Finite Volume Particle Method Research Articles

Eulerian vs Lagrangian Method for Low Computational Resources: A Comparison of 2D Dam Break Case

It is well known that computational fluid dynamics has been challenging for low-computational-resourced students and researchers. In this study, we performed a 2D dam break simulation by Eulerian approach-finite volume method of OpenFOAM and Lagrangian approach-finite volume particle method (FVP) in a low-specification personal computer. We compared those approaches’ results qualitatively and quantitatively against experimental data and measured their simulation time for 6 different grid sizes. We compared the visualization results and their pressure and velocity using ParaView and VisIt. At the same time, a quantitative comparison was made by determining the waterfront position each time using the Tracker video analyzer. It was found that OpenFOAM resulted in better visualization results, lower error by 28 - 68 %, and more reasonable pressure and velocity profiles. It can also simulate smaller grid sizes and 10 to 200 times faster than FVP, but it can’t produce the air-liquid interface’s sharpness as good as FVP. Thus, to simulate cases where interfaces are not important, Eulerian-based OpenFOAM is best suited to perform in a low-specification computer. HIGHLIGHTS One of the main challenge in CFD is that it needs a huge computational resources to get optimum results. For students or researchers with limited computational resources, which approaches can they used? Two approaches in CFD: Eulerian and Lagrangian methods-represented by OpenFOAM and Finite Volume Particle Method (FVP)-were performed in a personal laptop to simulate 2D dam break problem and their results are compared with the experimental data Qualitative and quantitative comparison shows that OpenFOAM is well suited for low computational resources users. However, FVP method has an advantage in terms of capturing the interface of the two phases involved in simulation. Thus, for phase-change phenomena where interface is important, it is strongly recommended to use FVP-though one might need a more sophisticated resources than a personal laptop GRAPHICAL ABSTRACT

Experimental and numerical investigations into molten-pool sloshing motion for severe accident analysis of sodium-cooled fast reactors: A review

Safety issues are particularly crucial for sodium-cooled fast reactors (SFRs). Data obtained from SFR safety analyses over recent years have shown that a specific type of sloshing motion probably occurs in the molten pool during core disruptive accidents (CDAs) of SFRs due to local neutronic power excursion or pressure developments, thereby significantly influencing recriticality. Recognizing the importance of improving the evaluation of CDAs of SFRs, extensive knowledge about this phenomenon has been garnered through experimental studies of their thermal-hydraulic mechanism and characteristics. Based on these studies, simulations using various numerical approaches, such as SIMMER code, the finite volume particle method, and the smoothed particle hydrodynamic method, have attempted to reproduce the sloshing motion under various experimental conditions to verify their reasonability and applicability, thereby promoting the development of SFR safety analysis. To provide useful references for future SFR safety analyses and assessments, we have systematically reviewed and summarized these experimental and numerical investigations into the thermal-hydraulic aspect of molten-pool sloshing motion. In addition, to enhance deeper and more comprehensive research into sloshing motion, we have also discussed future prospects. Knowledge gained from experimental and numerical investigations into molten-pool sloshing motion is valuable not only for improving and verifying SFR safety analysis codes but also for providing reference data for studies of sloshing motion in other fields of engineering.

A 3D particle-based simulation of heat and mass transfer behavior in the EAGLE ID1 in-pile test

The ID1 test was the final target test of the EAGLE experimental framework program. It was used to verify that during a core disruptive accident, the molten fuel could be discharged via wall failure of an inner duct in FAIDUS, a design concept for the sodium-cooled fast reactor. The ID1 results revealed that the wall failure behavior owed to the large heat flow from the surrounding fuel/steel mixture. The present study numerically investigated the heat transfer mechanisms in the test using the finite volume particle method in the three-dimensional domain. The thermal hydraulic behaviors during wall failure were reproduced reasonably. The present three-dimensional simulation mitigated inherent defects of our previous two-dimensional calculation and clarified that the solid fuel and liquid steel close to the outer surface of the duct can expose the duct to high thermal loads, resulting in the wall failure.

Application of finite volume particle method for axisymmetric modeling of droplet formation in dripping and Rayleigh regimes

An axisymmetric model has been developed in the finite volume particle method (FVPM). FVPM is a conservative, consistent, meshless particle method that incorporates properties of both smoothed particle hydrodynamics (SPH) and the mesh-based finite volume method (FVM). The surface tension effect amplifies capillary instability which is the main mechanism in dripping and jet disintegration. The simulations are performed in 2D cylindrical coordinates by only considering the liquid flow (one phase). The model is validated for free liquid droplet evolved from cylindrical state, dripping from a capillary tube, Rayleigh instability of capillary liquid cylinder columns, and Rayleigh breakup of viscous jets. The FVPM-predicted pressure and oscillating period are in good agreement with theoretical solution for a free droplet. The FVPM-computed dripping length shows good consistency with provided experimental data in literature. The predicted growth rate of capillary instability is in good agreement with analytical solutions for flows with different orders of Ohnesorge numbers. The numerical breakup length of jet with Weber numbers between 2.5 and 40 has been determined with good accuracy based on analytical experimental solution.

