Convection Patterns and Corresponding Critical Conditions in an Inclined Layer

NING Lizhong; WU Hao; NING Bibo; TIAN Weili; NING Jinghao

doi:10.21656/1000-0887.390102

Volume 40 Issue 4

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NING Lizhong, WU Hao, NING Bibo, TIAN Weili, NING Jinghao. Convection Patterns and Corresponding Critical Conditions in an Inclined Layer[J]. Applied Mathematics and Mechanics, 2019, 40(4): 398-407. doi: 10.21656/1000-0887.390102

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Convection Patterns and Corresponding Critical Conditions in an Inclined Layer

doi: 10.21656/1000-0887.390102

¹Institute of Water Resources and HydroElectric Engineering,Xi’an University of Technology, Xi’an 710048, P.R.China;²College of Civil Engineering and Architecture, Jiaxing University, Jiaxing, Zhejiang 314001, P.R.China;³Department of Architecture, Shanghai University, Shanghai 200444, P.R.China

Funds: The National Natural Science Foundation of China(10872164)

Received Date: 2018-04-02
Rev Recd Date: 2018-09-18
Publish Date: 2019-04-01

Abstract

Abstract

Through numerical simulation of the basic equations for 2D fluid mechanics, the convection patterns and the critical conditions for pattern transition in an inclined rectangular cavity with Prandtl number Pr=6.99 were studied. According to the variations of inclination angle θ and relative Rayleigh number Ra_r, the convection patterns in the inclined layer can be divided into the convection single-roll pattern, the multi-roll pattern filling the cavity and the multi-roll pattern in the transitional stage. With constant inclination angle θ,the system transforms from the multi-roll pattern filling the cavity to the single-roll pattern with the decrease of relative Rayleigh number Ra_r, where the convection amplitude and Nusselt number Nu increase with Ra_r. For Ra_r=9,the system transforms from the multi-roll pattern filling the cavity to the single-roll pattern with the increase of inclination angle θ,where the convection amplitude decreases with θ,and the Nusselt number increases with θ.The simulation results of the transition from multi-roll to single-roll patterns in plane θ_c-Ra_r show that, for Ra_r=2,the multi-roll pattern is not found in the cavity. For Ra_r=2.5 or so, the transition from the multi-roll pattern to the single-roll pattern appears in the cavity. The critical θ_c value for the transition from the multi-roll to the single-roll patterns increases with the decrease of Ra_r for θ_c<10. The θ_c value increases with Ra_r for θ_c>10, where θ_c increases rapidly with Ra_r for Ra_r≤5,and increases slowly with Ra_r for Ra_r>5. The relation between θ_c and Ra_rθ is similar to θ.
- inclined layer,
- convection pattern,
- Rayleigh number,
- critical inclination angle,
- streamline

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References(33)

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