Rik Wemmenhove

NUMERICAL SIMULATION OF SLOSHING IN LNG TANKS WITH A COMPRESSIBLE TWO-PHASE MODEL

The study of liquid dynamics in LNG tanks is getting more and more important with the actual trend of LNG tankers sailing with partially filled tanks. The effect of sloshing liquid in the tanks on pressure levels at the tank walls and on the overall ship motion indicates the relevance of an accurate simulation of the fluid behaviour. This paper presents the simulation of sloshing LNG by a compressible two-phase model and the validation of the numerical model on model-scale sloshing experiments. The details of the numerical model, an improved Volume Of Fluid (iVOF) method, are presented in the paper. The program has been developed initially to study the sloshing of liquid fuel in spacecraft. The micro-gravity environment requires a very accurate and robust description of the free surface. Later, the numerical model has been used for calculations for different offshore applications, including green water loading. The model has been extended to take two-phase flow effects into account. These effects are particularly important for sloshing in tanks. The complex mixture of the liquid and gas phase around the free surface imposes a challenge to numerical simulation. The two-phase flow effects (air entrapment and entrainment) are strongly affected by both the filling ratio of the tank and the irregular motion of the tank in typical offshore conditions. The velocity field and pressure distribution around the interface of air and LNG, being continuous across the free surface, requires special attention. By using a newly-developed gravity-consistent discretisation, spurious velocities at the free surface are prevented. The equation of state applied in the compressible cells in the flow domain induces the need to keep track on the pressure distribution in both phases, as the gas density is directly coupled to the gas pressure. The numerical model is validated on a 1:10 model-scale sloshing model experiment. The paper shows the results of this validation for different filling ratios and for different types of motion of the sloshing tank.Copyright

Application of a VOF Method to Model Compressible Two-Phase Flow in Sloshing Tanks

The growing transport of LNG in partially filled tanks raises the demand to have accurate methods to predict the fluid behaviour in these sloshing tanks and the effect of the sloshing fluid on the tanker motion. To examine the motion of the sloshing fluid, model experiments have been carried out on a scale of 1:10. Different tank filling ratios and types of motion have been tested to study the sloshing fluid behaviour for various sea states. The model experiments have been carried out to provide extensive validation material for the numerical method ComFLOW . The details of this improved Volume Of Fluid (iVOF) method are presented in the paper. The method resolves the governing equations in both fluids, one of them being compressible. The compressibility of the second phase is especially important for more violent flow conditions, when two-phase phenomena such as air entrapment and air entrainment occur frequently. Particular attention in the numerical method has been paid to the treatment of the flow variables around the interface, especially the density. The fluid is convected by means of a first-or second-order upwind scheme. The behaviour of the sloshing fluid strongly depends upon the regularity of the tank motion and the filling ratio of the tank. Video frames, wave probes and pressure transducers have been used to compare the fluid flow of simulation and experiment. Two-phase effects such as air entrapment are more common for increasing tank filling ratios and for more irregular tank motion. A realistic simulation of these effects is possible by modeling two-phase flow, especially when using a relatively fine grid and applying the less-dissipative second-order upwind scheme. Compared to the earlier paper on the numerical simulation of sloshing in LNG tanks [8], where the numerical method was validated for regular sway motion, more extensive attention is paid to the accuracy of the applied discretisation schemes in space and time. The results of different schemes are now evaluated for both regular and irregular sway and roll motion of LNG tanks.Copyright

CFD SIMULATION OF WAVE RUN-UP ON A SEMI-SUBMERSIBLE AND COMPARISON WITH EXPERIMENT

Use of CFD tools for industrial offshore applications is a common practice nowadays. So is the need for validation of such tools against experimental results. This paper presents one of the CFD tools, ComFLOW, which solves Navier-Stokes equations and employs an improved Volume of Fluid (iVOF) method to find temporary location of fluid’s free surface. The code is used to simulate flow around a semi-submersible offshore platform due to an incoming regular wave. In particular, wave run-up on the semi’s columns and under-deck fluid impact phenomena are investigated on high-accuracy computational grids with number of cells being in range of 10 millions. Results of numerical simulations are compared with experimental data and focus is on local fluid flow details in immediate vicinity of the platform. Wave run-up on the platform’s columns and fluid pressures at various locations, including under-deck impact, are reported and verified against the experiment for a range of incoming wave heights.Copyright

Modeling two-phase flow with offshore applications

With the trend towards offshore LNG production and offloading, sloshing of LNG in partially filled tanks has become an important research subject for the offshore industry. LNG sloshing may induce impact pressures on the containment system and may affect the motions of the LNG carrier.

Modeling the effect of nonuniform sediment on the dynamics of offshore tidal sandbanks

Tidal sandbanks are large-scale bed features present in many shallow shelf seas. Here we investigate the effect of nonuniform sediment on their dynamics, with a particular aim to explain observed surficial grain size variations over tidal sandbanks from a process-based modeling perspective. To this end, we use a linear stability analysis that describes the positive feedback mechanism between hydrodynamics, sediment, and the seabed responsible for sandbank formation on a horizontal shelf. In this model the sediment transport and bed evolution modules are extended by introducing an active layer and a bimodal sediment mixture. We include a dynamic hiding/exposure description of sediment transport, enhancing the transport of coarse grains and inhibiting the transport of finer grains. The model results show that for symmetrical tidal conditions, coarse grains tend to accumulate at the bank crests. Moreover, the growth rates of the perturbations increase compared to the case of uniform sediment, while the preferred wavelength and bank orientation remain unchanged. For asymmetrical tidal conditions we find a spatial phase shift between topography and the mean grain size fraction, indicating an accumulation of coarse grains on the lee side of the bank. The model results qualitatively agree with observations from banks on the Belgian continental shelf.

