Liquid Velocity Field Research Articles

Interaction of a liquid flow around a micropillar with a gas jet

An experimental study was conducted to investigate two-phase flow characteristics resulting from gas jet injection into a 225 μm high by 1500 μm wide microchannel. The jet was injected from a 25 μm wide slit on the downstream side of a 150 μm diameter pillar. The liquid Reynolds number (Re = ρUD/μ) based on pillar diameter ranged from 100 to 700, and the average gas momentum coefficient (ρjetUjetAjet/ρmainUmainAref), defined as the ratio of gas momentum to liquid momentum, ranged from 1.6 × 10−5 to 3.368 × 10−1. Flow visualization, micro particle image velocimetry (μPIV), and micro particle tracing velocimetry (μPTV) were used to elucidate the two-phase flow patterns, liquid velocity field, and bubble dynamics. Two modes of gas jets were observed in which bubbles either formed and detached at the pillar or formed an attached ligament that sheared bubbles from its trailing edge. The modes were determined to be primarily Reynolds number dependent. Both modes were observed to positively affect turbulent kinetic energy in the microchannel. The momentum coefficient of the gas jet had the most significant effect at low Reynolds numbers, when bubble formation took place at the pillar.

Phase-field model of solid-liquid phase transition with density difference and latent heat in velocity and elastic fields

We present a phase-field model of solid-liquid transitions with inhomogeneous temperature in one-component systems, including hydrodynamics and elasticity. Our model can describe plastic deformations at large elastic strains. We use it to investigate the melting of a solid domain, accounting for the latent heat effect, where there appears a velocity field in liquid and an elastic field in solid. We present simulation results in two dimensions for three cases of melting. First, a solid domain is placed on a heated wall, which melts mostly near the solid-liquid-wall contact region. Second, a solid domain is suspended in a warmer liquid under shear flow, which rotates as a whole because of elasticity and melts gradually. Cooling of the surrounding liquid is accelerated by convection. Third, a solid rod is under high compression in liquid, where slips appear from the solid-liquid interface, leading to a plastic deformation. Subsequently, melting starts in the plastically deformed areas, eventually resulting in the fracture of the rod into pieces. In these phase-transition processes, the interface temperature is kept nearly equal to the coexisting temperature T(cs)(p) away from the heated wall, but this local equilibrium is not attained near the the contact region. We also examine a first-order liquid-liquid phase transition under heating from a boundary in one-component liquids.

Characterization of plunging liquid jets: A combined experimental and numerical investigation

This paper presents a combined experimental and numerical study of the flow characteristics of round vertical liquid jets plunging into a cylindrical liquid bath. The main objective of the experimental work consists in determining the plunging jet flow patterns, entrained air bubble sizes and the influence of the jet velocity and variations of jet falling lengths on the jet penetration depth. The instability of the jet influenced by the jet velocity and falling length is also probed. On the numerical side, two different approaches were used, namely the mixture model approach and interface-tracking approach using the level-set technique with the standard two-equation turbulence model. The numerical results are contrasted with the experimental data. Good agreements were found between experiments and the two modelling approaches on the jet penetration depth and entraining flow characteristics, with interface tracking rendering better predictions. However, visible differences are observed as to the jet instability, free surface deformation and subsequent air bubble entrainment, where interface tracking is seen to be more accurate. The CFD results support the notion that the jet with the higher flow rate thus more susceptible to surface instabilities, entrains more bubbles, reflecting in turn a smaller penetration depth as a result of momentum diffusion due to bubble concentration and generated fluctuations. The liquid average velocity field and air concentration under tank water surface were compared to existing semi-analytical correlations. Noticeable differences were revealed as to the maximum velocity at the jet centreline and associated bubble concentration. The mixture model predicts a higher velocity than the level-set and the theory at the early stage of jet penetration, due to a higher concentration of air that cannot rise to the surface and remain trapped around the jet head. The location of the maximum air content and the peak value of air holdup are also predicted differently.

