Large Interfacial Deformations Research Articles

Improvement in the Accuracy and Efficiency of Smoothed Particle Hydrodynamics: Point Generation and Adaptive Particle Refinement/Coarsening Algorithms

Improvement in the Accuracy and Efficiency of Smoothed Particle Hydrodynamics: Point Generation and Adaptive Particle Refinement/Coarsening Algorithms

A two-field formulation for surfactant transport within the algebraic volume of fluid method

Surfactant transport plays an important role in many technical processes and industrial applications such as chemical reactors, microfluidics, printing and coating technology. High fidelity numerical simulations of two-phase flow phenomena reveal rich insights into the flow dynamics, heat, mass and species transport. In the present study, a two-field formulation for surfactant transport within the algebraic volume of fluid method is presented. The slight diffuse nature of representing the interface in the algebraic volume of fluid method is utilized to track the concentration of surfactant at the interface as a volumetric concentration. Transport of insoluble and soluble surfactants is investigated by tracking two different concentrations of the surfactant, one within the bulk of the liquid and the other one at the interface. These two transport equations are in turn coupled by source terms considering the ad-/desorption processes at a liquid–gas interface. Appropriate boundary conditions at a solid–fluid interface are formulated to ensure surfactant conservation, while also enabling to study the ad-/desorption processes at a solid–fluid interface. The developed numerical method is verified by comparing the numerical simulations with well-known analytical and numerical reference solutions and applied to a surfactant-laden drop in shear flow. The presented numerical methodology offers a seamless integration of surfactant transport into the algebraic volume of fluid method, where the latter has many advantages such as volume conservation and an inherent ability of handling large interface deformations and topological changes.

Extended Applications of the δ-SPH Model for the Numerical Study of Fluid–Soil Interactions

The fluid–soil interactions play a significant role in coastal and ocean engineering applications. However, there are still some complex mechanical problems with large deformations of water–soil interfaces to be solved. As a particle-based Lagrangian method, Smoothed Particle Hydrodynamics (SPH) is good at solving multiphase problems with large deformations of boundaries or interfaces. Therefore, in this work, the [Formula: see text]-SPH method is extended for the simulation of fluid–soil interacting problems. First, based on the weakly compressible assumption, the water is modeled as a viscous fluid while the soil is considered as a material with elastic–perfectly plastic behaviors. The [Formula: see text]-SPH method is implemented on the two phases separately, while the stress diffusive term only acts on the soil. The seepage force is introduced to model the interaction between two phases. After that, several numerical test cases with small to large interface deformations are presented. It is shown that the fluid–soil interacting model based on the [Formula: see text]-SPH model gives satisfying results compared with experimental data. Finally, the model is further extended for the simulation of vertical or oblique water jet scouring problems which demonstrates the potential applications of the SPH model for complex engineering problems.

Efficient solution of bimaterial Riemann problems for compressible multi-material flow simulations

When solving compressible multi-material flow problems, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular idea in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. The work presented in this paper aims to accelerate the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed, including (1) a change of integration variable through rarefaction fans, (2) storing and reusing integration trajectory data, (3) step size adaptation, and (4) constructing an R-tree on the fly to generate initial guesses. The performance of these acceleration methods is assessed using four example problems in underwater explosion, laser-induced cavitation, and hypervelocity impact. These problems exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. For all the problems, the acceleration methods are able to significantly reduce the computational cost without affecting solver robustness or solution accuracy. In different cases, the solution of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 81 times.

