Instability of a liquid jet in a high-frequency alternating electric field

Stability of a liquid (electrolyte) jet in a tangential electric field harmonically oscillating with a high frequency is considered under an assumption of an ideal liquid. It is demonstrated that it is possible to solve the electrodynamic and hydrodynamic parts of the problem inside the jet separately if the Peclet number based on the Debye layer thickness is small. Linear stability of the trivial solution of the problem is studied. A dispersion relation is derived, which is used to study the effect of the amplitude and frequency of electric field oscillations on jet stability. An increase in the amplitude of oscillations is demonstrated to exert a stabilizing effect, whereas an increase in frequency leads to insignificant destabilization of the jet.     

Stability of a viscous liquid microjet in DC and AC electric fields

The problem of the stability of a liquid electrolyte jet under the action of a tangential electric field is considered. The radii of these jets, usually observable in experiments, vary from nanoscales to microscales. In this study, we consider microjets with the characteristic thickness of the double ion layer near the interface much less than the jet radius. The stability problem is analytically solved with account for the presence of this small parameter. The assumption on the electric neutrality of the jet as a whole leads to an explicit expression for the surface electric charge induced by the external field. The solution of the hydrodynamic problem in the external domain closes the solution and gives the dependence of the disturbance growth rate on the wavenumber. The cases of DC and AC electric fields are qualitatively compared. The distinctive features of jet stabilization by an AC high-frequency electric field are discussed.     

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.     

Stability of Plane Flow of a Liquid Dielectric in a Transverse Alternating Electric Field

The effect of an alternating arbitrary-frequency electric field on the stability of convective flow of a dielectric liquid occupying a vertical layer is investigated within the framework of the electrohydrodynamic approximation when charge formation is associated only with the nonuniform liquid polarization. The stability thresholds are determined in the linear approximation using Floquet theory. The competition between the dielectrophoretic and thermogravitational instability mechanisms is explored. It is shown that in the case of a harmonically modulated field either quasiperiodic perturbations or perturbations synchronous with the external action may be the most dangerous. One further critical perturbation mode corresponding to the subharmonic response to variation of the external field develops for triangular modulation. In the limiting case of low-frequency modulation the asymptotic behavior of the critical parameters is investigated using the Wentzel-Kramers-Brillouin method.     

Containing liquid metal in a vacuum by circularly polarized magnetic field in the presence of a conducting jacket

In this article we study the possibility of stable containment of a liquid metal in a vacuum by a high-frequency circularly polarized magnetic field. It is considered that the oscillation frequency of the metal, in view of its inertia, is considerably less than the field rotation frequency. The problem is solved in the two-dimensional formulation. In the case of infinite conductivity of the liquid it is shown that by selecting the required distance of the metal from the jacket all possible disturbances may be stabilized. Then we consider the case of finite conductivity, but with high field frequency and with disturbances for which the skin layer oscillates together with the liquid as an elastic film, and it is shown that the stability criterion remains as before. Then the case of shortwave disturbances (small magnetic Reynolds numbers) is considered. These disturbances can be stabilized only by surface tension forces; therefore, for stability, it is necessary that the skin layer depth be sufficiently small.The author thanks Yu. I. Samoilenko for posing the problem and for his helpful discussions.     

Spreading of a liquid over a plane rigid substrate in an electric field

The influence of an electric field on spreading of a thin conducting liquid layer over a plane rigid substrate is investigated theoretically. The conductivity of the liquid is assumed to be so low that the effect of the magnetic field of the currents generated in the liquid under the action of the electric field can be neglected. The spreading is assumed to be so slow that the quasi-steady approximation can be used to calculate the electric field strength which can be considered to be equal to zero inside the liquid. Equations that describe variations in the layer shape are obtained in the lubrication theory approximation. The general formulation of the problem is considered. The solution of the problem is obtained in parametric form when the effect of the gravity force and the surface tension can be neglected. Variations in the layer thickness along the substrate are so smooth that the charge distribution over its surface can be assumed to be the same as that over the substrate surface in the absence of the liquid.     

The Model of Electric Connection of a Low-Conductivity Liquid in High-Frequency Electric Field

This paper describes the study of electroconvection of low-conductivity fluid in a capacitor with boundary conditions of adhesion on a solid surface in the case of rapid charge relaxation. The linear stability of fluid equilibrium in a constant electric field is investigated. The model describing the averaged fluid flow in a high-frequency electric field is obtained. The nonlinear regimes of electroconvection are described. A regime map is constructed. It is obtained that, depending on the frequency of the external field, the transition to chaotic state occurs through quasiperiodic or intermittent structures.     

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 (₀) is to destabilize the solutal convection.     

