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In the present study, the mixing fluids flow in the twin and circular mixers is investigated by using an improved robust weakly compressible Smoothed Particle Hydrodynamics method. In order to remove the Smoothed Particle Hydrodynamics complications and according to a predictive corrective scheme, a robust modified algorithm which uses the advanced second order discretization, pressure velocity decoupling, kernel gradient corrections and shifting algorithm is offered. After the verification and validation of the present algorithm for the moving boundary problems, the present algorithm is applied for investigation of the mixing behaviors of the two-blade circular and twin chamber mixers. By investigation of the mixing paths, the proper geometry for the two-blade mixers is proposed and examined. The effects of the rotation direction of the blades, geometry and Reynolds number on the mixing rate are investigated. The results show that the twin chamber mixer can improve the mixing performance over 60% in comparison with the circular chamber mixer while the case with circular chamber and same direction rotation of the blades has the weakest performance among the cases which have been examined.

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In this paper, breakup of liquid jet is simulated using smoothed particle hydrodynamics (SPH) which is a meshless Lagrangian numerical method. For this aim, flow governing equations are discretized based on SPH method. In this paper, SPHysics open source code has been utilized for numerical solutions. Therefore, the mentioned code has been developed by adding the surface tension effects. The proposed method is then validated using dam break with obstacle problem. Finally, simulation of two-dimensional liquid jet flow is carried out and its breakup behavior considering one-phase flow is investigated. Length of liquid breakup in Reyleigh regime is calculated for various flow conditions such as different Reynolds and Weber numbers and the results are validated by an experimental correlation. The whole numerical solutions are accomplished for both Wendland and cubic spline kernel functions and Wendland kernel function gave more accurate results. Effect of fluid viscosity is investigated in the breakup length of the fluid as well. The accomplished modeling presented that smoothed particle hydrodynamics (SPH) is an efficient method for simulation of liquid jet breakup phenomena.

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In this paper, the convection-diffusion process in a two-phase air-water flow is investigated. Two-phase flows of air and water are important and are widely used in the industrial applications. Simulation of such a flow needs a proper understanding of the interface between two phases where these is a change in fluids properties. Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian and meshless method which can simply detect the interface of multiphase flows. Here, we develop the open-source SPHyiscs2D code into two phase and implement the convection-diffusion equation by looking carefully at surface tension forces. To validate, first the still-water problem is investigated to ensure that the hydrostatic pressure at the interface is predicted and then the dam-break problem on an infinite bed is compared with the available experimental data. Results show that the combination of surface tension formulations and an additional artificial force gives a better result. Finally, the convection-diffusion process and the concentration distribution are shown for the air-bubble rising problem for different diffusive coefficients. It will be shown that the SPH method is a useful tool for studying multiphase flows and convection-diffusion processes.

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Dispersion of oil pollutants is one of the important topics of great concern which should be modeled for a wide range of hydrodynamic systems such as seas and oceans. In this paper, the effects of using booms on the oil plume are simulated using the Smoothed Particle Hydrodynamics (SPH) Method. The open-source SPHysics2D code is developed into two phase by adding the effects of surface tension and an added pressure term to the momentum equation. Several problems of plume dynamics are shown, and the performance of the developed code is evaluated. Firstly, the rising pattern of an oil plume with the density ratio of 0.8 is simulated where the results are compared with the analytical solution. Then, the rising pattern of a plume with density ratio of 0.1 is simulated and the time evolutions of the rising velocity and center of mass are shown. The simulation of the cnoidal wave on beaches is conducted and compared with an available experimental result. Finally, the effects of a boom with different angles on the oil plume dispersion are investigated. It will be shown that the SPH method could be an optimized method for the numerical simulation of the complex problems such as water wave dynamics and two-phase flows.

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The investigations of changes in bed surface of sediment due to the fluid flow and tracing sediment motion are complex and attractive for the researchers. In the recent decade, modeling of fluid flow using the Lagrangian methods, e.g. Smoothed Particle Hydrodynamics (SPH), is of interest. In this study, the open-source two dimensional SPHyiscs code is used to model the two phase Newtonian and non-Newtonian flows using the μ(I) visco-plastic model, which is obtained according to particle properties including inertia and friction coefficient. First, and in order to study the visco-plastic model, the one phase code is extended to non-Newtonian and the SPH results are compared with the experimental model of the collapsing granular column, where a harmonic interpolation is used for the viscosity of particles. In this stage, the comparison of the SPH model with the experimental data shows a good agreement. Then, the numerical method is utilized for the simulation of Newtonian dam-break fluid flow over a movable bed. The proposed model treat sediments as a non-Newtonian fluid using μ(I) model, by implementing the harmonic interpolation for the viscosity coupled with the Owen’s relation at the interface. Results show that the proposed model has a capability for simulating two-phase water sediment systems.

