Performances of Different Turbulence Models for Simulating Shallow Water Sloshing in Rectangular Tank

Abstract

Liquid sloshing is a common phenomenon in the transportation of liquid-cargo tanks. Liquid waves lead to fluctuating forces on the tank walls. If these fluctuations are not predicted or controlled, for example, by using baffles, they can lead to large forces and momentums. The volume of fluid (VOF) two-phase numerical model in OpenFOAM open-source software has been widely used to model the liquid sloshing. However, a big challenge for modeling the sloshing phenomenon is selecting a suitable turbulence model. Therefore, in the present study, different turbulence models were studied to determine their sloshing phenomenon prediction accuracies. The predictions of these models were validated using experimental data. The turbulence models were ranked by their mean error in predicting the free surface behaviors. The renormalization group (RNG) k–ε and the standard k–ω models were found to be the best and worst turbulence models for modeling the sloshing phenomena, respectively; moreover, the SST k–ω model and v2-f k-ε results were very close to the RNG k–ε model result.

Keywords

Volume of fluid / Turbulence models / Shallow water sloshing / Free surface / OpenFOAM / Liquid tanks / Renormalization group

References

[1] Brackbill J, Kothe DB, Zemach C. A continuum network method for modeling surface tension. J Comput Phys, 1992, 100(2): 335-354

[2] Chen YG, Price WG (2009) Numerical simulation of method for liquid sloshing in a partially filled container with inclusion of compressibility effects. Phys Fluids 21(112105):1-16. https://doi.org/10.1063/1.3264835, 112105

[3] Deshpande S, Anumolu L, Trujillo M. Evaluating the performance of the two-phase flow solver InterFoam. Comput Sci Discov, 2012, 5(014016): 1-37

[4] Godderidge B, Turnock S, Tan M, Earl C (2009) An vestigation of multiphase CFD modelling of a lateral sloshing tank. Computers and. Fluids, 38(2):183–193. https://doi.org/10.1016/j.compfluid.2007.11.007

[5] Hoang D, Steijn V, Portela L, Kreutzer M. Benchmark numerical simulations of segmented two-phase flows in microchannels using the volume of fluid method. Comput Fluids, 2013, 86(5): 28-36

[6] Hou L, Li F, Wu CJ. A numerical study of liquid sloshing in a two-dimensional tank under external excitations. J Mar Sci Appl, 2012, 2012(11): 305-310

[7] Kim S, Kim K, Kim Y. Comparative study on model-scale sloshing tests. J Mar Sci Technol, 2012, 17: 47-58

[8] Kim SY, Kim KH, Kim Y. Comparative study on pressure sensors for sloshing experiment. Ocean Eng, 2015, 94: 199-212

[9] Launder BE, Spalding DB. The numerical computation of turbulent flows. Com Meth Appl Mech Eng, 1974, 3(2): 269-289

[10] Lien FS, Kalitzin G. Computations of transonic flow with the v2-f turbulence model. Int J Heat Fluid Flow, 2001, 22: 53-61

[11] Lien FS, Chen WL, Leschziner MA (1996) Low-Reynolds-number eddy-viscosity modeling based on non-linear stress-strain/vorticity relations. Engineering Turbulence Modelling and Experiments 3:91–100

[12] Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J, 1994, 32(8): 1598-1605

[13] Ming PJ, Duan WY. Numerical simulation of models for sloshing in rectangular tank with VOF based on unstructured grids. J Hydrodyn, 2010, 22(6): 856-864

[14] Ozbulut M, Tofighi N, Goren O, Yildiz M. Investigation of wave characteristics in oscillatory motion of partially filled rectangular tanks. J Fluids Eng, 2018, 140(4): 041204-041215

[15] Saghi H, Ketabdari MJ. Numerical simulation of sloshing in rectangular storage tank using coupled FEM-BEM. J Mar Sci Appl, 2012, 11: 417-426

[16] Shadloo MS, Oger G, Le Touze D. Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: motivations, current state, and challenges. Comput Fluids, 2016, 136: 11-34

[17] Shamsoddini R, Abolpur B. Investigation of the effects of baffles on the shallow water sloshing in a rectangular tank using a 2D turbulent ISPH method. China Ocean Eng, 2019, 33(1): 94-102

[18] Shih TH, Liou WW, Shabbir A, Yang Z, Zhu J. A new k-ε eddy-viscosity model for high Reynolds number turbulent flows-model development and validation. Comput Fluids, 1995, 24(3): 227-238

[19] Wilcox DC. Formulation of the k-ω turbulence model revisited. AIAA J, 2008, 46(11): 2823-2838

[20] Wu CH, Chen BF, Hung TK. Hydrodynamic forces induced by transient sloshing in a 3D rectangular tank due to oblique horizontal excitation. Comput Math Appl, 2013, 65(8): 1163-1186

[21] Yakhot V, Orszag SA, Thangam S, Gatski TB, Speziale CG. Development of turbulence models for shear flows double expansion technique. Phys Fluids, 1992, 4(7): 1510-1520

[22] Zhao D, Hu Z, Chen G, Lim S, Wang S. Nonlinear sloshing in rectangular tanks under forced excitation. Int J Nav Archit Ocean Eng, 2018, 10(5): 545-565