Vibrational Convection Research Articles

Methods of experimental study of thermal convection in cavity subject to rotation and vibration

Vibrations of a non-isothermal fluid result in the generation of an averaged flows – “thermal vibrational convection”. The effect of vibrations changes qualitatively, and their effectiveness increases significantly under conditions of rotation. This makes vibrations an important tool for controlling the dynamics of non-isothermal systems and the intensification of heat and mass transfer in rotating cavities, which could be useful for optimization of various technological processes. The article describes methods used to study convection in rotating cylinders subject to vibrations. The cases of an annulus with boundaries at different temperatures and a cylinder filled with a heat-generating fluid are discussed. Experimental complex allows one to study thermal convection under the action of various factors, such as rotation, vibrations, librations, orientation of the axis of rotation, inertial waves, and others.•The vibrations of a non-isothermal fluid in a rotating cavity is an effective tool for intensification of heat transport due to the generation of intensive averaged flows•The developed experimental technique and setup provide the investigation of thermal vibrational convection in rotating cavities of various geometries in a wide range of governing dimensionless parameters

Trapping of plasma enabled by pycnoclinic acoustic force

Sound can hold partially ionized sulfur at the center of a spherical bulb. We use the sulfur plasma itself to drive a 180 dB re 20 $\ensuremath{\mu}\mathrm{Pa}$ sound wave by periodically heating it with microwave pulses at a frequency that matches the lowest order, spherically symmetric, acoustic resonance of the bulb. To clarify the trapping mechanism, we generalize acoustic radiation pressure theory to include gaseous inhomogeneities and find an interaction of high-amplitude sound with density gradients in the gas through which it propagates. This is the pycnoclinic acoustic force (PAF). Though generated by rapidly oscillating sound waves, it has a finite time average and manipulates the plasma through density gradients at its boundary. The PAF is essential for the description of the trap holding a plasma against its own buoyancy as well as understanding convection in the region outside the plasma. It has implications for pulse tubes, thermoacoustic engines, thermal vibrational convection in microgravity, combustion in the presence of sound, and the modeling of Cepheid variable stars.

Stability of quasi-equilibrium states and supercritical regimes of thermal vibrational convection of a Williamson fluid in zero gravity conditions

In this paper we investigate a linear stability of quasi-equilibrium states and supercritical regimes of thermal vibrational convection of a Williamson fluid between two rigid parallel plates, maintained at constant different temperatures in zero gravity conditions. Calculations are made for different angles of inclination of the vibration axis relative to the layer. It has been found that, as in the case of a Newtonian fluid, most dangerous are the hydrodynamic monotonic perturbations. Enhancement of viscoplastic properties of a fluid has a destabilizing effect at all angles of inclination of the vibration axis. An increase in the Prandtl number stabilizes the quasi-equilibrium states of the pseudoplastic fluids. In the viscoplastic limit, the critical value of the modified Rayleigh number, which determines the quasi-equilibrium stability threshold, does not depend on the Prandtl number and rheological parameters. The critical value of the perturbation wave number for pseudo- and viscoplastic fluids depends only on the angle of inclination of the vibration axis. The type of the convection excitation and the structure of the supercritical convective flows under longitudinal vibrations have been studied on the basis of full nonlinear equations of thermal vibrational convection. It has been found that the supercritical bifurcation takes place.

The Onset of Double-Diffusive Convection in a Superposed Fluid and Porous Layer Under High-Frequency and Small-Amplitude Vibrations

We numerically simulate the initiation of an average convective flow in a system composed of a horizontal binary fluid layer overlying a homogeneous porous layer saturated with the same fluid under gravitational field and vibration. In the layers, fixed equilibrium temperature and concentration gradients are set. The layers execute high-frequency oscillations in the vertical direction. The vibration period is small compared with characteristic timescales of the problem. The averaging method is applied to obtain vibrational convection equations. Using for computation the shooting method, a numerical investigation is carried out for an aqueous ammonium chloride solution and packed glass spheres saturated with the solution. The instability threshold is determined under two heating conditions—on heating from below and from above. When the solution is heated from below, the instability character changes abruptly with increasing solutal Rayleigh number, i.e., there is a jump-wise transition from the most dangerous shortwave perturbations localized in the fluid layer to the long-wave perturbations covering both layers. The perturbation wavelength increases by almost 10 times. Vibrations significantly stabilize the fluid equilibrium state and lead to an increase in the wavelength of its perturbations. When the fluid with the stabilizing concentration gradient is heated from below, convection can occur not only in a monotonous manner but also in an oscillatory manner. The frequency of critical oscillatory perturbations decreases by 10 times, when the long-wave instability replaces the shortwave instability. When the fluid is heated from above, only stationary convection is excited over the entire range of the examined parameters. A lower monotonic instability level is associated with the development of perturbations with longer wavelength even at a relatively large fluid layer thickness. Vibrations speed up the stationary convection onset and lead to a decrease in the wavelength of most dangerous perturbations of the motionless equilibrium state. In this case, high enough amplitudes of vibration are needed for a remarkable change in the stability threshold. The results of numerical simulation show good agreement with the data of earlier works in the limiting case of zero fluid layer thickness.

