Front Tracking Method Research Articles

Numerical simulation study of self-driven microdroplet on locally restrictive discontinuous wetting gradient surface using front tracking method

The motion of droplet on surface with discontinuous wetting gradient is of great importance for understanding lab-on-a-chip systems and other microfluidic devices. Different wetting gradients are known to be the main influencing factor in the droplet self-driven process, but the effect of different wall structures on the droplet migration process also deserves further investigation. In this paper, we analyze the self-driven process of liquid droplets on a local wetting gradient surface under microgravity conditions using front tracking method. The effects of different driving stripe lengths [Formula: see text], different restrictive stripe lengths [Formula: see text], and different surface wetting gradients Δcos⁡ θ on the droplet migration process and droplet morphology are analyzed. A theoretical formula that can predict the lateral spreading length of droplets is also proposed. The results show that different driving stripe length [Formula: see text] lengths and the wetting gradient Δcos θ have significant effects on the migration velocity of droplets, while different restrictive stripe length [Formula: see text] lengths have very significant effects on the final morphological characteristics of droplets. When restrictive stripe length [Formula: see text], the hindering effect generated by the restrictive region ΙΙΙ has more and more significant effects on the morphological structure of droplets in the migration process. When the correction factor ε = 0.735 in the prediction equation, the predicted value calculated by the theoretical equation has a good degree of similarity with the numerical simulation results.

Numerical study of head-on collision of two equal-sized compound droplets

Although on-axis collisions between compound droplets are involved in numerous technological applications, no detailed investigation of such collisions is yet available. To address this problem, the present work uses an axisymmetric front-tracking method to numerically explore the dynamics of on-axis collisions of compound droplets that contain one or more inner droplets. Two identical droplets are placed symmetrically on the midplane of a computational domain and made to make contact with an initial colliding velocity. Various parameters such as the Reynolds number Re, the Weber number We, the size of the inner droplets, the interfacial tension ratio, and the eccentricity are considered. Three primary outcomes are observed: complete coalescence (CC), outer coalescence (OC), and rebound (R) for Re = 4–256 and We = 1–128. CC is when both the inner and outer droplets coalesce, whereas OC is when only the outer droplets coalesce. R is when the droplets come into contact and then bounce back. Increasing Re or decreasing We enhances the CC pattern, as does increasing the size of the inner droplets or the interfacial tension ratio. The influence of the initial distance between the droplets is also investigated. Finally, regime diagrams related to these patterns of collision are also presented.

A numerical study of drop evaporation at high density ratios using Front-Tracking method

A numerical study of drop evaporation at high density ratios using Front-Tracking method

Numerical study of the effect of heat-flow coupling on interface instability based on front tracking

The interfacial instability of two-phase immiscible fluids in inclined tubes at constant temperature boundary conditions is numerically investigated by the front-tracking method. By analyzing the effects of inclination angle φ, Marangoni number (Ma), and Rayleigh number (Ra) on the interfacial instability, the interaction law between unstable interface fluctuation and heat transfer is studied. The results show that the larger the inclination angle, the easier the interface is destabilized, and the heat transfer at the interface will also decrease. In the comparison of inclination angles of 0°, 30°, 45°, and 60°, the heat transfer is more stable at 45°. The heat flux between fluids decreases with the increase of Ma number, and Ma number has little effect on the interfacial fluctuation. It mainly affects the interfacial morphology by changing the surface tension gradient at the interface, which is mainly reflected in the end of the convolution interface. The larger the Ma number, the more inward the interface develops. Ra number has an obvious inhibitory effect on the interfacial instability. The effect of Ra number on heat-flow transfer at the interface shows alternating changes. In the initial stage, the heat transfer between fluids in the inclined tube is greater than that in the horizontal tube, but in the later stage, the heat transfer is less than that in the horizontal tube.

Testing the INSIM-FT Proxy Simulation Method

This paper describes testing of the INSIM-FT proxy simulation method (interwell-numerical-simulation model improved with front-tracking method) to assess the dependencies between production and injection wells, as well as to assess the forecast of oil/liquid production by wells depending on their operation parameters. The paper proposes the approach of taking into account the influence of various production enhancement operations. The method was tested on a synthetic hydrodynamic model and on a sector of a real field. The results show a good match between historical data and simulation results and indicate significant computational efficiency compared to classical reservoir simulators.

