Top Free Surface Research Articles

Interfacial physico-chemical equilibrium control of lotus-type pore formation in solid

This study presents a challenging analysis of interfacial equilibrium conditions that control the evolution of lotus-type pores in both metals and nonmetals during solidification. It incorporates Henry’s or Sieverts’ law, affecting solute transfer at the cap and top free surface, and pore evolution. The significance of the directional and lightweight characteristics of lotus-type porous materials makes them vitally important in functional heat sinks, energy absorption, biomedical devices, and other applications. The study extends previous solute transfer models based on solute concentration deviations in the liquid from the top surface and convection-affected segregation at the advancing liquid–solid interface by further considering the effects of interfacial equilibrium conditions on pore development. Typical data selected for the dimensionless Henry’s law constant at the cap and top free surface is 0.175, while the Sieverts’ law constant at the cap and top free surface is 0.03. MATLAB Simulink and Simscape (version R2020b) with the solver ode113 are utilized to solve the resulting simultaneous system of unsteady first-order differential equations. The results show that the size of lotus-type pores increases as the Henry’s law constant at the cap decreases while the Henry’s law constant at the top free surface increases. Similar results are observed for Sieverts’ law. Lotus-type pores readily form as the Henry’s law constant at the cap increases while that at the top free surface decreases. The lotus pore length can also be determined and interpreted algebraically using solute content conservation. The model’s predictions closely match analytical findings previously validated by experimental data

Parametric Control via the Algebraic Expression of Lotus-Type Pore Shapes in Metals

Lotus-type porous metals, characterized by low densities, large surface areas, and directional properties, are contemporarily utilized as lightweight, catalytic, and energy-damping materials; heat sinks; etc. In this study, the effects of dimensionless working parameters on the morphology of lotus-type pores in metals during unidirectional solidification were extensively investigated via general algebraic expressions. The independent dimensionless parameters include metallurgical, transport, and geometrical parameters such as Sieverts’ law constant, a partition coefficient, the solidification rate, a mass transfer coefficient, the imposed mole fraction of a solute gas, the total pressure at the top free surface, hydrostatic pressure, a solute transport parameter, inter-pore spacing, and initial contact angle. This model accounts for transient gas pressure in the pore, affected by the solute transfer, gas, capillary, and hydrostatic pressures, and Sieverts’ laws at the bubble cap and top free surface. Solute transport across the cap accounts for solute convection at the cap and the amount of solute rejected by the solidification front into the pore. The shape of lotus-type pores can be described using a proposed fifth-degree polynomial approximation, which captures the major portions between the initial contact angle and the maximum radius at a contact angle of 90 degrees, obtained by conserving the total solute content in the system. The proposed polynomial approximation, along with its working parameters, offers profound insights into the formation and shape of lotus-type pores in metals. It systematically provides deep insights into mechanisms that may not be easily revealed with experimental studies. The prediction of a lotus-type pore shape is thus algebraically achieved in good agreement with the available experimental data and previous analytical results.

Effect of Marangoni flow during the solidification of a Fe-0.82wt.%C steel alloy

A two-phase Mixture model is proposed to simulate the liquid-solid phase transition of a Fe-0.82wt%C steel alloy under the effect of Marangoni flow. This model simplifies computations by solving a single momentum and enthalpy equation for the mixture phase using a three-dimensional finite volume method. The simulation involves solidifying a rectangular ingot (100 × 10 × 100 mm3) from the cold bottom surface towards the hot-free surface at the top. To facilitate heat exchange with the surrounding environment, a high heat transfer coefficient of h = 600 W/m2/K was applied on the bottom surface to establish an upward solidification direction. However, a lower heat transfer coefficient of 20 W/m2/K was applied on the top free surface, which was considered flat. This study aims to examine the effect of Marangoni flow generated by surface tension on flow and segregation patterns. The results show that the Marangoni flow emerges at the free surface and penetrates into the liquid depth, leading to the formation of hexagonal patterns along the liquid thickness. Upon full solidification, macro-segregation also exhibits hexagonal structures, mirroring the stationary hexagonal shapes generated by Marangoni flow.

