Two-phase Smoothed Particle Hydrodynamics Research Articles

Numerical Calculation of the Oil Flow in a Truck Rear Axle Transmission and the Influence of Gear-Induced Air Flow

Abstract For the reliable operation of a gearbox, consistently sufficient lubrication of tooth contacts and bearings is necessary. Thus, gearbox oil flow plays an important role. Additionally, air flow may affect the oil flow in the gearbox. The state of the art indicates that Computational Fluid Dynamics (CFD) enables targeted support of the gearbox development process at an early stage. Computational time plays a prominent role in practical applications due to associated costs. The particle-based Smoothed Particle Hydrodynamics (SPH) shows great potential for time-efficient calculations, especially with a simplified single-phase modeling approach. This study examines the influence of gear-induced air flow on gearbox oil flow, focusing on a test gearbox to identify a suitable modeling approach for a truck rear axle transmission. The results indicate that for the investigated operating conditions, the gear-induced air flow only impacts gearbox oil flow at higher circumferential speeds. For lower circumferential speeds, a single-phase SPH yields good results with significantly reduced computation times compared to the two-phase SPH. Applying the single-phase SPH to the truck rear axle transmission and comparing numerical results with experimental findings demonstrates a reliable representation of the oil flow characteristics.

Validation of multiphase water wave propagation using smoothed particle hydrodynamics

Water wave propagation is one of the classical problems in free surface flow that involved water and air. There are a lot of studies have been conducted on both experimental and numerical methods. One numerical method is computational fluid dynamics (CFD), which is divided into two major i.e. CFD mesh-based and meshfree. In this paper, smoothed particle hydrodynamics (SPH) is used to carry out a study of water wave propagation. SPH is a mesh-free CFD and Lagrangian approach that is suitable for free surface flow such as water waves. Two-phase SPH was used to reproduce long-distance propagation using a piston-type wavemaker. The wave probe was set 24.6 m in front of the wavemaker with a water depth is 0.75 m. The wave period is 1.15 s with an amplitude of the wavemaker is 33.0 mm. The simulation is carried out with a water and air phase (multiphase). The results indicate SPH is in reasonable agreement with experimental for the wave height, celerity, and amplitude.

Translational momentum of deformable submarine landslides off a slope

It has been reported that, in submarine landslides down a slope, only a small part of the landslide momentum was transferred to the tsunami while most was lost in the further propagation over the flat bed. The high momentum of landslides off a slope meant a long run-out and a great impact on underwater infrastructure. Nevertheless, little attention has been paid to the variation of momentum of deformable submarine landslides off a slope, i.e. the loss of momentum when the slides flow away from the slope over a flat bottom. In this paper, the translational momentum of deformable submarine granular landslides running down a non-erodible inclined bed is investigated with a two-phase smoothed particle hydrodynamics model. After flowing down the slope, the transport rate and flux of the landslide translational momentum along the propagation over the flat bottom are examined. The effects of physical variables of the slide, particularly the grain size, the initial compaction and the front intrusion angle on the variation of the translational momentum, are explored. Accordingly, scaling relations of the spatial-temporal maximum transport rate and flux of the landslide translational momentum, as well as those of the slide final run-out and the generated leading wave height, are proposed. These scaling relations, although based on numerical data of small-scale granular landslides, demonstrate a preliminary attempt to develop practical expressions in the framework of momentum for estimating the run-out of real submarine landslides and the impact on underwater infrastructure.

