Liquid Velocity Profiles Research Articles

Electrolubrication in liquid mixtures between two parallel plates

We describe theoretically ‘electrolubrication’ in liquid mixtures: the phenomenon whereby an electric field applied transverse to the confining surfaces leads to concentration gradients that alter the flow profile significantly. When the more polar liquid is the less viscous one, the stress in the liquid falls on two electric-field-induced thin lubrication layers. The thickness of the lubrication layer depends on the Debye length and the mixture correlation length. For the simple case of two parallel and infinite plates, we calculate explicitly the liquid velocity profile and integrated flux. The maximum liquid velocity and flux can be increased by a factor $\alpha$ , of order 10–100 or even more. For a binary mixture of water and a cosolvent, with viscosities $\eta _w$ and $\eta _{cs}$ , respectively, $\alpha$ increases monotonically with inter-plate potential $V$ and average ion content, and is large if the ratio $\eta _{cs}/\eta _w$ is large.

CFD modelling of the non-isobaric evaporation of cryogenic liquids in storage tanks

A new CFD model relevant to non-isobaric cryogen evaporation has been developed. It considers the heat influx, from the surroundings to the liquid and vapour phases, and the heat transfer between the phases. The phase change is modelled considering two contributions: an interfacial energy balance far from the tank wall, and by direct wall-to-liquid conduction near the wall. The model provides well resolved liquid and vapour temperature and velocity profiles, as well as pressure build-up and evaporation rates. It shows that below the vapour-liquid interface, liquid natural convection is dampened by thermal stratification, which is driven by the increase of the interfacial temperature due to increase in pressure. The pressure build-up is mainly governed by the heating of the vapour, particularly at the beginning of the evaporation. The model was used to analyse liquid velocity profiles for two different sets of experimental data for evaporation of liquid nitrogen by optimizing empirical parameters, namely the wall heat partitioning fraction and the overall heat transfer coefficients. The results show that a large fraction of the vapour heat ingress is not transferred to the vapour phase bulk. Instead, it is transported through the walls and transferred to the liquid at the liquid-vapour-wall contact point, driving phase change. Heat conduction from the walls to the interface has a significant effect, even for low heat fluxes, and cannot be neglected.

Systematic assessment of computational models for the prediction of flow fields in bubble columns

Systematic changes in interfacial forces, turbulence models for the continuous and dispersed phases, lift force coefficient, and bubble size distribution were used to evaluate, in terms of complexity, the performance of nine computational models in the simulation of the time-averaged axial liquid velocity and holdup profiles in a bubble column. The oscillation period of the gas plume was also included in this evaluation. The mesh used for the simulations was chosen after a convergence analysis carried out with four meshes. The finest mesh displayed the highest divergence from the experimental data. Such behavior indicates that the proper mesh for a simulation of a multiphase flow must consider other factors in addition to element size and the quality indicators. The standard, RNG, and realizable κ-ε models were used for the liquid phase, while an algebraic and the standard κ-ε were the models for the dispersed phase. The isotropic RNG model for the liquid phase achieved accurate predictions in the anisotropic region near the gas distributor. The algebraic approach for the gas phase produced data similar to those calculated with the standard model. The simultaneous presence of the lift and virtual mass forces led to reliable predictions, and a lift coefficient of 0.2 displayed better performance than 0.14. This coefficient produced an excessive dampening of the lift force and caused the simulations to lose accuracy. The population balances did not improve the predictions.

Effect of inlet gas and liquid velocity profiles on one-group interfacial area transport equation in a vertical large rectangular channel