A Lattice Boltzmann Front-Tracking Interface Capturing Method based on Neural Network for Gas-Liquid Two-Phase Flow

This paper presents a new method that accurately captures the interface of gas–liquid two-phase flow using a neural network-based lattice Boltzmann front-tracking interface capturing method. The motion of a single free-falling droplet is simulated using the Front Tracking Method (FTM), enabling the acquisition of information regarding the velocity field and interface points. The velocity field and interface points from the simulations are then utilised to generate input and output datasets for training the neural network (NN) models. Subsequently, the trained Bayesian regularised Back Propagation Neural Network (BRBPNN) model is integrated into the Lattice Boltzmann method (LBM), utilising the velocity field obtained from LBM simulation as input. The predicted LBM interface exhibits remarkable agreement with the FTM interface, as evidenced by a high correlation coefficient of 0.99945 for the ordinate value of the interface point in both methods. Therefore, the proposed method achieves precise positioning of the phase interface of LBM.

Measurement of internal diameters of capillaries and glass syringes using gravimetric and optical methods for microflow applications.

Microflow measurement devices are used in several science and health applications, mainly drug delivery. In the last decade, several new methods based on optical technology were developed, namely the front tracking and interferometric method, in which the knowledge of the inner diameter of the syringe or the capillary used is critical. Only a few National Metrology Institutes (NMIs) can perform inner diameter measurements below 1 mm, which requires expensive technology. Therefore, IPQ, in cooperation with CETIAT, CMI and UNIDEMI, under the EMPIR project 18HLT08 MeDDII - Metrology for Drug Delivery, developed new measurement methods for small inner diameter tubes based on the gravimetric principle and optical methods in order to simplify the apparatus used for this type of measurements without increasing uncertainty. The gravimetric experimental setup consists of measuring the liquid volume on a specific length of the glass tube. The optical method used is based on the front track principle that uses a high-resolution camera and ImageJ software, to determine the diameter at both ends of each capillary. To validate the developed methods, a comparison was performed between CETIAT, CMI and IPQ and the results obtained were all consistent. This work allowed the determination of inner diameter of syringes or capillaries using two different methods with relative expanded uncertainties from 0.1 to 0.5% (k=2), that can be applied for flow measurements using optical technology.

Front-tracking transition system model for traffic state reconstruction, model learning, and control with application to stop-and-go wave dissipation

Connected and Autonomous Vehicles is a technology that will be disruptive for all layers of traffic control. The Lagrangian, in-the-flow nature of their operation offers untapped new potentials for sensing and actuation, but also presents new fundamental challenges. In order to use these vehicles for traffic state reconstruction and control, we need suitable traffic models, which should be computationally efficient and able to represent complex traffic phenomena. To this end, we propose the Front-tracking Transition System Model, a cell-free modelling approach that can incorporate Lagrangian measurements, and has a structure that yields itself to on-line model learning and control. The model is formulated as a transition system, and based on the front-tracking method for finding entropy solutions to the Lighthill–Whitham–Richards model. We characterize the solution of this model and show that it corresponds to the solution of the underlying PDE traffic model. Algorithms for traffic state reconstruction and model learning are proposed, exploiting the model structure. The model is then used to design a prediction-based control law for stop-and-go wave dissipation using randomly arriving Connected and Autonomous Vehicles. The proposed control framework is able to estimate the traffic state and model, adapt to changes in the traffic dynamics, and achieve a reduction in vehicles’ Total Time Spent.