Numerical study on the dynamic characteristics of water entry of cavity body using two-phase SPH method

The air usually has a major influence on the water entry of a typical cavity body (cavity body is a hollow, cylindrical, semi-closed structure), which not only lowers the slamming load but also affects the dynamic characteristics of water entry. In this paper, a two-phase smoothed particle hydrodynamics (SPH) model for simulating the water entry of cavity body is presented. The SPH model combined with Riemann solver is improved to deal with the two-phase flows with the discontinuous quantities across the interface. One-sided Riemann problem is used to impose the fluid–structure interaction and a switch-function-based Riemann solver dissipation is formulated to improve the interfacial instability owing to the strong impact. The motion equations of rigid body are incorporated into two-phase SPH model to describe the motion of cavity body. The proposed model is validated by research on the test cases in the published literature. Finally, this work presents a study of water entry of cavity body by experiment and this two-phase SPH method. The dynamics phenomena in the coupling process between cavity body and two-phase flow are investigated. And the effects of air, mass, the sizes and incline angles of cavity body on the dynamic characteristics of cavity body and two-phase flows are shown. An improved two-phase SPH model was used to simulate the water entry of cavity body. The cavity body impacts the water surface and the cavity body is closed by the flooding water. It comes into being open air cavity and water jets. The jet walls protrude and the air cavity is closed. With the increase of the water entry depth, the complex hydrodynamic phenomena can be seen again. The sinking depth shows the law of fluctuation up and down with time.

Numerical Simulation of Long Duration Sloshing Using Smoothed Particle Hydrodynamics

The sloshing phenomenon is one of the events in a liquid carrier vehicle such as airplanes and ships. Sloshing is a dangerous phenomenon because sloshing can effect ship motions that create excessive motion in liquid carrier vehicles. Long duration sloshing is challenging problems to solve using smoothed particle hydrodynamics (SPH). Stable, accurate, and reliable computation time is tried to achieve by many researchers. In this study, long-duration sloshing in the prismatic tank is tried to reproduce using single-phase and two-phase SPH. Firstly, the experiment is carried out using prismatic tank, with three pressure sensors, and a forced oscillation machine. In this study, only roll motion is used to reproduce hydrodynamics pressure with a low filling ratio. The results show SPH could reproduce fairly hydrodynamics pressure with spurious pressure oscillation. Static pressure is well reproduced by SPH.

Single-phase and Two-phase Smoothed Particle Hydrodynamics for Sloshing in the Low Filling Ratio of the Prismatic Tank

The present study is to carry out a numerical sloshing using smoothed particle hydrodynamics (SPH) in the prismatic tank. Sloshing is a violent flow caused by the resonance of fluid in the tank by external oscillation. The prismatic tank was used to resemble a membrane LNG type carrier. The sloshing experiment was carried out using three pressure sensors, a camera high resolution, and four degrees of freedom forced oscillation machine. In this study, a filling ratio of 25% was used to reproduce sloshing in a low filling ratio. Only roll motion is used in the numerical simulation. Roll motion is directly imposing from the experiment displacement, and a comparison of hydrostatic and dynamic pressure was made to validate the SPH result. The time duration of the sloshing is the same as the experiment. Single-phase and multiphase SPH are conducted to reproduce sloshing in the prismatic tank. Sloshing was done both for the 2D and 3D domain. It shows that SPH has a good agreement with analytical and experimental results. The dynamic pressure is similar to an experiment through a spurious pressure oscillation exist. The dynamics pressure results show fairly for short time simulation and slightly decrease after that. The free surface deformation tendency is similar to experiment.

A smoothed particle hydrodynamics study on effect of coarse aggregate on self-compacting concrete flows

Coarse aggregates increase inhomogeneity and alter rheological properties of self-compacting concrete. In this work, the effect of coarse aggregates on self-compacting concrete is studied by considering its pipe flow. Self-compacting concrete is modelled as suspension of coarse aggregates in cement mortar and a two-phase Smoothed Particle Hydrodynamics (SPH) model is employed. Cement mortar, a yield-stress fluid, is modelled by fluid SPH particles, while each coarse aggregate is represented by a group of solid SPH particles, which moves as a rigid body. Simulation results show that, at the same volume fractions, the flow rate is higher for larger coarse aggregates, that is up to 24% in the investigated cases. Both effective yield stress and effective plastic viscosity of the concretes increase with the coarse aggregate content. Effective yield stress is smaller for bigger coarse aggregates. The reduction in effective yield stress is a consequence of bigger averaged gap between larger coarse aggregates through which the cement mortar flows.