The Impact of Marangoni and Buoyancy Convections on Flow and Segregation Patterns during the Solidification of Fe-0.82wt%C Steel.

Due to the high computational costs of the Eulerian multiphase model, which solves the conservation equations for each considered phase, a two-phase mixture model is proposed to reduce these costs in the current study. Only one single equation for each the momentum and enthalpy equations has to be solved for the mixture phase. The Navier-Stokes and energy equations were solved using the 3D finite volume method. The model was used to simulate the liquid-solid phase transformation of a Fe-0.82wt%C steel alloy under the effect of both thermocapillary and buoyancy convections. The alloy was cooled in a rectangular ingot (100 × 100 × 10 mm3) from the bottom cold surface to the top hot free surface by applying a heat transfer coefficient of h = 600 W/m2/K, which allows for heat exchange with the outer medium. The purpose of this work is to study the effect of the surface tension on the flow and segregation patterns. The results before solidification show that Marangoni flow was formed at the free surface of the molten alloy, extending into the liquid depth and creating polygonized hexagonal patterns. The size and the number of these hexagons were found to be dependent on the Marangoni number, where the number of convective cells increases with the increase in the Marangoni number. During solidification, the solid front grew in a concave morphology, as the centers of the cells were hotter; a macro-segregation pattern with hexagonal cells was formed, which was analogous to the hexagonal flow cells generated by the Marangoni effect. After full solidification, the segregation was found to be in perfect hexagonal shapes with a strong compositional variation at the free surface. This study illuminates the crucial role of surface-tension-driven Marangoni flow in producing hexagonal patterns before and during the solidification process and provides valuable insights into the complex interplay between the Marangoni flow, buoyancy convection, and solidification phenomena.

Numerical investigation of heat transfer enhancement in dielectric fluids through electro-thermo-capillary convection

In this study, a 2D numerical analysis was conducted to investigate electro-thermo-capillary convection in a 2D enclosure filled with a dielectric fluid. The enclosure had a free top surface and was subjected to buoyancy and electrical forces. The study considered a strong unipolar injection of electric charge (C = 10), a mobility number (M = 10), and a Prandtl number (Pr = 10). Calculations were performed for various thermal Rayleigh numbers (Ra) ranging from 5000 to 50,000, Marangoni numbers (Ma) varying from −5000 to 5000 and electric Rayleigh numbers (T) ranging from 100 to 800. The coupled equations governing the electro-thermo-convection problem (Navier-Stokes, energy, charge density transport, and the Maxwell-Gauss equations) were established and solved numerically using the FVM. This study involved mathematical modelling of complex and coupled phenomena, considering viscous, thermal, thermocapillary, and electrical instabilities. The findings showed a significant improvement in heat transfer with higher electrical and thermal Rayleigh numbers. Furthermore, the control of different forces led to an increase in the Nusselt number. Specifically, the application of thermal forces resulted in a 70% increase, while the use of thermocapillary forces led to a remarkable 169% increase. Additionally, electrical forces resulted in an impressive 224% increase. Multi-parameter correlations were established to estimate the Nusselt number as a function of the Marangoni, thermal and electrical Rayleigh numbers.

Diurnal heating and cooling of a sloping water body with vegetated shallow regions

In this work, diurnal heating, by solar radiation, and cooling in a sloping water body with vegetated shallow regions are investigated numerically. The sloping water body consists of a vegetated region with a bottom slope equal to 0.1 and a deep region with a horizontal bottom. The Volume-Averaged Navier-Stokes equations together with the Volume-Averaged Energy equation are solved numerically in the vegetated region. The latter has porosity equal to 0.85 (typical of aquatic plants found in lakes) and a length equal to the total length of the sloping region. At the top free surface, a time-dependent thermal forcing is applied, which is reduced in the vegetated region. Shallow water is considered with a maximum water depth being less than the penetration depth of the solar radiation. The non-vegetated sloping water body is also considered for validation purposes. The results (isotherms, streamlines, exchange flow rate), after ten full thermal forcing cycles, indicate significant vegetation effects on the daytime and night circulation and the exchange flow rates.