Bubbly flows appear in many heat and mass transfer equipment. The interfacial area concentration is a critical parameter in determining the performance of the heat and mass transfer systems. The one-dimensional one-group interfacial area transport equation (IATE) was developed based on area-averaged bubbly flow data collected under uniform inlet flow boundary conditions. The applicability of the IATE to the flow systems with non-uniform inlet flow boundary conditions was not comprehensively examined. This study investigated the effect of inlet liquid and gas velocity profiles on measured interfacial area concentration changes along the flow direction. The data used in this study were collected for vertical upward air-water two-phase flow in a rectangular channel with a gap length of 10 mm and width of 200 mm. The test conditions were the superficial gas velocity ranging from 0.0870 to 0.288 m/s and the superficial liquid velocity ranging from 0.515 to 2.53 m/s. The interfacial area concentrations with uniform and non-uniform inlet flow boundary conditions measured in a large vertical rectangular channel were compared under the same area-averaged flow rate conditions. Then, the predictive capability of the IATE to the bubbly flow test data with uniform and non-uniform inlet flow boundary conditions was assessed. Some non-uniform inlet flow boundary conditions, including channel-center peaking of liquid flow (CPF), channel-center peaking of gas flow (CPG), single-side-wall peaking of liquid flow (SPF), and single-side-wall peaking of gas flow (SPG), significantly affected the interfacial area concentration changes along the axial location at relatively high superficial gas or liquid velocity conditions. The IATE's predictive capability deteriorated for several non-uniform inlet flow boundary conditions, including double-side-wall peaking of gas flow (DPG) and single-side-wall peaking of liquid flow (SPF), specifically at relatively high superficial liquid velocity conditions. The maximum percentage error of the interfacial area concentration prediction by the IATE for these non-uniform inlet flow boundary conditions reached 75%.

Improvement of cleaning parameters of pipeline elements based on simulation of movement of solid magnetite particles in electrically conductive liquid

The unique properties of liquids that can interact with electric and magnetic fields are used in mechanical engineering, technology and medicine. The possibility of the influence of the magnetic field on the solid particles of the liquid in the pipeline allows cleaning of the solid walls of the pipeline, which is the object of the study. Magnetic liquids are solutions of ferromagnets in a liquid, and their physical properties in a magnetic field cause structural transformations in such liquids. The treatment of electrically conductive liquids in a magnetic field and their use for cleaning water from oil or oil residues are considered. On the basis of numerical modeling, the movement of solid particles of magnetite, which is part of an electrically conductive liquid, was investigated by jointly solving the equations of Reynolds, Maxwell, non-discontinuity and the turbulence model. The physical phenomena of the movement of solid particles of magnetite-based conductive liquid in various elements of the pipeline were determined, which improved the parameters of cleaning liquids contaminated with oil and oil. The magnetic particles of the electrically conductive liquid quite nicely fill the boundaries of the intersection if there is a flow reversal, as it happens in radiators. An increase in the intensity of the magnetic field leads to a change in the velocity profile of the conductive liquid, which prevents magnetite particles from penetrating close to the wall. An increase in the power of the magnetic field makes it possible to detach the contamination from the walls of the pipeline together with the solid particle of magnetite. A 73 % increase in wear in certain sections of the pipeline is due to the effect of the centrifugal force acting on the particle during rotation. The sudden expansion of the flow makes it difficult for particles to reach the pipe surfaces, which worsens the cleaning conditions. The number of particles on the surface is 82 % less compared to the absence of sudden expansion

Transient MHD flow of fractional Burger's fluid model through a parallel microchannel with heat transfer and slip boundary condition

The combined influence of magnetic field, electro-osmotic flow (EOF), and pressure gradient on the unsteady magnetohydrodynamic fluid flow through a parallel microchannel is investigated. The Burger's liquid model is used for the fractional partial differential equation, which allows us to study the behavior of viscoelastic liquid velocity profile in the parallel microchannel. The Laplace transform (LT) in concert with the Fourier cosine transform are used to obtain the analytical solution of the velocity profile. Furthermore, using the method of separation of variables, the energy equation, Joule heating, energy dissipation, and electromagnetic effects are calculated to obtain the temperature within the microchannel. The influence of some relevant parameters like heat transfer, temperature distribution, Hartmann number (Ha), and Brinkman number (Br) on fluid flow velocity are presented graphically and discussed. The results obtained show that temperature decreases with Ha and Br of the transverse electric field for slip flow. Close to the middle of the microchannel, fluid flow velocity increases with decrease in the delay time parameter value and increase in the Burger's parameter value, while the opposite trend is found for the velocity near to the middle of the microchannel. In addition, Burger's liquid is quite general, such that Oldroyd-B, Maxwell, and Newtonian liquids are readily obtained as limiting cases. The study is significant in the application fields of chemical analysis and biological analysis, drug delivery, bacteria detection, and some others.

