Session: 08-05-02 Free Surface Flows II

Paper Number: 81105

81105 - On Simulating Variability of Sloshing Loads in LNG Tanks 

The variability of local pressure measurements during liquid impacts in LNG tanks is notorious and considered to be insuperable. Even when carefully repeating a single impact wave, this variability is very large [1]. The wave shape before impact can be experimentally reproduced very precisely and with a smooth free surface, but repetitions always lead to large discrepancies in the local pressure measurements. The local variability of the loads is related to the free surface roughness and the liquid fragmentation resulting from the free surface instabilities that develop due the escaping gas, e.g., Kelvin-Helmholtz (shear), Rayleigh-Taylor (gravity) and Rayleigh-Plateau (surface tension).

 

The gas velocities tangent to the free surface induce shear forces along the surface which subsequently becomes unstable. The large variability of local loads is a malediction for liquid impact studies: it imposes many repetitions and long durations of the sloshing model tests for each condition in order to gather sufficiently large samples of pressure peaks for statistics. This variability also makes the experimental discrimination of the effect of any multiphase parameter (density ration, compressibility, phase transition) on impact loads more complex. Moreover, it prevents any serious experimental validation of numerical simulations for the local pressures. Despite its crucial influence, the development of free surface instabilities and its role in the variability of local pressures has not been studied in the context of wave impacts. The main challenges are (i) to capture both experimentally and numerically the development of the free surface instabilities; and (ii) to quantify their effect on the variability of local pressures.

 

Numerical modeling of the initiation of the free surface instabilities requires models for mass conservation, an averaged momentum equation, an equation of state, plus a model for capillary forces, as are available in the in-house developed CFD method ComFLOW. It models (in)compressible two-fluid flow on a staggered grid, with the acoustic part of the model solved implicitly. The spatial discretization of the Navier-Stokes equations generalizes the energy-preserving approach [2]. This discretization is stable, without numerical diffusion that might suppress the initiation of instabilities.

 

To conserve liquid mass, an accurate VOF-variant has been developed. Surface tension forces are modelled via the imposition of the Young-Laplace equation, where the jump condition is discretized using the ghost fluid method [3]. The interface curvature is computed using the local height function as developed for microgravity flow [4], where a parabolic interface reconstruction is required to ensure convergence of the curvature in space and time. Advection is performed with a modified FMPFA method [5].  Spurious velocities near the free surface are avoided by careful treatment of the (almost) discontinuities of the flow field.  With all these detailed physics, ComFLOW's adaptive local grid refinement and parallel execution are found essential. The model will be demonstrated on various simulations of breaking waves.  

 

[1]    Lafeber, W., H. Bogaert, and L. Brosset. Elementary Loading Processes (ELP) involved in breaking wave impacts: findings from the Sloshel project. 22^nd ISOPE Conf., Rhodes, Greece, 2012.

[2]    Verstappen, R.W.C.P. and A.E.P. Veldman. Symmetry-preserving discretization of turbulent flow. J. Comput. Phys., 2003, 187(1):343-368.

[3]    Liu, Xu-dong, R.P. Fedkiw, and M. Kang.  A boundary condition capturing method for Poisson's equation on irregular domains. J. Comput. Phys., 2000, 160:151-178.

[4]    Veldman, A.E.P., et al. The numerical simulation of liquid sloshing on board spacecraft. J.  Comput. Phys., 2007, 224(1): 82-99.

[5]    Owkes, M, and O. Desjardins. A mesh-decoupled height function method for computing interface curvature. J. Comput. Phys., 2015, 281:285-300.

 

Presenting Author: Arthur Veldman University of Groningen

Authors:

Ronald Remmerswaal University of Groningen
Arthur Veldman University of Groningen