Vol. 9 6, 2019 p 640-651


Article name, authors, abstract and keyword


Numerical method for identification of a hydraulic model of a pipeline linear section

Vladimir V. Zholobov a

a Pipeline Transport Institute, LLC (Transneft R&D, LLC), 47a, Sevastopolsky prospect, Moscow, 117186, Russian Federation

DOI: 10.28999/2541-9595-2019-9-6-640-651

Abstract: Introduction. In conditions of high-level fitting with measurement devices and powerful capabilities of modern computer facilities, the existing procedure for prediction calculation of hydraulic parameters during pipeline transportation appear to be unduly approximate. In this connection, adaptation of the most precise dependencies on actual conditions available in scientific and technical literature is relevant. By results of review of analytical dependencies for calculation of friction losses in the pressure pipelines, the dependence structure was established, which reflects most accurately the experimental data obtained by I. Nikuradze, where the resistance factor λ is described by the piecewise-continuous ratios reduced by O. M. Ayvazyan.
Methods. Selection is made as to hydraulic resistance factor structural dependency with the most high-level degree to generalization of the experiment results available in scientific and technical literature. Identification of free parameters included in the selected dependency for the hydraulic resistance factor, based on pressure measurement results, is conducted.
Results. The algorithm for numerical calculation was proposed, which would allow for recovering the values of parameters in structural dependency of resistance factor λ by means of multiple application of the known method for sensitivity functions and pressure measurement data in the pipeline linear section.
Discussion. The procedure for obtaining calculation system of the ordinary differential equations allowing for determining (and adjusting, if necessary) the corresponding parameters in the uniform structural dependency on λ factor for each fixed set of experimental data (pressure and flow rate), was demonstrated. Absence of nested loops is the feature of the proposed algorithm.
Conclusions. Dynamic monitoring of parameters in λ factor, based on proposed approach, allows for improving accuracy of prediction calculation for hydraulic pumping parameters and obtaining additional information on condition of medium filling the pipeline internal cavity.

Keywords: hydraulic resistance factor, sensitivity function, mean-square deviation, functional minimization.

For citation:
Zholobov V. V. Numerical method for identification of a hydraulic model of a pipeline linear section. Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktovScience & Technologies: Oil and Oil Products Pipeline Transportation. 2019;9(6):640651.

