Interface Velocity Research Articles

Accurate Prediction of Transport Coefficients of an Evaporating Liquid Drop

Abstract Numerical simulations were carried out to study the evaporation of a drop that is released into a parallel stream of fluid at a higher temperature. A coupled level-set and volume-of-fluid (CLSVOF) interface capturing method was deployed to capture the dynamic interface between the drop liquid and the surrounding fluid. Modified forms of mass, momentum, and energy equations were solved together with the species concentration equation. The pressure jump at the interface was handled by accurate estimation of the continuum surface force. The jumps in mass and energy at the interface were carefully resolved by considering appropriate source terms in the continuity and energy equations. At the interface, the procedure of velocity computation was incorporated by extending the liquid-phase velocity onto the entire domain and by calculating the Stefan flow to predict the interface velocity accurately. The calculation of the velocity using this step leads to the exact estimation of mass transfer through the interface. The model was validated against both temperature gradient-based and vapor mass concentration gradient-based evaporation test cases. Temporal histories of the average Nusselt number and Sherwood number during the lifetime of an evaporating drop were predicted in terms of the pertinent input parameters, namely, Reynolds number, Prandtl number, and Schmidt number.

DOPPLER OPTICAL PROBE FOR DROP SIZE, VELOCITY, AND FLUX MEASUREMENTS IN ASSISTED ATOMIZATION

For research as well as for process control, reliable drop size, velocity, and flux measurements are desirable in particular in dense, high-speed flows. A new optical probe has been recently manufactured by A2 Photonic Sensors company that combines an accurate phase detection capability (its latency length is small, about 6 µm) with the collection of a Doppler signal that provides the absolute velocity of an incoming gas-liquid interface. In this article, raw signals acquired over diverse flow conditions in terms of gas velocity and liquid concentration are analyzed. A dedicated signal processing routine is then proposed and optimized. The latter provides statistics on drop velocity and size. It also gives access to local liquid concentration and liquid flux. This Doppler probe combined with its processing has been tested in sprays produced from assisted atomization over a wide range of flow conditions. Transverse profiles of spray characteristics are presented for gas injection velocities ranging from 32 m/s to 283 m/s, for drops Sauter mean diameters D<sub>32</sub> varying from 37 µm to 275 µm, and for number densities-as estimated from liquid concentration and D<sub>32</sub>-comprised between 1 #/mm<sup>3</sup> and 218 #/mm<sup>3</sup>. The Doppler probe happens to be able to consistently detect chords as small as 4 µm, and to ensure a significant (up to 70%) fraction of direct velocity measurements. Besides, the injected liquid flow rate is recovered from the spatial integration of local liquid fluxes within 8% for gas velocities up to 50 m/s and within 17% for gas velocities above 90 m/s. Hence, the new Doppler probe combined with the proposed processing provides reliable statistics on drop velocity, size, and flux, and is a valuable tool for investigating dense, high-velocity, and fine sprays.

Pseudo-4D view of the growth and form of crystallographically ‘locked’ eutectic colonies

A number of fundamental questions remain unanswered regarding the interior structure of eutectic cells or colonies growing into a liquid. Here, we observe experimentally the solidification behaviour of an Al-Al2Cu eutectic as a model system using a novel imaging approach that combines in situ X-radiography and ex situ X-ray tomography. The former allows us to trace the solid-liquid interfaces while the latter enables us to visualize the solid-solid interfaces. When put together, we can visualize in 4D (i.e., three-dimensional space plus time) the development of a crystallographically ‘locked’ eutectic microstructure in the presence of an oscillatory eutectic-liquid velocity driven by thermosolutal convection. These details provide direct insight into the mechanism of the lamella-to-rod transition as the eutectic accommodates fluctuations in interfacial composition and growth velocity. We find that this morphological transition reflects a delicate balance between the motion of trijunctions and the stiffness of low-energy, solid-solid interfaces. Our pseudo-4D tomography approach holds broad appeal to the solidification science community, as it can temporally resolve the solidification process on the order of seconds and spatially resolves individual lamellae on the order of micrometres, thereby overcoming the space-time trade-off in conventional in situ X-ray tomography.

Adhesion and mechanical properties of poly(dimethylsiloxane) bottlebrush elastomers.