Shrinkage Deformation of Three Different Light Cure Composite Resin Using Image Correlation Method

The study performed were to measured the amount of shrinkage deformation of resin composites with and without bonding agent. The shrinkage defor mation of three types of composite resin (Ecusphere, Densply, CHARISMA) in cavities was studied using image correlation method. The cylindrical cavity in extracted teeth ( premolors) are to examine the shrinkage behavior on the top free surface. The cavities filled with resin after spreading a bonding agent are irradiated using LED unit, also performed on the cavities without bonding agent. One way analysis of variance and MOIRE analysis were used for statistical analysis. The shrinkage behavior was different in the cavities prepared with and without bonding agent. Polymerization of dental composites is characterized by heterogeneous deformation patterns with variable shrinkage values at different locations within the material.

Using Working Parameters to Control Formation and Shape of Lotus-Type Pores

The development and final shape of lotus-type pores can be manipulated in advance during unidirectional solidification in this study. Independent parameters considered are solidification rate, ambient pressure, and factor accounting for solute concentration at a selected reference state in liquid deviated from that at the top surface. Lotus-type porous materials have contemporarily been used in heat sinks, energy including shock, vibration, and sound absorption in aircraft engines, etc., which strongly depend on directions, distributions, and pore shapes in solid. This model accounts for transient gas pressure in the pore affected by solute transfer, gas, capillary and hydrostatic pressures, and Sieverts’ law or Henry’s law at the bubble cap and top surface. Solute transport across the cap self-consistently accounts for solute convection at the cap based on a reference concentration deviated from that at the top free surface, the amount of solute rejected by the solidification front into the pore, and the convection-affected concentration at the solidification front. The resulting simultaneous systems of unsteady first-order ordinary differential equations are solved by a MATLAB code. The length of lotus-type pores is also interpreted by the conservation of the solute content in the system. The predicted final shapes of lotus-type pores agree with algebraic results previously confirmed by available experimental data.

Enhancing efficiency and measuring sloshing in oscillating water column (OWC) systems: An experimental investigation of novel inlet geometry optimization and innovative measurement method

Sea wave characteristics could be the most crucial sloshing occurrence caused by OWCs. In this paper, an OWC with different inlet geometries has been investigated experimentally to optimize the performance and reduce sloshing. Eight wave gauges (WG) are applied to measure water free surface to determine the sloshing. The results showed that the converter performance decrease when sloshing occurs. To reduce sloshing, four inlet openings were installed at the inlet of OWC, and to achieve optimal efficiency in sloshing conditions, the geometry optimization done by genetic algorithm; then, the converter's performance with optimum inlet was experimentally investigated, sloshing phenomenon was observed in 4 frequencies in converter without opening; However, after installing the optimal opening, sloshing occurred in only one frequency, and also in this case, sloshing was 42 % reduced. The data correlation results showed a positive correlation between the frequency and the Top Free Surface of water inside the OWC (shown by a line called TFS) angle. At the same time, there is a negative correlation between the frequency and the flow rate, pressure difference, and power generated. The comparison of the converter results with opening and without opening shows that the correlation between frequency and other variables is always lower in the case with opening. Also, geometry optimization improved the sloshing frequency's 42.89 % performance.

Using a Magnetic Field to Reduce Thermocapillary Convection in Thin Annular Pools

This paper presents the investigation of thermocapillary convection in three-dimensional (3-D) thin pools with three cases of annular gaps containing silicon melt under a vertical magnetic field. The model was composed of two vertical walls: the inner is cold, and the outside is hot. Radiation is emitted upward from the free top surface, and the bottom is heated vertically. Both cases are considered in this study, electrically insulating all walls; and only the bottom wall is electrically conducting for three annular gaps. The governing equations were solved numerically through the finite volume method. The effects of different parameters such as the Hartmann number, annular gaps on the temperature distribution, the hydrothermal wave number, and azimuthal patterns, as well as the transition from 3-D steady to axisymmetric flows, were investigated. The results showed three hydrothermal waves are observed in a 3-D steady flow. It was also found that with the increasing Hartmann number, the azimuthal velocity, the temperature fluctuation, and the electric potential decreased. The results also revealed that a stronger magnetic field was needed for the transition from unsteady flow to a nonaxisymmetric steady flow and at the end to steady axisymmetric flow. The findings revealed that electromagnetic damping is more prominent when the bottom wall is electrically conducting than when all walls are insulating.

