Effect Of Gravity Modulation Research Articles

The effects of gravity modulation on fluid mixing. Part 1. Harmonic modulation

We study the effects of gravity modulation on the mixing characteristics of two interdiffusing miscible fluids initially in two vertical regions separated by a thin diffusion layer. We formulate the case of general gravity modulation of arbitrary orientation, amplitude , the flow is similar to a modulated lock exchange flow.

Stability of Gravity Driven Convection in a Cylindrical Porous Layer Subjected to Vibration

The linear stability theory is used to investigate analytically the effects of gravity modulation on convection in a homogeneous cylindrical porous layer heated from below. The linear stability results show that increasing the frequency of vibration stabilizes the convection. In addition the aspect ratio of the porous cylinder is shown to influence the stability of convection for all frequencies analysed. It was also observed that only synchronous solutions are possible in cylindrical porous layers, with no transition to subharmonic solutions as was the case in Govender (2005a) [Transport Porous Media 59(2), 227–238] for rectangular layers or cavities.

Stability of Solutal Convection in a Gravity Modulated Mushy Layer During the Solidification of Binary Alloys

The linear stability theory is used to investigate analytically the effects of gravity modulation on solutal convection in the mushy layer of solidifying binary alloys. The gravitational field consists of a constant part and a sinusoidally varying part, which is synonymous to a vertically oscillating mushy layer subjected to constant gravity. The linear stability results are presented for both the synchronous and subharmonic solutions. It is demonstrated that up to the transition point between the synchronous and subharmonic regions, increasing the frequency of vibration rapidly stabilizes the solutal convection. Beyond the transition point, further increases in the frequency tend to destabilize the solutal convection, but gradually. It is also demonstrated that the effect of increasing the ratio of the Stefan number and the solid composition (η 0 ) is to destabilize the solutal convection.

Linear Stability and Convection in a Gravity Modulated Porous Layer Heated from Below: Transition from Synchronous to Subharmonic Solutions

The linear stability theory is used to investigate analytically the effects of gravity modulation on convection in a homogenous porous layer heated from below. The linear stability results are presented for both the synchronous and subharmonic solutions and the exact point for the transition from synchronous to subharmonic solutions is computed. It is also demonstrated that increasing the excitation frequency rapidly stabilizes the convection up to the transition point from synchronous to subharmonic convection. Beyond the transition point, the effect of increasing the frequency is to slowly destabilize the convection.

Nonlinear parametrically excited surface waves in surfactant-covered thin liquid films

The effect of gravity modulation on the nonlinear evolution of long-wavelength disturbances at the free surface of a surfactant-covered thin liquid layer is studied. The surfactants, which are assumed to be insoluble, give rise to interfacial concentration gradients and associated Marangoni flow in the underlying liquid film. A coupled system of lubrication-theory-based evolution equations for the film height and surfactant concentration is solved numerically using spectral methods

Stability of Convection in a Gravity Modulated Porous Layer Heated from Below

The linear stability theory is used to investigate analytically the effects of gravity modulation on convection in a homogenous porous layer heated from below. The gravitational field consists of a constant part and a sinusoidally varying part, which is tantamount to a vertically oscillating porous layer subjected to constant gravity. The linear stability results are presented for the specific case of low amplitude vibration for which it is shown that increasing the frequency of vibration stabilises the convection.

Convection in Hele–Shaw cell with parametric excitation

The linear stability of a thin vertical fluid layer heated from below is considered. Here the gravitational field consists of two parts: a constant part and a time-dependent part varying periodically. The time-dependent part has been expressed in Fourier series. The effect of gravity modulation on the fluid layer is examined. Using an asymptotic analysis the convective threshold has been determined. Some comparisons are made with the known results.

Instability of long-wavelength disturbances on gravity-modulated surfactant-covered thin liquid layers

The effect of gravity modulation on long-wavelength disturbances at the free surface of a surfactant-covered thin liquid layer is analysed. The surfactants are assumed to be insoluble so that variations in their concentration along the free surface produce Marangoni flows in the underlying liquid. Lubrication theory is applied to obtain nonlinear partial differential equations that describe the behaviour of the free surface height and surfactant concentration, and the stability of these equations to small-amplitude disturbances is examined by applying Floquet theory. It is found that long-wavelength disturbances are destabilized by gravity modulation when surfactants are present, whereas such disturbances are stable when surfactants are absent. Results from additional calculations indicate that the instability becomes more difficult to excite as the Marangoni forces, body forces, capillary forces and surfactant diffusivity increase, and becomes easier to excite as the van der Waals forces increase.