Numerical study of a hollow pileup yielded by deposition of successive hollow droplets

Understanding the pileup formation process of sequentially deposited droplets is vital in advancing droplet-based printing technologies. While pileups of simple droplets have been extensively studied, knowledge of the hollow pileup formation is inadequate. This paper presents a fully resolved numerical analysis of the pileup formed by successively depositing incoming hollow droplets on a pre-solidified (or base) droplet on a supercool surface. An axisymmetric front-tracking method is used to handle the simulations. The pileup height increases as the incoming droplets coalesce, while the hollow cores may or may not merge. The pileup shape and its hollow configuration depend on parameters such as the Stefan number, Peclet number, Weber number, Fourier number, and the size and number of hollow cores. Varying these parameters does not affect the peak formation at the top of the pile caused by volume expansion during phase change, although the Fourier number has a strong influence on the mean aspect ratio and solidification time of the pileup. Increasing the deposition rate enhances the coalescence of hollow cores and reduces the mean aspect ratio of the pileup. Reducing the Stefan number also promotes hollow core coalescence, which decreases the mean aspect ratio. However, the size of the hollow core and the Peclet and Weber numbers have almost no influence on the outer shape of the hollow pileup. The effect of the number of incoming droplets on the pileup formation is also revealed.

Modeling and numerical study of particle-bubble-liquid flows using a front-tracking and discrete-element method

Particle-bubble-liquid flows widely exist in industrial processes, such as fluidized beds, flotation cells, and bubble column reactors, but the high-fidelity simulation of these flows is a great challenge. This paper developed a dynamic model for this three-phase system using a front-tracking and discrete-element method, where the behaviors of collision, attachment, and detachment between the particles and bubbles are included. The convergence and accuracy of this model were validated, and then the model was applied to simulate the transport behaviors of particle-bubble-liquid flows. The collision and attachment probabilities and the effects of particle size and properties on the collision, attachment, and flow behaviors were numerically investigated. The particle-bubble interaction simulations show that the collision probability and contact time increase with the increase of the size ratio of particle to bubble; hydrophilic particles can promote the bubble rising speed and even faster than that in the pure liquid; the attachment behavior greatly impedes the bubble rising but enhances the particle transport intensity. The bubbling simulations show that the wake of the rising bubble can induce the following bubble to move along a wave-like trajectory; the particles driven by a higher bubbling frequency present a higher lifting height and a stronger dispersion effect.

Using Adaptive Mesh Refinement strategies to investigate immiscible fluid flow in fractures

In this paper, we consider two Adaptive Mesh Refinement (AMR) methods to simulate flow through fractures using a novel multiphase model. The approach represents the fluid using a two-dimensional parallel-plate model that employs techniques adapted from lattice-Boltzmann simulations to track the fluid interface. We discuss different mesh refinement strategies for the model and compare their performance to that of a uniform grid. Results from the simulations show excellent agreement between the model and analytical solutions for both unrefined and refined meshes. We also present results from the study that illustrate the behavior of the AMR front-tracking method. The AMR model is able to accurately track the interfacial properties in cases where uniform fine meshes would significantly increase the simulation cost. The ability of the model to dynamically refine the domain is demonstrated by presenting the results from an example with evolving interfaces.Using the AMR model, we compute the relative permeability of immiscible two-phase flow in fractures. The results are successfully validated against the laboratory measurements. From this study, we introduce the interface specific surface area as a parameter to quantify the effect of flow pattern on the relative permeability. It is shown that by decreasing this parameter the fluids intervention decreases and the relative permeability curves approach the linear model.

Role of surfactant-induced Marangoni effects in droplet dynamics on a solid surface in shear flow

We address the dynamics of a surfactant-laden droplet on a solid surface in simple shear flow numerically. Our analysis uses the front-tracking method to take surfactant transport into account. The interfacial tension and the slip coefficient, both of which depend heavily on the surfactant concentration, are fully integrated into the generalized Navier boundary condition to model the moving contact lines. Accurate prediction of droplet motion indicates that the surfactant can change droplet behavior drastically. Surfactant-induced effects, such as interfacial tension reduction, the Marangoni stress, and wettability alternation, are investigated for various capillary numbers, surface wettabilities, elasticity numbers, and surface Péclet numbers. Deformation and motion of a sliding droplet are enhanced by the Marangoni effect, which is associated with an interfacial tension gradient. When the capillary number reaches a critical value, the sliding-to-detachment and detachment-to-pinch-off transitions occur. Both transitions can be triggered and accelerated by a surfactant, especially when convection is dominant. As a result, the critical capillary number decreases, but exhibits a non-monotonic relationship with the elasticity number and Péclet number. The mechanisms that underlie the effect of Marangoni stress are discussed by analyzing the distributions of the surfactant concentration and the hydrodynamic forces exerted on the droplet. Accumulation of surfactants near the receding contact line reverses the local concentration gradient, attempts to change its direction along the interface, and delays droplet detachment. Furthermore, the strong surfactant dilution reduces both the surfactant concentration and the interfacial tension gradient, and thereby increasing the critical value for droplet pinch-off.

