Smoothed Particle Hydrodynamics Model 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.

Numerical investigation of riser vibration induced by ice-water two-phase flow in icy regions by SPH method

In icy regions, the vibration induced by broken ice poses a hazard to risers, in addition to vortex-induced vibration (VIV). A numerical investigation has been conducted to explore the dynamic response of risers in seas with fragmented ice floes. Assuming the broken ice as a single rigid floating body bonded by particles, the flow with water and ice is considered a two-phase flow, which is established using the Smooth Particle Hydrodynamics (SPH) method based on the quasi-fluid model. Verification of the model was achieved by simulating the three-dimensional flow around a surface-piercing cylinder and VIV. Accurate predictions were made regarding hydrodynamic forces, uplift values of the free liquid surface at the front stagnation point of the cylinder, and riser motion. Furthermore, the SPH model was expanded to encompass the realm of ice-water structural interaction (IWSI) combined with the basic principle of bidirectional fluid-structure coupling, facilitating the simulation of riser vibration within ice-water flows. The results indicate that the ice load remained the principal contributor to the force on the vibrating riser, while the riser exhibited irregular motion, demonstrating a strong coupling between forces and riser movement.

A parallel multi-resolution Smoothed Particle Hydrodynamics model with local time stepping

Smoothed Particle Hydrodynamics (SPH) model has exhibited remarkable efficacy in addressing strongly nonlinear large deformation problems. However, the expensive computational cost could limit its application. To address this, we propose a novel parallel multi-resolution SPH model with a local time step strategy. This model integrates the multi-resolution model with a Message Passing Interface-based parallelization framework, wherein subdomains discretize the computational domain at varying resolutions. Meanwhile, a local fourth-order Runge-Kutta time integration scheme is introduced, enabling different subdomains to use different time steps. Subdomains of varying resolutions are devoid of overlapping regions, and changes in particle resolution at interfaces are achieved through a dynamic strategy involving particle merging and splitting. Besides that, we conducted a comparative analysis of different SPH discretization formats concerning their impact on the accuracy of multi-resolution particle discretization. Finally, several numerical tests were conducted to validate the accuracy and efficiency of the present multi-resolution SPH model.

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.

Numerical simulations of thermal capillary migration of a droplet on a temperature gradient wall with smoothed particle hydrodynamics method

Thermal capillary migration is a phenomenon due to the Marangoni effect, which refers to the spontaneous motion of a liquid on a non-isothermal surface. Numerical simulation of thermal capillary migration of a droplet is extremely difficult due to the multi-physics field coupling and the violent motion of the droplet surface. In this paper, an improved smooth particle hydrodynamics (SPH) method is developed for simulating thermal capillary migration of a droplet driven by thermal gradient. In improved SPH model, an improved continuous surface force model is proposed to enhance the accuracy and stability of surface tension force calculation by introducing an improved surface tangential force. The contact angle model is utilized to model the surface wettability. The SPH method for simulating the thermal fluid flow is developed based on the continuum, momentum, and energy equations. In addition, kernel gradient correction and particle shifting technique are utilized to improve the accuracy and stability of the SPH method. The correctness and effectiveness of the improved SPH method are verified by numerical examples. Moreover, the motions of a droplet driven by thermal gradient under different conditions are investigated. Comparing with the results obtained by experiments and other resources, we can conclude that the improved SPH model is effective in modeling the thermal capillary migration of a droplet.

Study on meso‑mechanical properties and failure mechanism of soil-rock mixture based on SPH model

This study adopts the Smoothed Particle Hydrodynamics (SPH) technique to accurately and efficiently replicate and forecast the mesoscopic behavior of soil-rock mixtures (SRM). It introduces a novel approach for generating rock blocks within the SRM, utilizing a method that randomly selects angles and lengths. In addition, this research proposes a method for discretizing any shaped region into free particles with specific material attributes, named the regional medium particle discretization method. It incorporates the Drucker-Prager constitutive model to develop the SPH numerical model for SRM. Furthermore, it examines the effects of different rock sizes and rock contents on the SRM's failure characteristics and mechanical properties. The findings revealed that, for identical rock contents, smaller rock samples exhibit a more dispersed failure surface with numerous secondary shear bands, whereas larger rock samples display a smoother and more concentrated failure surface. As the rock content decreases, shear bands typically form in the sample's center and are relatively straight. However, as the rock content increases, the shear bands' configuration becomes more intricate, often featuring multiple shear bands. This method offers a fresh perspective for exploring the mechanical properties of heterogeneous materials.

