Multiphase Smoothed Particle Hydrodynamics Research Articles

The simulation of droplet impact on liquid film evaporation in horizontal falling film evaporator based on smoothed particle hydrodynamics

Purpose In this paper, the complex flow evaporation process of droplet impact on the liquid film in a horizontal falling film evaporator is numerically studied based on smoothed particle hydrodynamics (SPH) method. The purpose of this paper is to present the mechanism of the water treatment problem of the falling film evaporation for the high salinity mine water in Xinjiang region of China. Design/methodology/approach To effectively characterize the phase transition problem, the particle splitting and merging techniques are introduced. And the particle absorbing layer is proposed to improve the nonphysical aggregation phenomenon caused by the continuous splitting of gas phase particles. The multiresolution model and the artificial viscosity are adopted. Findings The SPH model is validated qualitatively with experiment results and then applied to the evaporation of the droplet impact on the liquid film. It is shown that the larger single droplet initial velocity and the smaller single droplet initial temperature difference between the droplet and liquid film improve the liquid film evaporation. The heat transfer effect of a single droplet is preferable to that of multiple droplets. Originality/value A multiphase SPH model for evaporation after the droplet impact on the liquid film is developed and validated. The effects of different factors on liquid film evaporation, including single droplet initial velocity, single droplet initial temperature and multiple droplets are investigated.

Multiphase SPH analysis of a breaking wave impact on elevated structures with vertical and inclined walls

Elevated structures are prevalent along shorelines that are susceptible to storm surge flooding to improve coastal resilience. In this work, we explore the influence of front wall inclination on the pressures and forces attracted by an elevated structure in response to extreme wave impact. Multiphase smoothed-particle hydrodynamics was used to examine a typical two-story building 6 m high and 10 m long with three different frontal wall inclinations impinged by a single breaking wave propagating landwards (from left to right). Relative to a vertical surface, both positive (clockwise) and negative (counterclockwise) inclinations of the front wall altered breaking wave pressures depending on the structure's position relative to the still-water level (SWL). When the bottom of the structure is located below the SWL (negative air gap), a positive inclination decreased breaking wave loads by up to 21 %, while a negative inclination may result in 50 % higher pressure maxima. However, for a structure elevated above the SWL (positive air gap), negative and positive inclinations witnessed reductions to the pressure maxima of 35 % and 10 %, respectively, when compared with a vertical surface.

Numerical simulation of two-phase slug flows in horizontal pipelines: A 3-D smoothed particle hydrodynamics application

A fundamental difficulty of studying gas–liquid pipe flows is the prediction of the occurrence and characteristics of the slug flow regime, which plays a crucial role in the safety design of oil pipelines. Current empirical methods and one-dimensional computational models only achieve limited success. While 3-D numerical simulations are highly recommended, they have been very seldom used. We perform 3-D Lagrangian numerical simulations of gas–liquid pipe flows by adapting an existing multi-phase smoothed particle hydrodynamics (SPH) method based on a Riemann solver to achieve an efficient solver. To realize the high inlet velocities of gas and liquid an in- and outlet boundary condition is presented. The results are validated against existing experimental data, numerical simulations and analytical solutions. Multiple gas–liquid pipe flow patterns are predicted, namely, smooth stratified, stratified wavy, bubble flow, slug flow and bubble flow. Several principle characteristics of slug flows, e.g., pressure gradient, slug development and slug frequency are analyzed in a 3-D fully Lagrangian framework.

Study on the effect of cavity oscillation on wedge water entry with a multiphase smoothed particle hydrodynamics model

Previous Smoothed Particle Hydrodynamics (SPH) study on water entry issues has primarily been conducted for the load analysis of impact phase rather than the cavity oscillation effect because the calculation and simulation of this complex physical process are more complicated and time consuming. In order to increase computational efficiency and accuracy, the multiphase δ+-SPH model is combined with Adaptive Particle Refinement technology to investigate the whole process of the wedge's water entry. The hydrodynamic phenomena in the stages before cavity closure for the four cases with different Froude numbers (Fn) are compared and analyzed. After the cavity is pinched off, the wedge exhibits kinematic oscillation. Our test shows that the adoption of sound speed has a significant influence on the oscillation period and peak value of closed cavities in weakly compressible SPH calculations. Then, a suitable sound speed adoption is selected to simulate the oscillatory phenomenon accurately. Comparing the pressure profile with the surface pressure and acceleration of the wedge at the same time, it can be concluded that the oscillation of the hydrodynamic load on the wedge is caused by the pressure oscillation in the closed cavity. Especially for the case of low Fn, the pressure peak on the wedge's surface in the oscillation stage is even greater than the pressure load in the impact stage. The peak pressure of closed cavity is positively correlated with Fn and negatively correlated with Euler number (Eu). Finally, by analyzing the influence of wedge width and impact velocity, it is found that the oscillation period of the closed cavity is related to the morphology of the cavity. The larger the aspect ratio of the closed cavity, the longer the oscillation period.