Uniqueness and Weak-BV Stability for 2times 2 Conservation Laws

Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of small BV functions which are global solutions of this equation. For any small BV initial data, such global solutions are known to exist. Moreover, they are known to be unique among BV solutions verifying either the so-called Tame Oscillation Condition, or the Bounded Variation Condition on space-like curves. In this paper, we show that these solutions are stable in a larger class of weak (and possibly not even BV) solutions of the system. This result extends the classical weak-strong uniqueness results which allow comparison to a smooth solution. Indeed our result extends these results to a weak-BV uniqueness result, where only one of the solutions is supposed to be small BV, and the other solution can come from a large class. As a consequence of our result, the Tame Oscillation Condition, and the Bounded Variation Condition on space-like curves are not necessary for the uniqueness of solutions in the BV theory, in the case of systems with 2 unknowns. The method is L^2 based, and builds up from the theory of a-contraction with shifts, where suitable weight functions a are generated via the front tracking method.

Extrapolated Shock Fitting for Two-Dimensional Flows on Structured Grids

Over the years the development of structured-grid shock-fitting techniques faced two main problems: the handling of a moving discontinuity on a fixed background grid and the capability of simulating complex flow configurations. In the proposed work, the authors present a new shock-fitting technique for structured-grid solvers that is capable of overcoming the limitations that affected the different approaches originally developed. The technique presented here removes the tight link between grid topology and shock topology, which characterizes previous shock fitting as well as front tracking methods. This significantly simplifies their implementation and more importantly reduces the computational overhead related to these geometrical manipulations. Interacting discontinuities and shocks interacting with a solid boundary are discussed and analyzed. Finally, a quantitative investigation of the error reduction obtained with the approach proposed via a global grid convergence analysis is presented.

Application of the front tracking method in micro flow measuring devices

This work has the main objective to develop a calibration method for micro flow measuring devices based on the front tracking principle, in the Volume and Flow Laboratory (LVC) of the Portuguese Institute of Quality (IPQ), in a partnership with and the Department of Mechanical and Industrial Engineering (DEMI) of The New University of Lisbon under the project MeDD II – Metrology for Drug Delivery.The experimental setup consists of using a camera and Python software to track the distance traveled by the meniscus of a liquid inside a capillary tube and calculate the flow rate according to appropriated equations. Experimental tests using a flow generator and a flow meter were carried out for different flow rates. Two different setups with cameras of different specifications were tested.To validate the developed front tracking method, internal comparisons using a Nexus pump and a Sensirion meter were performed with the gravimetric and interferometric methods already implemented at LVC. The results obtained by these two comparisons were consistent.This new developed method can therefore be used to calibrate flow devices from 1000 μL/h down to 1 μL/h with an uncertainty value from 2% to 7% (k = 2). The calibration procedure is easy to apply and can be used for both syringe and flow meters. This method is simple to implement in a laboratory and the setup is relatively cheap compared to the gravimetric or interferometric method.Finally, the front tracking method was applied to the calibration of an implantable insulin pump used by diabetic patients.

Stability of solutions constructed by the wave front tracking method for conservation laws

We prove the Lloc1 stability of sequence of piecewise constant solutions constructed by the wave front tracking method for conservation laws. As a result, we can see concretely the convergence rate of sequence of piecewise constant solutions constructed by the wave front tracking method for conservation laws.

