Numerical study of the influence of surface defects on the stability of a cylindrical pipe containing fluid

S. A. Bochkarev ; S. V. Lekomtsev ; A. N. Senin

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 3, pp. 557-573.

Résumé

This paper is concerned with the dynamic behavior of an elastic cylindrical pipe with surface defects interacting with the internal flow of a compressible fluid. A defect in the form of a ring of rectangular cross-section is located on the inner or outer surface of an elastic body and characterized by its own set of physico-mechanical parameters. The behavior of an ideal compressible fluid is described using the potential theory, and the behavior of the pipe is considered in the framework of the linear theory of elasticity. The hydrodynamic pressure exerted by the fluid on the inner surface of the pipe (defect) is determined with the use of the Bernoulli equation. A mathematical formulation of the problem of the elastic body dynamics is based on the variational principle of virtual displacements, and the system of equations for a liquid medium is developed using the Bubnov-Galerkin method. For the numerical implementation of the algorithm, a semi-analytic version of the finite element method is used. The stability of the system is estimated based on the results of computation and analysis of complex eigenvalues for a coupled system of equations. Verification of the model is carried out for the case of an ideal pipe by comparing the obtained results with the known experimental and numerical data. The effect of the geometric and physico-mechanical parameters of the defect on the critical fluid velocity responsible for the loss of stability is studied for a cylindrical pipe clamped at both ends. It is shown that defects reduce the boundary of hydroelastic stability. It has been found that the defect located on the outer surface of the pipe exerts a greater impact on the system stability than it does when located on the wetted surface of the pipe.

Détail

Keywords: finite element method, theory of elasticity, surface defect, cylindrical pipe, hydroelastic stability, potential compressible flow.

Bibliographie

[1] Li X., Bai Y., Su C., Li M., “Effect of interaction between corrosion defects on failure pressure of thin wall steel pipeline”, Int. J. Pres. Ves. Pip., 138 (2016), 8–18 | DOI

[2] Silva R. C. C., Guerreiro J. N. C., Loula A. F. D., “A study of pipe interacting corrosion defects using the FEM and neural networks”, Adv. Eng. Softw., 38:11–12 (2007), 868–875 | DOI

[3] Khalajestani M. K., Bahaari M. R., “Investigation of pressurized elbows containing interacting corrosion defects”, Int. J. Pres. Ves. Pip., 123 (2014), 77–85 | DOI

[4] Ouglova A., Berthaud Y., François M., Foct F., “Mechanical properties of an iron oxide formed by corrosion in reinforced concrete structures”, Corrosion Sci., 48:12 (2006), 3988–4000 | DOI

[5] Vanaei H. R., Eslami A., Egbewande A., “A review on pipeline corrosion, in-line inspection (ILI), and corrosion growth rate models”, Int. J. Pres. Ves. Pip., 149 (2017), 43–54 | DOI

[6] Xu L., Cheng Y. F., “A finite element based model for prediction of corrosion defect growth on pipelines”, Int. J. Pres. Ves. Pip., 153 (2017), 70–79 | DOI

[7] Benjamin A. C., Freire J. L. F., Vieira R. D., Cunha D. J. S., “Interaction of corrosion defects in pipelines – Part 1: Fundamentals”, Int. J. Pres. Ves. Pip., 144 (2016), 56–62 | DOI

[8] Shariati M., Rokhi M. M., “Buckling of steel cylindrical shells with an elliptical cutout”, Int. J. Steel Struct., 10:2 (2010), 193–205 | DOI

[9] Sukhinin S. N., Shivrin M. V., “Axial rigidity study of multilayer composite cilidrical shells with local defects”, Compos. Mater. Construct., 2014, no. 1, 3–7 (In Russian)

[10] Lykhachova O., “Numerical simulation of axially compressed cylindrical shells with circular cutouts”, Mechanics Mechanical Eng., 20:3 (2016), 309–321 Available at (July 24, 2018) http://kdm.p.lodz.pl/articles/2016/20_3_9L.pdf

[11] Jiao P., Chen Z., Xu F., Tang X., Su W., “Effects of ringed stiffener on the buckling behavior of cylindrical shells with cutout under axial compression: Experimental and numerical investigation”, Thin Wall. Struct., 123 (2018), 232–243 | DOI

[12] Wang L., Ni Q., “Vibration of slender structures subjected to axial flow or axially towed in quiescent fluid”, Adv. Acoust. Vib., 2009 (2009), 432340 | DOI

[13] Païdoussis M. P., Slender Structures and Axial Flow, v. 1, Fluid-structure Interactions, Academic Press, London, 2014, 888 pp.; | DOI

[14] Païdoussis M. P., Slender Structures and Axial Flow, v. 2, Fluid-structure Interactions, Academic Press, London, 2016, 942 pp.; | DOI

[15] Zhang Y. L., Reese J. M., Gorman D. G., “Finite element analysis of the vibratory characteristics of cylindrical shells conveying fluid”, Comp. Methods Appl. Mech. Eng., 191 (2002), 5207–5231 | DOI | Zbl

[16] Zhang Y. L., Reese J. M., Gorman D. G., “Initially-tensioned orthotropic cylindrical shells conveying fluid: a vibration analysis”, J. Fluid. Struct., 16:1 (2002), 53–70 | DOI

[17] Zhang Y. L., Reese J. M., Gorman D. G., “A comparative study of axisymmetric finite elements for the vibration of thin cylindrical shells conveying fluid”, Int. J. Numer. Meth. Eng., 54:1 (2002), 89–110 | DOI | Zbl

[18] Uğurlu B., Ergin A., “A hydroelasticity method for vibrating structures containing and/or submerged in flowing fluid”, J. Sound Vib., 290:3–5 (2006), 572–596 | DOI

[19] Uğurlu B., Ergin A., “A hydroelastic investigation of circular cylindrical shells-containing flowing fluid with different end conditions”, J. Sound Vib., 318:4–5 (2008), 1291–1312 | DOI

[20] Uğurlu B., Ergin A., “The dynamics and stability of circular cylindrical shells containing and submerged in flowing fluid using a higher order boundary element method”, P. I. Mech. Eng. M.-J. Eng., 223:4 (2009), 489–502 | DOI

[21] Firouz-Abadi R. D., Noorian M. A., Haddadpour H., “A fluid–structure interaction model for stability analysis of shells conveying fluid”, J. Fluid. Struct., 26:5 (2010), 747–763 | DOI

[22] Bochkarev S. A., Lekomtsev S. V, “Numerical simulation of an elastic tube containing a flowing fluid”, PNRPU Mechanics Bulletin, 2011, no. 3, 5–14 (In Russian)

[23] Timoshenko S. P., Goodier J. N., Theory of elasticity, McGraw-Hill, New York, 1970, xxiv+567 pp. | Zbl

[24] Ilgamov M. A., Kolebaniia uprugikh obolochek, soderzhashchikh zhidkost' i gaz [Oscillations of elastic shells containing liqiud and gas], Nauka, Moscow, 1969, 182 pp. (In Russian)

[25] Bochkarev S.A., Matveenko V.P., “Numerical study of the influence of boundary conditions on the dynamic behavior of a cylindrical shell conveying a fluid”, Mech. Solids, 43:3 (2008), 477–486 | DOI

[26] Zienkiewicz O. C., The finite element method in engineering science, McGraw Hill, London, 1971, 521 pp. | Zbl

[27] Païdoussis M. P., Denise J.-P., “Flutter of thin cylindrical shells conveying fluid”, J. Sound Vib., 20 (1972), 9–26 | DOI