Dynamic hydraulic jump and retrograde sedimentation in an open channel induced by sediment supply: experimental study and SPH simulation

Mountainous torrents often carry large amounts of loose materials into the rivers, thus causing strong sediment transport. Experimentally it was found for the first time that when the intensive sediment motion occurs downstream over a gentle slope, the siltation of the riverbed is induced and the sediment particles can move upstream rapidly in the form of a retrograde sand wave, resulting in a higher water level along the river. To further study the complex mechanisms of this problem, a sediment mass model in the framework of the Smoothed Particle Hydrodynamics (SPH) method was presented to simulate the riverbed evolution, sediment particle motion, and the generation and development of dynamic hydraulic jump under the condition of sufficient sediment supply over a steep slope with varying angles. Because the sediment is not a continuous medium, the marker particle tracking approach was proposed to represent a piece of sediment with a marked sediment particle. The two-phase SPH model realizes the interaction between the sediment and fluid by moving the bed boundary particles up and down, so it can reasonably treat the fluid-sediment interfaces with high CPU efficiency. The critical triggering condition of sediment motion, the propagation of the hydraulic jump and the initial siltation position were all systematically studied. The experimental and numerical results revealed the extra disastrous sediment effect in a mountainous flood. The findings will be useful references to the disaster prevention and mitigation in mountainous rivers.

Experimental Validation of Single- and Two-Phase Smoothed Particle Hydrodynamics on Sloshing in a Prismatic Tank

This study aimed to validate the single-phase and two-phase smoothed particle hydrodynamics (SPH) on sloshing in a tank. There have been many studies on sloshing in tanks based on meshless particle methods, but few researchers have used a large number of particles because there is a limitation on the total number of particles when using only CPUs. Additionally, few studies have investigated the influence of air phase on tank sloshing based on two-phase SPH. In this study, a dedicated sloshing experiment was conducted at the National Research Institute of Fishing Engineering using a prismatic tank with a four-degrees-of-freedom forced oscillation machine. Three pressure gauges were used to measure local pressure near the corners of the tank. The sloshing experiment was repeated for two different filling ratios, amplitudes, and frequencies of external oscillation. Next, a GPU-accelerated three-dimensional SPH simulation of sloshing was performed using the same conditions as the experiment with a large number of particles. Lastly, two-dimensional sloshing simulations based on single-phase and two-phase SPH were carried out to determine the importance of the air phase in terms of tank sloshing. Based on systematic comparisons of the single-phase SPH, two-phase SPH, and experimental results, this paper presents a detailed discussion of the role of air-phase in terms of sloshing. The currently achievable accuracy when using SPH is demonstrated together with a few sensitivity analyses of SPH parameters.

Modified two-phase dilatancy SPH model for saturated sand column collapse simulations

The high mobility of landslides generates a serious risk of death and property damage. In this study, we develop a two-phase smoothed particle hydrodynamics (SPH) model based on mixture theory to investigate high mobility landslide mechanisms by simulating the process of saturated sand column collapse for different solid volume fractions and permeabilities. The dilatancy coefficient of volume fraction dependence and the Drucker-Prager criterion are introduced into an elastic-perfectly plastic model to describe the solid phase mechanic behavior, and the fluid phase is described as a slightly compressible Newtonian fluid. We present the deposition profile shape and apparent slope evolution trends of collapse examples for different initial solid volumes and permeability changes. We then analyze the effective stress, pore pressure, and velocity during the collapse process of extremely low permeability sand columns to explain the mechanism behind collapse evolution trends. We conclude that shear contraction behavior improves the mobility of the solid-fluid mixture by increasing the pore pressure and decreasing the effective stress, and vice versa. During the shear contraction process of column collapse, the lower permeability, slower seepage rate of the fluid phase, and lower pore pressure diffusion rate result in stronger mobility, but the larger drag force coefficient retards sand column collapse. Numerical simulation results show that the proposed model corrects some limitations of existing three-dimensional SPH models and can be applied to research the motion mechanism of solid-fluid mixtures such as landslides and debris flows.