Poly(dimethylsiloxane) (PDMS) bottlebrush elastomers (BBEs) are attractive soft materials with well-controlled bulk mechanical properties. However, their surface and interfacial properties have not been studied in depth. We report a detailed study of the adhesion of PDMS BBEs to glass using a contact adhesion test to determine the critical energy release rates, Gc, as a function of interfacial separation velocity. For BBEs, Gc for initiating separation, G0, was found to be independent of the crosslink density. We hypothesize that the monomer chemistry of side chains plays a primary role in defining surface properties for this materials system. After crack initiation, BBEs showed a significantly lower Gc and less velocity dependence than linear chain networks. Scaling analysis attributes these properties to the faster dissipative relaxation mechanisms within the BBEs. These findings demonstrate that the adhesion properties of BBEs can be finely tuned through the monomer chemistry and side chain length for potential applications.

An improved multiphase lattice Boltzmann flux solver with phase interface compression for incompressible multiphase flows

Numerical dissipation is ubiquitous in multiphase flow simulation. This paper introduces a phase interface compression term into the recently developed multiphase lattice Boltzmann flux solver and achieves an excellent interface maintenance. Here, the phase interface compression term only works in the interface region and is solved as the flux in finite volume discretization. At each cell interface, the interfacial compression velocity ur is determined by local reconstruction velocities of the multiphase lattice Boltzmann flux solver, which maintains the consistency of the flux evaluation. Meanwhile, the interfacial order parameter C in the phase interface compression term is obtained by the second order upwind scheme according to the interface normal direction. Numerical validation of the present model has been made by simulating the Zalesak problem, the single vortex problem, Rayleigh–Taylor instability, and bubble rising and coalescence. The obtained results indicate the validity and reliability of the present model.

A neural network-based data-driven local modeling of spotwelded plates under impact

Solving large structural problems with multiple complex localized behaviors is extremely challenging. To address this difficulty, both intrusive and non-intrusive Domain Decomposition Methods (DDM) have been developed in the past, where the refined model (local) is solved separately in its own space and time scales. In this work, the Finite Element Method (FEM) at the local scale is replaced with a data-driven Reduced Order Model (ROM) to further decrease computational time. The reduced model aims to create a low-cost, accurate and efficient mapping from interface velocities to interface forces and enable the prediction of their time evolution. The present work proposes a modeling technique based on the Physics-Guided Architecture of Neural Networks (PGANNs), which incorporates physical variables other than input/output variables into the neural network architecture. We develop this approach on a 2D plate with a hole as well as a 3D case with spot-welded plates undergoing fast deformation, representing nonlinear elastoplasticity problems. Neural networks are trained using simulation data generated by explicit dynamic FEM solvers. The PGANN results are in good agreement with the FEM solutions for both test cases, including those in the training dataset as well as the unseen dataset, given the loading type is present in the training set.

A Phase-Field Model for In-Space Manufacturing of Binary Alloys.

The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.

Non-equilibrium ordering of liquid crystalline (LC) films driven by external gradients in surfactant concentration

HypothesisGradients in the concentration of amphiphiles play an important role in many non-equilibrium processes involving complex fluids. Here we explore if non-equilibrium interfacial behaviors of thermotropic (oily) liquid crystals (LCs) can amplify microscopic gradients in surfactant concentration into macroscopic optical signals. ExperimentsWe use a milli-fluidic system to generate gradients in aqueous sodium dodecyl sulfate (SDS) concentration and optically quantify the dynamic ordering of micrometer-thick nematic LC films that contact the gradients. FindingsWe find that the reordering of the LCs is dominated by interfacial shearing by Marangoni flows, thus providing simple methods for rapid mapping of interfacial velocities from a single optical image and investigating the effects of confinement of surfactant-driven interfacial flows. Additionally, we establish that surface advection and surfactant desorption are the two key processes that regulate the interfacial flows, revealing that the dynamic response of the LC can provide rapid and potentially high throughput approaches to measurement of non-equilibrium interfacial properties of amphiphiles. We also observe flow-induced assemblies of microparticles to form at the LC interface, hinting at new non-equilibrium approaches to microparticle assembly. We conclude that dynamic states adopted by LCs in the presence of surfactant concentration gradients provide new opportunities for engineering complex fluids beyond equilibrium.

Computational investigation of vertical upflow boiling of liquid nitrogen and effects of bubble collision dispersion force

The present study investigates the performance of 2-D axisymmetric computational fluid dynamics (CFD) in predicting boiling characteristics of liquid nitrogen flowing vertically upwards along a uniformly heated circular tube. Investigation of the popular Volume of Fluid (VOF) model reveals (a) inaccurate surface tension calculation which degrades interface tracking, and (b) under-representation of bubble-to-bubble interaction, which stems from the innate nature of employing a single momentum equation in VOF. To alleviate VOF shortcomings, Coupled Level Set VOF (CLSVOF) is adopted in ANSYS FLUENT, including a user defined function to account for the crucial effects of bubble collision dispersion force. The CFD simulation results are validated against wall temperature and volume fraction results from prior benchmark experiments corresponding to four different wall heat flux conditions at nearly identical mass velocities. Predictions are also provided for axial variations of interfacial flow pattern, fluid temperature, and fluid velocity, flow characteristics that are very difficult to measure in cryogenic experiments. The CFD simulation results are shown to be highly accurate at predicting the nucleate boiling portion of the flow boiling curve.