Nonlinear convection regimes in superposed fluid and porous layers under vertical vibrations: Positive porosity gradients

We investigate the onset of average convection and its nonlinear regimes in a single-component fluid layer overlying a fluid-saturated porous layer. A heated from below cavity with a superposed fluid and a porous medium undergoes high-frequency and small-amplitude vertical vibrations in the gravitational field. Porosity of the medium decreases linearly with depth at a positive porosity gradient. Thermal vibrational convection equations are obtained by the averaging method and solved numerically. The shooting method, Galerkin method and finite-difference method are applied. It is shown that for small vibration accelerations, a convective flow is generated as short-wave rolls in the fluid layer overlying a porous medium. The heat flux undergoes abrupt changes as the supercriticality increases. It is due to the fluid flow penetrating into pores. A magnitude of the jump grows with the growth of vibration intensity. For sufficiently large vibration accelerations, the average convection is excited in the form of long-wave rolls that penetrate both layers. Here, the Nusselt number is 2–3 times higher than its value in the static gravity field.

Vibration effect on double-diffusive instability in an inhomogeneous porous layer underlying a binary fluid layer

A linear stability problem for mechanical equilibrium in an inhomogeneous fluid-saturated porous layer underlying a horizontal binary fluid layer is numerically simulated. The layers are subjected to high-frequency vertical vibration in a gravity field. Different values of temperature and concentration are fixed at the outer impermeable boundaries of the two-layer system. Porosity of a porous layer linearly depends on a transverse z-coordinate. Permeability is given by the Carman-Kozeny formula. To describe a fluid flow in layers, we use the vibrational convection equations written in the Boussinesq approximation and obtained by the averaging method. It is shown that when the fluid is heated from below, vibration effectively increases the equilibrium stability threshold and wavelength of its most dangerous perturbations. If a temperature gradient coincides with the direction of a concentration gradient for the heavier component of binary fluid, average convection is excited in an oscillatory manner. In the opposite case, there is a monotonic instability of equilibrium. Effects of the dimensionless porosity gradient mz and vibrational parameter pv on the instability threshold are studied. For pv<0.0134 and a fixed solutal Rayleigh number (-5⩽Rmc⩽15) an abrupt jump-like transition from the long-wave to short-wave most dangerous perturbations occurs as mz grows in the range of 0.030–0.162. Long-wave perturbations penetrate both layers. Short-wave perturbations mainly locate in the fluid layer. The transition is smoothed for pv>0.0134. When the fluid is heated from above, wavelength of critical perturbations smoothly varies with a change in pv and mz. A convective fluid flow arises monotonously and mostly in the form of long wavelength rolls (a wave number is of k<3.3). Vibration weakly lowers the equilibrium stability threshold in layers. The effect is most pronounced at high enough Rayleigh numbers (Rm=-40) for a porous medium with the porosity increasing with depth at mz=-0.2.

Convective stability of fluid in a rotating horizontal annulus

The convective stability of quasi-equilibriumof a fluid layer formed by two horizontal coaxial cylindrical surfaces which have different temperatures and rotate at the same angular velocity about the axis of symmetry is investigated theoretically and experimentally. Consideration is carried out from the standpoint of thermal vibrational convection caused by the average lifting force generated as a result of vibrations of a nonisothermal fluid with respect to the cavity. The vibrations are induced by an external field. The action of the centrifugal force field is also taken into account. Stability of mechanical quasi-equilibrium with respect to monotonic plane perturbations, which are, as shown experimentally, the most dangerous, is studied within the framework of the linear analysis. The stability boundaries are constructed for layers of various relative thickness in the plane of control parameters, the centrifugal and vibrational Rayleigh numbers. The thresholds of excitation of two-dimensional convective structures obtained experimentally are in good agreement with the theoretical ones.

