Lift force acting on single bubbles in linear shear flows

Lift coefficients, C_L, of single bubbles in linear shear flows are measured to investigate effects of the bubble shape, the liquid velocity gradient and the fluid property on C_L. The range of the Morton number, M, tested is from logM = − 6.6 to − 3.2. The shapes of bubbles are spherical and ellipsoidal. A correlation of bubble aspect ratio for single bubbles in infinite stagnant liquids proposed in our previous study can give good evaluations for bubbles in the linear shear flows. The C_L of spherical bubbles at low bubble Reynolds numbers, Re, depend on the dimensionless shear rate Sr and Re and decrease with increasing Re. These characteristics agree with the Legendre-Magnaudet correlation. The use of a single dimensionless group such as Re, the Eötvös number, the Weber number and the Capillary number cannot correlate C_L of non-spherical bubbles. The trend of the critical Re for the reversal of the sign of C_L is the same as that for the onset of oscillation of bubble motion, which supports the mechanism proposed by Adoua et al., at least within the range of −6.6 ≤ logM ≤ −3.2. An experimental database of C_L is provided for validation of available C_L models and CFD.     

Turbulent time and length scale measurements in high-velocity open channel flows

In high-velocity open channel flows, the measurements of air–water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air–water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8E+5 to 7.1E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air–water depth Y ₉₀. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95–0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.     

Analytical and experimental investigations of the pulsed air–water jet

This paper describes a new way of generating pulsed air–water jet by entraining and mixing air into the cavity of a pulsed water jet nozzle. Based on the theory of hydro-acoustics and fluid dynamics, a theoretical model which describes the frequency characteristic of the pulsed air–water jet is outlined aimed at gaining a better understanding of this nozzle for generating pulses. The calculated result indicates that as the air hold-up increases, the jet oscillation frequency has an abrupt decrease firstly, and then reaches a minimum gradually at α (air hold-up)=0.5, finally it gets increased slightly. Furthermore, a vibration test was conducted to validate the present theoretical result. By this way, the jet oscillation frequency can be obtained by analyzing the vibration acceleration of the equal strength beam affected by the jet impinging. Thereby, it is found that the experimental result shows similar trend with the prediction of the present model. Also, the relationship between vibration acceleration and cavity length for the pulsed water jet follows a similar tendency in accord with the pulsed air–water jet, i.e. there exists a maximum for each curve and the maximum occurs at the ratio of L/d₁ (the ratio of cavity length and upstream nozzle diameter) =2.5 and 2.2, respectively. In addition, experimental results on specimens impinged by the pulsed water jet and pulsed air–water jet show that the erosion depth increases slightly with air addition within a certain range of cavity length. Further, this behavior is very close to the vibration test results. As for erosion volume, the air entrained into the cavity significantly affects the material removal rate.     

Full-scale two-phase flow measurements on Athena research vessel

Measurements of gas volume fraction, bubble velocity, chord length and bubble size distributions were performed on the research vessel Athena II operating in Saint Andrew Bay in the gulf coast near Panama City, FL. Double tipped sapphire optical local phase-detection probes were used to acquire indicator functions downstream of the breaking bow wave, behind the masker and at the stern. These indicator functions were also taken at different depths, operating speeds and headings respect to the waves. The data processing includes the computation of velocity of individual bubbles and chord lengths, resulting in chord length distributions. These chord length distributions are used to obtain bubble size distributions using a novel procedure described in detail herein. Uncertainty analysis is performed for gas volume fraction, average bubble velocity and chord length. The results indicate that air entrainment increases with ship speed and sailing against the waves at all positions. The bow wave exhibits unsteady breaking that creates bubble clouds, which were characterized and identified by signal processing. At the stern a very strong dependence of bubble size with depth was found, with evidence that small bubbles (smaller than 500 μm) are transported through the bottom of the hull and reach the transom. The roller present at the transom, the associated strong unsteadiness and bubble entrainment are well captured, as indicated by the stern results, showing the frothy nature of the upper layer.     

