Heat and mass transfer characteristics of air bubbles and hot water by direct contact

 This paper has dealt with direct contact heat and mass transfer characteristics of air bubbles in a hot water layer. The experiments were carried out by bubbling air in the hot water layer under some experimental conditions of air flow rate, inlet air temperature and humidity as a dispersion fluid, and hot water temperature and hot water layer depth as a continuous fluid. Heat transfer and evaporation of water vapor from hot water to air bubbles occurred during air bubbles ascending into the hot water. Air bubble flow patterns were classified into three regions of independent air bubble flow, transition and air bubble combination growth. Non-dimensional correlation equations of direct contact heat and mass transfer between air bubbles and hot water were derived by some non- dimensional parameters for three regions of bubble flow pattern. Received on 14 July 2000 / Published online: 29 November 2001     

Flow in near-critical fluids induced by shock and expansion waves

Unsteady shock and expansion waves are proposed as means to produce flows near the liquid-vapor critical-point without imposing pressure gradients. By choosing appropriate initial conditions and wave speeds, near-critical post-wave conditions can be obtained. The post-shock conditions are shown to be stable with respect to perturbations in the pre-shock conditions. The initial conditions are sufficiently far from the critical-point to allow fast thermal equilibration, permitting the use of larger fluid volumes. Example calculations for the cases of an impulsively accelerated piston, of a shock tube, and of a Ludwieg-like tube are presented yielding flows up to 20 m/s in sulfur hexafluoride (SF₆), where the limit is due to the region of validity of the equation of state. The proposed setup also allows one to study shock wave propagation into near-critical fluids.Received: 13 August 2003, Revised: 7 October 2004, Published online: 4 February 2005[/PUBLISHED]PACS: 47.40.Nm, 47.50. + d, 47.55.Kf, 64.70.Fx, 64.60.HtCorrespondence to: S. Schlamp     

Effects of Bubbles on the Hydraulic Conductivity of Porous Materials – Theoretical Results

In a porous material, both the pressure drop across a bubble and its speed are nonlinear functions of the fluid velocity. Nonlinear dynamics of bubbles in turn affect the macroscopic hydraulic conductivity, and thus the fluid velocity. We treat a porous medium as a network of tubes and combine critical path analysis with pore-scale results to predict the effects of bubble dynamics on the macroscopic hydraulic conductivity and bubble density. Critical path analysis uses percolation theory to find the dominant (approximately) one-dimensional flow paths. We find that in steady state, along percolating pathways, bubble density decreases with increasing fluid velocity, and bubble density is thus smallest in the smallest (critical) tubes. We find that the hydraulic conductivity increases monotonically with increasing capillary number up to Ca 10^–2, but may decrease for larger capillary numbers due to the relative decrease of bubble density in the critical pores. We also identify processes that can provide a positive feedback between bubble density and fluid flow along the critical paths. The feedback amplifies statistical fluctuations in the density of bubbles, producing fluctuations in the hydraulic conductivity.     

Image analysis applied to study on frictional-drag reduction by electrolytic microbubbles in a turbulent channel flow

We investigate frictional-drag reduction with electrolytic microbubbles based on image measurement of a turbulent flow in a water channel at Re = 4800 (based on the half channel height). Microbubbles with a diameter ranging 30–200 μm can reduce frictional drag by as much as 30% relative to single-phase flow even at low void fractions (α ≈ 3 × 10⁻⁴); however, drag reduction is only effective within a limited downstream distance from an electrode array. Arrangement of the optical system allows us to measure the bubble-production rate by water electrolysis from images near the wall and to trace the motion of bubbles. We also measure velocity fields using particle-tracking velocimetry based on a shallow depth-of-field approach by segregating tracer particles from microbubbles. Vertically oscillating microbubbles likely represent interaction with vortical structures near the wall, and bubbles approaching the wall appear to induce negative streamwise velocity relative to the surrounding fluid. We relate the wall friction with the double integral of the Reynolds-stress profile and show that its variation due to microbubbles decreases the drag on the wall. Microbubbles tend to coalesce downstream resulting in a fewer bubbles but with greater size; accordingly, the oscillatory motion diminishes, and the frictional drag rather increases.     