Stability of thermovibrational convection of pseudoplastic fluid in plane vertical layer

Based on equations for thermal vibrational convection, the structure of the plane-parallel convective flow in a vertical layer of Williamson’s fluid is investigated. The layer is subjected to high frequency linear polarized vibrations directed along the layer. It is shown that with the growth of vibrations, the nonlinear-viscous properties of a pseudoplastic fluid stop producing the effect on the structure and intensity of its main flow, which becomes very similar to that of the Newtonian fluid. For the case of longitudinal high-frequency linear polarized vibrations, a linear stability problem is formulated and solved. This problem deals with the stability of the averaged plain parallel flow of the pseudoplastic Williamson’s fluid with respect to small periodic perturbations directed along the layer. Numerical calculations show that, as in the case of the Newtonian fluid, at small values of the Prandtl number the monotonic hydrodynamic perturbations are the most dangerous. With increasing Prandtl number, the oscillatory thermal perturbations become more dangerous. Strengthening of the pseudoplastic fluid properties leads to destabilization of the main flow relative to the both types of instabilities. The presence of vibrations, as in the case of the Newtonian fluid, causes the appearance of an additional vibration mode of instability and the relatively small values of the Graschof number corresponding to it. The influence of this vibration mode on the stability of the main flow is determined by the vibration frequency and the magnitude of a temperature gradient. Amplification of the vibration intensity leads to flow destabilization in all examined instability modes. For the given set of rheological parameters of Williamson’s fluid, there are critical values of the modified and vibration Graschof number, at which the averaged flow becomes absolutely unstable with respect to all types of the instabilities. The absolute destabilization of the main flow occurs at higher values of the vibration Graschof number compared to that for the Newtonian fluid.

On exact nonstationary solutions of equations of vibrational convection

On exact nonstationary solutions of equations of vibrational convection

Influence of gravitational and vibrational convection on the heat and mass transfer in the melt during crystal growth by the bridgman and floating zone methods

A comparative analysis of hydrodynamic and thermal processes during crystal growth by the Bridgman and floating zone methods under terrestrial conditions and in microgravity is performed by mathematical simulation. Specific features of the hydrodynamic state of the melt under axial vibrational perturbations of different frequency and intensity are studied. It is shown that the floating zone method is less sensitive to the Rayleigh–Taylor instability of a liquid-phase flow.

Вибрационные механизмы транспорта примеси в конвективных системах

The equations of vibrational convection for non-uniform molecular fluid mixtures have been derived when the diffusion coefficient depends on concentration of components. Equation system is received with the help of the averaging method in the limiting case of high frequencies and small values of amplitude. In a definite sense this one is identical mathematically to well-known equations system of thermal vibrational convection in an approximation of Zen’kovskaya and Simonenko. The problem of concentration field evolution in a plane infinite fluid layer has been solved numerically by the method of finite differences. The modeling situation with homogeneous one-dimensional source distribution of a heavy component on the solid boundary was considered. It was found that the high frequency vibrations can induce mean convective flow in a cavity even in the absence of a temperature inhomogeneity and in the case of weightlessness. At the same time vibrations cause the flow in the form of rolls which occupy the whole volume. The process of admixture ablation into the fluid has been considered for arbitrary oriented vibrations. It has been shown that in dependence on the direction of the vibration axes the process of admixture redistribution passes with various rates. First of all it is determined by the intensity degree of the averaged vibrational flow in a fluid. The modeling calculations were carried out for different values of the non-dimensional parameter which describes the dependence of diffusion coefficient on concentration. Numerical simulation demonstrates that most strong effect of admixture ablation takes place for longitudinal vibrations. On the other hand vibrations which are transversal to layer damps averaged flow. In this case the mass transfer has diffusive character. Also the dependence of mass transfer on diffusion coefficient is most pronounced for tangential vibrations.Received 27.07.2016; accepted 18.08.2016

Vibrational convection of ternary mixtures in rectangular cavities in zero gravity conditions

The present paper is devoted to the investigation of the onset and nonlinear regimes of the vibrational convection of ternary mixtures in rectangular cavities with rigid boundaries in zero gravity conditions. We consider translational linearly polarized vibrations of finite amplitude and frequency. The axis of vibrations is perpendicular to the temperature gradient. The problem is solved by finite difference method in the framework of 2D unsteady approach. Numerical data on the time evolution of instantaneous and average fields and characteristics of convective flows and concentration fields are obtained for different vibration intensities and aspect ratios.