A Semi-empirical correlation for stratified two-phase flow friction factors

The optimal design of two-phase flow pipes depends on various variables. Pressure drop and liquid hold-up are essential parameters in the appropriate design of pipes. These parameters can be estimated by numerical simulation of pipes. However, the simulation strongly depends on both phase frictions. Frictions are commonly calculated using friction factors, and various empirical correlations have been proposed to calculate friction factors, but most of these correlations are dependent on the experimental conditions.The present study proposes a semi-empirical friction factor model by modifying an existing model in the literature for stratified two-phase flows. Experimental data from various laboratories are taken to validate the interface shear stress, velocity profile and pressure gradient. Compared with previous models, the predicted velocity profiles and shear stresses are in better agreement with the experimental data.

Heterogeneous phase transformation pathways in additively manufactured Al-Ce-Mn alloys

Heat treatment of additively manufactured Al-Ce based multicomponent alloys leads to complex microstructure evolution. In this research, the ability to extend the phase transformation theories involving nucleation of a product phase from a heterogeneous multi-phase microstructure typical to that of additively manufactured samples is explored. The Al-10Ce-8Mn (wt%) was used as a model alloy system. Under additive manufacturing conditions different solidification microstructures were obtained due to spatial and temporal variations of thermal gradients (G) and liquid-solid interface velocities (R) within a given melt pool. Near the melt pool boundary (high G and low R, referred as MPB region), initially, Al20Mn2Ce forms from the liquid followed by a eutectic of FCC Al and Al11Ce3. In the melt pool interiors (low G and high R referred as ES region) a eutectic structure between FCC Al and Al20Mn2Ce is observed. During subsequent heat treatments, the MPB and ES regions transform into different sets of microstructures. In the MPB region, a fine globular microstructure containing FCC Al, Al11Ce3, Al6Mn, and Al12Mn results from the decomposition of Al20Mn2Ce. In the ES region a faceted Al51Mn7Ce4 plate phase results from the decomposition of Al20Mn2Ce. The formation of the Al51Mn7Ce4 phase within the eutectic microstructure at the boundaries of FCC Al and Al20Mn2Ce has not been reported in the literature. These two distinct phase transformation pathways are rationalized based on the role of driving force on the nucleation of (Al6Mn) and/or metastable intermetallic (Al51Mn7Ce4) phases at the interface of aluminum (FCC) and the non-equilibrium intermetallic (Al20Mn2Ce) phases.

Solution for the Dynamic Elastically Compressible Power-Law Strain Hardening Cylindrical Cavity-Expansion Problem

A closed form analytical solution for both the quasi-static or dynamic strain hardening cylindrical cavity-expansion (CCE) problems requires the plastic region to be incompressible. This is due to the fact that in both cases a hydrostatic stress state must be explicitly included in the strain hardening function, making an analytical solution intractable. Additionally, for the dynamic problem the elastic region must be compressible to avoid a logarithmic singularity at infinity. An alterative for the dynamic analytical formulation is to use the finite element method (FEM). With the FEM weak formulation, solutions for the radial stress at the cavity surface and the elastic–plastic interface interface velocity as functions of the cavity-expansion velocity can be obtained when both the strain hardening plastic and elastic regions are elastically compressible. In this study, a comparison is made using results from both analytical (strong formulations), and FE simulations for both strain hardening and perfectly plastic dynamic CCE problems. It is concluded that with increasing cavity-expansion velocities, the elastically compressible strain hardening FEM solution is less resistive than the corresponding closed form analytical solution with an incompressible plastic region. Additionally, it is shown that the elastic–plastic interface velocity asymptotes at the bulk wave speed for completely elastically compressible solutions. Furthermore, the completely elastically compressible solutions remain valid for cavity-expansion velocities beyond the critical cavity-expansion velocity associated with the closed-form analytical strain hardening solution.