Dynamics of a droplet in shear flow by smoothed particle hydrodynamics

The behavior of a droplet under shear flow in a confined channel is studied numerically using a multi-phase smoothed particle hydrodynamics (SPH) method. With an extensive range of Reynolds number, capillary number, wall confinement, and density/viscosity ratio between the droplet and the matrix fluid, we are able to investigate systematically the droplet dynamics such as deformation and breakup. We conduct the majority of the simulations in two dimensions due to economical computations, while perform a few representative simulations in three dimensions to corroborate the former. Comparison between current results and those in literature indicates that the SPH method adopted has an excellent accuracy and is capable of simulating scenarios with large density or/and viscosity ratios. We generate slices of phase diagram in five dimensions, scopes of which are unprecedented. Based on the phase diagram, critical capillary numbers can be identified on the boundary of different states. As a realistic application, we perform simulations with actual parameters of water droplet in air flow to predict the critical conditions of breakup, which is crucial in the context of atomization.

An improved multiphase SPH algorithm with kernel gradient correction for modelling fuel–coolant interaction

Fuel–coolant interaction (FCI) has a pivotal role in the development of core disruptive accident in a sodium-cooled fast reactor. The drastic deformation of multiphase interface in the FCI is hard to deal with in the traditional grid method. In this paper, an improved multiphase smoothed particle hydrodynamics (SPH) algorithm corrected with the kernel gradient correction (KGC) technique is presented for multiphase flow with a large density ratio and complex interfacial behaviors. The density discontinuity across the multiphase interface is described with the use of special volume, which only depends on the position information of adjacent particles. This multiphase SPH algorithm, which is troubled by an unstable and mixed-interface problem under a large density ratio, is significantly improved with the KGC technique. The accuracy and robustness of the improved method are demonstrated in the numerical simulations of the deformation of a square droplet, Rayleigh–Taylor instability, and bubble rising in water. The verified corrected multiphase SPH is applied to simulate the hydrodynamic behaviors of the general FCI and the interaction between fuels coated with stainless steel film and coolant. Boundary layer stripping, Rayleigh–Taylor instability, and Kelvin–Helmholtz instability are observed as important mechanisms of hydraulic fracturing. The fragments’ distribution and the influence of stainless steel film are analyzed. The existence of a stainless steel film has been shown to inhibit breakage.

Numerical investigation of solitary wave breaking over a slope based on multi-phase smoothed particle hydrodynamics

This study presents a numerical investigation of the solitary wave breaking over a slope by using the multi-phase smoothed particle hydrodynamics (SPH) method. Four different computational models are proposed to solve the gas-related far-field boundary conditions, and the model with the least disturbance to the internal flow field is selected. Since the artificial viscous coefficient can greatly affect the wave-breaking location, an empirical equation is fitted to quickly determine the optimal value of the artificial viscous coefficient. In addition, the turbulence model and three-dimensional effect on the wave breaking are discussed in this study. The results show that the present two-dimensional multi-phase SPH without a turbulence model can capture the macroscopic characteristics of the flow before the vortices convert to three dimensional flow structures caused by the wave breaking. Then, the processes of shoaling solitary wave breaking with different slopes and relative wave heights are simulated. Compared with the single-phase SPH, the multi-phase SPH is of great help in improving the prediction of wave breaking. A vortex similar to the Rankine Vortex is observed near the wave crest. Its intensity affects the pressure distribution of the gas, and its relative position to the wave crest is relevant to the energy transfer from the water to the gas. During the solitary wave propagating from deep water to shallow water, energy dissipation of gas and water shows four different stages. In the stage of energy dissipation, the gas can absorb the great energy from the water, which effectively dissipates the wave energy.