Experimental investigation of water laminar mixed-convection flow with sub-millimeter bubbles in a vertical channel

This paper describes flow and heat transfer characteristics of laminar mixed-convection flows of water with sub-millimeter bubbles in a vertical channel. We use thermocouples and a particle tracking velocimetry technique for the temperature and velocity measurements. The working fluid used is tap water, and hydrogen bubbles generated by electrolysis of the water are used as the sub-millimeter bubbles. The Reynolds number of the main flow ranges from 100 to 200. The ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection (the heat transfer coefficient ratio) ranges from 1.24 to 1.38. The heat transfer coefficient ratio decreases with the increase in the Reynolds number. We conclude from velocity measurements that this decrease is mainly caused by a decrease in the advection effect due to sub-millimeter bubbles.     

Transient deformation of an inviscid inclusion in a viscoelastic extensional flow

The transient deformation of a bubble in a viscoelastic extentional flow is analyzed by means of a finite element algorithm for viscoelastic moving boundary problems. Using the Oldroyd-B constitutive model, we find that bubbles in a viscoelastic fluid deform to the same steady-state configurations as bubbles in a Newtonian fluid at equal values of the far-field extensional stresses (corresponding to different stretch rates). Vapor bubbles in a developed extensional flow collapse more readily in the viscoelastic liquid than bubbles in Newtonian fluids because of the large compressive stresses associated with the viscoelastic liquid.     

On the interaction of Taylor bubbles rising in two-phase co-current slug flow in vertical columns: turbulent wakes

An experimental study on the interaction between Taylor bubbles rising through a co-current flowing liquid in a vertical tube with 32 mm of internal diameter is reported. The flow pattern in the bubble's wake was turbulent and the flow regime in the liquid slug was either turbulent or laminar. When the flow regime in the liquid slug is turbulent (i) the minimum distance between bubbles above which there is no interaction is 5D-6D; (ii) the bubble's rising velocity is in excellent agreement with the Nicklin relation; (iii) the experimental values of the bubble length compare well with theoretical predictions (Barnea 1990); (iv) the distance between consecutive bubbles varied from 13D to 16D and is insensitive to the liquid Reynolds number. When the flow regime in the liquid slug is laminar (i) the wake length is about 5D-6D; (ii) the minimum distance between bubbles above which there is no interaction is higher than 25D; (iii) the bubble's rising velocity is significantly smaller than theoretical predictions. These results were explained in the light of the findings of Pinto et al. (1998) on coalescence of two Taylor bubbles rising through a co-current liquid. Received: 2 February 2000 / Accepted: 15 March 2001     

Kinetic model for the motion of compressible bubbles in a perfect fluid

Collective behavior of compressible gas bubbles moving in an inviscid incompressible fluid is studied. A kinetic approach is employed, based on an approximate calculation of the fluid flow potential and formulation of Hamilton's equations for generalized coordinates and momenta of bubbles. Kinetic equations governing the evolution of a distribution function of bubbles are derived. These equations are similar to Vlasov's equations. Conservation laws which are direct consequences of the kinetic system are found. It is shown that for a narrowly peaked distribution function they form a closed system of hydrodynamical equations for the mean flow parameters. The system yields the analogue of Rayleigh–Lamb's equation governing oscillations of bubbles. A variational principle for the hydrodynamical system is established and the linear stability analysis is performed.     

Analysis of matching conditions at the boundary surface of a fluid-saturated porous solid and a bulk fluid: the use of Lagrange multipliers

The compatibility conditions matching macroscopic mechanical fields at the contact surface between a fluid-saturated porous solid and an adjacent bulk fluid are considered. The general form of balance equations at that discontinuity surface are analyzed to obtain the compatibility conditions for the tangent and normal components of the velocity and the stress vector fields. Considerations are based on the procedure similar to that used in the phenomenological thermodynamics for derivation of constitutive relations, where the entropy inequality and the concept of Lagrange multipliers are applied. This procedure made possible to derive the compatibility conditions for the viscous fluid flowing tangentially and perpendicularly to the boundary surface of the porous solid and to formulate the generalized form of the so called slip condition for the fluid velocity field, postulated earlier by Beavers and Joseph, J. Fluid. Mech. 30, 197–207 (1967). PACS 47.55.Mh Communicated by Y.D. Shikhmurzaev     

