Smoothed Particle Hydrodynamics Model Research Articles

Simulation of crude oil slick on ice infested sea water

A three-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) method is utilized to model such interactions. The effects from air and water are well captured using suitable force components and without explicit inclusion of air and water phases. This reduces the four-phase SPH model into a two-phase model, significantly reducing computational costs and potentially enabling the use of this model for large-scale simulations. This study includes two simulation domain size. The results show that the remained oil slick in the icy domain is completely depend on properties of different crude oils and current velocity. Then we performed a numerical experiment to study the effects of different ice parameters (e.g., ice concentration, floe shape) on the drift of fresh and weathered oil. Ice fields with the size of 750 m × 1350 m are used in the experiment. The ice concentration varies between 30%, 50% and 70%. Quadrilateral and circular ice floes, in addition to real-shape floes digitize from an aerial image are all used in the experiment. Oil spills of 1257 m3 are released in the open water and later drift into the ice under the influence of steady current of 50 cms. The type of spilled crude oil varies from fresh Troll B, Troll B 250 °C, and Troll B 250 °C and 75%emuls. The behavior of oil spills while crossing through the ice infested area are investigated by measuring the thickness of crude oil, the average and maximum distance traveled by crude oil.

Numerical simulation of dike failure using a GPU-based coupled DEM–SPH model

Dike failure includes a complex fluid–solid interaction process, which is one of the challenges in investigating dike failure problem. Given the characteristics of dike failure, a GPU-based coupled discrete element method (DEM)-smoothed particle hydrodynamics (SPH) model is proposed and adopted to simulate dike failure problems in this study. GPU parallel computing is involved in the proposed model and solid and fluid phases are modeled by DEM and SPH respectively. Overtopping-induced dike failure is numerically tested to validate the proposed model, and the computed motion of sediments and water and the dike surface profiles are in good agreement with experimental results. Then the proposed model is adopted to simulate seepage-induced dike failures, which have relatively covert behaviors compared with the overtopping-induced dike failure. The evolution of dike saturated zone and sediment displacement during this process is studied, and a sensitivity analysis of sediment diameter indicates that it has a great impact on the dike deformation. Finally, the effect of bottom drainage length on the development of seepage inside dike is investigated.

Investigation of dynamic contact between cold spray particles and substrate based on 2D SPH method

In cold spray, the study of the dynamic contact between the particle and the substrate in the high-velocity impact is essential during particle deposition. To entirely reveals the dynamic contact process, the SPH (Smoothed Particle Hydrodynamics) method is applied to virtual experiments to avoid the time-consuming and high costs in real experiments due to scale. In particular, an interface force model is proposed to completely describe the dynamic contact between the cold spray particles (CS particles) and substrate, which has the ability to eliminate the unphysical SPH particle penetration, rebounding phenomenon, and insufficient momentum transfer. The variation of the steady mean temperature of the CS particle surface with the initial velocity is analyzed and the critical velocity of particle deposition is successfully predicted. Furthermore, the effect of particle shapes on the deposition is discussed, which shows that the circular particles are more favourable to be deposited than the elliptical ones. The cold spray SPH model with the novel dynamic contact developed in this paper is in favor of understanding the mechanism of CS particles deposition and guiding the cold spray processes in a certain extent.

Research, analysis and optimization of the drive characteristics of the drive wheel of the machine tiller based on SPH method

Abstract The boat tiller (machine tiller) uses the floating working principle to make the hull and drive wheel bear the general tractor drive wheel load and drive two functions, respectively, so that it has good applicability in the operation of deep muddy foot water field, which greatly improves the tillage efficiency of China’s water field farming. The drive wheel is an important component of the machine tillage boat; its structural parameters have a significant impact on the driving performance and efficiency of the machine tillage boat. In this paper, combined with the kinetic analysis of the drive wheel, a single-wheel leaf-soil smooth particle hydrodynamic model of the drive wheel is constructed based on the SPH method, and the influence of the parameters of the wheel spurs of the drive wheel unit group on the driving performance is analyzed, and the drive wheel mechanism parameters with the best driving efficiency are finally obtained through simulation analysis. The research results show that the maximum propulsive force of the optimized single-wheel blade structure increases by 35.8% compared with that before optimization, the slip rate decreases by 3.9% compared with that before optimization, and the driving efficiency increases by 14.4% compared with that before optimization. The structural design and parameter selection of the drive wheel of the research results of this paper provides a certain theoretical basis, which is of great significance to the later improvement of the drive efficiency and performance of the drive wheel of the machine tiller in paddy soil.

