Simulation of fluid sloshing in a tank using the SPH and Pendulum methods
Simulacija pljuskanja kapljevine v cisterni po metodi hidrodinamike zglajenih delcev (SPH) in po metodah nihala
- Avtorji: Vesna Vidmar, Gregor Petkovšek, Dušan Žagar
- Citat: Acta hydrotechnica, vol. 31, no. 54, pp. 51-65, 2018. https://doi.org/10.15292/acta.hydro.2018.04
- Povzetek: V prispevku obravnavamo pljuskanja kapljevine v cisterni krožnega prečnega prereza med dvema tipičnima manevroma: vstopom in vožnjo skozi krožišče ter menjavo voznega pasu. Za simulacije nihanja kapljevine smo uporabili tri metode: modela kvazistatičnega nihala in modificiranega dinamičnega nihala s spremenljivo ročico ter model Tis-Isat, ki deluje po metodi hidromehanike zglajenih delcev (SPH – Smooth Particle Hydrodynamics). Za določitev praga prevrnitve pri prvem manevru smo izdelali in uporabili model poenostavljenega vozila s cisterno. Ujemanje nihanja kapljevine je bilo boljše pri drugem manevru, maksimalni odmik težišča kapljevine pa smo uspešno simulirali v obeh obravnavanih primerih. Vse tri metode pokažejo podobno obnašanje vozila s tekočim tovorom ob prevrnitvi, obe dinamični metodi, SPH in dinamično nihalo, pa dajeta znatno nižji prag prevrnitve. Pri SPH je prag prevrnitve nekoliko višji kot pri dinamičnem nihalu zaradi interakcije med delci kapljevine ter kapljevino in ostenjem. Primerjava rezultatov dinamičnih metod potrjuje uporabnost metode SPH za simulacije pljuskanja v tovornih cisternah, prav tako pa tudi prednosti metode SPH: opis nelinearne proste gladine v realnem času ter upoštevanje viskoznih procesov in mešanja v kapljevini.
- Ključne besede: metoda SPH, nihalo, nihanje kapljevine, zaprto območje, tekoči tovor, prag prevrnitve
- Polno besedilo: a31vv.pdf
- Viri:
- Abramson, H. N. (1966). The Dynamic Behavior of Liquids in Moving Containers. National Aeronautics and Space Administration, Washington.
- Aliabadi, S., Johnson, A., Abedi, J. (2003). Comparison of Finite Element and Pendulum Models for Simulation of Sloshing. Comput. Fluids 32, 535–545. https://doi.org/10.1016/S0045-7930(02)00006-3.
- Behr, M., Tezduyar, T. E. (1994). Finite Element Solution Strategies for Large-Scale Flow Simulations. Comput. Methods Appl. Mech. Eng. 112, 3–24. https://doi.org/10.1016/0045-7825(94)90016-7.
- Cao, X. Y., Ming, F. R., Zhang, A. M. (2014). Sloshing in a Rectangular Tank Based on SPH Simulation. Appl. Ocean Res. 47, 241–254. https://doi.org/10.1016/j.apor.2014.06.006.
- Casasanta, J. D. (2010). Rollover Stability Analysis of Commercial Semi-Tanker Trucks Utilizing a Trammel Pendulum Model to Simulate Fluid Sloshing. Available at: http://trid.trb.org/view.aspx?id=1221147#.VsV56HDmZUc.mendeley.
- Delorme, L. (2009). Sloshing Flows. Experimental Investigation and Numerical Simulations with Smoothed Particle Hydrodynamics. Technical University of Madrid (UPM).
- Džebo, E., Žagar, D., Četina, M., Petkovšek, G. (2013). Reducing the Computational Time of the Smoothed Particle Hydrodynamics Method with a Coupled 2-D/3-D Approach ‒ Skrajšanje računskega časa simulacij po metodi SPH z uporabo povezanega 2D/3D-modela (in Slovene). J. Mech. Eng. 59, 575–584. Available at: http://10.0.21.169/sv-jme.2013.944.
- Džebo, E., Žagar, D., Krzyk, M., Četina, M., Petkovšek, G. (2014). Different Ways of Defining Wall Shear in Smoothed Particle Hydrodynamics Simulations of a Dam-Break Wave. J. Hydraul. Res. 52, 453–464. https://doi.org/10.1080/00221686.2013.879611.
- Gingold, R. A., Monaghan, J. J. (1977). Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars. Mon. Not. R. Astron. Soc. 181, 375–389. https://doi.org/10.1093/mnras/181.3.375.
- Gomez-Gesteira, M., Rogers, B. D., Dalrymple, R. A., Crespo, A. J. C. (2010). State-of-the-Art of Classical SPH for Free-Surface Flows. J. Hydraul. Res. 48, 6–27. https://doi.org/10.1080/00221686.2010.9641242.
- Issermann, H. (1976). Overturning Limits of Articulated Vehicles with Solid and Liquid Loads, MIRA Trans. No. 22/76. England.
- Jena, D., Biswal, K .C. (2017). A Numerical Study of Violent Sloshing Problems with Modified MPS Method. J. Hydrodyn. Ser. B 29, 659–667. https://doi.org/10.1016/S1001-6058(16)60779-5.
- Jones, D.A., Belton, D. (2006). Smoothed Particle Hydrodynamics: Applications Within DSTO. Department of Defence, Australia. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.587.8046&rep=rep1&type=pdf.
- Kang, X., Rakheja, S., Stiharu, I. (2001). Effects of Tank Shape on the Roll Dynamic Response of a Partly Filled Tank Vehicle. Veh. Syst. Dyn. Available at: http://www.tandfonline.com/doi/abs/10.1076/vesd.35.2.75.2036#.VsV9sXXTouE.mendeley.