Control of Convection Patterning and Intensity in Shallow Cavities by Harmonic Vibrations

In this article the interplay among different types of flow (i.e. induced by driving forces of a different nature) is presented as a possible and “natural” means to control convection patterning and strength in shallow rectangular cavities of finite extent (A =length/height =4) filled with a low Prandtl number liquid (silicon, Pr =0.01). A variety of results concerning the possible spatial structure of the “mixed” states of steady Buoyant, Marangoni and Vibrational convection are discussed with the express intent of supporting the optimization of future experiments to be performed onboard the International Space Station.

Vibrational convection of heat-generating fluid in a rotating horizontal cylinder. The role of relative cavity length

Thermal convection of fluid with internal heat sources in a rotating horizontal cylinder with isothermal boundary and adiabatic ends is investigated experimentally. Under the action of gravity nonisothermal liquid oscillates in the cavity frame. These tidal oscillations generate the average mass force and, as a result, excite convection. The steady convection developing by this mechanism is called thermal vibrational. Centrifugal force in the considered case plays a stabilizing role. The objects of studying are the excitation thresholds of the averaged convection, heat transfer and the structure of convective flows. The parameters varying in the experiments are heat release rate, relative length of the cylinder and rotation velocity. It is found that the inertial waves which are generated near the ends of the cavity by tidal oscillations of nonisothermal liquid effect the convection. The intensity of flows excited by these waves is relatively low, but significant especially below the threshold of thermal vibrational convection. It is shown that the influence of inertial waves on heat transfer and structure of convective flows strongly depends on the cavity aspect ratio.

Experimental and numerical analysis of mass transfer in a binary mixture with Soret effect in the presence of weak convection.

One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.

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.

Stability of the rigid state of a generalized Newtonian fluid

The equations of thermal vibrational convection of a generalized Newtonian fluid are presented in the case of high-frequency vibration. A condition of quasi-equilibrium of the generalized Newtonian fluid is formulated: its particular case is the condition for rigid (quasi-solid) state. The rigid state stability is investigated for the infinite inclined layer of the nonlinearly viscous Williamson fluid. It is shown that, when heated from below, the rigid state may lose stability for layers oriented almost vertically or horizontally. High-frequency vibration stabilizes the fluid equilibrium state.

Onset of Vibrational Convection in a Binary Fluid Saturated Non-Darcy Porous Layer Heated from Above

A linear stability analysis is used to investigate the influence of mechanical vibration on the onset of thermosolutal convection in a horizontal porous layer heated and salted from above. Vibrations are considered with arbitrary amplitude and frequency. The Brinkman extended Darcy model is used to describe the flow and the Oberbeck-Boussinesq approximation is employed. Continued fraction method and Floquet theory are used to determine the convective instability threshold. It is found that the solutal Rayleigh number has the stabilizing effect. The existence of a closed disconnected loop of synchronous mode is predicted in the marginal curve for moderate values of solutal Rayleigh number and vibration amplitude.

Group properties and exact solutions of equations for vibrational convection of a binary mixture

A model of vibrational convection of a binary mixture with the thermodiffusion effect is considered. The symmetries of model equations are found, depending on the values of physical parameters. A partially invariant solution, which describes separation of the binary mixture in a thermodiffusion column, is constructed and studied. The influence of streamwise vibrations on the flow regime and separation of the mixture is investigated.

Averaging method and long-wave asymptotics in vibrational convection in layers with an interface

A scheme for applying an averaging method to the problem of convection in a two-layer system with an interface under the influence of high-frequency vibration is proposed. The derivation of the averaging equations is given, and the stability of the equilibrium of the averaged problem is considered. Long-wavelength asymptotics of steady and oscillatory instability are constructed. The results of numerical calculations for acetonitrile–n-hexane and silicone oil–fluorinert systems are given. The directions in which the investigation of thermovibrational convection in problems with free surfaces and interfaces can be continued, are indicated.