Numerical modeling and simulation of underwater explosions interacting with discrete rigid bodies

The smoothed particle hydrodynamics (SPH) method is widely used to simulate underwater explosion phenomena. However, previous studies have focused on the interaction between the underwater explosion and continuous structures (e.g., steel plates and dams), while studies on the interaction between the explosion and discrete objects (e.g., debris) have not been reported. In this study, a multi-media coupled model containing water, explosion gas, discrete objects, and steel plates is developed based on the SPH method. The discrete object is modeled as a rigid body with a certain shape, which is discretized by SPH particles. The interaction between the discrete object and the adjacent fluid particles is realized by the kernel approximation, while the collision between different objects is realized by the contact algorithm. To improve the numerical stability, an artificial viscous term containing a threshold switch is added to the SPH momentum equation, while a density dissipation term is introduced into the continuity equation to reduce the noise of the pressure field. Subsequently, the established SPH model is used to simulate the underwater explosion process containing discrete rigid bodies, and the effects of the distribution, stacking form, and number of rigid bodies on the propagation of shock waves, bubble expansion, and deformation of steel plates and the effect of damage are analyzed. The results show that the rigid body will hinder the propagation of shock waves, help reduce the peak pressure of the shock wave behind, and then affect the direction of the diffusion of the explosion energy. Shock waves would produce diffraction, reflection, and transmission when passing through the rigid bodies, and the superposition of various waves would make the pressure distribution near the liquid–gas interface irregular. The rigid bodies stacked above the explosives would enhance the damage effect of the explosion on the steel plates below, and the damage effect is affected by the stacking form. The established model can simulate the multi-medium coupling process in a unified framework without coupling other methods and can effectively restore the complex interaction process between underwater explosion, discrete object, and structure.

Dynamic Temperature Characteristics of Cathode Microprotrusion Under Electron Emission Based on Smoothed Particle Hydrodynamics

The study of dynamic temperature characteristics of cathode micro-protrusion under electron emission would be essential to the development of high-voltage vacuum systems. Owing to the multi-scale and multi-physics characteristics of the micro-protrusions under the electron emission, Smoothed Particle Hydrodynamics (SPH) method has become one of the feasible methods. In this paper, the SPH method is introduced to study the dynamic temperature characteristics of a micron scale micro-protrusion under the electron emission. First, the constitutive model and the equation of state with the material strength, and the coupling effect of the heat conduction, Joule heating, Nottingham effect and electron emission have been introduced into the SPH method. Then, a SPH model of the micro-protrusion under the electron emission with considering the temperature correction is established by combining the SPH method and thermal-field emission heating model. Compared with the Finite Element Method (FEM) and theoretical calculation, the SPH model of the micro-protrusion under the electron emission is verified. Based on the SPH model of the micro-protrusion, the dynamic temperature characteristics under the different conditions are quantitatively obtained and analyzed. The results of this paper may provide some useful reference for the vacuum insulation design and the insulation state evaluation of the high-voltage vacuum system.

Research on the Water Entry of the Fuselage Cylindrical Structure Based on the Improved SPH Model

During aircraft landing on water, the intense impact load may lead to significant local deformation of the fuselage skin. Ensuring the aircraft’s integrity and reliability is of paramount importance. This paper investigates the fuselage skin’s dynamic response during water entry. In the simulation of complex water entry problems, the smoothed particle hydrodynamics (SPH) method can fully leverage the advantages of the particle method. However, the traditional SPH method still suffers from the drawbacks of tensile instability, significantly affecting the computational accuracy. Therefore, this paper first introduces the improved SPH model addressing fluid and solid tensile instability issues. Furthermore, the Riemann-based contact algorithm at the fluid–solid interface is also demonstrated. Based on the above improved SPH model, the simulation of water entry of the elastic cylinder is performed to validate the efficacy of the improved SPH model. Then, the dynamic response characteristics of elastic fuselage skin and the skin–stringer–floor–column structure when it enters the water are analyzed, including the deformation features and slamming force. Lastly, based on the presented damage model, a study is conducted on the water entry of the metallic elastic–plastic skin–stringer–floor–column structure, analyzing the locations of failure and providing guidance for the structural safety design of engineering.