A numerical study of a suspended compound droplet solidifying under forced convection

In this study, we numerically investigate the solidification process of a suspended compound droplet in a cold environment under forced convection by a front-tracking method. The compound droplet consisting of an inner gas core (i.e., inner bubble) surrounded by a phase-change liquid shell (i.e., outer droplet) starts solidifying from a nucleus at its bottom. The phase-change interface evolves upward to form the solid shell with an upper conical outer surface due to volume expansion. We monitor main parameters such as the Reynolds number (Re) in the range of 25–200, the Stefan number (St) in the range of 0.05–1.6, the inner-to-outer radius ratio (Rio) in the range of 0.2–0.7, the solid-to-liquid density ratio (ρs1) in the range of 0.8–1.2, the nucleus size (r0/R) in the range of 0.05–0.3, the initial eccentricity (ε0) in the range of -0.15–0.3 and the growth angle (ϕgr) in the range of 0°–15°. It is found that an increase in St, ρsl or a decrease in ϕgr leads to a decrease in the height of the solidified droplet. In contrast, an increase in Re, r0/R, ε0 or Rio has a minor effect on the drop height after complete solidification. In contrast to ρsl, which has less influence on the solidification time, the change in the value of these parameters considerably modifies the solidification time. The inner and outer aspect ratios of the solidified droplet are also revealed.

Numerical Study of an Indicator Function for Front-Tracking Methods

In this paper, we present a detailed derivation and numerical investigation of an indicator function for front-tracking methods. We use the discrete Dirac delta function to construct an indicator function from a set of Lagrangian points and solve the resulting discrete Poisson equation with the zero Dirichlet boundary condition using an iterative method. We present several computational tests to investigate the effect of parameters such as distance between points, uniformity of the distance, and types of the Dirac delta functions on the indicator function.

Toward the Ultimate Goal on Simulating Multi-Phase Flows, Simulation of Film Boiling at High-Density Ratios

Abstract Flow boiling is a common phenomenon in modern technology and industries. A finite difference Front Tracking method is used to study film boiling on a flat plate subject to a constant heat flux. Large density ratios are examined (1000, 2000). The flow structure including the circulation zones, the vortex developing areas, and vortex pair generation are studied in detail. The numerical method is validated by comparing the result with the analytic solution for a simple problem. Large bubbles comparable to the computational domain are formed at large density ratios. The bubble either breaks up and departs from the rest of the gas, or a jet is formed depending on the heat flux imposed. It is found that the Nusselt number depends on the heat flux on the wall. Specifically, the Nusselt number decreases as the heat flux is raised. The Morton number also affects the Nusselt number in agreement with experimental correlations. The Nusselt number increases when the Morton number is raised. The results obtained agree with experimental correlations at relatively low heat fluxes. Agreement gets worse at large heat fluxes. Experimental correlations estimate larger Nusselt numbers compared to the present study. The flow enhances along the direction of the gravitational acceleration at large density ratios (2000). A wide neck is formed that stabilizes at a specific position inside the flow. The microstructure of the flow shows a vortex pair that develops beneath the root of the bubble at a large density ratio (2000).

Direct numerical simulation of film boiling on a horizontal periodic surface in three dimensions using front tracking

This study investigates film boiling on a horizontal periodic surface in three dimensions through direct numerical simulations. To solve the momentum and energy equations in both phases, a finite difference/front tracking method is used that accounts for inertia, viscosity, and interface deformation. The mathematical formulation and numerical method are presented. One of the challenging aspects of the front tracking method is breakup and coalescence of bubbles. Previous works continued the simulations up to the breakup and release of the bubble. We use an innovative topology changing algorithm to overcome this challenge. So, simulations are carried out over sufficiently long times to capture several bubble release cycles and to evaluate the quasi steady-state Nusselt number Nu¯. Effect of the Grashof and Jacob numbers on the interface dynamics, heat transfer, and fluid flow is studied. By increasing the Grashof number, buoyancy suppresses the viscous effect, so the average size of departing bubbles decreases, and the average Nusselt number increases. Wall superheat has direct influence on the Jacob number. At relatively low superheats, the bubbles are released periodically from the vapor film, but as the wall superheat increases, permanent vapor jets are formed and become thicker. However, the bubble size and the average Nusselt number decrease. The effect of unit cell size is investigated. It is observed that Nu¯ does not change much with unit cell size. To examine the effect of initial perturbation, single mode and multimode cases were simulated. The initial perturbation has no significant effect on the Nu¯. The density ratio was studied, and it is observed that the stationary steady state condition is reached at a shorter time.