[1] Loytsyansky L. G. Fluid and gas mechanics. Moscow: Nauka Publ.; 1970. 904 p. (In Russ.)
[2] Reynolds O. The dynamical theory of incompressible viscous fluids and the determination of the criterion. In: Problem of turbulence. MoscowLeningrad: ONTI NKTP Publ.; 1936. . 185227. (In Russ.)
[3] Prandtl L. Aerohydromechanics. Izhevsk: Regulyarnaya i Khaoticheskaya Dinamika Publ.; 2002. 572 p. (In Russ.)
[4] Nikuradse J. Regularity of turbulent flow in smooth pipes. In: Problem of turbulence. MoscowLeningrad: ONTI NKTP SSSR Publ.; 1936. . 75150. (In Russ.)
[5] Nikuradse J. Stromungsgesetze in rauchen Rohren. Forschung auf dem Gebiete des Ingenieurwesens. 1933(391):122. (In Germ.)
[6] Goncharov V. N. Uniform turbulent flow. MoscowLeningrad: Gosenergoizdat; 1952. 145 p. (In Russ.)
[7] Grishanin . V. Dynamics of channel flows. Leningrad: Gidrometeoizdat; 1979. 312 p. (In Russ.)
[8] Ayvazyan . . Basic hydraulics of the uniform flows. Moscow: Institute of Computer Researches Publ.; Izhevsk: Regulyarnaya i Khaoticheskaya Dinamika Publ.; 2006. 152 p. (In Russ.)
[9] Millikan C. B. A critical discussion of the turbulent flows in channels and circular tubes. Proceedings of the 5th Int. Congress for Applied Mechanics. Cambridge (Massachusetts, USA), September 1226, 1938. P. 386392. (In Russ.)
[10] Khintse I. . Turbulence, its mechanism and theory. Moscow: Fizmatgiz Publ.; 1963. 680 p. (In Russ.)
[11] Satkevich . . The theoretical basics of fluid dynamics. Part 2: Dynamics of liquid bodies. MoscowLeningrad: ONTI NKTP SSSR Publ.; 1934. 467 p. (In Russ.)
[12] Prandtl L. Neuere ergebnisse der turbulenzforschung. Zeitschrift des Vereines Deutscher Ingenieure. 1933(77): 105114. (In Germ.)
[13] Coles D. The law of the wake in turbulent boundary layers. J. Fluid. Mech. 1956;1(2):191226.
[14] Clauzer F. H. The turbulent boundary layer. Advances Appl. Mech. 1956;4:151.
[15] Zanoun E.-S., Durst F., Nagib H. Scaling laws for turbulent channel and pipe flows over a wide range of Reynolds numbers. Proc. of the 4th Int. Conf. on Heat Transfer, Fluid Mechanics and Thermodynamics. Cairo, Egypt, September 1922, 2005. Paper No. ZF2.
[16] Bryanskaya Y. V. Flow in a wall layer and beyond it (in a tube, canal, and boundary layer). Vestnik MGSU. 2010(24):6065. (In Russ.)
[17] Borovkov V. S., Volshanik V. V., Rylova I. . Features of velocity distribution in a turbulent flow. Vestnik MGSU. 2015(6): 103109. (In Russ.)
[18] Barenblatt G. I., Prostokishin V. M. Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data. Journal Fluid Mech. 1993(248):521529.
[19] Barenblatt G. I., Chorin A. J., Prostokishin V. M. Self-similar intermediate structures in turbulent boundary layers at large Reynolds numbers. Journal Fluid Mech. 2000(410):263283.
[20] Vysotsky L. I. A brief review of achievements in solving the problem of distribution of averaged velocities in canonical fluid flows. Nauchnoe obozrenie. Tekhnicheskie nauki = Scientific Review. Engineering Sciences. 2017(1):3658. (In Russ.)
[21] Buschmann M. H., Gad-el-Hak M. Turbulent boundary layers: reality and myth. Int. Journal of Computing Science and Mathematics. 2007;1(24):159176.
[22] Knopp T., Schanz D., Schröder A., Dumitra M., Cierpka C., Hain R., Kähler C. J. Experimental investigation of the log-law for an adverse pressure gradient turbulent boundary layer flow at Reθ=10000. Flow, Turbulence and Combustion. 2014(92):451471.
[23] George W. K. Is there a universal log law for turbulent wall-bounded flows? Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2007(365):789806.
[24] Baykov V. N. Universal velocity distribution in water flows under different hydraulic-resistance regimes. Vestnik MGSU. 2009(4):1922. (In Russ.)
[25] Bryanskaya Y. V. Refinement of turbulent flow velocity characteristics. Inzhenerno-stroitelny zhurnal = Construction Engineering Journal. 2013(6):3138. (In Russ.)
[26] Lobanov I. . Theory of hydraulic resistance in direct round tubes with rough walls. Otraslevye aspekty tekhnicheskikh nauk = Industry-specific Aspects of Engineering Sciences. 2012(4):413. (In Russ.)
[27] Yanyshev D. S. Application of the Lambert function in the theory of turbulent friction. Trudy MAI: electronic journal. 2015. Issue 50 [accessed 2019 Feb 07]. http://trudymai.ru/upload/iblock/98a/primenenie-funktsii-lamberta-v-teorii-turbulentnogo-treniya.pdf?lang=ru&issue=50. (In Russ.)
[28] Kondratyev A. S., Nha T. L., Shvydko P. P. The Colebrook White general formula in pipe flow for arbitrary sand roughness of pipe wall. Fundamentalnye issledovaniya = Fundamental Research. 2017(1):7478. (In Russ.)
[29] Kondratyev A. S., Nha T. L., Shvydko P. P. Engineering method of calculation of hydraulic drag coefficient and velocity profile for an arbitrary sand roughness of the pipe wall. Gidravlika = Hydraulics: electronic scientific journal. 2016. Issue 2. (In Russ.)
