Liquid Velocity Field Research Articles

Nonlinear corrections to the oscillation mode frequencies of an ideal liquid charged jet

An analytical asymptotic expression is derived for the time evolution of an ideal incompressible conducting liquid jet with a uniformly charged surface that moves with a constant velocity along the symmetry axis of an undisturbed cylindrical surface. The expression is obtained in the third order of smallness in jet oscillation amplitude under the conditions when the initial deformation of the equilibrium jet surface is specified by one (axisymmetric or nonaxisymmetric) mode. Analytical expressions are also found for the positions of internal nonlinear degenerate three-and four-mode resonances, which are typical of nonlinear corrections to the equilibrium shape of the jet, liquid velocity field potential in the jet, and electrostatic field near the jet, and also for a nonlinear frequency correction. It is established that the nonlinear oscillations of the jet take place about a surface depending on the type of initial (generally asymmetric) deformation rather than about the equilibrium cylindrical shape.

Fluid Flow in A Four-strand Bloom Continuous Casting Tundish with Different Flow Modifiers

Fluid flows in a four-strand tundish for bloom continuous casting have been investigated with physical modeling and mathematical simulation methods. The liquid steel flow velocity fields in the former tundish and the optimal one with a turbulence inhibitor and newly-designed baffles were numerically calculated and the flow characteristics in the two cases and other tundish configurations were measured in the physical modeling. The results in the physical modeling experiments showed that large difference in the Residence Time Distribution (RTD) curves of two outlets in one side of the former configuration tundish existed. It was found from the numerical calculation of the velocity fields in the tundishes that with the former tundish configuration velocities and turbulent degree of the liquid steel flow in the impact zone of the tundish were large due to the high velocities of liquid steel from the long shroud of the ladle, which caused in lining corrosion and slag entrapment due to the surface eddies. Asymmetric velocity field in the tundish with the former baffles formed and short circuit flow existed in one side of the four-strand tundish. For the optimal configuration of the tundish with a turbulence inhibitor and newly-designed baffles, very similar RTD curves of the two outlets in the same side of the tundish were achieved. The velocities and turbulent degree in the impacting zone of the tundish were depressed and quiet and symmetric molten steel flow was obtained. Eddies on surface and short circuit flow in the optimal tundish disappeared. Such improvement of liquid steel flow in the tundish would increase the ability of inclusion removal. Turbulence inhibitors should be used with other well-designed flow control devices for effective improvement to fluid flow characteristics in tundishes.

Motion of a magnetic flow follower in two‐phase flow — application to the study of airlift reactor hydrodynamics

AbstractA low‐cost and simple magnetic particle tracer method was adapted to characterize the hydrodynamic behavior of an internal‐ and an external‐loop airlift reactor (ALR). The residence time distribution of three magnetic particles differing in diameter (5.5, 11.0 and 21.2 mm) and with a density very close to that of water was measured in individual reactor sections. The measured data were analyzed and used to determine the velocity of the liquid phase. Validation of the experimental results for liquid velocity was done by means of the data obtained by an independent reference method. Furthermore, analysis of the differences found in the settling velocity of the particle in single‐liquid and gas‐liquid phases was carried out, using a simplified 3D momentum transfer model. The model considering particle‐bubble interaction forces resulting from changes in the liquid velocity field due to bubble motion was able to predict satisfactorily the increase in the particle settling velocity in the homogeneous bubbly regime. The effective drag coefficient in two‐phase flow was found to be directly dependent on particle Reynolds number to the power of − 2 but independent of gas flow‐rate for all particle diameters studied. Based on the experimental and theoretical investigations, the valid exact formulation of the effective buoyancy force necessary for the calculation of the correct particle settling velocity in two‐phase flow was done. In addition, recommendations concerning the use of flow‐following particles in internal‐loop ALRs for liquid velocity measurements are presented. Copyright © 2006 Society of Chemical Industry

Comprehensive experimental investigation of the hydrodynamics of large-scale, 3D, oscillating bubble plumes

