Evolution of finite perturbations in a viscoelastic relaxing liquid with gas bubbles

The propagation of one-dimensional perturbations in a viscoelastic relaxing liquid containing gas bubbles is investigated within the framework of the homogeneous model of the medium when the wavelength of the perturbation is much larger than the distance between the bubbles and the bubble radius. The evolution of stationary and nonstationary waves is investigated analytically and with the use of numerical integration; shock waves are also investigated. The results are compared with the behavior of perturbation waves in a Newtonian liquid with gaseous inclusions. The models of the gas-liquid medium [1, 2] are generalized to the case when the liquid phase is a viscoelastic liquid, for example, a weak aqueous solution of polymers. The propagation of longwave perturbations of finite amplitude in such a mixture is investigated using the technique developed in [3].     

Numerical simulation of shock propagation in a polydisperse bubbly liquid

The effect of distributed bubble nuclei sizes on shock propagation in a bubbly liquid is numerically investigated. An ensemble-averaged technique is employed to derive the statistically averaged conservation laws for polydisperse bubbly flows. A finite-volume method is developed to solve the continuum bubbly flow equations coupled to a single-bubble-dynamic equation that incorporates the effects of heat transfer, liquid viscosity and compressibility. The one-dimensional shock computations reveal that the distribution of equilibrium bubble sizes leads to an apparent damping of the averaged shock dynamics due to phase cancellations in oscillations of the different-sized bubbles. If the distribution is sufficiently broad, the phase cancellation effect can dominate over the single-bubble-dynamic dissipation and the averaged shock profile is smoothed out.     

Enhancement of channel wall vibration due to acoustic excitation of an internal bubbly flow

The effect of an internal turbulent bubbly flow on vibrations of a channel wall is investigated experimentally and theoretically. Our objective is to determine the spectrum and attenuation rate of sound propagating through a bubbly liquid flow in a channel, and connect these features with the vibrations of the channel wall and associated pressure fluctuations. Vibrations of an isolated channel wall and associated wall pressure fluctuations are measured using several accelerometers and pressure transducers at various gas void fractions and characteristic bubble diameters. A waveguide-theory-based model, consisting of a solution to the three-dimensional Helmholtz equation in an infinitely long channel with the effective physical properties of a bubbly liquid is developed to predict the spectral frequencies of the wall vibrations and pressure fluctuations, the corresponding attenuation coefficients and propagation phase speeds. Results show that the presence of bubbles substantially enhances the power spectral density of the channel wall vibrations and wall pressure fluctuations in the 250–1200 Hz range by up to 27 and 26 dB, respectively, and increases their overall rms values by up to 14.1 and 12.7 times, respectively. In the same frequency range, both vibrations and spectral frequencies increase substantially with increasing void fraction and slightly with increasing bubble diameter. Several weaker spectral peaks above that range are also observed. Trends of the frequency and attenuation coefficients of spectral peaks, as well as the phase velocities are well predicted by the model. This agreement confirms that the origin of enhanced vibrations and pressure fluctuations is the excitation of streamwise propagating pressure waves, which are created by the initial acoustic energy generated during bubble formation.     

Cell model for gas absorption with first-order irreversible chemical reaction and heat release in gas-liquid bubbly media

A model for mass and heat transfer during physical gas absorption in gas-liquid bubbly medium suggested in [1] is generalized for a case of chemical absorption accompanied by heat release. Diffusion and thermal interactions between bubbles are taken in to account in the approximation of a cellular model of a bubbly medium whereby a bubbly medium is viewed as a periodic structure consisting of identical spherical cells with periodic boundary conditions at a cell boundary. Distribution of concentration of the dissolved gas, temperature distribution in liquid and rates of mass and heat transfer during nonisothermal chemical absorption of a soluble pure gas from a bubble by liquid are determined. In the limiting case of chemical absorption without heat release the derived formulas recover the expressions for isothermal chemical absorption. In the limiting case of physical absorption with heat release the derived formulas recover the expressions for nonisothermal absorption obtained in [1].     