Computational modeling and analysis of the interfacial debonding in copper/copper and copper/polyether-ether-ketone coatings deposited by cold spraying

Cold Spraying (CS) is a promptly developing solid-state additive material deposition technique that is frequently used for high-value metallic component repair. The purpose of this research is to investigate the interfacial adhesion strength of cold-sprayed copper (Cu) coatings deposited on Cu and polyether-ether-ketone (PEEK) substrates for repair applications. In light of this, we propose a computational framework that accounts for both of the two main failure mechanisms, i.e., failure at the Cu/Cu interface caused by plasticity and damage initiation and failure at the Cu/PEEK interface due to brittle crack. Towards this end, different damage models are employed to describe the ductile damage of bulk materials, and a large deformation Cohesive Zone Model (CZM) is developed to model Cu/Cu interface debonding, allowing for stable calculations under large interfacial deformation. The Virtual Crack Closure Technique (VCCT) is used to simulate brittle debonding failure of the Cu/PEEK coating. The threshold stresses for coating debonding, found experimentally, are successfully compared to the numerical predictions. Such debonding modeling techniques might be useful for predicting coating behavior and bonding strength in cold spraying under various loading situations and material combinations.

Research Progress of SPH Simulations for Complex Multiphase Flows in Ocean Engineering

Complex multiphase flow problems in ocean engineering have long been challenging topics. Problems such as large deformations at interfaces, multi-media interfaces, and multiple physical processes are difficult to simulate. Mesh-based algorithms could have limitations in dealing with multiphase interface capture and large interface deformations. On the contrary, the Smoothed Particle Hydrodynamics (SPH) method, as a Lagrangian meshless particle method, has some merit and flexibility in capturing multiphase interfaces and dealing with large boundary deformations. In recent years, with the improvement of SPH theory and numerical models, the SPH method has made significant advances and breakthroughs in terms of theoretical completeness and computational stability, which starts to be widely used in ocean engineering problems, including multiphase flows under atmospheric pressure, high-pressure multiphase flows, phase-change multiphase flows, granular multiphase flows and so on. In this paper, we review the progress of SPH theory and models in multiphase flow simulations, discussing the problems and challenges faced by the method, prospecting to future research works, and aiming to provide a reference for subsequent research.

Numerical simulation of three-fluid Rayleigh-Taylor instability using an enhanced Volume-Of-Fluid (VOF) model: New benchmark solutions

The main objective of the present study is to introduce two novel benchmark solutions namely: two-dimensional three-fluid Rayleigh-Taylor Instability problems, aiming to provide an up-to-date data set and a unique fundamental insight into morphology and hydrodynamic behavior of coupled Rayleigh-Taylor-Kelvin-Helmholtz instability phenomenon. To this end, the Volume-Of-Fluid (VOF) model is adopted to probe the complex configurations and kinetic processes of highly nonlinear multi-fluid flow problems with large topological changes and moving interfaces. However, to improve the performance and accuracy of the classical VOF model and preserve monotonicity for the density and viscosity, a novel high-order bounded advection scheme is first proposed in the context of the Total Variation Diminishing and Normalized Variable Diagram (TVD-NVD) constraints and then is utilized for the discretization of the convection terms in the Navier-Stokes and transport equations. To further increase the accuracy of the numerical simulations, the second-order PLIC-ELVIRA is implemented for the reconstruction of the physical discontinuity between phases and the determination of its curvature. Furthermore, to enhance the consistency and stability of the classical VOF model in handling incompressible multi-fluid flows, a novel semi-iterative pressure-velocity coupling algorithm is constructed by the combination of the standard PISO and SIMPLEC algorithms and is then applied to ensure mass conservation in each grid cell. To demonstrate the versatility and robustness of the proposed model in dealing with the multiphase flows involving large interface deformation and breaking phenomena, a series of canonical test cases such as dam-break over a dry bed with and without stationary obstacle, 2D three-fluid rising bubble, two-fluid and three-fluid Rayleigh-Taylor Instability are adopted. In the last stage, an improved VOF model is applied to solve two new three-fluid Rayleigh-Taylor Instability benchmark problems on a staggered grid system. The results of this study can provide a wide panorama on the improvements of standard VOF model and may be utilized as benchmark solutions for validation of various CFD tools or simply to understand more complex related multi-fluid flows.

