Ra=107, Ta=108, and Raw=106

Figure 5

(a) 3D streamtraces, (b) streamlines at the central x-z plane, (c) streamlines at the central y-z plane, (d) 3D isotherms, and (e) isotherms in the central x-z plane at Ra=107, Ta=108, and Raw=105

Figure 4

(a) 3D streamtraces, (b) streamlines at the central x-z plane, (c) streamlines at the central y-z plane, (d) 3D isotherms, and (e) isotherms in the central x-z plane at Ra=107, Ta=106, and Raw=103

Figure 3

(a) 3D streamtraces, (b) streamlines at the central x-z plane, (c) streamlines at the central y-z plane, (d) 3D isotherms, and (e) isotherms in the central x-z plane at Ra=107, Ta=102, and Raw=10−1

Figure 2

(a) 3D streamtraces, (b) streamlines at the central x-z plane, (c) streamlines at the central y-z plane, (d) 3D isotherms, and (e) isotherms in the central x-z plane at Ra=107, Ta=0, and Raw=0

Figure 1

Schematic of the geometry of the domain

Figure 9

Variation in the (a) Θ¯ and (b) Θrms at Ra=107, Ta=0, and Raw=0, Ta=102 and Raw=10−1, Ta=106 and Raw=103, Ta=108 and Raw=105, Ta=108 and Raw=2×105, and Ta=108 and Raw=106

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