Development and assessment of five-component wall boiling heat flux partitioning model

A mechanistic framework of wall boiling model with the total heat flux partitioned into five components, i.e. solid quenching, sliding-induced transient conduction, lift-off induced transient conduction, evaporation and single-phase convection, is developed and implemented into the unsteady two-fluid solver in the OpenFOAM. As important sub-models, bubble departure diameter, lift-off diameter and sliding length are calculated based on force balance analysis. A two-phase wall function is employed to account for the effect of nucleated bubbles on the near-wall turbulence. The developed model framework is assessed with the DEBORA experiment with the R12 as work fluid at the pressure of 1.46 MPa and 2.62MPa. The assessment indicates that the two-phase wall function improves prediction of liquid and vapor velocity profile and that the void fraction, the liquid and wall temperature can be well predicted. Under the condition of lower pressure and higher surface heat flux, bubble grows faster, which increases bubble departure and lift-off diameter. Higher liquid mass flux increases quasi-steady drag force and shear lift force, which consequently reduces the bubble departure and lift-off diameter. Due to large nucleation site spacing, relatively large sliding length appears in the lower-pressure cases. Nucleation awaiting time dominates the bubble departure frequency which increases steeply when the near-wall liquid approaches saturated. Comparing with the RPI model, the current model predicts relatively small evaporation heat flux. The predicted solid quenching and transient conduction heat flux induced by bubble lift-off are less significant in all the cases. The calibrated algebraic bubble size model can be adequate in the simulation of subcooled boiling at high pressure condition.

Interelectrode Distance Analysis in the Water Defluoridation by Electrocoagulation Reactor

In this research, the effect of the interelectrode distance (d) in the electrocoagulation (EC) reactor was studied. The experiments were carried out with varying d in values of 3, 5, and 9 mm during the treatment of water contaminated with fluoride (F−). The response variables analyzed were the treatment time necessary to reduce the residual concentration of F− to 1.5 mg L−1, the number of aluminum hydroxides formed, the potential drop in the reactor terminals, and the electric power consumption of the reactor. The software FLUENT version 6.3 was employed to simulate the liquid velocity profiles achieved in the reactor chamber. The results obtained show that the liquid velocity increases in the interelectrode spaces to 0.48, 0.65, and 0.86 m s−1 for interelectrode distances of 9, 5, and 3 mm, respectively, which favors not only the formation of flocs but also the elimination of fluoride. With a shorter interelectrode distance, the EC reactor not only consumes less electrical energy but also fewer electrodes, and the dispersion of generated flocs in the reactor chamber is major, which is more important than the quantity of flocs generated in it.

Analysis of Fractional Thin Film Flow of Third Grade Fluid in Lifting and Drainage via Homotopy Perturbation Procedure

Analysis of thin film flows is an important topic in fluid dynamics due to the large number of industrial applications such as food processing, chip manufacturing, irrigation, oil refining process, painting finishing, etc. Analysis involves studying the effects of various parameters in absolute conditions. These parameters may be film thickness, volumetric flux, liquid velocity profile, viscosity, shear stress, gravity, density, and different boundary formations. We have expanded the formulations of non-Newtonian third grade fluid for lifting and draining in fractional space. Fractional calculus along with Homotopy Perturbation Method is used for the solution and analysis purposes. The suitability and consistency of the solutions is determined by detecting residuals in each case. Velocity profile, average velocity, and volume flow for lifting and drainage cases are calculated. To the best of authors knowledge, thin film flow of fractional third grade fluid is not attempted before in lifting and drainage. Investigation shows increase in value of fractional parameter that decreases the velocity profile in lifting while increases the velocity in drainage scenario. Also, the frictional parameter and the gravitational parameter have opposite, while material constant has direct relationship with the velocity profile in lifting case. All the parameters showed inverse effect on the velocity in drainage case.

