Liquid Pool Depth Research Articles

Analysis of the interfacial evolution characteristics of hollow droplet impact on a liquid pool

The impact dynamics of a hollow droplet on a liquid pool have significant implications across various industrial applications. This study employs numerical simulations to explore the dynamic evolution of the interface during the impact of a hollow droplet on a liquid pool. The investigation focuses on the effects of varying the hollow ratio Dr and liquid pool depth h* while maintaining a constant volume of liquid within the droplet shell. The findings reveal that both the hollow ratio Dr and pool depth h* critically influence the formation of ejecta + lamella, and vortex rings after the impact of a hollow droplet on a liquid pool. The confinement effect of the pool bottom can influence the evolution of the splashing, while the internal air in the hollow droplet can absorb a part of the impact energy during the collision. Specifically, at shallow pool depths, the interface primarily evolves into ejecta + lamella structures, whereas at greater pool depths, vortex ring formation is predominant. Furthermore, an increase in the hollow ratio leads to a reduction in the critical pool depth hc* at which the transition between these interfacial modes occurs. These findings indicate that, in practical applications involving the impact of hollow droplets on liquid pools, sufficient attention should be given to the pool depth. This enhances our understanding of the bottom pressure, droplet impact, and vortex formation, which is of significant relevance to related industrial technologies.

Effects of operating parameters on single-stage ultrasonic separation of ethanol from its aqueous solutions

The effects of operating parameters on separation of ethanol from its aqueous solutions using ultrasonic atomization were investigated in a single-stage process. With an experimental setup similar to those used in previous work, we measured the degree of enrichment and the combined molar collection rate of ethanol and water for a single combination of the ultrasound power and frequency at 126 combinations of bulk liquid depth, composition, and temperature; carrier-gas inlet/outlet elevation and flow rate; and collection temperature. Enrichment depends strongly on bulk liquid composition, reaching a maximum at an ethanol mole fraction below 0.1, with the maximum enrichment depending on bulk liquid depth and inlet/outlet elevation. The collection rate depends strongly on inlet/outlet elevation and bulk liquid pool depth, and for high ethanol mole fractions is nearly independent of bulk liquid composition. Enrichment and collection rate increase with increasing bulk liquid temperature and decreasing collection temperature. The fact that increasing the carrier-gas flow rate increases the collection rate and decreases enrichment is interpreted in terms of size-selective transport of drops from the ultrasonically-generated fountain where they are atomized, to the cold trap where they are collected. The results are discussed in terms of operating parameters, transport phenomena (including evaporation and gravitational settling of atomized drops), the ultrasonically-induced fountain, and previously reported drop-size distributions. The duration of the experiments, conducted in batch, was such that the results should be relevant to both batch and continuous-flow operation. The work provides guidance and critical data for process scale-up.

On the hydrostatic limit for thin film flow with applications to thermosyphons

Heat pipes frequently encounter challenges in effectively returning condensed liquid from the condenser to the evaporator through capillary pumping, which limits their overall efficacy. When capillary pumping becomes irrelevant due to factors like the absence of wick, or overfilling, the heat pipe is more properly termed as thermosyphon. In a close-to-horizontal orientation, the driving force for liquid return in a thermosyphon relies on the difference in liquid pool depth between the evaporator and condenser. An excessively deep liquid pool in the condenser can hinder radial heat transfer, necessitating a design that favours intermediate-depth liquid pools. This study utilizes a theoretical approach based on the lubrication approximation to the Navier–Stokes equations to determine the fill ratio that maximizes thermosyphon performance. We explore the relationship between this fill ratio and factors such as the axial temperature difference along the thermosyphon. Our analysis thereby highlights the hydrostatic-driven flow limit in the thermosyphon as an analogue to the capillary limit in heat pipes. Regarding the hydrostatic limiting curve as an alternative to the capillary limiting curve offers valuable insights for enhancing thermosyphon performance and provides means of comparing the performance of one vs. the other passive heat transfer device.

Numerical Simulation of White Spot Formation in Vacuum Arc Remelting

Coupling fluid flow, heat transfer, solidification, and particle dissolution behavior, the white spot formation in the vacuum arc remelting process is simulated. The effect of particle initial diameter, dropping position, and dropping height on the remelting behavior is investigated. The results show that the particle from the electrode drops through the arc zone with gravity force and the diameter is reduced in the high‐temperature zone. As the diameter is lower than 5 mm, the particle completely dissolves and the white spot formation can be eliminated. The particle dissolution is less affected by the liquid pool depth, but it is mainly affected by the high‐temperature zone distribution, which is closely related to the electric arc generation. Because of the limited high‐temperature zone near the ingot side surface, the particle from the ingot crown is more difficult to remelt, compared with that from the electrode. Moreover, it is found that the dropping height obviously affects the particle remelting behavior. As the dropping height decreases from 25 to 0, the particle critical diameter that can fully dissolve increases from 4.2 to 6.6 mm.