A dendritic freezing model for in-flight supercooled large droplets impingement and solidification

Supercooled large droplets (SLD) solidification is a complex multi-physics process of great importance for assessing in-flight icing problems. In this work, a multiphase smoothed particle hydrodynamics (SPH) formulation of SLD impingement and solidification is further enriched by incorporating a freezing model for dendrites growth. The solver is validated against available experimental data of SLD impingement on ice surfaces at low speeds and then applied to test cases with various supercooling degrees and impact speeds to explore their effects on residual ice layers. This work completes a comprehensive toolset for parametric studies of single SLD impingement and solidification and paves the way for macroscopic models that can enrich in-flight icing CFD codes.

A partitioned continuous surface stress model for multiphase smoothed particle hydrodynamics

A density partitioned continuous surface-stress (CSS) model is presented within a multi-phase smoothed particle hydrodynamics (SPH) framework. We follow the original work of Adami et al. (2010) [1] to partition the surface-tension force from a zeroth-order consistent continuum surface-stress model. As a consequence of the scaled surface-tension force, both the surface-tension based artificial speed of sound and the numerical time step criteria can be relaxed for phase interfaces with high density ratio. A new color-gradient treatment and a static contact angle based surface-stress boundary condition is introduced to incorporate wetting behavior. All models are validated by comparison to analytical solutions of several surface-tension dominated flows. The resulting scheme is demonstrated to handle both capillary and Marangoni forces for high density and viscosity ratios.

Investigation on the bouncing and coalescence behaviors of bubble pairs based on an improved APR-SPH method

Bubbles rising in fluids are widespread in many engineering fields. In this paper, the bouncing and coalescing of two bubbles rising side by side are studied based on a multi-phase smoothed particle hydrodynamics (SPH) model. An improved adaptive particle refinement (APR) scheme is applied in the SPH model to make the numerical simulation sufficiently accurate and efficient. The effect of the surface-tension model is firstly verified, then various testing cases including the rising of a single bubble and two horizontally positioned bubbles are carried out and validate the numerical model well. Furthermore, the interaction between two three-dimensional bubbles rising side by side is studied considering the effects of viscous forces (with the Reynolds number Re), surface tensions (with the Eotvos number Eo), and the initial centroid distance of the two bubbles (Γ). The motion and the deformation of the bubbles are displayed and the mechanism of the bubbles' interaction is discussed. The results reveal that for the lower Eotvos number cases indicating a larger surface tension effect, the surface tension force increases dramatically when the two bubbles collide with each other and coalesce.

Two-dimensional smoothed particle hydrodynamics (SPH) simulation of multiphase melting flows and associated interface behavior

ABSTRACT Heat transfer and phase change in multiphase media involve complex behavior such as multi-physics coupling, unsteady interfaces, and boundary generation/disappearance. The smoothed particle hydrodynamics (SPH) method is used to simulate multicomponent problems (initially solid material surrounded by a fluid) characterized by heat transfer, solid–liquid phase change, and multiphase flow. First, the interface behavior of the melted liquids and ambient fluids are simulated by a multiphase SPH model, where corrected algorithms and techniques are adopted to provide a stable simulation for the interface with a large density ratio. The wetting effect of the solid surface by melted liquids is considered by extending the continuum surface force model to three phases including solid, melted liquid and ambient fluid. Second, a thermal dynamics model is incorporated with the multiphase SPH model. The solid–liquid phase change occurs in a small temperature interval in which the latent heat is incorporated using the equivalent heat capacity. Third, the numerical model is validated using several benchmark examples. Five specially configured cases are simulated to demonstrate the robustness, adaptability, and stability of the model. The intriguing phenomena of evolution of the fluid interface of melted liquids, accumulation of thin-layer liquids, and melted droplet formation are reproduced.

