Collapse of a single bubble in a Shvedov-Bingham fluid under pulsating external pressure

The behavior of a spherical bubble in an ideal fluid, a viscous medium, and an incompressible viscoplastic medium with a yield stress is studied numerically and analytically when a time-varying periodic pressure is exerted at a sufficient distance from the surface of the bubble. Various modes of collapse are examined and classified. The critical values of the key parameters that characterize the behavior of this system are found; one of these parameters is the dimensionless frequency of external pressure fluctuations.     

Experimental investigation of the interaction between a pulsating bubble and a rigid cylinder

In this paper, the behavior of a bubble near a rigid cylinder is studied experimentally as the positions of bubble induction change, and several cylinders with different diameters are used in the experiment. The main results are as follows. The behavior of a bubble near a rigid cylinder is distinct from that near a rigid plate. When the cylinders are laid in deep water, there will occur three kinds of typical bubble shapes as the distance between bubble and cylinder increases. And the bubble shapes are different as the diameter of cylinder varies. When the cylinders are laid near a free surface, the behaviors of bubble near cylinders with different diameters are similar. For a certain distance between bubble and free surface, as the distance between bubble and cylinder increases, "double jet", "inclined jet" and "downward jet" will take place successively.     

Interactions between a central bubble and a surrounding bubble cluster

The interaction of multiple bubbles is a complex physical problem. A simplified case of multiple bubbles is studied theoretically with a bubble located at the center of a circular bubble cluster. All bubbles in the cluster are equally spaced and own the same initial conditions as the central bubble. The unified theory for bubble dynamics [35] is applied to model the interaction between the central bubble and the circular bubble cluster. To account for the effect of the propagation time of pressure waves, the emission source of the wave is obtained by interpolating the physical information on the time axis. An underwater explosion experiment with two bubbles of different scales is used to validate the theoretical model. The effect of the bubble cluster with a variation in scale on the pulsation characteristics of the central bubble is studied.     

Interaction between a circular inclusion and a symmetrically branched crack

The interaction problem between a circular inclusion and a symmetrically branched crack embedded in an infinite elastic medium is solved. The branched crack is modeled as three straight cracks which intersect at a common point and each crack is treated as a continuous contribution of edge dislocations. Green's functions are used to reduce the problem into a system of singular equations consisting of the distributions of Burger's dislocation vectors as unknown functions through the superposition technique. The resulting integral equations are solved numerically by the method of Gauss-Chebychev quadrature. The proposed integral equation approach is first verified for two limiting cases against the literature. More effort is paid on the effect of inclusion on both the Mode I and Mode lI stress intensity factors at the branch tips. The effect of inclusion on the branching path is also investigated.     

Mass transfer from a pulsating drop

The primary difficulty in solving the problem of mass transport through an isolated drop (or bubble) moving in a fluid medium at high Reynolds numbers lies in the extreme complexity of the hydrodynamic pattern of the phenomenon. For sufficiently high velocities a separation of the external flow will occur in the rear portion of the drops and bubbles, which leads to the appearance of a turbulent wake and a sharp increase of the hydrodynamic resistance. Beginning with those dimensions for which the resistance force acting per unit surface of the drop or bubble from the external medium becomes greater than the capillary pressure, the surface of the drops and bubbles begins to deform and pulsate. The local variations of the surface tension, resulting either from the process of convective diffusion or from adsorption of surface-active substances, have a large effect on the hydrodynamics of drops and bubbles (particularly on the deformation of their surface) [1, 2], The presence of vortical, and possibly even turbulent, motion within the drops and bubbles may, under certain conditions [1], lead to their fractionation.Naturally, at the present time such complex hydrodynamics cannot be described by exact quantitative relations. Several authors have attempted to solve this problem approximately within the framework of certain assumptions. In particular [3–6], a theory was developed for the boundary layer on the surface of spherical and ellipsoidal gaseous bubbles moving in a liquid, studies were made [7, 8] of the hydrodynamics of drops located in a gas flow and the conditions were found for which fractionation of such drops takes place. Of considerable practical interest is the development of the theory of mass transfer in pulsating drops and bubbles and finding in explicit form the dependence of the mass transfer coefficients on the hydrodynamic characteristics of these systems. Until this relationship is established, every theory which ignores the effect of hydrodynamics on the mass transfer rate from an individual drop or bubble cannot be considered in any way well-founded. This relates particularly to the theories [9, 10] which consider mass transfer in systems with concentrated streams of drops and bubbles. The present paper is devoted to the study of mass transport through the surface of an isolated drop in an irrotational gas or liquid stream for large Peclet numbers P.In conclusion the authors wish to thank V. G. Levich for his helpful discussions.     