Experiments on thermocapillary-buoyancy convection of medium Prandtl number liquids in annular pools heated from inner cylinder

A series of terrestrial experiments on thermocapillary-buoyancy convection of medium Prandtl number liquids (Pr = 6.7-25.2) were performed in annular pools with different depths and a heated inner cylinder. The temperature fluctuation pattern on the free surface was recorded by the schlieren method. Experimental results indicate that thermocapillary-buoyancy convection could weaken and the critical Marangoni number of the flow transition increases with the Prandtl number. When the flow destabilizes, the rotating petal-like structure and the spoke pattern appear respectively in the annular pools with the depths of 4-5 mm and 6-8 mm. As the Marangoni number increases, the flow becomes oscillating as a result of the thermal perturbation induced by the thermocapillary effects. Besides, with the increasing liquid pool depth, the strengthened buoyancy force has an impact on the basic flow and the thermal fields. Thus, the temperature fluctuation frequency of the oscillating petal-like structure is more than that of the oscillating spoke pattern. Different from the cylindrical geometry heated from the outer cylinder, the radial waves and the petals appear respectively near the outer cylinder and the inner cylinder. Furthermore, the wavenumber decreases as the liquid pool depth increases.

Symmetry breaking of Worthington jets by gradients in liquid pool depth

We investigate the impact of a vertically falling droplet onto a non-uniform liquid depth having a linear slope of the bottom substrate. Here, we report that the resulting jet direction is inclined to the shallow liquid depth after the droplet impact, which is found to be markedly distinct from a vertically falling droplet onto a uniform liquid bath. From experimental and numerical results, we observe that initially the cavity grows almost axisymmetrically, and then, when it retracts, asymmetric capillary waves exhibit. The asymmetric cavity reversal leads to the inclined jet ejection that is related to pressure distribution and velocity of the interface. For the systematic study, we explore the jet dynamics by varying the surface tension, the droplet size, the droplet impact speed, the inclination angle of the bottom substrate, and the depth of the liquid bath. Finally, we provide a simple scaling model to predict the inclination angle of the resulting jet after the drop impact on the inclined liquid pool.

MODELLING OF SELECTIVE LASER MELTING PROCESS FOR ADDITIVE MANUFACTURING

The proposed model is a numerical tool for designing processing windows suitable to metal alloy. The model is validated fitting experimental measures of track width, depth and cross sectional area from three literature sources. Effective liquid pool thermal conductivity laser absorptivity and depth of application of laser energy are here considered as fitting parameters. Laser absorptivity and depth of application of laser energy result to rise almost linearly with increasing specific energy.. The obtained results give confidence about the possibility of using the model as a predicting tool after further calibration on a wider range of metal alloys.

ELECTRON-BEAM MELTING OF INGOTS OF TiAl SYSTEM INTERMETALLICS

Performance of scientific-technical researches at the E. O. Paton Electric Welding Institute of the NAS of Ukraine have been directed on development of technology for manufacture of titanium aluminide –based alloys using the method of electron-beam melting (EBM). The mathematical models of heat state and evaporation of alloying elements in EBM were developed. The results of calculations of heat state using the mathematical model allowed determining a dependence of depth of liquid pool on different melting rates. The mathematical models of processes of evaporation in EBM of titanium aluminide ingots were used for plotting the nomograms, which help to determine the necessary content of alloying element of the alloy in the initial charge for acquiring the necessary concentration of this element in ingot at set technological parameters of melting. In scopes of designed mathematical models there were investigated different technological modes of electron-beam melting of ingots based on titanium aluminide. The optimum EBM modes, at which a solidification front approaches to flat, were determined. At that, more uniform distribution of the additives on ingot section and volume is provided as well as level of stressed state is reduced. The works were carried out on manufacture of titanium aluminide based-ingots with addition of refractory as well as volatile alloying elements. Composition and structure of produced ingots were examined. It is shown that electron-beam melting allows getting chemically homogeneous ingots based on titanium aluminide and is a perspective method for production of such class materials.

