Free Liquid Surface Research Articles

Bubble dynamics and deformation of free liquid surface in aerated liquid storage tanks

OpenFOAM was utilized for analyzing bubble behavior and deformation of free liquid surface due to bubble formation and bursting in a rectangular container. Influence of three system parameters, orifice diameter, number of orifices and spacing between orifices, on various bubble dynamics and deformation of gas-liquid interface is presented. The study also incorporates information on bubble formation, bubbling frequency, and orientation of bubbles. Considering different orifice spacing, bubbling synchronicity is also reported. Details regarding interaction of wakes during bubble coalescence for single, double and triple inlet orifices are presented. The deformation of free liquid surface due to bubble formation and bursting is quantified using a new parameter called deformation index (D L * ). The analyses indicate that the frequency of bubble detachment is augmented with increase in orifice diameter and number of orifices. However, bubble detachment frequency is reduced when orifice spacing increased. Orientation of detached bubbles keeps on changing for larger orifice spacing. Results show that variations of these geometric parameters have substantial influence on free liquid surface deformation due to bubble bursting and other bubble behavior. Using results of these studies, one can develop a bubble-generating device for optimal performance.

Unveiling Carbon Dioxide and Ethanol Diffusion in Carbonated Water-Ethanol Mixtures by Molecular Dynamics Simulations.

The diffusion of carbon dioxide (CO) and ethanol (EtOH) is a fundamental transport process behind the formation and growth of CO bubbles in sparkling beverages and the release of organoleptic compounds at the liquid free surface. In the present study, CO and EtOH diffusion coefficients are computed from molecular dynamics (MD) simulations and compared with experimental values derived from the Stokes-Einstein (SE) relation on the basis of viscometry experiments and hydrodynamic radii deduced from former nuclear magnetic resonance (NMR) measurements. These diffusion coefficients steadily increase with temperature and decrease as the concentration of ethanol rises. The agreement between theory and experiment is suitable for CO. Theoretical EtOH diffusion coefficients tend to overestimate slightly experimental values, although the agreement can be improved by changing the hydrodynamic radius used to evaluate experimental diffusion coefficients. This apparent disagreement should not rely on limitations of the MD simulations nor on the approximations made to evaluate theoretical diffusion coefficients. Improvement of the molecular models, as well as additional NMR measurements on sparkling beverages at several temperatures and ethanol concentrations, would help solve this issue.

An Oblate Spheroid Base Isolator and Floating Surface Diaphragm for Seismic Protection of Liquid Storage Tank

ABSTRACT Base shear and sloshing response control in ground-supported circular cylindrical liquid storage tank is achieved by oblate spheroid base isolation (OSBI) system used along with floating surface diaphragm on the contained liquid. The new base isolation system, OSBI proposed herein is based on rolling-friction mechanism in ellipsoidal-shaped isolators in both the horizontal axes. The surface diaphragm is proposed to float on the free liquid surface to control the sloshing amplitude. The tank is analyzed using the coupled acoustic-structural (CAS) approach in finite element method (FEM). In order to have conformity of the present FE model, the FEM results are compared with the mechanical lumped-mass model of the tank (without surface diaphragm). The seismic response is investigated for the tank subjected to harmonic and real-earthquake excitations. The parameters considered for the analysis are the aspect ratio of the tank, eccentricity of the isolator, and thickness of the diaphragm. The seismic response quantities evaluated are base shear, sloshing displacement, and impulsive hydrodynamic pressure in the tank. Further, to study the effectiveness of the OSBI, the seismic responses of the tank subjected tri-directional components are compared with the two horizontal bi-directional components of the earthquakes. Also, the sloshing displacement with and without surface diaphragm in the non-isolated and base-isolated tanks are compared. From the results, it is observed that the OSBI system is efficient in mitigating the seismic responses in the tanks and the surface diaphragm is efficient in controlling the sloshing displacement. The superior performance of the proposed isolator depends on the design parameters, namely, eccentricity, and coefficient of rolling friction selected. The effectiveness of the surface diaphragm depends on the choice of material and thickness adopted.

Inclined free-surface liquid jet impingement on semi-cylindrical convex curved and flat surfaces: Heat transfer characteristics

An experimental study was performed to understand heat transfer characteristics of inclined liquid jet impingement on heated semi-cylindrical convex curved and flat surfaces in free surface configuration (unconfined). In experiments, curvature ratio of D/d = 7 along with the flat surface (D/d → ∞) were considered, here d is the hydraulic diameter of the circular pipe used to produce a liquid jet, and D is the cylindrical surface's diameter. Jet to plate spacing (H) was held constant to 24 mm (H/d = 4). Results are presented for four different inclination angles [0° (orthogonal jet), 15°, 30°, 45°], and Reynolds numbers (17,036 to 42,590). Applicability of inclined jet impingement on a curved and flat surface, their advantage, disadvantages in terms of heat removal rate (Nusselt number) are discussed. A Parametric study was performed by varying Reynolds number, inclination angle, and curvature ratios (D/d) to understand these parameters' effect on heat transfer. Findings revealed that higher inclination angle cases (θ = 30° and θ = 45°) could give an overall high heat removal rate from the cylindrical surface as compared to the orthogonal jet case, especially for higher Reynolds numbers. However, there are no advantages in terms of the heat removal rate by using an inclined jet for lower Reynolds number cases.