Effect of weak compressibility of a fluid on bubble-bubble interaction in strong acoustic fields

The effect of weak compressibility of a fluid on the interaction between spherical bubbles in a strong acoustic field is considered. A small parameter ɛ which represents the ratio of the characteristic velocity of radial oscillations of the bubbles to the speed of sound in the fluid is used as a parameter characterizing the fluid compressibility. The equations governing the interaction between two bubbles are derived with an accuracy O(ɛ) in the case in which the ratio of the characteristic velocities of their translational and radial motions is of the order of ɛ. It is shown that neglecting the fluid compressibility effect due to the bubble interaction can lead to either enhancement or attenuation of their radial oscillations following the main compression stage, variation in the oscillation frequency, the bubble approach velocity, and the velocity of the spatial motion of the coupled pair, and the bubble approach and collision rather than their moving away from one another with the formation of a coupled pair.     

Flow around individual Taylor bubbles rising in stagnant polyacrylamide (PAA) solutions

The flow around single Taylor bubbles rising in stagnant non-Newtonian solutions of polyacrylamide (PAA) polymer was studied using a technique employing simultaneous particle image velocimetry (PIV) and shadowgraphy. Solutions with different weight percentages of polymer, varying from 0.01 to 0.80 wt.%, were used to cover a wide range of flow regimes. The rheological fluid properties and pipe dimension yielded Reynolds numbers between 2 and 1160, and Deborah numbers up to 115. The shape of the bubbles rising in the different solutions was compared and quantified by fitting correlations. The flow around the nose of the bubbles was found to be similar for all conditions studied. Velocity profiles were measured and analysed in the liquid film around the bubbles. A comparison of bubble wake flow patterns was made. For the 0.10 and 0.20 wt.% PAA solutions, long wakes with a recirculation region were observed. Below the wakes, a flow of stretched liquid was found. Negative wakes were also observed for the more concentrated solutions.     

Computational study of steady streaming from oscillating microbubbles with uniform and wavy wall motions

Steady streaming flow fields of a 5 μm bubble oscillating with uniform radial wall motion and a 500 μm bubble oscillating with wavy wall motion were simulated using a computational fluid dynamics method that incorporated fluid–structure interactions. The steady streaming flow fields for both bubbles were calculated, and they exhibited upward jet flow with two symmetrical counter-rotating vortices. The maximum streaming velocity ranged from a few to tens of millimeters per second. The simulated flow fields were compared with the theory and experimental measurements using particle image velocimetry. The simulation results agreed well with the theoretical and experimental data. Therefore, the proposed computational method would provide a useful tool to predict steady streaming flow fields of oscillating bubbles.     

Dye-bubble interactions in an open channel flow

An innovative technique has been developed to visualize the effect that a localized surface reaction has in an open channel flow field. The working fluid is hexanoic acid mixed with mineral oil, and it flows over an aluminum plate embedded with sodium metal. Hexanoic acid and sodium metal react to form hydrogen gas and hexanoic salt. The hydrogen gas forms bubbles that rise to the surface and are convected downstream by the fluid. The rising bubbles induce the formation of counter-rotating vortices that straddle the reaction site. Bubble entrainment stretches and bends the dye filaments, and buoyancy transports the bubbles away from the reaction. The products of the reaction introduce velocity fluctuations into an otherwise laminar flow, inducing what has been described by some researchers as pseudoturbulence. Downstream of the reaction, far away from the disturbances caused by the buoyant bubbles, the velocity fluctuations dampen out and the flow relaminarizes.     