Techniques of PIV in stratified two-phase headers

The stratification of two fluid phases, namely gas and liquid, within flow distribution devices, such as headers, that have side or bottom oriented fluid pipe connections, or discharges, has shown relevance to loss-of-coolant accidents in nuclear power plants. Under critical conditions the gas phase could entrain into the predominantly liquid discharge flow causing the fluid quality to be dramatically affected. This condition is referred to as the onset of gas entrainment (OGE) phenomenon and it occurs at a specific critical liquid height which changes with the Froude number. The liquid velocity field at the OGE is of importance, for example, to theorists who may find a semi-empirical approach to model this phenomenon. Stereoscopic particle image velocimetry (PIV) technique is an excellent candidate for non-intrusively investigating the velocity field. The liquid-phase velocity field was investigated for three discharge Froude numbers at the OGE. It was found that the stereoscopic PIV could be used to extract the velocity field experimentally, yet a high degree of error was found in the region closest to the discharge. The relative error was determined through conservation of mass by comparing the flow rate obtained with the PIV data to that obtained using a flow meter. In summary it was found that the number of image planes used, the resolution of the image planes, and consequently the number of vectors used to calculate the flow rate, all contributed a great deal to the relative error.

The effect of gas-injector location on bubble formation in liquid cross flow

Liquid flows incorporating small-size bubbles play a vital role in many industrial applications. In this work, an experimental investigation is conducted on bubble formation during gas injection from a microtube into the channel of a downward liquid cross flow. The tip of the air injector has been located at the wall (wall orifice) and also at several locations from the wall to channel centerline (nozzle injection). The size, shape, and velocity of the bubbles along with liquid velocity field are measured using a shadow-particle image velocimetry/particle tracking velocimetry system. The process of bubble formation for the wall orifice and the nozzle injection configurations is physically explained. The effect of variation in water and air flow rates on the observed phenomena is also investigated by considering water average velocities of 0.46, 0.65, and 0.83 m/s and also air average velocities of 1.32, 1.97, 2.63, and 3.29 m/s. It was observed that shifting the air injector tip toward the center of the channel resulted in the coalescence of some of the preliminary bubbles and the formation of larger bubbles termed secondary and multiple bubbles. Increase in air flow rate and reduction in water flow rate also intensify the rate of bubble coalescence. A correlation-based model is also suggested to overcome the shortcoming of the available models in the literature which are developed to only estimate the size of the preliminary bubbles. The model predicts the percent of the preliminary, secondary, and multiple bubbles along with the average size of secondary and multiple bubbles as a function of nozzle position within a cross flow.

Interaction between a cavitation bubble and shear flow

The deformation of a cavitation bubble in shear and extensional flows is studied numerically. The Navier–Stokes equations are solved to observe the three-dimensional behaviour of the bubble as it grows and collapses. During the collapse phase of the bubble, two re-entrant jets are observed on two sides of the bubble. The re-entrant jets are not the result of interaction with a solid wall or free surface; rather, they are formed due to interaction of the bubble with the background flow. Effects of the viscosity, surface tension and shear rate on the formation and strength of re-entrant jets are investigated. Re-entrant jets with enough strength break up the bubble into smaller bubbles. Post-processing and analysis of the results are done to cast the disturbance by the bubble on the liquid velocity field in terms of spherical harmonics. It is found that quadrupole moments are created in addition to the monopole source.

Advanced PIV/LIF and shadowgraphy system to visualize flow structure in two-phase bubbly flows

Particle image velocimetry (PIV) is a promising technique to measure dispersed phase size, dispersed phase hold-up and velocity of both the phases. The current work reports measurement of the shape, size, velocity and acceleration of bubbles using shadowgraphy, and liquid velocity measurement obtained using PIV/LIF with fluorescent tracer particles. Measurements were performed in a narrow rectangular column at moderate gas hold-up (∼5%) with wide variation of bubble sizes (0.1–15 mm). The liquid velocity field was subjected to 2D discrete wavelet transform (DWT) to visualize the flow structures in the bubbly flow. Further, the slip velocity of individual bubbles was obtained from the DWT filtered liquid velocity field. The results are compared with the slip velocity correlations reported in literature for single bubbles rising in quiescent water. The comparison shows the difference in slip velocity of single bubbles and bubbles rising in swarm. The scale wise decomposition obtained from DWT was also used to quantify the liquid velocity field in terms of wavenumber spectrum. The velocity and acceleration measurements are demonstrated on a single spherical cap bubble rising in quiescent water. The measurements show the potential of the 2D acceleration measurement to facilitate the estimation of unsteady drag on bubbles.

