Numerical simulation of sloshing in rectangular storage tank using coupled FEM-BEM

Abstract

Sloshing of liquid can increase the dynamic pressure on the storage sidewalls and bottom in tanker ships and LNG careers. Different geometric shapes were suggested for storage tank to minimize the sloshing pressure on tank perimeter. In this research, a numerical code was developed to model liquid sloshing in a rectangular partially filled tank. Assuming the fluid to be inviscid, Laplace equation and nonlinear free surface boundary conditions are solved using coupled FEM-BEM. The code performance for sloshing modeling is validated against available data. To minimize the sloshing pressure on tank perimeter, rectangular tanks with specific volumes and different aspect ratios were investigated and the best aspect ratios were suggested. The results showed that the rectangular tank with suggested aspect ratios, not only has a maximum surrounded tank volume to the constant available volume, but also reduces the sloshing pressure efficiently.

Keywords

rectangular storage tank / sloshing phenomenon / aspect ratio / coupled FEM-BEM

References

[1] Belakroum R., Kadja M., Mai T.H., Maalouf C. An efficient passive technique for reducing sloshing in rectangular tanks partially filled with liquid. Mechanics Research Communications, 2010, 37: 341-346

[2] Celebi M.S., Akyildiz H. Nonlinear modeling of liquid sloshing in moving rectangular tank. Ocean Engineering, 2002, 29: 1527-1553

[3] Chen B.F., Chiang H.W. Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank. Ocean Engineering, 2000, 27: 953-977

[4] Chen B.F., Nokes R. Time-independent finite difference analysis of fully non-linear and viscous fluid sloshing in a rectangular tank. Journal of Computational Physics, 2005, 209: 47-81

[5] Curadelli O., Ambrosini D., Mirasso A., Amani M. Resonant frequencies in an elevated spherical container partially filled with water: FEM and measurement. J. Fluids Structure, 2010, 26: 148-159

[6] Frandsen J.B. Sloshing motions in excited tank. Journal of Computational Physics, 2004, 106: 53-87

[7] Gavrilyuk I.P., Lukovsky I.A., Timokha A.N. Linear and nonlinear sloshing in a circular conical tank. Fluid Dynamics Research, 2005, 37: 399-429

[8] Hasheminejad S.M., Ghabeigi A.M. Sloshing characteristics in half-full horizontal elliptical tanks with vertical baffles. Applied Mathematical Modeling, 2012, 36: 57-71

[9] Jung J.H., Yoon H.S., Lee C.Y., Shin S.C. Effect of the vertical baffle height on the liquid sloshing in a three-dimensional rectangular tank. Ocean Engineering, 2012, 44: 79-89

[10] Karamanos S.A., Patkas L., Platyrrachos M.A. Sloshing effects on the seismic design of horizontal-cylindrical and spherical industrial vessels. J. Pressure Vessel Technology, 2006, 128: 328-340

[11] Lee D.H., Kim M.H., Kwon S.H., Kim J.W., Lee Y.B. A parametric sensitivity study on LNG tank sloshing loads by numerical simulation. Ocean Engineering, 2007, 34: 3-9

[12] Liu D., Lin P. Three-dimensional liquid sloshing in a tank with baffles. Ocean Engineering, 2009, 36: 202-212

[13] Mciver P. Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth. J. Fluid Mech., 1989, 201: 243-257

[14] Nakayama T., Washizu K. Boundary element analysis of nonlinear sloshing problems, 1984, Newyork: Elsevier Applied Science Publishers

[15] Panigrahy P.K., Saha U.K., Maity D. Experimental studies on sloshing behavior due to horizontal movement of liquids in baffled tanks. Ocean Engineering, 2009, 36: 213-222

[16] Papaspyrou S., Valougeorgis D., Karamanos S.A. Refined Solution of externally induced sloshing in half-full spherical containers. J. Eng. Mech., 2003, 129: 1369-1379

[17] Papaspyrou S., Karamanos S.A., Valougeorgis D. Response of half-full horizontal cylinders under transverse excitation. J. Fluid Struct., 2004, 19: 985-1003

[18] Papaspyrou S., Valougeorgis D., Karamanos S.A. Sloshing effects in half-full horizontal cylinders vessels under longitudinal excitation. J. Appl. Mech., 2004, 71: 255-265

[19] Patkas L., Karamanos S.A. Variational solutions of externally-induced sloshing in horizontal-cylindrical and spherical vessels. J. of Eng. Mech., 2007, 133: 641-655

[20] Pirker S., Aigner A., Wimmer G. Experimental and numerical investigation of sloshing resonance phenomena in a spring-mounted rectangular tank. Chemical Engineering Science, 2012, 68: 143-150

[21] Shekari M.R., Khaji N., Ahmadi M.T. A couple BE-FE study for evaluation of seismically isolated cylindrical liquid storage tanks considering fluid-structure interaction. Journal of Fluids and Structures, 2009, 25: 567-585

[22] Wiesche S.A.D. Sloshing dynamics of a viscous liquid in a spinning horizontal cylindrical tank. Aerospace Science Technology, 2008, 12: 448-456

[23] Yue B.Z. Nonlineaqr coupling dynamics of liquid filled spherical container in microgravity. J. Applied Mathematics and Mechanics (English edition), 2008, 29: 1085-1092