Numerical analysis of thermosolutal flows in a cavity with gravity modulation effects

In this work, a two-dimensional thermosolutal convection flow under a sinusoidal gravity modulation (g-jitter) field is studied to understand the effects of the periodic source on flow field, as well as heat and mass transfer mechanisms. A semi-implicit projection finite element method is adopted to solve the transient Navier–Stokes, energy and species concentration equations. The fingering regime and the diffusive regime are explored for a series of gravity modulation frequencies. Two types of flow evolution, synchronous and subharmonic responses, are obtained for different frequencies. Distribution of unstable responses for the singly unstable condition is in agreement with the literature predict. The results show that heat and mass transfer rates are affected by the response type. For a subharmonic variation flow field, the overall Nusellt number and Sherwood number exhibit larger values. In addition, the augmenting condition in combining thermally driving force and solutally driving force is analyzed for a practical crystal material and displays a different response distribution from those in the fingering regime and the diffusive regime.

Stability of return thermocapillary flows under gravity modulation

The effect of gravity modulation on the stability of a time-harmonic parallel flow in a slot geometry is studied. A constant temperature gradient applied along the length of a slot with a flat free interface at the top drives a steady thermocapillary return flow. A vertical time-harmonic gravity modulation drives a time-periodic buoyant return flow. The relative strength of the two components is characterized by the Marangoni number Ma and the Rayleigh number Ra, respectively. There is potential for Rayleigh–Bénard, shear, and hydrothermal wave instabilities. The linear stability for two-dimensional rolls is studied and the stability boundaries are obtained by Floquet theory. Stability diagrams in the Ra–Ma plane are obtained for fixed modulation frequency and various Prandtl numbers and a disturbance kinetic-energy analysis is used to determine the instability mechanism. Buoyant and hydrothermal instabilities are found at small Ma and small Ra, respectively, whereas shear instabilities are found not to be important in the parameter regime studied. The two active mechanisms are found to either reinforce or oppose each other in different parameter regimes. This leads to regions of stability in the Ra–Ma plane where flows are stable due to the combined effect of buoyancy and thermocapillarity whereas a purely buoyant or a purely thermocapillary flow at the same Ra or Ma would be unstable. These results are contrasted with those obtained by Nield [J. Fluid Mech. 19, 341 (1964)] in the case of steady gravity, for which thermocapillarity and buoyancy reinforce each other.

Effect of gravity modulation on the stability of convection in a vertical slot

The nature of instability occurring in a differentially heated infinite slot under steady gravity depends only on the Prandtl number of the contained Boussinesq fluid. For fluids with Pr < 12.5, the instability is shear dominated and onsets in a steady convection mode; for fluids with Pr > 12.5, the instability is buoyancy dominated and onsets in an oscillatory mode. In this paper, we examine the effect of gravity modulation on the stability characteristics of convection in an infinite slot with both kinds of fluids, in particular, Pr = 1 and Pr = 25. Using the method of Sinha & Wu (1991), we are able to obtain accurate results without excessive numerical integration in the linear stability analysis by Floquet theory. Results show that, for Pr = 1, at a non-dimensional oscillation frequency ω = 20, the critical state alternates between the synchronous and subharmonic modes. At higher frequencies, ω > 100, all critical states occur in the synchronous mode. For Pr = 25, with a modulation amplitude ratio of 0.5, resonant interaction occurs in the neighbourhood of ω = 2σc, where σc is the oscillation frequency of the instability at the critical state under steady gravity. This resonant interaction is destabilizing, with the critical Grashof number being reduced by approximately 20% from that at steady gravity. It is due to the presence of a detached subharmonic branch of the marginal stability curve. In frequency ranges where the detached subharmonic branch is absent, the critical state is in the quasi-periodic mode consisting of two waves of different oscillation frequencies whose sum is the forcing frequency. An analysis of the rate of change of the perturbation kinetic energy shows that, for Pr = 1, the instability is shear dominated regardless of the mode of oscillation, synchronous or subharmonic. Similarly, for Pr = 25, the instability is buoyancy dominated whether it is in the quasi-periodic or subharmonic mode. The mode switching is a response to the forcing and is independent of the dominant mechanisms of instability.

Effect of gravity modulation on the onset of convection in a fluid and porous layer

Effect of gravity modulation on the onset of convection in a fluid and porous layer

Effect of gravity modulation on the onset of convection in a fluid and porous layer

The stability of a horizontal fluid and fluid-saturated porous layer heated from below is examined for the case of a time-dependent buoyancy force generated by gravity modulation. A linear stability analysis is performed to show that the gravity modulation can significantly affect the stability limits of the system. A method based on small amplitude of the modulation proposed by Venezian is used to compute the critical value of Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of the modulation, Prandtl number and porous parameter. It is found that the low frequency g-jitter can have a significant effect on the stability of the system. The Darcy limit and viscous flow limit are obtained as degenerate cases of the Brinkman model. Finally, an asymptotic analysis is presented for small and large frequencies.

