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Research Papers

Low Order Continuum-Based Liquid Sloshing Formulation for Vehicle System Dynamics

[+] Author and Article Information
Liang Wang, Ahmed A. Shabana

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

Jesús R. Jiménez Octavio

Mechanical Engineering Department,
Comillas Pontifical University,
Madrid 25-28015, Spain

Cheng Wei

Department of Astronautics Engineering,
Harbin Institute and Technology,
Harbin, Heilongjiang 150001, China

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 9, 2014; final manuscript received June 6, 2014; published online January 21, 2015. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 10(2), 021022 (Mar 01, 2015) (10 pages) Paper No: CND-14-1041; doi: 10.1115/1.4027836 History: Received February 09, 2014; Revised June 06, 2014; Online January 21, 2015

The objective of this investigation is to develop a low order continuum-based liquid sloshing model that can be successfully integrated with multibody system (MBS) algorithms. The liquid sloshing model proposed in this investigation allows for capturing the effect of the distributed inertia and viscosity of the fluid. The fluid viscous forces are defined using the Navier–Stokes equations. In order to demonstrate the use of the approach presented in this study, the assumption of an incompressible Newtonian fluid is considered with a total Lagrangian approach. Fluid properties such as the incompressibility condition are formulated using a penalty method. The low order model that captures the effect of the distributed fluid inertia on the vehicle dynamics is developed in this investigation using the floating frame reference (FFR) formulation. The use of this approach allows for developing an inertia-variant fluid model that accounts for the dynamic coupling between different modes of the fluid displacements. The matrix of position vector gradients and its derivative are formulated using the FFR kinematic description. The position and velocity gradient tensors are used to define the Navier–Stokes stress forces. The proposed liquid sloshing model is integrated with a MBS railroad vehicle model in which the rail/wheel interaction is formulated using a 3D elastic contact formulation that allows for the wheel/rail separation. Several simulation scenarios are used to examine the effect of the distributed liquid inertia on the motion of the railroad vehicle. The results, obtained using the sloshing model, are compared with the results obtained using a rigid body vehicle model. The comparative numerical study presented in this investigation shows that the effect of the sloshing tends to increase the possibility of wheel/rail separation as the forward velocity increases, thereby increasing the possibility of derailments at these relatively high speeds.

Copyright © 2015 by ASME
Topics: Fluids , Sloshing , Vehicles
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References

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Figures

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Fig. 1

FFR coordinate system

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Fig. 2

FE coordinate systems

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Fig. 3

Fluid element boundary constraints

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Fig. 5

The S-shape curved track

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Fig. 6

Lateral displacement of the rear wheelset with forward velocity of 25 m/s (56 mph) (—▪— rigid body, —△— flexible body)

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Fig. 7

Lateral displacement of the rear wheelset with forward velocity of 35 m/s (78 mph) (—▪— rigid body, —△— flexible body)

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Fig. 8

Lateral displacement of the rear wheelset with forward velocity of 60 m/s (134 mph) (—▪— rigid body, —△— flexible body)

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Fig. 9

Lateral displacement of the car body with forward velocity of 60 m/s (134 mph) (—▪— rigid body, —△— flexible body)

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Fig. 10

Normal contact force on the right wheel of the rear wheelset of the rear bogie in the rigid body model with forward velocity of 60 m/s (134 mph)

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Fig. 11

Normal contact force on the right wheel of the rear wheelset of the rear bogie in the fluid body model with forward velocity of 60 m/s (134 mph)

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Fig. 12

Change of the fluid shape due to sloshing

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Fig. 13

Lateral displacement of the rear wheelset with respect to the track (—▪— rigid body, —△— fluid body)

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Fig. 14

Change of the center of mass with respect to the track (—▪— rigid body, —△— fluid body)

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Fig. 15

Normal contact force of the right wheel of the rear wheelset of the rear bogie (—▪— rigid body, —△— fluid body)

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Fig. 16

Normal contact force of the left wheel of the rear wheelset of the rear bogie (—▪— rigid body, —△— fluid body)

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Fig. 17

Lateral displacement of the car body using different damping coefficients (— c = 0, - - - c = 50, - · - ·  - ·  c = 100, ······ rigid model)

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