Wave interactions with multi-float structures: SPH model, experimental validation, and parametric study

This paper proposes a new type of multi-float structures which comprise several serially arranged box-type modules. Adjacent modules are connected at the top corners using hinges, while rubber bumpers are placed at the bottom corners to absorb the collision energy. The whole structure is anchored to the seabed with mooring lines. A Smoothed Particle Hydrodynamics (SPH) model is established to study the wave interactions with such multi-float structures. In the SPH model, the Navier-Stokes equations are solved for the wave motion and the multi-degree-of-freedom motion of the structure is tracked by applying the Newton's second law to rigid bodies. A light spring model is used to evaluate the mooring forces, while the collision forces between adjacent modules are calculated according to the force-compression relation of the rubber bumpers. Besides, a continuity restriction on the linear acceleration is applied to the hinge connectors between adjacent modules. To validate the proposed SPH model, a laboratory experiment is conducted regarding the hydrodynamic performance of a three-float structure. Then, the SPH model is applied to a multi-float design scenario, from which useful findings have been obtained for engineering practice.

Development of a two-dimensional coupled smoothed particle hydrodynamics model and its application to nonlinear wave simulations

This paper presents a two dimensional two-way coupled model combining Smoothed Particle Hydrodynamics (SPH) based on the Navier–Stokes equations (NSE) and OceanWave3D based on the fully nonlinear potential flow theory (FNPT) in order to efficiently simulate non-linear waves and wave–structure interaction problems. The two models are strongly coupled in space and time domains using a fixed overlapping zone, wherein the information from both solvers is exchanged by relaxation functions. In the SPH model, an open relaxation boundary, which is implemented as open and relaxation zones, is used in the coupling region. Horizontal velocity and free surface elevation in the open and relaxation zones are obtained from OceanWave3D, while vertical velocity and density in the open zones are interpolated from the relaxation region. OceanWave3D requires the free surface elevation and vertical velocity at the free surface from SPH in the coupled region. The coupled model is tested by modelling a regular wave, irregular wave and wave over a submerged bar and an oscillating water column (OWC) device. The results demonstrate that the coupled model can produce satisfactory results with less computational time than the SPH-only model.

Comparison of finite element and smoothed-particle hydrodynamics models in the simulation of hypereutectic Al-Si alloy friction surfacing: calibrations from experiments

Comparison of finite element and smoothed-particle hydrodynamics models in the simulation of hypereutectic Al-Si alloy friction surfacing: calibrations from experiments

Data-driven modeling of sluice gate flows using a convolutional neural network

Abstract Predicting the flow field around sluice gates is essential for controlling water levels and discharges in open channels and rivers. Smooth particle hydrodynamics (SPH) models can satisfactorily reproduce such free-surface flows, but they typically require long computational time and extensive computational resources. In this work, we propose a convolutional neural network (CNN) to predict the flow field around a sluice gate. A validated SPH model is used to carry out extensive simulations, and the generated data set is used to train and test CNN-based models. The results demonstrated that the developed CNN can accurately reproduce sluice gate flows, with R2 values exceeding 90% and significantly reducing the computational costs. Furthermore, various traditional machine learning algorithms comprising adaptive neuro-fuzzy inference system, genetic programing, multigene genetic programing, and one-dimensional CNN were also evaluated, and a comparison of the results showed that the developed CNN performed better than the traditional data-driven algorithms in predicting sluice gate flows. Therefore, the proposed method is a promising tool for providing rapid prediction of the spatial distribution of flow fields near the sluice, and potentially for predicting other spatially distributed hydrologic variables.

Numerical simulation of buoyancy–driven flow in a human stomach geometry: Comparison of SPH and FVM models

The primary functions of the stomach, including mixing, digestion, and emptying, are affected by the spatial distribution of content properties, and how this distribution changes in response to gravity and wall contraction forces. One aspect that is not well studied is the buoyancy effects that result from content with heterogenous density. A buoyancy–driven flow in a non–deforming stomach is simulated using the Smoothed Particle Hydrodynamics (SPH) and Finite Volume Method (FVM). An aqueous liquid layer is initially placed above a fatty layer of the same volume. The buoyancy effect driven by gravity and strongly influenced by the stomach shape, causes the fat to rise to the top layer and the aqueous liquid to sink to the bottom. Rayleigh–Taylor Instability (RTI) is well–captured in the SPH model in the initial interface flow development. Some detailed flow behaviours are slightly different between the two models once the bulk turnover flow is established, but both models show that the separation process happens rapidly (within 6 s) in the curved geometry of the stomach. The final phase separation is more complete in the FVM compared with the SPH. Sensitivity analysis is conducted in both models to examine the solution accuracy. This work suggests that buoyancy driven flow effects, which have not been investigated previously, occur on a much shorter timescale (6 s) than peristaltic (20 – 60 s) and digestion timescales (hours). This result may help basic understanding of digestive processes and be used to guide food and drug design.