Note on the propagation of disturbances in a liquid containing gas bubbles

Summary In a liquid containing gas bubbles the speed of sound is less than that in each phase separately. Using the equations of motion for a homogeneous liquid containing gas bubbles it is shown that the dominating attenuation of an infinitesimal disturbance is that due to the second viscosity. In the propagation of a finite compressive disturbance an expression for the time required for the disturbance to display shock characteristics is found in terms of the initial disturbance profile and the liquid-gas ratio.     

Turbulent shear stress profiles in a bubbly channel flow assessed by particle tracking velocimetry

Particle tracking velocimetry (PTV) is applied to a bubbly two-phase turbulent flow in a horizontal channel at Re = 2 × 10⁴ to investigate the turbulent shear stress profile which had been altered by the presence of bubbles. Streamwise and vertical velocity components of liquid phase are obtained using a shallow focus imaging method under backlight photography. The size of bubbles injected through a porous plate in the channel ranged from 0.3 to 1.5 mm diameter, and the bubbles show a significant backward slip velocity relative to liquid flow. After bubbles and tracer particles are identified by binarizing the image, velocity of each phase and void fraction are profiled in a downstream region. The turbulent shear stress, which consists of three components in the bubbly two-phase flow, is computed by analysis of PTV data. The result shows that the fluctuation correlation between local void fraction and vertical liquid velocity provides a negative shear stress component which promotes frictional drag reduction in the bubbly two-phase layer. The paper also deals with the source of the negative shear stress considering bubble’s relative motion to liquid.     

On two-phase flow patterns and transition criteria in aqueous methanol and CO2 mixtures in adiabatic,rectangular microchannels

This paper presents flow map investigations of adiabatic two-phase flow in square cross-sectioned, 200 μm deep microchannels fabricated in silicon, employing laser induced fluorescence microscopy. The influence of surface tension and nozzle geometry on the flow pattern transition was investigated using two nozzle widths (orifices of 30 μm and 50 μm, respectively) and methanol–water solutions with CO₂ as the gas phase. It was found and quantified that smaller nozzle geometries and smaller liquid surface tension promote the propagation of capillary gas bubbles at lower superficial gas and liquid velocities. Within the measurement domain of superficial gas (0.01–0.625 m/s) and liquid (0.0005–0.5000 m/s) velocities, we observed dispersed bubbly, regularly ordered bubbly, wedging, slug and annular flows, thus extending the experimental knowledge base to smaller superficial liquid velocities by almost two orders of magnitude. With the help of the flow maps presented herein, we were able to characterize the observed regularly ordered bubbly flow as the transition regime between dispersed bubbly and wedging flow. The results of the present investigation are of direct relevance to the operation of small-scale direct methanol fuel cells.     

Shock structure in bubbly liquids: comparison of direct numerical simulations and model equations

Shock wave structure in a bubbly mixture composed of a cluster of gas bubbles in a quiescent liquid with initial void fractions around 10% inside a 3D rectangular domain excited by a sudden increase in the pressure at one boundary is investigated using the front tracking/finite volume method. The effects of bubble/bubble interactions and bubble deformations are, therefore, investigated for further modeling. The liquid is taken to be incompressible while the bubbles are assumed to be compressible. The gas pressure inside the bubbles is taken uniform and is assumed to vary isothermally. Results obtained for the pressure distribution at different locations along the direction of propagation show the characteristics of one-dimensional unsteady shock propagation evolving towards steady-state. The steady-state shock structures obtained by the present direct numerical simulations, which show a transition from A-type to C-type steady-state shock structures, are compared with those obtained by the classical Rayleigh–Plesset equation and by a modified Rayleigh–Plesset equation accounting for bubble/bubble interactions in the mean-field theory.      

Fluctuation characteristics of bubbly liquid flow in converging-diverging nozzle

The pressure fluctuation characteristics in bubbly liquid flow in a converging-diverging nozzle are interpreted on the basis of the previous theoretical results concerning the possible wave modes in bubbly liquid flow and their properties. The experiment is performed in a visual blowdown facility using water and nitrogen gas. The intensity and power spectrum density of the pressure fluctuations are measured, as well as the velocities of liquid and bubbles, the void fraction and the chord length of bubbles. All the fluctuation characteristics and their relation with the main stream condition are compatible with the theoretical predictions. The instability of the convection mode in the presence of the velocity slip and the cut off of the propagation modes in moderate frequency are demonstrated.     