An extensive study of the most important hydrodynamic characteristics of fairly large-scale bubble plumes was conducted using several measurement techniques and a variety of tools to analyze the data. Particle image velocimetry (PIV), double-tip optical probes (OP) and photographic techniques were extensively applied to measure bubble and liquid velocities, void-fraction and bubble sizes. PIV measurements in a vertical plane crossing the centre of the injector provided the instantaneous velocity fields for both phases, as well as hydrodynamic parameters, such as the movement of the axis of the plume and its instantaneous shape. Statistical studies were performed using image processing to determine the distribution of the apparent instantaneous plume diameter and centreline position. An important finding was that there is little instantaneous spreading of the bubble plume core; the spreading of the time-averaged plume width (as measured from the time-averaged void-fraction and time-averaged liquid velocity fields) is largely due to plume meandering and oscillations. The liquid-phase stress tensor distributions obtained from the instantaneous velocity data indicate that, for the continuous phase, these stresses scale linearly with the local void-fraction in the range of 0.5% < α < 2.5%. The bubbles were found to be ellipsoidal, with shape factor e ≈ 0.5.

A hybrid method for bubble geometry reconstruction in two-phase microchannels

Understanding bubble dynamics is critical to the design and optimization of two-phase microchannel heat sinks. This paper presents a hybrid experimental and computational methodology that reconstructs the three-dimensional bubble geometry, as well as provides other critical information associated with nucleating bubbles in microchannels. Rectangular cross-section silicon microchannels with hydraulic diameters less than 200 lm were fabricated with integrated heaters for the flow experiments, and the working liquid used was wa- ter. Bubbles formed via heterogeneous nucleation and were observed to grow from the silicon side walls of the channels. Two-dimensional images and two-component liquid velocity field measurements during bubble growth were obtained using micron-resolution particle image velocimetry (lPIV). These measurements were combined with iterative three-dimensional numerical simulations using finite element software, FEMLAB. The three- dimensional shape and location of the bubble were quantified by identifying the geometry that provided the best match between the computed flow field and the lPIV data. The reconstructed flow field through this process reproduced the experimental data within an er- ror of 10-20%. Other important information such as contact angles and bubble growth rates can also be estimated from this methodology. This work is an important step toward understanding the physical mechanisms behind bubble growth and departure.

Atomization by jet impact

The formation and fragmentation of liquid sheets resulting from the oblique collision of two identical cylindrical jets is investigated. The liquid expands radially from the impacting point forming a sheet in the form of a bay leaf bounded by a thicker rim. The sheet shape, rim size and liquid velocity field are quantified and represented analytically. External harmonic perturbations of the injection conditions reveal the nature of the rim destabilization and of its coupling with the sheet. Flow perturbations in the incident jets lead to sheet thickness modulations which trigger the fragmentation of the rim via the formation of liquid ligaments whose dynamics is described. The breakup of these ligaments induce both the shape and width of the drop size distribution in the spray formed by this process.

Simulations of the kettle reboiler shell side thermal-hydraulics with different two-phase flow models

A computational fluid dynamics approach is presented for the simulation and analyses of the kettle reboiler shell side thermal-hydraulics with two different models of two-phase flow – the mixture and two fluid model. The mixture model is based on solving one momentum equation for two-phase mixture flow and a closure law for the calculation of the slip between gas and liquid phase velocities. In the two fluid modeling approach the momentum balance is formed for each phase, while the gas-liquid interaction due to momentum exchange at the interface surface is predicted with an empirical correlation for the interface friction coefficient. In both approaches the two-phase flow is observed as two inter-penetrating continua. The models are solved for the two-dimensional geometry of the kettle reboiler shell side vertical cross section. The computational fluid dynamics numerical method based on the SIMPLE type algorithm is applied. The results of both liquid and vapor velocity fields and void fraction are presented for each modeling approach. The calculated void fraction distributions are compared with available experimental data. The differences in the modeling approaches and obtained results are discussed. The main finding is that the void fraction distribution and two-phase flow field strongly depends on the modeling of the slip between liquid and gas phase velocity in mixture model or on the interface friction model in two fluid model. The better agreement of the numerically predicted void fraction with the experimental data is obtained with the two fluid model and an interfacial friction model developed for the conditions of two-phase flows in large volumes of kettle reboilers or different designs of steam generators.

