Simulation Of Free Surface Flows Research Articles

Simulations of free-surface flows with an embedded object by a coupling partitioned approach

This article describes numerical investigations of the flow and wave patterns under stationary or moving submerged objects in a viscous fluid. To incorporate the effects of the free motion objects as well as the free surface, the modified height function scheme is implemented to accurately capture the configurations of free surfaces. For dealing with complex submerged objects in the fluid, a hybrid Cartesian/immersed boundary method is adopted to allow imposition of the solid boundary conditions with a linear interpolation approach. The considered physical model is developed for incompressible, unsteady free-surface flows to satisfy the condition of volume conservation based on the staggered finite-difference spatial discretization. Possible free-surface configurations are described by a high-order flux corrected transport model to maintain the sharp interface and in the mean time to eliminate the surface numerical oscillations. Finally several examples are provided to assess the performance of the developed numerical model. Four numerical validated examples are used to respectively demonstrate the proposed schemes. They are (1) the flow past a circular cylinder, (2) in-line oscillating circular cylinder in a fluid, (3) liquid sloshing in a partially filled rectangular tank and (4) the oscillatory sloshing tank over a shaking table to test the total volume preservation. In addition, two more numerical experiments are carried out to simulate (5) the free-surface flows with the embedded solid body subject to stationary horizontal cylinder and (6) free-surface simulations induced by an oscillating moving object. Both tested cases show encouraging results as well by the present algorithm.

An embedded level set method for sharp-interface multiphase simulations of Diesel injectors

We propose a comprehensive approach for treating complex wall boundaries in two-phase, free-surface flow simulations on a Cartesian adaptive grid. The external gas–liquid interface is handled by the well-known combined level-set volume-of-fluid (CLSVOF) method. The new element is the coupling with the wall boundary representation using a second level-set function. The no-slip boundary condition at the walls is enforced by properly populating the ghost cells of a narrow band inside the solid body, using a simple and numerically robust treatment of the contact line. In this framework, merging and separation of multiple solid bodies are easily accommodated. Verification tests with grid convergence analysis are presented for a stationary/oscillating body in single-phase flow and for a drop on an inclined plane. Two examples demonstrate the suitability of the proposed approach to study liquid injection. The first is a validation study with data from a scaled-up Diesel injector, to demonstrate how the seamless calculation of internal flow and jet primary atomization can be accomplished. The second is a demonstration of transient atomization response to a measured three-dimensional needle displacement of the injector.

A new adaptive Cartesian-grid CIP method for computation of violent free-surface flows

A new adaptive Cartesian-grid for the CIP (constrained interpolation profile) method is proposed and applied to two-dimensional numerical simulations of violent free-surface flows. The CCUP (CIP combined and unified procedure) method is employed and combined with this adaptive Cartesian-grid for robust and efficient computation. This adaptive grid is capable of tracking regions where flows vary violently, and a much finer grid is then concentrated automatically on these regions to adapt to the violent changing of the flow. Unlike the abacus-like Soroban grid which is an adaptive meshless grid with complicated algorithms and inefficiency of evaluation of frequently computed spatial derivatives, the present approach not only simplifies computational algorithm but also enhances efficiency of frequently-computed spatial derivatives. It is also different from most of the remeshing schemes that no additional CPU-time for the value-mapping from the old grid to the new grid is taken in this adaptive grid system provided that the advection velocity is interpolated, since the value-mapping process is accomplished simultaneously within the advection process. To validate the accuracy and efficiency of this newly-proposed CFD model, several two-dimensional benchmark problems are performed, and the results are compared with experimental measurements and other published numerical results. Numerical simulations show that the proposed numerical model is robust, accurate, and efficient for strongly nonlinear free-surface flows.

Hybrid boundary condition combined with data assimilation for simulations of free surface flows using lattice Boltzmann method

In this paper, we combine the single-phase lattice Boltzmann method (LBM) including the hybrid boundary condition with the assimilation of experimental data into a simulation. This combination improves the accuracy of numerical simulations of violent free surface flows performed using the LBM. An unknown wall effect parameter used in the hybrid boundary condition is determined through iterative calculations to minimize the objective function that measures the discrepancy between the simulation and measurement. The present method is applied to a dam failure problem involving a very large deformation of a free surface. We confirm that the method proposed in this study can optimally incorporate the hybrid boundary condition into the LBM without ad hoc specification of the wall effect parameter.

