A two-phase flow model coupling with volume of fluid and immersed boundary methods for free surface and moving structure problems

A numerical model based on the two-phase flow model for incompressible viscous fluid with a complex free surface has been developed in this study. The two-step projection method is employed to solve the Navier–Stokes equations in the numerical solutions, and finite difference method on a staggered grid is used throughout the computation. The two-order accurate volume of fluid (VOF) method is used to track the distorted and broken free surfaces. The two-phase model is first validated by simulating the dam break over a dry bed, in which the numerical results and experimental data agree well. Then 2-D fluid sloshing in a horizontally excited rectangular tank at different excitation frequencies is simulated using this two-phase model. The results of this study show that the two-phase flow model with VOF method is a potential tool for the simulation of nonlinear fluid sloshing. These studies demonstrate the capability of the two-phase model to simulate free surface flow problems with considering air movement effects.

In this paper, the lattice Boltzmann method-large eddy simulation (LBM-LES) model was combined with the volume of fluid (VOF) method and used to simulate vortex flow in a typical pump intake. The strain rate tensor in the LES model is locally calculated utilizing nonequilibrium moments based on Chapman–Enskog expansion, and the bounce-back scheme is used for nonslip condition on the solid wall and VOF method for the free surface. The evolution of all kinds of cells on the free surface is based on the mass exchange in the VOF method, i.e., lattice Boltzmann-single phase (LB-SP) free surface model. The introduction of the external force terms is established through adding corresponding expressions on the right of the lattice Boltzmann equation (LBE), and by modifying the velocity. The predicted vortex flow patterns (core location and strength of the vortex) and velocity correlate with the experiments undertaken with the physical model. A comparison of the results demonstrates the feasibility and stability of the model and the numerical method in predicting vortex flows inside pump intakes. The model developed and presented in this paper provides a new analysis method of vortex flow patterns in pump intake from a mesoscopic perspective, enriches the relevant technologies, and makes corresponding contributions to further engineering applications.

A two-phase flow model has been developed to study three-dimensional breaking waves over complex topography, including the wave pre-breaking, overturning and post-breaking processes. The large-eddy simulation approach has been adopted in this study, where the model is based on the filtered Navier–Stokes equations with the Smagorinsky sub-grid model being used for the unresolved scales of turbulence. The governing equations have been discretized using the finite volume method, with the PISO algorithm being employed for the pressure–velocity coupling. The air–water interface has been captured using a volume of fluid method and the partial cell treatment has been implemented to deal with complex topography in the Cartesian grid. The model is first validated against available analytical solutions and experimental data for solitary wave propagation over constant water depth and three-dimensional breaking waves over a plane slope, respectively. Furthermore, the model is used to study three-dimensional overturning waves over three different bed topographies, with three-dimensional wave profiles and surface velocities being presented and discussed. The overturning jet, air entrainment and splash-up during wave breaking have been captured by the two-phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems over complex topography.

When cylindrical tanks installed in the ground, such as oil tanks and liquid storage tanks, receive strong seismic waves, including the long-period component, motion of the free liquid surface inside the tank called sloshing may occur. If high-amplitude sloshing occurs and the waves collide with the tank roof, it may lead to accidents such as damage to the tank roof or outflow of internal liquid. Therefore, it is important to predict the wave height of sloshing generated by an earthquake input. Sloshing is vibration of the free liquid surface, and when the sloshing wave height is small, it can be approximated with a linear vibration model. In that case, the velocity-response-spectrum method using velocity potential can estimate the sloshing wave height under an earthquake input. However, when the sloshing wave height increases and the sloshing becomes nonlinear, it is necessary to evaluate the wave height using other methods such as numerical analysis. Taking into consideration that design earthquake levels tend to increase and the use of seismic isolation mechanisms has continued to spread in recent years, it is possible that the long-period components of an earthquake input which act on cylindrical tanks will also increase. Therefore, although it is thought that the evaluation of nonlinear sloshing wave height is important, there are few examples which quantitatively evaluate the wave height of nonlinear sloshing. In this study, as a simple evaluation technique of a nonlinear sloshing wave height, the applicability of the correction coefficient proposed by Shimada et al. was examined based on the flow analysis which used Volume of Fluid (VOF) method. Moreover, it was studied that the VOF method can be used to evaluate nonlinear sloshing wave height and sloshing wave crest impact pressure acting on the fixed roof of a tank. Shaking table tests will continue to be carried out in order to verify the applicability of the simple evaluation technique of nonlinear sloshing wave height. Results from flow analysis code will also be validated against these test results.

