Vibration effect on convection onset in a system consisting of a horizontal pure liquid layer and a layer of liquid-saturated porous medium

The onset of convection in a system of two horizontal layers (a pure liquid and a porous medium saturated with the same liquid) heated from below under the action of vertical vibration is investigated. For describing the free thermal convection, in the liquid layer the Boussinesq approximation and in the porous layer the Darcy-Boussinesq approximation are used. In the limiting case of a thin liquid layer, effective boundary conditions on the upper boundary of the porous layer with account for convection in the liquid layer are obtained and it is shown that vibration has a stabilizing effect, whereas the presence of a liquid layer leads to destabilization. For an arbitrary liquid to porous layer thickness ratio the onset of convection is investigated numerically. In the case of a thin liquid layer there are two (short-and long-wave) unstable modes. In the case of thick layers the neutral curves are unimodal. Vibration has a stabilizing effect on perturbations with any wave number but affects short-wave perturbations much more strongly than long-wave ones.     

Dynamics of electroconvective structures in a weakly conducting liquid

The finite-amplitude evolution of electroconvective structures in a weakly conducting liquid with an electroconductive charge formation mechanism is examined. The liquid is in the electrostatic field of a horizontally placed capacitor and is heated from below, and the electric charge time constant is much shorter than the characteristic hydrodynamic time. The interaction between the electroconductive convection and thermogravitational convection is considered. The evolution of the supercritical structures is investigated by direct numerical simulation using the finite-difference method. The bifurcations leading to the formation of stationary and wave liquid flows are analyzed. Nonlinear modes of stationary convection and traveling waves with different space-time patterns are identified and investigated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 20–27, May–June, 2008.     

Vibrational convection in a saturated porous medium in the absence of thermal equilibrium between the solid and liquid phases

Thermal vibrational convection in a saturated porous medium is theoretically studied on the basis of a thermal nonequilibrium model, in accordance with which the temperatures of the porous medium and the saturating liquid can be different. In the high-frequency vibration approximation the averaged equations of convection are derived. The dependence of the vibration force direction on the interphase heat transfer coefficient and the vibration frequency is established. Vibrational convection in a cylindrical layer is studied. It is shown that, depending on the interphase heat transfer coefficient, the flows of two types differing in the liquid circulation direction can exist.     

Flow and heat exchange in the neighborhood of a subterranean pipeline

The present study considers flow and heat exchange in the neighborhood of a subterranean pipeline on irrigated sector of a route. The flow is caused by thermal convection of the liquid in the field of gravitational forces, this convection being connected with the cooling or heating of the liquid near the surface of the pipeline.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 51–56, November–December, 1987.     

Influence of buoyancy in a mixed convection liquid metal flow for a horizontal channel configuration

This article presents the direct numerical simulation (DNS) of mixed convection turbulent heat transfer in a horizontal channel case for liquid lead. Cartesian mesh is used and the incompressible Navier-Stokes equations are discretized with highly accurate finite difference sixth-order compact schemes to perform the DNS. The influence of mixed convection in liquid metal with Prandtl number equal to 0.025 and Reynolds number equal to 4667 has been studied by varying the Richardson number (Ri = 0, 0.25, 0.50, 1.00). The obtained results are extensively analyzed and discussed in this article. In particular, large-scale circulation is observed under the influence of buoyancy. Compared to the forced convection case (Ri = 0), stronger velocity fluctuations are noticed that highlight the fact that turbulence is strongly enhanced with the increasing buoyancy. It also proves that the thermal plumes rising up from the hot wall of the channel activate the cross-stream eddies. Moreover, temperature fluctuations are found to be more homogeneously distributed with increasing buoyancy effects and mixing is more effective in the center of the channel. In addition, compared with forced convection, mixed convection has shown enlargement of the large-scale structures that only appear in the temperature field for low Prandtl number fluids. Extensive results of flow and temperature fields are analyzed and presented.     

Thermocapillary convection in a plane liquid layer with concentration heat sources

Thermocapillary instability of a plane liquid binary-mixture layer with time-dependent surface tension is studied under weightlessness conditions. The liquid is heated (or cooled) due to heat release by an active admixture. The heat release rate is proportional to the active-component concentration. The admixture is transported by convection and diffusion. The active component “burns up” with time. The neutral curves for monotonous and oscillating disturbances are found for different values of the nondimensional parameters. Some nonlinear convection regimes are studied numerically by a finite-difference method. The dependence of the convective flow intensity on the Marangoni number is determined. The phase portraits of unsteady regimes are found.     