Solute segregation affected by transport properties during a bubble entrapment in upward solidification

Abstract The effects of transport properties on segregation of a dissolvable gas, for example, carbon dioxide in water in the presence of an entrapping bubble during upward unidirectional solidification is numerically investigated. Microporosity and inter-related solute segregation are two common defects detrimental to mechanical properties of components, especially to fatigue performance, strength and ductility. In this work, transport processes between the bubble, liquid and solid affected by mass, momentum, energy, and concentration Eqs. are solved by finite element schemes provided from the commercial COMSOL code. The results find that solute concentration in solid and liquid surrounding the pore increases with decreasing Henry's law constant and gravitational acceleration, and increasing surface tension and solid thermal conductivity. Solute gas concentration on the top free surface is insensitive to that in the pore rather than that in liquid and solid away from the pore. Apex cap becomes non-spherical affecting solidification rate and shape of the solidification front as ambient pressure at the top free surface and gravitational acceleration increase. Contact angle versus location of the solidification front predicted from this work and Abel's Eq. agrees well. Solute segregation encountered by pore formation is controllable.

Natural convection due to surface cooling in sloping water bodies with vegetation

Natural convection induced by surface cooling in sloping water bodies with vegetation is investigated numerically. The sloping water body consists of a vegetated region with a bottom slope equal to 0.1 and a deep region with a horizontal bottom. The volume-averaged Navier–Stokes equations together with the volume-averaged energy equation are solved numerically in the vegetated region. Submerged vegetation has an equivalent porosity of 0.85. The vegetation length is either equal to the total or half the sloping region. A differential cooling is applied at the top free surface with a varying heat loss rate between the two regions. The non-vegetated sloping water body is also considered for validation purposes. The results indicate that, when cooling is reduced in the vegetated region (a) there is a time delay for the establishment of the quasi-steady regime and (b) the exchange flow rate and the gravity current's velocity decreases with increasing vegetation length. When cooling is completely blocked, different circulation patterns are developed.

Marangoni convection in a dielectric fluid layer with an AC electric field and nonuniform volumetric heat source due to incident radiation

AbstractThe role of a uniform AC electric field and a nonuniform volumetric heat source arising due to an external incident radiation on the onset of Marangoni convection in a horizontal layer of an incompressible dielectric fluid is investigated. The bottom rigid surface is fixed at a constant temperature while the top free surface at which the surface tension acts is considered to be nondeformable and a Robin boundary condition on the perturbation temperature is invoked. The nonuniform internal heating within the fluid layer alters the conduction temperature profile from linear to nonlinear in the vertical coordinate. The linear stability of the quiescent basic solution is studied with respect to normal mode disturbances. The resulting stability eigenvalue problem with variable coefficient is solved numerically using the Galerkin method. The impact of governing parameters on the instability of the system is discussed thoroughly. The forces causing instability reinforce together and are found to be tightly coupled. It is observed that the strength of nonuniform heat source and the electric Rayleigh number is to hasten, while an increase in the Biot number is to delay the onset of Marangoni electroconvection. Finally, the results obtained under the limiting cases are shown to be in good agreement with those published earlier.

MHD Effect on the Thermocapillary Silicon Melt Flow in Various Annular Enclosures

AbstractTo simulate thermocapillary magnetohydrodynamic (MHD) convection in different shallow annular enclosures filled with silicon melt, a 3D numerical approach using an implicit finite volume formulation is used. Radiation is emitted upward from the annular enclosure's free top surface, the bottom one heated vertically and is subjected to an external magnetic field. The steady and unsteady thermocapillary MHD flow in four annular enclosures (R = 0.5, 0.6, 0.7, and 0.8) field is studied. The effects of varying the annular gaps, R, on the hydrothermal wave number and azimuthal pattern are obtained. The effects of the magnetic field on azimuthal velocity, temperature disturbances, and the transition from oscillatory to steady flow are also depicted. The results reveal that: hydrothermal waves m = 4, m = 6 and m = 8 are observed in steady flow for R = 0.7, R = 0.6 and R = 0.5, respectively. Oscillatory flows dominated by a hydrothermal wave m = 3 are found also when R = 0.8. The azimuthal velocity and temperature fluctuations at the free surface decrease as the magnitude of the magnetic field (Ha) increases, and the oscillatory flow would turn steady when Ha exceeds a critical value.