气泡夹带对壁面油膜流动特性的影响

油-气润滑系统工作过程中,润滑油膜受微油滴冲击和压缩空气扰动影响易形成气泡夹带现象,气泡夹带行为将对壁面润滑油膜层的形成及流动过程产生重要影响。基于VOF数值模拟方法,对含气泡油膜沿倾斜壁面的流动行为进行研究,考察了气泡的存在对油膜形态和流动速度的影响规律,以及气泡破裂阶段空腔邻域内流体压力变化特性。研究表明,油膜夹带气泡的形变和迁移诱发气泡周围微流场的速度扰动现象,导致气液界面处产生非均匀速度梯度分布,进而引发油膜表面的形态波动。气泡发生破裂时,油膜空穴部位发生明显的正负压力波动现象,气泡附近壁面将承受一定的交变载荷作用。     

Turbulence,dynamic similarity and scale effects in high-velocity free-surface flows above a stepped chute

In high-velocity free-surface flows, air entrainment is common through the interface, and intense interactions take place between turbulent structures and entrained bubbles. Two-phase flow properties were measured herein in high-velocity open channel flows above a stepped chute. Detailed turbulence measurements were conducted in a large-size facility, and a comparative analysis was applied to test the validity of the Froude and Reynolds similarities. The results showed consistently that the Froude similitude was not satisfied using a 2:1 geometric scaling ratio. Lesser number of entrained bubbles and comparatively greater bubble sizes were observed at the smaller Reynolds numbers, as well as lower turbulence levels and larger turbulent length and time scales. The results implied that small-size models did underestimate the rate of energy dissipation and the aeration efficiency of prototype stepped spillways for similar flow conditions. Similarly a Reynolds similitude was tested. The results showed also some significant scale effects. However a number of self-similar relationships remained invariant under changes of scale and confirmed the analysis of Chanson and Carosi (Exp Fluids 42:385-401, 2007). The finding is significant because self-similarity may provide a picture general enough to be used to characterise the air–water flow field in large prototype channels.     

The Effect of Bubbly Oil on the THD Lubrication of Tilting-pad Journal Bearings Subjected to Rotating Unbalance Load

Little work has been published on the contribution of entrained air and/or gas bubbles on the lubricant viscosity and hence on the hydrodynamic performance of bearings. In this work, a thermo-hydrodynamic analysis of the performance of dynamically loaded tilting-pad journal bearing lubricated by bubbly oil is carried out. The non-steady Reynolds equation for compressible fluid and the energy equation are solved iteratively using finite difference method to study the effect of air bubbles on the bearing performance characteristics. The effect of bubbles content on the lubricant viscosity is considered.The results showed that the value of maximum pressure slightly increases with increasing the bubble ratio up to 0.2, while the film thickness deteriorates at very high bubble content. The pressure peak moves in the downstream direction with the increase of bubble ratio ₁, which would be of great importance in deciding the pivot location in tilting-pad bearings.     

Simulating air entrainment and vortex dynamics in a hydraulic jump

The air entrainment characteristics of three separate Froude number hydraulic jumps are investigated numerically using an unsteady RANS, realizable k–ε turbulence model, with a Volume of Fluid treatment for the free surface. Mean velocity profiles, average void fraction, and Sauter mean diameter compare favorably with experimental data reported in literature. In all simulations, time-averaged void fraction profiles show good agreement with experimental values in the turbulent shear layer and an accurate representation of interfacial aeration at the free surface. Sauter mean diameter is well represented in the shear layer, and free surface entrainment results indicate bubble size remains relatively unchanged throughout the depth of the jump. Several different grid resolutions are tested in the simulations. Significant improvements in void fraction and bubble size comparison are seen when the diameter to grid size ratio of the largest bubbles in the shear layer surpasses eight. A three-dimensional simulation is carried out for one Froude number jump, showing an improvement in the prediction of entrained air and bubble size compared with two-dimensional results at a substantial increase in computation time. An analysis of three-dimensional vorticity shows a complex interaction between spanwise and streamwise vortical structures and entrained air bubbles. The jump is similar to a turbulent mixing layer, constrained by the free surface, with vortex pairing and subsequent fluctuations in free surface elevation. Downstream fluctuations of the toe are associated with a roll up of the primary spanwise vortex, fluctuations of the free surface, and counter-rotating streamwise vortex pairs. The action of these flow structures is likely responsible for the improvement in three-dimensional results.     

