Simulation Of Free Surface Research Articles

Three-Dimensional Simulation of Tsunami Run Up Around Conical Island Using Smoothed Particle Hydrodynamics

The large-scale laboratory experiments were performed in a 30 m-wide, 25 m-long, and 60 cm-deep wave basin. Waves were realistically created in the tank by a horizontal wave generator with 60 different paddles each 46 cm-wide and moving independently. These experiments provided run-up observations for validating numerical models and supplemented comparisons with analytical results. Smoothed particle hydrodynamics (SPH) is a popular meshfree, Lagrangian method with attractive features in modelling fluid dynamics. The SPH method is capable of dealing with problems with free surface, deformable boundary, moving interface, wave propagation and solid simulation. A weakly incompressible fluid flow SPH model was employed in this paper to investigate the run-up heights of nearshore tsunamis in the vicinity of a circular island. The predicted numerical results have been verified by comparing to available laboratory measurements. A good agreement has been observed.

Enhancement of heat and mass transfer performance on humidification tower using injection of different carrier gases into water bed

The present study is presented an approach attempting for enhancement of heat and mass transfer between a continuous gas phase and liquid phase in a non-packed humidification towers by injection of different carrier gases such as air, carbon dioxide and helium through water bed. The computational technique utilized was a three-dimensional Navier-Stokes solver in the laminar flow regime with free-surface simulation in Piecewise Linear Interface Construction method to compute density variation on the two-dimensional two-phase flow field and pressure on a water bed. This work studied the influence of the operating conditions such as the water bed temperature and carrier gas type on the overall gas phase heat and mass transfer coefficient. The present study included also determining the overall pressure drop of the carrier gases through water bed, consumed power and humidification efficiency. It has been found that the mass transfer coefficient increases with increasing carrier gas molecular weight. The heat transfer coefficients are more than 5 times for carbon dioxide than air flow and less for helium than air, about 50% flow at water bed temperature 353K. The mass transfer coefficients are more than 2.5 times for helium than air and less for carbon dioxide than air, about 50% at water bed temperature 353K. The obtained maximum humidification efficiency of the helium was about 87%. The pressure drop was about 51.4kPa for helium and 47.2kPa for carbon dioxide at a water bed temperature 353K. The consumed power was about for helium about 45.45W and for carbon dioxide was 41.25W at a water bed temperature 353K. The comparison between the numerical and other experimental results shows a good matching of outlet humidity ratios for air as a carrier gas except that the numerical values were slightly smaller than experimental ones. This may be attributed to the laminar flow computation without including turbulence effects and the two-dimension computational model consideration.

Applicable sloping range and bottom smoothing treatment for σ-based modeling of wave propagation over rapidly varying topography

Accurate modeling of nonlinear wave propagation over mildly or rapidly varying topography is an important topic in costal/ocean engineering. This study examines the applicable sloping ranges and proposes a bottom smoothing treatment for the σ-based modeling framework. An efficient non-hydrostatic σ model is chosen to be validated against a series of experiments with various slopes from 1:20 to 1:∞. The measured and simulated free surface time series are compared and analyzed using both one- and two-dimensional short-time Fourier transform. The reflection rate and high harmonic generation including a recurrence behavior are characterized and discussed. Overall, the excellent agreement reveals the applicability of the σ-based model along with an appropriate 1:0.5 virtual slope to the wave problems with vertical (or extremely steep) bottom topography.

Study of Error Propagation in Free Surface Simulations

Study of Error Propagation in Free Surface Simulations

Second Order Upwind Lagrangian Particle Method for Euler Equations

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. Numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.

Numerical simulation of ductile fracture based on mean field homogenization method: Modeling and implementation

A mean filed homogenization method at large deformation is presented to describe the damage softening effects due to nucleation and growth of voids during ductile fracture. The developed homogenization frame is combined with the Nucleation-And-Growth model and the percolation theory based coalescence model for describing ductile damage evolution. A semi-implicit numerical algorithm is developed to solve the ductile damage model. Based on the model, we have carried out numerical simulations of the spall fracture of a Al 2024-T4 plate and a Ti–6Al alloy plate under impact loads. The simulated free surface velocity profiles show good agreement with experimental measures.

