Three-dimensional Smoothed Particle Hydrodynamics Research Articles

Characterizing Drop-Wall Interactions of Engine Fuels at Engine-Relevant Conditions Using Smoothed Particle Hydrodynamics

Abstract In an internal combustion engine, interactions of fuel droplets and heated walls can significantly affect the combustion process and engine performance. The formation and characteristics of secondary droplets from drop-wall interactions are functions of various factors such as fuel properties, impact velocity, ambient conditions, and wall temperature. Understanding the impact behavior is important to optimize the distribution of the fuel-air mixture for efficient and clean combustion and to develop a comprehensive spray-wall interaction model. In this study, three-dimensional smoothed particle hydrodynamics (SPH) simulations are performed to investigate the interactions of fuel droplets with a heated wall at atmospheric and elevated pressures over a range of Weber numbers (We). The SPH model is validated using available experimental data. Secondary atomization is characterized by using size distributions for different fuels. The resulting droplets vary in size, where secondary droplets are mostly below 7 μm in diameter. Following these cases, this paper qualitatively describes the impact process and proposes empirical correlation relating the mean secondary droplet size to ambient pressure in the film-boiling regime. Postimpingement vaporization characteristics are also analyzed and compared for fuels with drastically different vapor pressures.

A three-dimensional smoothed particle hydrodynamics analysis of multiple retrogressive landslides in sensitive soil

Numerical modelling and analysis of three-dimensional multiple retrogressive landslides of Saint-Jude landslide in sensitive clay is conducted. The investigations of the three-dimensional effects in determining the extent of landslides are concerned. To accurately simulate the extremely large deformation caused by progressive soil failure, a special form of SPH formulation known as finite particle method (FPM) is adopted. A hypoelastic–plastic model with strain softening is implemented to capture the key feature of the mechanical behaviour of the sensitive clay in undrained condition. The multiple progressive failure process, the final run-out stretch, and the retrogression distance of the Saint-Jude landslide are compared quantitatively with the data from site investigation. Furthermore, three-dimensional effects and influences of various factors, including slope morphology and soil properties, are discussed for better understanding of the development of retrogressive landslides in sensitive soil.

Numerical investigation of vehicle wading based on an entirely particle-based three-dimensional SPH model

Vehicle wading problems have received increasing attention from the automotive community in recent years because of the prosperous developments of electric vehicles, for which the performance of water tightness can be more important than conventional fuel vehicles. This paper presents an attempt to simulate vehicle wading problems based on an entirely meshless framework by using Smoothed Particle Hydrodynamics (SPH). First of all, an easy-to-implement but effective strategy is proposed to prevent the penetration between fluid particles and a wall boundary modeled by a set of solid particles when the distribution quality of the solid particles is poor. Subsequently, a comparative study is conducted to assess the feasibility and applicability of the SPH and Finite Volume (FV) methods in solving vehicle wading problems. Furthermore, the wading dynamics of a vehicle passing a puddle under different combinations of wading speeds and accumulating water depths is also investigated and discussed in detail by using the SPH method. It is suggested that the SPH method can be regarded as a potential candidate for solving vehicle wading problems, especially for those situations where the free-surface evolution during the wading process is particularly concerning.

Direct imposition of the wall boundary condition for weakly compressible flows in three-dimensional smoothed particle hydrodynamics simulations

This study introduces a novel method for imposing wall boundary conditions in smoothed particle hydrodynamics (SPH). SPH is a particle method based on the Lagrangian approach, primarily employed in fluid analysis as a part of numerical computation methods. Due to its ability to discretize space using particles, SPH excels in handling analyses of free surface flow or multiphase flow with intricate boundary surfaces. However, there is a drawback in modeling wall boundaries using particles, as resolving the particle deficiency problem necessitates multi-layered boundary particles to be arranged behind the wall boundary. This leads to difficulties in implementing complex shapes and adds computational expense. To address this issue, this study suggests the use of boundary segments for wall boundary modeling and specifically employs triangular segments for three-dimensional expansions. For robust application of boundary conditions, a method considering both Poisson's equation and geometric configurations is proposed. The proposed method is independent of the segment density, which facilitates efficient and flexible modeling. In addition, by imposing accurate boundary conditions from the wall, the stability and accuracy of the solution are enhanced. The performance of the proposed method is validated through numerical examples, compared with various analytical and experimental results.

