DYNAMIC STABILITY OF A STRAIGHT PIPE CONVEYING PULSATILE FLOW UNDER THERMAL LOADS

Lolov, D.S.; Lilkova-Markova, Sv.V.

doi:10.15593/perm.mech/2023.2.01

DYNAMIC STABILITY OF A STRAIGHT PIPE CONVEYING PULSATILE FLOW UNDER THERMAL LOADS

D.S. Lolov, Sv.V. Lilkova-Markova

Author details

D.S. Lolov
University of Architecture, Sofia, Bulgaria
Sv.V. Lilkova-Markova
University of Architecture, Sofia, Bulgaria

https://doi.org/10.15593/perm.mech/2023.2.01

Pipes conveying fluid are considered as a fundamental dynamical problem in the field of fluid-structure interaction. They are widely used in the petroleum industry, in nuclear engineering, aviation and aerospace, in nanostructures. This article investigates the effect of temperature load on the dynamic stability of a straightpipe conveying pulsatile flow. The fluid velocity is a harmonic function of time. The Galerkin method is applied for the solution of the differential equation of the transverse vibrations of the pipe. The differential equation is reduced to a first-order differential equation system. The system of differential equations is transformed and rewritten in a matrix form. The harmonic function of the fluid velocity allows the Floquet theory to be applied in order to investigate the dynamic stability of the system. The static scheme of the investigated pipe is a beam with restricted horizontal and vertical displacements at both of its ends. A numerical solution for a straight pipe conveying fluid with specified geometric and physical characteristics has been carried out. The temperatureload and the constant fluid rate are considered as parameters of the problem. The results show that the temperature load affects the vibrational characteristics of the pipe, as well as its critical velocity.

Keywords

pipefluiddynamic stabilitythermal loadpulsatile flow.

Bibliography

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27.Jung D, Chung J. In-plane and out-of-plane motions of an extensible semi-circular pipe conveying fluid. Journal of Sound and Vibration, 2008, Vol.311(1), pp.408–420. Scholar
28.Liu G., Li S., Karney B.Y. Vibration analysis of curved pipes conveying fluid. Proceedings of the ASME 2014 Pressure Vessels & Piping Conference, Anaheim, California, USA. 2014, Vol.3. Scholar
29.Lolov D., Lilkova-Markova Sv. Free vibrations out-of-plane of curved planar pipe conveying fluid in two cases of supporting. Annual of UACEG, Mathematics. Mechanics. 2006, Vol. 72(2), pp.123-128. Scholar
30.Liang F., Yang X.-D., Bao R.-D., Zhang W. Frequency Analysis of Functionally Graded Curved Pipes Conveying Fluid. Advances in Materials Science and Engineering. 2016, Vol.2016, Article ID 7574216. Scholar
31.Zhao Q., Sun Z. Flow-induced vibration of curved pipe conveying fluid by a new transfer matrix method. Engineering applications of computational applied mechanics. 2018, Vol. 12(1), pp. 780-790. Scholar
32.Zhao Q., Sun Z. In-plane forced vibration of curved pipe conveying fluid by Green function method. Applied Mathematics and Mechanics (English Edition). 2017, Vol.38(10), pp. 1397-1414. Scholar
33.Wu J., Shih P. The dynamic analysis of a multispan fluid-conveying pipe subjected to external load. Journal of sound and vibration. 2001, Vol.239(2), pp. 201-215. Scholar
34.Chicone C. Ordinary Differential Equations with applications, Springer Science+ Business, 1999 Scholar
35.Inspeger Т., Horvath R. Pendulum with harmonic variation of the suspension point. Periodica Polytechnica. 2000, Vol. 44, pp. 39-46. Scholar
36.Akulenko L.D., Georgievskii D.V., Nesterov S.V. Spectrum of Transverse Vibrations of a Pipeline Element under Longitudinal Load. Doklady Physics. 2016, Vol. 61 (3), pp. 129–132. Scholar
37.Gay-Balmaz F., Georgievskii D., Putkaradze V. Stability of Helical Tubes Conveying Fluid. Journal of Fluids and Structtures. 2018. Vol 78 (2), pp. 146–174. Scholar
38.Il’ichev A.T. Dynamics and spectral stability of soliton-like structures in fluid-filled membrane tubes. Russian Math. Surveys. 2020. Vol 75 (5), pp. 843–882 Scholar