Power particles

This paper introduces a new particle-based approach to incompressible fluid simulation. We depart from previous Lagrangian methods by considering fluid particles no longer purely as material points, but also as volumetric parcels that partition the fluid domain. The fluid motion is described as a time series of well-shaped power diagrams (hence the name power particles ), offering evenly spaced particles and accurate pressure computations. As a result, we circumvent the typical excess damping arising from kernel-based evaluations of internal forces or density without having recourse to auxiliary Eulerian grids. The versatility of our solver is demonstrated by the simulation of multiphase flows and free surfaces.

A New Method to Simulate Free Surface Flows for Viscoelastic Fluid

Free surface flows arise in a variety of engineering applications. To predict the dynamic characteristics of such problems, specific numerical methods are required to accurately capture the shape of free surface. This paper proposed a new method which combined the Arbitrary Lagrangian-Eulerian (ALE) technique with the Finite Volume Method (FVM) to simulate the time-dependent viscoelastic free surface flows. Based on an open source CFD toolbox called OpenFOAM, we designed an ALE-FVM free surface simulation platform. In the meantime, the die-swell flow had been investigated with our proposed platform to make a further analysis of free surface phenomenon. The results validated the correctness and effectiveness of the proposed method for free surface simulation in both Newtonian fluid and viscoelastic fluid.

오픈 소스 라이브러리를 이용한 수치수조 구현 및 적용

In this paper, ship performance prediction solver was developed using open source computational fluid dynamics (CFD) libraries. The mass- and momentum-conservation equations and turbulent model with a wall function for the turbulent closer were considered. The volume fraction transport equation with a high-resolution interface capturing scheme were selected for free-surface simulation. The predicted wave pattern around KRISO container ship (KCS) using developed program showed good agreement against existing experimental data. For the revolution of a propeller in the propulsive test, general grid interface (GGI) library was used. The predicted propulsive performance showed 7 % difference against experimental data. Two-phase mixture model was developed to simulate a cavitation and applied to a propeller. The sheet cavitation on the propeller was predicted well. From results, the potential of the numerical tank developed by open source libraries was verified by applying it to KCS.

On a potential‐velocity formulation of incompressible Navier‐Stokes equations

AbstractComputational fluid dynamics has emerged as an essential investigative tool in nearly every field of technology. Despite a well‐developed mathematical theory and the existence of readily available commercial software codes, computing solutions to the governing equations of fluid motion remains challenging, especially due to the non‐linearity involved. Additionally, in the case of free surface film flows the dynamic boundary condition at the free surface complicates the mathematical treatment notably.Recently, by introduction of an auxiliary potential field, a first integral of the two‐dimensional incompressible Navier‐Stokes equations has been constructed leading to a set of equations, the differential order of which is lower than that of the original equations [1]. A useful application to free surface simulation was found in [2]. Moreover the new formulation is naturally extendible to three dimensions via tensor calculus, involving a non‐unique symmetric tensor potential. The corresponding degrees of freedom can be used in order to achieve a numerically convenient representation. Finally an efficient staggered‐grid finite difference scheme is applied to a Stokes flow problem in a 3D lid‐driven cavity to demonstrate the capabilities of the new approach. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes

This work is related with the implementation of a finite volume method to solve the 2D Shallow Water Equations on Graphic Processing Units (GPU). The strategy is fully oriented to work efficiently with unstructured meshes which are widely used in many fields of Engineering. Due to the design of the GPU cards, structured meshes are better suited to work with than unstructured meshes. In order to overcome this situation, some strategies are proposed and analyzed in terms of computational gain, by means of introducing certain ordering on the unstructured meshes. The necessity of performing the simulations using unstructured instead of structured meshes is also justified by means of some test cases with analytical solution.

