Interaction of the thermovibrational and thermocapillary convection mechanisms

Thermal convection in microgravity induced by the combined action of thermocapillary forces and vibrations is considered. In the high-frequency approximation the thermovibrational forces are written for the case in which isothermal mixing of the fluid is unimportant. The authors' own work and new results of investigating the effect of vibration on thermocapillary instability, of numerically modeling the heat and mass transfer in open cavities and of experiments on the vibrational suppression of surface deformation are reviewed. The prospects for the practical application of the results obtained are discussed.     

Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure

The main objective of this article is to study the effect of magnetic field on the combined buoyancy and surface tension driven convection in a cylindrical annular enclosure. In this study, the top surface of the annulus is assumed to be free, and the bottom wall is insulated, whereas the inner and the outer cylindrical walls are kept at hot and cold temperatures respectively. The governing equations of the flow system are numerically solved using an implicit finite difference technique. The numerical results for various governing parameters of the problem are discussed in terms of the streamlines, isotherms, Nusselt number and velocity profiles in the annuli. Our results reveal that, in tall cavities, the axial magnetic field suppresses the surface tension flow more effectively than the radial magnetic field, whereas, the radial magnetic field is found to be better for suppressing the buoyancy driven flow compared to axial magnetic field. However, the axial magnetic field is found to be effective in suppressing both the flows in shallow cavities. From the results, we also found that the surface tension effect is predominant in shallow cavities compared to the square and tall annulus. Further, the heat transfer rate increases with radii ratio, but decreases with the Hartmann number.     

Experiments on buoyancy driven convection in non-Newtonian fluid

Summary Buoyancy-driven convection in horizontal layers of dilute water solutions of ionic and nonionic polyacrylamides confined between rigid, parallel, conducting surfaces was studied experimentally. By determining the temperature difference at the point where convection first sets in, values of the zero shear rate viscosity were calculated in good agreement with those obtained from rheogoniometer data. Beyond this point, the heat transfer characteristics of the solutions and the associated convective flow patterns were found to be rather similar to those of a viscous Newtonian fluid forRayleigh numbers up to 5 × 10⁴, the range covered by the present experiments. However, theNusselt numbers at any givenRayleigh number were slightly but consistently higher than those of a Newtonian fluid of comparable viscosity. Also, the regularity of the flow patterns was more pronounced.

---

Zusammenfassung Experimentell wurde die auf dem Auftrieb beruhende Konvektion in horizontalen Schichten verdünnter Wasserlösungen von ionischen und nichtionischen Polyacrylamiden zwischen festen, parallelen, leitfähigen Oberflächen untersucht. Durch Bestimmung der Temperaturdifferenz an dem Punkt, an dem die Konvektion einsetzt, wurden die Viskositätswerte für die Schergeschwindigkeit Null in guter Übereinstimmung mit den Ergebnissen aus Rheogoniometermessungen ermittelt. Die Wärmeübergangseigenschaften der Lösungen und die konvektiven Stromlinienbilder erweisen sich nach diesem Punkt als sehr ähnlich einer viskosen newtonschen Flüssigkeit fürRayleigh-Zahlen bis 5 · 10⁴. Die hier durchgeführten Experimente beziehen sich auf diesen Bereich. DieNusselt-Zahlen sind für jede gegebeneRayleigh-Zahl immer etwas größer als die für eine newtonsche Flüssigkeit mit vergleichbarer Viskosität. Außerdem war die Gleichmäßigkeit der Stromlinienbilder ausgeprägter.

     

Oscillating thermocapillary convection regimes driven by a point heat source

The stability of an axisymmetric thermocapillary flow driven by a point heat source located in the neighborhood of the free surface of a fluid filling a deep tank is investigated theoretically and experimentally. It is shown that for certain values of the depth and power of the heat source thermocapillary convection becomes unstable with respect to oscillating perturbations of the surface shape. Perm’, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 92–103, March–April, 2000.     

Particle-image-velocimetry applied to thermocapillary convection

Thermocapillary convection is studied experimentally using particle-image-velocimetry for flow visualization and analysis. This method offers the advantage of measuring the entire flow field (velocity field, streamlines etc.) in a selected plane within the fluid at a given instant of time in contrast to point by point methods like laser-Doppler-velocimetry (LDV). The paper describes the method and presents quantitative results for different Marangoni numbers.Presented in part at the VIIth European Symposium on Materials and Fluid Sciences in Microgravity, Oxford University, UK, September 10–15, 1989     

Experimental study on thermocapillary convection

In the present paper, the experimental studies on thermocapillary convection are reviewed. The author‘s interest is mainly focused on the onset of oscillatory thermocapillary convection,the features of oscillatory flow pattern, and the critical Marangoni number related with temperature and free surface oscillation. The coordinated measurement in a microgravity environment of a drops haft is also addressed.     

