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Tytuł artykułu

Mathematical model and numerical computations of transient pipe flows with fluid-structure interaction

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Transient flows in closed conduits are of interest from over a century, but the dynamic interaction between the fluid and the pipe is taken into consideration more thoroughly just from a few decades. A standard model of the phenomenon consists of fourteen first order partial differential equations (PDE), two for a one-dimensional (1D) liquid flow and twelve for 3D pipe motion. In many practical cases however, a simpler four equations (4E) model can be used, where 1D longitudinal pipe movement is assumed. A short description of waterhammer event with fluidstructure interaction taken into account is presented in the article. The 4E mathematical model is presented in detail with the assumptions and main algorithms of computer program that has been developed. Two phase flow is assumed not to take place, but the friction between the liquid and the pipe wall are taken into consideration. A method of characteristics (MOC) with time marching procedure is employed for finding the solutions, but instead of direct solving the resulting finite difference equations (FDE) the “wave method” is proposed. Some other important elements of the algorithm are presented and selected results of numerical computations as well.
Rocznik
Tom
Strony
77--94
Opis fizyczny
Bibliogr. 24 poz., rys., tab.
Twórcy
autor
  • The Szewalski Institute of Fluid Flow Machinery, Polish Academy of Sciences, Hydraulic Machinery Department, ul. J. Fiszera 14, 80-231 Gdańsk, Poland
Bibliografia
  • [1] Wylie E.B., Streeter V.L.: Fluid Transients. McGraw-Hill, 1978.
  • [2] Almeida A.B., Koelle E.: Fluid Transient in Pipe Networks. Comp. Mech. Publ, Southampton – Boston & Elsevier AS, London 1992.
  • [3] Adamkowski A.: Transients in fluid-flow systems of rotor water machines. Scientific Journals of the IFFM (Institute of Fluid-Flow Machinery PAS) 534/1493/2004, Gdańsk 2004 (in Polish).
  • [4] Ghidaoui M., Ming Zao, McIlnnis D., Axworthy D.: A review of water hammer theory and practise. Applied Mechanics Review 58(2005), 49–76.
  • [5] Wiggert D.C., Hatfield F.J., Stuckenbruck S.: Analysis of liquid and structural transients in piping by the method of characteristics. Trans. ASMEJournal of Fluids Engineering 109(1987),161–165.
  • [6] Tijsseling A.S.: Fluid-structure interaction in liquid-filled pipe systems: a review. Journal of Fluids and Structures 10(1996), 109–146.
  • [7] Wang Z.M., Tan S.K.: Coupled analysis of fluid transient and structural dynamic responses of a pipeline system. Journal of Hydraulic Research 35(1997), 1, 119–131.
  • [8] Zhang L., Tijsseling A.S., Vardy A.E.: FSI analysis of liquid filled pipes. Journal of Sound and Vibration 224(1999), 69–99.
  • [9] Wiggert D., Tijsseling A.: Fluid transients and fluid-structure interaction in flexible liquid-filled piping. Applied Mechanics Review 54(2001), 455–481.
  • [10] Adamkowski A., Lewandowski M.: Experimental examination of unsteady friction models for transient pipe flow simulation. Trans. ASME Journal of Fluids Engineering 128(2006).
  • [11] Lewandowski M.: Friction models in waterhammer analyses. PhD thesis, IFFM, Gdańsk 2008 (in Polish).
  • [12] Budny D.D., Wiggert D.C., Hatfield F.J.: The influence of structural damping on internal pressure during a transient pipe flow. Journal of Fluids Engineering – ASME 113(1991), 424–429.
  • [13] Bergant A., Simpson A.R., Tijsseling A.S.: Water hammer with column separation: A historical review. Journal of Fluids and Structures 22(2006), 135–171.
  • [14] Timoshenko S., Young D.H.: Vibration Problems in Engineering, 3rd ed. Nostrad Comp., 1955.
  • [15] Meirovitch L.: Analytical Methods in Vibrations. The Macmillan Company, New York 1967.
  • [16] Gutowski R., Swietlicki W.: Dynamics and Vibrations of Mechanical Systems. PWN, Warsaw 1986 (in Polish).
  • [17] Cowper G.R.: The shear coefficient in Timoshenko’s beam theory. Journal of Applied Mechanics – ASME (1966), 335–340.
  • [18] Hutchinson J.R.: Shear coefficients for Timoshenko beam theory. Journal of Applied Mechanics – ASME 68(2001), 87–92.
  • [19] Henclik S.: Mathematical description and numerical algorithms of computer program for transient flows and FSI modelling (not published). IFFM internal report No. 369/09 (also 694/08), Gdańsk 2009 (in Polish).
  • [20] Quarteroni A., Valli A.: Numerical Approximation of Partial Differential Eaquations. Springer Verlag, Berlin – Heidelberg 1994.
  • [21] Bjoerck A., Dahlquist G.: Numerical Methods. PWN, Warsaw 1987 (in Polish). (Also English ed. Prentice Hall, 1974).
  • [22] Adamkowski A.: Analysis of transient flow in pipes with expanding and contracting sections. Journal of Fluids Engineering – ASME 125(2003).
  • [23] Tijsseling A.S.: Water hammer with fluid structure interaction in thick-walled pipes. Computer and Structures 85(2007), 844–851.
  • [24] Adamkowski A., Lewandowski M.: A new method for numerical prediction of liquid column separation accompanying hydraulic transients in pipelines. Journal of Fluids Engineering – ASME 131(2009).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWM8-0006-0004
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