Three-dimensional two-phase flow model of proton exchange membrane fuel cell with parallel gas distributors

A non-isothermal, steady-state, three-dimensional (3D), two-phase, multicomponent transport model is developed for proton exchange membrane (PEM) fuel cell with parallel gas distributors. A key feature of this work is that a detailed membrane model is developed for the liquid water transport with a two-mode water transfer condition, accounting for the non-equilibrium humidification of membrane with the replacement of an equilibrium assumption. Another key feature is that water transport processes inside electrodes are coupled and the balance of water flux is insured between anode and cathode during the modeling. The model is validated by the comparison of predicted cell polarization curve with experimental data. The simulation is performed for water vapor concentration field of reactant gases, water content distribution in the membrane, liquid water velocity field and liquid water saturation distribution inside the cathode. The net water flux and net water transport coefficient values are obtained at different current densities in this work, which are seldom discussed in other modeling works. The temperature distribution inside the cell is also simulated by this model.

Responses of Taxus cuspidata to hydrodynamics in bubble column bioreactors with different sparging nozzle sizes

Studying bioreactor hydrodynamics under growth conditions holds great significance in the scale-up of plant cell cultures. In this study, a 3D Laser Doppler Anemometer (LDA) system was used to measure liquid velocity fields in bubble columns with different nozzle sizes, and their hydrodynamic stresses were calculated by liquid velocity fluctuation components. The magnitude of axial normal Reynolds stress was higher compared to other directions, varying from 2.0Pa to 7.2Pa. The maximum axial normal stress took place near the gas–liquid interface, followed by the sparger where bubbles form and the bulk flow area where bubbles rise, suggesting from a hydrodynamic perspective that cell damage occurs mainly at the gas–liquid interface. Reynolds stresses at the gas–liquid interface increased with decreasing nozzle size of distributor. Taxus cuspidata cultured in bubble columns with larger nozzle sizes showed better performance with respect to cell growth and viability, which matched well with hydrodynamics fluctuation in bubble columns with different nozzle sizes. The correlation of cellular response with hydrodynamics may be helpful in optimizing bioreactor design and scale-up of plant cell culture.

Uniform Flow in Bubble Columns

Uniform bubbly flow in a 15 cm bubble column is investigated. We use a special needle sparger consisting of 559 separate needles, uniformly distributed over the bottom. With this sparger, we can ensure that all bubbles generated are of the same size and that the bubble injection is very uniform over the entire bottom of the column. Detailed experiments are reported, using optical glass fibers to measure the local gas fraction and bubble size and velocity and using laser Doppler anemometry to measure the liquid axial velocity field. We find that the homogeneous flow regime extends up to a gas fraction of 55% well beyond the predictions of theory. The superficial gas velocity at which the homogeneous regime looses its stability depends on the water quality: fresh water looses its stability much earlier than old water. However, the gas fraction as a function of the superficial gas velocity is in the homogeneous regime independent of the water quality. The overall gas fraction can be described by a Richardson...

Local characteristics of hydrodynamics in draft tube airlift bioreactor

Airlift column reactors have been widely used in bioprocesses. The design, scale-up, and performance evaluation of such reactors all require extensive and accurate information about the gas–liquid flow dynamics, particularly as computational fluid dynamics (CFD) has become more popular in the last decade. However, due to the limitation of most conventional techniques for gas–liquid flow dynamics measurement, only global hydrodynamic parameters (e.g., cross-sectionally averaged liquid circulation velocity, overall gas holdup, and overall mass transfer rate) have been extensively studied. The local flow characteristics (e.g., the macro-mixing and the turbulence intensity) remain unclear. In this study, we use the computer automated radioactive particle tracking (CARPT) technique to investigate the details of the multiphase flow dynamics in a draft tube airlift bioreactor, such as the liquid velocity field, turbulent kinetic energy field, distributions of shear stresses, etc. The flow structures in the whole reactor, as well as the structure in individual regions, i.e., the top, the bottom, the riser, and the downcorner are also characterized. We found significantly large turbulent kinetic energy in the top and the bottom regions, with spots of very high shear stress, which were also found in the vicinity of the sparger. The results also suggest that the top and bottom clearances have significant effects on the flow structures, which may have substantial effects on the bioreactor performance.