A hybrid smoothed-particle hydrodynamics model of oxide skins on molten aluminum

A computational model of aluminum melting is proposed which captures both the thermal fluid-solid phase transition and the mechanical effects of oxidation. The model hybridizes ideas from smoothed particle hydrodynamics and bonded particle models to simulate both hydrodynamic flows and solid elasticity. Oxidation is represented by dynamically adding and deleting spring-like bonds between surface fluid particles to represent the formation and rupture of the oxide skin. Various complex systems are simulated to demonstrate the adaptability of the method and to illustrate the significant impact of skin properties on material flow. Initial comparison to experiments of a melting aluminum cantilever highlights that the computational model can reproduce key qualitative features of aluminum relocation.

Microstructural smoothed particle hydrodynamics model and simulations of discontinuous shear-thickening fluids

Despite the recent interest in the discontinuous shear-thickening (DST) behavior, few computational works tackle the rich hydrodynamics of these fluids. In this work, we present the first implementation of a microstructural DST model in smoothed particle hydrodynamic (SPH) simulation. The scalar model was implemented in an SPH scheme and tested in two flow geometries. Three distinct ratios of local to non-local microstructural effects were probed: zero, moderate, and strong non-locality. Strong and moderate cases yielded excellent agreement with flow curves constructed via the Wyart–Cates (WC) model, with the moderate case exhibiting banding patterns. We demonstrate that a local model is prone to a stress-splitting instability, resulting in discontinuous stress fields and poor agreement with the WC model. The mechanism of stress splitting has been explored and contextualized by the interaction of local microstructure evolution and the stress-control scheme. Analytic solutions for a body-force-driven DST channel flow have been derived and used to validate the SPH simulations with excellent agreement in velocity profiles. Simulations carried out at increasing driving forces exhibited a decrease in flow. We showed that even the simple scalar model can capture some of the key properties of DST materials, laying the foundation for further SPH study of instabilities and pattern formation.

Smoothed particle hydrodynamics approach for modelling submerged granular flows and the induced water wave generation

In this study, we develop a Smoothed Particle Hydrodynamics (SPH) 2D-model for simulating fully submerged granular flows and their arising water waves. The granular particles are characterised by a non-Newtonian flow pattern, following a Casson constitutive law, generalised by applying the infinitesimal strain theory to avoid numerical singularities inherited from the original law. The implementation of this rheological model on the weakly compressible viscous Navier-Stokes equations enables the simultaneous modelling of the motion of granular flows and their resulting water waves, establishing a monolithic representation of fluid-structure coupling. The novelty of this model lies in the numerical continuity of the generalised rheological model based mainly on the yield stress criterion, which is computed purely from the mechanical properties of granular materials, including internal friction, cohesion, and viscosity coefficients. The proposed SPH model is validated through two benchmarks available in the literature, representing a submarine landslide along an inclined plane and an immersed granular column collapse. The outcomes of our study illustrate the effectiveness of the proposed model in accurately predicting the motions of submerged granular masses and their resulting water waves, which is crucial for accurately predicting the behaviour of underwater landslides and other natural hazards.

Continuous Feed Grinding Milling Process of Soda-Lime Glass Using Smoothed-Particle Hydrodynamics

A smoothed-particle hydrodynamics (SPH) modeling technique was applied in conjunction with the Johnson–Holmquist (JH-2) ceramic material constitutive model to replicate the fracture of soda-lime glass in a milling manufacturing process. Four-point bending tests were conducted to validate the soda-lime glass bulk material properties prior to its implementation in ABAQUS CAE™ Explicit (Version 2017). The JH-2 material constitutive model replicated the fracture load and time to fracture for the four-point bending load cases as per ASTM C158. This study showed how SPH in combination with a validated JH-2 material model in a milling process simulation was able to replicate the output size distribution at 5000 and 6500 revolutions per minute (RPM). For operations at 3000 RPM or lower, it was shown that it is necessary to include additional effects in the model, such as fluid–structure interactions, to improve the correlation with the experimental data. The SPH model was validated through an experimental campaign using high-speed cameras and a particle Camsizer. The experimental results clearly indicate a direct relation between the mill’s RPM and the output particle size distribution.