Experimental assessment of scale effects affecting two-phase flow properties in hydraulic jumps

A hydraulic jump is the rapid transition from a supercritical to subcritical free-surface flow. It is characterised by strong turbulence and air bubble entrainment. New air–water flow properties were measured in hydraulic jumps with partially developed inflow conditions. The data set together with the earlier data of Chanson (Air bubble entrainment in hydraulic jumps. Similitude and scale effects, 119 p, 2006) yielded similar experiments conducted with identical inflow Froude numbers Fr ₁ = 5 and 8.5, but Reynolds numbers between 24,000 and 98,000. The comparative results showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. The present comparative analysis demonstrated quantitatively that dynamic similarity of two-phase flows in hydraulic jumps cannot be achieved with a Froude similitude. In experimental facilities with Reynolds numbers up to 10⁵, some viscous scale effects were observed in terms of the rate of entrained air and air–water interfacial area.     

Air transport in chute flows

The air bubble rise velocity in still water depends mainly on the bubble size and is basically influenced by buoyancy, viscosity and surface tension. In high-speed flows the number of forces acting on air bubbles increases with turbulence, non-hydrostatic pressure gradient, shear forces, bubble clouds and free-surface entrainment. Air bubbles in these flows are used for cavitation protection of hydraulic structures such as chutes, spillways and bottom outlets. Here, air is normally added by means of aerators upstream of regions where the cavitation number falls below a critical value mainly to reduce the sonic velocity of the fluid and cushion the cavitation bubble collapse process. The distance between successive aerators depends basically on the bubble rise velocity. Until today, the bubble rise velocity in high-speed flows was not thoroughly investigated because of limited laboratory instrumentation. The present project focused on the streamwise development of air concentrations in high-speed flows along a 14 m long model chute. The bubble rise velocity was indirectly derived from the air detrainment gradient of the air concentration contour lines downstream of an aeration device. It accounts for the main hydraulic parameters chute slope, Froude number and air concentration. It is demonstrated that the bubble rise velocity in high-speed flow and stagnant water differ significantly due to fracturing processes, turbulence, and the ambient air concentration.     

Characterisation of gas-liquid two-phase flow in minichannels with co-flowing fluid injection inside the channel,part II: gas bubble and liquid slug lengths,film thickness,and void fraction within Taylor flow

Current research proofs the potential of apparatuses containing minichannel flow structures to intensify gas-liquid-solid contacting processes. The excellent heat and mass transfer in these devices as well as a sharp RTD mainly result from the Taylor flow regime. A proper design of corresponding contactors requires precise information on the provided interfacial areas. However, the characterisation of gas-liquid Taylor flow with industrially relevant fluids at elevated pressure and created by capillary injection devices gained little attention so far.This work analyses adiabatic gas-liquid Taylor flow in a square minichannel of 1.0 mm hydraulic diameter using water, water-glycerol, or water-ethanol mixtures as liquid phase and hydrogen or nitrogen as gas phase to cover a broad range of material parameters. In the mixing zone located within the flow channel, gas was injected into the co-flowing liquid by so-called capillary injectors with variable inner diameter (0.184, 0.317, 0.490 mm).Two different bubble forming mechanisms were identified leading to a complex interaction between physical properties of the fluids, geometrical parameters and the observed gas bubble and liquid slug lengths. According to the Pi-theorem, these lengths were affected by 6 dimensionless groups, namely (u_G,s/ u_L,s), Re_L, We_L, (d_In,CI/ d_h), (d_Ou,CI / d_h), and Θ^*. Based on more than 370 experimental data, novel correlations to predict gas bubble and liquid slug lengths were developed.     

Development of self-aeration process for supercritical chute flows

When a high-velocity flow discharges into a chute, air is entrained through the free surface. This is relevant to the development of self-aeration for mixture flow. In this study, the air concentration was measured in the self-aerated developing region for various initial flow velocities, depths, and chute slopes. The effect of hydraulic conditions on the bottom self-aeration process was analyzed. Increasing the initial flow velocity and depth was found to increase the rate of air diffusion into the water flow. This positive correlation indicates that flow turbulence is a key factor for the self-aeration development process. The Reynolds number of the flow was found to be an appropriate hydraulic condition for describing self-aeration development. In addition, the constraint of buoyancy on air bubble diffusion into the chute bottom decreased as the chute slope was increased, which made the development process for bottom self-aeration more pronounced. A new empirical equation is presented for predicting the development process of bottom self-aeration in open channel flows.     

