Bubble–wall interaction and two-phase flow parameters on a full-scale boat boundary layer

Full scale bubbly flow experiments were performed on a 6 m flat bottom survey boat, measuring the void fraction, bubble velocity and size distributions as the bubbles naturally entrained at the bow of the boat interact with the boat’s boundary layer. Double-tip sapphire optical probes capable of measuring bubbles down to 50 μm in diameter were specifically designed and built for this experiment. The probes were positioned under the hull at the bow near the bubble entrainment region and at the stern at the exit of the bottom flat plate. Motorized positioners were used to vary the probe distance to the wall from 0 to 50 mm. The experiments were performed in fresh water (Coralville Lake, IA) and salt water (Panama City Beach, FL), at varying velocities with most data analysis performed at 10, 14 and 18 knots. The results indicate that the bubbles interact significantly with the boundary layer. At low velocity in fresh water, bubble accumulation under the hull and coalescence are evident by the presence of large bubbles at the stern. At high speeds bubble breakup dominates and very small bubbles are produced near the wall. It is also observed that salt water inhibits coalescence, even at low boat speeds. The void fraction increases with speed beyond 10 knots and peaks near the wall. Bubble velocities show slip with the wall at all speeds and exhibit large RMS fluctuations, increasing near the wall.     

Bubble size distribution prediction for large-scale ship flows: Model evaluation and numerical issues

Prediction of the bubble size distribution in the wake of a ship is important to analyze its acoustic signature. To achieve CFD simulation of dynamic ships with moving control surfaces and rotating propellers in waves, a robust implementation is paramount. In this work a mass conserving multigroup discretization strategy of the Boltzmann transport equation for polydispersed bubbly flows is presented, as well as an analysis of available breakup and coalescence models. Modifications of the discrete equations for the fixed pivot method at the boundaries are introduced that guarantee exact bubble mass conservation. The role of the time stepping scheme in the conservation of mass and number of bubbles is discussed. Though the conservation properties of the discrete system of equations are satisfied provided they are solved exactly, in practice an iterative procedure must be used since the ODE’s are non-linear. Three iterative schemes are proposed and they are analyzed in terms of robustness and efficiency. Breakup, coalescence and dissolution models are analyzed from the numerical point of view. Available models of breakup and coalescence are studied finding appropriate choices for ship applications. Other models are appropriate as well, but are more costly numerically. As appropriate for ship applications, an extension to the model of Prince and Blanch for salt water is proposed and analyzed. The final model is tested against experimental data and computations by other researchers, and convergence properties in bubble size discretization is studied. It is found that for salt water the final steady state is dependent on the initial condition since there is a range of sizes for which coalescence and breakup are both negligible.     

Numerical study of bubble rise and interaction in a viscous liquid

In this article, the flow instabilities during the rise of a single bubble in a narrow vertical tube are studied using a transient two-dimensional/axisymmetric model. To predict the shape of the bubble deformation, the Navier-Stokes equations in addition to an advection equation for liquid volume fraction are solved. A modified volume-of-fluid technique based on Youngs' algorithm is used to track the bubble deformation. To validate the model, the results of simulations for terminal rise velocity and bubble shape are compared with those of the experiments. The effect of different parameters such as initial bubble radius, channel height, liquid viscosity and surface tension on the shape and rise velocity of the bubble is investigated.     

The structure of water-air bubble grid turbulence in a square duct

Local measurements of void fraction and continuous phase velocity field in water-air bubble, grid turbulence were conducted in a channel of vertical, square test section. The measured statistics indicate that, due mainly to the interaction of mean shear with the dispersed phase, the turbulence structure of the flow is modified. The observed change is characterized by a strong spatial dependence of void fraction and liquid flow properties, and the emergence of two spatial regions controlled by different physical processes. Intensity measurements indicate significant departure from isotropy in the flow. Two distinct regimes corresponding to low and high values of void fraction have been also identified. The autocorrelation and spectra measurements indicate that for low void fraction the scales of turbulence decrease while for higher values of void fraction increase again and inverse cascade is observed.     

