Document Type : Research Paper


Sirjan University of Technology


Liquid sloshing is a common phenomenon in the transporting of liquid tanks. Liquid waves lead to fluctuating forces on the tank wall. If these fluctuations are not predicted or controlled, they can lead to large forces and momentum. Baffles can control liquid sloshing fluctuations. One numerical method, widely used to model the liquid sloshing phenomena is Smoothed Particle Hydrodynamics (SPH). Because of its Lagrangian nature, SPH is suitable for simulating free surface flow. In the present study, a relatively accurate Incompressible SPH (ISPH) method improved by kernel gradient correction tensors, particle shifting algorithms, turbulence viscosity calculations, and free surface particle detectors is applied for the free surface flow modeling. In comparison to the other SPH Simulations and experimental data, these results show that the present algorithm is effective for simulating free surface problems. The present algorithm has been applied to simulate liquid sloshing phenomena, while the aim of this study is the investigation of vertical and horizontal baffle effects on the control and damping of liquid sloshing. Results show that for vertical baffles, baffle size has a major role in sloshing fluctuation damping. For horizontal baffles, also including size, the baffle base position has a significant role in liquid sloshing fluctuation damping. When horizontal baffle is near the free surface, sloshing fluctuation-damping increases.

Graphical Abstract

Numerical investigation of vertical and horizontal baffle effects on liquid sloshing in a rectangular tank using an improved incompressible smoothed particle hydrodynamics method


Main Subjects

 [1]    L. B. Lucy, “A numerical Approach to the Testing of the Fission Hypothesis”, The Astronomical Journal, Vol. 82, pp. 1013-1024, (1977).

[2]     R. A. Gingold, and J. J. Monaghan, “Smoothed Particle Hydrodynamics: Theory and Application to Non-spherical Stars”, Monthly Notices of the Royal Astronomical Society, Vol. 181, pp. 375-389, (1977).

[3]     R. A. Gingold, and J. J. Monaghan, “Kernel estimates as a basis for general particle methods in hydrodynamics,” Journal of Computational Physics, Vol.46, No. 3, pp. 429-453, (1982).

[4]     J. P. Morris, P. J. Fox, and Y. Zhu, “Modeling low Reynolds number incompressible flows using SPH”, Journal of Computational Physics, Vol. 136, No. 1, pp. 214-226, (1997).

[5]     M. Sefid, R. Fatehi, and R. Shamsoddini, “A modified smoothed particle hydrodynamics scheme to model the stationary and moving boundary problems for Newtonian fluid flows,” Journal of Fluids Engineering, Vol. 137, No. 3, pp. 031201-9, (2014).

[6]     M. S. Shadloo, A. Zainali, S. H. Sadek, and M. Yildiz, “Improved incompressible smoothed particle hydrodynamics method for simulating flow around bluff bodies”, Computer Methods in Applied Mechanics and Engineering, Vol. 200, No. 9-12, pp. 1008-1020, (2011).

[7]     M. R. Hashemi, R. Fatehi, and M. T. Manzari, “SPH simulation of interacting solid bodies suspended in a shear flow of an Oldroyd-B fluid,” Journal of Non-Newtonian Fluid Mechanics, Vol. 166, No. (21-22), pp. 239-1252. (2011).

[8]     R. Shamsoddini, N Aminizadeh, and M Sefid, “An improved WCSPH method to simulate the non-Newtonian Power-Law Fluid Flow Induced by motion of a Square Cylinder”, Computer Modeling in Engineering & Sciences, Vol. 105, No. 3, pp. 209-230, (2015).

 [9]    A. Farrokhpanah, B. Samareh, and J. Mostaghimi, “Applying Contact Angle to a Two-Dimensional Multiphase Smoothed Particle Hydrodynamics Model”, Journal of Fluids Engineering, Vol. 137, No. 4, pp. 041303-12, (2015).

[10]   M. S. Shadloo, A. Zainali, and M. Yildiz, “Simulation of single mode Rayleigh–Taylor instability by SPH method”, Computational Mechanics, Vol. 51, No. 5, pp. 699-715. (2013).

[11]   R. Shamsoddini, M. Sefid, and R. Fatehi, “Lagrangian simulation and analysis of the micromixing phenomena in a cylindrical paddle mixer using a modified Weakly Compressible Smoothed Particle Hydrodynamics Method”, Asia-Pacific Journal of Chemical Engineering, Vol. 10, No. 1, pp. 112-122, (2015).

[12]   R. Shamsoddini, M. Sefid, and R. Fatehi, “ISPH modelling and analysis of fluid mixing in a microchannel with an oscillating or a rotating stirrer”, Engineering Applications of Computational Fluid Mechanics, Vol. 8, No. 2, pp. 289-298, (2014).

[13]   R. Shamsoddini, and M. Sefid, “Lagrangian simulation and analysis of the power-law fluid mixing in the two-blade circular mixers using a modified WCSPH method,” Polish Journal of Chemical Technology, Vol. 17, No. 2, pp. 1-10, (2015).