A weakly compressible smoothed particle hydrodynamics framework for melting multiphase flow

In this study, the transient process of solid–liquid phase change is modeled and simulated by the multiphase smoothed particle hydrodynamics (SPH) method. First, to simulate the interfacial behaviors of melt liquids, the multiphase SPH model is established for immiscible viscous fluids with a large density ratio, where the environmental liquid surrounding the solid phase is considered, and the surface tension of the melt liquid can be accurately modeled by the continuum surface force method. Based on the multiphase model, the thermal dynamics model is incorporated to describe the heat conduction process. The solid–liquid phase change is realized by directly switching the state of the concerned SPH particle, where the absorbed latent heat is computed by the phase change model. Second, the model is validated by several simulation cases, including the Stefan problem, hydrostatic pressure of the evolving fluid interface, rising of two bubbles, and square droplet deformation, and the effects of numerical parameters on simulation accuracy and stability are also discussed. Third, the integrated SPH model is applied to simulate molten droplet formation and dropping processes. The results show that an initial solid–liquid interface disappears during the melting process, and new liquid–liquid interfaces gradually form and evolve under the action of surface tension, gravity, and viscosity. Phenomena such as thin-layer fluid dynamics and capillary instabilities are also reproduced, showing the effectiveness of the model for handling multiphase flow with heat conduction and phase change.

A stable SPH model with large CFL numbers for multi-phase flows with large density ratios

The discontinuity across interface of multi-phase flows with large density ratios usually poses great challenges for numerical simulations. The smoothed particle hydrodynamics (SPH) is a meshless method with inherent advantages in dealing with multi-phase flows without the necessity of tracking the moving interfaces. In this paper, we develop a new weakly-compressible SPH model for multi-phase flows with large density ratios while allowing large CFL numbers. In the present SPH model, the continuity equation is first modified by eliminating the influence from particles of different phases based on the simple fact that different phases will not contribute when calculating the density for immiscible multi-phase flows; thus, the modified continuity equation will only consider the influence from neighboring particles of the same phase. The pressure and density of the particles of other phases are then re-initialized by using the Shepard interpolation function. The present multi-phase SPH model has been tested by four numerical examples, including the two-phase hydrostatic water, standing waves, liquid sloshing, and dam breaking. It has been demonstrated that the present multi-phase SPH model can obtain satisfactory results stably, even at large CFL numbers, and this means that large time steps can be employed. Therefore, the present multi-phase SPH model can significantly save computational cost through using large time steps, especially for large-scale problems with a large number of particles.

Simulating multi-phase sloshing flows with the SPH method

In this paper, the intense sloshing flow is simulated by Smoothed Particle Hydrodynamics (SPH) method successfully. First, the traditional SPH method is used for the simulation of sloshing process; and the obtained results for free surface shape and pressure evolution are in good agreement with the experimental data. Then, the δ-SPH method and particle shifting technique (PST) are introduced in the traditional SPH model to improve its stability and accuracy in simulating sloshing flow. Air phase does have an inescapable influence on water phase in intense sloshing process. Thus, an improved multiphase SPH model with pressure correction algorithm is utilized for interfacial sloshing simulation. The stability, accuracy and conservation of pressure correction algorithm are validated by the cases of hydrostatic test and dam breaking test. Besides, the comparison results show that unphysical pressure transmission at the interface between two fluids with large density ratio is effectively suppressed. Finally, the effect of air is considered in the multiphase flow simulation of sloshing process with presented multiphase δ-SPH and pressure correction utilized. The phenomenon that air phase is involved into inner water flow and then moves, rolls and rises in it is replicated accurately. It is found that both the shape of free surface and the air cavities during the slamming phase are well captured, which proves that the integrated multiphase SPH is effectively utilized for the simulation of such multiphase problem as sloshing.

Multiphase smoothed particle hydrodynamics modeling of diffusive flow through porous media

This paper presents a numerical model using smoothed particle hydrodynamics for simulating diffusive flow in porous media with spatially varying porosity, especially when high permeability permits fast flow. The governing equations are based on a two-phase mixture theory that describes porosity in terms of stationary solid particles carrying information about volume fraction. The diffusion equation is first validated by application to two-dimensional diffusion within a square box. The continuity and momentum equations taking account of porosity are then validated by simulating Darcy seepage flow in a U-tube filled with a porous medium. Good agreement between numerical results and predicted data is obtained, demonstrating the validity of the multiphase model. Finally, the model is applied to diffusion in a two-dimensional dam-break flow through a porous structure.