Solute dispersion in a pulsating flow

The one-dimensional model proposed by Taylor [1] of the dispersion of soluble matter describes approximately the distribution of the solute concentration averaged over the tube section in Poiseuille flow. Aris [2] obtained more accurately the effective diffusion coefficient in Taylor's model and solved the problem for the general case of steady flow in a channel of arbitrary section. Many papers have been published in the meanwhile devoted to particular applications of this theory (for example, [3–5]). Various dispersion models have been constructed [6–8] that make the Taylor—Aris model more accurate at small times and agree with it at large times. The acceleration of the mixing of the solute considered in these models in the presence of the simultaneous influence of molecular diffusion and convective transport also operates in unsteady flows. In particular, the presence of velocity pulsations influences the growth of the dispersion even if the mean flow velocity is equal to zero at every point of the flow. In the present paper, the Taylor—Aris theory is extended to the case of laminar flows with periodically varying flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 24–30, September–October, 1982.     

Lifetime of a superheated liquid

The mathematical relationship between the lifetime of a superheated liquid and temperature is investigated. The energy equation is solved in conjunction with a non-equilibrium vapor formation model in order to specify the temperature variation of the liquid during the nucleation process. It is shown that the expectation time of a uniformly superheated liquid decreases with increasing temperature. The limit of superheat in the liquid is then identified as the liquid temperature above saturation at which boiling takes place almost instantaneously. Results compare favorably with classical nucleation kinetic data.     

Numerical analysis of a symmetrically heated vertical channel with obstruction

 In this paper, a numerical investigation of laminar natural convection flows in a vertical channel with obstructions is carried out. The main purpose was to analyze the effects of the locations of symmetric obstructions. The computations were performed in a two-dimensional domain and a symmetric uniform wall temperature has been taken as thermal boundary condition. The governing equations were solved using a control volume method and the SIMPLER algorithm for the velocity–pressure coupling was employed. The profiles of the local Nusselt number were given for three different locations of the obstructions. The variation of the average Nusselt number and inlet flow rate versus the modified Rayleigh number were investigated. The results demonstrated that the average Nusselt number decreases as the distance of the obstructions from the inlet increases. Received on 17 January 2000     

Lifetime of a narrow channel in a liquid

Lifetime determination is considered for a narrow channel in a liquid collapsing in response to gravitational and capillary forces. Working formulas are derived to relate the lifetime to the properties of the liquid and the channel parameters. The calculations are compared with experiments on the effects of a focused high-power electron beam acting on a liquid and solid.Translated from Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 121–129, January 1974.     

Visualization of a confined accelerated bubble

High-speed photography was used to study the collapse of a confined two-dimensional, air cavity in water, subjected to a propagating pressure disturbance. The 5–6 mm diameter cavity was confined in a rectangular duct. A sustained pressure disturbance was created by an accelerating piston in contact with the water 240 mm away from the bubble. The pressure increased from 0.1 MPa to about 0.12 MPa with a rise time of the order of 2 ms. The pressure pulse was not reflected until its arrival at the end of the duct, 320 mm from the piston. A microjet was produced at the proximal wall which penetrated the distal cavity wall, thereby producing a pair of bubbles which was thought to be regions of intense vorticity. The features of such confined bubble collapse were not found in previous investigations of unconfined bubble accelerations by weak pressure disturbances. Confinement apparently intensified the effect of the disturbance significantly. Received 18 August 1998 / Accepted 12 May 1999     

Internal gravityWaves excited by a pulsating source of perturbations

The problem of constructing uniform asymptotics for the far fields of internal gravity waves generated by a pulsating localized source of perturbations in finite-depth stratified medium flow is considered. The solutions obtained describe the wave perturbations both inside and outside the wave fronts and can be expressed in terms of the Airy function and its derivatives. Numerically calculated wave patterns of the excited wave fields are presented.     

Numerical investigation of a laminar pulsating flow in a rectangular duct

A pulsating laminar flow of a viscous, incompressible liquid in a rectangular duct has been studied. The motion is induced under an imposed pulsating pressure difference. The problem is solved numerically. Different flow regimes are characterized by a non‐dimensional parameter based on the frequency (ω) of the imposed pressure gradient oscillations and the width of the duct (h). This, in fact, is the Reynolds number of the problem at hand. The induced velocity has a phase lag (shift) with respect to the imposed pressure oscillations, which varies from zero at very slow oscillations, to 90° at fast oscillations. The influence of the aspect ratio of the rectangular duct and the pulsating pressure gradient frequency on the phase lag, the amplitude of the induced oscillating velocity, and the wall shear were analyzed. Copyright © 1999 John Wiley & Sons, Ltd.     