Energy conservation during single droplet impact on deep liquid pool and jet formation

This paper investigates the impact of single droplets impinged into a deep liquid pool at atmospheric pressure. The single-droplet dynamics of three impinging liquid samples with different surface tensions, viscosities, and densities were experimentally investigated. The time evolution from droplet impingement on the pool surface to jet formation was recorded by a high-speed video camera. The impact velocity and droplet diameter were varied as 1.0–3.2 m/s and 1.8–3.0 mm respectively, and the liquid-pool depth was fixed at 30 mm. The cavity volume was affected by the impact parameters, indicating a clear correlation between drop diameter and impact velocity. For the water droplets, the jet volume was decreased and increased under lower and higher impact velocity conditions, respectively. For ethanol droplets, the jet volume increased at higher impact velocity and larger droplet diameter. To gain deeper physical insight into the jet formation, the energy balance of droplet impingement onto the liquid pool surface was estimated. Approximately 28% of the impact energy was invested in cavity formation, regardless of the liquid properties. The remaining energy was most likely dissipated or consumed at the surface. All of the cavity energy in all samples was consumed in jet formation.

Experimental study on the effect of surface evaporation on the thermocapillary-buoyancy convection in a shallow annular pool

In order to understand effect of surface evaporation on thermocapillary-buoyancy convection, a series of experiments on thermocapillary-buoyancy convection in a shallow annular pool with different surface evaporation rates have been conducted. The annular pool is subjected to a radial temperature gradient, and the inner and outer radii are respectively 20 mm and 40 mm. The 0.65 cSt silicone oil has been selected as the working fluid for its relatively strong volatility. Results show that the surface evaporation rate depends mainly on Marangoni number and the average temperature of the working fluid. At a weak evaporation, the critical Marangoni number increases with the increase of the surface evaporation rate and the liquid pool depth, i.e. the surface evaporation and buoyancy effects can suppress the flow destabilization. When the three-dimensional flow appears, the temperature fluctuation from the hydrothermal waves and the free surface fluctuation of the liquid layer are regular and coincident. However, in the case of the rapid evaporation, the vapor recoil can directly trigger the flow instability. Furthermore, the temperature fluctuation is weakened significantly, and the surface fluctuation of the liquid layer become irregular due to the vapor recoil effect.

Development and calibration of a CFD-based model of the bed fusion SLM additive manufacturing process aimed at optimising laser parameters

The main concern deriving from the Selective Laser Melting technique is attaining a fully dense part out of the interconnected tracks. The right choice of process parameters is of fundamental importance to get a porosity free component. In this work a model has been developed simulating the printing process with the aim of creating a simple numerical tool for designing processing windows suitable to metal alloys of any composition. The applied simplified approach makes the model use as much practical as possible, while keeping the physical description representative. The model has been calibrated fitting experimental measures of track width, depth and cross sectional area taken from three literature sources, referring to: Ti6Al4V, Inconel 625 and Al7050. Effective liquid pool thermal conductivity, laser absorptivity and depth of application of laser energy are the fitting parameters. Laser absorptivity and depth of application of laser energy result to rise almost linearly with increasing specific energy; the slopes of the three analyzed alloys result very close to each other. The obtained results give confidence about the possibility of using the model as a predicting tool after further calibration on a wider range of metal alloys.

Continuous harvesting of microalgae biomass using foam flotation

Biomass harvesting and dewatering are major operational costs that constrain the development and expansion of the industrial use of microalgae; particularly for low value biofuels. In this study we demonstrate, for the first time, a surfactant-aided foam flotation column that is designed and optimised for the continuous harvest of microalgae not only to improve the productivity of microalgae biomass but also as an attempt to overcome the trade-off between recovery efficiency and enrichment in batch and semi-batch foam flotation. The following operational parameters were optimised; surfactant concentration, air flow rate, feed flow rate, column height, liquid pool depth, and sparger type. Additionally, the effects of cell surface characteristics (hydrophobicity, zeta potential, and contact angle) were investigated on Chlorella vulgaris flotation performance. Hydrophobicity was enhanced using three surfactants; the cationic cetyltrimethylammonium bromide (CTAB), the anionic sodium dodecyl sulphate (SDS), and the non-ionic TWEEN®20; with CTAB producing the greatest enhancement. Surfactant concentration, column height, and air flow rate had the greatest effect on the algae concentration factor (CF) and recovery efficiency (RE). The optimised design (CTAB = 35 mg L−1, air flow rate = 1 L min−1, feed flow rate = 0.1 L min−1, column height = 146 cm, liquid pool depth = 25 cm, with a fine porous sparger) yielded RE of 95, 93, and 89% with 173, 271, and 143-fold biomass enrichments for freshwater C. vulgaris and marine Isochrysis galbana and Tetraselmis suecica microalgae respectively. Achieving high RE for freshwater and in the case of marine microalgae (irrespective of ionic strength) at moderate surfactant dosages, gives foam flotation the advantage of being a growth media independent harvesting process. The process had a very low power consumption (0.052 kWh m−3 of algae culture). Our findings demonstrate the potential for continuous, low cost, scalable flotation harvesting with particular relevance for the biofuels, water and wastewater treatment industries.