[14]   R. Shamsoddini, M. Sefid, R. Fatehi, “Incompressible SPH modeling and analysis of non-Newtonian power-law fluids, mixing in a microchannel with an oscillating stirrer”, Journal of Mechanical Science and Technology, Vol. 30, No. 1, pp. 307-316, (2016).

[15]   M.R. Hashemi, , R. Fatehi, and M.T. Manzari, “A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows”, International Journal of Non-Linear Mechanics, Vol. 47, No. 6, pp. 626-638, (2012).

[16]   M. Doring, Y. Andrillon, B. Alessandrini, and P. Ferrant, 2003, “SPH Free Surface Flow Simulation,” 18th International Workshop on Water Waves and Floating Bodies, At Le Croisic, France, (2003).

[17]   D. Violeau, and R. Issa, “Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview”, International Journal for Numerical Methods in Fluids, Vol. 53, No. 2, pp. 277-304. (2007).

[18]   M. Gomez-Gesteira, B.D. Rogers, A. J. C. Crespo, R.A., Dalrymple, M. Narayanaswamy, and J. M. Dominguez, “SPHysics - development of a free-surface fluid solver- Part 1: Theory and Formulations”, Computers & Geosciences, Vol. 48, pp. 289-299, (2012).

[19]   E. S. Lee, C. Moulinec, R. Xu, D. Violeau, D. Laurence, and P. Stansby, “Comparisons of Weakly Compressible and Truly Incompressible Algorithms for the SPH Mesh Free Particle Method”, Journal of Computational Physics. Vol. 227, No. 18, pp. 8417-8436, (2008).

[20]   R. L. Bass, E. B. Bowles, R. W. Trudell, J. Navickas, J. C. Peck, N. Yoshimura, S. Endo, and B. F. M. Pots, “Modeling Criteria for Scaled LNG Sloshing Experiments”, Journal of Fluids Engineering, Vol. 107, No. 2, pp. 272-280, (1985).

[21]   F. T. Dodge, and D. D. Kana, “Dynamics of Liquid Sloshing in Upright and Inverted Bladdered Tanks”, Journal of Fluids Engineering, Vol. 109, No. 1, pp. 58-63, (1987).

[22]   L. Hou, F. Li, and C. Wu, “A Numerical Study of Liquid Sloshing in a Two-dimensional Tank under External Excitations”, Journal of Marine Science and Application, Vol. 11, pp. 305-310, (2012).

[23]   B. Godderidge, S. Turnock, M. Tan, and C. Earl, “An investigation of multiphase CFD modelling of a lateral sloshing tank”, Computers & Fluids, Vol. 38, No. 2, pp.183-193, (2009).

[24]   X. Y. Cao, F. R. Ming, and A. M. Zhang, “Sloshing in a rectangular tank based on SPH simulation”, Applied Ocean Research, Vol. 47, pp. 241-254, (2014).

[25]   H. Gotoh, A. Khayyer, T. Ikari, H. Arikawa, and K. Shimosako,“On enhancement of Incompressible SPH method for simulation of violent sloshing flows”, Applied Ocean Research, Vol. 46, pp. 104-115, (2014).

[26]   S. De Chowdhury, and S. A. Sannasiraj, “Numerical simulation of 2D sloshing waves using SPH with diffusive terms”, Applied Ocean Research, Vol. 47, pp. 219-240, (2014).

[27]   J. R. Shao, H. Q. Li, G. R. Liu, and M. B. Liu, “An improved SPH method for modeling liquid sloshing dynamics”, Computers & Structures, Vol. 100-101, pp. 18-26, (2012).

[28]   W. Dehnen, and H. Aly, “Improving Convergence in Smoothed Particle Hydrodynamics Simulations without Pairing Instability”, Monthly Notices of the Royal Astronomical Society, Vol. 425 (2), pp. 1068-1082, (2012).

[29]   J. Bonet, and T. S. Lok, “Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulation”, Computer Methods in Applied Mechanics and Engineering Vol. 180, pp. 97-115, (1999).

 [30]  A. M. Aly, and S. W. Lee, “Numerical simulations of impact flows with incompressible smoothed particle hydrodynamics”, Journal of Mechanical Science and Technology, Vol. 28, No. 6, pp. 2179-2188, (2014).

[31]   R. Shamsoddini and N. Aminizadeh, “Incompressible Smoothed Particle Hydrodynamics Modeling and Investigation of Fluid Mixing in a Rectangular Stirred Tank with Free Surface”, Chemical Engineering Communications, Vol. 204, No. 5, pp. 563-572, (2017).

[32]   S. Koshizuka, and Y. Oka, “Moving-particle semi-implicit method for fragmentation of compressible fluid”, Nuclear Science Engineering, Vol. 123, pp. 421-434, (1996).

[33]   M. Hinatsu, “Experiments of two-phase flows for the joint research,” Proceedings of the SRI-TUHH mini-workshop on numerical simulation of two-phase flows, National Maritime Research Institute & Technische Universität Hamburg–Harburg, NMRI; (2001).