A two-phase boundary-layer model for laminar mixed-convection condensation with a noncondensable gas on inclined plates

A finite-volume-based numerical model for mixed-convection laminar film condensation from a flowing mixture of a vapor and a heavier noncondensable gas on inclined isothermal flat plates is presented. The full boundary layer equations for the liquid film and the vapor-gas mixtures (including liquid inertia and energy convection terms) are solved implicitly with appropriate liquid-mixture interface conditions. Results were obtained for three mixtures, covering wide ranges of liquid Prandtl number and free-stream gas concentration in the forced-convection, mixed-convection and free-convection flow regimes. The effects of liquid inertia were found to be significant only for low-Prandtl-number fluids and lower gas concentrations. The effects of liquid energy convection were found to be significant only for high-Prandtl-number fluids and to be most significant for mixed-convection condensation. Received on 3 March 1998     

Effects of strong compressibility in natural convective flows through porous media with a near-critical fluid

The dynamics and heat transfer in a porous medium occupied by a liquid with parameters in the neighborhood of the critical point of “liquid-gas” transition are simulated numerically within the framework of the equations of dynamics of a porous medium with a compressible liquid phase and the Van-der-Waals equation of state. Adiabatic heating of the liquid phase in a porous layer initiated by a jump in temperature on one of the boundaries is investigated under microgravity conditions. Thermo-gravitational convection in the unsteady and steady-state regimes is simulated in rectangular domains and the effect of adiabatic heating on convection is studied. Calibration relations between the Rayleigh-Darcy and Prandtl numbers in the basic system of equations and their real analogs are obtained. A comparison is made with convection in a porous media occupied by a perfect gas.     

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 convective patterns and their role in the enhancement of evaporation from pores

The present work investigates the evaporation process from a liquid meniscus formed in capillary tubes of various sizes. A very strong convection within the liquid phase is observed; it is proposed that the non-uniform evaporation from the meniscus leads to a temperature gradient along the interface causing a surface tension gradient, which is the driving mechanism for the convection. The observed convection is shown to be clearly correlated to the evaporation rate and the volatility of the liquid. Unlike Marangoni convection observed by imposing a temperature gradient, this is a self-induced driving gradient caused by evaporative cooling effect.The Marangoni roll in the liquid phase has been visualized and characterized using seeding particles. It is shown in the present study that the observed convection contribute in enhancing the heat–mass transfer from the pore. The experimental results show that when the meniscus recedes inside the pore, the convection slows down and eventually stops. A theoretical model is developed to describe the temperature gradient, which establishes due to the evaporative cooling effect between the centre and the wedge of the meniscus. The results of the model show a good qualitative agreement with the experimental observations.     

Thermocapillary convection in a horizontal layer of liquid

An exact solution is found for the equations for free convection in a planar horizontal layer of liquid with a constant temperature gradient at the boundaries. Two cases of boundary conditions for the velocity are considered: 1) the liquid is bounded by two solid planes, 2) the upper surface of the liquid is free, and the surface tension is a function of temperature.     

Marangoni convection in a cylinder of finite size

This paper considers a liquid in a finite-size cylinder in which Marangoni instability occurs. The upper boundary of the liquid is free and deformable. The problem of the occurrence of convection in a cylindrical container is solved using the method of separation of variables. A homogeneous differential equation of the sixth order with constant coefficients and complex boundary conditions is obtained. An analytical expression for critical Marangoni numbers is derived for the case of monotonic perturbations. The case is considered where the liquid in the cylinder is weightless.     

液封液桥内热毛细对流的数值模拟

建立了液封液桥(不相溶混的双层同轴液柱)内热毛细对流的物理数学模型,采用涡量-流 函数法、利用有限差分格式对微重力条件下液封液桥内热毛细对流进行了数值模拟,得到了 双层液柱主流区的温度场和流场,证实了液封技术能削弱液桥主流区的热毛细对流,从而提 高浮区晶体生长质量,找出了液封厚度以及内、外层流体物性参数比对液桥内热毛细对流的 影响规律.     

Combined convection of a viscoplastic liquid in a plane vertical layer

The combined (free and induced) convection of a viscoplastic Shvedov-Bingham liquid in a plane vertical layer is considered. The influence of the temperature dependence of the yield shear stress on the conditions of occurrence of the flow and the stationary convection regime in the case of heating from the side is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–113, November–December, 1979.     

Thermal convection in a viscoelastic liquid

The onset of convection in a layer of viscoelastic liquid heated from below is investigated. It is shown that the nature of the convective solution depends strongly on the particular constitutive relation used to characterize the viscoelasticity. For certain models and certain parameter ranges the convection is supercritical and stable, while for other models and parameter ranges it can be subcritical and unstable. It is suggested that observations of convective behavior can provide a test for constitutive relations proposed for a particular liquid. A Fourier representation of the solution to the nonlinear problem is developed which is shown to admit aperiodic, or chaotic, solutions in a specific truncation that generalizes the classical Lorenz system for the Newtonian Bénard problem.     