Measurement of Averaged Liquid Velocity Field around Large Bubbles Using UVP

An Ultrasonic Velocity Profile monitor (UVP) measurement was performed to measure the averaged liquid velocity field in front of, around and behind the large bubble rising in stagnant water in a round pipe of inner diameter D=54 mm in order to obtain fundamental information for the gas liquid two-phase slug flows. Two ultrasonic transducers were used for the measurement to get velocity vectors. The measured results are presented and compared with some existing studies on the corresponding phenomena. In the liquid film near the bubble nose, velocity profiles are presented and compared with existing studies. The different of D may affect some features. The parameter z/D is found more dominant than z for this phenomenon. In the liquid phase behind the bubble tail or the wake region, a large ring vortex is recognized. The effect of bubble length on the vortex is also discussed. The upward velocity at the pipe axis agrees well the predicted results by an existing prediction.

Measurement of Averaged Liquid Velocity Field around Large Bubbles Rising in Stagnant Water in Round Pipe Using UVP

An ultrasonic velocity profile monitor (UVP) measurement was performed to measure the average liquid velocity field around a large bubble rising in stagnant water in a round pipe of inner diameter D=54mm in order to obtain fundamental information for gas-liquid two-phase slug flows. Two ultrasonic transducers were set at different directions to obtain velocity vectors. The measured results are presented and compared with the results of some previous studies on the corresponding phenomena. In the liquid film near the bubble nose, the difference in bubble length does not affect the acceleration. The parameter z/D is more dominant than z itself, particularly when z/D is less than unity. In the wake region, a large ring vortex is recognized. The upward velocity at the pipe axis agrees well with previously predicted results. The effect of bubble length on the vortex length is also discussed.

Effect of Interfacial Velocity Fluctuations on the Enhancement of the Mass-Transfer Process in Falling-Film Flow

To investigate the relationship between surface instability and mass-transport behavior, a laser Doppler anemometer (LDA) system was used to measure the liquid velocity components in a falling film, even very close to the liquid surface. The experimental results show that the presence of countercurrent gas flow tends to reduce and flatten the liquid velocity in the surface region and that the maximum liquid velocity might occur at some distance from the interface. The fluctuating liquid velocity field shows a maximum at a position of 0.8−1.0 in the dimensionless liquid film thickness, and a fluctuation frequency is obtained. Interfacial mass transport in a falling film is strongly dependent on interfacial small-scale convection. The experimental mass-transfer rates are larger than those predicted by penetration theory. The enhanced liquid Sherwood number, ShL, was calculated, and the predicted values were found to be in agreement with the experimental data.

Estimation of the liquid velocity field in two-phase flows using inverse analysis and particle tracking velocimetry

In bubbly two-phase flow, the gas phase and liquid phase have different flow fields. The relative velocity of the two phases depends on the motion characteristic of the bubbles. The mathematical expression for the motion of a small bubble at low Reynolds number is already established. Using the equation, the liquid velocity along the trajectory of the bubble is calculated inversely using the motion equation. Whole field liquid flow structure is also estimated using a spatial and/or temporal interpolation method. This paper proposes an algorithm for estimating the liquid phase flow field from measurement data on bubble motion. In order to verify this principle, Taylor–Green vortex flow and Karman vortex shedding from a square cylinder have been chosen. The results reveal that by combining the inverse analysis and PTV with the spatio-temporal post-processing algorithm one can reconstruct well the carrier phase flow of the gas–liquid two-phase flow.

Effect of the microscale wall topography on the thermocapillary convection within a heated liquid film

Thin films, which are frequently used for cooling of electronic devices and other components, can be ruptured by thermocapillarity leading to appearance of uncontrolled dry patches that significantly reduce the heat and mass transfer characteristics. Microstructured wall surfaces often improve the performance of such devices. However, the effect of the wall microstructure on the heated film dynamics has not been studied to date. When the temperature of the wall differs from that of ambient gas, the presence of a wall microstructure leads to a temperature gradient along the liquid–gas interface. This is a result of the film thickness inhomogeneity resulting from the microstructure. Thus, a thermocapillary convection develops even in the undisturbed state. In the present paper, the thermocapillary film flow on a horizontal microstructured wall is studied in the framework of the long-wave theory and numerically using the volume of fluid method. The predictions of the liquid velocity fields from the above two methods are compared. It is found that the flow is characterized by a steady roll motion. The gas–liquid interface is found to deform in such a way, that the liquid tends to accumulate within the groove. A film stability analysis is also performed. It is found that the wall microstructure destabilizes the film.

