Articles

Dynamics of a fluid-filled curvilinear pipeline

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  • Computing Center of Far-Eastern Branch, Russian Academy of Sciences, Khabarovsk 680000, Russia

Received date: 2017-08-14

  Revised date: 2017-12-29

  Online published: 2018-06-01

Supported by

Project supported by the Russian Science Foundation (No. 18-11-00021)

Abstract

A mathematical model is presented, and numerical experiments are performed to describe the mechanics of the slow movement of a pipeline. The problem reduction algorithm to one-dimensional formulation is offered. Results of numerical experiment for the model problem are adduced. The proposed mathematical model is found to adequately describe the dynamics of known phenomena of pipes. The cross-sections of the extended curvilinear thin-walled pipeline are numerically demonstrated to experience warping, which has experimental confirmation in the literature.

Cite this article

V. A. RUKAVISHNIKOV, O. P. TKACHENKO . Dynamics of a fluid-filled curvilinear pipeline[J]. Applied Mathematics and Mechanics, 2018 , 39(6) : 905 -922 . DOI: 10.1007/s10483-018-2338-9

References

[1] Feodosiev, V. I. Advanced Stress and Stability Analysis:Worked Examples, Springer-Verlag, Berlin/Heidelberg (2005)
[2] Towhata, I. Geotechnical Earthquake Engineering, Springer-Verlag, Berlin/Heidelberg (2008)
[3] Paidoussis, M. P. Fluid-structure interactions. Slender Structures and Axial Flow, Academic Press, San Diego/London (1998)
[4] Bai, Y. Pipelines and Risers, Elsevier, Amsterdam (2003)
[5] Bashurov, V. V., Vaganova, N. A., Kropotov, A. I., Pchelintsev, M. V., Skorkin, N. A., and Filimonov, M. Y. Nonlinear model of a pipeline in a gravity field with an ideal fluid moving through it. Journal of Applied Mechanics and Technical Physics, 53(1), 43-48(2012)
[6] Liu, R., Wang, W. G., Yan, S. W., and Wu, X. L. Engineering measures for preventing upheaval buckling of buried submarine pipelines. Applied Mathematics and Mechanics (English Edition), 33(6), 781-796(2012) https://doi.org/10.1007/s10483-012-1586-6
[7] Liu, R., Liu, W. B., Wu, X. L., and Yan, S. W. Global lateral buckling analysis of idealized subsea pipelines. Journal of Central South University, 21(1), 416-427(2014)
[8] Wang, B. and Zhou, J. Strain analysis of buried steel pipelines across strike-slip faults. Journal of Central South University of Technology, 18(5), 1654-1661(2011)
[9] Kim, J. Harmonic axisymmetric thick shell element for static and vibration analyses. KSME International Journal, 18(10), 1747-1754(2004)
[10] Rodrigues, M. R., Zouain, N., Borges, L., and de Souza, N. E. A. A continuum-based mixed axisymmetric shell element for limit and shakedown analysis. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 36(1), 153-172(2014)
[11] Sun, J., Xu, X., Lim, C. W., and Tan, V. B. C. An energy conservative symplectic methodology for buckling of cylindrical shells under axial compression. Acta Mechanica, 224(8), 1579-1592(2013)
[12] Zubov, L. M. Equations of nonlinear dynamics of elastic shells in cylindrical Eulerian coordinates. Doklady Physics, 61(5), 218-222(2016)
[13] Rukavishnikov, V. A. and Tkachenko, O. P. Numerical and asymptotic solution of the equations of propagation of hydroelastic vibrations in a curved pipe. Journal of Applied Mechanics and Technical Physics, 41(6), 1102-1110(2000)
[14] Rukavishnikov, V. A. and Tkachenko, O. P. Nonlinear equations of motion of an extensible underground pipeline:derivation and numerical modeling. Journal of Applied Mechanics and Technical Physics, 44(4), 571-576(2003)
[15] Rukavishnikov, V. A. and Tkachenko, O. P. Effect of the pipe curvature on internal elastic wave propagation. Computational Mathematics and Mathematical Physics, 50(11), 1886-1894(2010)
[16] Rukavishnikov, V. A. and Tkachenko, O. P. Numerical analysis of the mathematical model of hydroelastic oscillations in a curved pipeline. Mathematical Models and Computer Simulations, 3(4), 508-516(2011)
[17] Rukavishnikov, V. A. and Tkachenko, O. P. Approximate solution to the nonlinear problem of an underground pipeline deformation. Journal of Applied and Industrial Mathematics, 6(1), 100-110(2012)
[18] Sedov, L. I. A Course in Continuum Mechanics, Vol. 4, Translation from the Russian (ed. Radok, J. R. M.), Wolters-Noordhoff, Groningen (1971)
[19] Sasic, R. and Sasic, S. A new approach to the velocity field investigation in case of the entry flow in curved pipes with circular cross section. Acta Mechanica, 140, 103-117(2000)
[20] Novozhilov, V. V. and Radok J. R. M. Thin Shell Theory (Paperback, Softcover Reprint of the Original 1st ed. 1964), Springer-Verlag, Netherlands (2014)
[21] Goto, S. I. Amplitude equations for a linear wave equation in a weakly curved pipe. Journal of Physics A:Mathematical and Theoretical, 42(44), 445205(2009)
[22] Nikuradse, J. Laws of Flow in Rough Pipes, Technical Memorandum 1292, Translation of "Strömungsgesetze in Rauhen Rohren."\VDI-Forschungsheft 361. Beilage zu "Forschung auf dem Gebiete des Ingenieurwesens"\Ausgabe B Band 4, July/August 1933, NACA, Washington (1950)
[23] Loitsyanskii, L. G. Mechanics of Liquids and Gases, Pergamon Press, Oxford/New York (1966)
[24] Landau, L. D. and Lifshitz, E. M. Fluid Mechanics (Volume 6 of A Course of Theoretical Physics), Butterworth-Heinemann, Oxford (1987)
[25] Havil, J. Gamma:Exploring Euler's Constant, Princeton University Press, Princeton (2003)
[26] Widjaja, B. and Lee, S. H. H. Flow box test for viscosity of soil in plastic and viscous liquid states. Soils and Foundations, 53(1), 35-46(2013)
[27] Gol' Denveizer, A. L., von Karman, T., and Dryden, H. L. Theory of Elastic Thin Shells:Solid and Structural Mechanics, Elsevier, New York (2014)
[28] Popov, Y. P. and Samarskii, A. A. Difference Methods for Solving Problems Gas Dynamics (in Russian), Nauka, Moscow (1992)
[29] Vlasov, V. Z. The General Principles of Construction of The Technical Theory of Shells (in Russian)/Vlasov, V. Z. Selected Works, Vol. 2, RAS, Mocsow, 467-503(1963)
[30] Timoshenko, S. P. Strength and Vibrations of Structural Elements (in Russian), Nauka, Moskow, 284-291(1975)
[31] Timoshenko, S. P. Strength of Materials, Part I:Elementary Theory and Problems, 3rd ed., D. Van Nostrand Company, Princeton (1955)
[32] Athisakul, C., Monprapussorn, T., Pulngern, T., and Chucheepsakul, S. The effect of axial extensibility on three-dimensional behavior of tensioned pipes/risers transporting fluid. Proceedings of the Eighth ISOPE Pacific/Asia Offshore Mechanics Symposium, the International Society of Offshore and Polar Engineers, Bangkok, 97-104(2008)
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