Three-Dimensional Smooth Particle Hydrodynamics Modelling of Liquid–Sediment Interaction at Coastline Region

The three-dimensional liquid–sediment system of a coastline was investigated using experimental and numerical approaches. A scaled-down model of the coastline was numerically studied using smooth particle hydrodynamics (SPH). The flow dynamics and the impacts of the wave frequency and the seaward slope angle on the breaking wave characteristics of the two-phase liquid–sediment interaction were parametrically studied. A particle image velocimetry (PIV) experiment was conducted to validate the SPH predictions. It was found that the flow profiles obtained by the PIV and SPH are in good agreement both qualitatively and quantitatively. The maximum velocity of the fluid flow was recorded as 0.5623 m/s in the SPH simulation, but as 0.5860 m/s in the PIV experimental, with a percentage difference of 4.21%. Subsequently, it was found that the breaking wave characteristic is surging at the wave frequency range of f<0.15 Hz, plunging at 0.15<f<0.55 Hz, and spilling at 0.55<f≤1.0 Hz. It was also established that at a particular Froude number, it is observed that spilling, plunging, and surging wave breakers are produced at low, mid, and high seaward slope angles, respectively. Meanwhile, increasing the Froude number increases the tendency to produce spilling or plugging breaking waves, irrespective of the slope angle. Ultimately, this study has demonstrated the presented methodology’s usefulness in investigating coastlines’ liquid–sediment interaction properties.

Comprehensive Analysis of the Failure Potential of a Motorway Landslide in Dabu County, China

Because the failure potential of a landslide is difficult to assess, a motorway landslide that has obviously deformed was used as a case study in this research. Several multi-integrated geotechniques, including field investigation, drilling, electrical resistivity tomography (ERT), stability analysis, and numerical simulations, were used to achieve this goal. Field investigation with drilling was used to roughly determine the failure potential mass boundary and the material composition ERT technique was further used to distinguish the structure and composition of underground materials; the results agreed well with the field investigation, as well as the drilling data in the lithology judgement. The above investigations also showed the failure potential mass is in a slow sliding state and the slip surface roughly follows the contact zone between the upper soil and bedrock. Next, stability analysis based on the limit equilibrium method (LEM) was used to judge the current stability status of the slope, and its factor of safety (FOS) was 1.2 under the natural condition, 1.05 under the earthquake condition, and 1.15 under the rainfall condition. Based on the assessed potential slip surface and digital elevation data, a three-dimensional smoothed particle hydrodynamics (SPH) model was used to simulate the failure potential process. The dynamic information of the run-out behavior, including velocity, movement distance, and frictional energy, can be obtained, which is useful for hazard prediction.

The role of the drag force in the gravitational stability of dusty planet-forming disc – II. Numerical simulations

ABSTRACT Young protostellar discs are likely to be both self-gravitating, and to support grain growth to sizes where the particles decoupled from the gas. This combination could lead to short-wavelength fragmentation of the solid component in otherwise non-fragmenting gas discs, forming Earth-mass solid cores during the Class 0/I stages of young stellar object evolution. We use three-dimensional smoothed particle hydrodynamics simulations of two-fluid discs, in the regime where the Stokes number of the particles St > 1, to study how the formation of solid clumps depends on the disc-to-star mass ratio, the strength of gravitational instability, and the Stokes number. Gravitational instability of the simulated discs is sustained by local cooling. We find that the ability of the spiral structures to concentrate solids increases with the cooling time and decreases with the Stokes number, while the relative dynamical temperature between gas and dust of the particles decreases with the cooling time and the disc-to-star mass ratio and increases with the Stokes number. Dust collapse occurs in a subset of high disc mass simulations, yielding clumps whose mass is close to linear theory estimates, namely 1–10 M⊕. Our results suggest that if planet formation occurs via this mechanism, the best conditions correspond to near the end of the self-gravitating phase, when the cooling time is long and the Stokes number close to unity.

Three-dimensional smoothed particle hydrodynamics modeling of near-shore current flows over rough topographic surface

In this study, a three-dimensional (3D) numerical model based on the smoothed particle hydrodynamics (SPH) approach was developed to simulate the near-shore current flows over a rough topographic surface in the coastal area, where the flows are shallow and demonstrate strong turbulent characteristics. The numerical program is based on the open-source code SPHysics (http://www.sphysics.org), and two major improvements are made to treat the turbulence and rough boundary effects: A modified sub-particle-scale (SPS) eddy viscosity model is developed to address the turbulence transfer of flows, and a drag force equation is included in the momentum equations to account for the influence of roughness element on the bed and lateral boundaries. The computed results of flow velocity, shear stress, and free surface characteristics are compared with the laboratory measurements for a variety of test conditions. It has shown that the present SPH model can accurately simulate 3D-free surface near-shore current flows over a realistic topography with roughness.