Influence of the lift force on the stability of a bubble column

This work investigates the role of the lift force for the stability of a homogeneous bubble column. Instabilities caused by the lift force may be one important reason for the transition from homogeneous to heterogeneous bubble column. On rising bubbles the lift force acts in a lateral direction, when gradients of the liquid velocity are present. Non-uniform liquid velocity fields may be induced if the gas fraction is not equally distributed, e.g. caused by local disturbances. This feedback mechanism is studied in the paper. It was found, that a positive lift coefficient (small bubbles) stabilizes the flow, while a negative coefficient (large bubbles) leads to unstable gas fraction distributions, and thus it favours the appearance of a heterogeneous bubble column regime. The turbulent dispersion force has always a stabilizing action, i.e., it partially compensates the destabilization induced by a negative lift coefficient. A stability analysis for a mono-dispersed system nevertheless showed, that influence of the lift force is much larger, compared to the influence of the turbulent dispersion force, if only bubble induced turbulence is considered. Thus, the stability condition is practically the positive sign of the lift force coefficient. The extension of the analysis to two bubbles classes, from which one being small enough to have a positive lift coefficient, results in a minimum fraction of small bubbles needed for stability. Finally a generalized criterion for N bubble classes and for a continuous bubble size distribution is given.

Application of high frame-rate neutron radiography to liquid-metal two-phase flow research

Liquid metal two-phase flows in metallic vessels were studied by using high frame-rate neutron radiography. Both a bubble column and a gas-lift loop arrangement have been considered. Liquid velocity field of two-phase flow in a flat bubble column with rectangular cross-section was measured precisely by the particle tracking velocimetry. In a gas-lift loop, simultaneous measurements of void fraction by using high frame-rate neutron radiography and four-sensor probe were also performed to observe the bubble-probe interaction. Asymmetric Abel inversion was applied to compare the radial void fraction profiles. Measured radial void fraction profiles obtained by neutron radiography and electrical conductivity probe agreed well with each other. From these measurements, the measurement error and basic characteristics of gas–liquid metal two-phase flow were clarified.

Nonlinear analytical asymptotic investigation of oscillations of nonaxisymmetric modes of a charged jet of an ideal liquid

A jet of an ideal incompressible conducting liquid with a uniformly charged surface is considered. The jet moves at a constant velocity along the symmetry axis of its unperturbed cylindrical surface. An analytical expression for the jet shape is derived as a function of time for the excitation of nonaxisymmetric modes at the initial instant. The solution is found in the second order of smallness with respect to the amplitude of capillary oscillations of the jet. In the same approximation, the liquid velocity field in the jet and the distribution of the electric field in the jet region are determined. Second-order corrections to the analytical expressions for the jet shape and potentials of the liquid velocity field in the jet and the electrostatic field around the jet have resonant forms determined by the conditions of their interaction with the solutions of the first order of smallness.

CFD Analysis of Electric Submersible Pumps (ESP) Handling Two-Phase Mixtures

The behavior of electric submersible pumps (ESP) handling two-phase flow is a subject of primary concern, especially in the petroleum industry, where significant amounts of free gas may be found in oil wells production. In the past, several attempts were made to predict the performance of such kind of pumps, nevertheless, limited success has been achieved due to the complex flow dynamics inside the impeller. Geometry, gas void fraction (GVF) and suction pressure seem to be the main parameters affecting ESP performance. Furthermore, the higher the GVF of the mixture is, the higher the degradation of head that is experienced by the pump. So far, this complex phenomenon has not been well understood. In the present work, a two fluid model is used in three-dimensional (3D) CFD simulations to obtain the pressure, liquid and gas velocity fields as well as the GVF distribution inside an ESP impeller of known geometry; using flow rates, bubble diameter and GVF at the suction as independent variables and an incompressible fluid hypothesis. The gas pocket in the impeller blade reported by other researchers is obtained and comparison with experimental results shows good agreement. The obtained variables from the simulations are the cornerstone that allows the prediction of the performance curve of the pump for different GVF and such, lets the head degradation of the pump be estimated.