Measuring and investigating the effect of sloshing on the performance of an OWC wave energy converter by means of a novel experimental approach

Renewable energy development could be an appropriate method to tackle the problems caused by fossil fuels. In this regard, an Oscillating Water Column (OWC) with a scale of 1:10 has been studied in this research. Sloshing is an unwanted phenomenon in OWC. Therefore in order to study sloshing, A Novel experimental approach for measuring free surface profile inside OWC by considering the effect of wave characteristics and sloshing was investigated experimentally in this paper. Eight wave gauges were installed at the top of the converter to study the hydrodynamic behaviour. The results showed that an increase in frequency raises the possibility of sloshing. However, up to the frequency of 0.37, the TFS (Top Free Surface) angle increase is insignificant. As frequency approaches 0.37, suddenly TFS angle rises, and sloshing occurs at frequencies of 0.37–0.80. Also, dead volumes are formed on TFS (some positive and negative volumes formed on free surface which cancel each other). Therefore if TFS angle is more than 3.85°, the sloshing is happened, and the converter's performance decreases severely. In the best conditions, efficiency and power are 53.7% and 192.2 W, respectively, and in sloshing area, efficiency and power are 8.3% and 35 W, respectively.

Free Vibration Analysis of Stiffened Lock Gate Coupled with Reservoir Fluid considering Linearised Free Surface Condition

The effect of surrounding reservoir fluid on the stiffened lock gate structure is investigated using the finite element method. A single stiffener is used to stiffen the plate, which is placed edge to edge along the height on the plate's center nodal line. Mindlin’s plate bending and Euler’s beam theories are used to formulate plate and stiffener, respectively. The stiffened lock gate material is assumed to be isotropic, homogeneous, uniformly thick and elastic in nature. The fluid is assumed to be incompressible and inviscid, resulting in an irrotational flow field. The fluid domain's top free surface is assumed to be linear based on Airy’s linear wave theory. The far boundary of the fluid domain is truncated numerically close to the lock gate to control the size of computation without influencing the results, very much. It is truncated by solving the Laplace equation using Fourier half range cosine series expansion in the finite element formulation. Pressure and displacement are considered as nodal variables for the fluid domain and the lock gate, respectively. The interaction between the fluid domain and the lock gate is established by finite element formulation and transformed into a computer code, written in FORTRAN. The natural frequencies of clamped and simply supported stiffened lock gates are evaluated by the varying extent of the fluid. Both stiffened and unstiffened gates are compared. The results are beneficial to the engineers/designers when the gate structure is subjected to cataclysmic events.

On the competition of transverse and longitudinal modes of Marangoni convection in a three-dimensional layer of viscoelastic fluid

Within the vast array of applications encompassed by viscoelastic fluids, some lack of knowledge seems to affect the non-linear behavior of Marangoni convection when its typical initial unicellular and steady states are taken over by more complex flow configurations. These still hide a not-fully understood competition of complex and diverse physical mechanisms that determine the prevailing macroscopic behavior. In the present study, relevant insights are sought from consideration of the classical differentially heated rectangular layer of liquid with adiabatic bottom and top free surface. It is shown that, for increasing values of the Marangoni number and/or the elasticity parameter, this problem offers a multifaceted spectrum of different outcomes depending on the non-trivial interplay established between two distinct categories of disturbances (transverse and longitudinal). These are studied using a diversity of model types in which some processes are on or off to discern selectively their effect in the laminar state and their contribution to the evolution of the system toward chaos. The characteristic marks by which the ensuing elastic turbulence can be distinguished from the companion Kolmogorov counterpart are highlighted through analysis of the emerging scaling laws in the velocity spectrum and the sensitivity of these to the intensity of the driving force and the considered elasticity level. It is shown that these two forms of turbulence can coexist in the considered problem.