Behaviors of sliding bubbles in an inclinable turbulent channel flow investigated by optoacoustic measurement

Bubbles sliding in the vicinity of inclined walls are experimentally investigated to understand their fundamental behavior inside a turbulent boundary layer. A qualitative visualization confirms that the bubble shape varies with changes in channel inclination. An optoacoustic measurement technique is adopted to investigate the sliding motion of the bubbles. The diameters and advection velocities of individual bubbles are obtained from particle-tracking-type image processing, while the liquid velocity profiles in the bubbly flow and the maximum distance between the wall and bottom of the bubble are obtained using an ultrasound pulsed Doppler method. The combined measurement confirms that the effect of buoyancy on the slip velocity of the bubble is enhanced by an increase in inclination. Moreover, the drag and buoyancy determine the bubble shape in the inclined condition. The drag coefficient is derived from the measured variables using a force balance equation between drag and buoyancy, and we reveal that the drag coefficient increases with the inclination angle up to 35°. Finally, we propose a modeling equation for the drag coefficient in terms of the Weber number, inclination angle, and ellipticity of the bubble. This equation is applicable to bubbles inside turbulent boundary layers.

Spill-Free Transfer and Stabilization of Viscous Liquid

This article studies the feedback stabilization problem of the motion of a tank that contains an incompressible, Newtonian, viscous liquid. The control input is the force applied on the tank and the overall system consists of two nonlinear partial differential equations and two ordinary differential equations. Moreover, a spill-free condition is required to hold. By applying the control Lyapunov functional methodology, a set of initial conditions (state space) is determined for which spill-free motion of the liquid is possible by applying an appropriate control input. Semi-global stabilization of the liquid and the tank by means of a simple feedback law is achieved, in the sense that for every closed subset of the state space, it is possible to find appropriate controller gains, so that every solution of the closed-loop system initiated from the given closed subset satisfies specific stability estimates. The closed-loop system exhibits an exponential convergence rate to the desired equilibrium point. The proposed stabilizing feedback law does not require measurement of the liquid level and velocity profiles inside the tank and simply requires measurements of 1) the tank position error and tank velocity, 2) the total momentum of the liquid, and 3) the liquid levels at the tank walls. The obtained results allow an algorithmic solution of the problem of the spill-free movement and slosh-free settlement of a liquid in a vessel of limited height (such as water in a glass) by a robot to a prespecified position, no matter how full the vessel is.

Experimental Investigations and Numerical Assessment of Liquid Velocity Profiles and Turbulence for Single- and Two-phase Flow in a Constricted Vertical Pipe

In this work, the capabilities of state-of-the-art turbulence models are compared for a three-dimensional flow (3D) field within a constricted vertical pipe. The considered flow domain is a vertical pipe section with a baffle-shaped flow constriction which leads to the development of a jet flow through and a recirculation flow region behind the constriction. Different Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) models were tested for single- and two-phase flow simulations. In the two-phase simulations, bubble-induced turbulence (BIT) was also considered by adding source terms in the k and ε/ω equations. The results are validated against experimental data. We employed hot-film anemometry (HFA) for liquid velocity measurement and combined it with ultrafast X-ray computed tomography (UFXCT), which provides gas phase data. Based on the local phase-indicator function obtained from the tomographic image data, we can correct HFA signals, which become corrupted by bubble contacts. We found that for single-phase flow all RANS models predict axial velocity well while radial velocity prediction is inadequate. LES models, however, achieve a better prediction of the latter. For two-phase flow, the axial component of the liquid velocity is well captured by all RANS models and the radial component of the liquid velocity is predicted better than for single-phase flow. In general, the computationally less costly RNG k-ε model performs similar to the SSG RSM model and can therefore be recommended for simulation of complex flow scenarios.

Numerical and Experimental Investigations of Horizontal Turbulent Particle-Liquid Pipe Flow.

