Research Papers

A Total Lagrangian ANCF Liquid Sloshing Approach for Multibody System Applications

[+] Author and Article Information
Cheng Wei

Department of Aerospace Engineering,
Harbin Institute of Technology,
92 W. Dazhi Street,
359 Mail Box, Heilongjiang,
Harbin 150001, China
e-mail: weicheng@hit.edu.cn

Liang Wang

Department of Mechanical and
Industrial Engineering,
University of Illinois at Chicago,
842 W. Taylor Street,
Chicago, IL 60607

Ahmed A. Shabana

Department of Mechanical and
Industrial Engineering,
University of Illinois at Chicago,
842 W. Taylor Street,
Chicago, IL 60607
e-mail: shabana@uic.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 19, 2014; final manuscript received September 27, 2014; published online April 16, 2015. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 10(5), 051014 (Sep 01, 2015) (10 pages) Paper No: CND-14-1171; doi: 10.1115/1.4028720 History: Received July 19, 2014; Revised September 27, 2014; Online April 16, 2015

The objective of this investigation is to develop a total Lagrangian nonincremental liquid sloshing solution procedure based on the finite element (FE) absolute nodal coordinate formulation (ANCF). The proposed liquid sloshing modeling approach can be used to avoid the difficulties of integrating most of fluid dynamics formulations, which are based on the Eulerian approach, with multibody system (MBS) dynamics formulations, which are based on a total Lagrangian approach. The proposed total Lagrangian FE fluid dynamics formulation, which can be systematically integrated with computational MBS algorithms, differs significantly from the conventional FE or finite volume methods which are based on an Eulerian representation that employs the velocity field of a fixed control volume in the region of interest. The ANCF fluid equations are expressed in terms of displacement and gradient coordinates of material points, allowing for straightforward implementation of kinematic constraint equations and for the systematic modeling of the interaction of the fluid with the external environment or with rigid and flexible bodies. The fluid incompressibility conditions and surface traction forces are considered and derived directly from the Navier–Stokes equations. Two ANCF brick elements, one is obtained using an incomplete polynomial representation and the other is obtained from a B-spline volume representation, are used. The new approach ensures the continuity of the displacement gradients at the nodal points and allows for imposing higher degree of continuity across the element interface by applying algebraic constraint equations that can be used to eliminate dependent variables and reduce the model dimensionality. Regardless of the magnitude of the fluid displacement, the fluid has a constant mass matrix, leading to zero Coriolis and centrifugal forces. The analysis presented in this paper demonstrates the feasibility of developing an efficient nonincremental total Lagrangian approach for modeling sloshing problems in MBS system applications in which the bodies can experience large displacements including finite rotations. Several examples are presented in order to shed light on the potential of using the ANCF liquid sloshing formulation developed in this study.