[30] Mingalev I. V., Mingalev O. V., Mingalev V. S. Generalized Newtonian rheological model for laminar and turbulent flows. Matematicheskoe modelirovanie = Mathematical Modeling. 1999;11(11):3963. (In Russ.)
[31] Wilcox D. C. Turbulence Modeling for CFD. La Canada (): DWC Industries Inc.; 1998. 540 p.
[32] Pavlovsky V. . On one phenomenological alternative to the hypothesis of the mixing path length. In: Models of continuum mechanics: collection. Physical mechanics. Issue 7. B. V. Filippov, editor. Saint Petersburg: Publ. House of St Petersburg University; 1998. P. 2135. (In Russ.)
[33] Chistov A. L. Unified laminar turbulent differential model of incompressible viscous liquid flows. Vestnik of Saint Petersburg University. Series 10. 2008(4):103106. (In Russ.)
[34] Pavlovsky V. . Various forms of transformations of the Navier Stokes equations. Problems of saving fuel and energy resources at industrial enterprises and thermal power plants: interuniversity collection of scientific papers. Saint Petersburg: SPbGTURP Publ.; 2007. P. 511. (In Russ.)
[35] Pavlovsky V. . On the calculation of pulsation characteristics of turbulent flows. Journal of Applied Mechanics and Technical Physics. 1988(3):114122. (In Russ.)
[36] Pavlovsky V. . Applications of the unified phenomenological laminar and turbulent model for the calculation of non-isothermal fluid flows in pipes. Proc. of the Scientific and Technical Conference The Shipbuilding Education and Science. Saint Petersburg: SPbGMTU; 2003. P. 3337. (In Russ.)
[37] Pavlovsky V. ., Shestov . V. Application of f-turbulence model for calculation of internal tasks of hydrodynamics and heat and mass transfer. Proc. of the Third All-Russian intersectoral scientific and technical conference Actual Problems of Marine Energy. Saint Petersburg: Publ. House f SPbMTU; 2014. 181 . (In Russ.)
[38] Dupuit J. Traite theorique et pratique de la conduite et de la distribution des eaux. Paris: Carilian-Goeury et Dalmont, 1854. (In French.)
[39] Darcy H. Recherches experimentales relatives au mouvement de leau dans les tuyaux. Paris: Mallet-Bachelier, 1857. 268 p. (In French.)
[40] Darcy H. P. G., Bazin H. Recherches Hydrauliques. 1ère et 2ème parties. Paris: Imprimerie Impériales, 1865. (In French.)
[41] Du Buat P. L. G. Principes dhydraulique et de pyrodynamique. 3e édition révisée en 3 vol. Paris: Firmin Didot, 1816. (In French.)
[42] Bakhmetev B. . On the uniform fluid motion in channels and pipes. Leningrad: Kubuch Publ.; 1929. 244 p. (In Russ.)
[43] Biel R. Über den Druckhöhenverlust bei der Fortleitung tropfbarer und gasförmiger Flüssigkeiten. Mitteilungen über Forschungsarbeiten auf dem Gebiete des Ingenieurwesens. Heft 44. Berlin: Springer Verlag, 1907. (In Germ.)
[44] Idelchik I. . Handbook of hydraulic resistances. By ed. . . Shteinberg. 3rd ed., revised and enlarged. Moscow: Mashinostroenie Publ.; 1992. 672 p. (In Russ.)
[45] Chernikin . V. Generalized formula for hydraulic resistance coefficient of pipelines. Transport i khranenie nefteproduktov = Transportation and Storage of Oil Products. 1997(45):2022. (In Russ.)
[46] Chernikin V. ., Chernikin . V. Generalized formula for calculating the friction factor of pipelines for light oil products and low viscosity oils. Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktovScience &Technologies: Oil and Oil Products Pipeline Transportation. 2012(4):6466. (In Russ.)
[47] Chernikin . V. n hydraulic calculation of pipelines according to L. S. Leybenzons formula. Neftyanoe khozyajstvo = Oil Industry. 1996(4):6566. (In Russ.)
[48] Chernikin . V. On determination of pressure losses in pipelines by the generalized formula. Nauka i tekhnologiya uglevodorodov = Hydrocarbon Science and Technology. 1999(4):1315. (In Russ.)
[49] Morozova N. V., Korshak . . Pipeline hydraulic calculations and border Reynolds numbers. Neftegazovoe delo = Oil and Gas Business. 2007;5(1):120125. (In Russ.)
[50] Chernikin . V., Talipov R. F. About Colebrook equation using at pipelines hydraulic calculation by generalized formula. Truboprovodnyi transport: teoriya i praktika = Pipeline Transport: Theory and Practice. 2010(4):1416. (In Russ.)
[51] Seleznev V. E., Aleshin V. V., Pryalov S. N. Mathematical modeling of pipeline networks and channel systems: methods, models and algorithms. Moscow: MAKS Press; 2007. 695 p. (In Russ.)
[52] Voevodin . F., Nikiforovskaya V. S. Numerical method for solving some inverse problems of hydraulics. Vodnye resursy = Water Resources. 1981(3):114118. (In Russ.)
[53] Bondar D. V., Zholobov V. V., Varybok D. I., Nadezhkin O. S. About the testing of the leak detecting algorithms based on the sensitivity function. Neftegazovoe delo = Oil and Gas Business: online media. 2018(4): 194233. (In Russ.)