Electric-Field-Driven Ion Emission from the Free Surface of Room Temperature Ionic Liquids.

Electric-field-driven ion emission from the free surface of a planar room-temperature ionic liquid (RTIL) film was studied by using molecular dynamics simulations. We calculated ion emission rate (je) as a function of the electric field normal to the RTIL/vacuum surface (En) and found that the logarithm of je over the charge density on the surface (σ) is proportional to En1/2, in agreement with classical ion evaporation theories. The composition of emitted ions includes monomers and dimers. It was found that the monomer has to move across two barriers before emission. The fraction of dimers was found to depend on the external field and ion-ion interactions. We further performed replica exchange molecular dynamics simulations and identified different metastable states of the emitting ion near the liquid film. Our results showed that En and molecular details of ion/surface determine the rate and composition of ion emission from RTIL/vacuum surfaces. Fundamental insights revealed in this study form the basis to improve ion evaporation theories and performance of electrospray applications ranging from space propulsion to nanomanufacturing.

Numerical Simulation of the Instability of a Non-Isothermal Liquid Film in Film Devices

This work presents results of numerical simulation of the instability of vertical liquid film flow at moderate Reynolds numbers in the framework of partial differential equation of the state of the free surface of the liquid film. Equation coefficients include different physicochemical factors such as surface tension parameter and Marangoni parameter. Python scripts are used for computation of wave characteristics, instability regions of liquid films and liquid films free surface state. Computational experiments were carried out for the vertical water and alcohol films. Results could be used in the design or modernization of existing equipment and in the design of technological processes in liquid films.

Analysis of gas entrainment phenomenon from free liquid surface for a sodium-cooled fast reactor design (Velocity profile and Strouhal number in a flow field)

Analysis of gas entrainment phenomenon from free liquid surface for a sodium-cooled fast reactor design (Velocity profile and Strouhal number in a flow field)

The planar spread of a liquid jet and hydraulic jump on a porous layer

The flow of a planar liquid free surface jet impinging on a porous layer is theoretically examined, with particular emphasis on the influence of porosity ϕ, stress jump coefficient χ, and depth of the porous layer on the super- and sub-critical regions. Despite the numerous studies in the literature on the flow over a porous medium, the jet impingement on a porous layer has not been studied. An averaging integral approach is adopted to capture the flow in the developing boundary-layer and fully viscous regions upstream of the hydraulic jump. Asymptotic analyses for small distance from impingement, small porosity, and small porous layer depth are also conducted, elucidating the various mechanisms behind the behavior predicted numerically. We find a domain of validity for the stress jump coefficient χ in which numerical and experimental values of χ from the literature seem to fall. The transition point, where the outer edge of the boundary layer intersects the film surface, moves downstream with increasing porosity and stress jump coefficient accompanied by a drop in the film thickness. While the height of the hydraulic jump generally decreases with increasing ϕ for any permeability, the jump location decreases for small χ and increases for large χ.

Numerical Simulation of a Radial Free Surface Liquid Jet Impinging on a Heated Surface

Impinging liquid jets have been demonstrated to be an effective means of providing high heat transfer rates, and widely used in designing cooling systems for electronic modules, plastic manufacturi ...

The effect of convection on the position of the free liquid surface under zero and terrestrial gravity

Theresults of numerical modelinghas based on the solution of Navier-Stokes equations for convection oftwo-layer system air-water are presented.The influence of thermo-capillary and gravitational convection on the deformation and time averaged position of the interface of air-water system under sudden lateral heating of a square-section cavity are shown.

Effect of Radiation Force on a Flexible Spherical Particle at the Free Liquid Surface*

The effect of the radiation force on a spherical drop of an ideal liquid in the vicinity of the free boundary of the liquid when an acoustic wave is normally incident on the liquid surface is studied. As a result, the liquid sphere is located in the field of standing acoustic wave of pressure with the node at the free liquid surface. The measure of interaction is the radiation force: the time-average integral over the pressure in the external fluid caused by the acoustic wave over the surface of the sphere. The approach assuming the use of the velocity field potential obtained by solving the linear diffraction problem when determining the pressure in the liquid is used. It is established that there are frequencies of the incident wave at which the radiation force does not act on the spherical drops, which, therefore, will be stationary.