Modeling of the microconvective contribution to wall heat transfer in subcooled boiling flow

In the present work, the two-phase turbulent boundary layer in subcooled boiling flow is investigated. The bubbles in the near-wall region have a significant effect on the dynamics of the underlying liquid flow, as well as on the heat transfer. The present work develops a single-fluid model capable of accounting for the interactions between the bubbles and the liquid phase, such that the two-phase convective contribution to the total wall heat transfer can be described appropriately even in the framework of single-fluid modeling. To this end, subcooled boiling channel flow was experimentally investigated using a laser-Doppler anemometer to gain insight into the bubble-laden near-wall velocity field. It was generally observed that the streamwise velocity component was considerably reduced compared to the single-phase case, while the near-wall turbulence was increased due to the presence of the bubbles. Since the experimentally observed characteristics of the liquid velocity field turned out to be very similar to turbulent flows along rough surfaces, it is proposed to model the near-wall effect of the bubbles on the liquid flow analogously to the effect of a surface roughness. Incorporating the proposed approach as a dynamic boundary condition into a well-established mechanistic flow boiling model makes it possible to reflect adequately the contribution of the microconvection to the total wall heat transfer. A comparison against the experimental data shows good agreement for the predicted wall shear stress as well as for the wall heat flux for a wide range of wall temperatures and Reynolds numbers.

静止水中を上昇する単一大気泡周囲液相流れ場への管内径の変化が及ぼす影響

The measuring method of the averaged liquid velocity fields around a large bubble rising in stagnant liquid in a vertical round pipe using Ultrasonic Velocity Profile monitor (UVP), which the authors have developed in the previous report, was applied to make clear the effect of pipe inner diameter, D, on the velocity field in this report. Two ultrasonic transducers inclined +20 degrees and -20 degrees from the horizontal line, respectively, were used for the measurement to get two dimensional velocity vectors. Three pipes of D = 32, 42 and 54mm were used in the measurement. According to the measured results, the velocity fields in the liquid phase above the large bubble, in the liquid film around the large bubble, and in the wake were presented and discussed, focusing especially on the effect of pipe inner diameter D.

Hydrodynamics of Taylor flow in noncircular capillaries

In this work, volume of fluid (VOF) technique, one computational fluid dynamics (CFD) method, was used to investigate the upward Taylor flow in vertical square and equi-triangular capillaries. For saving computation time, the simulations were carried out in a moving frame of reference attached to Taylor bubbles. The main flow parameters, involving bubble size and shape, liquid film thickness, velocity field and two-phase relative velocity, were studied as functions of capillary number. The numerical simulations were in good agreement with previous reports and showed that the flow in the sides and corners of polygonal capillaries were different. A comparative study was also conducted on Taylor flow in square and equi-triangular capillaries and their circular counterparts, where the influence of capillary geometry on the characteristics of Taylor flow was illustrated clearly.

Purely irrotational theories for the viscous effects on the oscillations of drops and bubbles

In this paper, we apply two purely irrotational theories of the motion of a viscous fluid, namely, viscous potential flow (VPF) and the dissipation method to the problem of the decay of waves on the surface of a sphere. We treat the problem of the decay of small disturbances on a viscous drop surrounded by gas of negligible density and viscosity and a bubble immersed in a viscous liquid. The instantaneous velocity field in the viscous liquid is assumed to be irrotational. In VPF, viscosity enters the problem through the viscous normal stress at the free surface. In the dissipation method, viscosity appears in the dissipation integral included in the mechanical energy equation. Comparisons of the eigenvalues from VPF and the dissipation approximation with those from the exact solution of the linearized governing equations are presented. The results show that the viscous irrotational theories exhibit most of the features of the wave dynamics described by the exact solution. In particular, VPF and DM give rise to a viscous correction for the frequency that determines the crossover from oscillatory to monotonically decaying waves. Good to reasonable quantitative agreement with the exact solution is also shown for certain ranges of modes and dimensionless viscosity: For large viscosity and short waves, VPF is a very good approximation to the exact solution. For ‘small’ viscosity and long waves, the dissipation method furnishes the best approximation.

