This study presents a comprehensive full dynamic model designed for simulating liquid sloshing behavior within cylindrical tank structures. The model employs a discretization approach, representing the liquid as a network of interconnected spring-damper-mass systems. Key aspects include the adaptation of liquid discretization techniques to cylindrical lateral cross-sections and the calculation of stiffness and damping coefficients. External forces, simulating various vehicle maneuvers, are also integrated into the model. The resulting system of equations is solved using Maple Software with the Runge-Kutta-Fehlberg method. This model enables accurate prediction of liquid displacement and pressure forces, offering valuable insights for tank design and fluid dynamics applications. Ongoing refinement aims to broaden its applicability across different liquid types and tank geometries.
References
[1]
Abramson, H.N. (1966) The Dynamic Behavior of Liquids in Moving Containers. NASA SP-106.
[2]
Ranganathan, R., Ying, Y. and Miles, J.B. (1993) Analysis of Fluid Slosh in Partially Filled Tanks and Their Impact on the Directional Response of Tank Vehicles. SAE Technical Paper 932942, 39-45. https://doi.org/10.4271/932942
[3]
El Damatty, A.A. and Sweedan, A.M.I. (2006) Equivalent Mechanical Analog for Dynamic Analysis of Pure Conical Tanks. Thin-Walled Structures, 44, 429-440. https://doi.org/10.1016/j.tws.2006.03.016
[4]
Noui, O. (2012). Étude et modélisation des citernes en aluminium pour les véhicules routiers. Mémoire de maîtrise, Université du Québec à Chicoutimi. https://doi.org/10.1522/030341785
[5]
Provot, X. (1995) Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior. National Institute for Research in Computer Science and Control (France).
[6]
Balci, M. and Foroosh, H. (2006) Real-Time 3D Fire Simulation Using a Spring-Mass Model. 2006 12th International Multi-Media Modelling Conference, Beijing, 4-6 January 2006, 8. https://doi.org/10.1109/mmmc.2006.1651309
[7]
Mesit, J., Guha, R. and Chaudhry, S. (2007) 3D Soft Body Simulation Using Mass-Spring System with Internal Pressure Force and Simplified Implicit Integration. Journal of Computers, 2, 34-43.
[8]
Bouazara, M., Noui, O. and Richard, M.J. (2014). 3D Dynamical Model for Liquid Motion Simulation in a Partially Filled Tank. Volume 4A: Dynamics, Vibration, and Control, Montreal, 14-20 November 2014. https://doi.org/10.1115/imece2014-36211
[9]
Dodge, F.T. (2008) The New Dynamic Behaviour of Liquids in Moving Containers. Southwest Research Institute (SRI), San Antonio, Texas.
[10]
Kang, X. (2001) Optimal Tank Design and Directional Dynamic Analysis of Liquid Cargo Vehicles under Steering and Braking. Ph.D. Thesis, Concordia University Canada.
[11]
Noui, O., Bouazara, M. and Richard, M.J. (2016) Study of Liquid Motion and Pressure Forces Applied on the Walls of Partially Filled Moving Tank. Volume 4A: Dynamics, Vibration, and Control, Phoenix, 11-17 November 2016. https://doi.org/10.1115/imece2016-65170
[12]
Maple (2016) Maplesoft, a Division of Waterloo Maple Inc., Waterloo, Ontario.
[13]
Fehlberg, E. (1969) Low-Order Classical Runge-Kutta Formulas with Step Size Control and Their Application to Some Heat Transfer Problems. NASA Technical Report 315.
[14]
Fortin, A. (2015) Analyse numérique pour ingénieurs. 5th Edition, Presses Internationales Polytechnique.
[15]
Toumi, M., Bouazara, M. and Richard, M.J. (2009) Impact of Liquid Sloshing on the Behaviour of Vehicles Carrying Liquid Cargo. European Journal of Mechanics-A/Solids, 28, 1026-1034. https://doi.org/10.1016/j.euromechsol.2009.04.004
