0
Research Papers

Fluid-Conveying Flexible Pipes Modeled by Large-Deflection Finite Elements in Multibody Systems

[+] Author and Article Information
J. P. Meijaard

Laboratory of Mechanical
Automation and Mechatronics,
University of Twente,
Enschede NL-7500 AE, The Netherlands;
Olton Engineering Consultancy,
Enschede NL-7514 BC, The Netherlands
e-mail: J.P.Meijaard@utwente.nl

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 15, 2013; final manuscript received July 5, 2013; published online October 9, 2013. Assoc. Editor: Johannes Gerstmayr.

J. Comput. Nonlinear Dynam 9(1), 011008 (Oct 09, 2013) (7 pages) Paper No: CND-13-1007; doi: 10.1115/1.4025353 History: Received January 15, 2013; Revised July 05, 2013

The modeling and simulation of flexible multibody systems containing fluid-conveying pipes are considered. It is assumed that the mass-flow rate is prescribed and constant and the pipe cross section is piecewise uniform. An existing beam element capable of handling large motions is modified to include the effect of the fluid flow and the initial curvature of the pipe. The modified element is incorporated in a finite-element based multibody system dynamics program, which takes care of the connection with other parts of the system and the simulation. The element is applied in several test problems: the buckling of a simply supported pipe, the flutter instability of a cantilever pipe, and the motion of a curved pipe that can rotate about an axis perpendicular to its plane. As a three-dimensional example, a Coriolis mass-flow rate meter with a U-shaped pipe is considered.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Païdoussis, M. P., 1998, Fluid–Structure Interactions: Slender Structures and Axial Flow, Vol. 1, Elsevier, New York.
Benjamin, T. B., 1961, “Dynamics of a System of Articulated Pipes Conveying Fluid I. Theory,” Proc. R. Soc. London, Ser. A, 261, pp. 457–486. [CrossRef]
Benjamin, T. B., 1961, “Dynamics of a System of Articulated Pipes Conveying Fluid II. Experiments,” Proc. R. Soc. London, Ser. A, 261, pp. 487–499. [CrossRef]
Irschik, H., and Holl, H. J., 2002, “The Equations of Lagrange Written for a Non-Material Volume,” Acta Mech., 153, pp. 231–248. [CrossRef]
Gregory, R. W., and Païdoussis, M. P., 1966, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid I. Theory,” Proc. R. Soc. London, Ser. A, 293, pp. 512–527. [CrossRef]
Gregory, R. W., and Païdoussis, M. P., 1966, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid II. Experiments,” Proc. R. Soc. London, Ser. A, 293, pp. 528–542. [CrossRef]
Bajaj, A. K., and Sethna, P. R., 1984, “Flow Induced Bifurcations to Three-Dimensional Oscillatory Motions in Continuous Tubes,” SIAM J. Appl. Math., 44, pp. 270–286. [CrossRef]
Stangl, M., Gerstmayr, J., and Irschik, H., 2009, “A Large Deformation Planar Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation,” ASME J. Comput. Nonlinear Dyn., 4, p. 031009. [CrossRef]
Sultan, G., and Hemp, J., 1989, “Modelling of the Coriolis Mass Flowmeter,” J. Sound Vib., 132, pp. 473–489. [CrossRef]
Mehendale, A., 2008, “Coriolis Mass Flow Rate Meters for Low Flows,” Ph.D. thesis, University of Twente, Enschede, The Netherlands.
Meijaard, J. P., 1996, “Validation of Flexible Beam Elements in Dynamics Programs,” Nonlinear Dyn., 9, pp. 21–36. [CrossRef]
Jonker, J. B., and Meijaard, J. P., 2013, “A Geometrically Non-Linear Formulation of a Three-Dimensional Beam Element for Solving Large Deflection Multibody System Problems,” Int. J. Non-Linear Mech., 53, pp. 63–74. [CrossRef]
Cowper, G. R., 1966, “The Shear Coefficient in Timoshenko's Beam Theory,” ASME J. Appl. Mech., 33(2), pp. 335–340. [CrossRef]
Jonker, J. B., and Meijaard, J. P., 1990, “SPACAR—Computer Program for Dynamic Analysis of Flexible Spatial Mechanisms and Manipulators,” Multibody Systems Handbook, W.Schiehlen, ed., Springer-Verlag, Heidelberg, Germany, pp. 123–143.
Jonker, J. B., Aarts, R. G. K. M., and van Dijk, J., 2009, “A Linearized Input–Output Representation of Flexible Multibody Systems for Control Synthesis,” Multibody Syst. Dyn., 21, pp. 99–122. [CrossRef]
Pratap, R., 2006, Getting Started with MATLAB7: A Quick Introduction for Scientists and Engineers, Oxford University, New York.
Cheesewright, R., and Shaw, S., 2006, “Uncertainties Associated With Finite Element Modelling of Coriolis Mass Flow Meters,” Flow Meas. Instrum., 17, pp. 335–347. [CrossRef]
Feynman, R. P., 1985, “Surely You're Joking, Mr. Feynman!”: Adventures of a Curious Character, Norton, New York.
Païdoussis, M. P., 1997, “Fluid–Structure Interactions Between Axial Flows and Slender Structures,” Proceedings of the 19th International Congress of Theoretical and Applied Mechanics, T.Tatsumi, E.Watanabe, and T. Kambe, eds., Kyoto, Japan, Aug. 25–31, 1996, Elsevier, Amsterdam, pp. 427–442.
Hamel, G., 1949, Theoretische Mechanik, eine einheitliche Einführung in die gesamte Mechanik, Springer-Verlag, Berlin.
Samer, G., and Fan, S.-C., 2010, “Modeling of Coriolis Mass Flow Meter of a General Plane-Shape Pipe,” Flow Meas. Instrum., 21, pp. 40–47. [CrossRef]
Misra, A. K., Païdoussis, M. P., and Van, K. S., 1988, “On the Dynamics of Curved Pipes Transporting Fluid. Part I: Inextensible Theory,” J. Fluids Struct., 2, pp. 221–244. [CrossRef]
Misra, A. K., Païdoussis, M. P., and Van, K. S., 1988, “On the Dynamics of Curved Pipes Transporting Fluid. Part II: Extensible Theory,” J. Fluids Struct., 2, pp. 245–261. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Simply supported pipe

Grahic Jump Location
Fig. 3

Transient tip deflection for a cantilever pipe with m· = 30kg/s; dashed-dotted: two elements; dashed: four elements; fully drawn: eight elements

Grahic Jump Location
Fig. 4

Semicircular rotating pipe

Grahic Jump Location
Fig. 5

Angular velocity of a rotating curved pipe; dotted: EI = 10 Nm2; dashed-dotted: EI = 100 Nm2; dashed: EI = 1000 Nm2; fully drawn: rigid

Grahic Jump Location
Fig. 6

U-shaped mass-flow rate meter pipe. The sensors are at the positions S1 and S2.

Grahic Jump Location
Fig. 7

Dimensionless natural circular frequency as a function of the dimensionless mass-flow rate for a water-filled pipe with b = 3a; fully drawn: present study; dashed: from Ref. [9]

Grahic Jump Location
Fig. 8

Time difference of zero crossing between the two measurement points as a function of the mass-flow rate

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In