The influence of obliquely perforated dual-baffles on sway induced tank sloshing dynamics

This paper examines the influence of oblique perforated baffles on the sloshing dynamics of rectangular liquid storage tanks. The analysis presented accounts for sway induced hydrodynamic forces and entropy generation. Internal liquid free surface oscillation is modelled by the volume of fluid method. The effect of baffle geometric parameters, orientation and porosity on loads is examined and numerical results are compared against a set of experiments. Consequently, an engineering method suggesting the optimum size, angle of inclination and topology of baffles for the case of a rectangular tank is presented. It is shown that implementation of optimized oblique porous dual baffles may reduce sloshing loads by up to 15%.

Heat transfer characteristics of free surface water jet impingement on a curved surface

Impinging jet studies are available in the literature, which involves air as a working fluid or water in the submerged jet configuration. However, literature is scarce for free surface liquid jet impingement. In this work, heat transfer characteristics of free surface water jet impingement on a convex uniformly heated semi-cylindrical curved surface is presented. In experiments, two different curvature ratios, D/d are considered, where d is the inner diameter of circular nozzle pipe, and D is the outer diameter of the semi-cylindrical convex surface. Jet to surface distance was fixed to H/d=4 (d=6 mm). Reynolds number ranging from 17036 to 42590 were considered for experimental study. Nusselt number contours are presented for three different Reynolds numbers and two different curvature ratios, in which one case was D/d=∞ (flat surface). Present investigation revealed that surface curvature effects heat removal rate near the stagnation point. Heat transfer away from the impact in the circumferential direction is found to be affected by curvature, especially for higher Reynolds number (Re=42590).

Free-Surface Liquid Lithium Flow Modeling and Stability Analysis for Fusion Applications

Liquid metal plasma facing components are considered an attractive design choice for fusion devices including pilot plants. Virtual prototyping of such devices includes modeling of free-surface flow of the electrically conductive liquid, which requires computational fluid dynamics (CFD) and magnetohydrodynamics (MHD) simulations. Numerical tools capable of simulating flows and heat transfer in the free-surface MHD flow were developed at PPPL based on the customized ANSYS CFX. MHD is introduced using a magnetic vector potential approach. Free-surface flow capabilities are available in the code and were tested. Special stabilization procedures were derived and applied to improve convergence of the momentum equations with the source terms due to the Lorentz force and surface tension. Important characteristics of the fusion-relevant liquid metal flow is free surface smoothness and stability. Heat flux from the plasma impacts the liquid surface at a very acute angle, so any change of the free surface from axisymmetry can dramatically increase the local heat flux density and thus create excessive evaporation of liquid lithium into the plasma, which is detrimental to operations. Stability analysis of the liquid metal film flow was performed to determine applicable flow regimes. Thin film flow along horizontal wall is considered. Effects of gravity, magnetic field, and surface tension are included in the analysis.

Inductive level sensor: experiment and calculation

A non-contact induction technique for registering the free sufrace position of liquid metal is studied numerically and experimentally. A localized inductive level sensor (ILS) generates an alternating magnetic field and measures the resulting magnetic field. If an electrically conductive medium appears in the sensitive area of the sensor, this field changes. In the experiment, signals from the ILS were measured for a rotating cylinder with a beveled upper boundary, for different frequencies of alternating current, supplying the sensor generating coil. A set of calibration curves was obtained, that can be used to determine the cylinder rotation angle from the signal. In the numerical simulations, the three-dimensional fields of magnetic induction were obtained. The influence of the alternating current frequency, as well as the cylinder rotation angle on the ILS measurement, was studied. Numerical simulations show that increasing current frequency results in higher ILS sensitivity. The numerical and experimental results are in agreement. The developed technique is applicable for measuring the oscillation frequency of the liquid metal free surface.

Optimizing the spray characteristics of an ultrasonic droplet generator with continuously variable operating frequency

Ultrasonic spraying is utilized in a diversity of industrial processes and biomedical applications, including nanomaterial synthesis and inhalation drug delivery. Ultrasonic droplet generators transfer energy into bulk liquids using acoustic waves to break the free liquid surface into extremely fine microdroplets. We have previously reported an approach that combines ultrasonic actuation, resonant operation, and acoustic wave focusing for efficient spraying of liquids (e.g., low surface tension fuels, high viscosity inks, and suspensions of biological cells). Microfabricated devices comprised a piezoelectric transducer, sample reservoir, and an array of acoustic horn structures with microscale orifices. Orifice size dictated droplet size, and the fixed reservoir geometry restricted operation to specific device resonant frequencies. Here, we incorporate a continuously variable reservoir height that enables dynamic adjustment of operating parameters (e.g., to improve spray efficiency or to tune the droplet size in real-time). Finite element analysis is used to predict the harmonic response of the system for a range of reservoir heights from 0.5 to 3 mm (corresponding to operating frequencies from 0.5 to 2.5 MHz). Spray quality is optimized regarding uniformity and stability of active nozzles for arrays with 10, 20, and 40 μm orifices, and model results are used to explain observed behaviors.