Bubble collapse in solid-liquid two-phase fluid

Equations of motion for bubble collapse in solid-liquid two-phase fluid have been derived, in which the resistance coupling effects between the liquid and solid particles have been considered. The motion of particles during the bubble collapse and the effects of particles on bubble collapse have been calculated and discussed. Qualitative relations between the concentration and the size of the particles and the rate of bubble collapse have been obtained. Institute of Water Conservancy and Hydroelectric Power Research     

水气两相流中稀疏气泡流动速度场的数字图像测量初探

由空压机提供的气体通过—排微小直径的喷嘴进入静止水体，形成水气两相流流场。在单相PIV和PTV技术的基础上，研究稀疏气液两相流情况下气泡的速度场分布。PIV算法采用快速傅立叶互相关分析法，而PTV算法需要获得每幅图像中每个气泡的形心，根据连续图像中的粒子对，计算速度。用PIV和PTV两种算法处理求出气泡的速度并对两种方法进行比较，其最终研究成果可应用于流体及多相流的流量测技术，提高我们进行低密度气液两相流相关研究的测量水平。同时为水气两相流的数值分析和理论研究提供流场测试的数据。     

Bouncing and Coalescence of Bubble Pairs Rising at High Reynolds Number in Pure Water or Aqueous Surfactant Solutions

The encounter of bubble pairs of O(1 mm) in both pure water and aqueous surfactant solutions was studied experimentally. In pure water, two equally sized bubbles were found to coalesce if the Weber number, W = V² R/, based on the velocity of approach, V, was below a critical value, W_cr = 0.18, where and are the density and surface tension of the liquid respectively and R the equivalent radius of the bubbles. After coalescence bubbles perform volume and shape oscillations.When W_cr is exceeded, bubbles bounce. After bouncing, bubbles can either coalesce or separate without coalescing. This was found to depend on the Weber number, based on the rise velocity U, We = U² R/. If this number was below a critical value, bubbles coalesced after bouncing. The relative motion of the bubbles was found to be damped out by acoustic damping due to surface oscillations rather then by viscosity.If We was above a critical value, which was close to that for path instability of a single bubble (We = 3.3), the bubbles separated after bouncing. This is probably caused by shedding of vortices which dominate the relative motion of the bubbles. This mechanism may cause bubbles in bubbly flows not aggregating in horizontal planes, as was found in calculations based on potential flow theory. For modelling bubbly flows it will therefore be essential to incorporate the influence of vorticity.When surfactants are added to the water it was found that bubbles are prevented to coalesce above a critical concentration, which is nearly identical to that of single rising bubbles. Above this critical concentration, bubbles behave as rigid spheres and trajectories cannot be predicted by potential flow theory.     

The interaction of background ocean air bubbles with a surface ship

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.     

Effects of coalescence and breakup on the steady-state morphology of an immiscible polymer blend in shear flow

The steady-state morphology of an immiscible polymer blend in shear flow has been investigated by optical microscopy techniques. The blend is composed by poly-isobutylene (PIB) and poly-dimethylsiloxane (PDMS) of comparable viscosity. Experiments were performed by means of a home-made transparent parallel plate device. The two plates can be independently counterrotated, so that sheared droplets of the dispersed phase can be kept fixed with respect to the microscope point of view, and observed for long times. The distribution of drops and their average size were measured directly during flow at different shear rates and for different blend compositions. It was found that the average drop size in steady-state conditions is a decreasing function of the applied shear rate, and does not depend on blend composition for volume fractions up to 10%. Experiments have proved that, in the shear rate range which could be investigated, the stationary morphology is controlled only by coalescence phenomena, droplet breakup playing no role in determining the size of the dispersed phase. More generally, it has been shown that the steady-state morphology is a function not only of the physical parameters of the blend and of the shear rate, but also of the initial conditions applied to the blend. The steady-state results reported in this paper constitute the first direct experimental confirmation of theoretical models which describe the mechanisms of shear-induced drop coalescence.     

气液两相流中气泡运动速度场的PIV分析与研究

粒子图像测速技术（PIV）作为一种无扰、瞬态、全场速度测量方法，已被广泛应用于液体或气体的单相流流速场测定。对于两相流PIV技术，目前还处于起步阶段，本文应用PIV技术的基本原理，对静止液体中的气泡运动速度进行了分析，并对有关气液两相流测量问题进行了探讨。     

Numerical simulation of bubble breakup phenomena in a narrow flow field

Based on the boundary integral method, a 3D bubble breakup model in a narrow flow field is established, and a corresponding computation program is developed to simulate the symmetrical and asymmetrical bubble breakup. The calculated results are compared with the experimental results and agree with them very well, indicating that the numerical model is valid. Based on the basic behavior of bubbles in a narrow flow field, the symmetrical and asymmetrical bubble breakup is studied systematically using the developed program. A feasibility rule of 3D bubble breakup is presented. The dynamics of sub-bubbles after splitting is studied. The influences of characteristic parameters on bubble breakup and sub-bubble dynamics are analyzed.     

An experimental investigation of outflow of liquids from single-outlet vessels

This paper considers the outflow of a liquid from a single outlet vessel, i.e. a vessel in which the outflowing liquid is displaced by another fluid which enters the vessel through the same opening. The simplest possible arrangement is investigated: a sealed axisymmetric cylindrical vessel with an outlet in its base, in which water is displaced by air.