1.Belhadi A., Boukhalfa A., Belalia S.A. Free vibration modeling of single-walled carbon nanotubes using the differential quadrature method. Mathematical modeling of engineering problems. 2017, Vol. 4 (1), pp. 33-37. Scholar
2.Reddy, C.D., Lu C., Rajendran S., Liew K.M. Free vibration analysis of fluid conveying single-walled carbon nanotubes. Applied Physics Letters. 2007, Vol. 90, pp. 133122. Scholar
3.Yoon, J., Ru C., Mioduchowski A. Vibration and instability of carbon nanotubes conveying fluid. Composites Science and Technology. 2005, Vol.65 - pp. 1326 - 1336. Scholar
4.Lolov D.S., Lilkova-Markova Sv. V. Dynamic stability of double-walled carbon nanotubes. Journal of the Serbian Society for Computational Mechanics. 2018, Vol.12(1), pp.1-8. Scholar
5.Yoon J., Ru C.Q., Mioduchowski A, Flow-induced flutter instability of cantilever CNTs. Int. J. Solids Struct. 2006, Vol.43, pp. 3337–3349. Scholar
6.Yoon J., Ru C.Q., Mioduchowski A, Vibration and instability of CNTs conveying fluid. Compos. Sci. Technol. 2005, Vol. 65, pp. 1326–1336. Scholar
7.Wang X.Y., Wang X., Sheng G.G. The coupling vibration of fluid-filled carbon nanotubes. J. Phys. D: Appl. Phys. 2007, Vol.40, pp.2563–2572. Scholar
8.Dong K., Wang X. Wave propagation in carbon nanotubes under shear deformation. Nanotechnology. 2006, Vol. 17, pp. 2773–2782. Scholar
9.Dong K., Wang X., Sheng G.G. Wave dispersion characteristics in fluid-filled carbon nanotubes embedded in an elastic medium. Model. Simul. Mater. Sci. Eng. 2007, Vol.15, pp. 427–439. Scholar
10.Jeong W., Soo Y., Jeong S.,Lee S., Yoo W. Stability Analysis of a pipe conveying periodically pulsating fluid using finite element method. JSME International Journal. 2006, Vol. 49, pp. 1116-1122. Scholar
11.Paidoussis M. Fluid-structure interactions: Slender Structures and Axial flow, Academic Press, London, 1998. Scholar
12.Paidoussis M., Issid N. Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration. 1974, Vol. 33(3), pp. 267-284. Scholar
13.Deng Q., Yang Z. Wave propagation in submerged pipe conveying fluid. Acta Mechanica Solida Sinica. 2019, Vol.32(4), pp. 483-498. Scholar
14.Lolov D. S., Lilkova-Markova Sv. Dynamic stability of a fluid-immersed pipe conveying fluid and resting on a damped Winkler elastic foundation. Proceedings of XI International Conference Industrial Engineering and Environment Protection 2021 (IIZS 2021), October 7-8th, 2021, Zrenjanin, Serbia. pp.49-55. Scholar
15.Hellum A., Mukherjee R., Hull A. Flutter instability of a fluid-conveying fluid-immerced pipe affixed to a rigid body. Journal of Fluids and Structures. 2011, Vol.27, pp. 1086-1096. Scholar
16.Lin W., Qiao N. Vibration and stability of an axially moving beam immersed in fluid. International Journal of Solids and Structures. 2008, Vol. 45, pp. 1445-1457. Scholar
17.Huang Q., Lin T., Safarpour M. Flow-induced vibration attenuation of a viscoelastic pipe conveying fluid under sinusoidal flow, using a nonlinear absorber. Mechanics Based design of Structures and Machines. 2020, Vol. 50, pp. 1673-1703. Scholar
18.Liang F., Gao A., Yang X.D. Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans. Applied Mathematical Modeling. 2020, Vol. 83, pp. 454-469. Scholar
19.Askarian A.R., Permoon M.R., Shakouri M. Vibration analysis of pipes conveying fluid resting on a fractional Kelvin-Voigt viscoelastic foundation with general boundary conditions. International Journal of Mechanical Sciences. 2020. Vol. 179, pp. 105702. Scholar
20.Cao J., Liu Y., Liu W. The effect of two cases of temperature distributions on vibration of fluid-conveying functionally graded thin-walled pipes. Journal of Strain Analysis. 2018, Vol. 53(5), pp. 324-331. Scholar