- Kolaei, A., Rakheja, S., Richard, M. J. (2015). Three-Dimensional Dynamic Liquid Slosh in Partially-Filled Horizontal Tanks Subject to Simultaneous Longitudinal and Lateral Excitations. Eur. J. Mech. / B Fluids 53, 251–263. https://doi.org/10.1016/j.euromechflu.2015.06.001.
- Kolaei, A., Rakheja, S., Richard, M. J. (2014). Range of Applicability of the Linear Fluid Slosh Theory for Predicting Transient Lateral Slosh and Roll Stability of Tank Vehicles. J. Sound Vib. 333, 263–282. https://doi.org/10.1016/J.JSV.2013.09.002.
- Liu, G. R., Liu, M. B. (2003). Smoothed Particle Hydrodinamics: a Meshfree Particle Method. World Scientific Publishing. Available at: http://www.worldscientific.com/worldscibooks/10.1142/5340.
- Lucy, L. B. (1977). A Numerical Approach to the Testing of the Fission Hypothesis. Astron. J. 82, 1013–1024.
- Martin, J. C., Moyce, W. J. (1952). An Experimental Study of the Collapse of Liquid Columns on a Rigid Horizontal Plane. Philos Trans Soc, A 244, London, 312–324.
- Modaressi-Tehrani, K., Rakheja, S., Sedaghati, R. (2006). Analysis of the Overturning Moment Caused by Transient Liquid Slosh Inside a Partly Filled Moving Tank. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 220, 289–301. https://doi.org/10.1243/09544070D01705.
- Molteni, D., Colagrossi, A. (2008). Oblique Impact of a Jet on a Plane Surface Solved by SPH: Suggestions to Improve the Results of the Pressure Profiles, in: 3rd ERCOFTAC SPHERIC Workshop on SPH Applications. 1–5.
- Monaghan, J. J. (1992). Smoothed Particle Hydrodynamics. Annual Review of Astronomy and Astrophysics, 543–574.
- Monaghan, J.J., Lattanzio, J.C. (1985). A Refined Particle Method for Astrophysical Problems. Astron. Astrophys. 149, 135–143.
- Okamoto, T., Kawahara, M. (1990). Two-Dimensional Sloshing Analysis by Lagrangian Finite Element Method. Int. J. Numer. Methods Fluids 11, 453–477. https://doi.org/10.1002/fld.1650110502.
- Petkovšek, G., Džebo, E., Četina, M., Žagar, D. (2010). Application of Non-Discrete Boundaries with Friction to Smoothed Particle Hydrodynamics. J. Mech. Eng. 56, 307–315.
- Rajar, R. (1972). Recherche theorique et experimentale sur la propagation des ondes de rupture de barrage dans une vallee naturelle. University Paul Sabatier.
- Rakheja, S., Ranganathan, R. (1993). Estimation of the Rollover Threshold of Heavy Vehicles Carrying Liquid Cargo: A Simplified Approach. Int. J. Heavy Veh. Syst. 1. https://doi.org/https://doi.org/10.1504/IJHVS.1993.054646.
- Ramaswamy, B., Kawahara, M., Nakayama, T. (1986). Lagrangian Finite Element Method for the Analysis of Two-Dimensional Sloshing Problems. Int. J. Numer. Methods Fluids 6, 659–670. https://doi.org/10.1002/fld.1650060907.
- Ranganathan, R., Rakheja, S., Sankar, S. (1993). Directional Response of a B-Train Vehicle Combination Carrying Liquid Cargo. J. Dyn. Syst. Meas. Control 115, 133–139. http://dx.doi.org/10.1115/1.2897388.
- Rattaya, J. V. (1965). Sloshing of Liquids in Axisymmetric Ellipsoidal Tanks, AIAA paper.
- Salem, M.I. (2000). Rollover Stability of Partially Filled Heavy-Duty Elliptical Tankers Using Trammel Pendulums to Simulate Fluid Sloshing. West Virginia University.
- Shao, J. R., Li, H. Q., Liu, G. R., Liu, M. B. (2012). An Improved SPH Method for Modeling Liquid Sloshing Dynamics. Comput. Struct. 100–101, 18–26. https://doi.org/10.1016/j.compstruc.2012.02.005.
- Strandberg, L. (1978). Lateral Stability of Road Tankers, VTI rapport. Sweden. Available at: https://trid.trb.org/view.aspx?id=74044.
- Verlet, L. (1967). Computer “Experiments” on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Phys. Rev. 159, 98–103. https://doi.org/10.1103/PhysRev.159.98.
- Vidmar, V. (2012). Simulations of Fluid Movement in a Tank Using the SPH and Pendulum Methods ‒ Simulacija gibanja kapljevin v cisterni po metodi SPH in metodi nihala (in Slovenian). Fakulteta za gradbeništvo in geodezijo. Available at: http://drugg.fgg.uni-lj.si/3755/1/GRU_3217_Vidmar.pdf.
- Vorobyev, A., Kriventsev, V., Maschek, W. (2011). Simulation of Central Sloshing Experiments with Smoothed Particle Hydrodynamics (SPH) Method. Nucl. Eng. Des. 241, 3086–3096. https://doi.org/10.1016/j.nucengdes.2011.05.020.
- Wu, G. X., Ma, Q. W., Eatock Taylor, R. (1998). Numerical Simulation of Sloshing Waves in a 3D Tank Based on a Finite Element Method. Appl. Ocean Res. 20, 337–355. https://doi.org/10.1016/S0141-1187(98)00030-3 .