Motion of a bubble in a viscous liquid

The discussion concerns steady-state flow of a viscous fluid around a spherical bubble at small Reynolds number R. Asymptotic matching [1] provides a way of calculating the resistance force, which agrees well with the measured force for R < 5. The rate of growth or dissolution of the bubble is calculated on the assumption that the Péclet number is large.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 107–111, January–February, 1971.We are indebted to V. G. Levich for a discussion.     

Flow enhancement mechanisms of a pulsating flow of non-Newtonian liquids

Summary The pipe flow of non-Newtonian liquids under a fluctuating pressure gradient is considered. Adopting a generalized Maxwell model with full relaxation spectrum and considering only weak-sense stationary pressure-gradient noises, it is shown that there are two mechanisms involved in the flow enhancement: an inelastic and a dynamic mechanism. Both depend on the shear-thinning properties of the liquid in steady and oscillatory flows. For one-frequency pressuregradient noises, the flow enhancement increases with increasing frequency of fluctuation if the modulus of the complex viscosity is a decreasing function of the frequency. Since almost all polymeric liquids are shear-thinning in oscillatory shear flows, this investigation serves as a possible explanation for the data collected byBarnes, Townsend andWalters (1971). This, however, does not necessarily ensure that the constitutive model adopted in this study is free of defect in a general flow field.

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Zusammenfassung Es wird die Rohrströmung einer nicht-newtonschen Flüssigkeit bei fluktuierendem Druckgefälle betrachtet. Für ein verallgemeinertes Maxwell-Modell mit beliebigem Relaxations-Spektrum wird bei Beschränkung auf kleine Schwankungen des Druckgradienten um einen stationären Mittelwert gezeigt, daß zwei Mechanismen zur Steigerung des Durchflusses beitragen, ein unelastischer und ein dynamischer Mechanismus. Beide hängen von den Scherentzähungs-Eigenschaften der Flüssigkeit bei stationären und oszillierenden Beanspruchungen ab. Für eine harmonisch-periodische Druckstörung nimmt die Durchflußsteigerung mit wachsender Schwankungsfrequenz zu, wenn der Betrag der komplexen Viskosität eine mit der Frequenz abnehmende Funktion darstellt. Da nahezu alle Polymerflüssigkeiten bei oszillierenden Scherströmungen Scherentzähung aufweisen, liefert diese Untersuchung eine mögliche Erklärung für die vonBarnes, Townsend undWalters (1971) zusammengestellten Ergebnisse. Dies bedeutet aber nicht notwendigerweise, daß das hier angenommene Modell auch für die Beschreibung allgemeinerer Strömungsfelder angemessen ist.

     

Forced convection with laminar pulsating flow in a tube

The heat transfer model of laminar pulsating flow in a tube in rolling motion is established. The correlations of velocity, temperature and Nusselt number are obtained. The effects of several parameters on Nusselt number are investigated. The theoretical results are consistent with experimental data. Then the results are evaluated with Nield and Kuznetsov’s results. It is found that Nield and Kuznetsov’s results are not applicable for the laminar pulsating flow in nuclear power systems in ocean environments.     

Start-up and steady thermal oscillation of a pulsating heat pipe

As a novel electronic cooling device, pulsating heat pipes (PHPs) have been received attention in recent years. However, literature survey shows that no studies were carried out on the start-up and steady thermal oscillation of the PHPs. In the present paper, the copper capillary tube was being bended to form the snake-shaped PHP. Heating power was applied on the heating section, and transferred to the condensation section and dissipated to the environment by the pure natural convection. The inside diameter of the capillary tube is 2.0 mm and the working fluid is selected as FC-72. A high speed data acquisition system was used to detect the start-up and steady thermal oscillation of the PHP. Two types of the start-up process were observed: a sensible heat receiving start-up process accompanying an apparent temperature overshoot followed by the steady thermal oscillation at low heating power, and a smooth sensible heat receiving start-up process incorporating a smooth oscillation period at high heating power. For the steady thermal oscillation, also two types were found: the random thermal oscillation with a wide frequency range, indicating the random distribution of the vapor plug and liquid slug inside the capillary tube at low heating power, and the quasi periodic thermal oscillation with the same characteristic frequency for both heating section and condensation section, indicating the uniform distribution of the vapor plug and liquid slug inside the capillary tube at high heating power. The power spectral density (PSD) was used to analyze the thermal oscillation waves. The frequency corresponds to the time that a couple of adjacent vapor plug and liquid slug passing through a specific wall surface.