The loading on a vertical cylinder in steep and breaking waves on sheared currents using smoothed particle hydrodynamics

Waves and currents coexist in a wide range of natural locations for the deployment of offshore structures and devices. This combined wave–current environment largely determines the loading of vertical surface piercing cylinders, which are the foundations typically used for offshore wind turbines along with many other offshore structures. The smoothed particle hydrodynamics (SPH) code DualSPHysics is used to simulate focused waves on sheared currents and assess subsequent loading on a vertical cylinder. Outputs from another numerical model are used to define the SPH inlet–outlet boundary conditions to generate the wave–current combinations. A modified damping zone is used to damp the waves, but allow the currents to exit the domain. Numerical results are validated against experimental measurements for surface elevation and associated loading on the cylinder. Four phase repeats are used in the SPH model to understand the harmonic structure of the surface elevation at the front face of the cylinder and associated loading. It is shown that the SPH model provides agreement with experimental measurements of harmonic components for both force and elevations. Taking advantage of the SPH method, wave amplitudes were increased up to, and beyond, the breaking threshold highlighting a complex relationship between peak force and wave phase, requiring detailed investigation. The numerical modeling of interactions of steep and breaking waves on sheared currents with the cylinder demonstrates the SPH model's capability for modeling highly nonlinear fluid–structure interaction problems.

Coupling SPH with a mesh-based Eulerian approach for simulation of incompressible free-surface flows

This paper presents a coupling algorithm for the simulation of incompressible free-surface flows over the near and far fields by solving the Navier-Stokes equations. The coupling combines the Smoothed Particle Hydrodynamics (SPH) with the Finite Difference (FD) method implemented on structured Eulerian grids. Based on the domain decomposition, the SPH is applied to the near-field core region for modeling with high-fidelity the severe free-surface deformation and even fragmentation of flow, while the FD method is used to resolve the remaining far-field region with relatively high efficiency. The primary purpose of the hybrid approach is to mitigate the computational load of SPH applications through combination with a mesh-based Eulerian method while maintaining high accuracy for both the near-field and far-field simulations. Two-way coupling between the FD and SPH models is achieved by the overlapping region between the computational subdomains, in which the Eulerian solutions and the Lagrangian solutions are coupled with each other through interpolation in the overlapping region for the fluid transfer and free-surface movement between the near-field and far-field regions. The proposed algorithm is validated by several test cases, showing favorable accuracy, convergence, and applicability in the simulation of wave interactions with complex bathymetry and structures.

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.

Numerical simulation of conduction problem with evaporation based on a SPH model improved by a fractional order convection-diffusion equation

Smoothed particle hydrodynamics (SPH) simulations of phase transitions are not accurate because of the decrease in liquid particles at the end of the evaporation phase transition. In this paper, we establish a numerical model of droplet evaporation suitable for SPH by introducing a time fractional-order convection–diffusion equation. This model was used to study the evaporation process of droplets under different environments, and the stationary evaporation of droplets was simulated by combining convection–diffusion equations of different orders to determine the optimal order. The results conformed to the “D2 Law,” confirming the effectiveness and accuracy of our method. The model was then used to study the phase transition process of droplets impacting flat and curved surfaces. Among the tested equations, the 0.1-order convection–diffusion equation had the best correction effect on the evaporation model. This equation improved the accuracy of the calculation and had a good corrective effect for both static evaporation and the evaporation of droplets impacting flat and curved surfaces.

A class of second-derivatives in the Smoothed Particle Hydrodynamics with 2nd-order accuracy and its application to incompressible flow simulations