A REVIEW OF SMOOTHED PARTICLE HYDRODYNAMICS FAMILY METHODS FOR MULTIPHASE FLOW

With meshfree and fully Lagrangian features of particle methods, smoothed particle hydrodynamics (SPH) is suitable to achieve high-accurate simulations of multiphase flows with large interfacial deformations, discontinuities, and multi-physics. Multiphase flow simulations with SPH methods have been reported abundantly and the specific implementations are much different. In this review, the basic SPH method and issues about fluid pressure, surface tension and solid boundary are discussed. And various implementations of SPH for multiphase flow simulation are mainly summarized as: (1) Lagrangian solver for the two-fluid model (TFM): The two phases are discreterized into two independent groups of SPH particles and coupled by the explicit interphase interaction; (2) multiphase SPH: The multiphase SPH method is considered as the natural extension of SPH method on multiphase flow simulation, and the interphase interaction is implicitly described by SPH parameters; (3) coupling of SPH and other discrete methods: The two phases with large differences each adopt different discrete methods to give play to the advantages of different Lagrangian methods; and (4) coupling of SPH and grid-based methods: The grid method handles the simple main-flow to obtain the balance between accuracy and efficiency. Also, some issues associated with SPH simulations of multiphase flows, such as the physicalization of simulation parameters and the improvement of accuracy and efficiency, are suggested as requiring attention.

Numerical Simulations of Red-Blood Cells in Fluid Flow: A Discrete Multiphysics Study

In this paper, we present a methodological study of modelling red blood cells (RBCs) in shear-induced flows based on the discrete multiphysics (DMP) approach. The DMP is an alternative approach from traditional multiphysics based on meshless particle-based methods. The proposed technique has been successful in modelling multiphysics and multi-phase problems with large interfacial deformations such as those in biological systems. In this study, we present the proposed method and introduce an accurate geometrical representation of the RBC. The results were validated against available data in the literature. We further illustrate that the proposed method is capable of modelling the rupture of the RBC membrane with minimum computational difficulty.

Eulerian Model for Simulating Multi-Fluid Flows with an Arbitrary Number of Immiscible Compressible Components

A ($$2N+1$$)-equation model to simulate the flow of N ($$\textit{N}\ge 3$$) immiscible compressible fluids separated with interfaces is proposed. The model is based on the single velocity diffuse-interface method and includes $$N-1$$ advection equations for fluid volume fractions. Solving the advection equations with a non-linear high-order scheme commonly results in the violation of the non-negativity constraint that any arbitrary partial sum of volume fractions should be in the interval [0, 1]. First, it is shown that this constraint can be met if the $$N-1$$ advection equations are solved for some rational functions of volume fractions rather than for volume fractions themselves. The non-linear sub-cell slope reconstruction (MUSCL-type and THINC) with the proposed rational advection functions is proved to be non-oscillatory and provide the distribution of volume fractions satisfying the non-negativity constraint. Second, it is proved that the PV property (preservation of constant-pressure and constant-velocity equilibrium) is maintained providing that linear functions of volume fractions are used in the advection equations. We suggest two ways for resolving the contradiction in choosing the advection functions (functions of volume fractions) in accordance with the non-negativity constraint and the PV property. We also adopt two numerical methods—the Roe-type scheme and the HLLC scheme to solve the governing equations. Finally, the proposed numerical model is tested with several benchmark problems. The results obtained demonstrate robustness and effectiveness of the proposed numerical approach in solving multi-fluid flows with large interface deformations.