A Eulerian–Eulerian computational fluid dynamics approach is used in conjunction with appropriate auxiliary models for turbulence and solid dynamic properties to study the complex turbulent flow of particle–liquid suspensions in a horizontal pipe. Numerical simulations of the detailed flow field are fully and successfully validated using a unique experimental technique of positron emission particle tracking. The study includes nearly neutrally buoyant as well as dense particles, ranging from small to large at low to high concentrations, conveyed by a Newtonian liquid. Results are analyzed in terms of radial particle and liquid velocity profiles as well as particle distribution in the pipe. The approach provides predictions with a high degree of accuracy. Particle behavior can be classified into three categories depending on their size and particle–liquid density ratio. An analysis of the forces governing the two-phase flow is used to interpret the phenomena observed.

Can Simultaneous PIV In The Gas And Liquid Phases Provide Insight Into The Transfer Of Momentum Between The Two Phases?

Understanding the interaction between a gas shearing over a liquid film and the liquid film is essential if we wish to use modeling to optimize systems to decrease environmental impact, increase efficiency, and hence productivity. To this end, PIV is used to simultaneously study the velocity fields in the gas and liquid fields to better understand the interaction between the two phases. The methodology is detailed in the paper, and initial results show that the film shape changes as the flow increases from 2.2 m/s to 4.7 m/s. This change can be seen to be from a 2D surface wave regime to a 3D wave regime. In the 2D regime, the liquid film is linear in shape, and the averaged and conditionally averaged velocity profiles of the gas and liquid velocity are equal at the interface. In the 3-D regime, the averaged liquid and gas velocity profiles are no longer equal at the average interface height. Instead, they coincide at the 2.5% percentile of the local height distribution. The conditionally averaged velocity profiles show significant differences as the film height changes. It is suggested that this would mean the use of average profiles for validating CFD in similar situations might need to be reviewed.

The use of PIV methods in the study of two-phase flows in small diameter channels

The PIV (Particle Image Velocimetry) method is one of the optical, non-invasive measurement methods for measuring fluid velocity and can be used in the study of two-phase gas-liquid flows to determine velocity fields. The velocity distribution of the liquid and gas phases influences the formation of two-phase flow structures and, consequently, the mechanisms of energy and moment exchange in the two-phase flow. The article concerns the application of the PIV method to the assessment of hydrodynamic phenomena occurring during two-phase flow realized in pipe minichannels with an internal diameter d > 2 mm. Fluorescent marker particles with a density close to that of water were used in the research. The preliminary tests were carried out on the adiabatic water-air mixture. The research aimed to check the applicability of PIV methods also in non-adiabatic flows. As a result of preliminary studies, velocity maps of the liquid phase, histograms and velocity profiles in the vertical section of the tested minichannel were obtained.

Lift coefficient of bubble sliding inside turbulent boundary layers in an inclinable channel flow

The behavior of bubbles traveling in the proximity of a tilted wall is studied experimentally to understand the fundamental sliding motion of bubbles inside turbulent boundary layers along an inclined wall. The qualitative visualization of sliding bubbles confirms the contribution of bubble buoyancy on the sliding motion for negative and positive inclinations of the channel. An opto-acoustic combined measurement technique is adopted to explore the sliding motion. Liquid velocity profiles in the bubbly flow and the distance between the wall and bottom of the bubble are obtained using the ultrasound pulsed Doppler method, while the bubble diameters and velocities are obtained from particle-tracking type image processing. The combined measurements reveal that the velocity of bubbles decreases under the negative slope condition and increases under the positive slope condition due to opposite buoyancy effects. In addition, the distance between the wall and bottom of the bubble increases with an increase in negative inclination. The lift coefficient is derived from the measured variables using a force–balance equation among the buoyancy, lift, and surface tension. Finally, we propose modeling equations for the lift coefficient expressed in terms of the Reynolds, Weber, and Bond numbers, which apply to the bubbles inside boundary layers.