Experimental and numerical investigations on the microstructural features and mechanical properties of explosively welded aluminum/titanium/steel trimetallic plate

In this paper, 3A21Al/TA1/CCSB composite plate was fabricated successfully by explosive welding to improve the bond strength. The microstructure characteristics of aluminum/titanium and titanium/steel bonding interfaces were systematically investigated by two-step numerical simulation and SEM/EBSD characterizations. Firstly, the SPH (Smoothed Particle Hydrodynamics) and Lagrange methodology were used to simulate and calculate the collision velocity and collision angle, establishing an accurate impact condition. Secondly, the SPH model was used to simulate the high-speed oblique impact welding process. The simulation results reproduce the formation of wavy interface, vortex zone and jet, which are consistent with the experimental results. Combined with SEM, EBSD, and EDS analysis, continuous and uniform wavy structures were found at different interfaces of the composite plate, showing significantly different wave lengths and amplitudes. Dynamic recovery and recrystallization took place at the bonding interfaces which showed refined grain with different preferred orientations. The observed structural characteristics and the thermodynamic state predicted by SPH simulation inferred the evolutions of microstructures (including morphologies, micro defects, grain structures). The tensile strength and fracture elongation of the trimetallic plate reach 448.2 MPa and 14.15%, respectively. In addition, the shear strengths of each interface far exceed the corresponding acceptable standard values.

Co-Extrusion of Dissimilar Aluminum Alloys via Shear-Assisted Processing and Extrusion

Bimetallic tubes are used when a component requires more than one performance requirement, for instance, strength/creep resistance and oxidation/corrosion resistance. Shear-assisted processing and extrusion (ShAPE) can be used to fabricate extrudates that are comparable or superior in performance relative to conventionally manufactured extrudates. For the first time, ShAPE has been successfully employed in producing bimetallic Al tubing consisting of 6061 and 7075 Al alloys. Both light and electron microscopy techniques were used to investigate the integrity of the tubes, especially the interface between the core and cladding of the bimetallic tubes. Void-free bimetallic tubes were produced using ShAPE. Quantification of tube integrity was carried out with tensile testing under as-extruded and post-aged conditions. All the bimetallic tubes in the as-extruded samples exhibited uniform elongation above 5% with good tensile strength. Key insights such as material flow during bimetallic tube extrusion were obtained from the characterization of remnant billet and simulation results from a smoothed particle hydrodynamics model.

Smoothed particle hydrodynamics modelling of particle-size segregation in granular flows

In this work, smoothed particle hydrodynamics (SPH) is employed to investigate the segregation evolution in granular flows. We first provide the Lagrangian description-based governing equations, including the linear momentum conservation and the segregation–diffusion equation. Then the hybrid continuum surface reaction scheme is introduced to formulate the concentration-related inhomogeneous Neumann boundary condition on the free and wall surfaces. We follow a two-stage strategy to advance boundary particle searching and normal direction identification. Moreover, $C^1$ consistency is considered based on the Taylor series to obtain accurate segregation flux gradient along the boundary. Our SPH model is validated with a shear box experiment. The model is then applied to investigate the segregation mechanism in bidisperse-sized granular flows in a rotating drum.

Numerical investigations on water entry and/or exit problems using a multi-resolution Delta-plus-SPH model with TIC

As a classical Fluid-Structure Interaction (FSI) problem, water entry and/or exit of marine structures involve large deformations of free-surface and splashing, which have long been a great challenge for numerical modeling. Smoothed Particle Hydrodynamics (SPH) is a meshless Lagrangian particle method that has natural advantages in dealing with the non-linear variation of free-surface and moving interfaces. However, the characteristics of weakly-compressible SPH itself may lead to deficiencies such as pressure noise, tensile instability, heterogeneous particle distributions and computational inefficiency. Therefore, in this work, an acoustic damper term is formulated in the momentum equation to eliminate the amount of acoustic pressure waves induced by liquid impacts. Meanwhile, the Adaptive Particle Refinement (APR) is applied to obtain sufficiently fine particle resolution and reduce the computational cost. For the tensile instability issues induced by negative pressures, especially at the water exit stage, the Tensile Instability Control (TIC) is adopted into the SPH simulations to suppress its adverse impact. Furthermore, the Particle Shifting Technique (PST) is beneficial to the two schemes above, and it is also employed in this study. That is to say, PST can effectively solve the problem of particle disorder, which increases the accuracy and robustness of APR and reduces the momentum conservation error caused by TIC. Finally, we propose an improved Free-Surface Detection Method (FSDM) to allow the flow separation from the structure surface at the water entry stage that is impacted by PST. The fairly good agreements between the numerical results and the experimental data indicate the present SPH model can be treated as a reliable numerical tool for accurately solving such problems of structures penetrating fluid interfaces.