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Investigation of multi-physics problems such as flow-structure interaction (FSI) in free surface is very important in mechanical engineering, whereas numerical simulations of such problems have been widely conducted by researchers. The implementations of CFD in engineering applications are most of the time based on the Eulerian description. In this method, one can focus on flows at a fixed spatial point x at time t and any flow variable Φ is expressed as Φ (x, t). This description has been studied for over fifty years and is clearly understood. Most of commercial codes have been developed by using finite difference, finite element and finite volume approaches. Simulating free surface flow with most Eulerian CFD methods is potentially very difficult as explicit treatment of the free surface is required. Moreover, The problems of most Eulerian and mesh-based numerical methods for complex free surface deformations involves difficulties and complexities of various boundaries remeshing as well as moving boundaries and exact determination of free- surface fluid. Another description of study of CFD is the Lagrangian method where one can follow the history of an individual fluid parameter through the time. In the Lagrangian methods, any flow variable is expressed as Φ (x0, t), where the point vector x0 of the particle at the reference time t = 0. Smoothed Particle Hydrodynamics (SPH) is a meshless and fully Lagrangian method which is able to simulate the FSI problems due to its simplicity and capability, as there is no special treatment needed for the free surface. The current problem in hydrodynamic science and fluid engineering is studied as a complex phenomenon in free-surface flow. Smoothed Particle Hydrodynamics (SPH) is a flexible Lagrangian and meshless technique for CFD simulations initially developed by Lucy (1977) and Gingold and Monaghan (1977) to simulate the nonaxisymmetric phenomena in astrophysics. In recent years, the SPH method has been very popular in fluid mechanics, e.g. multiphase flows,3 heat conduction,4 underwater explosions, free-surface flows, etc. In this method, each particle carries an individual mass, position, velocity, internal energy and any other physical quantity. The Lagrangian nature of SPH would lead this method to be well suited to problems with large deformations and distorted free surfaces. Simplicity, robustness and relative accuracy in comparison with other numerical methods are the main advantages of using SPH.10 Moreover, the SPH method can handle fully nonlinear, multiply-connected free-surface problems and extend computations beyond wave breaking, which need complex treatments in other grid-based methods, e.g. Volume of Fluid (VoF).In this approach the computational domain is formed by a set of particles. Each particle represents macroscopic volume of fluid conveying information about the mass, density, pressure, speed, position and the other parameters related to the nature of the flow. However, the computational cost is a disadvantage of SPH because the time step is small because of the explicit integration scheme in a weakly compressible formulation. This method has been successfully applied to a range of free-surface problems which involve breaking and splashing up There is a choice of SPH formulation in the literature mostly expressed in weakly compressible forms where pressure is obtained from the equation of state In this research, SPH is used to investigate the flow-structure interaction in free surface. First, the simulation of dam break problem on a dry and infinite bed is shown and compared with the experimental data. Then, and after implementing the governing equations, the vibration of a beam is studied. Finally, the dam break problem on an elastic gate is shown. Comparison between the SPH results and available numerical and experimental data shows that the SPH method is useful method for simulating the FSI problem.

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The precision and speed of numerical simulations of physical phenomena has led to their increasing use in designing and research applications. These precision and speed are owed to the improvements in numerical methods and significant advancements in computing power of CPUs and GPUs.
Particle-based methods are some of the most recently developed numerical simulation methods. Development of these methods has been long delayed due to the need for a relatively high computational effort.
Particle-based methods can be considered as a subset of Meshless Methods. In nonlinear computational methods, mathematical equations in the problem domain are estimated only by nodes, and contrary to the case about the nodes in FEM and FDM methods, there is no need for these nodes to be connected to each other by a mesh. If the nodes are particles that carry physical properties, such as mass and stiffness, and simulations proceed on the basis of updating trajectory and physical properties of particles, then the method is called a particle-based method. Particle-based methods include molecular dynamics (MD), Discrete Element Method (DEM), Smoothed Particle Hydrodynamics (SPH), and Lattice Boltzmann Method (LBM). The number of studies and computer codes developed based on these methods has grown dramatically over the past two decades.
Among particle-based methods, DEM method is mainly used to model solid objects and fractures and in some cases it has been used to model granular materials like soil. While most of the applications of SPH method include numerical solution of the Navier-Stokes equations in fluid dynamic problems. Despite their differences, both DEM and SPH methods are particle-based methods and so there have been successful attempts to integrate them into a single application.
In current study, a computer code called “QUANTA” is introduced. In this software, the researchers have tried to integrate the SPH method with another particle-based method called Bonded Particle Method (BPM). BPM is based on DEM and was originally developed to model rock and soil mechanics phenomena. The main modification applied to DEM is the ability to consider cohesion among particles, which plays a significant role in simulating the behavior of rocks and soils.
QUANTA is being developed with the goal of providing a tool to simulate two-dimensional solid, fluid, and multi-phased interactive environments for research purposes. In this software, the solid environment is modeled using the BPM algorithm and the fluid environment is modeled using the SPH algorithm by solving Navier-Stokes equations. Depending on the problem at hand, BPM and SPH particles interact with each other by equations based on momentum or pressure. The code is developed using Visual C ++ programming language and has the ability to perform parallel computations with a remarkable speed.
To verify the software, a few simple and frequently used problems in the literature were chosen. A cantilever beam was modeled and loaded to verify BPM part of the software. Poiseuille and shear cavity problems were used to verify the SPH part. In order to verify the interaction of these two algorithms, a solid cylinder was modeled once in a wind tunnel travelling at supersonic speeds and then against the flow of a viscous fluid. According to the results of these numerical modellings, the software can be deemed successful in simulating the sample problems.
While simulation with particle methods requires more computational effort than common methods such as finite element and finite difference, the particle-based and micromechanical nature of these methods and their ability to model large-scale deformations and complex behaviors has, in many cases, made them logical choices for simulation. As the next steps of this study, the authors are developing new equations for interaction and equations of state to improve the software performance.