Random trilobe packing using rigid body approach and local Gas-Liquid hydrodynamics simulation through CFD with experimental validation

It is quite difficult to measure the local information of the gas/liquid flow inside random packed extrudate catalyst beds in a large scale. Obtaining the local information through computational fluid dynamic (CFD) simulations in such system is also difficult due to the complexity of random particle packing and two-phase flow simulation. An efficient packing scheme was implemented to randomly pack 2917 trilobe particles (10 cm in height) in a 2-inch column to represent the trickle bed reactor (TBR) based on the rigid body approach. The generated geometry was used to define the computational domain for the two-phase hydrodynamics simulation based on the volume of fluids (VOF) approach. This hydrodynamics modelling study is paired with an experimental study using our in-house developed advanced measurement techniques based on optical fiber probes, which allowed to determine local liquid velocity and saturation profiles. The experimental measurements were used for local validation of the implemented model.

Modification of the equation for mass flow rate (mass) measurement of liquid with account of dynamic influencing factors

The paper introduces theoretical foundations for the method of transferring units of mass and volume of liquid in the flow, mass and volumetric liquid flow rates using the indirect measurement method. The equation for measuring the mass flow rate (mass) was modified in terms of assessing the dynamic influencing factors caused by transient processes: liquid flow rate fluctuations and turbulent pulsations, unevenness of the liquid velocity profile in the nozzle exit of the diverter. The modified equation was derived from the continuity equation in physical and mathematical modeling of hydrodynamic processes of liquid flow in the nozzle exit of the diverter using mathematical statistics methods. The main uncertainty sources of calibration units with weighing devices were identified. The results of the approbation of the method of transferring units of mass and volume of liquid in the flow, mass and volumetric liquid flow rates were obtained on calibration units with weighing devices in a wide range of geometric and operating parameters. A comparison of the expanded measurement uncertainty of the calibration unit with weighing devices when transferring units of mass and volume of liquid in the flow, mass and volumetric liquid flow rates, determined using the method of indirect measurements and comparison testing with a transfer standard, was performed.

Ultrasonic Measurement of Two-Dimensional Liquid Velocity Profile Using Two-Element Transducer

The flow field or multidimensional velocity distribution of the coolant in fuel rod bundles of the reactor core in pressurized water reactors (PWRs) is an important parameter that is revealed through experimental investigations. This paper presents the two-dimensional (2D) velocity profile measurement using a two-element ultrasonic transducer with both elements acting as a transceiver. The size of the transducer is minimized for compactness, leading to a narrow sound field appropriate for applications in fuel rod bundle flow. Furthermore, the transducer’s sound pressure is evaluated via simulations and experimental measurements. In order to confirm the ability of the ultrasonic velocity profiler (UVP) with a two-element transducer, the experimental measurement is conducted in turbulent horizontal pipe flow. The 2D velocity vector profile is obtained, and then the measurement in swirling flow is conducted. The 2D velocity profile in an axial and radial plane is obtained utilizing the UVP measurement. Lastly, the ability of the UVP to derive the 2D velocity profile in the narrow area of the rod bundles is demonstrated.

Evaluation of velocity fields in horizontal gas-liquid intermittent flows using Stereoscopic-PIV and instantaneous masking procedure

The main goal of this work was to obtain well-converged liquid velocity profiles for intermittent gas-liquid flows in a horizontal pipe. To this end, air and water with superficial velocities of JG = 0.5 m/s and JL = 0.3, 0.4 and 0.5 m/s, respectively, were driven into a 18-m acrylic test section with an inner diameter of 40 mm. All three-components of the velocity vectors were measured in a pipe cross-section using a highfrequency stereoscopic PIV system, together with the laser induced fluorescence technique. Photogates were used to measure the unit cell translational velocity, as well as to trigger data acquisition, allowing the calculation of ensemble-averaged velocity fields at specific positions, referenced to the gas-bubble nose tip position. An instantaneous image masking procedure was implemented, allowing the determination of non-dimensional ensemble-averaged velocity profile in the liquid film, referenced to gas-bubble boundary. The high-frequency system employed allowed the determination of the influence of the faster-moving gas bubble on the liquid velocity field in the plug region. The data presented are relevant to the validation and improvement of one-dimensional two-phase numerical models, as well as to better understand this complex flow.