Electrohydromagnetic instability of superposed fluids

The problem of stability of superposed viscous liquids subject simultaneously to electric and magnetic fields is investigated using the normal mode analysis. A configuration of an electrically conducting liquid topped by a dielectric liquid is envisaged in a downward gravity field. The electric field is assumed along the gravity field, while the magnetic field is taken to be either along or normal to the electric field. Criteria of instability are derived in both cases. It is found that a vertical electric field has a destabilizing influence and renders an otherwise stable configuration (bottom heavy arrangement) unstable for small wavelengths, while the effect of the magnetic field is stabilizing.     

Parametric instability of a nonuniformly heated horizontal layer of liquid dielectric in a variable electric field

The parametric instability of a nonuniformly heated horizontal layer of liquid dielectric with free isothermal boundaries in a transverse electric field is studied analytically. An instability map is obtained. It is shown that instability can develop at some critical electric field strength which depends on the frequency and is several times greater than the critical strength of the constant electric field.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 184–186, September–October, 1993.     

Fluid–structure interaction during the impact of a cylindrical shell on a thin layer of water

A two-dimensional unsteady analysis of an elastic circular cylindrical shell that enters a thin layer of an ideal incompressible liquid is considered. The cylinder initially touches the liquid free surface at a single point and then penetrates the liquid layer at a constant vertical velocity. The problem is coupled because the liquid flow, the shape of the elastic shell and the geometry of the contact region between the body and the liquid must be determined simultaneously. The flow region is subdivided into four complementary regions that exhibit different properties: the region beneath the entering body surface, the jet root, the spray jet, and the outer region. A complete solution is obtained by matching the solutions within these four subdomains. The structural analysis is based on the normal-mode method. Strain-time histories of the inner surface of the cylinder are of particular interest. In the case of a very flexible shell three distinct regimes of the impact process were found. For a high impact velocity the lower part of the shell flattens and the shell does not enter the water. For a moderate impact velocity the shell reaches the bottom and an effect of “fluid capture” may occur. For a low impact velocity the shell penetrates the liquid, but the size of the contact region decreases before the shell reaches the bottom. This behaviour corresponds to exit or “reflection” of the shell from the water layer.     

The study of self-sustained oscillating plane jet flow impinging upon a small cylinder

 Experimental studies of a plane jet impinging upon a small circular cylinder are conducted by hot-wire measurements. The cylinder is located on the jet centerline within the potential-core region. The jet–cylinder interactions on the instability shear layer frequency, the cylinder wake shedding frequency, and the induced self-sustained oscillation phenomenon are carefully investigated. Test data indicate that the self-sustained flow oscillation is mainly generated by the resonant effect of the flow between the jet exit and the cylinder. Its resonant frequency is found to vary linearly and exhibits jump-stage pattern as a function of the distance between the jet exit and the cylinder. The feedback mechanism and the hydrodynamic instability theorem are proposed to predict correctly the frequency jump position, wave number and the convection speed of the self-sustained oscillating flow for different jet exit velocities. Received: 15 July 1998/Accepted: 9 December 1998     

Parametric excitation of waves on the surface of an inviscid liquid

A study is made of the stability of the equilibrium of the free surface of an infinite layer of inviscid incompressible liquid executing oscillations along the vertical axis. The problem is solved in the nonlinear formulation by series expansion with respect to the amplitude of the excitation. Soft and hard excitation regimes of the surface waves are obtained. The stability of the regimes is investigated. It is shown that the plane wave formed on the surface of the liquid is unstable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–75, September–October, 1982.I thank V. A. Briskman for suggesting the problem and for constant interest in the work and also A. A. Nepomnyashchii for discussing the results.     

Experimental and numerical study on flow characteristics and heat transfer of an oscillating jet in a channel

A fluidic oscillator can produce self-induced and self-sustaining oscillating jet by fluid supply without moving parts. This device has attracted research interest in heat and mass transfer enhancement in recent years. In the current study, a double-feedback fluidic oscillator was numerically investigated based on three-dimensional unsteady Reynolds-averaged Navier-Stokes equations (3D-URANS) while the operating fluid is an incompressible flow. Then, the results were validated with experimental data by two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) and thermographic phosphor thermometry (TPT) for the velocity and temperature field, respectively. A grid sensitivity study was done by comparison of instantaneous and time-averaged flow fields. Additionally, the proper orthogonal decomposition (POD) method was used to find the phase information of the oscillating jet, and fast Fourier transform (FFT) analysis was used to find the frequency of the oscillating jet to validate the numerical results. The effect of the working fluid was also studied. Finally, in order to determine the effect of the Reynolds number on heat transfer enhancement, the Q-criterion was calculated to provide detailed insight into the oscillating mechanism. The results show that the non-dimensional frequency of oscillation is independent of either the working fluid or mass flow rate. Additionally, for a given fluid, increasing Re causes strong vortices and increases the frequency of oscillation. However, the convection heat transfer did not change significantly when varying the mass flow rate because the convection velocity of vortices increases as the mass flow rate is enhanced. A comparison with a free jet reveals that the oscillating jet in a channel is useful in terms of covering a larger area.     