Particle simulation of nugget formation process during steel/aluminum alloy dissimilar resistance spot welding and thickness estimation of intermetallic compounds

A steel/aluminum alloy dissimilar resistance spot welding process was simulated by a three-dimensional smoothed particle hydrodynamics method. Furthermore, the time-dependent increase in the intermetallic compound thickness at the joint interface was estimated using the obtained numerical data of temperature history. As a result, the steel sheet started to melt from the center of the sheet in the thickness direction. The convection in the molten aluminum alloy caused by the electromagnetic force promoted the heat transfer at the solid-liquid interface because the temperature gradient becomes steeper. Moreover, the maximum thickness of the intermetallic compound was estimated to be approximately 1 µm. These results support the validity of the computational model developed in this study for simulating the nugget formation process during dissimilar resistance spot welding and estimating the intermetallic compound thickness.

Accretion rates in hierarchical triple systems with discs

ABSTRACT Young multiple systems accrete most of their final mass in the first few Myr of their lifetime, during the protostellar and protoplanetary phases. Previous studies showed that in binary systems the majority of the accreted mass falls on to the lighter star, thus evolving to mass equalization. However, young stellar systems often comprise more than two stars, which are expected to be in hierarchical configurations. Despite its astrophysical relevance, differential accretion in hierarchical systems remains to be understood. In this work, we investigate whether the accretion trends expected in binaries are valid for higher order multiples. We performed a set of three-dimensional smoothed particle hydrodynamics simulations of binaries and of hierarchical triples (HTs) embedded in an accretion disc, with the code phantom. We identify for the first time accretion trends in HTs and their deviations compared to binaries. These deviations, due to the interaction of the small binary with the infalling material from the circumtriple disc, can be described with a semi-analytical prescription. Generally, the smaller binary of an HT accretes more mass than a single star of the same mass as the smaller binary. We found that in an HT, if the small binary is heavier than the third body, the standard differential accretion scenario (whereby the secondary accretes more of the mass) is hampered. Reciprocally, if the small binary is lighter than the third body, the standard differential accretion scenario is enhanced. The peculiar differential accretion mechanism we find in HTs is expected to affect their mass ratio distribution.

Three-Dimensional Smooth Particle Hydrodynamics Modeling and Experimental Analysis of the Ballistic Performance of Steel-Based FML Targets.

In this paper, shields made of 1.3964 stainless steel bonded to a fiber laminate were subjected to ballistic impact response of 7.62 × 51 mm ŁPS (light projectile with a lead core) projectiles. Additionally, between the steel sheet metal and the laminate, a liquid-filled bag was placed, which was a mixture of ethylene glycol (C2H6O2) with 5 wt.% SiO2 nanopowder. Numerical modeling of the projectile penetrating the samples was carried out using the finite element method in the Abaqus program. The elasto-plastic behavior of the projectile material and the component layers of the shields was taken into account. Projectile penetration through glycol-filled bag has been performed using the smooth particle hydrodynamics technique. The morphology of the penetration channel was also analyzed using a scanning electron microscope. For the shield variant with a glycol-filled bag between the steel and laminate plates, the inlet speed of projectile was 834 m/s on average, and 366 m/s behind the sample. For the variant where there was no glycol-filled bag between the steel and laminate plates, the inlet and outlet average velocities were 836 m/s, after 481 m/s, respectively. Referring to the steel-glycol-laminate and steel-laminate variants, it can be concluded that the laminate-glycol-laminate is more effective.

Characteristics of iceberg calving-generated waves based on three-dimensional SPH simulations

Large-scale icebergs calving into water often generate waves that may threaten human lives or passing ships. The formation and evolution of such three-dimensional (3D) waves in the near field are still not fully understood. In this paper, a 3D numerical model based on the Smoothed Particle Hydrodynamics (SPH) open source code DualSPHysics was established to simulate the generation and evolution processes of waves caused by icebergs calving into water. The model is validated with available large-scale laboratory tests. The 3D characteristics in the near field of the waves are presented and analyzed in detail. The results indicate that iceberg calving can generate three main waves: a leading wave produced by the initial entry of the iceberg into the water; a second wave induced by the collapse of the water jet; and a third wave caused by the resurfacing of the iceberg. The reflux tail blocked by the reflux front may appear prior to the second wave, which can develop into a constantly changing wavefront, and then form a step-like flow structure in the near field by linking these two wavefronts. The shapes of the multiple wavefronts outlined by the leading wave and the trailing waves in the near field are closely related to the iceberg geometry. However, the wavefronts gradually develop into a semicircular shape in the far field irrespective of the iceberg geometry. These findings are helpful for hazard assessments of iceberg calving-generated waves. • A rigid body–fluid coupled SPH model is established to simulate three-dimensional iceberg calving-generated waves (ICGW). • The three-dimensional characteristics of ICGWs in the near field are presented. • ICGW consists of three main waves: a leading wave; a second wave by water jet; and a third wave by resurfacing. • The generation and evolution processes of the multiple wavefronts are outlined.