Dynamics of a Taylor bubble in steady and pulsatile co-current flow of Newtonian and shear-thinning liquids in a vertical tube

A computational analysis is carried out to ascertain the effects of steady and pulsatile co-current flow, on the dynamics of an air bubble rising in a vertical tube containing water or a solution of Carboxymethylcellulose (CMC) in water. The mass fraction (m_f) of CMC in the solution is varied in the range 0.1% ⩽ m_f ⩽ 1% to accommodate zero-shear dynamic viscosities in the range 0.009–2.99 Pa-s. It was found that the transient and time-averaged velocities of Taylor bubbles are independent of the bubble size under both steady as well as pulsatile co-current flows. The lengths of the Taylor bubbles under the Newtonian conditions are found to be consistently greater than the corresponding shear-thinning non-Newtonian conditions for any given zero-shear dynamic viscosity of the liquid. In contrast to observations in stagnant liquid columns, an increase in the dynamic viscosity of the liquid (under Newtonian conditions) results in a concomitant increase in the bubble velocity, for any given co-current liquid velocity. In shear-thinning liquids, the change in the bubble velocity with an increase in m_f is found to be relatively greater at higher co-current liquid velocities. During pulsatile shear-thinning flows, distinct ripples are observed to occur on the bubble surface at higher values of m_f, the locations of which remain stationary with reference to the tube for any given pulsatile flow frequency, while the bubble propagated upwards. In such a pulsatile shear-thinning flow, a localised increase in dynamic viscosity is accompanied near each ripple, which results in a localised re-circulation region inside the bubble, unlike a single re-circulation region that occurs in Newtonian liquids, or shear-thinning liquids with low values of m_f. It is also seen that as compared to frequency, the amplitude of pulsatile flow has a greater influence on the oscillating characteristics of the rising Taylor bubble. The amplitude of oscillation in the bubble velocity increases with an increase in the CMC mass fraction, for any given value of pulsatile flow amplitude.     

Bubble formation in co-fed gas–liquid flows in a rotor-stator spinning disc reactor

The gas–liquid flow in a rotor-stator spinning disc reactor, with co-feeding of gas and liquid, is studied for high gas volumetric throughflow rates and high gas/liquid volumetric flow ratios. High speed imaging and spectral analysis of pressure drop signals are employed to analyse the flow. Two mechanisms of bubble formation are observed, one due to gas overpressure leading to large irregular bubbles, and one due to liquid turbulent vortices leading to small, well-defined bubbles. The two mechanisms lead to three distinct gas dispersion regimes, distinguished by their characteristic oscillations in pressure drop. At low rotational Reynolds numbers (Re_ω < 0.4 · 10⁶), in the gas spillover regime, the gas is dispersed as large bubbles only. Above this critical Re_ω, small bubbles are sheared off as well, thus forming a heterogeneous dispersion. At sufficiently high Re_ω, depending on the gas flow rate, the gas is homogeneously dispersed as small bubbles. The maximum gas flow that can be dispersed as small bubbles is linearly proportional to the local energy dissipation rate. The understanding of the bubble formation mechanisms and pressure signature allows prediction and detection of the prevailing hydrodynamic regime in scaled up spinning disc reactors and for different reaction fluids.     

Turbulence measurements in the bubbly flow region of hydraulic jumps

A hydraulic jump is characterized by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air–water flow measurements were performed in a large-size facility using two types of phase-detection intrusive probes: i.e. single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent integral time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of Chanson [H. Chanson, Bubbly flow structure in hydraulic jump, Eur. J. Mech. B/Fluids 26 (3) (2007) 367–384], providing the turbulent scales of the eddy structures advecting the air bubbles in the developing shear layer. The length scale L_xz is an integral air–water turbulence length scale which characterized the transverse size of the large vortical structures advecting the air bubbles. The experimental data showed that the dimensionless integral turbulent length scale L_xz/d₁ was closely related to the inflow depth: i.e. L_xz/d₁ = 0.2–0.8, with L_xz increasing towards the free-surface.     

Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers

The transition from supercritical to subcritical open channel flow is characterised by a strong dissipative mechanism called a hydraulic jump. A hydraulic jump is turbulent and associated with the development of large-scale turbulence and air entrainment. In the present study, some new physical experiments were conducted to characterise the bubbly flow region of hydraulic jumps with relatively small Froude numbers (2.4 < Fr₁ < 5.1) and relatively large Reynolds numbers (6.6 × 10⁴ < Re < 1.3 × 10⁵). The shape of the time-averaged free-surface profiles was well defined and the longitudinal profiles were in agreement with visual observations. The turbulent free-surface fluctuation profiles exhibited a peak of maximum intensity in the first half of the hydraulic jump roller, and the fluctuations exhibited some characteristic frequencies typically below 3 Hz. The air–water flow properties showed two characteristic regions: the shear layer region in the lower part of the flow and an upper free-surface region above. The air–water shear layer region was characterised by local maxima in terms of void fraction and bubble count rate. Other air–water flow characteristics were documented including the distributions of interfacial velocity and turbulence intensity. The probability distribution functions (PDF) of bubble chord time showed that the bubble chord times exhibited a broad spectrum, with a majority of bubble chord times between 0.5 and 2 ms. An analysis of the longitudinal air–water structure highlighted a significant proportion of bubbles travelling within a cluster structure.     

Convective transport of air bubbles in strong hydraulic jumps

A hydraulic jump is a flow singularity characterised by a significant amount of air entrainment in the shear zone. The air is entrapped at the jump toe that is a discontinuity between the impinging flow and the roller. The impingement point is a source of air bubbles, as well as a source of vorticity. Herein the convective transport of air bubbles in the jump roller is re-visited. Some analytical extension is presented and the theoretical results are compared with some laboratory experiments conducted in a large-size facility operating at large Froude numbers. The turbulent air bubble mixing coefficient was found to increase linearly with increasing distance and be independent of the Froude and Reynolds numbers. Overall the study highlighted some seminal features of the air–water shear layer in hydraulic jumps with large Froude numbers (5.1 < Fr₁ < 11.2). The air bubble entrainment in the mixing zone was a convective transport process, although there was some rapid flow de-aeration for all Froude numbers.     

Characteristic lengths and maximum entropy estimation from probe signals in the ellipsoidal bubble regime

The bubble size, surface and volume distributions in two and three phase flows are essential to determine energy and mass transfer processes. The traditional approaches commonly use a conditional probability density function of chord-lengths to calculate the bubble size distribution, when the bubble size, shape and velocity are known. However, the approach used in this paper obtains the above distributions from statistical relations, requiring only the moments inferred from the measurements given by a sampling probe. Using image analysis of bubbles injected in a water tank, and placing an ideal probe on the image, a sample of bubble diameter, shape factor and velocity angle are obtained. The samples of the bubble chord-length are synthetically generated from these variables. Thus, we propose a semi-parametric approach based on the maximum entropy (MaxEnt) distribution estimation subjected to a number of moment constraints avoiding the use of the complex backward transformation. Therefore, the method allows us to obtain the distributions in close form. The probability density functions of the most important length scales (D, D₂₀, D₃₀, D₃₂), obtained applying the semi-parametric approach proposed here in the ellipsoidal bubble regime, are compared with experimental measurements.     

Air–water flow characteristics in high-velocity free-surface flows with 50% void fraction

High-velocity free-surface flows are complex two-phase flows and limited information is available about the interactions between air and water for void fractions of about 50%. Herein a detailed experimental study was conducted in the intermediate flow region (C ∼ 50%) on a stepped spillway and the microscopic air–water flow characteristics were investigated. The results showed differences in water and droplet chord times with comparatively larger number of air chord times (0–2 ms), and larger number of water chord times (2–6 ms). A monotonic decrease of particle chord modes was observed with increasing bubble count rates. Several characteristic time scales were identified based upon inter-particle arrival time analyses of characteristic chord time classes as well as spectral analyses of the instantaneous void fraction signal. Chord times of 3–5 ms appeared to be characteristic time scales of the intermediate flow region having similar time scales compared to the local correlation and integral turbulent time scales and to time scales associated with bubble break-up and turbulent velocity fluctuations. A further characteristic time scale of 100 ms was identified in a frequency analysis of instantaneous void fraction. This time scale was of the same order of magnitude as free-surface auto-correlation time scales suggesting that the air–water flow structure was affected by the free-surface fluctuations.