Planar shadow image velocimetry for the analysis of the hydrodynamics in bubbly flows

In order to allow for more reliable modelling of microscale processes in turbulent bubbly flows, detailed experiments in a laboratory-scale double loop facility and a bubble column with a diameter of 140 mm were performed. The range of bubble mean diameters considered in the measurements was between 2 and 4 mm. The average gas volume fraction was in the range between 0.5 and 5% for different experiments. To allow simultaneous measurements of bubble size, bubble velocity and liquid velocity field, a combined system of planar shadow imaging, particle tracking velocimetry (PTV) and particle image velocimetry (PIV) for online measurements was developed and applied. The measurements of the liquid phase velocities were realized by seeding the flow with polyamide tracer particles having a mean diameter of 65 μm. A background illumination was established by using an array of 551 LEDs with a size of 160 mm by 100 mm. A double image CCD camera with macro optics was used to record the images of tracers and bubbles simultaneously. Because of the small depth of field of the macro camera optics (<4 mm for the bubbles), it was possible to discriminate between bubbles and tracer particles inside and outside the camera's focal plane using the gradient of grey values. A set of digital image filters was applied to perform phase discrimination between bubbles and tracer particles, i.e. to obtain separate double images for bubbles and tracer, respectively. The contour of in-focus bubbles was determined using an edge detecting Sobel filter and a spline interpolation technique. Thereby, the bubble size, shape and orientation could be derived. The bubble velocity was obtained by applying PTV and the continuous phase velocity field was determined by PIV, using a successive refinement of the interrogation area. By recording and evaluating at least 500 double images, it was possible to determine bubble size distributions and mean as well as fluctuating velocities for both phases. Thereby, detailed data on the hydrodynamics of bubble-driven flows are provided.

Finite Element Analysis of Sloshing in Rectangular Liquid-filled Tanks

The focus of the present paper is on the development of a finite element formulation to investigate the sloshing of liquids in partially filled rigid rectangular tanks undergoing base excitation. The liquid domain is discretized into two-dimensional four-node rectangular elements with the liquid velocity potential representing the nodal degrees of freedom. Liquid sloshing effects induced by both steady-state harmonic and arbitrary horizontal base excitation are investigated in terms of the slosh frequencies, liquid velocity field, free surface displacement and hydrodynamic forces acting on the tank walls. The model is employed to study the effects of inserting a bottom-mounted vertical rigid baffle, as well as side-mounted horizontal baffles that are wholly immersed in the liquid region, in an attempt to investigate their viability in acting as slosh suppression devices.

3D macrosegregation simulation with anisotropic remeshing

The article presents a three-dimensional coupled numerical solution of momentum, mass, energy and solute conservation equations, for binary alloy solidification. The interdendritic flow in the mushy zone is assumed to obey the Darcy's law. Microsegregation is governed by the lever rule, assuming local equilibrium at phase interfaces. The resulting energy and solute advection–diffusion equations are solved using the Streamline-Upwind/Petrov–Galerkin (SUPG) finite element method. A SUPG-PSPG velocity-pressure formulation is applied for the momentum equation. The full algorithm was implemented in the 3D code THERCAST, together with an anisotropic remeshing method. Two applications have been considered: a small ingot of Pb-48wt%Sn alloy and a large steel ingot. The numerical results of these two cases are presented with the evolution of temperature, liquid velocity, and solute concentration fields during solidification. To cite this article: S. Gouttebroze et al., C. R. Mecanique 335 (2007).

Short-term dynamics of a density interface following an impact

A tube filled with a perfectly wetting liquid falls axially under its own weight. In its gravity-free reference frame, the liquid interface is deformed by surface tension into a hemispherical shape. On impact of the tube on a rigid floor, the interface curvature reverses violently, forming a concentrated jet. If the contact angle at the tube wall is such that the interface is flat, the liquid rebounds as a whole with the tube, with no deformation. We analyse this phenomenon using an impulse pressure description, providing an exact description of the initial liquid velocity field at the impact, supported by high-speed image velocimetry measurements. This initial dynamics is insensitive to liquid surface tension and viscosity.

Magnetically stabilized bed reactor for selective hydrogenation of olefins in reformate with amorphous nickel alloy catalyst

A magnetically stabilized bed (MSB) reactor for selective hydrogenation of olefins in reformate was developed by combining the advantages of MSB and amorphous nickel alloy catalyst. The effects of operating conditions, such as temperature, pressure, liquid space velocity, hydrogen-to-oil ratio, and magnetic field intensity on the reaction were studied. A mathematical model of MSB reactor for hydrogenation of olefins in reformate was established. A reforming flow scheme with a post-hydrogenation MSB reactor was proposed. Finally, MSB hydrogenation was compared with clay treatment and conventional post-hydrogenation.