Velocity field measurement in gas–liquid metal two-phase flow with use of PIV and neutron radiography techniques

To establish reasonable safety concepts for the realization of commercial liquid-metal fast breeder reactors, it is indispensable to demonstrate that the release of excessive energy due to re-criticality of molten core could be prevented even if a severe core damage accident took place. Two-phase flow due to the boiling of fuel-steel mixture in the molten core pool has a larger liquid-to-gas density ratio and higher surface tension in comparison with those of ordinary two-phase flows such as air–water flow. In this study, to investigate the effect of the recirculation flow on the bubble behavior, visualization and measurement of nitrogen gas-molten lead bismuth in a rectangular tank was performed by using neutron radiography and particle image velocimetry techniques. Measured flow parameters include flow regime, two-dimensional void distribution, and liquid velocity field in the tank. The present technique is applicable to the measurement of velocity fields and void fraction, and the basic characteristics of gas–liquid metal two-phase mixture were clarified.

Velocity field measurement in gas?liquid metal two-phase flow with use of PIV and neutron radiography techniques

To establish reasonable safety concepts for the realization of commercial liquid-metal fast breeder reactors, it is indispensable to demonstrate that the release of excessive energy due to re-criticality of molten core could be prevented even if a severe core damage accident took place. Two-phase flow due to the boiling of fuel-steel mixture in the molten core pool has a larger liquid-to-gas density ratio and higher surface tension in comparison with those of ordinary two-phase flows such as air–water flow. In this study, to investigate the effect of the recirculation flow on the bubble behavior, visualization and measurement of nitrogen gas-molten lead bismuth in a rectangular tank was performed by using neutron radiography and particle image velocimetry techniques. Measured flow parameters include flow regime, two-dimensional void distribution, and liquid velocity field in the tank. The present technique is applicable to the measurement of velocity fields and void fraction, and the basic characteristics of gas–liquid metal two-phase mixture were clarified.

Dispersion And Coalescence Of Two Pulses OfSpherical Solid Particles Dropped SuccessivelyInto An Initially Quiescent Liquid

The penetration, dispersion and eventual coalescence of two pulses of monosized spherical solid particles dropped successively into an initially quiescent. fluid is examined numerically. Solid particle motion is modelled via a Eulerian Eulerian, multiphase, finite volume approach, within a cylindrical geometry. Flow of the solid and liquid phases is coupled numerically and inter-particle interactions are modelled using a solids pressure expression. The dispersion of single and double pulses of micron sized spherical particles were undertaken for comparison. In the case of two successive pulses of solids, the first pulse of solids is found to form a closed torus which is subsequently penetrated by the second pulse. Thereafter, the two pulses combine to form a larger closed torus which then expands slowly as it descends through the domain. It was found that the initial coalescence of the two pulses is solely due to the liquid velocity field created by the entry of the first pulse of solids, the entry of the second pulse simply serves to enhance t,hat field. The entry of a second pulse of solids provides additional momentum to the domain, enhancing the recirculation. It is found that after the initial coalescence of the successive pulses, the dispersive evolution of the closed torus and tail is very similar to that of a single pulse. These results are in good qualitative agreement with related experimental work. Transactions on Engineering Sciences vol 42, © 2003 WIT Press, www.witpress.com, ISSN 1743-3533

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

The rise of a buoyant bubble and its interaction with a target horizontal wall is simulated with a 2-D numerical code based on the Boundary Element Method (BEM). Developed from a viscous potential flow approximation, the BEM takes into account only the part of the energy dissipation related to the normal viscous stresses. Hence, a simple analytical model based on lubrication approximation is coupled to the BEM in order to compute the drainage of the interstitial liquid film filling the gap between the bubble and the near wall. In this way the bubble–wall interaction is fully computed: the approach stage, the bubble deformation stage and, depending on the values of the Reynolds number and the Weber number, the rebound and the bubble oscillations. From computation of both the bubble interface motion and the liquid velocity field, a physical analysis in terms of energy budget is proposed. Though, in the present study, the bubble under consideration is basically supposed to be a 2-D gaseous cylinder, a comparison between our numerical results and the experiments of Tsao and Koch (1997) enlightens interestingly the physics of bouncing.