Simulation of Two-Phase Flow in Sloshing Tanks

The CFD simulation tool ComFLOW is applied to study the effect of tank motions on two-phase flow phenomena inside a sloshing tank. An improved VOF method is used to assure an accurate description of the fluid displacement. With a novel “gravity-consistent” density averaging method, spurious velocities near the free surface can be avoided. Comparison of simulations with measurements show that compressibility of the air should be included for accurate simulations; the agreement is quite good on a relatively coarse mesh.

Extreme Wave Impact on Offshore Platforms and Coastal Constructions

Hydrodynamic wave loading on structures plays an important role in areas such as coastal protection, harbor design and offshore constructions (FPSO’s, mooring), and there is a need for its prediction up to a detailed level (max./min. pressures, duration of pressure peaks, shear stresses, etc.). In close cooperation with industry, long-year joint-industry projects are carried out to develop a numerical simulation method: the CFD method ComFLOW. The two major application areas are the prediction of extreme wave forces on offshore platforms and offloading vessels, and the prediction of impact forces on coastal protection structures. The paper will present a short overview of the method, some recent results and future plans.Copyright

Numerical Simulation of Sloshing in a Tank, CFD Calculations Against Model Tests

Simulation of liquid dynamics in an LNG tank is studied numerically. The applied CFD code solves Navier-Stokes equations and uses an improved Volume of Fluid (iVOF) method to track movement of fluid’s free surface. Relative advantages of using two different fluid models, single-phase (liquid+void) and two-phase (liquid+compressible gas) are discussed, the latter model being capable of simulating bubbles and gas entrapped in liquid. Furthermore, the 1st and 2nd order upwind differencing schemes are used with both physical models leading to a total of four possible approaches to solve the problem. Numerical results are verified against experimental data from large scale (1:10) sloshing experiments of 2D section of an LNG carrier. The CFD vs. experiment comparison is shown for tank filling rates of practical interest, ranging from 10% to 95%, and includes both fluid height and fluid pressure exerted on tank walls. A visual comparison in form of computer animation frames, synchronised with camera-made movies taken during the experiments is included as well. Finally, an exhaustive computational grid convergence study is presented for lower filling rates of the tank.Copyright

HYDRODYNAMIC WAVE LOADING ON OFFSHORE STRUCTURES SIMULATED BY A TWO-PHASE FLOW MODEL

The numerical simulation of hydrodynamic wave loading on different types of offshore structures is important to predict forces on and water motion around these structures. This paper presents a numerical study of two-phase flow over a sloping bottom with the presence of breaking waves. The details of the numerical model, an improved Volume Of Fluid (iVOF) method, are presented in the paper. The program has been developed initially to study the sloshing of liquid fuel in satellites. This micro-gravity environment requires a very accurate and robust description of the free surface. Later, the numerical model has been used for calculations of green water loading and the analysis of anti-roll and sloshing tanks, including the coupling with ship motions. The model has been extended recently to take two-phase flow effects into account. Two-phase flow effects are particularly important near the free surface, where loads on offshore structures strongly depend on the interaction between different phases like air and water. Entrapment of air pockets and entrainment of bubble clouds have a cushioning effect on breaking wave impacts. The velocity field around the interface of air and water, being continuous across the free surface, requires special attention. By using a newly-developed gravity-consistent discretisation, spurious velocities at the free surface are prevented. Thus far, the second air phase has been treated as incompressible. Taking compressibility effects into account requires a pressure-density relation for grid cells containing air. The expansion and compression of air pockets is considered as an adiabatic process. The numerical model is validated on several test cases. In this paper special attention will be paid to the impact of a breaking wave over a sloping bottom.Copyright

NUMERICAL INVESTIGATION OF SLOSHING IN A TANK, STATISTICAL DESCRIPTION OF EXPERIMENTS AND CFD CALCULATIONS

Numerical study of liquid dynamics in an LNG tank is presented. The available data from large scale (1:10) sloshing experiments of 2D section of an LNG carrier reveal large scatter in recorded values of peak pressures. The experimental data is analysed from statistical point of view in order to obtain distributions of the pressure peaks. Then the entire experimental data record is reproduced numerically by CFD simulations and it is shown that pressure peaks obtained numerically display scatter of values as well. A statistical description of the numerically obtained record is provided and compared with description derived from the experimental data. The applied CFD code ComFLOW solves Navier-Stokes equations and uses an improved Volume of Fluid (iVOF) method to track movement of fluid’s free surface. Two different fluid models, single-phase (liquid+void) and two-phase (liquid+compressible gas) can be applied, the latter model being capable of simulating bubbles and gas entrapped in liquid. For low tank filling rate discussed in the paper (10%) the single-phase approach is sufficient. Comparison of statistical properties of experimental and numerical records is offered.Copyright