Effect of gravity modulation on natural convection in a vertical slot

Abstract The effect of a sinusoidal gravity modulation on natural convection of fluids with constant property, in vertical slots of aspect ratio of 20 and 15, is studied numerically by a finite difference method. The gravity modulation is characterized by the nondimensional amplitude Rg and nondimensional frequency ωf. We find a low frequency g-modulation has a strong effect on the fluid flow but little effect on the heat transfer rate. The flow of air usually enters a periodic state after two cycles of g-modulation, much faster than that of large Prandtl number fluids. The response is generally in the synchronous mode, except at ωf = 10 and Rg = 1 for air where it appears to be subharmonic. For a multicellular primary flow of air, g-modulation at ωf = 25 and Rg = 1 changes the multicellular primary flow to a unicellular one, demonstrating significant stabilizing effect. For high Prandtl number fluids, a flow pattern, consisting of horizontal secondary cells, preceded the onset of the commonly observed vertical secondary cells. At low modulation frequencies, stability of convection is enhanced as demonstrated by the increase in the critical Grashof number, by approximately 154% at Rg = 1.6 and ωf = 40. The temperature remains unchanged within the cycle of the modulation, totally different from the case of air, and gives a critical gradient approximately 0.56 at the center.

Fluid dynamics of slender, thin, annular liquid jets

AbstractPerturbation methods are used to obtain the one‐dimensional, asymptotic equations that govern the fluid dynamics of slender, thin, inviscid, incompressible, axisymmetric, irrotational, annular liquid jets from the Euler equations. It is shown that, depending on the magnitude of the Weber number, two flow regimes are possible: an inertia‐dominated one corresponding to large Weber numbers, and a capillary regime for Weber numbers of the order of unity. The steady equations governing these two regimes have analytical solutions for the liquid's axial velocity component and require a numerical integration to determine the jet's mean radius for inertia‐dominated jets. The one‐dimensional equations derived in this paper are shown to be particular cases of a hydraulic model for annular liquid jets, and this model is used to determine the effects of gravity modulation on the unsteady fluid dynamics of annular liquid jets in the absence of mass injection into the volume enclosed by the jet and mass absorption. It is shown that both the convergence length and the pressure coefficient are periodic functions of time which have the same period as that of the gravity modulation, but undergo large variations as the amplitude, frequency and width of gravitational pulses is varied.

Convective stability of gravity-modulated doubly cross-diffusive fluid layers

A stability analysis is undertaken to theoretically study the effects of gravity modulation and cross-diffusion on the onset of convection in horizontally unbounded doubly diffusive fluid layers. We investigate the stability of doubly stratified incompressible Boussinesq fluid layers with stress-free and rigid boundaries when the stratification is either imposed or induced by Soret separation. The stability criteria are established by way of Floquet multipliers of the amplitude equations. The topology of neutral curves and stability boundaries exhibits features not found in modulated singly diffusive or unmodulated multiply diffusive fluid layers. A striking feature in gravity-modulated doubly cross-diffusive layers is the existence of bifurcating neutral curves with double minima, one of which corresponds to a quasi-periodic asymptotically stable branch and the other to a subharmonic neutral solution. As a consequence, a temporally and spatially quasi-periodic bifurcation from the basic state is possible, in which case there are two incommensurate critical wavenumbers at two incommensurate onset frequencies at the same Rayleigh number. In some instances, the minimum of the subharmonic branch is more sensitive to small parameter variations than that of the quasi-periodic branch, thus affecting the stability criteria in a way that differs substantially from that of unmodulated layers.

Natural convection with thermocapillary and gravity modulation effects in low-gravity environments

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The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double-diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

Experiment Study of the Effect of Gravity Modulation on the Growth Process in Vapor Phase

Experiment Study of the Effect of Gravity Modulation on the Growth Process in Vapor Phase

The effect of gravity modulation on solutal convection during directional solidification

During directional solidification of a binary alloy at constant velocity, thermosolutal convection may occur due to the temperature and solute gradients associated with the solidification process. For vertical growth in an ideal furnace (lacking horizontal gradients) a quiescent state is possible. For a range of processing conditions, the thermal Rayleigh number is sufficiently small that the stabilizing role of the thermal field during growth vertically upwards may be neglected, and only solutal convection need be considered. The effect of a time-periodic vertical gravitational acceleration (or equivalently vibration) on the onset of solutal convection is calculated based on linear stability using Floquet theory. We find that a stable base state can be destabilized due to modulation, while an unstable state can be stabilized. The flow and solute disturbance fields show both synchronous and subharmonic temporal response to the driving sinusoidal modulation.