Numerical simulation of single droplet dynamics in three-phase flows using ISPH

In this study, a new surface tension formulation for modeling incompressible, immiscible three-phase fluid flows in the context of incompressible smoothed particle hydrodynamics (ISPH) in two dimensions has been proposed. A continuum surface force model is employed to transform local surface tension force to a volumetric force while physical surface tension coefficients are expressed as the sum of phase specific surface tension coefficients, facilitating the implementation of the proposed method at triple junctions where all three phases are present. Smoothed color functions at fluid interfaces along with artificial particle displacement throughout the computational domain are combined to increase accuracy and robustness of the model. In order to illustrate the effectiveness of the proposed method, several numerical simulations have been carried out and results are compared to analytical data available in literature. Results obtained by simulations are compatible with analytical data, demonstrating that the ISPH scheme proposed here is capable of handling three-phase flows accurately

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Early Career Award, “New Dimension Reduction Methods and Scalable Algorithms for Multiscale Nonlinear Phenomena,” and Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4)

Modelling of immiscible liquid-liquid systems by Smoothed Particle Hydrodynamics

Immiscible fluid systems are ubiquitous in industry, medicine and nature. Understanding the phase morphologies and intraphase fluid motion is often desirable in many of these situations; for example, this will aid improved design of microfluidic platforms for the production of medicinal formulations. In this paper, we detail a Smoothed Particle Hydrodynamics (SPH) approach that facilitates this understanding. The approach includes surface tension and enforces incompressibility. The approach also allows the consideration of an arbitrary number of immiscible phases of differing viscosities and densities. The nature of the phase morphologies can be arbitrary and change in time, including break-up (which is illustrated) and coalescence. The use of different fluid constitutive models, including non-Newtonian models, is also possible. The validity of the model is demonstrated by applying it to a range of model problems with known solutions, including the Young-Laplace problem, confined droplet deformation under a linear shear field, and a droplet falling under gravity through another quiescent liquid. Results are also presented to illustrate how the SPH model can be used to elucidate the behaviour of immiscible liquid systems

Improved multiphase smoothed particle hydrodynamics

Smoothed Particle Hydrodynamics (SPH) is a relatively new meshless numerical approach which has attracted significant attention in the last 15 years. Compared with the conventional mesh-dependent computational fluid dynamics (CFD) methods, the SPH approach exhibits unique advantages in modeling multiphase fluid flows and associated transport phenomena due to its capabilities of handling complex material surface behavior as well as modeling complicated physics in a relatively simple manner. On the other hand, as SPH is still a developing CFD tool, it is vital to investigate its attributes, namely, advantages or potential limitations in modeling different multiphase flow problems to further understand and then improve this technique. Toward this end, this work aims to design a computational code using SPH method for the simulation of multiphase flows. In this work, we present numerical solutions for flow over an airfoil and square obstacle using both weakly compressible and incompressible SPH method with an improved solid boundary treatment approach, referred to as Multiple Boundary Tangents (MBT) method. It is shown that the MBT boundary treatment technique is very effective for tackling boundaries of complex shapes. Also, we have proposed the usage of the repulsive component of the Leonard Jones Potential (LJP) in the advection equation to repair particle fracture occurring in SPH method due to the tendency of SPH particles to follow the stream line trajectory. This approach is named as the artificial particle displacement method. Furthermore, the proposed method is totalized for the multiphase uid systems and implemented accordingly. The presented model is validated by solving Laplace's law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. Then, the problem descriptions and solutions for two important hydrodynamic instabilities namely, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, are provided along with their brief analytical linear stability analysis to describe the accuracy and the limitation of the numerical scheme. The long time evolution for both cases are investigated and the comparison between the simulation results and existence theories are provided in details. Finally, we have presented a model to study the deformation of a droplet suspended in a quiescent fluid subjected to the combined effects of surface tension and electric field forces. The electrostatics phenomena are coupled to hydrodynamics through the solution of a set of Maxwell equations. The relevant Maxwell equations and associated interface conditions are simplified relying on the assumptions of the so called leaky dielectric model. All governing equations and the relevant jump and boundary conditions are discretized in space using the SPH method with improved interface and boundary treatments. Numerical results are validated by two highly credential analytical results which are frequently cited in the literature

Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows

Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) are increasingly popular and attractive methods that propose efficient multiphase formulations, each one with its own strengths and weaknesses. In this context, when it comes to study a given multi-fluid problem, it is helpful to rely on a quantitative comparison to decide which approach should be used and in which context. In particular, the simulation of intermittent two-phase flows in pipes such as slug flows is a complex problem involving moving and intersecting interfaces for which both SPH and LBM could be considered. It is a problem of interest in petroleum applications since the formation of slug flows that can occur in submarine pipelines connecting the wells to the production facility can cause undesired behaviors with hazardous consequences. In this work, we compare SPH and LBM multiphase formulations where surface tension effects are modeled respectively using the continuum surface force and the color gradient approaches on a collection of standard test cases, and on the simulation of intermittent flows in 2D. This paper aims to highlight the contributions and limitations of SPH and LBM when applied to these problems. First, we compare our implementations on static bubble problems with different density and viscosity ratios. Then, we focus on gravity driven simulations of slug flows in pipes for several Reynolds numbers. Finally, we conclude with simulations of slug flows with inlet/outlet boundary conditions. According to the results presented in this study, we confirm that the SPH approach is more robust and versatile whereas the LBM formulation is more accurate and faster