It is shown experimentally that the average liquid discharge velocity is independent of the liquid level in the vessel and the shape of the outlet for the range of outlets employed; it increases weakly with both the diameter of the vessel and the diameter of the outlet.     

Some Aspects of the Lift Force on a Spherical Bubble

Several situations in which a spherical bubble experiences a lift force are examined, especially through the use of computational results obtained by solving the full Navier–Stokes equations. The lift force is computed over a wide range of Reynolds number for the case of pure shear flow, pure strain and solid body rotation. Using these results, the validity of asymptotic solutions derived in the limit of low Reynolds number or inviscid flow is discussed. A general expression of the lift force valid for low to moderate shears is proposed. It is shown that for such shears, the lift force in a complex flow can be predicted by superposing the results obtained in pure strain flow and solid body rotation flow. Finally, the interaction force experienced by two bubbles rising side-by-side is studied. The computational results reveal that, at variance with the predictions of potential theory, the sign of this force changes when the Reynolds number or the separation distance between the bubbles decreases below a critical value. All these results are discussed in terms of vorticity. The respective role played by the vorticity generated at the bubble surface and by the one that is eventually present in the unperturbed flow is emphasized.     

A non-dualistic unified field theory of gravitation,electromagnetism and spin

The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrödinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-M) theory needs to be geometrized. The crux of the matter is, however not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrödinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Tonnelat. By allowing the metric formds ²=g dx ^v x ^v and the non-degenerate two-formF=(1/2> _l) dx ^vdx ^vto enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an external gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.     

A first order relaxation model for the prediction of the local interfacial area density in two-phase flows

Many energy production and chemical processes involve vapor/liquid two-phase flows. Mass and energy are often exchanged between the vapor and the liquid phases, and the fluid mechanics of the two-phase system is strongly influenced by the exchange of momentum between each phase. Significantly, the transport of mass, energy and momentum between the phases takes place across interfaces. Therefore the interfacial area density (i.e. the interfacial area per unit volume) has to be accurately known in order to make reliable predictions of the interfacial transfers. Indeed, the interfacial area density must be known for both steady and transient two-phase flows. It is the purpose of this paper to present a first order relaxation model which is derived from the Boltzmann transport equation, and which accurately describes the evolution of interfacial area density for bubbly flows. In particular, the local, instantaneous interfacial area densities and volume fractions are predicted for vertical flow of a vapor/liquid bubbly flow involving both bubble clusters and individual bubbles.     

Pressure waves in a tube filled with a bubbly mixture with a nonuniform cross-sectional bubble distribution

The evolution of pressure waves in a tube filled with a gas-liquid medium with a stepped cross-sectional bubble distribution is investigated. The calculations are compared with experimental data. It is shown that in the case of a nonuniform bubble distribution, due to the appearance of transverse flows, the pressure pulse is damped faster than for a uniform distribution. The interaction of pressure waves with a bubble cluster in a tube filled with liquid is also analyzed.     

Bubble dynamics and interactions with a pair of micro pillars in tandem

This study investigates flow patterns and bubble dynamics of two-phase flow around two 100 μm diameter circular pillars in tandem, which were entrenched inside a horizontal micro channel. Bubble velocity, trajectory, size, and void fraction were measured using a high speed camera and analyzed using a particle tracking velocimetry method. A range of gas and liquid superficial velocities were tested, resulting in different bubbly flow patterns, which were consistent with previous studies. These flow patterns were altered as they interacted with the pillars. Depending on the relative transverse location of bubbles to the pillars, and through bubble–bubble interaction, the flow sometimes returned to its original state. It was also determined that the pillars altered both the bubble trajectory and void fraction, especially in the pillars region.     

A New Approach in Modeling Phase Distribution in Fully Developed Bubbly Pipe Flow

Turbulent two-phase flow equations are derived and solved for fully developed pipe flow using a composite eddy-viscosity model and a new void-fraction equation. The void fraction profile is first specified from experiments and the velocity field is calculated to validate the eddy-viscosity model. Consequently, a new equation is presented for calculation of the void fraction. This void-fraction equation incorporates the gradient of turbulent normal stresses in the radial direction, the conventional lift force, and a contribution from the unsteady drag force. The implications of this new equation, for the bubbly flow regime, are investigated by calculating the void-fraction distribution for a given velocity field. Inclusion of the normal turbulent stresses in the radial direction is shown to simulate correctly the experimentally observed trends of the phase distribution, both for upward and downward bubbly flow, without the need for a fictitious term such as the so called ``lubrication force'. This revised version was published online in July 2006 with corrections to the Cover Date.