This paper aims to evaluate the effects of the opening width of a dam site on the evolution of partial dam-break waves over a fixed dry bed. The volume of fluid (VOF) method was used to scrutinize the propagation of the dam-break free surface. The model was validated using experimental data provided in the literature. At the same time, a sensitivity analysis was conducted on the size of the mesh cells and the turbulence model. However, the large eddy simulation (LES) method showed the highest accuracy among all the models. The results affirmed the crucial role of the opening width of the dam site in the flow characteristics. In this direction, diminishing the opening width results in a reduction of the wave-front travel distance, free surface gradient within the reservoir, outflow discharge values, damping the outflow hydrographs and decreasing the Froude number values at the dam site. Conversely, this leads to an increase in the air bubbles entrained within the wave and results in energy dissipation across the downstream channel.

An improved implicit direct-forcing immersed boundary method (DF-IBM) is presented for simulating incompressible flows around complex rigid structures undergoing arbitrary motion. The current approach harnesses the pressure implicit with splitting of operators algorithm to handle the fluid–solid system's dual constraints in a segregated manner. As a result, the divergence-free condition is preserved throughout the Eulerian domain, and the no-slip velocity boundary condition is exactly enforced on the immersed boundary. A new pressure Poisson equation (PPE) is derived, incorporating the boundary force where the no-slip condition is already met, enabling the use of fast iterative PPE solvers without modifications. The improvement involves integrating Lagrangian weight methods having better reciprocity over the IBM-related linear operators with the implicit formulation. An additional force initialization scheme is introduced to further boost the algorithm's performance. The method's accuracy, efficiency, and capability are verified through various stationary and moving immersed boundary cases. The results are validated against experimental and numerical data from the literature. The proposed improvements seamlessly integrate into existing incompressible fluid solvers with minimal adjustments to the original system equations, highlighting their ease of implementation.

Challenges and opportunities in modelling of proton exchange membrane fuel cells (PEMFC)

In order to examine the feasibility of direct simulation of bubbly flows, the applicability of the VOF (volume of fluid) method to the analyses of a single rising bubble was examined in this study. Calculated bubble shapes and terminal velocities under wide ranges of Eotvos number and Morton number were compared with the experimental data summarized by Grace et al. Except for the cases when bubble shapes are spherical-cap and skirted, the VOF method could predict them well by assigning only eight cells to the bubble diameter. Hence, it was confirmed that some modification of this method will enable us to simulate bubbly flows directly under a wide-range of flow conditions. Moreover, the relation between a bubble shape and velocity distribution was examined within the ranges in which the VOF method is valid. It was found that the secondary vortex appearing in wobbling bubbles induces the velocity component normal to the bubble interface, and this velocity is one of the causes of the wobbling shape of the bubble.

A three-dimensional non-hydrostatic coupled model for free surface – Subsurface variable – Density flows