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The coastal waves caused by landslide in the lake of reservoir dams can threaten the safety of the dam. Therefore, the exact recognition of hydraulic flow due to coastal waves has always been of interest to researchers. So far, extensive laboratory and numerical research has been devoted to it. Also, the phenomenon of landslide in the lake of dams and rivers, and the production and propagation of waves resulting from it, is one of the most important and complex issues in the field of hydraulic engineering. Today, the expansion of numerical relations and the modeling process have somewhat contributed to a rational understanding of these phenomena. In this research, a Lagrangian method is used for solving governing equations. Initially, the hydrodynamic method is defined as an explicit three-step incompressible smoothed particle hydrodynamic. This method, by replacing the fluid with a set of particles, provides an approximate solution to the fluid dynamics equations. In this simulation, there are a series of arbitrary interpolation points that can be assumed to be fluid particles. All variables are calculated by these points and are calculated by an interpolation function. In order to validate the method, the dam break problem on dry bed and the subsurface landslide problem have been used. In the first issue, the correlation coefficient of 0.9998, the mean absolute error of 0.5426 and the efficiency coefficient of the Nash-Sutcliff model 0.974 for the calculated parameters indicate that the model is accurately calibrated, which demonstrates the high capability of this method in simulating free surface fluids and wave-related phenomena. Also, comparing the measured results with the experimental data in the sub-surface landslide simulation showed that the correlation and mean square error correlation coefficients were 0.95 and 0.0071 respectively, which indicates the high accuracy of the model in calculating the water surface profile caused by landslide subsurface. The results showed that at times after 2 seconds, numerical waves tended to release more than its experimental state, with a difference between the ranges of 5 to 10 cm. This is due to the turbulence of the free surface of water causing the flow of complexity. For smaller body weights and deeper depths of submergence, these differences will be lower in scope.
Then three landslide modeling scenarios were designed and implemented. In this study, slopes and non-rigid bodies were considered as a rheological material (pseudoplastic fluid) and entered into modeling as Carreau Yasuda non-Newtonian fluid. The results were reported at 0.3 and 0.6 seconds, and then they were analyzed.
The innovation aspect of this research is that the study of non-rigid slopes during landslide and falling and sliding of non-rigid bodies on them, as well as the production and propagation of waves from it, have not been investigated so far. The purpose of this paper is simulation and review it by an explicit three-step incompressible smoothed particle hydrodynamic. On the other hand, the choice of non-Newtonian Carreau Yasuda fluid to simulate the slope and non-rigid body is another aspect of the innovation of the present study.

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In the present study, solid particle erosion of Ti-6Al-4V alloy under the impact of spherical alumina particles with a diameter of 85 microns was analyzed using experimental studies and smoothed particle hydrodynamics (SPH) modeling. The erosive behavior of this alloy was simulated as impacts on micro-scale and based on Johnson-Cook constitutive equations. This research focuses on the effect of particle velocity and impact angle on erosion rate as the most critical factors. Additionally, the results of this model are validated by empirical results under-considered conditions. At the end of the article, based on the alloy properties, the velocity of particles, and impact angle, a prediction equation was presented on erosion rate in the studied range of velocity and impact angle. This study indicates a power-law equation between the velocity of particles and the erosion rate, where the power is independent of impact angle. Furthermore, in all the velocity and angle ranges, the maximum erosion rate was associated with the angle of 45^o. Therefore, the critical angle in erosion is also independent of the velocity of particles.

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The initial position of particles in Smoothed Particle Hydrodynamics (SPH) method can play an important role in reducing numerical errors and its efficiency. In this research, based on water level variation modeling, and using previous modeling experiences with SPH method, six common particle distributions as: SC square distribution, Triangular distribution, distribution based on WVT algorithm, distribution based on Greedy algorithm, hexagonal distribution and distribution based on Fibonacci algorithm have been investigated. Based on the results of the pressure, velocity, and the free surface level at different times according to the physical model, the average total modeling error for each of the models (the difference between the values obtained from the modeling and the results of the laboratory model) has been presented. According to the obtained results, it was determined that the two hexagonal and Fibonacci particle distributions have the lowest average modeling error (10.2% and 11.1%, respectively). In addition, based on the obtained results, the WVT model has a lower modeling error (about 14%) than the remaining three models, i.e., square, triangular, and Greedy distributions. Therefore, since in this phenomenon, the two initial distributions of hexagonal and Fibonacci particles have less modeling error than other distributions, it is recommended to use these two initial distributions in modeling the water level variation phenomenon using the SPH method.