Coupling of the meshless finite volume particle method and the finite element method for fluid–structure interaction with thin elastic structures

A novel fluid–structure interaction (FSI) scheme is developed in this article, with the meshless finite volume particle method (FVPM) for fluid dynamics and the finite element (FE) solver FEBio for solid mechanics. Like smoothed particle hydrodynamics (SPH), FVPM is based on compactly supported particle kernels, but kernels are interpreted as a partitioning of volume, leading to a scheme with properties of both SPH and classical finite volume methods. Particle methods are advantageous for fluid modelling in FSI of highly deformable structures, as the particles can conform to the dynamic geometry of the fluid–structure interface. In FVPM, in particular, particles are rigorously truncated by boundaries, and the novel FSI scheme incorporates a sharp interface between the fluid and solid. A new method is described which avoids the possibility of unphysical communication between fluid particles separated by a thin structure. The method proposed here ensures that particles interact with the correct neighbour particles and boundaries, regardless of the particle overlap with the thin structure, allowing for particle size that can be chosen independently of structure thickness. The new method is validated for a hydrostatic water column on an elastic plate, a dam-break with elastic gate, a dam-break with a downstream elastic wall, and a 2-D model of a heart valve leaflet. In the latter two cases, the structure thickness is less than the particle diameter by a factor of up to 16. The results agree well with experimental data from the literature for fluid velocity field and solid deformation. Where quantitative data is available, the numerical results converge with decreasing particle size.

Numerical simulations of Pelton turbine flow to predict large head variation influence

In the framework of the new feed-in-tariff system in Switzerland for Small Hydropower Plants (SHP), the aim of the SmallFLEX project, led by HES-SO Valais and performed in collaboration with EPFL, WSL, EAWAG, PVE, and FMV, is to show how SHP can provide winter peak energy and ancillary services, whilst remaining eco-compatible. The pilot and demonstrator site selected is the new small hydropower plant of Gletsch-Oberwald (KWGO) owned by FMV and commissioned end of 2017. This run-of-river power plant is equipped with two six-jet Pelton turbine units featuring a maximum power of 7 MW each.The addition of flexibility can be reached by using existing volumes of the power plant: the settling basin, the forebay chamber as well as part of the headrace tunnel. By consequence, the turbine head will undergo variations. To ensure that these variations will not cause any damages to the Pelton runner, the influence of the available head is investigated by numerical simulations. The simulations are carried out using two different software. OpenFOAM, which is based on a Finite Volume Method (FVM), is used for computing the flow inside the distributor until the jet. GPU-SPHEROS, which is based on Arbitrary Lagrangian-Eulerian (ALE) Finite Volume Particle Method (FVPM) is utilized to compute the interaction between the jet and Pelton buckets.Mixing the two aforementioned approaches, i.e. mesh-based FVM and particle-based FVPM, the overall torque T of the present six-jet Pelton runner can be reconstructed for different rated heads and discharges. The predicted torque fluctuations can then be considered for an estimation of the structural fatigue damage of the runner.

Application of particle-based numerical analysis to the practical design of Pelton turbine

For the design optimization of the Pelton turbine, it is highly demanded to investigate the flow inside the turbine casing, which includes the water jet from the nozzles, the interaction between the jet and rotating runner, and the flow ejected from the bucket outlet, in various operating ranges. The behavior of the flow, however, is very complicated due to its unsteadiness and free surface. Further, the experimental observation in the model test is challenging because of the high time resolution requirement and the obstruction by the splashing water inside the turbine housing. In this regard, the numerical analysis is considered as a powerful method to approach the flow behavior in the Pelton turbine. Conventionally, the grid-based numerical analysis is applied to the calculation of the flow for its practical design. However, with the gird-based methods, a huge amount of fine elements is required to capture the unsteady behavior of the water free surface and the tiny splashing water particles. Increasing the number of elements directly results in higher computational costs, which makes it difficult to consider the splashing water in the process of practical design. From this point of view, the GPU-accelerated finite volume particle method is applied to the investigation of the flow in this research. It is firstly confirmed that the particle-based numerical result has a good agreement with the experimental result by the comparison of the turbine characteristics. Furthermore, several evaluations of the flow based on the analysis for the practical design are introduced in the paper.

