Roel Luppes

The numerical simulation of liquid sloshing on board spacecraft

The subject of study is the influence of sloshing liquid on the dynamics of spacecraft. A combined theoretical and experimental approach has been followed. On the one hand, CFD simulations have been carried out to predict the combined liquid/solid body motion. Basically a volume-of-fluid (VOF) approach is followed, however with improvements in the treatment of the free liquid surface: these cover the surface reconstruction and displacement and the calculation of surface tension effects by means of a local height function. Also attention has been paid to the stability of the numerical coupling between solid-body dynamics and liquid dynamics. On the other hand, in-orbit experiments have been carried out with the Sloshsat FLEVO satellite. The paper describes a first comparison between theoretical predictions and experimental findings.

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

CFD Simulations of a Semi-Submersible With Absorbing Boundary Conditions

The CFD tool COMFLOW is suitable for simulations of two-phase flows in offshore applications. COMFLOW solves the Navier-Stokes equations in both water and (compressibl e) air. The water surface is advected through a Volume-of-Flui d method, with a height-function approach for improved accur acy. By employing Absorbing Boundary Conditions (ABC), boundaries can be located relatively close to an object, wit hout influencing outgoing waves or generating numerical reflections that affect the waves inside the flow domain. Tradition ally, boundaries are located far from the obstacle to avoid reflect ions; even when numerical damping zones are used. Hence, with the ABC approach less grid points are required for the same accuracy, which reduces the computing time considerably. Simulations of a semi-submersible model are compared to measurements. The overall agreement is reasonably good, fo r a wide range of wave conditions. The ABC performs well; numeri cal reflections are almost absent. Moreover, computing time s reduce with a factor four compared to damping zone techniques.

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

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.

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.

Rayleigh instability of the inverted one-cell amphibian embryo

The one-cell amphibian embryo is modeled as a rigid spherical shell containing equal volumes of two immiscible fluids with different densities and viscosities and a surface tension between them. The fluids represent denser yolk in the bottom hemisphere and clearer cytoplasm and the germinal vesicle in the top hemisphere. The unstable equilibrium configuration of the inverted system (the heavier fluid on top) depends on the value of the contact angle. The theoretically calculated normal modes of perturbation and the instability of each mode are in agreement with the results from ComFlo computational fluid dynamic simulations of the same system. The two dominant types of modes of perturbation give rise to axisymmetric and asymmetric sloshing of the cytoplasm of the inverted embryos, respectively. This work quantifies our hypothesis that the axisymmetric mode corresponds to failure of development, and the asymmetric sloshing mode corresponds to development proceeding normally, but with reversed pigmentation, for inverted embryos.

Turbulence Modeling, Local Grid Refinement and Absorbing Boundary Conditions for Free-Surface Flow Simulations in Offshore Applications

To study extreme hydrodynamic wave impact in offshore and coastal engineering, the VOF-based CFD simulation tool ComFLOW is being developed. Recently, much attention has been paid to turbulence modeling, local grid refinement, wave propagation and absorbing boundary conditions. The turbulence model has to cope with coarse grids as used in industrial applications. Thereto a blend of a QR-model and a regularization model has been designed, in combination with a dedicated wall model. Local grid refinement is based on a semi-structured approach. Near refinement interfaces special discretization stencils have been designed. The computational domain is restricted to the close environment of the objects studied. To suppress unphysical reflections, special generating and absorbing boundary conditions have been designed. The combined performance of the new ingredients will be demonstrated with several applications. For validation, experiments have been carried out at MARIN.

Efficient Computation and Modeling of Viscous Flow Effects in ComFLOW

In offshore applications, details of viscous flow effects can become relevant when predicting e.g. drag forces on the columns of oil drilling rigs, or the flow around a semisubmersible in figure 1. This motivates a novel approach for efficiently simulating viscous flow effects at high Reynolds numbers with the CFD simulation tool ComFLOW.In ComFLOW, the Navier–Stokes equations can be solved for one-phase and for two-phase flow. The equations are discretized second-order in space, and second-order in time. An Improved Volume-of-Fluid (IVOF) algorithm is used for free-surface advection and reconstruction [1, 2].Modeling viscous flow effects in high Reynolds number flows requires a turbulence model that provides accurate results on coarse grids. We pursue to achieve a high local grid resolution in a computationally efficient manner. Both approaches are tested for flows around a square cylinder: grid refinement at Reynolds numbers 10 and 100, and the turbulence model at Reynolds number 22,000.Copyright