21.Ameen K.A., Al-Dulaimi M.J., Hatem A.A. Experimental study of vibration on pipe conveying fluid at different end conditions for different fluid temperatures. Engineering and Technology Journal. 2019, Vol. 37, pp. 512-515. Scholar
22.Li B., Wang Z., Jing L. Dynamic response of pipe conveying fluid with lateral moving supports. Shock and Vibration. 2018, Vol. 2018, pp. 1-17. Scholar
23.Al-Waily M., Al-Baghdadi M., Al-Khayat R. Flow Velocity and Crack Angle Effect on Vibration and Flow Characterization for Pipe Induced Vibration. International Journal of Mechanical & Mechatronics Engineering. 2017, Vol. 17(5), pp. 19-27. Scholar
24.Siba M., Wahmahmood W., Zakinuaw M., Rasani R., Nassir M. Flow-induced vibrations in pipes: challengess and solutions – a review. Journal of Engineering Science and Technology. 2016, Vol. 11(3), pp. 362-382. Scholar
25.Faal R., Derakhshan D. Flow-Induced Vibration of Pipeline on Elastic Support. Procedia Engineering. 2022, Vol. 14, pp. 2986-2993. Scholar
26.Shiwen L., Ronghui H., Zhao Y., Jiarui W., Shuang C., Jianyong L., Yi L. Numerical Simulation Research on Flow-Induced Vibration Characteristics of Fluid-Conveying Pipe Network. Nuclear Power Engineering. 2022, Vol. 43(1), pp. 187-191. Scholar
27.Jung D, Chung J. In-plane and out-of-plane motions of an extensible semi-circular pipe conveying fluid. Journal of Sound and Vibration, 2008, Vol.311(1), pp.408–420. Scholar
28.Liu G., Li S., Karney B.Y. Vibration analysis of curved pipes conveying fluid. Proceedings of the ASME 2014 Pressure Vessels & Piping Conference, Anaheim, California, USA. 2014, Vol.3. Scholar
29.Lolov D., Lilkova-Markova Sv. Free vibrations out-of-plane of curved planar pipe conveying fluid in two cases of supporting. Annual of UACEG, Mathematics. Mechanics. 2006, Vol. 72(2), pp.123-128. Scholar
30.Liang F., Yang X.-D., Bao R.-D., Zhang W. Frequency Analysis of Functionally Graded Curved Pipes Conveying Fluid. Advances in Materials Science and Engineering. 2016, Vol.2016, Article ID 7574216. Scholar
31.Zhao Q., Sun Z. Flow-induced vibration of curved pipe conveying fluid by a new transfer matrix method. Engineering applications of computational applied mechanics. 2018, Vol. 12(1), pp. 780-790. Scholar
32.Zhao Q., Sun Z. In-plane forced vibration of curved pipe conveying fluid by Green function method. Applied Mathematics and Mechanics (English Edition). 2017, Vol.38(10), pp. 1397-1414. Scholar
33.Wu J., Shih P. The dynamic analysis of a multispan fluid-conveying pipe subjected to external load. Journal of sound and vibration. 2001, Vol.239(2), pp. 201-215. Scholar
34.Chicone C. Ordinary Differential Equations with applications, Springer Science+ Business, 1999 Scholar
35.Inspeger Т., Horvath R. Pendulum with harmonic variation of the suspension point. Periodica Polytechnica. 2000, Vol. 44, pp. 39-46. Scholar
36.Akulenko L.D., Georgievskii D.V., Nesterov S.V. Spectrum of Transverse Vibrations of a Pipeline Element under Longitudinal Load. Doklady Physics. 2016, Vol. 61 (3), pp. 129–132. Scholar
37.Gay-Balmaz F., Georgievskii D., Putkaradze V. Stability of Helical Tubes Conveying Fluid. Journal of Fluids and Structtures. 2018. Vol 78 (2), pp. 146–174. Scholar
38.Il’ichev A.T. Dynamics and spectral stability of soliton-like structures in fluid-filled membrane tubes. Russian Math. Surveys. 2020. Vol 75 (5), pp. 843–882 Scholar

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Published: 23 June 2023
Issue date: 23 June 2023
Issue: No. 2 (2023)

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DYNAMIC STABILITY OF A STRAIGHT PIPE CONVEYING PULSATILE FLOW UNDER THERMAL LOADS

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