Thermal Gravitational Convection Research Articles

Mathematical and Numerical Modelling of Microconvection in the Long Rectangular Domains

The thermal gravitational convection of liquids under conditions of microgravity is studied in a 2D long rectangular domain elongated in the direction of the gravity force. The liquid is located between two solid regions of equal thickness. The solid parts are heat conducting. The mathematical modelling of the coupled problem is presented. Two mathematical models of convection are used to describe a motion of liquid: the classical Oberbeck-Boussinesq model and the microconvection model of isothermally incompressible liquid. The numerical experiments of convection are performed and demonstrate the qualitative and quantitative differences in the flow characteristics.

Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 1: Rayleigh–Bénard systems

Secondary and oscillatory instabilities in thermal gravitational convection have been the focus of intensive studies over recent years due to their relevance in materials science, and in particular, in the field of crystal growth from the melt. The purpose of the present discussion is to provide a comparative and critical review of the subject through examination of existing studies and very recent contributions. It complements earlier reviews (Lappa, 2005) that were limited to the survey of steady three-dimensional symmetry breaking effects and/or the primary bifurcation of the flow. To cite this article: M. Lappa, C. R. Mecanique 335 (2007).

Mathematical modeling and experimental investigation of the effect of temperature gradients on crystallization processes under terrestrial and space conditions

Mathematical modeling of the processes of heat and mass transfer during directed crystallization under terrestrial and space conditions is performed on the basis of experimental data on the temperature distribution (boundary conditions). Convective processes are described by the system of Oberbeck-Boussinesq equations together with the heat-conduction equation (the Stefan problem). A dependence of the intensity of thermal gravitational convection on the radial and axial temperature gradients is established. It is shown that one of the necessary conditions for the growth of homogeneous semiconductor crystals under both terrestrial and zero-gravity (on board spacecraft) conditions is the absence of the free surface of a melt (the Marangoni convection) and optimization of the temperature gradients (first of all, the radial gradient).

Application of the Eigenfrequency of a Convective Cell to Determination of the Frequency Characteristics of Oscillatory Thermal Gravitational and Thermocapillary Convection in Closed Volumes

The notion of the eigenfrequency of a convective cell has been introduced and three methods for determination of this parameter in numerical experiments have been proposed. The effect of resonance of the stream function in the field of a rotating gravity vector (this effect has been found earlier) is used for thermal gravitational convection in a square cavity. Thermocapillary convection is investigated in a rectangular cavity and in a cylinder. In these cases use is made of the resonance effect and the variation of the parameters with eigenfrequency under the action of a heat flux harmonically oscillating and acting on the free surface of the liquid. The correspondence between the obtained eigenfrequencies of the convective cell and the frequencies of oscillatory convection, obtained in numerical calculations and experiment, has been established.

Stability of the equilibrium of a flat layer in a microconvection model

The stability of the equilibrium state of a flat layer bounded by rigid walls is studied using a microconvection model. The behavior of the complex decrement for long‐wave perturbations has an asymptotic character. Calculations of the full spectral problem were performed for melted silicon. Unlike in the classical Oberbeck–Boussinesq model, the perturbations in the microconvection model are not monotonic. It is shown that for small Boussinesq parameters, the spectrum of this problem approximates the spectra of the corresponding problems for a heat‐conducting viscous fluid or thermal gravitational convection when the Rayleigh number is finite.

Filtration convection in a high-frequency vibration field

The effect of high-frequency translational vibrations on the occurrence of filtration convection in a plane horizontal layer of a viscous incompressible liquid saturating a porous medium is studied. Constant temperature is maintained at the boundaries of the layer. It is established that for any vibration direction different from the vertical (transverse) direction, convection in gravity and thermal gravitational convection under both heating from above and heating from below can arise. In the case of reduced gravity, values of the vibration parameter that lead to transition to zero gravity are established. The results are obtained from an analysis of the averaged equations of filtration convection, derived for an arbitrary region.

Specific features of the behavior of a liquid and a liquid-gas system under conditions of near-weightlessness

The results of investigating specific features of the behavior of a liquid subject to thermal gravitational convection in the inner, outer and coupled problems under conditions of near-weightlessness are generalized. The results of calculating the flows in a liquid-gas system in a variable acceleration vector field are presented.

Microconvection in a vertical layer

In the case of very weak gravity the classical Oberbeck-Boussinesq approximation is not valid for describing thermal gravitational convection. This was pointed out in [1] where a new model was proposed under the assumption that the fluid is isothermal and incompressible. In this model the velocity vector is no longer solenoidal. Below, on the basis of this model we analyze the convective motion in a vertical layer, on the rigid boundaries of which a heat flux that depends on time only is prescribed. It is found that the nonsolenoidal character of the velocity does not lead to considerable restructuring of the steady-state convection. At the same time, the patterns of the unsteady, in particular, periodic convective flow calculated within the framework of the classical and the new models differ significantly.

Thermal gravitational convection in a variable vector field of small accelerations

The use of nearly weightless states in the manufacture of materials can allow for improvement of structure and for uniformity of mixture distribution in samples [1-3]. In the absence of gravity, small accelerations due to various perturbations play a primary role in the evolution of gravitational convection. Small accelerations are related to the rigidity characteristics of structures and are periodic in nature, where the vector for small accelerations g continuously changes in quantity and direction over time. In many cases, this change can to some degree of accuracy be considered as the rotation of a vector with a constant modulus and angular velocity in some fixed plane

Influence of Thermal Gravitational Convection on Solidi Fication Processes

AbstractThe aim of these experiments in the Gradient Furnace with Quenching device (GFQ) during the German D-1 Mission was to study the influence of thermal convection on– the diffusion in the melt ahead of the solidification front in an AlCu-alloy– the stability of a smooth solidification front in an Al-Cualloy and– the morphology of the solidification front in an AlSi-alloyduring the directional solidification of the binary alloys AlCu with 0.3 wght.-% Cu and AlSi with 7.0 wght.-% Si. Altogether five samples had been successfully processed during the D1-Mission. After getting the complete values from the process data (above all the velocity of the solidification front and the temperature gradient) reference experiments were made in the same GFQ under lg-conditions.Additional experiments under lg with a transparent fluid were done to obtain information about the thermal convection in a cylindrical cell while measuring temperature distribution at the same time.A first result having the same crystallization condition is the more than twice thicker diffusion boundary layer in AlCu 0,3-specimen than in the lg-reference specimen. The diffusion coefficient and the dendritic morphology are to be determined. The evaluation of all specimens (flight- and lg-samples) is not finished in the moment.

Effect of thermal gravitational convection on flame propagation over a fuel surface

The effect of thermal gravitational convection on flame propagation velocity and stability was determined by comparison of experimental results obtained by changing gravitational conditions while maintaining other external conditions constant. The fuel materials used were series BF glues. Interferograms were produced to study the alcohol vapor concentration field above the drying glue surface. Under conditions of normal gravity, flame behavior changes markedly. The flame loses stability and its structure becomes complex and strictly periodically repetitive. Experiments under conditions of weightlessness revealed that in the absence of gravity, relaxation combustion is impossible.