Numerical study on free surface flow of liquid metal lithium for IFMIF

The IFMIF presents an intense neutron source to develop fusion reactor materials. The free surface flow of a liquid metal Li is planned as a target irradiated by two deuteron beams to generate intense neutrons and it is thus important to obtain information on the surface wave characteristic for the safety and the efficiency of system in the IFMIF. We have been studying on surface wave characteristics numerically using computational fluid dynamics code in order to establish the mechanism of the formation and the development of the free surface wave of the Li jet. This paper reports results of the Li free surface flow simulation using large eddy simulation and volume of fluid as the turbulence model and the interface tracking method, respectively, including the inside of a two-staged contraction nozzle. In our simulation, two cases of velocities of 9 and 15m/s at the nozzle exit were conducted as the flow condition from the nozzle exit to 20mm downstream. It is found that the surface wave transits to the three-dimensional wave mode induced by both longitudinal and transverse vortices at the position of 15mm downstream in the case of the velocity of 15m/s.

Free-surface flow simulations for discharge-based operation of hydraulic structure gates

We combine non-hydrostatic flow simulations of the free surface with a discharge model based on elementary gate flow equations for decision support in the operation of hydraulic structure gates. A water level-based gate control used in most of today's general practice does not take into account the fact that gate operation scenarios producing similar total discharged volumes and similar water levels may have different local flow characteristics. Accurate and timely prediction of local flow conditions around hydraulic gates is important for several aspects of structure management: ecology, scour, flow-induced gate vibrations and waterway navigation. The modelling approach is described and tested for a multi-gate sluice structure regulating discharge from a river to the sea. The number of opened gates is varied and the discharge is stabilized with automated control by varying gate openings. The free-surface model was validated for discharge showing a correlation coefficient of 0.994 compared to experimental data. Additionally, we show the analysis of computational fluid dynamics (CFD) results for evaluating bed stability and gate vibrations.

Modelling and simulation of the sea-landing of aerial vehicles using the Particle Finite Element Method

In this paper the Particle Finite Element Method (PFEM) is applied to the simulation of the sea-landing of an unmanned aerial vehicle (UAV). The problem of interest consists in modelling the impact of the vehicle against the water surface, analyzing the main kinematic and dynamic quantities (such as loads exerted upon the capsule at the moment of the impact). The PFEM, a methodology well-suited for free-surface flow simulation is used for modelling the water while a rigid body model is chosen for the vehicle. The vehicle under consideration is characterized by low weight. This leads to difficulties in modelling the fluid–structure interaction using standard Dirichlet–Neumann coupling. We apply a modified partitioned strategy introducing the interface Laplacian into the pressure Poisson's equation for obtaining a convergent FSI solution. The paper concludes with an industrial example of a vehicle sea-landing modelled using PFEM.

Simulation of free-surface flow using a boundless grid

Physically based fluid simulation in recent years has been successful for small-scale fluids such as liquid in a cubic cavity. However, for boundless free-surface flow of large scale and irregular area, there is a critical trade-off between simulation efficiency and accuracy because of the restriction of the traditional regular computational grids. This paper introduces boundless computational grids based on hierarchical runlength encoding to simulate large-scale free-surface flow. We first modeled the free-surface flow with a lattice Boltzmann method, and calculated the surface curvature in the update process. We then introduced an effective method with which to calculate the surface curvature according to the surface tension so that the surface detail was enhanced, and obtained the curvature of each surface effectively as it was extracted. Furthermore, we dynamically compressed and indexed the computational cells with the improved hierarchical run-length encoding algorithm, so that the grid expands dynamically according to the fluid flow and the computational resources used were proportional to the volume of the fluid. Finally fluids in different situations were simulated realistically. The proposed method makes the best of the computational resources to perform the simulation with high resolution, and dynamically allocates resources so that the fluid can expand in random directions without boundaries, which is suited to the simulation of large-scale visual scenes.

A diffuse interface method for complex three-dimensional free surface flows

In this article the weakly compressible two-phase diffuse interface method (DIM) for the simulation of complex two-dimensional non-hydrostatic free surface flows proposed by Dumbser in [24] is extended to three-dimensional unstructured tetrahedral meshes. As in the 2D case, a reduced version of the Baer–Nunziato model for compressible multiphase flows is used. The physical model is closed by the Tait equation of state for water and can be implemented easily into existing compressible codes based on high resolution shock capturing finite volume schemes. Since the proposed model is fully three-dimensional, it includes the fluid accelerations in gravity direction and hence does not assume a hydrostatic pressure distribution, like the classical shallow water equations. Furthermore, the 3D two-phase model can naturally deal also with breaking waves. To solve the system of conservation laws of mass and momentum coupled with the non-conservative evolution equation of the fluid volume fraction, a high order path-conservative one-step WENO finite volume scheme is applied, together with a new generalized Osher-type Riemann solver at the element interfaces. The accurate Riemann solver in combination with a high order finite volume approach leads to a simple but sharp resolution of the free surface.A thorough comparison of experimental reference data with the computational results obtained for a large set of three-dimensional test cases shows the suitability of the present approach for the accurate simulation of complex three-dimensional free surface flows. The use of a compressible flow model allows the method to simulate both, low speed and high speed free surface flow problems, which makes the approach applicable to a very wide class of environmental and industrial free surface flow problems.