3D Numerical Simulation of the Var Consumable Electrode Melting Process

A 3D numerical model was set up to simulate the formation and dynamics of the liquid metal film under the consumable electrode during VAR process. In the present paper, the implementation of this model is described. It was developed using the open source computational fluid dynamics (CFD) software OpenFOAM. The model solves coupled momentum and energy equations combined with a volume of fluid (VOF) method to track the liquid metal free surface. The melting of the electrode material is modeled with an enthalpy-porosity approach. The electric power supplied by the arc is supposed to be uniformly distributed over the surface of the electrode tip. For a given electric arc power, the model enables to quantitatively predict the dripping rate and hence the overall melt rate. Besides the thermal behavior of the electrode, simulation results illustrate the dynamics of the liquid film and the transfer mechanisms of the liquid metal during VAR melts performed with short and long interelectrode gaps.

Development of a novel tuned liquid damper with floating base for converting deep tanks into effective vibration control devices

Despite the proven effectiveness of tuned liquid dampers (TLDs), readily available liquid storage tanks are rarely utilized for vibration control of laterally-excited structures, as these are deep tanks with low inherent damping. Further, the fluctuation in liquid level in these tanks also causes variation in the fundamental sloshing frequency, leading to detuning. To overcome these problems, a novel TLD with floating base (TLD-FB) is proposed, in which a constant and shallow liquid level is maintained between the free liquid surface and the floating base. The liquid above the floating base acts as a conventional shallow TLD that always remains tuned to the structural frequency. The paper demonstrates how the TLD-FB can be incorporated into a water storage tank system on an example building without disturbing its functionality and achieves structural response reduction, despite water level fluctuations in the tanks.

Inhibiting bulging deformation of liquid metal free surface by magnetic pressure

A new method was presented to inhibit bulging deformation and fluctuation of free surface by magnetic pressure. A research combined with numerical and experimental methods was conducted to investigate the feasibility and inhibition efficiency. The parameters including magnetic flux density, frequency and action area of magnetic pressure were analyzed. The results show that the method is feasible, and the bulged free surface is fully inhibited by the proper magnetic pressure. The inhibition efficiency increases as the increase in magnetic flux density and frequency, which shows a linear relationship with the magnetic flux density. The frequency has a great influence on the inhibition efficiency when the frequency is changed from 0.15 to 5.00 kHz. However, the frequency more than 5.00 kHz has little influence on the inhibition efficiency and is recommended in application process. When the ratio of the action area to the area of bulged free surface is 0.8, the best inhibition is achieved. However, when the ratio is more than 1.2, a distinct W-shaped free surface is observed. The surficial and internal flow is strengthened with proper magnetic pressure imposed. Moreover, under the action of magnetic pressure, the fluctuation amplitude of free surface decreases from 4.0 to 1.2 mm and the main fluctuation with frequency of 2.34 Hz is dispersed into several minor fluctuations with frequency of 0.4–4.3 Hz.

Thermocapillary deformations of a two-layer system of liquids under laser beam heating

Heat and mass transfer in a bilayer system of viscous incompressible liquids with interfaces have been studied theoretically and experimentally. Thermocapillary convection and interface deformations have been induced by an intense thermal exposure on the free boundary due to the action of a laser beam. The evolution of the interfaces and liquid behavior have been experimentally investigated. The static profile of the liquid – liquid interface and free surface have been measured using the laser-sheet technique. The scheme of the experiment and parameters of the physical system have been presented. The theoretical study of the system dynamics includes the development of a correct mathematical model in the framework of continuum mechanics and creation of an effective numerical algorithm, validated with the help of new experimental results. An outline of the numerical method has been given. The proposed approach allows one to describe the characteristics of the arising flows, to predict the shape of thermocapillary deformations of the liquid interfaces, and to analyze the interaction of the thermal gravitational and thermocapillary convection. The mechanisms causing the occurrence of the decaying oscillations that were first discovered by the authors have been discussed. The results of the numerical study for a two-layer system of the “silicone oil – glycerin” type are in good agreement with the experimental data, and enable to estimate the influence of the upper layer thickness on the features of fluid motion and to forecast the rupture time of the top liquid under local heating at the free boundary. The rupture time depends on the rate at which the threshold temperature difference in the top layer sets in. For systems with relatively large thickness of the upper layer the appearance of a stable profile of the thermocapillary flexure on the free surface without layer breakdown is characteristic.