Derivation of phenomenological turbulence theory in liquid with small additives of drag reducing agents



Published May 31, 2020
Nikita N. Golunov Mikhail V. Lurie


Paper considers the issue of deriving the phenomenological turbulence theory in liquids treated with small additives of drag reducing agent. It also proposes the concept that for practical purposes, it is the phenomenological theory, which is relevant, since it determines the parameters of the phenomenon in question in the absence of detailed knowledge of the

mechanisms of additives action, which, despite many years of intensive studies, remain either unknown or not fully understood. Different additives have different effects on shear turbulence in pipes and channels and, accordingly, change the integral characteristics of the turbulent flow in different ways. Some additives affect only the narrow wall-bounded areas of the flow without changing the turbulent viscosity in the flow core, while others act throughout the entire flow volume and significantly change the turbulent viscosity. Additives of the first type affect a turbulent flow by changing the boundary conditions in known models without changing the model coefficients. Additives of the second type change both the boundary conditions and the coefficients of the model itself. It is shown that the von Karman modified theory (model) of shear turbulence is equally suitable for describing the turbulent flow of a liquid with additives of the both first and second types. The universal drag equation with experimentally determined transfer coefficients that follows from this model enables calculating the hydraulic drag coefficient depending on the properties of the drag reducing agent used.


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Golunov NN, Lurie MV. Derivation of phenomenological turbulence theory in liquid with small additives of drag reducing agents. PST [Internet]. 2020May31 [cited 2020Aug.8];4(2(4):118-25. Available from:


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Pipeline, turbulent flow, hydraulic drag, drag reducing agent, phenomenological turbulence theory, turbulent viscosity,von Karman constant, universal equation, roughness.

[1] Kobets G. F. On physical justification of the mechanism of drag reduction by polymer additives. In: The effect of polymer additives and surface elasticity on the wall-bounded turbulence. Novosibirsk: Nauka Publ.; 1978. P. 24–44. (In Russ.)
[2] Pilipenko V. N. The effect of additives on wallbounded turbulent flows. Itogi nauki I tekhniki. Mekhanika zhidkosti i gaza = Results in Science and Technics. Fluid mechanics. Vol. 15. P. 156–257. Moscow: VINITI of USSR Academy of Sciences; 1980. (In Russ.)
[3] Belousov Y. P. Drag reducing additives for hydrocarbon liquids. Novosibirsk: Nauka Publ.; 1986. 144 p. (In Russ.)
[4] Nadolink R. H., Haigh W. W. Bibliography on skin friction reduction with polymers and other boundary-layer additives. Applied Mechanics Reviews. 1995;4 (7):351–460.
[5] Manfield P. D., Lawrence C. J., Hewitt G. F. Drag reduction with additives in multiphase flow. A Literature Survey, Multiphase Science and Technology. 1999;11(3):197–221.
[6] Ge W. Studies on the nanostructure, rheology and drag reduction characteristics of drag reducing cationic surfactant solutions. Ph. D. Thesis. The Ohio state university, 2008.
[7] Bakhtizin R. N., Gareev M. M., Lisin Y. V., Manzhai V. N., Mastobaev B. N., Nesyn V. G., Sunagatullin R. Z. Nanotechnology for lowering the hydraulic resistance in pipelines. St. Petersburg: Nedra Publ.; 2018. 352 p. (In Russ.)
[8] Sedov L. I., Vasetskaya N. G., Ioselevitch V. A. On calculation of turbulent boundary layers with low additions of polymers. In. Turbulent flows. Moscow: Nauka Publ.; 1974. (In Russ.)
[9] Gorin Y., Norbery D. Turbulent flow of dilute polymer solutions. Inzhenerno-physichesky zhurnal = Journal of Engineering Physics. 1995;27(5):830–838. (In Russ.)
[10] Sedov L. I., Vasetskaya N. G., Ioselevitch V. A., Pilipenko V. N. On Hydrodynamic Drag Reduction Using Polymer Additives. In: Mechanics of turbulent flows. Moscow: Nauka Publ.; 1980. P. 7–29. (In Russ.)
[11] Vasetskaya N. G., Ioselevitch V. А. On deriving a semi-empirical theory of turbulence of dilute polymer solutions. Izvestia of the USSR Academy of Sciences. Fluid and gas mechanics. 1970(2):136– 146. (In Russ.)
[12] Povkh I. L., Stupin A. B., Maksyutenko S. N., Aslanov P. V., Simonenko A. P. Features of turbulent flows of solutions of micelle-forming surfactants. In: Mechanics of turbulent flows. Moscow: Nauka Publ.; 1980. P. 44–69. (In Russ.)
[13] Sedov L. I., Pilipenko V. N., Karaschenko V. N. Reduction of turbulent resistance in suspensions and emulsions flow. In: Mechanics of non-homogeneous and turbulent flows: collection of proceedings; ed. by acad. V.V. Struminsky. Moscow: Nauka Publ.; 1989. P. 5–15. (In Russ.)
[14] Pilipenko V. N., Mikhailer А. G. The drag reduction mechanism and heat transfer in turbulent flows with dissimilar additives. In: Heat Mass Transfer – VI: Proceedings of the All-Union Conference. Minsk: Heat and Mass Transfer Institute of NAS of Belarus; 1980. Vol. 6.4.2. P. 89–94. (In Russ.)
[15] Ivanyuta Y. F., Chekalova L. А. Study of the velocity profile of turbulent flows of dilute polymer solutions in the pipe. Inzhenerno-Fizicheskii Zhurnal = Journal of Physical Engineering. 1974;(26)5:799–806. (In Russ.)
[16] Ginevsky А. S., Ioselevich V. А., Kolesnikov А. V. Methods of turbulent boundary layer calculation. Itogi nauki i tekhniki. Mekhanika zhidkosti i gaza =Results in Science and Technics. Fluid Mechanics. Vol. 11. Moscow: VINITI of USSR Academy of Sciences; 1978. P. 156–257. (In Russ.)
[17] Kokhanovsky A. Y., Toropetsky K. V., Ulyanov V. N., Borisov G. A., Usov E. V. Modelling of the fluid flow in the presence of drag reducing additives. Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov–Science & Technologies: Oil and Petroleum Products Pipeline Transportation. 2018;8(1):30–35. (In Russ.)
[18] Lurie M. V., Podoba N. A. Modification of the Karman theory for the calculation of shear turbulence. Reports of the Academy of Sciences of the USSR. 1984;27 (3):570–575. (In Russ).
[19] Lurie M. V. Theoretical foundations of pipeline transport of oil, petroleum products and gas. Moscow: Nedra Publ.; 2017. 478 p. (In Russ.)
[20] Golunov N. N. Hydrodynamic justification of von Karman theory application for calculating the hydraulic drag of pipelines with rough walls in the presence of drug reducing agents. Territorija “NEFTEGAZ” = Oil and Gas Territory. 2018(10):66–70. (In Russ.)
Original Work