Abstract
A mathematical model of the flow of a thin layer of heavy liquid under an elastic shell filled with gas is constructed. By means of mass exchange with the environment, the gas phase is active and maintains self-organized wave motion in the liquid layer. The conditions under which small perturbations are transformed into quasiperiodic wave packets of finite amplitude which move in the same direction are found. It is shown that the structure of the waves is similar to that of roll waves in open channels.
Similar content being viewed by others
References
G. B. Whitham, Linear and Nonlinear Waves (New York, Wiley, 1974).
R. F. Dressler, “Mathematical Solution of the Problem of Roll-Waves in Inclined Open Channels,” Comm. Pure Appl. Math. 2, 149–194 (1949).
A. Dyment and A. Boudlal, “A Theoretical Model for Gas–Liquid Slug Flow in Down Inclined Ducts,” Int. J. Multiphase Flow 30, 521–550 (2004).
A. Boudlal and V. Yu. Liapidevskii, “Stability of Regular Roll Waves,” Vychisl. Tekhnol. 10 (2), 3–14 (2005).
D. J. Needham and J. H. Merkin, “On Roll Waves Down an Open Inclined Channel,” Proc. Roy. Soc. London, Ser. A 394, 259–278 (1981).
C. Kranenburg, “On the Evolution of Roll Waves,” J. Fluid Mech. 245, 249–261 (1992).
G. L. Richard and S. L. Gavrilyuk, “A New Model of Roll Waves: Comparison with Brock’s Experiments,” J. Fluid Mech. 698, 374–405 (2012).
V. Yu. Liapidevskii and A. A. Chesnokov, “Mixing Layer under the Free Surface,” Prikl. Mekh. Tekh. Fiz. 55 (2), 127–140 (2014)
V. Yu. Liapidevskii and A. A. Chesnokov, J. Appl. Mech. Tech. Phys. 55 (2), 299–310 (2014)].
D. Barnea and Y. Taitel, “Interfacial and Structural Stability of Separated Flow,” Int. J. Multiphase Flow 25, 387–414 (1994).
E. Kordyban, “Horizontal Slug Flow: a Comparison of Existing Theories,” Trans. ASME, J. Fluids Eng. 112 74–83 (1990).
V. Yu. Liapidevskii, “Structure of Roll Waves in Two-Layer Flows,” Prikl. Mat. Mekh. 64 (6), 976–982 (2000).
A. Boudlal, “Roll Waves and Plugs in Two-Layer Flows,” Europ. J. Appl. Math. 19, 1–19 (2007).
V. Yu. Liapidevskii, “Roll Waves in a Gas–Liquid Medium,” Prikl. Mekh. Tekh. Fiz. 43 (2), 39–42 (2002)
V. Yu. Liapidevskii, J. Appl. Mech. Tech. Phys. 43 (2), 204–207 (2002)].
V. Yu. Liapidevskii and V. M. Teshukov, Mathematical Models of Propagation of Long Waves in an Inhomogeneous Liquid (Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2000) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A. Boudlal, V.Yu. Liapidevskii.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 4, pp. 3–11, July–August, 2015.
Rights and permissions
About this article
Cite this article
Boudlal, A., Liapidevskii, V.Y. Roll waves in channels with an active gas phase. J Appl Mech Tech Phy 56, 541–548 (2015). https://doi.org/10.1134/S002189441504001X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S002189441504001X