Numerical simulation of 3D sloshing flow in partially filled LNG tank using a coupled level-set and volume-of-fluid method

doi:10.1016/j.oceaneng.2015.04.083

Ocean Engineering

Volume 104, 1 August 2015, Pages 10-30

https://doi.org/10.1016/j.oceaneng.2015.04.083 Get rights and content

Highlights

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The 3D sloshing flow is modeled by a coupled Level-Set and Volume-of-Fluid (CLSVOF) method.
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The predicted impact pressures are in good agreement with the experimental data.
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The CLSVOF method can capture the violent sloshing flow patterns.
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The CLSVOF method can preserve good local and stable mass conservation.

Abstract

The motion induced 3D sloshing flow in partially filled LNG tank was investigated using a new coupled Level-Set and Volume-of-Fluid (CLSVOF) method incorporated into Finite-Analytic Navier–Stokes (FANS) method. In addition to accurately simulating the sloshing pattern inside LNG tank, impact pressures acting upon tank wall were also predicted by the CLSVOF method. Furthermore, the predicted impact pressures were compared with the corresponding experimental data and another numerical data by the pure level set method with global mass conservation scheme. The comparisons showed the CLSVOF method is capable of predicting the accurate sloshing induced impact and capturing the violent sloshing flow including wave breaking, jet formation, gas entrapping and liquid-gas interactions. The CLSVOF method also demonstrated the prominent feature in local and stable mass conservation.

Introduction

As the demand for natural gas increases, liquefied natural gas (LNG) carriers with supersize cargo capacity are becoming the trend in the world fleet of LNG carriers. Most of the current LNG carriers have adopted the membrane-type LNG cargo tank design. Since the supersize LNG carriers operate under a wide range of filling conditions, they are prone to varying degrees of violent sloshing inside the tanks depending on the sea condition. Sloshing flow can produce localized high impact loads, which may lead to severe structural damage on tank walls and ceiling. Hence, it is essential to investigate sloshing phenomena for the design of membrane-type tank structure and for the operation safety, especially under partially filled conditions. For the analysis of sloshing, model test (Faltinsen et al., 2000, Lee et al., 2005, Lee et al., 2006) has been known as the most reliable method in predicting the maximum impact loads. However, uncertainty exists when the measured impact loads from model test are scaled up to the prototype, due to the scale effects associated with some unmatched parameters such as fluid viscosity, density ratio between liquid and ullage gas, ullage pressure and wall elasticity.

Numerical methods are alternative tools in the analysis of sloshing problems inside LNG tanks. Any appropriate numerical method must be able to handle arbitrary interface behavior. The Marker and Cell (MAC) method, the Volume-of-Fluid (VOF) method, and the Level-Set (LS) method have been successfully applied to capture the profile of the interface in LNG sloshing flow. Arai et al. (2002) used the MAC method to compute sloshing impact pressure in simulations. Nam and Kim (2006) used the smoothed particle hydrodynamics (SPH), which is developed from the MAC scheme, to solve the two-dimensional sloshing flows. Kim, 2001, Kim, 2004 used the SOLA-SURF program to simulate the sloshing problem in rectangular and prismatic tanks. Loots et al. (2004) presented an improved Volume of Fluid (iVOF) method to numerically produce the dynamics of sloshing in LNG tanks, with several improvements in the treatment of spikes for the pressure signals. Wemmenhove et al. (2005) extended iVOF method to incorporate two-phase flow and improved the method to simulate the effect of gas bubbles of different sizes. Yu et al. (2007) performed the Level-Set Reynolds-Averaged Navier–Stokes (RANS) method for the simulation of liquid sloshing in 2D and 3D LNG tanks.

For LNG sloshing flow problem, there are two major requirements that must be fulfilled. The first is to preserve the mass conservation. Since sloshing flow develops inside an enclosed tank, the mass conservation of liquid fluid (LNG) is the fundamental task for simulation and it also directly affects the predicted impact pressure on the wall. The other requirement is to accurately capture the violent sloshing flow pattern on the basis of mass conservation. The sloshing flow is a complicated and violent flow, especially when the exciting frequency is close to the natural frequency of the liquid fluid. Part of the liquid–air interface may break up into discontinuous droplets and small air bubbles might be trapped in the liquid fluid. Each of the interface capturing methods has its own advantages and disadvantages. Although the MAC method can achieve high accuracy, it requires colossal computer storage and computational time to track all the markers. The VOF method has its unique capability to keep the mass conservation, but it lacks accuracy for the calculations of the surface normal and curvature of the interface due to the VOF functions behaving as step functions. The LS method is celebrated for its capability in capturing the sharp and smooth interface, but it is not able to preserve mass conservation because of the numerical dissipation across the interface. However, a coupled method can take advantage of the strengths of the two coupled methods, and is superior to either single method. It is natural to use the coupled Level-Set and Volume-of-Fluid (CLSVOF) method for the LNG sloshing flow simulation. In this method, the interface is reconstructed from the VOF method to preserve the mass conservation and the geometric properties are evaluated by the LS method.

