Pattern selection in Rayleigh-Bénard convection with nonlinear viscoelastic fluids

Zheng, Xin; Hagani, Fouad; Boutaous, Mhamed; Knikker, Ronnie; Xin, Shihe; Siginer, Dennis A.

doi:10.1103/physrevfluids.7.023301

Cited by 8 publications

(10 citation statements)

References 26 publications

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“…A recently developed in-house solver was adopted to solve the governing equations. The capability of this solver to simulate VRBC has been shown in our previous work 21,34,35,45 . Various validation tests have been done.…”

Section: Numerical Proceduresmentioning

confidence: 93%

“…In the work of Zheng et al 35 , Park and Ryu 36 , Park and Lee 49 on HVRBC, an oscillating convection, which exhibits strong spatio-temporal periodicity, takes place with Γ = 2 and a certain range of β and Wi. The time-dependent convective cells show standing wave characteristics in space in the pattern of H2R (two cells) meaning that there is no mass exchange between cells.…”

Section: B Oscillating Convection Structuresmentioning

confidence: 98%

“…After that, the branches of T 3R grow from the bifurcation H1. Considering the oscillating flow configuration in HVRBC 35 , we guess that there may be a certain Ra range where H2R and H3R may coexist. To obtain another pattern, we take the stable solution H2R of HVRBC as the initial value and raise the inclination to α = 2 • .…”

Section: A Pattern Selection and Bifurcation Diagramsmentioning

confidence: 99%

“…There is clearly a distinction between weakly elastic VRBC which shows similarities to the NRBC and strongly elastic VRBC with much more interesting behavior, regular flow reversal for instance. The distinction extends to the convection onset and the corresponding pattern selection which depends on the rheological parameters Wi and β 34,35 . Similar dependency is also found by Park and Ryu 36 , Park, Shin, and Sohn 37 also arrived at similar findings through linear and nonlinear stability analysis.…”

Section: Introductionmentioning

confidence: 99%

“…The influence of the parameters (α, Wi) on TVRBC in the vicinity of the convection onset is explored in detail. We work with an aspect ratio of Γ = 2 because flow patterns in a 2 : 1 cavity with strongly elastic fluids show a rich variety compared with aspect ratios Γ = 1 and Γ > 3 35,36 about the critical Rayleigh number (Rac).…”

Section: Introductionmentioning

confidence: 99%

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Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity

et al. 2023

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The oscillating onset of the Rayleigh-Bénard convection (RBC) with viscoelastic fluids in a slightly tilted 2-dimension (2D) rectangular cavity with aspect ratio Γ = 2 was investigated for the first time via direct numerical simulation. A series of simulations were conducted in the plane of the Rayleigh number (Ra) and the tilt angle (α ∈ [0◦,5◦]) with three Weissenberg numbers (Wi = (0.1,0.15,0.2)) at a fixed Prandtl number Pr = 7.0. The evolutionary path of the oscillating convection onset in the (Wi,α)-plane was determined and corresponding complex flow structures were observed. The inclination of the box delays the onset of the oscillations and the corresponding Rayleigh number Rac as compared to the horizontal configuration. Oscillating flow structures acquire the attributes of a traveling wave. A specific feature of the oscillating convection in the case of the horizontal cavity, the periodicity in space and time exists in the inclined box case as well. But, the evolution of the oscillatory flow structure is very different from the horizontal case in that the counter-clockwise cell assimilates the clockwise cell.

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Section: Numerical Proceduresmentioning

confidence: 93%

Section: B Oscillating Convection Structuresmentioning

confidence: 98%

Section: A Pattern Selection and Bifurcation Diagramsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity

et al. 2023

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Oscillatory one-roll and two-roll solutions in laminar viscoelastic Rayleigh-Bénard convection in a square cavity

Maurya,

Singh,

Kumar

2024

Journal of Non-Newtonian Fluid Mechanics

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Pattern selection and heat transfer in the Rayleigh–Bénard convection near the vicinity of the convection onset with viscoelastic fluids

et al. 2023

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The effect of viscoelasticity on the flow and heat transport in the Rayleigh-Bénard convection (RBC) in a rectangular with horizontal periodic boundary is investigated via direct numerical simulation. The working fluid is described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model that is able to capture some of the most important polymeric flow behaviors. Numerical simulations are conducted at a low concentration β = 0.9, where β = μs/μ0, μs is the solvent viscosity, μ0 = μs + μp is sum of μs and the polymer viscosity μp. A parametric analysis is performed to understand the influence of the Weissenberg number Wi, the viscosity ratio β and the extension length L on the oscillating mode of the viscoelastic RBC. It is found that both Wi and β weakly inhibit the convection onset and the transition from steady to oscillatory convection. The amplitude and frequency of the oscillations in the oscillatory flow regime are both suppressed. However, the elastic nonlinearity may make the flow transition irregular and even may bring about the relaminarization or lead to the convection cells traveling in the horizontal direction. The extension length L may induce multiple pairs of roll flow patterns at a specific setting of (Ra, Wi). Heat transport is reduced by elasticity but still obeys the power law with Ra if the flow pattern has one pair of rolls. However, heat transfer enhancement occurs if multiple pairs of rolls are induced.

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Pattern selection in Rayleigh-Bénard convection with nonlinear viscoelastic fluids

Cited by 8 publications

References 26 publications

Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity

Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity

Oscillatory one-roll and two-roll solutions in laminar viscoelastic Rayleigh-Bénard convection in a square cavity

Pattern selection and heat transfer in the Rayleigh–Bénard convection near the vicinity of the convection onset with viscoelastic fluids

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