Determining critical flow parameters for the Poiseuille, Couette and Taylor – Couette flows
Authors: Kondratiev A.S., Ogorodnikov K.F.
Published in issue: #6(102)/2020
DOI: 10.18698/2308-6033-2020-6-1985
Category: Mechanics | Chapter: Mechanics of Liquid, Gas, and Plasma
Based on a detailed analysis of the known Dou method for determining the critical parameters of a Newtonian fluid flow during the transition of a laminar flow regime to a turbulent one, an alternative to determining the critical Reynolds number for the Poiseuille and Couette flows in cylindrical, coaxial and flat channels, the article proposes a new mathematical justification of the Dou method leading to simpler calculation relations, while preserving the initial ideas about the physical conditions of the transition. New computing expressions for determining the critical Dou number for the generalized Poiseuille – Couette flow in a flat channel not considered by Dou are obtained. Analytical expressions for calculating critical parameters for the Taylor – Couette flow approximating experimental results for critical Reynolds numbers are given, as well as calcula-ted values of critical Dou numbers.
References
[1] Schlichting H. Boundary-layer theory. New York, McGraw-Hill Publ., 1955, 535 p. [In Russ.: Schlichting H. Teoriya pogranichnogo sloya. Moscow, Nauka Publ., 1974, 712 p.].
[2] Drazin F. Vvedeniye v teoriu gidrodinamicheskoy ustoychivosti [Introduction to the theory of hydrodynamic stability]. Moscow, Fizmatlit Publ., 2005, 288 p.
[3] Makarov K.A. Inzhenernyy zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2014, iss. 1 (25). DOI: 10.18698/2308-6033-2014-1-1185
[4] Ayvazyan O.M. Universalnyy energeticheskiy kriteriy ustoychivosti ravnomernykh laminarnykh techeniy vyazkoy neszhimayemoy zhidkosti [Universal energy criterion for the stability of uniform laminar flows of a viscous incompressible fluid]. Moskcow; Izhevsk, NITs «Regulyarnaya i khaoticheskaya dinamika» IKI Publ., 2008, 128 p.
[5] Dou H.S., Khoo B.C., Tsai H.M. Journal of Petroleum Science and Engineering, 2010, vol. 73, no. 1-2, pp. 41–47.
[6] Kondratyev A.S., Ovsyannikov V.M., Olofinsky E.P., Stepin B.S., Chinenkov I.A. Transportirovanie vodougolnykh suspenziy: gidrodinamika i temperaturnyy rezhim [Transportation of water-coal suspensions: hydrodynamics and temperature conditions]. Moscow, Nedra Publ., 1988, 213 p.
[7] Dou H.S. International Journal of Non-linear Mechanics, 2006, vol. 41, pp. 512–517.
[8] Dou H.S., Khoo B.C. Modern Physics Letters B, 2009, vol. 23, no. 3, pp. 457–460.
[9] Dou H.S., Khoo B.C. Modern Physics Letters B, 2010, vol. 24, no. 13, pp. 1437–1440.
[10] Dou H.S., Khoo B.C. Advances in Applied Mathematics and Mechanics, 2011, vol. 3, no. 2, pp. 165–180.
[11] Mukund V., Hof B. Journal of Fluid Mechanics, 2018, vol. 839, pp. 76–94.
[12] Trefethen L.N., Trefethen A.E., Reddy S.C., Driscoll T.A. Science, 1993, vol. 261, pp. 578–584.
[13] Grossmann S. Reviews of Modern Physics, 2000, vol. 72, pp. 603–618.
[14] Dou H.S., Khoo B.C., Yeo K.S. International Journal of Thermal Sciences, 2007, vol. 46, no. 2, pp. 262–275.
[15] To Xuan Zoan. Struktura szhimayemykh vikhrevykh techeniy Kuetta — Teylora. Diss. cand. fiz.-mat. nauk [The structure of compressible vortex flows of Couette — Taylor. Cand. phys. and math. sci. diss.]. Moscow, MFTI Publ., 2014, 104 p.
[16] Dou H.S., Khoo B.C., Yeo K.S. International Journal of Thermal Sciences, 2008, vol. 47, no. 11, pp. 1422–1435.
[17] Dou H.S. International Journal of Physical Sciences, 2011, vol. 6, no. 6, pp. 1411–1425.