A coupled fluid-solid SPH approach to modelling flow through deformable porous media

In this paper, a computational framework based on the mesh-free smoothed particle hydrodynamics (SPH) method is developed to study the coupled behaviour of fluid and solid in a deformable porous medium. The mathematical framework developed herein is derived from the Biot's two-phase mixture theory in which the solid is modelled as an elasto-plastic material and the pore-fluid as an incompressible fluid. The key feature of the proposed numerical framework is that both solid and fluid phases are solved simultaneously in two different Lagrangian discretisations (or two different sets of Lagrangian particles) using their own governing equations that are linked through several laws of physics. The capability of the SPH method to model large deformation of the solid materials enables the framework to account for the permeability change due to the dilatant shear behaviour of the solid phase. To obtain a stable and accurate SPH solution for the pore-fluid, an incompressible SPH (ISPH) approach is adapted to correctly simulate the pore-pressure distribution of the fluid phase inside the porous medium. The proposed coupled SPH framework is firstly validated against analytical and solutions obtained using finite element method (FEM) for a submerged soil medium subjected to a gravitational load and a seepage flow through an elastic embankment, respectively. Then, it is employed for the simulation of flows through rockfill dams and an embankment failure induced by seepage flows. Simulation results predicted by SPH show very good agreements with analytical, FEM and experimental results. This suggests that the proposed two-phase SPH framework is a promising approach for future studies of coupled problems that involve complex water free-surface/seepage flows and large deformation of soils which are difficult to be modelled using traditional FEM-based coupled two-phase flow models.

Two-phase smooth particle hydrodynamics modeling of air-water interface in aerated flows

The large deformations associated with air and water interactions are critical factors that affect the hydrodynamic characteristics of hydraulic structures. As a type of Lagrange meshless particle method, smoothed particle hydrodynamics (SPH) has been shown to have many advantages when modeling the interface flow and tracing the free surface because the particles inherit the velocity, mass, and density properties. Significant theoretical and numerical studies have been performed recently in this area. In the present study, a two-phase SPH framework was developed based on these previous studies and we explored its capacity to capture the main features of large density ratio aerated flows. The cohesive pressure was included only in the momentum equation of the air phase for additional amendments to ensure the stability and accuracy of the two-phase SPH model. Three case studies were performed to test the performance of the two-phase SPH model. A convergence study demonstrated the need to balance the CPU time consumption and the real-time requirements. A dam-break simulation based on pressure variation in the air pocket showed the superior analytical performance of the two-phase model compared with the single-phase model. The results of a hydraulic jump simulation were compared with the theoretical results in order to understand the collision between the solid and liquid using the SPH method more clearly. Thus, the consistency between the simulation and the theoretical and experimental results demonstrated the feasibility and stability of the two-phase SPH framework.

Two-phase SPH simulation of fluid–structure interactions

In this paper, a two-phase Smoothed Particle Hydrodynamics (SPH) method is used to simulate the fluid–structure interactions with violent deformation of the free surface. An improved solid boundary treatment is proposed based on the accurate pressure interpolations of the inner fluid particles. The model performance is validated by sloshing in a water tank and dam break flow impact on a vertical wall. In the practical model applications, a two-dimensional wedge entry into the static water is studied, for which the flow fields of water and air phases are computed simultaneously. It has been found that both the water flow around the wedge cavity and the air flow inside are reasonably predicted. Also the two-phase model has been found to accurately provide the flow features throughout the entire entry process, while the single-phase model can only predict the flows before the closure of the cavity due to the lack of air modeling. Besides, a laboratory experiment on the wedge entry has also been carried out for the validation purposes.

