Numerical study of subcritical Rayleigh–Bénard convection rolls in strongly shear-thinning Carreau fluids

Jenny, Mathieu; Plaut, Emmanuel; Briard, Antoine

doi:10.1016/j.jnnfm.2015.03.002

Cited by 20 publications

(55 citation statements)

References 19 publications

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“…In a quite different system, Rayleigh-Bénard thermoconvection, a similar asymptotic regime has been found by Jenny et al (2015) for strongly shear-thinning Carreau fluids: the onset of thermoconvection rolls becomes subcritical, and the critical Rayleigh number constructed on the bulk average of the viscosity is roughly constant. This proves, generally, the relevance of the bulk averaged mean viscosity in shear-thinning fluids.…”

Section: Concluding Discussionsupporting

confidence: 71%

Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

2017

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In order to model the transition to turbulence in pipe flow of non-Newtonian fluids, the influence of a strongly shear-thinning rheology on the traveling waves with a threefold rotational symmetry of Faisst & Eckhardt (2003); is analyzed. The rheological model is Carreau's law. Besides the shear-thinning index n C , the dimensionless characteristic time λ of the fluid is considered as the main non-Newtonian control parameter. If λ = 0, the fluid is Newtonian. In the relevant limit λ → +∞, the fluid approaches a power-law behaviour. The laminar base flows are first characterized. To compute the nonlinear waves, a Petrov-Galerkin code is used, with continuation methods, starting from the Newtonian case. The axial wavenumber is optimized and the critical waves appearing at minimal values of the Reynolds number Re w based on the mean velocity and wall viscosity are characterized. As λ increases, these correspond to a constant value of the Reynolds number based on the mean velocity and viscosity. This viscosity, close to the one of the laminar flow, can be estimated analytically. Therefore the experimentally relevant critical Reynolds number Re wc can also be estimated analytically. This Reynolds number may be viewed as a lower estimate of the Reynolds number for the transition to developed turbulence. This demonstrates a quantified stabilizing effect of the shear-thinning rheology. Finally, the increase of the pressure gradient in waves, as compared to the one in the laminar flow with the same mass flux, is calculated, and a kind of 'drag reduction effect' is found.

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Section: Concluding Discussionsupporting

confidence: 71%

Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

2017

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“…It is worth noting that in the Carreau fluid case, the heat transfer is increased with decreasing n as shown by Refs. and . Contrarily to the Herschel‐Bulkley model, in the Carreau case, the decrease in effective viscosity is larger when n decreases.…”

Section: Resultsmentioning

confidence: 90%

“…It is not surprising as one knows that shear‐thinning fluids can involve subcritical bifurcation as shown in Refs. . A theoretical study has also shown the possibility of subcritical bifurcation in yield stress fluids in the case of the Rayleigh‐Bénard Poiseuille flow for low values of Reynolds number.…”

Section: Resultsmentioning

confidence: 94%

Natural convection in shear‐thinning yield stress fluids in a square enclosure

Magnin

Métivier

2015

AIChE Journal

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International audienceThe influence of viscoplastic rheological features on the Rayleigh-Bénard convection is investigated by numerical means in order to compare with first experimental results given by Darbouli et al. The fluid is modeled by a regularized Herschel-Bulkley law which is often used to fit numerous pasty fluids. Natural convection in a two-dimensional square cavity heated from below is considered. Critical values of Oldroyd number Od and yield number Y are provided. Numerical results highlight a stabilizing effect of the yield stress as well as a destabilizing effect of increasing shear-thinning coefficient n as the increase in n enhances the heat transfer in the range of our calculations. Unyielded regions are located in the square corners of the cavity and in the cavity where convection occurs. The unyielded zones size increases with the increase in Od and can invade all the cavity for sufficiently large values of Od

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“…the influence of nonlinear decrease of the viscosity with the shear rate. This feature, when it is sufficiently strong, leads to a subcritical bifurcation (Lamsaadi, Naimi & Hasnaoui 2005;Solomatov & Barr 2006, 2007Balmforth & Rust 2009;Albaalbaki & Khayat 2011;Alloui et al 2013;Benouared, Mamou & Ait-Messaoudene 2014;Bouteraa et al 2015;Jenny, Plaut & Briard 2015). Indeed, in the presence of a finite amplitude perturbation, the viscosity decreases reducing by this way the viscous damping.…”

Section: Case Of Non-newtonian Fluids: Influence Of Shear-thinning Efmentioning

confidence: 99%

Stability of hexagonal pattern in Rayleigh–Bénard convection for thermodependent shear-thinning fluids

et al. 2020

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Numerical study of subcritical Rayleigh–Bénard convection rolls in strongly shear-thinning Carreau fluids

Cited by 20 publications

References 19 publications

Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

Natural convection in shear‐thinning yield stress fluids in a square enclosure

Stability of hexagonal pattern in Rayleigh–Bénard convection for thermodependent shear-thinning fluids

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