An enhanced weakly-compressible MPS method for free-surface flows

Similar to other particle methods, the Weakly-Compressible MPS (WC-MPS) is known to suffer from numerical instabilities and unphysical pressure fluctuations. Here we develop, adapt and evaluate a series of enhancement techniques to improve the stability and accuracy of this numerical approach. This includes a new conservative pressure gradient formulation and its conjugate form of the continuity equation supplied with a new diffusive term to reduce the numerical error related to the false diffusion. As a regularization technique, we have also adapted and modified the particle shifting algorithm (with near-surface special treatment) in combination with the pair-wise particle collision method to avoid particle clustering and associated noises. The impact of each of these enhancement techniques is evaluated and quantified using popular benchmark cases, i.e. hydrostatic pressure tank, elliptical water drops, rotating square patch of fluid, and dam-break problems. While the results confirm the effectiveness of all the enhancement techniques, the additional diffusive term is found to play a key role in increasing stability and eliminating the high-frequency pressure noises. Furthermore, results show that for the cases with large interfacial deformations, the developed particle shifting algorithm is essential for maintaining the smoothness of the free-surface region and avoiding unwanted fragmentation.

Numerical study of the shear-thinning effect on the interaction between a normal shock wave and a cylindrical liquid column

Based on adaptive mesh refinement, the SIM (Sharp-Interface Method) is utilized to numerically study the interaction between a shock wave and a liquid column as well as the evolution of the flow field. The SIM consists of the LSM (Level Set Method) and the GFM (Ghost Fluid Method). The LSM tracks the gas-liquid interface, and the GFM generates the virtual domains near the interface based on the gas-liquid interface condition. The hybridized GFM has been developed by integrating the Riemann GFM and the modified GFM together, which ensures the accuracy of the interface Riemann problem in the small deformation region of the interface while ensuring that the large interface deformation can be processed correctly. By comparing with the experimental results and the numerical results in previous literature, the good agreement shows that the above algorithm can accurately simulate the interactions between shock waves and liquid columns along with achieving the evolutions of the sharp gas-liquid interfaces. Based on the algorithm above, the interactions between the shock waves and the inviscid, the Newtonian, and the shear-thinning liquid columns are simulated, respectively. The numerical results indicate that the viscous effect can cause the bending of the liquid column and large deformation in the high shearing region. However, the shear thinning effect alleviates the bending and the deformation of the liquid column in the high shear region.

Probing the adsorption/desorption of amphiphilic polymers at the air-water interface during large interfacial deformations.

Hydrophobically modified polymers are good candidates for the stabilization of liquid interfaces thanks to the high anchoring energy of the hydrophobic parts. In this article we probe the interfacial anchoring of a series of home-made hydrophobically modified polymers with controlled degree of grafting by studying their behavior upon large area dilations and compressions. By comparing the measured interfacial tension to the one that we expect in the case of a constant number of adsorbed monomers, we are able to deduce whether desorption or adsorption occurs during area variations. We find that the polymer chains with the longest hydrophobic grafts desorb at larger compressions compared to the polymers with the shortest grafts, because of their larger desorption energy. Furthermore, for a given graft length, we observe more desorption for polymers with the highest grafting densities. We attribute this counter intuitive result to the fact that at high grafting densities, the length of the polymer loops is shorter, and hence the elastic penalty upon compression is larger for these layers, leading to a faster desorption. Comparing the elastic penalty to thermal energy, kBT, enables deducing a critical grafting density above which desorption of grafts is expected upon compression, which is consistent with our experimental results. In the case of large area dilations, the experiments reveal that the number of adsorbed anchors remains constant in the case of chains with a low grafting density while chains with the highest degree of grafting seem to show some degree of adsorption during the dilatation. Therefore, in these highly grafted chains there may be unadsorbed grafts remaining in the vicinity of the interface, which may adsorb quickly at the interface upon dilatation.

A New Interface Identification Technique Based on Absolute Density Gradient for Violent Flows

An identification technique for sharp interface and penetrated isolated particles is developed for simulating two-dimensional, incompressible and immiscible two-phase flows using meshless particle methods in this paper. This technique is based on the numerically computed density gradient of fluid particles and is suitable for capturing large interface deformation and even topological changes such as merging and breaking up of phases. A number of assumed particle configurations will be examined using the technique, including these with different level of randomness of particle distribution. The tests will show that the new technique can correctly identify almost all the interface and isolated particles, and also show that it is better than other existing popular methods tested.