半浮区液桥热毛细振荡流

采用非定常、三维直接数值模拟方法研究大Pr数半浮区液桥热毛细对流从定常流向振荡流的过渡过程．文中详细描述了热毛细振荡流的起振和振荡特征,给出了液桥横截面上振荡流的流场和温度分布．在地面引力场条件下计算的结果与地面实验的结果进行比较,得出液桥水平截面上的流场和温度分布图样以一定的速度旋转,自由表面固定点处流体的环向流速正、负交替变化的一致结论．     

Effect of surface electric current on the electrohydrodynamic flow inside and outside a spherical drop

The problem of electrohydrodynamic flow of a viscous, low-conducting, polarizable liquid inside and outside a spherical drop in an applied homogeneous constant electric field is analytically solved with account for the effect of both surface conduction current and surface convection current. The influence of the drop deformation on the field and the flow is neglected. The solution is obtained in the form of asymptotic expansions in a small parameter corresponding to weak surface convection electric currents.     

Numerical study of convection of a liquid heated from below

The equilibrium of a liquid heated from below is stable only for small values of the vertical temperature gradient. With increase of the temperature gradient a critical equilibrium situation occurs, as a result of which convection develops. If the liquid fills a closed cavity, then there is a discrete sequence of critical temperature gradients (Rayleigh numbers) for which the equilibrium loses stability with respect to small characteristic disturbances. This sequence of critical gradients and motions may be found from the solution of the linear problem of equilibrium stability relative to small disturbances. If the temperature gradient exceeds the lower critical value, then (for steady-state heating conditions) there is established in the liquid a steady convective motion of a definite amplitude which depends on the magnitude of the temperature gradient. Naturally, the amplitude of the steady convective motion cannot be determined from linear stability theory; to find this amplitude we must solve the problem of convection with heating from below in the nonlinear formulation. A nonlinear study of the steady motion of a liquid in a closed cavity with heating from below was made in [1]. In that study it was shown that for Rayleigh numbers R which are less than the lower critical value R_c steady-state motions of the liquid are not possible. With R>R_c a steady convection arises, whose amplitude near the threshold is small and proportional to (R–R_c)^1/2 (the so-called soft instability)-this is in complete agreement with the results of the phenom-enological theory of Landau [2, 3].Primarily, various versions of the method of expansion in powers of the amplitude [4–8] have been used, and, consequently, the results obtained in those studies are valid only for values of R which are close to R_c, i. e., near the convection threshold.It is apparent that the study of developed convective motion far from the threshold can be carried out only numerically, with the use of digital computers. In [9, 10] the numerical methods have been successfully used for the study of developed convection in an infinite plane horizontal liquid layer.The present paper undertakes the numerical study of plane convective motions of a liquid in a closed cavity of square section. The complete nonlinear system of convection equations is solved by the method of finite differences on a digital computer for various values of the Rayleigh number, the maximal value exceeding by a factor of 40 the minimal critical value R_c. The numerical solution permits following the development of the steady motion which arises with R>R_c in the course of increase of the Rayleigh number and permits study of the oscillatory motions which occur at some value of the parameter R. The heat transfer through the cavity is studied. The corresponding linear problem on equilibrium stability is solved approximately by the Galerkin method.     

Capillary and gravitational convection in a droplet immersed in a nonuniformly heated liquid

Under the conditions of the Plato technique, the problem of convection in a droplet immersed in a nonuniformly heated liquid is solved analytically. The influence of gravitational convection on the thermocapillary flow is studied. In the linear approximation with respect to the Marangoni and Grashof numbers and their product, the shape of the droplet and the displacement of its center of the mass are obtained.Perm. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–51, July–August, 1996.     

Numerical study of evaporation by mixed convection of a binary liquid film flowing down the wall of two coaxial cylinders

Evaporation by mixed convection of a binary liquid film flowing down the external wall of a vertical cylinder has been investigated numerically. Two cases were considered: one where the cylinder wall is soaked with a liquid, and another where a liquid film flows along this wall. Heat, mass and momentum transfer in the liquid film and the vapor phase are modelled by mixed convection equations. In order to locate the liquid–vapor interface, a suitable coordinate transformation is carried out with suitable variables. The discretization of the dimensionless equations by an implicit difference scheme leads to a system of algebraic equations, which are solved by using Gauss algorithm for the momentum conservation equations and Thomas algorithm for the energy and diffusion conservation equations. The film thickness is calculated by the Newtons method. Results show, in particular, that the film thickness cannot be neglected and that the latent heat transfers are increasingly significant as the liquid film components become more volatile.