Surrogate model approach for stochastic prediction of sloshing-induced pressure based on SPH with FORM

ABSTRACT An efficient method to predict extreme pressures considering the sloshing in a rectangular tank subjected to in-plane irregular rotational motions is proposed. First Order Reliability Method (FORM) is applied to evaluate the probability distribution of pressure, while the open-source Smoothed-Particle Hydrodynamics (SPH) code DualSPHysics is used for obtaining time-domain pressures. To attain an efficient extreme value prediction, a simplified surrogate model is formulated so that the SPH results are represented with fast computations. An efficient extreme value prediction is achieved without directly using SPH to the series calculations with various stochastic variables during FORM. FORM results are validated by comparing the reliability index with the Monte Carlo Simulation. Finally, the difference in the sloshing-induced impact pressures evaluated by the two-dimensional and three-dimensional SPH under the most probable wave episodes obtained by FORM is presented, and then the applicability of the present surrogate model to the three-dimensional SPH is demonstrated.

On three-dimensional SPH modelling of large-scale landslides

Lagrangian particle-based smoothed particle hydrodynamics (SPH) is increasingly widely used in landslide modelling. This paper investigates four important issues not addressed by previous studies on SPH modelling of large-scale landslides, i.e., convergence property, influence of constitutive parameters, scale effect and friction reduction, and influence of different treatments of the viscous effect. The GPU-acceleration technique is employed to achieve high-resolution three-dimensional (3D) modelling. The Baige landslide is investigated by comparing numerical results with field data, and detailed analyses on the four issues are provided. Suggestions on particle resolution, constitutive parameter, and formulations of viscous discretization are also presented for future SPH modelling of large-scale landslides.

Growth and dissipation of Be star discs in misaligned binary systems

ABSTRACT We use a three-dimensional smoothed particle hydrodynamics code to simulate growth and dissipation of Be star discs in systems where the binary orbit is misaligned with respect to the spin axis of the primary star. We investigate six different scenarios of varying orbital period and misalignment angle, feeding the disc at a constant rate for 100 orbital periods, and then letting the disc dissipate for 100 orbital periods. During the disc growth phase, we find that the binary companion tilts the disc away from its initial plane at the equator of the primary star before settling to a constant orientation after 40–50 orbital periods. While the mass-injection into the disc is ongoing, the tilting of the disc can cause material to reaccrete on to the primary star prematurely. Once disc dissipation begins, usually the disc precesses about the binary companion’s orbital axis with precession periods ranging from 20 to 50 orbital periods. In special cases, we detect phenomena of disc tearing, as well as Kozai–Lidov oscillations of the disc. These oscillations reach a maximum eccentricity of about 0.6, and a minimum inclination of about 20○ with respect to the binary’s orbit. We also find the disc material to have highly eccentric orbits beyond the transition radius, where the disc changes from being dominated by viscous forces, to heavily controlled by the companion star, in contrast to its nearly circular motion inwards of the transition radius. Finally, we offer predictions to how these changes will affect Be star observables.

Hiding Signatures of Gravitational Instability in Protoplanetary Disks with Planets

Abstract We carry out three-dimensional smoothed particle hydrodynamics simulations to show that a migrating giant planet strongly suppresses the spiral structure in self-gravitating disks. We present mock Atacama Large Millimeter/submillimeter Array (ALMA) continuum observations that show that in the absence of a planet, spiral arms due to gravitational instability are easily observed. Whereas in the presence of a giant planet, the spiral structures are suppressed by the migrating planet resulting in a largely axisymmetric disk with a ring and gap structure. Our modeling of the gas kinematics shows that the planet’s presence could be inferred, for example, using optically thin 13C16O. Our results show that it is not necessary to limit the gas mass of disks by assuming high dust-to-gas mass ratios in order to explain a lack of spiral features that would otherwise be expected in high-mass disks.

