The Rayleigh–Bénard problem in intermediate bounded domains

1993 ◽  
Vol 254 ◽  
pp. 375-400 ◽  
Author(s):  
F. Stella ◽  
G. Guj ◽  
E. Leonardi
Keyword(s):  
Flow Pattern ◽  
Quantitative Comparison ◽  
Flow Structures ◽  
Bounded Domains ◽  
Oscillatory Regime ◽  
Rectangular Container ◽  
Two Dimensional Flow ◽  
Convection Rolls ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The stationary instabilities of flow patterns associated with Rayleigh–Bénard convection in a 3 × 1 × 9 rectangular container are extensively investigated by numerical simulation. Two types of spatial instabilities of the base convection rolls are predicted in the transition from steady two-dimensional flow to the unsteady oscillatory regime; these instabilities depend on the Prandtl number. For Pr = 0.71 the soft-roll instability is found at moderate Rayleigh number Ra. The results obtained confirm the importance of this flow pattern as a continuous mechanism for steady transition from one wavenumber to another. For Pr = 15, cross-roll instability is obtained, which at larger Ra leads to bimodal convection. For this value of Pr the soft-roll flow pattern is found at intermediate Ra. At higher Ra a new flow structure in which cross-rolls are superimposed on the soft roll is obtained. The effects of the various flow structures on the heat transfer are given. A quantitative comparison with previous experimental and theoretical findings is also presented and discussed.

scholarly journals From zonal flow to convection rolls in Rayleigh–Bénard convection with free-slip plates

2020 ◽  
Vol 905 ◽  
Author(s):  
Qi Wang ◽  
Kai Leong Chong ◽  
Richard J. A. M. Stevens ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Zonal Flow ◽  
Bénard Convection ◽  
Benard Convection ◽  
Convection Rolls ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract

scholarly journals A model for near-wall dynamics in turbulent Rayleigh–Bénard convection

1998 ◽  
Vol 373 ◽  
pp. 221-254 ◽  
Author(s):  
S. ANANDA THEERTHAN ◽  
JAYWANT H. ARAKERI
Keyword(s):  
Similarity Solution ◽  
Critical Length ◽  
Two Dimensional ◽  
Velocity Fluctuations ◽  
Bénard Convection ◽  
Benard Convection ◽  
Two Dimensional Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Near Wall

Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh–Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh–Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.

Rayleigh–Bénard convection in liquid metal layers under the influence of a horizontal magnetic field

2002 ◽  
Vol 453 ◽  
pp. 345-369 ◽  
Author(s):  
ULRICH BURR ◽  
ULRICH MÜLLER
Keyword(s):  
Magnetic Field ◽  
Heat Transport ◽  
Convective Heat ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Horizontal Magnetic Field ◽  
Two Dimensional Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

This article presents an analytical and experimental study of magnetohydrodynamic Rayleigh–Bénard convection in a large aspect ratio, 20[ratio ]10[ratio ]1, rectangular box. The test fluid is a eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr≈0:02. The experimental setup covers Rayleigh numbers in the range 103< Ra<8×104 and Chandrasekhar numbers 0[les ]Q[les ]1.44×106 or Hartmann numbers 0[les ]M[les ]1200, respectively.When a horizontal magnetic field is imposed on a heated liquid metal layer, the electromagnetic forces give rise to a transition of the three-dimensional convective roll pattern into a quasi-two-dimensional flow pattern in such a way that convective rolls become more and more aligned with the magnetic field. A linear stability analysis based on two-dimensional model equations shows that the critical Rayleigh number for the onset of convection of quasi-two-dimensional flow is shifted to significantly higher values due to Hartmann braking at walls perpendicular to the magnetic field. This finding is experimentally confirmed by measured Nusselt numbers. Moreover, the experiments show that the convective heat transport at supercritical conditions is clearly diminished. Adjacent to the onset of convection there is a significant region of stationary convection with significant convective heat transfer before the flow proceeds to time-dependent convection. However, in spite of the Joule dissipation effect there is a certain range of magnetic field intensities where an enhanced heat transfer is observed. Estimates of the local isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport is accompanied by the formation of strong non-isotropic time-dependent flow in the form of large-scale convective rolls aligned with the magnetic field which exhibit a simpler temporal structure compared to ordinary hydrodynamic flow and which are very effective for the convective heat transport.

scholarly journals The effect of surfactant solutions on flow structures in turbulent Rayleigh-Benard convection

2018 ◽  
Vol 22 (Suppl. 2) ◽  
pp. 507-515 ◽  
Author(s):  
Tongzhou Wei ◽  
Weihua Cai ◽  
Changye Huang ◽  
Hongna Zhang ◽  
Wentao Su ◽  
...  
Keyword(s):  
Experimental Study ◽  
Large Scale ◽  
Particle Image ◽  
Surfactant Solution ◽  
Flow Structures ◽  
Large Scale Circulation ◽  
Surfactant Solutions ◽  
Image Velocimetry ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper presents an experimental study on the flow structures in turbulent Rayleigh-B?nard convection with surfactant solutions. The shadowgraph visualization was used to obtain the plumes and the velocity field was measured using particle image velocimetry. The results show that the size of plumes in surfactant solution case is larger than that in Newtonian fluid case and it needs more time for surfactant solution case to start convection. The large-scale circulation fails to form in surfactant solution case and the convection velocity is smaller. A decrease of the measured Nusselt number is observed in surfactant solution case. The above phenomena are caused by the shear-shinning and elastic chara cteristics of surfactant solution.

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