A GPU-based hydrodynamic simulator with boid interactions

We present a hydrodynamic simulation system using the GPU compute shaders of DirectX for simulating virtual agent behaviors and navigation inside a smoothed particle hydrodynamical (SPH) fluid environment with real-time water mesh surface reconstruction. The current SPH literature includes interactions between SPH and heterogeneous meshes but seldom involves interactions between SPH and virtual boid agents. The contribution of the system lies in the combination of the parallel smoothed particle hydrodynamics model with the distributed boid model of virtual agents to enable agents to interact with fluids. The agents based on the boid algorithm influence the motion of SPH fluid particles, and the forces from the SPH algorithm affect the movement of the boids. To enable realistic fluid rendering and simulation in a particle-based system, it is essential to construct a mesh from the particle attributes. Our system also contributes to the surface reconstruction aspect of the pipeline, in which we performed a set of experiments with the parallel marching cubes algorithm per frame for constructing the mesh from the fluid particles in a real-time compute and memory-intensive application, producing a wide range of triangle configurations. We also demonstrate that our system is versatile enough for reinforced robotic agents instead of boid agents to interact with the fluid environment for underwater navigation and remote control engineering purposes.

Numerical studies of complex fluid-solid interactions with a six degrees of freedom quaternion-based solver in the SPH framework

Six-degree-of-freedom (6-DOF) motions of structures widely exist in aeronautics and ocean engineering. It is significant to study the 6-DOF motion for simulating the trajectory and impact load of structures. This paper uses the smoothed particle hydrodynamics (SPH) method combined with some modified numerical techniques to simulate the fluid-solid interactions (FSI), then a quaternion-based method is adopted to simulate the free motion of rigid bodies, where the calculation process of 6-DOF motions based on quaternion is elaborated in detail. The accuracy of this method is verified through two benchmark tests, including water entry of a cuboid and skipping stone, which can prove the pressure calculation and motion prediction of rigid bodies are consistent with the experimental results. At last, the 6-DOF ditching process of a seaplane is simulated by the quaternion method embedded in the SPH model, and the simulation results are consistent with those simulated by the finite volume method (FVM). The above three tests demonstrate that the SPH model combined with a 6-DOF quaternion-based solver can accurately solve FSI problems from basic to complex at different scales. Besides, the SPH model shows significant advantages in capturing large-deformed free surfaces and splashing droplets compared with Eulerian-grid-based methods.

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.

Numerical simulation of dry laser derusting process based on SPH method

Laser cleaning is an efficient, environmental-friendly, and non-contact surface treatment technology. Laser radiation and heating cause the surface material to heat up and gasify, separating it from the substrate. Traditional mesh-based numerical methods are difficult to effectively simulate the evolution of erosion crater and the splashing phenomenon. In this study, a meshfree method, the smoothed particle hydrodynamics (SPH) method, is used to establish the numerical model of the interaction between the laser beam and the targeted material and to investigate the removal process of the rust layer under different laser operating conditions. In consideration of the coupling effect of laser absorption, heat transfer, and material phase change, the SPH modeling procedure and corresponding numerical scheme for heat transfer and heat-absorption-induced phase change are introduced. Additionally, a surface particle detection algorithm and surface normal vector calculation method are proposed to accurately compute the complex surface geometry of the erosion crater, which realizes the dynamic coupling of laser-energy absorption and laser-beam direction. The established SPH model is then used to simulate the temperature distribution of the rust layer under the action of a laser beam, and the influence of laser energy, beam overlap rate, and beam direction on the removal efficiency is analyzed. This study applies the meshfree SPH method to the study of laser rust removal process, verifies the accuracy of the surface detection algorithm, captures the spatter behavior of material particles after phase change, and reflects the advantages of the meshfree method in solving such problems.

SPH simulations and experimental investigation of water flow through a Venturi meter of rectangular cross-section

The flow of water through a horizontal small-scale Venturi tube of rectangular cross-section is simulated using a modified version of the open-source code DualSPHysics, which is based on Smoothed Particle Hydrodynamics (SPH) methods. Water is simulated using the Murnaghan-Tait equation of state so that weak compressibility is allowed. The hydrodynamics is coupled to a Large-Eddy Simulation (LES) turbulence model. The convergence properties of SPH are improved by adopting a C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{2}$$\\end{document} Wendland function as the interpolation kernel, increased number of neighboring particles and non-reflective open boundary conditions at the outlet of the Venturi tube. The flow structure and differential pressure as well as the mainstream velocity profiles at different stations are compared with calibrated experimental data. A resolution independence test shows that good convergence to the experimental measurements is achieved using four million particles. At this resolution the simulations predict the experimental centerline velocity profile along the Venturi meter for a volumetric flow rate of ten liters per minutes (lpm) with a root-mean-square error of 4.3%. This error grows to 7.1% when the volumetric flow rate increases to 25 lpm. The predicted differential pressure matches the experimental data with errors varying from 1.4% (for 10 lpm) to 6.8% (for 25 lpm). Cross-sectional velocity profiles within the throat and divergent sections differ from the experimental measurements in less than 5.5%. In general, it is shown that the SPH model can provide an efficient and accurate method for recalibrating flow meters at moderately high Reynolds numbers instead of using costly experimental tests.

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.