SPH simulations of three-dimensional non-Newtonian free surface flows

In this paper, the smoothed particle hydrodynamics (SPH) method is extended to deal with three-dimensional (3D) non-Newtonian flows with complex free surfaces, in which the viscosity is modeled using the Cross model. In order to alleviate the so-called tensile instability which leads to particle clustering and unphysical fracture in fluid stretching, an artificial stress term is particularly incorporated into the momentum equation. For convenience in implementation of wall boundary condition in 3D, an enhanced treatment of solid boundaries is proposed to improve the computational performance. Parallelization is also developed to ensure affordable computational time of simulations involving millions of particles. The proposed SPH algorithm is validated by solving the Hagen–Poiseuille flow and comparing the SPH results with the available analytical solutions. To demonstrate the ability of the numerical method in simulating 3D non-Newtonian flows with free surfaces, three challenging engineering applications, including the impacting droplet, molding injection of a thin plate mold and a Z-shaped mold, and jet buckling, are investigated. It is found that the shear-thinning behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and fairly accurate and agrees well with the available data.

Numerical simulation of sloshing with large deforming free surface by MPS-LES method

Moving particle semi-implicit (MPS) method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation (LES) by coupling with a sub-particle-scale (SPS) turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is “neighbor particle”. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no “neighbor particles” in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.

Numerical simulation of unsteady free surface flow and dynamic performance for a Pelton turbine

Different from the reaction turbines, the hydraulic performance of the Pelton turbine is dynamic due to the unsteady free surface flow in the rotating buckets in time and space. This paper aims to present the results of investigations conducted on the free surface flow in a Pelton turbine rotating buckets. The unsteady numerical simulations were performed with the CFX code by using the Realizable k-ε turbulence model coupling the two-phase flow volume of fluid method. The unsteady free surface flow patterns and torque varying with the bucket rotating were analysed. The predicted relative performance at five operating conditions was compared with the field test results. The study was also conducted the interactions between the bucket rear and the water jet.

Adaptive simulation of free surface flows with discrete least squares meshless (DLSM) method using a posteriori error estimator

PurposeThe purpose of this paper is to propose an adaptive refinement strategy based on a posteriori error estimate for the efficient simulation of free surface flows using discrete least squares meshless (DLSM) method.Design/methodology/approachA pressure projection method is employed to discretize the governing equations of mass and momentum conservation in a Lagrangian form. The semi‐discretized equations are then discretized in space using the DLSM method, in which the sum of squared residual of the governing equations and their boundary conditions are minimized with respect to the unknown nodal parameters.FindingsSince the position of the free surface is of great significant in free surface problems, a posteriori error estimator which automatically associates higher error to the nodes near the free surface is proposed and used along with a node moving refinement strategy to simulate the free surface problems more efficiently. To test the ability and efficiency of the proposed adaptive simulation method, two test problems, namely dam break and evolution of a water bubble, are solved and the results are presented and compared to those of analytical and experimental results.Originality/valueError estimate and adaptive refinement have been mostly used in confined and steady‐state flow. Here in this paper, a new attempt has been made to use these concepts in moving boundary problem.

Patterns of gravity induced aggregate migration during casting of fluid concretes

In this paper, aggregate migration patterns during fluid concrete castings are studied through experiments, dimensionless approach and numerical modeling. The experimental results obtained on two beams show that gravity induced migration is primarily affecting the coarsest aggregates resulting in a decrease of coarse aggregates volume fraction with the horizontal distance from the pouring point and in a puzzling vertical multi-layer structure. The origin of this multi layer structure is discussed and analyzed with the help of numerical simulations of free surface flow. Our results suggest that it finds its origin in the non Newtonian nature of fresh concrete and that increasing casting rate shall decrease the magnitude of gravity induced particle migration.