Simulations of globular clusters within their parent galaxies: multiple stellar populations and internal kinematics

ABSTRACT Using three-dimensional smoothed particle hydrodynamics simulations, we investigate the formation of multiple stellar populations (MSPs) in globular clusters (GCs) within the context of their parent galaxies. In our scenario, the second generation (2G) of stars originate from both asymptotic giant branch (AGB) polluters and pristine gas accreted from the host galaxy. Previous theoretical and numerical studies have demonstrated that this ‘AGB with dilution’ model has the potential to alleviate several problems faced by the classical AGB scenario. However, the accretion of pristine gas on to the GC has yet to be investigated within the context of the parent galaxy. This paper presents the preliminary results from our original simulation code which models GC formation from giant molecular clouds in a host galaxy, and subsequent gas accretion on to the GC. By simulating the genesis of the 2G over a 370 Myr time frame, we demonstrate that the fraction of 2G stars are inextricably linked to the GC’s environment. Our simulations rationalize the wide variety of abundance patterns, kinematics, and 2G concentrations by altering the initial conditions of both the GC progenitor and the host galaxy itself. Most notably, we reproduce a positive correlation between the fraction of 2G stars and the initial mass of the cluster. We discuss the physical implications of our scenario and compare our simulations with observations of the Galactic GC 47 Tucanae (47 Tuc). Finally, we present scaling relations that encompass the wider GC population and serve as a reference for future observations.

Planet migration in self-gravitating discs: survival of planets

ABSTRACT We carry out three-dimensional smoothed particle hydrodynamics simulations to study whether planets can survive in self-gravitating protoplanetary discs. The discs modelled here use a cooling prescription that mimics a real disc, which is only gravitationally unstable in the outer regions. We do this by modelling the cooling using a simplified method such that the cooling time in the outer parts of the disc is shorter than in the inner regions, as expected in real discs. We find that both giant (>MSat) and low-mass (<MNep) planets initially migrate inwards very rapidly, but are able to slow down in the inner gravitationally stable regions of the disc without needing to open up a gap. This is in contrast to previous studies where the cooling was modelled in a more simplified manner where, regardless of mass, the planets were unable to slow down their inward migration. This shows the important effect the thermodynamics has on planet migration. In a broader context, these results show that planets that form in the early stages of the discs’ evolution, when they are still quite massive and self-gravitating, can survive.

Role of baffle shape on debris flow impact in step-pool channel: an SPH study

Drainage channels with step-pool system are widely used to control debris flow. The blocking of debris flow often gives rise to local damage at the steps and baffles. Hence, the estimation of impact force of debris flow is crucial for designing step-pool channel. Existing empirical models for impact pressure prediction cannot consider the influence of baffle shape. In this work, a three-dimensional smoothed particle hydrodynamics (SPH) study on the impact behavior of debris flows in step-pool systems is presented, where debris material is modeled using the regularized Bingham model. The SPH method is first checked using the results from two laboratory tests. Then, it is used to investigate the influence of baffle shape and flow density. Numerical results show that the impact pressure at the first baffle highly depends on the baffle shape; however, the largest impact pressure usually occurs at subsequent baffles due to the violent impact induced by jet flows. The peak impact pressure at the first baffle initially grows with increasing flow density; however, it starts to drop as density is beyond a threshold. Based on the numerical results, an empirical relation considering the influence of baffle shape is proposed for better prediction of debris impact pressure.

Star–disc alignment in the protoplanetary discs: SPH simulation of the collapse of turbulent molecular cloud cores

ABSTRACT We perform a series of three-dimensional smoothed particle hydrodynamics (SPH) simulations to study the evolution of the angle between the protostellar spin and the protoplanetary disc rotation axes (the star–disc angle ψsd) in turbulent molecular cloud cores. While ψsd at the protostar formation epoch exhibits broad distribution up to ∼130°, ψsd decreases (≲ 20°) in a time-scale of ∼104 yr. This time-scale of the star–disc alignment, talignment, corresponds basically to the mass doubling time of the central protostar, in which the protostar forgets its initial spin direction due to the mass accretion from the disc. Values of ψsd both at t = 102 yr and t = 105 yr after the protostar formation are independent of the ratios of thermal and turbulent energies to gravitational energy of the initial cloud cores: α = Ethermal/|Egravity| and γturb = Eturbulence/|Egravity|. We also find that a warped disc is possibly formed by the turbulent accretion flow from the circumstellar envelope.