Observations of vortex breakdown in an open cylindrical container with a rotating bottom

A laser induced fluorescent dye technique was used to visualize the steady-state flow driven by a rotating bottom in an open, cylindrical container. The flow behaviour and the vortex breakdown conditions were studied as a function of the container aspect ratio H/R and the Reynolds number Re = R ²/v. Like in the closed container configuration, previously studied by Vogel (1968) and Escudier (1984), vortex breakdown occurs in a certain parameter range (H/R, Re). However, in the free surface configuration vortex breakdown conditions as well as the forms of the breakdown bubbles differ notably from what is observed in the closed container configuration. In particular, it is found that as Re is increased, the breakdown bubbles get attached to the free surface and grow in diameter.     

Quasi-static bubble in a yield stress fluid: elasto-plastic model

The influence of the yield stress of Carbopol® gel dispersions on the behaviour of quasi-static bubbles was investigated. Many fluids, from many different industrial fields, have yield stress behaviour. Most of them contain gas bubbles. To study bubble behaviour in such suspensions, a transparent model fluid (dispersion of Carbopol® in water) was used. The experimental device allowed to quasi-statically increase bubble internal pressure with small pressure step to reach a maximum target internal pressure and the pressure setpoint was inverted to return to the initial pressure. Hysterical behaviour of the bubbles was highlighted as they did not regain their initial shape because of yield stress. We show that the rheological behaviour is related to the internal pressure, bubble geometry and yield stress in quasi-static conditions. A modification of the Laplace law depending on the yield stress of the fluid and bubble sphericity was proposed and validated.     

Dynamics of microbubble oscillators with delay coupling

Two vibrating bubbles submerged in a fluid influence each others’ dynamics via sound waves in the fluid. Due to finite sound speed, there is a delay between one bubble’s oscillation and the other’s. This scenario is treated in the context of coupled nonlinear oscillators with a delay coupling term. It has previously been shown that with sufficient time delay, a supercritical Hopf bifurcation may occur for motions in which the two bubbles are in phase. In this work, we further examine the bifurcation structure of the coupled microbubble equations, including analyzing the sequence of Hopf bifurcations that occur as the time delay increases, as well as the stability of this motion for initial conditions which lie off the in-phase manifold. We show that in fact the synchronized, oscillating state resulting from a supercritical Hopf is attracting for such general initial conditions.     

An analysis of the structure of laminar separation bubbles in swept infinite geometries

The influence of sweep on the general structure of short separation bubbles in strictly laminar flow fields on swept infinite geometries is investigated by theoretical analysis and direct numerical simulations (DNS). In this situation the ‘independence principle’ of the Navier–Stokes equations for incompressible flow enforces a unique topology for the mean flow, which includes the much better understood unswept separation bubbles as a special case: swept laminar separation bubbles form leading edge parallel streamtubes with a spanwise outflow and a helical motion inside directed parallel to the separation line. If chordwise inflow conditions are kept constant, their cross-sections stay independent of a rising sweep angle, as the spanwise velocity field is then merely superimposed over the unchanged flow of the corresponding unswept case. Their mean flow field follows strict scaling rules that may be derived analytically from the generic 45°-solution, as confirmed by DNS-results for a series of pressure-induced separation bubbles subjected to a systematic variation of the sweep angle between 0° and 60°.     

Mass transfer during gas absorption in a vertical gas-liquid slug flow with small bubbles in liquid plugs

A model is developed for the analysis of mass transfer during isothermal absorption in a vertical gas-liquid slug flow at large Reynolds numbers with liquid plugs containing small bubbles. Simple formulas for mass flux from the N-th unit cell of gas-liquid slug flow and for total mass flux from N unit cells are derived. In the limiting case the derived formulas for mass transfer during gas absorption in a slug flow with liquid plugs containing small bubbles recover the derived expressions for mass transfer in slug flow without small bubbles in the liquid plugs. Using the developed model recommendations concerning the design of the absorber operating in a slug flow regime are suggested. Received on 28 July 1997     

Subsonic and transonic flow field in two-dimensional de laval nozzles

This paper presents solutions of subsonic and transonic flow fields in two-dimensional De Laval nozzles with preassinged contraction ration ₁, expansion ration ₂, and throat wall radiusR _*. The effects of the contraction and the expansion angle on nozzle flow, the transformation of flow pattern of a De Laval nozzle in the throat region, and the conditions of occurrence and the governing parameters of the supersonic bubbles are discussed.