Numerical simulation of heat transfer behavior in EAGLE ID1 in-pile test using finite volume particle method

The EAGLE ID1 test was performed by the Japan Atomic Energy Agency to demonstrate the effectiveness of fuel discharge from a fuel subassembly with an inner duct structure. The experimental results suggested that the early duct wall failure observed in the test was initiated by high heat flux from the molten pool and the post-test analyses showed that the high heat flux may be enhanced effectively by molten steel. In this study, the mechanisms of heat transfer were analyzed using a fully Lagrangian approach based on the finite volume particle method. A series of physical behaviors in the pool were simulated to investigate the effect of the behaviors on molten pool-to-duct wall heat transfer in ID1 test. The present 2D particle-based simulation demonstrated that a large thermal load on the duct wall can be caused by direct contact of the liquid fuel releasing nuclear heat and high-temperature liquid steel.

Application of a particle-grid hybrid method in multiphase flow calculation

ABSTRACT In this paper, a new particle-grid hybrid method is used for numerical simulations of the gas-liquid two phase flow. In this method, the main area of the fluid is calculated via the constrained interpolated profile/multi-moment method (CIP/MM FVM), and the interface of the two phases is calculated by the finite volume particle method (FVP). In the numerical calculation, the particles are distributed in the dense one of the two phases, and only near the interface. Through calculations of the dam break, single bubble rise and bubble coalescence, the reliability and accuracy of the method in multiphase flow simulation have been verified.

Particle transport velocity correction for the finite volume particle method for multi-resolution particle distributions and exact geometric boundaries

The finite volume particle method (FVPM) is a meshless computational fluid dynamics (CFD) method, where the fluid domain is represented by a set of overlapping particles, and boundaries are defined as exact geometries. Particle-based CFD methods, such as smoothed particle hydrodynamics (SPH) and FVPM, are susceptible to non-uniform particle distributions, which result in errors. Particle regularisation techniques, based on displacement or particle transport velocity, improve particle distributions. Here, improvements are made to the previous particle regularisation methods in SPH and FVPM. The method presented here takes advantage of the arbitrary Lagrangian-Eulerian nature of FVPM and applies a small correction to the particle transport velocity. It incorporates a novel symmetric formulation to maintain specified spatially varying resolution. Difficulties associated with the FVPM definition of the geometric boundaries are overcome, in that the correction method automatically adjusts to varying geometry segment size, without requiring fictitious boundary particles, as in SPH. The method is evaluated in a static multi-resolution test, cylinder in flow, and dambreak flow. Results show that the method yields improved particle distribution with few voids, with improved wall pressure results in the dambreak. The method maintains multi-resolution and adaptive particle distributions and is insensitive to the resolution of boundary geometry.

GPU-accelerated numerical analysis of jet interference in a six-jet Pelton turbine using Finite Volume Particle Method

The Pelton turbine is an impulse turbine typically installed for high head hydroelectric power plants. For a site with a rated head H and discharge Q, a higher specific speed turbine results in a more compact generating unit with reduced manufacturing costs but requires a larger number of jets. However, by increasing the number of jets and specific speed, the water jets tend to interfere, creating a significant energy loss. In the present research, the interaction between two adjacent jets in a six-jet Pelton runner is simulated using a GPU-accelerated particle-based in-house solver based on the 3-D Finite Volume Particle Method (FVPM). The numerical simulations are performed at eight operating points ranging fromN/NBEP=0.89 to N/NBEP=1.31,where N is the runner rotational speed, and BEP is the Best Efficiency Point. The torque and efficiency trends, as well as the speed range in which the jets interfere, are well-captured, which provides confidence in the use of the numerical simulations for the design optimization of Pelton turbines. The simulations, in particular, evidence a significant torque and efficiency drop at high rotational speeds, due to jet interference. Furthermore, jet disturbance yields load fluctuations at rotational speeds both lower and higher than the NBEP, which is likely to amplify fatigue damage. Both phenomena are worth considering that in the design process of a Pelton machine.