Validation of the S‐CLSVOF method with the density‐scaled balanced continuum surface force model in multiphase systems coupled with thermocapillary flows

SummaryThree numerical methods, namely, volume of fluid (VOF), simple coupled volume of fluid with level set (S‐CLSVOF), and S‐CLSVOF with the density‐scaled balanced continuum surface force (CSF) model, have been incorporated into OpenFOAM source code and were validated for their accuracy for three cases: (i) an isothermal static case, (ii) isothermal dynamic cases, and (iii) non‐isothermal dynamic cases with thermocapillary flow including dynamic interface deformation. Results have shown that the S‐CLSVOF method gives accurate results in the test cases with mild computation conditions, and the S‐CLSVOF technique with the density‐scaled balanced CSF model leads to accurate results in the cases of large interface deformations and large density and viscosity ratios. These show that these high accuracy methods would be appropriate to obtain accurate predictions in multiphase flow systems with thermocapillary flows. Copyright © 2016 John Wiley & Sons, Ltd.

Mesh-free SPH modeling of sediment scouring and flushing

A two-phase mesh-free Lagrangian model, based on the Smoothed Particle Hydrodynamics (SPH) method, is developed and evaluated for the continuum-based study of sediment-water system (a dense submerged granular flow system). The case studies are (a) sediment scouring downstream of a wall-jet, and (b) reservoir sediment flushing, both of great interest of engineers and researchers. The mesh-free Lagrangian nature of the SPH method makes the model capable of dealing with the large interfacial deformations involved in these complex water-sediment flow systems. Water and sediment materials are both treated as continuum and the governing equation of their motion are solved on a Lagrangian frame using SPH formulation. A pressure-dependent viscoplastic rheological model is used to describe the behavior of the sediment phase. A combination of Mohr–Coulomb and Shields yielding criteria (in place of commonly used Mohr–Coulomb yield criteria) is employed to determine the critical stress above which the sediment material behaves as a viscous fluid. Effect of this combination on the model results is investigated. To validate the developed numerical model, this study also provides some original experimental measurements for the test cases of this study. The results show the good compatibility of the numerical and experimental water and bed profiles. The sediment feature such as scouring and deposition areas (for wall-jet scouring case) and the sediment failure slope (for the flushing test case) are reproduced by the developed SPH model, with a good degree of accuracy. The numerical results as well as experimental measurements of this study not only provide an insight into better understanding of the complicated mechanism of sediment transport induced by rapid flow discharge, but also provide a reliable numerical tool and benchmark for simulation of such problems.

Electro-osmosis of superimposed fluids in the presence of modulated charged surfaces in narrow confinements

In the present study, we attempt to analyse the electro-osmotic flow of two superimposed fluids through narrow confinements in the presence of axially modulated surface charges. We attempt to solve for the flow structure as well as the interface deformation by both analytical and numerical techniques. Approximate analytical solutions are obtained through asymptotic analysis for low deformations, whereas numerical solutions are obtained by applying the phase field formalism; the numerical solutions are obtained for small as well as large interfacial deformations. The analytical solutions are derived only for the transient deformation of the interface, neglecting the transience in the flow, i.e. the flow is assumed to be quasisteady. The numerical solutions, however, are derived including the effects of inertia and transients in the flow. We attempt to compare our analytical and numerical results and explore the effects of several physico-chemical parameters on the deformation of the interface as well as the nature of the flow. Our analysis reveals that parameters such as the modulation wavelength, surface tension (described through the capillary number), viscosity ratio, permittivity ratio and extent of asymmetry in the potential on the two walls are the major contributors to the deformation and the resulting flow features.