In this paper, we propose a class of decoupled first- and second-derivatives models for the Smoothed Particle Hydrodynamics (SPH) method, which were inspired by the Lagrangian Differencing Dynamics (LDD) (Bašić et al., 2018) and (Bašić et al., 2022) and arranged to the SPH framework. Being extensions of existing gradient and Laplacian SPH models, the proposed decoupled models include the cross-derivatives, which are crucial to ensure 2nd-order accuracy. Under the framework of the proposed class of decoupled models, we defined five second-derivative models, here termed, Naïve (NI), Block Diagonal (BD), SUM, Part Inverse (PI), and Full Inverse (FI). Among these models, only the NI and BD have equivalences in existing models, while the other three are completely original. Therefore, we believe that, besides the development of new models, this work may provide a standard classification for second-derivative models in SPH. In addition, applying the FI model into the first-derivative model, we propose the first instance of a 2nd-order accurate gradient model in SPH.Then, we demonstrated that the convergence rate of the truncation error decreases the higher the order of the model, and the results were investigated for different particle disorder levels. After that, we applied the proposed derivative models to incompressible fluid flow simulations for validation. The validation includes four famous benchmark tests: the lid-driven cavity, the Kármán vortex behind a cylinder, the rotating square patch, and the dam break problem. The first two tests are used to discuss the accuracy of the spatial derivative models without a free surface, while the third test already includes the effects of the free surface, where particle disorder is more severe. All examples demonstrate the robustness and accuracy of our proposed spatial derivatives at 2nd-order accuracy. Since the combination of the FI Laplacian model and the 2nd-order gradient model can satisfy 2nd-order accuracy, we expect this to be the second generation of SPH formulations, which we call SPH(2).

A Numerical Study of Aero Engine Sub-idle Operation: From a Realistic Representation of Spray Injection to Detailed Chemistry LES-CMC

High altitude relight is a matter of increasing importance for aero engine manufacturers, in which combustion plays literally a vital role. In this paper we want to evaluate the predictive capability of a combined Smoothed Particle Hydrodynamics (SPH) and Large Eddy Simulation with Conditional Moment Closure (LES-CMC) approach for a spray combustion process at these extreme conditions. The focus is on the SPH modelling of the kerosene primary atomization, the extraction of realistic spray boundary conditions for LES-CMC and the effect of the spray on combustion. Interestingly, it will be demonstrated that the fragment size distributions resulting from the airblast atomization are characterized by bimodal behaviour during the relight process and that small and large fragments differ significantly in their dynamical behavior. This is shown to affect the combustion in the Central Recirculation Zone (CRZ). Very large fragments are even able to supersede the flame from the CRZ, such that endothermic pyrolysis becomes dominant, but simultaneously essential to sustain and stabilize the remaining flame with reactive pyrolysis species. The study proves the ability of our methodology for extreme operating conditions, in which experimental insights are hardly possible.

Study on movement characteristics of snow-wind flow based on SPH method

Snowstorm disasters seriously endanger human life and the social economy. In order to find out the influence of the sublimation of snow on motion characteristic of snow-wind flow, based on Smoothed Particle Hydrodynamics (SPH), this paper simulates motion to propose the method and basic theory of the SPH model of snow-wind flow. The basic idea of the SPH method is to decompose the computational domain into independent particles. These computational particles carry their physical properties. And it can move with the governing equations, which is consistent with the discrete nature of snow particles. According to the advantages of the SPH method and the characteristics of snow flow, this paper improves and rectifies SPH theory, so that SPH shows its unique advantages in dealing with the coupling of two substances in the snow two-phase flow. This new model can able to achieving two functions: moisture diffusion and snow particle physical properties change with time and environment. And it can dynamically display the movement state of the salting snow particles of the whole snow-wind flow process to obtain each particle's speed, trajectory, and mass change. In this paper, the dynamic characteristics of snow particle swarm motion behavior are obtained through the microscopic analysis of a single snow particle motion physical quantity.

Mesh-free simulation of height and energy transfer of landslide-induced tsunami waves

The landslide-induced tsunami wave poses a threat to human society and the living environment by causing disasters such as run-up of water surfaces and overtopping of dams. In this paper, we systematically investigated the relationship between landslide properties and induced tsunami wave characteristics as well as the energy transfer between the landslide and waves. A meshless smoothed particle hydrodynamics (SPH) framework was presented and validated with four experiments of different landslide types. The validations indicate that the SPH model is capable of reproducing the complex processes of tsunami wave generation induced by both rigid and deformable landslides. Then we perform numerical simulations of 162 landslide-induced waves scenarios with varying landslide deformability, relative initial positions, densities, landslide size, and downstream water depths using the validated SPH model. The results show that the effect of density and initial water depth on the maximum wave height can be disregarded, while the effective landslide volume has a significant effect. The analysis of the kinetic and potential energy of the induced waves reveals that energy transfer occurs rapidly, which mainly increases the potential energy of the water downstream. We also find an exponential relationship between landslide potential energy reduction and maximum wave height. These findings provide valuable insights into the landslide-induced tsunami waves and enhance risk assessment and mitigation efforts.