Experimental study on Prandtl number dependence of thermocapillary-buoyancy convection in Czochralski configuration with different depths

A series of experiments on thermocapillary-buoyancy convection in Czochralski configuration with different liquid depths have been conducted. Prandtl numbers of the working fluids vary from 10 to 29 and the depth of the liquid pool is between 1.5 mm and 8 mm. Results show that the critical Marangoni number increases with the increase of the liquid pool depth. Prandtl number has a little impact on the critical Marangoni number for the shallow liquid pool, but a significant influence for the deep liquid pool. The flow pattern transits from the concentric multi-rolls to the hydrothermal waves in the shallow liquid pool with the increase of Marangoni number. Furthermore, with the increase of Prandtl number and the liquid pool depth, the hydrothermal waves can be suppressed, and thus the concentric multi-rolls flow pattern is easier to appear. In deep liquid pools, the number of the spokes decreases with the increase of Marangoni number and the liquid pool depth, and the spokes move from the crystal edge to the crucible sidewall. In addition, the radical waves close to the crystal edge have been observed at deep liquid pools and large Marangoni numbers.

Non-stationary heat model for electron beam melting and refining – An economic and conservative numerical method

An economic and conservative numerical method is proposed for discretization and numerical simulation of non-stationary heat model concerning electron beam melting and refining (EBMR) of metals. The numerical model and optimization problems are developed to analyze and compare experiments and numerical data and to aid in understanding and optimizing EBMR. The axis-symmetric problem is decomposed into two locally one-dimensional problems. For the two problems, implicit and absolutely stable schemes are built for which the decomposition method gives rate of convergence of order one for both the space and time variables. The obtained discrete problems lead to linear systems of equation with three-diagonal matrixes which are solved via Thomas method. Proposition for the stability and realization of Thomas method is proved for one of the two one-dimensional problems. Criteria, related to the geometry of the crystallization front, for improvement of the quality of the obtained material after EBMR are discussed. Approaches for discretization of the criteria over the numerical solution of the model are proposed. Comparison between experimental and simulation results is made and the model is validated against liquid pool depth and diameter. Through applying the developed numerical scheme and criteria, optimization of the EBMR of copper ingots is achieved. Results for the best technological regime parameters according to the chosen criteria for the investigated ranges of the e-beam power and the beam radius are given. The results indicate that the model is able to quantitatively predict the liquid pool geometry and the optimization criteria, based on the profile, are able to propose optimal process parameters.

Modeling of the Vacuum Arc Remelting Process for Estimation and Control of the Liquid Pool Profile

Vacuum arc remelting (VAR) is an industrial metallurgical process widely used throughout the specialty metals industry to cast large alloy ingots. The final ingot grain structure is strongly influenced by the molten metal pool profile, which in turn depends on the temperature distribution in the ingot. A reduced-order model of the solidifying ingot was developed specifically for dynamic control and estimation of the depth of molten liquid pool atop the ingot in a VAR process. This model accounts only for the thermal aspects of the system ignoring other physical domains such as fluid flow and electromagnetic effects. Spectral methods were used to obtain a set of nonlinear dynamic equations which capture the transient characteristics of liquid pool profile variations around a quasi-steady operating condition. These nonlinear equations are then linearized and further simplified by suppressing fast modes. The resulting system was used to construct a linear-quadratic-gaussian (LQG) controller which was tested in a laboratory-scale furnace showing a good performance. A high-fidelity physics-based model is used in real-time to provide information about the solidifying ingot and potential solidification defects.

