Thermocapillary-buoyancy convection in a shallow cavity heated from the side

Shevtsova, Valentina; Nepomnyashchy, Alexander; Legros, Jean–Claude

doi:10.1103/physreve.67.066308

Cited by 84 publications

(49 citation statements)

References 24 publications

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“…The first intriguing feature is that, at the first critical point, it bifurcates from a 2D stationary solution to a 2D time-dependent one. This represents excitation of the m ¼ 0 mode when the perturbation spreads along the z axis, parallel to the temperature gradient as in extended cavities or thin layers [12]. In the considered case of long liquid bridge (À ¼ 1:8) the wave m ¼ 0 appears as a critical one at Ma …”

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confidence: 97%

New Flow Regimes Generated by Mode Coupling in Buoyant-Thermocapillary Convection

2009

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We report on a new nonlinear dynamics occurring in a confined cylindrical column filled with fluid (liquid bridge) and heated from above. We demonstrate and analyze the novel oscillatory flow state created by the interaction of two hydrothermal waves of different origins: one propagates vertically from the cold towards the hot side (m ¼ 0) and another is traveling in the azimuthal direction (m ¼ 1). Their interaction leads to an exotic flow structure: during a part of the oscillation period the resulting wave propagates in a given azimuthal direction, whereas during the rest of the period it moves in the opposite direction. A new bimodal flow regime is found to exist over a parameter range where these modes have comparable influence. The phase diagrams, obtained by three-dimensional nonlinear simulations, are reported. They shed light on the instability mechanism and criteria of the existence of novel states. DOI: 10.1103/PhysRevLett.102.134503 PACS numbers: 47.20.Ky, 05.45.Àa, 47.54.Bd, 47.55.nk The investigation of the Rayleigh-Bénard and RayleighMarangoni convection has played a crucial role in the development of the nonlinear stability theory for planar spatially extended systems [1]. Recently, significant progress has been achieved in understanding the nonlinear regimes of buoyant-thermocapillary convection in cylindrical columns [2,3]. The latter problem can be considered as a paradigmatic example of nonlinear dynamics in essentially nonparallel flows. The mechanisms of instability have a universal character. Therefore, it is of a general interest, far beyond its direct applications in engineering. Because of the periodicity of the problem in the azimuthal direction, the spectrum of azimuthal wave numbers is discrete. The hydrothermal waves, which are developed due to the oscillatory instability of a steady axisymmetric flow, are characterized by integer values of the azimuthal wave number m. Typically, above the critical point, a 3D oscillatory flow starts as a finite-amplitude standing or traveling (TW) wave. When the thermal stresses increase, the nonlinear dynamics is determined mostly by the interaction of modes with m ¼ 1 and m ¼ 2, e.g., [2,3].Still, the role of the simplest, axisymmetric oscillatory mode m ¼ 0, is somehow elusive, and there is no agreement on that subject up to now. Xu and Davis However, these measurements were performed above the threshold of the 3D oscillatory regime, where modes with m ! 1 are present. Numerical simulations for aspect ratio close to unity À $ 1 also could not reveal the m ¼ 0 as being critical, e.g., [2,9,10]. In short liquid bridges the rigid walls impose a strong constraint to the appearance and spreading of axial waves.In the present Letter, we clarify the question of the existence of axisymmetric wavy motions, and analyze the consequences of the interaction between the modes with m ¼ 0 and m ¼ 1 that leads to novel, highly nontrivial, flow regimes. Our analysis also explains the enigmatic flow regime with alternating directions of hot or cold spot's moti...

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confidence: 97%

New Flow Regimes Generated by Mode Coupling in Buoyant-Thermocapillary Convection

2009

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“…Let us remark that this idealised basic flow should di¤er from the return flow in any experiment in which sidewalls will change these profiles [24]. Nevertheless, experimental flow far from the sidewalls should not di¤er substantially from that idealised flow in su‰ciently wide systems. '…”

Section: The Basic Statementioning

confidence: 99%

“…Moreover, Schwabe et al [11], Burguete et al [20], Garnier [21], Garnier et al [22,23] find two wave regimes, one for very thin layers (typically h < 1:4 mm) and another for thicker layers. Finally, Shetsova et al [24] investigated numerically a finite two-dimensional cavity heated from the side, and analysed the interplay between the steady cell created near the hot wall and the hydrothermal waves.…”

Section: Introductionmentioning

confidence: 99%

Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids

Pérez–García

Madruga

Echebarria

et al. 2004

Journal of Non-Equilibrium Thermodynamics

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The stability of a liquid layer with an undeformable interface open to the atmosphere, subjected to a horizontal temperature gradient, is theoretically analysed. Buoyancy and surface tension forces give rise to a basic flow for any temperature difference applied on the system. Depending on the liquid depth, this basic flow is destabilised either by an oscillatory instability, giving rise to the so-called hydrothermal waves, or by a stationary instability leading to corotating rolls. Oscillatory perturbations are driven by the basic flow and therefore one must distinguish between convective and absolute thresholds. The instability mechanisms as well as the di¤erent regimes observed in experiments are discussed. The calculations are performed for a fluid used in recent experiments, namely silicone oil of 0.65 cSt ðPr ¼ 10Þ. In particular, it is shown that two branches of absolute instability exist, which may be related to the two types of hydrothermal waves observed experimentally.

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“…Those results agree to that obtained by Weisloger etc. [14][15] , who studied the capillary driven flow in a circular tube experimentally.…”

Section: Discussionmentioning

confidence: 99%

Experiment Investigation on Fluid Transportation Performance of Propellant Acquisition Vanes in Microgravity Environment

Zhuang¹,

Li²,

Luo

et al. 2014

International Journal of Fluid Machinery and Systems

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The propellant acquisition vane (PAV) is a key part of a vane type surface tension propellant management device (PMD), which can manage the propellant effectively. In the present paper, the fluid transportation behaviors for five PAVs with different sections were investigated by using microgravity drop tower test. Further, numerical simulation for the propellant flow in a PMD under microgravity condition was also carried out based on VOF model, and showed the similar flow pattern for PAVs to the experiment. It is noted that the section geometry of PAVs is one of the main factors affecting the fluid transportation behavior of PMD. PAVs with bottom length ratio of 5/6 and 1/2 have larger propellant transportation velocity. Based on the experiments, there were two stages during the process of propellant transportation under microgravity environment: liquid relocation and steady transportation stage. It is also recognized that there is a linear correlation between liquid transportation velocity and relative time's square root. Those results can not only provide a guideline for optimization of new vane type PMDs, but also are helpful for fluid control applications in space environment.

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Thermocapillary-buoyancy convection in a shallow cavity heated from the side

Cited by 84 publications

References 24 publications

New Flow Regimes Generated by Mode Coupling in Buoyant-Thermocapillary Convection

New Flow Regimes Generated by Mode Coupling in Buoyant-Thermocapillary Convection

Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids

Experiment Investigation on Fluid Transportation Performance of Propellant Acquisition Vanes in Microgravity Environment

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