Abstract
Initiation of turbelence is associated with disturbances of finite intensity [1]. Some attempts, as in [2], have been made to treat this region analytically. The nonuniformity of the local stability * of laminar fluid flow over the tube cross section has been established experimentally [3,4, 1]. On this finding is based the interpretation of a number of turbulent transition phenomena, including a characteristic singularity of the relationship between the resistance coefficient of rough tubes and the Reynolds number under transient conditions [5].
Expression (1.1) introduced as a measure of stability, and the criterion q* yield satisfactory quantitative results.
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References
H. Schlichting, Entstehung der Turbulenz, Springer, Berlin, 1959.
E. M. Khazen, “Contribution to the theory of turbulence in inhomogeneous flows,” Dokl. AN SSSR, vol. 147, no. 1, 1962.
M. Sibulkin, “Transition from turbulent to laminar pipe flow,” Phys. Fluids, vol. 5, no. 3, 1962.
J. C. Rotta, “Experimenteller Beitrag zur Entstehung turbulenter Strömung im Rohr,” Ing.-Arch., vol. 24, no. 4, 1956.
L. G. Loitsyanskii, Mechanics of Liquids and Gases [in Russian], Fizmatgiz, Moscow, 1959.
L. Schiller, Strömung in Rohren, Akad. Verlagsgesellschaft, Leipzig, 1932.
Modern Developments in Fluid Dynamics, vol. 1, Clarendon Press, Oxford, 1938.
S. J. Davies and C. M. White, “An experimental study of the flow of water in pipes of rectangular section,” Proc. Roy. Soc., ser. A, vol. 119, no. 781, p. 92, 1928.
L. Schiller, “Über den Strömungswiderstand von Rohren verschiedenen Querschnitts und Rauhigkeitsgrades,” Z. angew. Math. und Mech., vol. 3, no. l, 1923.
R. Winkel, “Die Wasserbewegungen in Leitungen mit Ringsspalt-Durchflussquerschnitt,” Z. angew. Math. und. Mech., vol. 3, no. 4, 1923.
T. Lonsdale, “The flow of water in the annular space between two coaxial cylindrical pipes,” Philos. Mag. and J. Sci., ser. 6, vol. 46, no. 271, p. 163, 1923.
F. C. Lea and A. G. Tadros, “Flow of water through a circular tube with a central core and through rectangular tubes,” Philos. Mag. and J. Sci., ser. 7, vol. 11, no. 74, p. 1235, 1931.
A. Fage, “The influence of wall oscillations, wall rotation and entry eddies on the breakdown of laminar flow in an annular pipe,” Proc. Roy. Soc., ser. A, vol. 165, no. 923, p. 520, 1938.
J. Laufer, “The structure of turbulence in fully developed pipe flow,” NACA, TN 1174, 1954.
M. K. Likht and I. A. Rozhanskaya, “Classes of disturbances in hydrodynamic instability studies,” Summaries of Reports to the Third All-Union Conference on Theoretical and Applied Mechanics [in Russian], Nauka, Moscow, 1968.
E. G. Feindt, “Untersuchungen über die Abhängigkeit des Umschlages laminar-turbulent von der Oberflächenrauhigkeit und der Druckverteilung,“Jahrbuch 1956 der schiffsbautechnische Gesellschaft, vol. 50, p. 180, 1956.
Rayleigh, “On the dynamics of revolving fluids,” Proc. Roy. Soc., ser. A, vol. 93, no. 648, p. 148, 1916.
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Kuznetskii, R.S., Likht, M.K. General stability criterion for laminar tube flow. J Appl Mech Tech Phys 10, 587–593 (1969). https://doi.org/10.1007/BF00916215
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DOI: https://doi.org/10.1007/BF00916215