Advancements in free surface RANSE simulations for sailing yacht applications

The analysis of yacht hulls performance using RANSE based free surface simulations has become an accepted approach over the last decade. Access to this technology has been eased by the development of user-friendly software and by the increase of computational power. Results are widely accepted as superior to previous non-viscous approaches and have to compete with towing tank results in terms of accuracy. However, many practical applications suffer from a numerical smearing of the free surface interface between air and water which can be described as numerical ventilation. This problem occurs when the intersection between bow and calm water surface forms an acute angle and is further pronounced if the stem is rounded or blunt. It is therefore especially linked to sailing yacht applications. The problem manifests itself as a non-physical suction of the air–water mixture under the yacht hull, causing a significant under-prediction of viscous resistance. While this is the easily observable appearance of the problem, a second issue is its effect on wave resistance. It can be shown that wave damping is significantly increased, causing a prediction of wave resistance which is also too low. The paper provides a review of the Volume-of-Fluid method. It discusses the resultant implications for practical applications. A remedy to circumvent the problem is described and its impact on the accuracy of the result is shown. Simulations on an identical appended hull with and without interface smearing are compared. Effects on free surface visualization and numerical accuracy are shown. The paper finishes with a thorough verification and validation of a fully appended yacht in accordance with ITTC standards.

Influence of fluid properties on bubble formation, detachment, rising and collapse; Investigation using volume of fluid method

Numerical simulations have been carried out to investigate the formation and motion of single bubble in liquids using volume-of-fluid (VOF) method using the software platform of FLUENT 6.3. Transient conservation mass and momentum equations with considering the effects of surface tension and gravitational force were solved by the pressure implicit splitting operator (PISO) algorithm to simulate the behavior of gas-liquid interface movements in the VOF method. The simulation results of bubble formation and characteristics were in reasonable agreement with experimental observations and available literature results. Effects of fluid physical properties, operation conditions such as orifice diameter on bubble behavior, detachment time, bubble formation frequency and bubble diameter were numerically studied. The simulations showed that bubble size and bubble detachment times are linear functions of surface tension and decrease exponentially with the increase in liquid density. In contrast, only a small influence of the fluid viscosity on bubble size and detachment time was observed. Bubble collapse at a free surface simulation with VOF method was also investigated.

Benchmarking of Navier–Stokes codes for free surface simulations by means of a solitary wave

The paper presents a benchmark of four freely available solvers for Navier–Stokes equations: Gerris, OpenFOAM, Thétis and Truchas. These models are selected because they have been reported to deal successfully with oceanographic and coastal engineering applications. The benchmark includes two free surface problems: propagation of a solitary wave and runup of a solitary wave on a plane beach. The fluids are inviscid, which allows a detailed study of energy conservation and comparison of the results with a reference solution given by a boundary integral solver. The Navier–Stokes solvers use the finite volume discretization and free surface capturing techniques based on the volume-of-fluid (VOF) method. In the first benchmark test, we investigate the influence of numerical dissipation and other spurious effects on the energy balance of the wave. In the second problem, we focus on the runup heights and compare them with the reference solution. The beach in the runup problem is represented with a solid body immersed in the Cartesian mesh. The solid boundaries are described with a VOF type approach or a staircase representation, depending on the features of the solver. In addition to the immersed boundary description a couple of body fitted meshes are tested for the runup case.

Weak Formulations with Upwind Shift for Calculation of Free Surface Corrections and Simulation of Steady-State Forming Problems

For many material forming processes steady-state formulations allows reducing numerical simulation time by an order of magnitude with respect to more conventional approaches. In the presented approach, the steady regime is iteratively computed by a free surface algorithm that alternates computations of the metal forming flow over a known geometry and known contact surfaces, with computations of domain corrections to satisfy free and contact surface conditions. Several weak formulations of the second problem equations are investigated to get a robust algorithm suitable for parallel computations with unstructured meshes. Analytical problems show the necessity to introduce an upwind shift within these weak formulations. Contact inequations enforces this necessity by requiring a more dramatic shift. A robust and accurate algorithm is so obtained, which is successfully applied to 3D complex metal forming processes like rolling. In the wire drawing application, computational time is reduced by more than fifteen with respect to the incremental calculation of the steady-state.

Application of a new concept for multi-scale interfacial structures to the dam-break case with an obstacle

New results of a generalized concept developed for the simulation of two-phase flows with multi-scale interfacial structures are presented in this paper. By extending the inhomogeneus Multiple Size Group-model, the concept enables transitions between dispersed and continuous gas morphologies, including the appearance and evanescence of one of these particular gas phases. Adequate interfacial transfer formulations, which are consistent with such an approach, are introduced for interfacial area density and drag. A new drag-formulation considers shear stresses occurring within the free surface area.The application of the concept to a collapsing water column demonstrates the breakup of continuous gas into a polydispersed phase forming different bubble sizes underneath the free surface. Thus, both resolved free surface structures as well as the entrainment of bubbles and their coalescence and breakup underneath the surface can be described in the same time. The simulations have been performed with the CFD-code CFX 14.0 and will be compared with experimental images.The paper will further investigate the possible improvement of such free surface simulations by including sub-grid information about small waves and instabilities at the free surface. A comparison of the results will be used for a discussion of possible new mass transfer models between filtered free surface areas and dispersed bubble size groups as part of the future work.