Solidification of hypereutectic and hypoeutectic binary alloys with buoyancy and surface tension driven natural convection

Convection patterns and evolution of macrosegregation during solidification of hypereutectic and hypoeutectic NH₄CL-H₂O binary systems in rectangular side chilled ingots have been numerically investigated. Under the conditions of pure thermal/solutal convection, without a free surface, solidification of NH₄CL 70%-H₂O hypereutectic alloy is characterized by the formation of channels and A-segregates, while solidification of NH₄CL 10%-H₂O hypoeutectic alloy is characterized by the formation of circulation cells in the narrow melt and V-segregates. Surface tension effects during solidification of NH₄CL 70%-H₂O results in establishing a counterclockwise rotating cell at the cavity top, changing the number and orientation of developed channels, and creating an area of negative segregation at the cavity top. During solidification of NH₄CL 10%-H₂O, surface tension effects increase the intensity of flow and results in a higher degree of macrosegregation. Received on 9 June 1998     

Characteristics of thermocapillary convection in two-component fluids

The linear problem of convective instability near the surface of a stratified two-component liquid medium (for example, saline sea water) is considered. The specificity of the problem consists in need to take into account both background stratifications and a difference in the transfer coefficients and boundary conditions for two substances (heat and admixture concentration), as well as the thermocapillary effect. It is shown that there is a vast region of monotonic instability in the medium stable in accordance with all criteria previously known. The two-component nature of the medium makes the development of anomalously intense perturbations deeply penetrating into the hydrostatically stable medium possible. A dimensionless instability criterion is formulated and neutral curves are calculated.     

Characteristics of surface oscillation in thermocapillary convection

The characteristics of surface oscillation in a rectangular pool of silicone oil have been investigated experimentally. The horizontal cross-section of the pool is 52 mm × 36 mm, and the depth of the silicone oil layer is in the range of 1.1-4.8 mm. The applied temperature difference between the two sidewalls leads to shear flow along the free surface from hot to cold and a back flow in the underlying layer. With the increase of the temperature difference, the original steady flow will become unstable to unsteady flow. A CCD laser displacement-sensor with high resolution is used to measure the position of the liquid surface dynamically. And the Hilbert-Huang transform is chosen to analyze the experiment data which is nonlinear and non-stationary. The characteristics of surface oscillation have been obtained. And the relationship of the characteristics with the temperature difference and liquid layer depth has been discussed in details.     

On the regularity of some thermocapillary convection models

The classical model of confined thermocapillary convection is analyzed. Its vorticity singularity, independent of the contact angle, leads to infinite pressure values at contact lines, forbidding any numerical use of the Laplace equation to calculate free surface shapes. Four models are explored to overcome this difficulty: an explicit polynomial filtering, a Navier slip at the solid boundaries, an interface viscosity model and the combination of slip and interface viscosity. Regular solutions are obtained with the first and last approaches. Only the last one is based on physical considerations and, by the introduction of physical length scales, avoids infinite pressure values at the contact line.     

Temporal and spatial elements of thermocapillary convection in floating zones

We investigated experimentally spatio-temporal convective flow phenomena in cylindrical liquid bridges [floating-(half-)zones] of liquids with different Prandtl-numbers (NaNO₃?Pr=7; C₂₄H₅₀?Pr=49; C₃₆H₇₄?Pr=65). The convective flow is driven by thermocapillary forces (TC-forces) and buoyancy forces. The zones were heated from above (ΔT, Ma>0) or from below (ΔT, Ma<0) to couple both effects in different ways. Optical evaluations (view from above and view from the front) in connection with thermocouple (tc) measurements (tc-tips distributed over one half of the free surface) made it possible to get very new ideas of spatio-temporal flow structures in the considered convective system. In this article we deal with some transitionary temporal phenomena accompanying the system’s way to chaotic behaviour. We present results supplementary to well-known transitions to chaos (i.e. quasi-periodic and period-doubled flow states) and introduce some very special events. Here all considerations are based on a primarily “temporal way of thinking”. We then try to illuminate several flow situations primarily from a more “spatial point of view”. Possible spatio-temporal convective flow structures are discussed by accompanying the system from a laminar flow state up to the onset of chaotic motion. Starting with former ideas of spatio-temporal flow situations we recognize 2D- and 3D-stationary flows, “pulsating” and “rotating” modes m=1 and 2, different spatial reasons for quasi-periodic and period-doubled temporal behaviour and different spatial mechanisms that cause spatio-temporal chaotic structures in the system considered. One should realize the ambiguity of a certain time-signal with respect to various spatial structures. Additionally we find out that a revision of the interpretation of very complicated Ma/Ma _c (A)-state maps now becomes necessary. These state maps show the present flow state (e.g. a time-dependent, quasi-periodic or chaotic one) depending on the geometrical parameter aspect ratio A (i.e. the zone length) and the TC-force (i.e. the Marangoni-number).     

