Thermal instabilities in a yield stress fluid: Existence and morphology

Davaille, Anne; Gueslin, Blandine; Maßmeyer, A.; Giuseppe, Erika Di

doi:10.1016/j.jnnfm.2012.10.008

Cited by 41 publications

(55 citation statements)

References 35 publications

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“…Unyielded regions may be further categorized as being stationary or in motion, with the former typically abutting a wall of the flow domain. This paper is motivated by the recent experimental study of Davaille et al (2013) in which thermal plumes are induced in a stationary viscoplastic fluid reservoir (rectangular tank), by means of localized heating applied at the lower wall of the tank. In natural convection, buoyancy forces resulting from thermal expansion induce fluid motion.…”

Section: Introductionmentioning

confidence: 99%

“…A review of the vast body of research on Newtonian plumes can be found in Ribe, Davaille & Christensen (2007). To the best of authors' knowledge, the first experimental studies of viscoplastic plumes were conducted very recently by Davaille et al (2013).…”

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confidence: 99%

“…This temperature history was not produced using any particular mathematical function. Instead it was derived from the temperature history of the heater in the experiments of Davaille et al (2013) and was only provided for a very limited number of simulations. This significantly limits the possibility of quantitative benchmarking against their work.…”

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confidence: 99%

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Thermal plumes in viscoplastic fluids: flow onset and development

2015

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The purely conductive state in configurations such as the Rayleigh-Bénard one is linearly stable for yield stress fluids at all Rayleigh numbers, Ra. However, on changing to localized heater configurations the static background state exists only if the yield stress is sufficiently large. Otherwise, thermal plumes may be induced in a stationary viscoplastic fluid layer, as illustrated in the recent experimental study of Davaille et al. (J. Non-Newtonian Fluid Mech., vol. 193, 2013, 144-153). Here, we study an analogous problem both analytically and computationally, from the perspective of an ideal yield stress fluid (Bingham fluid) that is initially stationary in a locally heated rectangular tank. We show that for a non-zero yield stress the onset of flow waits for a start time t s that increases with the dimensionless ratio of yield stress to buoyancy stress, denoted B. We provide a precise mathematical definition of t s and approximately evaluate this for different values of B, using both computational and semianalytical methods. For sufficiently large B B cr , the fluid is unable to yield. For the flow studied, B cr ≈ 0.00307. The critical value B cr and the start time t s , for B < B cr , are wholly independent of Ra and Pr. For B < B cr , yielding starts at t = t s . The flow develops into either a weakly or a strongly convective flow. In the former case the passage to a steady state is relatively smooth and monotone, resulting eventually in a steady convective plume above the heater, rising and impinging on the upper wall, then recirculating steadily around the tank. With strongly convecting flows, for progressively larger Ra we observe an increasing number of distinct plume heads and a tendency for plumes to develop as short-lived pulses. Over a certain range of (Ra, B) the flow becomes temporarily frozen between two consecutive pulses. Such characteristics are distinctly reminiscent of the experimental work of Davaille et al. (J. Non-Newtonian Fluid Mech., vol. 193, 2013, 144-153). The yield stress plays a multifaceted role here as it affects plume temperature, size and velocity through different mechanisms. On the one hand, increasing B tends to increase the maximum temperature of the plume heads. On the other hand, for larger B → B cr , the plume never starts.

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Section: Introductionmentioning

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Thermal plumes in viscoplastic fluids: flow onset and development

2015

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“…Finally, a number of authors have recently studied the onset of natural convection experimentally using solutions of Carbopol (e.g. Darbouli et al 2013;Davaille et al 2013;Kebiche, Castelain & Burghelea 2014). …”

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A novel heat transfer switch using the yield stress

2015

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International audienceWe explore the feasibility of a novel method for the regulation of heat transfer across a cavity, by using a controllable yield stress in order to suppress the convective heattransfer. Practically, this type of control can be actuated with electro-rheological ormagneto-rheological fluids. We demonstrate that above a given critical yield stressvalue only static steady regimes are possible, i.e. a purely conductive unyielded fluidfills the cavity. We show that this limit is governed by a balance of yield stressand buoyancy stresses, here described by B. With proper formulation the criticalstate can be described as a function of the domain geometry, and is independent ofother dimensionless flow parameters (Rayleigh number, Ra, and Prandtl number, Pr).On the theoretical side, we examine the conditional stability of the static regime.We derive conservative conditions on disturbance energy to ensure that perturbationsfrom a static regime decay to zero. Assuming stability, we show that the kineticenergy of the perturbed field decays to zero in a finite time, and give estimatesfor the stopping time, t0. This allows us to predict the response of the system insuppressing advective heat transfer. The unconditional stability is also considered forthe first time, illustrating the role of yield stress. We focus on the hydrodynamiccharacteristics of Bingham fluids in transition between conductive and convectivelimits. We use computational simulations to resolve the Navier–Stokes and energyequations for different yield stresses, and for different imposed controls. We showthat depending on the initial conditions, a yield stress less than the critical value canresult in temporary arrest of the flow. The temperature then develops conductivelyuntil the fluid yields and the flow restarts. We provide estimates of the hydrodynamictimescales of the problem and examples of flow transitions. In total, the theoreticaland computational results establish that this methodology is feasible as a control, atleast from a hydrodynamic perspective

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“…Whether time-invariant or not, and whether coupled to the flow or independently prescribed, the body force determines how the momentum balance is affected by purely viscous stresses, yield stress and the body force, and hence allows for different dynamic behaviours; e.g. recent studies have illustrated the possibility of delayed flow 55 onset when the driving force is the buoyancy due to temperature differences in the domain [6,7,8]. In naturally convecting flows, the forcing is coupled with the flow field.…”

Section: Introductionmentioning

confidence: 99%