Interfacial deformation and jetting of a magnetic fluid

An attractive technique for forming and collecting aggregates of magnetic material at a liquid–air interface by an applied magnetic field gradient was recently proposed, and its underlying principle was studied theoretically and experimentally (Tsai et al., 2013): when the magnetic field is weak, the deflection of the liquid–air interface has a steady shape, while for sufficiently strong fields, the interface destabilizes and forms a jet that extracts magnetic material. Motivated by this work, we develop a numerical model for the closely related problem of solving two-phase Navier–Stokes equations coupled with the static Maxwell equations. We computationally model the forces generated by a magnetic field gradient produced by a permanent magnet and so determine the interfacial deflection of a magnetic fluid (a pure ferrofluid system) and the transition into a jet. We analyze the shape of the liquid–air interface during the deformation stage and the critical magnet distance for which the static interface transitions into a jet. We draw conclusions on the ability of our numerical model to predict the large interfacial deformation and the consequent jetting, free of fitting parameters.

Interface instability mechanism of an annular viscous liquid sheet exposed to axially moving inner and outer gas

The interface instability mechanism of an annular viscous liquid sheet exposed to axially moving inner and outer gas is investigated. Sheet instability and breakup have been investigated using a nonlinear spatial instability analysis. A perturbation expansion method is used with the initial amplitude of the disturbance as the perturbation parameter. The evolution of the two gas–liquid interfaces is tracked until the sheet breaks up and the breakup length is determined. The model is validated by comparison with available experimental data. To investigate the interface instability mechanism of an annular viscous liquid sheet, the effects of velocity difference between gas and liquid, annular curvature on the annular sheet instability have been studied. The results show that both first-order and second-order maximum disturbance growth rates increase with increase in velocity difference between gas and liquid, and annular liquid sheet curvature. Also, with increasing velocity difference between gas and liquid, large interface deformations occur and the breakup length of the annular viscous liquid sheet becomes shorter. The shear effect difference between the outer and inner sides of the annular liquid sheet is the source of instability.

A Modified SPH Model for Simulating Water Surface Waves

As a flexible Lagrangian particle method, smoothed particle hydrodynamics (SPH) can easily capture large interface deformation, breaking, merging and splashing, which is quite suitable for the simulation of water surface waves. The classic weakly compressible smoothed particle hydrodynamics (WCSPH) algorithm for incompressible fluid flow usually needs small time steps to ensure numerical stability, which makes it computational time consuming. The major reason is that the pressure is linked with the density deviation which should be zero everywhere in incompressible fluid flows. Generally, the equation of state for a weakly compressible fluid is adopted to simulate incompressible fluid. To enforce the incompressibility, the stiffness of fluid is set to be large enough to keep the density deviation less than an allowable error. That will lead to a problem that a tiny error of computed density will cause a large pressure error and further numerical instability. In order to obtain rational pressure distribution and good computational efficiency as well, a new algorithm is proposed considering that flow field is globally incompressible from the view of spatial averaged flow field and weakly compressible locally due to the computational error from the view of particles. The basic conception of the proposed modified SPH is to split the pressure into a global part and local fluctuating part. The global part of pressure or the spatial averaged pressure on the resolution of background mesh is obtained by solving the pressure Poisson equation based on the velocity divergence free condition. The local fluctuating pressure is related to the local particle density variation by solving the local pressure Poisson equation, which is applied to maintain particles’ spacing in relative equilibrium. Based on this idea, formulas for the spatial averaged pressure and local fluctuating pressure are derived. The spatial averaged pressure is used as a primary estimation of the pressure gradient force and then the local fluctuating pressure is added as a correction of local density deviation. The proposed algorithm is verified by simulating the classic dam broken problem and then applied to simulate water wave breaking. A comparison of the particle configurations with previous studies at different times is shown. Good agreement between the present results and the previous results can be found. A discussion on computational efficiency is also carried out. The result shows that the proposed algorithm has better stability and can greatly reduce the computational time cost.