Natural convection of three-dimensional non-Newtonian nanofluids with Marangoni effects and inclined magnetic fields

Based on the various applications of the influence of the magnetic field in the convection flow especially in the inclined case, a very large number of published investigations can be found. Nevertheless, those studies were devoted to the case of two-dimensional included magnetic fields. For the three-dimensional (3D, for short) case, there are no attempts to examine these impacts. To this end, this investigation aims to present a formulation for the inclined magnetic field in case of the 3D non-Newtonian power-law nanofluids flow under the Marangoni effects. The basic aide is depending on introducing three inclination angles with X − , Y − ,and Z-axis for the magnetic strength, namely, ηx, ηy and ηy, respectively. These angles satisfy the mathematical relation cos2ηx + cos2ηy + cos2ηz = 1. The flow domain is considered as 3D cubic enclosures with a top free surface that has linear distributions of the tension as a function in the concentration and temperature. The finite volume (FV) technique with 3D SIMPLE (Semi-Implicit Method for Pressure Linked Equations) technique is used to treat the mathematical formulations. The major findings disclosed that the inclination angles 0–90-90 and 45–90-45 give the higher double-diffusive comparing to the other values of the inclination angles. During variation of the inclination angles, the average Nusselt number; Nuav has a rate of changes up to 13.21% while the average Sherwood number; Shav reaches 380.21%.

The effect of confinement and material heterogeneities on the dynamics of a granular medium subjected to impact loading

Compared with the mechanics of continua that has been established well, the mechanical characteristics of granular particles, in particular, the dynamic ones, have not been thoroughly clarified yet. Therefore, in our previous preliminary study, dynamic stress transfer as well as wave and fracture development in granular media has been recorded using the experimental technique of dynamic photoelasticity in conjunction with high-speed cinematography. Penny-shaped particles have been prepared by a digital laser cutter and piled on a rigid horizontal plane to form a model slope with some inclination angle. The two-dimensional slope has been subjected to dynamic impact on its top free surface. From the experimentally recorded particle motion and transient stress evolution, two dissimilar failure patterns have been identified. One is the complete collapse of the slope or mass flow due to unidirectional force-chain-like stress transfer, and the other one is the toppling-type separation of the slope face caused by broadly expanding two-dimensional waves. Whichever occurs seems to be governed by the temporal profile of the energy given by the impact. Here, in order to investigate the effect of confinement and possibly material heterogeneities on granular dynamics, first, experimentally, solid plates are additionally placed on some boundaries of the model slopes. It is found that stress transfer and dynamic motion in the confined granular medium is largely controlled by the additional solid boundaries. Then, in order to numerically confirm the above experimental observations, the open source code ESyS-Particle is employed. The numerical results compare well with the experimental ones if the parameters required for the numerics are carefully and properly selected.

Gravity Governs Shear Localization in Confined Dense Granular Flows.

The prediction of flow profiles of slowly sheared granular materials is a major geophysical and industrial challenge. Understanding the role of gravity is particularly important for future planetary exploration in varying gravitational environments. Using the principle of minimization of energy dissipation, and combining experiments and variational analysis, we disentangle the contributions of the gravitational acceleration, confining pressure, and layer thickness on shear strain localization induced by moving fault boundaries at the bottom of a granular layer. The flow profile is independent of the gravity for geometries with a free top surface. However, under a confining pressure or if the sheared layer withstands the weight of the upper layers, increasing gravity promotes the transition from closed shear zones buried in the bulk to open ones that intersect the top surface. We show that the center position and width of the shear zone and the axial angular velocity at the top surface follow universal scaling laws when properly scaled by the gravity, applied pressure, and layer thickness. Our finding that the flow profiles lie on a universal master curve opens the possibility to predict the quasistatic shear flow of granular materials in varying gravitational environments.