Unsteady thermocapillary convection in a nonuniformly heated fluid layer

In many technological processes, thin extended layers of nonuniformly heated fluid are used [1–3]. If they are sufficiently thin, thermocapillary forces have a decisive influence on the occurrence and development of motion of the fluid [4–6]. Investigation of convective motion in such a layer is of great interest for estimating the intensity of heat and mass transfer in technological processes. This paper is a study of unsteady thermocapillary motion in a layer of viscous incompressible fluid with free surface in which a thermal inhomogeneity is created at the initial time. Approximate expressions are obtained for the fields of the velocity, temperature, and pressure in the fluid, and also for the shape of the free surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1991.     

On thermocapillary convection of a liquid in a floating zone

A new approach to the study of the thermocapillary convection of a liquid in a floating zone is proposed. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 69–73, May–June, 1998.     

Axisymmetric thermocapillary convection in a slowly rotating annular cylindrical container

In a slowly rotating annular cylindrical container the free liquid surface (liquid-gas interface) is subjected to a temperature gradient in radial direction. The temperature dependent surface tension creates a shear stress on the interface which is transmitting a thermocapillary convection in the bulk of the liquid. For constant temperature T ₁ of the inner and T ₂ of the outer wall a steady Marangoni convection takes place, exhibiting a double vortex ring of equal directional flow. For time-oscillatory temperatures of the walls a time-dependent thermocapillary convection appears, which will create on the free liquid surface various wave patterns. They shall, depending on the forcing frequency of the temperature, exhibit resonance peaks. The velocity distribution and the response magnitude inside the container has been determined. Received on 3 September 1997     

Investigation of thermocapillary and thermogravitational convection in a fluid with local heating

The results of a numerical solution of the problem of the unsteady convective motion generated in a fluid layer by the formation at the initial instant of a heated zone in the form of a thin cylindrical column, extending from the surface into the interior of the fluid, are presented. The problem is formulated with allowance for both thermocapillary and thermogravitational convection. The influence of the thermocapillary and thermogravitational effects on the fluid motion for various layer thicknesses is subjected to parametric analysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 25–29, November–December, 1989.     

Onset of oscillatory thermocapillary convection in systems with a deformable interface

Oscillatory interfacial instability is investigated with allowance for the deformation of the interface. The possibility of two types of oscillations being excited is established. One of these is similar to the well-known type in systems with a plane interface, while the other is determined by the oscillations of the deformable surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 11–16, July–August, 1991.     

3D PTV measurement of oscillatory thermocapillary convection in half-zone liquid bridge

Three-dimensional (3D) reconstruction of a unique particle motion in oscillatory thermocapillary convections in a small-sized half-zone liquid bridge with a radius of O (1 mm) was carried out by applying 3D particle tracking velocimetry (PTV). By placing a small cubic beam splitter above a transparent top rod, simultaneous observation of the particles in the bridge by use of two CCD cameras was realized. Reconstruction of the 3D trajectories and the particle velocity fields in several types of oscillatory flow regimes was conducted successfully for a sufficiently long period without losing particle tracking.     

Dissolved gas effects on thermocapillary convection during boiling in reduced gravity environments

The mechanisms by which thermocapillary convection arises during boiling of nominally pure fluids in low-g environments are currently not known. It has recently been suggested that small amounts of dissolved gas within the bulk liquid can accumulate within the vapor bubble, forming localized concentration gradients that results in a temperature gradient to form along the liquid–vapor interface that drives thermocapillary convection. This hypothesis was tested by boiling > 99.3% pure n-perfluorohexane with and without noncondensible gas in a low-g environment using a 7.0 × 7.0 mm² microheater array to measure time and space resolved heat transfer at various wall superheats. The thermocapillary convection around the primary bubble that formed in the gassy fluid was found to be much weaker than in the degassed fluid, and the primary bubble diameter was much larger in the gassy fluid due to the accumulation of noncondensible gas within the bubble. The results suggest that the accumulation of noncondensible gas in the bubble can result in temperature variations along the interface but due to the increased vapor/gas bubble size, the driving thermocapillary temperature gradient along the interface is significantly reduced and result in much weaker thermocapillary flow. The highest CHF values in a reduced gravity environment (19 W/cm²) occurred when the fluid was highly subcooled and degassed.