Since the initial implementation of the CLSVOF method by Sussman and Puckett (2000) in the Cartesian coordinate system, several improvements have been made to extend the method to curvilinear coordinates for simulation of violent free surface flow around complex geometries. Jang et al. (2007) generalized the volume-of-fluid formulation of the CLSVOF method to curvilinear coordinates by carrying out interface reconstruction and propagation in the computational domain. The level-set re-distance procedure for the LS function in CLSVOF method was also extended by Wang et al. (2009) based on the reconstructed surface in the computational domain. More recently, Zhao and Chen (2014) developed a new inter-grid mass conservation technique for an overset grid system including embedding, overlapping and matching grids. The new technique includes VOF estimation scheme on overset interior boundary and mass conservation scheme across non-matching overset grid blocks. The CLSVOF method for overset gird system has been verified by several benchmark test cases with excellent local mass conservation and accurate surface simulations.

In the present study, the new CLSVOF method for overset grid system of Zhao and Chen (2014) is employed as the interface-capturing method and incorporated into Finite-Analytical Navier–Stokes (FANS) method (Chen et al., 1990, Chen and Yu, 2009) for time-domain simulation of sloshing in a three-dimensional membrane-type LNG tank. An effective volume-correction scheme is designed for the CLSVOF method, to compensate for the mass change and to maintain a divergence-free velocity filed. The sloshing impact loads on membrane-type LNG tank wall are predicted by the present CLSVOF method, and are compared with the numerical result obtained by the pure level set method and the experimental data.

Section snippets

Governing equations

The LS function, specified as ϕ, is a smooth function and is initialized to the signed distance from the interface (Osher and Sethian, 1988). The value is zero on an interface, negative in air, and positive in liquid. The VOF function, defined as C, represents the volume fraction of liquid phase in a computational cell (Hirt and Nichols, 1981). Its value is between zero and one in those cells cut by interface. The value is either zero or one if the cell does not contain interface. Moreover,

Numerical methods

In the present study, Eq. (1) and Eq. (2) are rewritten into the transformed domain $ξ^{i} = (ξ, η, ζ)$ as following, $\frac{\partial ϕ}{\partial t} + U \frac{\partial ϕ}{\partial ξ} + V \frac{\partial ϕ}{\partial η} + W \frac{\partial ϕ}{\partial ζ} = 0$ $\frac{\partial (J C)}{\partial t} + (J U) \frac{\partial C}{\partial ξ} + (J V) \frac{\partial C}{\partial η} + (J W) \frac{\partial C}{\partial ζ} = 0$ where $U^{i} = (U, V, W)$ are the contravariant velocity components in the transformed domain; J is the Jacobian of transformation from the physical domain to the transformed domain and J represents the physical volume for each computational cell.

The present study has distinct numerical schemes for advection equations of the LS function

Experimental and numerical setups

Fig. 1 shows the schematic of the tank geometry: the dimension of the tank in full scale is 37.9 m×43.72 m×26.75 m (tank breadth×tank length×tank height). More precisely, the lower and upper chamfer angles ( $γ_{l}, γ_{u}$ ) are equal to 135°; the lower chamfer height $h_{l}$ is 3.77 m; and the upper chamfer height $h_{u}$ is 8.63 m. The filling level $H %$ is specified in terms of $d / h$ .

The experiment with a 1/70 scale model of full scale tank was carried out by Lee et al. (2006). The dimension of the 1/70 scale model is

Results and discussion

All of the study cases are normally performed for 20 periods. Due to the three-dimensional instability, there occur the drastically different impact pressures among the sensor locations and their mirror image locations. In order to provide a complete understanding of the three-dimensional sloshing flow, the number of the sensors is increased to 48 in numerical simulations. These 48 sensors in Fig. 4 located not only at the original 17 sensor locations in Fig. 2, but also at original sensors׳

Summary and conclusions

In the present study, the CLSVOF method in conjunction with the Finite-Analytical Navier–Stokes (FANS) flow solver has been implemented for the simulation of violent 3D sloshing flows induced by the transverse and longitudinal motions of LNG tank. The predicted impact pressures by the CLSVOF are in good agreement with the corresponding experimental data. For low filling levels, the sloshing flow is prone to violent free surface motions with high impact pressures upon the vertical side walls.

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Numerical simulation of 3D sloshing flow in partially filled LNG tank using a coupled level-set and volume-of-fluid method

Highlights

Abstract

Introduction

Section snippets

Governing equations

Numerical methods

Experimental and numerical setups

Results and discussion

Summary and conclusions

J. Comput. Phys.

J. Comput. Fluid.

J. Comput. Phys.

J. Comput. Phys.

Appl. Ocean Res.

J. Comput. Phys.

J. Comput. Phys.

Int. J. Multiph. Flow.

A technique for stable numerical computation of hydrodynamic impact pressure in sloshing simulation

J. Soc. Nav. Archit. Jpn.

Solutions of Reynolds-averaged Navier–Stokes equations for three-dimensional incompressible flow

J. Comput. Phys.

CFD simulation of compressible two-phase sloshing flow in a LNG tank

Ocean. Syst. Eng.

Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth

J. Fluid Mech.