An interface-resolved phase-change model based on velocity decomposition

An interface-resolved phase-change model is proposed in the interface-capturing framework based on the coupled level-set and volume of fluid (CLSVOF) method. A velocity decomposition method is employed to ensure the numerical stability and accuracy of interface propagation. Specifically, the velocity u is decomposed into the potential part u˜ associated with the phase change and the remaining rotational part u¯. The potential velocity u˜ is computed by solving a Poisson equation. A modified momentum equation is derived to solve the rotational-part velocity u¯, which is divergence-free. The momentum equation is solved using the Computational Air-Sea Tank (CAS-Tank) developed previously by Yang et al. [1]. To evolve the interface and ensure the mass conservation, a continuous interfacial velocity uΓ is constructed by adding the velocity uˆ associated with the volume change of liquid (or gas) to u¯, where uˆ is computed by solving a Poisson equation with constant coefficient. The proposed method is verified in the context of the two-dimensional (2D) droplet with constant evaporation rate, one-dimensional (1D) Stefan and sucking problems, 2D droplet evaporation at saturation temperature, 2D droplet evaporation below saturation temperature, and a three-dimensional (3D) evaporating droplet falling under the gravity. The results show that the proposed method is accurate and stable. The numerical method is also validated by simulating an evaporating droplet falling under the gravity and the numerical results are found to be in agreement with the results in the literature. The interaction of two evaporating droplets is also simulated in a 3D domain to show the capability of the proposed method in solving 3D problems.

Determination of self-adaptive slip rate at tool/workpiece interface in numerical model of friction stir welding

As a key parameter affecting the heat generation and the interface material velocity, the interface slip rate is a prerequisite for numerical simulation of friction stir welding of lightweight materials. The contact state on the tool/workpiece interface is related to friction stress and material yield strength, and a new calculation method of the self-adaptive interface slip rate was established. The interface velocity of material flow, heat generation due to friction and plastic deformation near the tool and temperature distribution were analyzed quantitatively. The calculated self-adaptive interface slip rate has a wider range than the previous used one, from a sticking dominant for the material near the inner part of the shoulder to a sliding dominant for the material near the edge of the shoulder. With application of this improved method determining the slip rate, the material flow velocity at the tool/workpiece interface is roughly in a "M" shape, which first increases and then decreases as the radial distance rises, and the maximum interfacial material velocity no longer appears at the shoulder edge. The experiments were made to validate the method. The slip rate distribution at tool/workpiece interface in (a) Previous mode; (b) Improved mode.

Dynamics of condensate film in the vicinity of a pulling vapor stream

This article introduces eight possible film configurations that appear when a rising vapor stream condenses on a vertical surface. These configurations include hanging film, falling film, falling film with zero interface velocity, partly falling film, bidirectional film, partly rising film, transition film, and rising film. We develop a theoretical framework to predict condensate dynamics and heat transfer. The results show that the entire film morphology depends on a subcooling parameter (H) and a characteristic number (ϒN). Here, ϒN is the ratio of the relative Froude number and the film Reynolds number, which increases continuously from falling to rising configurations. Our analysis shows that a falling film's heat transfer and condensation rates increase as subcooling (H) increases. However, increasing H for partly falling films reduces the condensation rate, hindering the overall heat transfer. We demonstrate that the falling films produce the maximum condensate within a particular range of H; however, the maximum shifts to transition films beyond this range. As H increases, the transition films are attained at a smaller ϒN. We have identified five physical mechanisms that subtly govern the film dynamics: gravity, wall shear, interfacial shear, near wall mass-flux deficit, and interfacial mass entrainment. Concurrent participation of these mechanisms yields complex streamlines and spiral vortices.

Two-phase free-surface flow interaction with moving bodies using a consistent, momentum preserving method

The numerical prediction of two-phase flows with an interface is challenging, to a considerable extent because of the high density ratio at the interface. Numerical results become affected by momentum losses, diverging spurious interface velocities, free surface distortion, and even numerical instability. To prevent issues like these, consistent momentum and mass transport with an additional continuity equation were introduced.In this article, we describe how a consistent discretization was incorporated into our own method and extended for fluid-structure interaction (FSI) with moving rigid bodies. The new method was tested against benchmark simulations from literature confirming that consistent transport modeling gives a significant improvement compared to non-consistent modeling for the dynamics of two-phase flows.Newly devised proof of principle FSI simulations with momentum transfer from fluid to body in the presence of a high-density ratio between fluids are introduced that could serve as a benchmark for future studies. The simulations demonstrate that consistent modeling gives an order of magnitude improvement in terms of momentum conservation compared to non-consistent modeling.Simulations with the new method are also compared to FSI experiments from literature. Results obtained with the consistent method are closer to the measurements than results of the non-consistent method.The merit of consistent modeling with and without FSI becomes especially apparent for two-phase flows with a high-density ratio between fluids.