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Dodge, F. T., and Kana, D. D., 1966, “Moment of Inertia and Damping of Liquid in Baffled Cylindrical Tanks,” J. Spacecraft Rockets, 3(1), pp. 153–155. [CrossRef]
Kana, D. D., 1987, “A Model for Nonlinear Rotary Slosh in Propellant Tanks,” J. Spacecraft Rockets, 24(2), pp. 169–177. [CrossRef]
Kana, D. D., 1989, “Validated Spherical Pendulum Model for Rotary Liquid Slosh,” J. Spacecraft Rockets, 26(3), pp. 188–195. [CrossRef]
Pinson, L. D., 1964, “Longitudinal Spring Constants for Liquid Propellant Tanks With Ellipsoidal Ends,” NASA TN D-2220, November.
Warner, R. W., and Caldwell, J. T., 1961, “Experimental Evaluation of Analytical Models for the Inertias and Natural Frequencies of Fuel Sloshing in a Circular Cylindrical Tanks,” NASA TN D-856.
Ranganathan, R., Rakheja, S., and Sankar, S., 1989, “Steady Turning Stability of Partially Filled Tank Vehicles With Arbitrary Tank Geometry,” ASME J. Dyn. Sys. Meas. Control, 111(3), pp. 481–489. [CrossRef]
Zheng, X., Li, X., and Ren, Y., 2012, “Equivalent Mechanical Model for Lateral Liquid Sloshing in Partially Filled Tank Vehicles,” Math. Prob. Eng., 2012, Article ID 162825. [CrossRef]
Aliabadi, S., Johnson, A., and Abedi, J., 2003, “Comparison of Finite Element and Pendulum Models for Simulation of Sloshing,” Comput. Fluids, 32(4), pp. 535–545. [CrossRef]
Versteeg, H. K., and Malalasekera, W., 2007, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, 2nd ed., Pearson/Prentice Hall, Upper Saddle River, NJ.
Reddy, J. N., and Gartling, D. K., 2001, The Finite Element Method in Heat Transfer and Fluid Dynamics, 2nd ed., CRC Press, Boca Raton, FL.
Zienkiewicz, O. C., Nithiarasu, P., Taylor, R. L., and Ebrary Inc., 2005, The Finite Element Method for Fluid Dynamics, 6th ed., Elsevier Butterworth-Heinemann, Amsterdam/Boston.
Anderson, J. D., 1995, Computational Fluid Dynamics: The Basics With Applications, McGraw-Hill, New York.
Zikanov, O., and Ebrary Inc., 2010, Essential Computational Fluid Dynamics, Wiley, Hoboken, NJ.
Son, G., 2005, “A Level Set Method for Incompressible Two-fluid Flows With Immersed Solid Boundaries,” Numer. Heat Transfer, Part B, 47(5), pp. 473–489. [CrossRef]
Sussman, M., Smereka, P., and Osher, S., 1994, “A Level Set Approach for Computing Solutions to Incompressible 2-phase Flow,” J. Comput. Phys., 114(1), pp. 146–159. [CrossRef]
Gingold, R. A., and Monaghan, J. J., 1977, “Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars,” Mon. Not. R. Astron. Soc., 181(2), pp. 375–389. [CrossRef]
Liu, M. B., and Liu, G. R., 2010, “Smoothed Particle Hydrodynamics (SPH): An Overview and Recent Developments,” Arch. Comput. Meth. Eng., 17(1), pp. 25–76. [CrossRef]
Negrut, D., Tasora, A., Mazhar, H., Heyn, T., and Hahn, P., 2012, “Leveraging Parallel Computing in Multibody Dynamics,” Multibody Sys. Dyn., 27(1), pp. 95–117. [CrossRef]
Idelsohn, S. R., Onate, E., Pin, F. D., and Calvo, N., 2006, “Fluid-Structure Interaction Using the Particle Finite Element Method,” Comput. Meth. Appl. Mech. Eng., 195(17–18), pp. 2100–2123. [CrossRef]
Pin, F. D., Idelsohn, S., Oñate, E., and Aubry, R., 2007, “The ALE/Lagrangian Particle Finite Element Method: A New Approach to Computation of Free-Surface Flows and Fluid-Object Interactions,” Comput. Fluids, 36(1), pp. 27–38. [CrossRef]
Wang, L., Octavio, J. R. J., Wei, C., and Shabana, A. A., “Low Order Continuum-Based Liquid Sloshing Formulation for Vehicle System Dynamics,” ASME J. Comput. Nonlinear Dyn. (in press).
Shabana, A. A., 1998, “Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics,” Nonlinear Dyn., 16(3), pp. 293–306. [CrossRef]
Wei, C., and Shabana, A. A., 2014, “Continuum-Based Liquid Sloshing Model for Vehicle Dynamics,” Department of Mechanical and Industrial Engineering, University of Illinois, Chicago, IL, Technical Report No. MBS2014-1-UIC.
Spencer, A. J. M., 1980, Continuum Mechanics, Longman, London, England.
Shabana, A. A., 2012, Computational Continuum Mechanics, 2nd ed., Cambridge University, Cambridge, UK.
Olshevskiy, A., Dmitrochenko, O., and Kim, C. W., 2013, “Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation,” ASME J. Comput. Nonlinear Dyn., 9(2), p. 021001. [CrossRef]
Ogden, R. W., 1984, Non-Linear Elastic Deformations, Dovers Publications, Mineola, NY.
Shabana, A. A., 2014, Dynamics of Multibody Systems, 4th ed., Cambridge University, Cambridge, UK.
Yu, J., Wojtan, C., Turk, G., and Tap, C., 2012, “Explicit Mesh Surfaces for Particle Base Fluids,” Eurographics, 31(2), pp. 815–824. [CrossRef]
Thürey, N., Wojtan, C., Gross, M., and Turk, G., 2010, “A Multiscale Approach to Meshbased Surface Tension Flows,” ACM Trans. Graphics, 29(4), p. 48. [CrossRef]


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Fig. 1

The 8-node brick fluid element

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Fig. 2

Continuity at the element interface

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Fig. 3

C1 Interface discontinuity in two-IPAE mesh

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Fig. 4

C1 Continuity after applying continuity constraints

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Fig. 6

Boundary conditions

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Fig. 7

Fluid element in a container

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Fig. 8

Fluid/ground surface interaction using one element (a) IPAE example and (b) BSAE example

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Fig. 9

Fluid/ground surface interaction using an eight-IPAE mesh: (a) Without continuity constraints and (b) with continuity constraints

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Fig. 10

The Z component of rx of node number 10 in eight-IPAE mesh (—▪— continuity, Δ without continuity)

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Fig. 11

Effect of surface tension using eight-IPAE mesh

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Fig. 12

Sloshing problem solution using one element [23]

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Fig. 13

Sloshing problem using the FFR formulation



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