Cavitating flows in fluid machineries always present complicated phase morphologies including a wide range of interface length scales. In the present work, an Eulerian–Lagrangian cavitation model is proposed for simulating the unsteady cavitating flow and investigating the multiscale cavitating flow features in a convergent-divergent test section. Most importantly, a two-way transition algorithm is newly developed mainly based on the shape of resolved cavities and the relative size of microscale bubbles compared to the cells, for taking the transition between microscale discrete bubbles and macroscale vapor cavities into consideration. The transient flow field of the two-phase system is described by the filtered Navier–Stokes equation and the sub-grid scale model. The volume of fluid (VOF) method and a discrete bubble model (DBM) are combined for simulating resolvable water-vapor interfaces and unresolvable discrete bubbles, respectively. Applying the proposed multiscale modeling framework, the dissipated bubbles caused by the collapse of shedding cavities that are unable to be represented by the VOF method are well predicted. The results show that the VOF-DBM model is less sensitive to the mesh resolution compared to the VOF method and it is found the dissipated bubbles are transporting around the vortex core region. Detailed bubble dynamics including DBM to VOF and VOF to DBM transitions and the interaction between macroscale cavities and microscale bubbles are well presented, indicating that the proposed VOF-DBM model is a promising approach to reveal the multiscale cavitation characteristics within limited computing resources.

A new approach to aircraft ditching analysis by coupling free surface lattice Boltzmann and immersed boundary method incorporating surface tension effects

Ocean conditions can cause the steam generator in nuclear-powered ship to heave, sway and tilt with the ship, causing the free liquid surface in the steam generator to fluctuate and causing additional fluctuations of pressure and water level. In this paper, the CFD method is used to numerically study the fluctuation characteristics of the free liquid surface during the sloshing process of the secondary side liquid in the steam generator under the action of external force. The free liquid surface is tracked by using the VOF (Volume of Fluid Method) method, and additional inertial force is added through the UDF (User Define Function) to simulate rolling conditions. First, the simulation results of the numerical model in this study are compared with the experimental results, and the results are in good agreement, which verifies the reliability of the numerical model to analyze the liquid sloshing problem. Then, through numerical simulation, the fluctuation characteristics of the free liquid surface and the change of the water level and the pressure in the steam generator under different excitation periods are obtained. The results show that the liquid sloshing process in the steam generator exhibits periodic changes, and due to the complexity of the structure of the steam generator, the instability and nonlinearity of the liquid sloshing are enhanced.

본 연구에서는 규칙파동장에 있어서 인장계류된 원형부유체의 파랑응답해석에 2차원 Navier-Stokes solver에 기초한 새로운 수치파동수조모델을 제안하였다. 본 수치파동수조모델에서는 이동구조물과 유체와의 상호작용을 해석하기 위하여 직각좌표계에서 임의형상의 불투과경계를 갖는 구조물과 유체와의 연성해석이 가능한 IBM(Immersed Boundary Method)과 자유수면 추적을 위한 VOF(Volume of Fluid)법을 결합하였다. 부유체운동에 대한 수치결과를 기존의 FAVOR(Fractional Area Volume Obstacle Representation)법에 의한 계산결과 및 수리실험과 비교하였다. 게다가, 수치모델의 보다 자세한 검증을 위하여 원형부유체의 동요 및 자유수면변동에 관한 수리모형을 추가로 실시하였고, 제안된 수치모델의 범용성과 타당성을 검증하기 위하여 직사각형부유체에 대한 수치 및 수리실험도 병행하였다. 이로부터 추정된 수치계산결과는 실험결과를 잘 재현하고 있는 것으로 판단되었다. In the present study, we proposed a new numerical wave tank model to analyze the vertical tension-leg circular floating bodies, using a 2-D Navier-Stokes solver. An IBM(Immersed Boundary Method) capable of handling interactions between waves and moving structures with complex geometry on a standard regular Cartesian grid system is coupled to the VOF(Volume of Fluid) method for tracking the free surface. Present numerical results for the motions of the floating body were compared with existing experimental data as well as numerical results based on FAVOR(Fractional Area Volume Obstacle Representation) algorithm. For detailed examinations of the present model, the additional hydraulic experiments for floating motions and free surface transformations were conducted. Further, the versatility of the proposed numerical model was verified via the numerical and physical experiments for the general rectangular floating bodies. Numerical results were compared with experiments and good agreement was archived.

Non-convex analytical and geometrical tools for volume truncation, initialization and conservation enforcement in VOF methods

Two phase flow regime identification using infrared sensor and volume of fluids method