Liquid holdup modeling analysis in horizontal gas–liquid slug flow

In slug flow, the wetted wall fraction and liquid holdup of the liquid film section are key parameters affecting the mass transfer and radial velocity distribution of the liquid film, the friction pressure drop, the momentum transfer between the two phases, and heat transfer characteristics. A modified wetted wall fraction and liquid holdup model based on the modified apparent rough surface (MARS) model is proposed in this study, which considers the friction coefficient and shear stress on the gas–wall, liquid–wall and gas–liquid interfaces and introduced the modified average interface velocity of the liquid film. Air–water slug flow experiments were in a 50 mm diameter acrylic glass pipe equipped with a high-speed camera. The edge detection operator was optimized to obtain the wetted wall fraction and liquid holdup at the liquid film section based on image analysis technology. A comparative analysis of the model performance shows that the mean absolute percentage error (MAPE) of the wetted wall fraction model is 9.4%, and the 96.1% relative deviations are within the ±20% error band. The MAPE of the liquid holdup model is 8.04%, and 93.4% relative error is within the ±25% error band. The modified MARS model has good prediction ability for the wetted wall fraction and liquid holdup of the gas–liquid slug flow.

Significance of Brinkman and Stokes system conjuncture in human knee joint

Stokes’s equation in the fluid domain and Brinkman’s equation in the porous media are combined in the current study which is designated by the Stokes-Brinkman coupling. The current paper gives a theoretical analysis of the Stokes-Brinkman coupling. It has been shown that such a model is a good match for the knee joint. A flow model has been investigated in order to get a better understanding of the convective diffusion of the viscous flow along the articular surfaces between the joints. The Beavers and Joseph slip conditions which are a specific boundary condition for the synovial fluid are used to solve the governing system of partial differential equations for the synovial fluid and the results are provided here. We develop formulas for the interfacial velocity for both flow through special slip condition and analyse the link between the slip parameters alpha and beta . Thus, the damping force due to the porous medium naturally when we non-dimensionalize, some parameter which are controlling the structure like, beta and alpha . Through the development of an analytical solution and numerical simulation (using the finite volume approach) it is hoped that the mechanisms of nutritional transport into the synovial joint will be better understood. According to the data the average concentration has a negative connection with both the axial distance and the duration spent in the experiment. Many graphs have been utilized to gain understanding into the problem’s various characteristics including velocity and concentration, among others. Hyaluronate (HA) is considered to be present in porous cartilage surfaces and the viscosity of synovial fluid fluctuates in response to the amount of HA present.

Numerical study of satellite droplet formation in dripping faucet

• Dynamic relation between the liquid/gas interface, pressure and velocity profile has been investigated. • Physics of capillary wave generation in liquid filament has been analyzed. • Satellite drop generation depends on the acceleration and distribution of the axial velocity at the cone-filament junction. • Satellite drop is less likely to be formed at high inlet velocity and low surface tension coefficient. Dynamics of primary and satellite drop formation has wide engineering applications. Drop formation from a vertical capillary tube in air goes through various stages that include necking, bifurcation, recoil, wave generation and secondary necking and bifurcation. In this study, the problem has been studied numerically where the free surface of the pendant drop is tracked by a coupled level set and volume-of-fluid method with the surface tension force determined by the continuum surface force model. The evolution of the complete droplet separation process has been simulated. The numerical results have been compared with published experimental data. The mechanism for the recoiling of the liquid filament after droplet detachment and the subsequent formation of a satellite droplet has been studied and dynamic correlation among liquid/gas interface topology, velocity and pressure field has been investigated. Bell shaped distribution of axial velocity profile and fast acceleration at the cone-filament junction has been found to lead to satellite drop generation. Parametric studies on the effects of inlet velocity, surface tension coefficient and viscosity have been performed. Satellite droplet is less likely to be formed at high inlet velocity and low surface tension coefficient. Viscosity, on the other hand, has been found to play an important role on the shape of liquid filament and satellite droplet. These findings can help better understanding of drop-on-demand liquid dispensing, inkjet printing, spray combustion and many more engineering applications.

Kinetic coefficient for ice–water interface from simulated non-equilibrium relaxation at coexistence

In the theory of solidification, the kinetic coefficient multiplies the local supercooling to give the solid-liquid interface velocity. The same coefficient should drive interface migration at the coexistence temperature in proportion to a curvature force. This work computes the ice-water kinetic coefficient from molecular simulations starting from a sinusoidal ice-water interface at the coexistence temperature. We apply this method to the basal and prismatic ice planes and compare results to previous estimates from equilibrium correlation functions and simulations at controlled supercooling.