Thermocapillary convection stability in a cylindrically-symmetric two-phase system

Thermocapillary flows in an infinitely long liquid cylinder surrounded by a coaxial gas layer with a controlled flow rate and the stability of such flows are investigated. In the layers a constant axial temperature gradient is maintained. An exact solution of the equations of motion describing the steady-state flow in this two-phase system is derived. Possible flow regimes and their stability in the linear approximation are studied. It is shown that in the liquid phase the thermocapillary flow can be completely stopped by the gas flow at the expense of the interaction between mechanical stresses at the interface. The results obtained indicate the possibility of controlling thermocapillary flows and their stability by means of gas flows.     

Effect of a rotating magnetic field on convection in a horizontal fluid layer

The stability of mechanical equilibrium of a horizontal layer of conducting fluid in the presence of a magnetic field rotating in a horizontal plane is considered. Both finite field rotation frequencies and the limiting case of high frequencies are investigated. It is shown that the magnetic field stabilizes the equilibrium. The dependence of the critical perturbation wavelength on the field strength is non-monotonic, and with increase in the magnetic field strength the mode of most dangerous perturbations changes from long-to short-wave type. Nonlinear three-dimensional convection regimes are calculated numerically. It is found that at finite supercriticalities and a sufficiently strong magnetic field the rolls and the hexagonal cells may be stable simultaneously.     

Convective stability of a horizontal rotating fluid layer with distributed heat sources

The results of investigating the convective instability of a horizontal layer of rotating fluid, created by a temperature difference applied at the boundaries of the layer and by heat sources distributed according to various laws, are presented. It is shown that, when the other parameters of the problem are fixed, an increase in the internal heat release lowers the limits of both monotonic and oscillatory stability of the layer, increases the wave number and reduces the neutral oscillation frequency. An increase in source concentration towards the center of the layer intensifies the effect. As the strength of the internal heat sources and their concentration towards the center of the layer increase, the oscillating convection that develops at the stability limit when the Prandtl number is low and the rotation fairly fast is first replaced by monotonic convection and then ceases altogether.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 21–28, January–February, 1989.     

Effect of electrohydrodynamic interaction on the stability of a flat plate laminar boundary layer

The stability of a unipolarly charged electrohydrodynamic boundary layer on a flat dielectric plate along which an electric current flows between electrodes located on the plate is investigated within the framework of the linear theory. The solution of the steady-state problem is obtained on the basis of methods developed earlier for conditions typical of aerodynamical experiments and various electric currents and electrode voltages. The effect of the interaction between perturbations of the electric and hydrodynamic flow parameters on the flow stability is estimated within the framework of the locally homogeneous approximation. This effect turns out to be insignificant under the conditions considered. It is shown that steady-state electrohydrodynamic action on the main flow makes it possible to obtain “accelerating” velocity profiles with increased absolute values of the second derivative in the transverse direction. This ensures a significant increase in the critical Reynolds numbers of loss of stability and a narrowing of the growing perturbation wavenumber range.     

The onset of convection in a viscoelastic liquid saturated anisotropic porous layer

The linear stability of a viscoelastic liquid saturated horizontal anisotropic porous layer heated from below and cooled from above is investigated by considering the Oldroyd type liquid. A generalized Darcy model, which takes into account the viscoelastic properties, the mechanical and thermal anisotropy is employed as momentum equation. The critical Rayleigh number, wavenumber, for stationary and oscillatory states and frequency of oscillation are determined analytically. It is shown that oscillatory instabilities can set in before stationary modes are exhibited. The effect of the viscoelastic parameter, the mechanical and thermal anisotropy parameters and specific heat ratio on the linear stability of the system is analyzed and presented graphically.     

Mechanism of self-oscillations in a supersonic jet impact onto an obstacle. 2. Obstacle with no spike

Results of the numerical solution of the problem of impingement of an overexpanded supersonic jet onto an obstacle are reported. The mass-flow-rate mechanism of self-oscillations is revealed. This mechanism consists of periodic changes in the regimes of gas inflow and outflow from the separation region to the jet around this region. It is shown that the shock-wave structure of the impinging supersonic jet exerts a significant effect on the amplitude of self-oscillations.