Journal issues: 4/2015
Language: (RU, EN)
8 September, 2015
SCALING DETECTION IN A PIPELINE WITH FLUID UNDER PRESSURE USING NATURAL FREQUENCIES OF FLEXURAL VIBRATIONS
Federal State Budget Scientific Institution, R.R. Mavlyutov Institute of Mechanics, Ufa Scientific Centre, Russian Academy of Sciences, Ufa, the Russian Federation
Pipelines can form scale deposits on their walls. Erosion-corrosion processes in pipelines are characterized by the fact that deposition of corrosion products in some of their portions occurs simultaneously with wall thinning in the others.
In this paper consideration is given to natural frequencies of flexural vibrations in a pipeline clamped at both ends and subjected to the action of tension force. The pipeline has wall scale deposits and is filled with fluid under pressure. The scale deposits are supposed to be uniformly distributed on the inner surface of the pipeline. Here, the Kirchhoff’s equation for flexural vibrations is applied. The frequency equation has been derived from the equation that dictates the type of flexural vibrations and also the boundary conditions for a pipeline clamped at its ends. Solutions have been found to the primal problem to determine the first and the second natural frequencies of flexural vibrations in the pipeline for the given scale density in the pipeline, axial force, wall thickness, inside pressure of the pipeline and uniform scale thickness on the pipe wall as well as to the inverse problem to determine scale density on the pipe wall and deposition thickness using two natural frequencies of flexural vibrations in the pipeline.
It has been found that an increase in the density of scale deposits on the pipe wall results in smaller natural frequencies of pipe flexural vibrations. Besides, the research has shown that a reduction in the pipe inside area or an increase in the scale thickness results in smaller natural frequencies of pipe flexural vibrations. Using two natural frequencies of pipe flexural vibrations we can determine the density of scale deposits on the pipe wall and pipe inside area or scale thickness.
The investigation outcomes can be applied to assess axial loading and pipe wall thickness using two natural frequencies of flexural vibrations.
- Sidorov B.V., Martynov S.A. Recommended technology of diagnostics of buried pipelines. Control. Diagnostics, 2005, no. 12, p. 18–19. [in Russian].
- Gladwell G.M.L. Inverse problems in vibration. – Dordrecht, Boston, London: Kluwer Academic Publishers, 2004. (Russian edition: Gladwell G.M.L Obratnye zadachi teorii kolebaniy. – Moscow–Izhevsk: NITs , 2008. 608 p.).
- Guangming Dong, Jin Chen. Vibration analysis and crack identification of a rotor with open cracks. – Japan Journal of Industrial and Applied Mathematics, 2011, vol. 28, no. 1, p. 171–182.
- Akopyan V.A., Cherpakov A.V., Rozhkov E.V., Solovyev A.N. Integral diagnostic feature for identifying damage in the elements of rod constructions. – Control. Diagnostics, 2012, no 7, p. 50–56. [in Russian].
- Yunwei Zhang, Guozheng Yan. Detection of gas pipe wall thickness based on electromagnetic flux leakage. Defectoscopy, 2007, no. 2, p. 78–89.
- Kulikov V.V. Wall thickness of a pipe loaded with pressure. 2009, no 7, p. 6–8. [in Russian].
- Kucheryavyy V.I., Milkov S.N. Reliability calculations for a compressed portion in a gas pipeline in the presence of longitudinal cracks. 2011, no. 3, p. 112–116. [in Russian].
- Khakimov A.G. Determination of fluid density and inner pressure in a pipeline using natural frequencies of flexural vibrations. 2014, no. 1, p. 37–43. [in Russian].
- Baranenko V.I., Yanchenko Yu.A. Erosion-corrosion damage in the elements of pipeline systems at the nuclear power plants with RBMK-1000 reactors. – Teploenergetika, 2010, no. 5, p. 26–33. [in Russian].
- Musakaev N.G., Urazov R.R., Shagapov S.Sh. Dynamics of hydrate formation during natural gas transportation. Teplofizika i aeromekhanika, 2006, vol. 13, no. 2, p. 295–302. [in Russian].
- Wang Wenda, Huang Qiyu, Huang Jun, Pang Quan, Fu Jun, Wang Fenghui. Study of paraffin wax deposition in seasonally pigged pipelines. – Chemistry & Technology of Fuels & Oils, 2014, no 1 (581), p. 27–33. [in Russian].
density of scale deposits; flexural vibrations; natural frequencies; pipe inside area; primal and inverse problems; scaled pipeline; изгибные колебания; плотность отложений; площадь в свету трубы; прямая и обратная задачи; собственные частоты; трубопровод DOI 10.17122/ogbus-2015-4-151-171 References to this article (GOST) Khakimov A.G. SCALING DETECTION IN A PIPELINE WITH FLUID UNDER PRESSURE USING NATURAL FREQUENCIES OF FLEXURAL VIBRATIONS // Electronic scientific journal "Oil and Gas Business". 2015. №4. P.151-171. URL: http://ogbus.ru/issues/4_2015/ogbus_4_2015_p151-171_KhakimovAG_ru_en.pdf