Application of background pressure with kinematic criterion for free surface extension to suppress non-physical voids in the finite volume particle method

Lagrangian particle methods such as smoothed particle hydrodynamics (SPH) and the finite volume particle method (FVPM) can suffer from non-physical voids in the spatial discretisation, due to the inability of numerical particles to deform as continuum fluid elements can. It is known that the situation can be improved for wall-bounded flows in SPH by adding a uniform background pressure to ensure positive absolute pressure everywhere. In this article, we investigate the application of background pressure in FVPM, and show that numerical voids grow under negative pressure and collapse under positive pressure. To use this technique in free-surface flow, however, the background pressure must be applied as an atmospheric pressure at the free surface. A kinematic criterion for free surface extension (KCFSE) to differentiate physical free surfaces from new numerical voids has been developed, supplementing the inherent capability of FVPM to identify free-surface particles robustly. The novel method enables background pressure to be applied at physical free surfaces and throughout the fluid, but not in non-physical voids, facilitating the suppression of such spurious voids. The KCFSE is validated for a translating square cylinder inside a rectangular numerical domain, with and without a free surface, and liquid in an oscillating rectangular tank.

GPU-accelerated Pelton turbine simulation using finite volume particle method coupled with linear eddy viscosity models

The numerical investigation of the unsteady flow patterns around a Pelton bucket can be helpful to improve the overall turbine efficiency by optimizing the bucket design based on identified loss mechanisms. Since the flow is highly turbulent, modeling the effect of turbulence can bring about improved predictions. In this paper, two RANS-based eddy viscosity models (namely the standard and realizable k-ε) have been implemented as a module in a particle-based in-house solver, GPU-SHPEROS. A scalable wall function based on the log-law has been utilized to model the flow in the near-wall region. The solver has been accelerated on GPUs and is based on the Finite Volume Particle Method (FVPM), which is a locally conservative and consistent particle-based method including many of the attractive features of both particle-based methods (e.g. SPH) and conventional mesh-based methods (e.g. FVM). As a mesh-free method based on the Arbitrary Lagrangian Eulerian (ALE) formulation, FVPM is robust in handling free surface flows and large boundary deformations, such as the ones found in rotating Pelton buckets. The validation of the turbulence models implementation within FVPM is presented for internal and free surface flows. Then, the effectiveness of the turbulence models in the case of rotating Pelton buckets is assessed by comparing the predicted torque time histories to experimental data acquired on a model-scale test rig.

An ALE pairwise-relaxing meshless method for compressible flows

In this paper, we present a pairwise-relaxing meshless (PRM) method for solving the Euler equations of compressible flows within the Arbitrary Lagrangian Eulerian (ALE) framework. Derived from the moving particle semi-implicit (MPS) method and the finite volume particle (FVP) method, the PRM approximates the derivatives from the value defined at the midpoint of each interacting particle pairs through a kernel-based formulation. Pairwise-relaxing constants are introduced to the kernels to provide degree of freedom to enforce the Taylor-series consistency condition while mass, momentum and energy are conserved exactly. An upwind high-order reconstruction scheme via a corrective procedure and variable cut-off radius is also developed for this PRM method. The HLLC approximate Riemann solver is adopted to solve Riemann problem. One and two-dimensional numerical tests are presented to demonstrate the performance of the PRM method.

FVPM simulation of scratching induced by a spherical indenter

This article presents a single particle scratching simulation using the Finite Volume Particle Method (FVPM). FVPM is a variant of the well-known Smooth Particles Hydrodynamics method (SPH) which is locally conservative and consistent, what’s more it features advantages of mesh-free methods for handling moving interfaces and multi-scale interpolation. The test material is represented by overlapping particles and data exchanges occur through the interfaces. The indenter is modeled as a rigid sphere whose path is a straight horizontal line. The resulting surface topography as well as constraints and scratching efforts have been numerically studied. The FVPM simulation code assessed in this article has been found suitable for the scratching simulation based on a comparison with other results from the literature. The presented results suggest the possibility to simulate more complex surface finishing operations. Manufacturing processes based on abrasion material removal, such as the grinding process, will be considered in the future.

A model for surface tension in the meshless finite volume particle method without spurious velocity

A surface tension model has been developed in the finite volume particle method (FVPM). FVPM is a conservative, consistent, meshless particle method that incorporates properties of both smoothed particle hydrodynamics and the mesh-based finite volume method. Surface tension force is applied only on free-surface particles, which are inexpensively and robustly detected using the FVPM definition of interparticle area, analogous to cell face area in the finite volume method. We present a model in which the direction of the pairwise surface tension force is approximated by the common tangent of free-surface particle supports. The new surface tension model is implemented in 2D. The method is validated for formation of an equilibrium viscous drop from square and elliptical initial states, drops on hydrophobic and hydrophilic walls, droplet collision, and impact of a small cylinder on a liquid surface. Results are practically free from parasitic current associated with inaccurate curvature determination in some methods.