An improved time-dependent nonlocal electron heat-flux model and its verification by laser-driven Al foil acceleration experiment

In hydrodynamics simulation of laser driven systems, the time-dependent nonlocal electron heat-flux models predict the saturation (flux inhibition) and delocalization of the heat-flux automatically. Therefore it avoids commonly used time and space-independent ad hoc flux limiting. Previously proposed analytical nonlocal heat-flux model of Luciani et al. [Phys. Rev. Lett., 51, p-1664, (1983)] which fits the results of numerical Fokker–Planck calculations is simple and straight forward to implement in a fluid code. The proposed expression, however, is a convolution of Spitzer–Harm heat-flux with a delocalization kernel which depends on classical electron collision mean free path. This is rigorously valid for high temperature non-degenerate plasmas. However, in laser driven systems, the energy transport due to electron thermal conduction is important in regions between the critical density and ablation surface where the plasma is mostly degenerate. We have improved this nonlocal heat-flux model by using a wide-range electron collision frequency model valid from warm-dense matter (degenerate plasmas) to fully ionized plasmas. The effect of this improved nonlocal heat-flux model on the free-surface velocity of laser-accelerated Al foils of thickness 2–10 μm is studied by using a two-dimensional radiation hydrodynamics code. The simulated free surface velocities are compared with our experimental results for laser intensities in the range 4 × 1013–3 × 1014 W/cm2. Preliminary analysis shows that the simulation results obtained with improved nonlocal heat-flux model yields better agreement with our experimental values.

Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions

The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases, but in a simplified way. An experimental validation is given by an example of gravity driven flow of a particle suspension.

Numerical Modelling of the Hydrodynamics and Total Dissolved Gas Downstream of Hells Canyon Dam

A computational fluid dynamics model was developed to predict the flow pattern and total dissolved gas (TDG) distribution downstream of Hells Canyon Dam on the border of Idaho and Oregon, USA. Free surface simulations in the tailrace were carried out to predict spillway jet regimes with and without deflectors. Model results agreed with deflector performance curves obtained in a 1:48 laboratory scale model. The distribution of TDG was predicted with a mixture model that accounts for the two-phase flow in the tailrace and the mass transfer between bubbles and water. Attenuation of the turbulence at the free-surface and the effect of the bubbles on the turbulence was included to capture water attraction towards spillway surface jets, which affects the amount of water exposed to bubbles and downstream TDG dilution. The model takes into account changes in bubble size with dissolution and pressure. Good agreement was obtained between predicted TDG and available measurements in the field.

시스템 식별기법을 활용한 파압과 해수면 모델링

A System Identification method to develop parametric models linking free surface elevation and wave pressure is presented and two models are built allowing for either wave pressure or free surface elevation simulation. Linear, time invariant model structures with static nonlinearities are assumed and solutions are sought in a form of autoregressive model with extra input (ARX). An arbitrary chosen free-surface elevation and wave pressure dataset is used for estimation of the models, which are subsequently verified against datasets with similar pressure gauge depth but different free-surface elevation spectra due to different meteorological conditions. It is shown that freesurface simulation using System Identification methods can perform better than traditional linear transfer function derived from linear wave theory (LTF), while wave pressure simulation quality using presented methods is generally similar to that obtained with corrected LTF. 핵심용어: system identification, wind waves, free surface elevation, sea wave pressure, autoregressive model, ARX model, linear transfer function, wind wave spectrum, free surface records, pressure records, ì‹œìŠ¤í œ 식별법, 풍파, 해수면, í•´ì €íŒŒì••, 자기회기모형, ARX 모형, ì„ í˜•ì „ì†¡í•¨ìˆ˜, 풍파스펙트럼, 해수면 시계열자료, 파압 시계열자료