A three-dimensional steady state thermal fluid model of jumbo ingot casting during electron beam re-melting of Ti–6Al–4V

A 3-D coupled thermal-fluid model describing mass, momentum and energy transport within a Ti–6Al–4V rolling ingot cast in an (Electron Beam Cold Hearth Remelting) EBCHR process has been developed to describe steady state casting conditions. The model incorporates a number of the physical phenomena inherent to the industrial process, including a metal inlet in the center of one of the narrow faces, complex boundary conditions based on industrial practice, buoyancy driven flow within the liquid and flow attenuation using a Darcy momentum source term within the mushy zone. The model ignores turbulence in the liquid pool and Marangoni (surface tension) driven surface flows. The model has been validated against liquid pool depth and profile measurements made on an experimental casting seeded with insoluble dense markers and doped with dense alloy additions. Comparisons have also been made to video images taken of the top surface during casting. The results indicate that the model is able to quantitatively predict the steady state sump depth and profile and is able to qualitatively predict aspects of the top surface temperature distribution. The model has also been used to conduct a process heat balance and sensitivity analyses. The process heat balance conducted on the model domain indicates that at steady state the liquid metal inlet contributes 88% of the total power input, while the electron beam provides net 12% after accounting for radiation losses from the top surface; 62% of the heat is lost through the ingots sides and the balance is lost via bulk transport of sensible heat through the bottom of the domain. The results of the sensitivity analysis on pool depth indicate that casting rate has the largest effect followed by metal inlet superheat. The thermal, flow and pressure fields predicted by the steady state model serves as the initial conditions for a transient hot-top model, which is the subject of a forth-coming paper.

Process intensification of foam fractionation by successive contraction and expansion

Enrichment in foam fractionation is enhanced by reducing the liquid flux while maintaining the flux of bubble surfaces. We show that it is possible to do so in a continuous foam fractionation column by inserting a plate into the foam layer and forcing the foam through a narrower tube (foam riser) mounted at the centre of the plate. A 35% reduction in liquid flux was observed by using a single plate-foam riser assembly in a foam stabilised by 0.52 g/L sodium dodecyl sulphate solution, and the liquid rejected from the foam due to the presence of the foam riser had the same concentration as the feed solution. However, due to the nature of the adsorption isotherm of SDS, the enrichment enhancement measured in the experiments hererin was modest. The mechanism of the foam riser plate was explained by invoking recent theoretical studies on pneumatic foam. It was demonstrated that the reduction in liquid flux was affected by sudden expansion of the flow area causing a rejection of interstitial liquid to the top of the plate and extracted, whence it was recycled back to the feed. Preliminary experiments on the effect of liquid pool depth and foam height on interfacial adsorption were also carried out to demonstrate that the insertion of the plate does not affect the adsorption of the target substance to the bubble surface in the current system. It was found that equilibrium could be achieved within 0.2 m of liquid pool depth or foam height, however the equilibrium surface excess on a rising bubble in the liquid pool is roughly 51% of the equilibrium value on a quiescent interface, while that in the foam layer is roughly 73% of the equilibrium value on a quiescent interface.

Mould powder selection for thin slab casting

Mould powders play an important role in the stability of the continuous casting process. The main functions of mould powders are to provide sufficient lubrication and to control the horizontal heat transfer. Because process control of thin slab casting is more stringent, it is generally assumed that mould powder properties become more critical as well.In 2000, the Direct Sheet Plant at Corus IJmuiden (DSP) commissioned a thin slab caster designed for casting speeds up to 6 m min−1. During commissioning, several operational problems were encountered with mould powders, i.e. insufficient liquid pool depth and the formation of rims/lumps. To investigate the operational mould powder problems, some of the mould powders were characterised using physical and mineralogical methods. The results were linked to operational experiences. It was concluded that for thin slab casting, a stable slag formation is obtained with a proper choice of free carbon and an even distribution of the carbon particles within the granules. The physical properties of mould powders are not as critical as expected when the additional mineralogical requirements are taken into account.

Modelling of a single drop impact onto liquid film using particle method

AbstractThe process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: rC = [c(t − t0)]0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.

The Effects of VAR Processing Parameters on Solidification Microstructures in Ti Alloys by Computer Simulation

VAR process is required to control its various operating parameters. Heat transfer simulation has been accomplished to understand development of solidification micro and macro-structures during VAR process in Ti alloys. Optimum VAR process parameters could be also estimated in this study. It was found that macro-structures were closely related to the shape and depth of liquid pool, and solidification parameters, such as temperature gradient, heat flux, solid fraction. The cooling rates were higher at bottom, top, and center part respectively. As cooling rates increased, the <TEX>$\alpha$</TEX> phase decreased in length, width and fraction. In order to evaluate which parameter affects the result of heat transfer calculation most sensitively, the sensitivities of input parameters to the simulation result were examined. The pool depth and cooling rate showed more sensitive to the temperature of the molten metal, heat transfer coefficient, and liquidus respectively. Also, these thermal properties became more sensitive at higher temperatures.