Hydrothermal waves in Marangoni convection in a cylindrical container

Ezersky, Alexander; Garcimartín, Ángel; Burguete, Javier; Mancini, H.; Pérez–García, C.

doi:10.1103/physreve.47.1126

Cited by 63 publications

(43 citation statements)

References 6 publications

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“…When the bifurcation is stationary, the emerging pattern consists of a 3D structure of rolls whose axes are parallel to the radial coordinate (radial rolls) and in the oscillatory case, the axes are tilted with respect the radial axis. These results coincide with those obtained experimentally [12,13,14].…”

Section: Introductionsupporting

confidence: 93%

“…One type is formed by corotative rolls such as those reported in experiments [12,13,14], and in similar theoretical studies [21]. The second kind of solution has similar features to those of the return flow described in [20].…”

Section: Discussionsupporting

confidence: 55%

“…This set up corresponds to the experiment reported in Ref. [12], and also it is comparable to similar experiments in rectangular containers [13,14]. In [15] a similar problem is treated theoretically, however in this work rotation is considered and the gravity field is along the radial coordinate.…”

Section: Introductionsupporting

confidence: 69%

“…This result is similar to that obtained in experiments reported in Refs. [12,13,14], where co-rotative rolls perpendicular to the gradient are found as well. These results coincide with those obtained in Ref.…”

Section: Results On the Basic Statementioning

confidence: 59%

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Thermal convection in a cylindrical annulus heated laterally

Hoyas

Herrero

Mancho

2002

J. Phys. A: Math. Gen.

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In this paper we study thermoconvective instabilities appearing in a fluid within a cylindrical annulus heated laterally. As soon as a horizontal temperature gradient is applied a convective state appears. As the temperature gradient reaches a critical value a stationary or oscillatory bifurcation may take place. The problem is modelled with a novel method which extends the one described in [10]. The Navier Stokes equations are solved in the primitive variable formulation, with appropriate boundary conditions for pressure. This is a low order formulation which in cylindrical coordinates introduces lower order singularities. The problem is discretized with a Chebyshev collocation method easily implemented and its convergence has been checked. The results obtained are not only in very good agreement with those obtained in experiments, but also provide a deeper insight into important physical parameters developing the instability, which has not been reported before.

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Section: Introductionsupporting

confidence: 93%

Section: Discussionsupporting

confidence: 55%

Section: Introductionsupporting

confidence: 69%

Section: Results On the Basic Statementioning

confidence: 59%

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Thermal convection in a cylindrical annulus heated laterally

Hoyas

Herrero

Mancho

2002

J. Phys. A: Math. Gen.

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“…As the heating increased they also found a transition to a multicellular flow, composed by corotating rolls, the intensity of which decreases as one moves away from the hot wall. Similar results were obtained by Ezersky et al [13] and de Saedeleer et al [14]. The first observations of hydrothermal waves were reported by Daviaud and Vince [15] who used a shallow layer of silicone oil of 0.65 cSt ðPr ¼ 10Þ in a narrow rectangular channel heated horizontally across the shorter side.…”

Section: Introductionsupporting

confidence: 83%

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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Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

Li¹,

Peng

et al. 2004

Cryst. Res. Technol.

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In order to understand the nature of surface spoke patterns on silicon melt in industrial Czochralski furnaces, a series of unsteady three-dimensional numerical simulations were conducted for thermocapillary-buoyancy flow of silicon melt in annular pool (inner radius r i =15 mm, outer radius r o =50 mm, depth d=3mm). The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. Results show that a small temperature difference in the radial direction generates steady roll-cell thermocapillary-buoyancy flow. With large temperature difference, the simulation can predict three-dimensional oscillatory flow, which is characterized by spoke patterns traveling in the azimuthal direction. The small vertical heat flux (3W/cm 2 ) does not have significant effects on the characteristics of this oscillatory flow. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined.

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Hydrothermal waves in Marangoni convection in a cylindrical container

Cited by 63 publications

References 6 publications

Thermal convection in a cylindrical annulus heated laterally

Thermal convection in a cylindrical annulus heated laterally

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

Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

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