Bubble dynamics: a review and some recent results

Several aspects of small-amplitude oscillations of bubbles containing gas, vapor, or a gas-vapor mixture are discussed. An application to pressure-wave propagation in a bubbly liquid is described. Nonlinear forced oscillations are considered in the light of recent research on forced oscillations of nonlinear systems. The growth of vapor bubbles, an extension of the Rayleigh-Plesset equation to non-Newtonian liquids and appreciable mass transfer at the interface, and a boundary integral numerical method for nonspherical cavitation bubble dynamics are also briefly discussed.     

Acoustic Waves of Various Geometry in Multi-Fraction Bubbly Liquids

The propagation of acoustic waves of various geometry in mixtures of a liquid and a disperse phase consisting of small bubbles which differ from one another by both the radii and the thermophysical properties is investigated. A systemof differential equations of motion of the mixture is written and the dispersion relation is derived. The dispersion curves are constructed and damping of the pressure pulses is compared for the plane, cylindrical, and spherical waves in the bubbly liquids considered. The theory is compared with the experimental data.     

Turbulent flow structure and bubble distribution in an axisymmetric nonisothermal impinging gas-liquid jet

The flow structure of a bubbly impinging jet in the presence of heat transfer between the two-phase flow and the surface is numerically investigated on the basis of the Eulerian approach. The model uses the system of Reynolds-averaged Navier–Stokes equations in the axisymmetric approximation written with account for the inverse effect of the bubbles on the average and fluctuating flow parameters. The influence of the gas volumetric flow rate ratio and the dimensions of the bubbles on the flow structure in a gas-liquid impinging jet is studied, In the presence of gas bubbles the liquid velocity is higher than the corresponding value in the single-phase flow. A considerable, more than twofold, anisotropy between the axial and radial turbulent fluctuations in the gas-liquid impinging jet is shown to exist. An addition of air bubbles leads to a considerable growth in the liquid velocity fluctuations in the two-phase flow (up to 50% compared with the single-fluid liquid impinging jet). An increase in the disperse phase dimensions leads to intensification of turbulence of the liquid.     

Dynamics of soluble gas bubbles

The problem of the mass, thermal and dynamic interaction between a bubble containing a soluble gas and a liquid is considered. It is shown that this problem can be reduced to the problem of the behavior of a vapor bubble with phase transitions investigated in detail in [1–3]. Expressions are obtained for the rate of decay of the radially symmetric oscillations of the bubbles due to the solubility of the gas in the liquid. The effective coefficients of mass transfer between the radially pulsating bubbles and the liquid are determined. A numerical solution is obtained for the problem of the radial motion of a bubble created by a sudden change of pressure in the liquid which, in particular, corresponds to the behavior of the bubbles behind the shock front when a shock wave enters a bubble screen.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 52–59, November–December, 1985.     

Dynamic film thickness between bubbles and wall in a narrow channel

The present paper describes a novel technique to characterize the behavior of the liquid film between gas bubbles and the wall in a narrow channel. The method is based on the electrical conductance. Two liquid film sensors are installed on both opposite walls in a narrow rectangular channel. The liquid film thickness underneath the gas bubbles is recorded by the first sensor, while the void fraction information is obtained by measuring the conductance between the pair of opposite sensors. Both measurements are taken on a large two-dimensional domain and with a high speed. This makes it possible to obtain the two-dimensional distribution of the dynamic liquid film between the bubbles and the wall. In this study, this method was applied to an air–water flow ranging from bubbly to churn regimes in the narrow channel with a gap width of 1.5 mm.     

气液两相流压力波传播速度研究

将双流体模型用于绝热无相的管道气液两相流,依据小扰动线化分析原理,导出了压力波波数Ｋ方程通过对不同空隙率下肉体上压力波小随角频率变化的计算,研究了虚拟质量力和狭义相间阻力对压力波波速及其人色散性的影响。对泡状流和弹状流压力波波速的计算结果与前人的测量结果作了比较,两者符合良好。