Extensions of the meshless finite volume particle method (FVPM) for static and dynamic free-surface flows

The Finite Volume Particle Method (FVPM) is a meshless method that incorporates features of both Smoothed Particle Hydrodynamics and the Finite Volume Method. Here, two new formulations are presented which enhance its performance in simulation of free surface flows. One is a method for determining the velocity of the free surface, making use of a partial Riemann problem to analyse the flow between the particle barycentre and the geometric free surface. The second is a well-balanced formulation for gravity forces that enables hydrostatic equilibrium to be preserved exactly. Results are presented for hydrostatic, 1D impact, dambreak and deep-water standing wave test cases. Computations display convergence and good agreement with experimental data. The new methods recover exact hydrostatic equilibrium, improve robustness and reduce acoustic pressure fluctuations in dambreak flows, and reduce dissipation.

GPU-accelerated 3-D Finite Volume Particle Method

In previous works (Jahanbakhsh et al., CMAME 298 (2016): 80–107, Jahanbakhsh et al., CMAME 317 (2017): 102–127; see [1] and [2]), the authors introduced SPHEROS, a 3-D particle-based solver based on the Finite Volume Particle Method (FVPM) featuring a spherical top-hat kernel. In the present research, the authors present algorithms and optimization procedures that allowed to significantly accelerate computations by taking advantage of the computational power of Graphics Processing Units (GPUs). The new accelerated solver, GPU-SPHEROS, has been developed in CUDA and runs entirely on GPU, are presented. All the parallel algorithms and data structures have been designed specifically for the GPU many-core architecture. A roofline model has been utilized to assess the performance of the kernels and apply appropriate optimization strategies. In particular, the neighbor search algorithm, accounting for almost a third of the overall compute time, features an efficient Space-Filling Curve (SFC) as well as an optimized octree construction procedure. The memory-bound interaction vector computation, accounting for almost two thirds of the overall compute time, features fixed-size memory pre-allocation and an efficient data ordering to reduce memory transactions and cost of dynamic memory operations i.e. allocation and deallocation. As a case study, the numerical simulation results of water jet deviation by the rotating buckets in a Pelton turbine is presented and compared to available experimental data. For that case, a speedup by a factor of almost six times has been achieved on a single NVIDIA® Tesla™ P100-SXM2-16 GB GPU with GP100 Pascal architecture compared to a dual CPU node equipped with two Broadwell Intel® Xeon® E5-2690 v4 CPUs with 28 total physical cores.

Accuracy and stability enhancements in the incompressible finite-volume-particle method for multiphase flow simulations

For the simulation of multiphase flows, an incompressible finite volume particle (IFVP) method is proposed that offers enhanced accuracy and stability. A high-order multiphase Laplacian operator is derived by combining the gradient model and divergence model. To produce enhanced accuracy, neighboring dummy particle is introduced in each dimension of the calculation and used for the discretization of the gradient model. The error-compensating terms produced by introducing these dummy particles assist in the higher-order calculations of the gradient operator. Consequently, accuracy of the Laplacian operator is enhanced consistently by these error-compensating terms. Compared to the single dummy particle introduced for two-dimensional calculations in our previous work (Liu et al., 0000), the proposed high-order scheme is more generalized and can be applied in the calculation of arbitrary dimensions. This enhanced multiphase scheme provides accurate and stable calculations of multiphase flows characterized by high density ratios. An advantage of this scheme is that the separation of two liquids of similar density is easily handled as well. Results of several numerical simulations are given to demonstrate its validity and enhanced performance.

A novel approach to surface tension modelling with the Finite Volume Particle Method

Surface tension plays a key role in many applications such as spraying, diffusion in porous media, birds drinking, etc. But simulation of surface tension is challenging because it involves a moving interface, topology changes, and triple lines where the dynamic contact angle is generally unknown. Surface tension is a macroscopic force resulting from microscopic interactions. Based on recent developments of the Finite Volume Particle Method, we propose a surface tension formulation directly derived from the macroscopic force for a single-phase configuration. Each particle represents a physical volume of fluid, and the free-surface is the union of the free-surfaces for each particle. Motion of these particles will cause a deformation of the free-surface and change its energy. Through analytical computation of these changes, the surface tension force is modelled by a particle–particle interaction that does not involve parameters other than a constant surface tension γ and the equilibrium contact angle at the triple line, θe. After a formal derivation of the force, we use it in various drop applications to validate its behaviour, both qualitatively and quantitatively. We also show that empirical dynamic contact angle models can advantageously be replaced by a physically meaningful surface roughness model. In this case, the roughness parameter has to be empirically evaluated.