TOTAL VOLUME CONSERVATION IN NUMERICAL SIMULATION OF LIQUID SLOSHING PHENOMENA IN PARTIALLY FILLED CONTAINERS

A computational model is developed for incompressible, 2-dimensional, unsteady free surface flows to study the conditions of total volume conservation. Free surface tracking methods used in the numerical simulation of unsteady free surface flows may introduce sources or sinks resulting in changes in total fluid volume in the computational domain. The model is based on finite volume discretization of the Navier-Stokes equations coupling momentum and mass conservation. Free surface position is tracked using VOF method. Possible free surface cell configurations and a solution procedure for continuity are described. Liquid sloshing in a partially filled rectangular containers are simulated. Numerical solutions preserving total volume are presented. Computed free surface profiles are verified by experimental. The Navier-Stokes equations are assumed to hold in the liquid domain and have been solved numerically in developed two-dimensional grids, while the dynamical effects in the ideal gas are disregarded. Also all of the vortexes generated in the flow have been modelled and analyzed numerically. Comparisons of the computed results with exact solutions showed that the method is capable of achieving high accuracy and efficiency with minimal computational effort.DOI: http://dx.doi.org/10.5755/j01.mech.18.4.2326

A practical numerical framework for free surface flows based on CLSVOF method, multi-moment methods and density-scaled CSF model: Numerical simulations of droplet splashing

We propose a practical numerical framework for free surface flows with surface tension force. The numerical framework consists of the CLSVOF (coupled level set and volume-of-fluid) method, the THINC/WLIC (tangent of hyperbola for interface capturing/weighted line interface calculation) scheme, multi-moment methods (CIP-CSL and VSIAM3) and the density-scaled CSF (continuum surface force) model. We also propose an efficient implementation algorithms of the density-scaled CSF model and a curvature interpolation technique, based on the level set method. The framework is validated through three benchmark problems (equilibrium drop, Rayleigh–Taylor instability and single bubble rising) and comparisons with an experiment of droplet splashing. The numerical framework can well capture free surface flows with complex interface geometries like droplet splashing. The proposed surface force algorithms, especially the level set based curvature interpolation technique, play a key role in numerical simulations of free surface flows with complex interface geometries.

The dynamics of liquid drops and their interaction with solids of varying wettabilities

Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation free-surface flows is confirmed by a comparison with previous numerical studies for the large amplitude oscillations of free liquid drops. Our code's ability to produce high resolution benchmark calculations for dynamic wetting flows is then demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the process which go beyond the resolution available to experimental analysis. Strong interfacial effects which are observed at the microfluidic scale are then harnessed by designing surfaces of varying wettability that allow new methods of flow control to be developed.

On enhanced non-linear free surface flow simulations with a hybrid LBM–VOF model

In this paper, we present extensions, extensive validations and applications of our previously published hybrid volume-of-fluid-based (VOF) model for the simulation of free-surface flow problems. For the solution of the flow field, the lattice Boltzmann method is used, where the free surface is represented by a VOF approach. The advection equation for the VOF fill level is discretized with a finite volume method, on the basis of a 3D Piecewise Linear Interface Reconstruction (PLIC) algorithm. The model is validated for several standard free surface benchmarks, such as breaking dam scenarios and a free falling jet. Finally, the hybrid algorithm is applied to the simulation of a wave breaking by overturning during shoaling, which is considered to be a demanding test case, especially for VOF solvers. In this case, the flow field is initialized early in the shoaling process with a solitary wave solution from inviscid, irrotational potential flow. The wave breaking process is then simulated with the 3D transient and turbulent LBM–VOF solver. All validation and benchmark tests confirm the accuracy of the proposed hybrid model.

GPU를 이용한 효율적인 비압축성 자유표면유동 해석

This paper presents incompressible Navier-Stokes solution algorithm for 2D Free-surface flow problems on the Cartesian mesh, which was implemented to run on Graphics Processing Units(GPU). The INS solver utilizes the variable arrangement on the Cartesian mesh, Finite Volume discretization along Constrained Interpolation Profile-Conservative Semi-Lagrangian(CIP-CSL). Solution procedure of incompressible Navier-Stokes equations for free-surface flow takes considerable amount of computation time and memory space even in modern multi-core computing architecture based on Central Processing Units(CPUs). By the recent development of computer architecture technology, Graphics Processing Unit(GPU)`s scientific computing performance outperforms that of CPU`s. This paper focus on the utilization of GPU`s high performance computing capability, and presents an efficient solution algorithm for free surface flow simulation. The performance of the GPU implementations with double precision accuracy is compared to that of the CPU code using an representative free-surface flow problem, namely. dam-break problem.

Dynamic particle refinement in SPH: application to free surface flow and non-cohesive soil simulations

In this paper, we present a dynamic refinement algorithm for the smoothed particle Hydrodynamics (SPH) method. An SPH particle is refined by replacing it with smaller daughter particles, which positions are calculated by using a square pattern centered at the position of the refined particle. We determine both the optimal separation and the smoothing distance of the new particles such that the error produced by the refinement in the gradient of the kernel is small and possible numerical instabilities are reduced. We implemented the dynamic refinement procedure into two different models: one for free surface flows, and one for post-failure flow of non-cohesive soil. The results obtained for the test problems indicate that using the dynamic refinement procedure provides a good trade-off between the accuracy and the cost of the simulations.