Study on the wedge penetrating fluid interfaces characterized by different density-ratios: Numerical investigations with a multi-phase SPH model

Bodies penetrating fluid interfaces is a classical issue that has been considerably investigated, especially for water entry problems, because of its relevance to slamming phenomena in ocean and coastal engineering. This paper is dedicated to investigating the water entry problems of a wedge characterized by different density-ratios using multi-phase Smoothed Particle Hydrodynamics (SPH) simulations. The SPH model is combined with an Adaptive Particle Refinement (APR) incorporating with a phase-switch correction to improve the numerical accuracy and computational efficiency of simulations. Firstly, an SPH simulation for a classical water entry process of a wedge is employed as a benchmark to validate the accuracy and stability of the utilized SPH model. Subsequently, the mechanisms of the spatiotemporal cavity behaviors for different density-ratios are simulated and discussed in detail. It is demonstrated that the cavity evolutions during penetrating and motion characteristics of the wedge are significantly affected by density-ratios. It is also suggested that the presented multi-phase SPH model with APR can be treated as a reliable numerical tool for solving such problems in terms of complex fluid interfaces behind moving structures.

SPH simulation of supercooled large droplets impacting hydrophobic and superhydrophobic surfaces

Hydrophobic and superhydrophobic coatings are of great interest to the aerospace community as a measure to mitigate performance losses due to ice formation in flight. To numerically investigate the supercooled large droplets (SLDs) impacting such coated surfaces, a multiphase smoothed particle hydrodynamics (SPH) solver is developed by solving the Euler momentum equations for fluid dynamics, the energy equation for heat transfer and a latent heat model for phase changes. A continuum surface tension term is included in the momentum equations and a robust contact angle model that corrects the surface tension near triple-phase points is proposed to calculate the non-wetting effects of surfaces. The present solver is capable of modeling droplets impacting, spreading, retracting on and/or rebounding from hydrophobic/superhydrophobic surfaces, with heat transfer and phase change. It is first validated against the evolution of droplets on solid surfaces of various contact angles and then applied to droplets impacting hydrophobic and superhydrophobic surfaces at different temperatures. This work investigates SLD impingement and solidification on hydrophobic and superhydrophobic coatings and provides a base for the numerical experimentation of a single SLD icing behavior at in-flight speeds.

Simulation of droplet spreading on surfaces with asymmetrical wettability using multiphase Smoothed Particle Hydrodynamics (SPH)

Simulation of droplet spreading on surfaces with asymmetrical wettability using multiphase Smoothed Particle Hydrodynamics (SPH)

Extended computation of the viscous Rayleigh-Taylor instability in a horizontally confined flow.

In this article, the classical Rayleigh-Taylor instability is extended to situations where the fluid is completely confined, in both the vertical and horizontal directions. This article starts with the two-dimensional (2D) viscous periodic case with finite height where the effect of adding surface tension to the interface is analyzed. This problem is simulated from a dual perspective: first, the linear stability analysis obtained when the Navier-Stokes equations are linearized and regularized in terms of density and viscosity; and second, looking at the weakly compressible version of a multiphase smoothed particle hydrodynamics (WCSPH) method. The evolution and growth rates of the different fluid variables during the linear regime of the SPH simulation are compared to the computation of the eigenvalues and eigenfunctions of the viscous version of the Rayleigh-Taylor stability (VRTI) analysis with and without surface tension. The most unstable mode, which has the maximal linear growth rate obtained with both approaches, as well as other less unstable modes with more complex structures are reported. The classical horizontally periodic (VRTI) case is now adapted to the case where two additional left and right walls are included in the problem, representing the cases where a two-phase flow is confined in a accelerated tank. This 2D case where no periodic assumptions are allowed is also solved using both techniques with tanks of different sizes and a wide range of Atwood numbers. The agreement with the linear stability analysis obtained by a Lagrangian method such as multiphase WCSPH is remarkable.

SPH simulation of the 2007 Chehalis Lake landslide and subsequent tsunami

A multi-phase smoothed particle hydrodynamics (SPH) formulation in combination with a granular rheological model is applied to simulate the 2007 Chehalis Lake landslide and the subsequent tsunami. The model is implemented within the open-source 3D code GPUSPH. The lake geometry is built using the British Colombia Hydro (BCH) topography and bathymetry surveys, and the landslide initial geometry is reconstructed from pre- and post-failure geological profiles under the assumption of constant thickness across the entire width. The water and the landslide are treated as immiscible continua, discretized in two distinct sets of SPH particles with different mass and behaviour laws. The landslide material is modelled as a continuum whose shear stresses obey a friction law that takes its granular nature into consideration. A sensitive analysis for various physical parameters is carried out, and numerical results are checked by comparing run-up heights to BCH's surveys.