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.
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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