Smoothed Particle Hydrodynamics Simulation of Water-Soil Mixture Flows

AbstractA two-phase smoothed particle hydrodynamics (SPH) mixture model to simulate water-soil interactions is presented. In this model, each phase of the mixture satisfies its own conservation equations of mass and momentum. The water is considered as a Newtonian fluid and the soil is modeled as an elastic-perfectly plastic material. Drucker-Prager criterion is employed to test the yielding of the soil and an associated flow rule is adopted to describe the soil behavior after yielding. Interactions between water and soil are modeled by the viscous drag force according to Darcy’s law. With this mixture model, it is possible to investigate the temporal and spatial evolutions of the volume fractions of both phases. This study first examines the proposed SPH mixture model for two single-phase flows, i.e., water dam break and sand column collapse, respectively. The drag force model is also tested using the problem of flow in porous media. Then its application to the problem of soil excavation by high-velocity...

Two-phase SPH modelling of waves caused by dam break over a movable bed

This paper describes the application of the Smoothed Particle Hydrodynamics (SPH) method for modeling two dimensional waves caused by dam break over a movable bed in two dimensions. The two phase SPH method is developed to solve the Navier-Stokes equations. Both fluid and sediment phases are described by particles as weakly compressible fluids and the incompressibility is achieved by the equation of state. The sediment phase is modeled as a non-Newtonian fluid using three alternative approaches of artificial viscosity and Bingham Model. In this paper, the new formulations for two-phase flows are proposed. The numerical results obtained from the developed SPH model show acceptable accuracy with comparison to experimental data.

Two-phase SPH modelling of advective diffusion processes

This paper deals with a two-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) technique for the evaluation of the concentration field of pollutants in water. A SPH model is formulated to solve the fickian diffusion equation applied to pollutants with the same density as the water. A lagrangian SPH formalism of the advective diffusion equation is also developed for pollutant-water, taking into account the effects of molecular diffusion and natural advection induced by differences between the fluid densities. These equations are coupled with the fluid mechanics equations. Attention is paid to the numerical aspects involved in the solution procedure and to the optimization of the model parameters. Environmental engineering problems concerning diffusion and natural advection phenomena occur in the presence of a pollutant in still water. Numerical tests referring to a strip and a bubble of contaminant in a water tank with different initial concentration laws have been carried out. The results obtained by the proposed SPH models are compared with other available SPH formulations, showing an overall better agreement with standard analytical solutions in terms of spatial evolution of the concentration values. Capabilities and limits of the proposed SPH models to simulate advective diffusion phenomena for a wide range of density ratios are discussed.

Mass transfer in eccentric binaries: the new oil-on-water smoothed particle hydrodynamics technique

To measure the onset of mass transfer in eccentric binaries, we have developed a two-phase smoothed particle hydrodynamics (SPH) technique. Mass transfer is important in the evolution of close binaries, and a key issue is to determine the separation at which mass transfer begins. The circular case is well understood and can be treated through the use of the Roche formalism. To treat the eccentric case, we use a newly developed two-phase system. The body of the donor star is made up from high-mass water particles, whilst the atmosphere is modelled with low-mass oil particles. Both sets of particles take part fully in SPH interactions. To test the technique, we model circular mass-transfer binaries containing a 0.6 M-circle dot donor star and a 1 M-circle dot white dwarf; such binaries are thought to form cataclysmic variable ( CV) systems. We find that we can reproduce a reasonable CV mass-transfer rate, and that our extended atmosphere gives a separation that is too large by approximately 16 per cent, although its pressure scale height is considerably exaggerated. We use the technique to measure the semimajor axis required for the onset of mass transfer in binaries with a mass ratio of q = 0.6 and a range of eccentricities. Comparing to the value obtained by considering the instantaneous Roche lobe at pericentre, we find that the radius of the star required for mass transfer to begin decreases systematically with increasing eccentricity.