Abstract
A planar analog of conical flows is considered: an inviscid incompressible fluid flow around a wedge tip. A class of conical flows is found where vorticity is transported along streamlines by the potential component of velocity. Problems of a wave “locked” in the corner region and of a flow accelerating along the rib of a dihedral angle are considered. By analogy with an axisymmetric quasi-conical flow, a planar quasi-conical flow of the fluid is determined, namely, the flow inside and outside the region bounded by tangent curves described by a power law. Conditions are found where vorticity and swirl produce a significant effect. An approximate solution of the problem of the fluid flow inside a “zero” angle is obtained.
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References
U. Frisch, Turbulence. The Legacy of A. N. Kolmogorov, Cambridge University Press, Cambridge (1995).
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland, Amsterdam (1977).
J. Fernandez-de la Mora, R. Fernandes-Feria, M. Peres-Saborid, and A. Barrero, “Conically similar swirling flows at high Reynolds numbers,” Quart. J. Mech. Appl. Math., 52, Part 1, 1–53 (1999).
F. I. Frankl and E. A. Karpovich, Gas-Dynamics of Slender Bodies [in Russian], Gostekhteoretizdat, Moscow-Leningrad (1948).
S. K. Betyaev, “Conical and quasi-conical flows of an incompressible fluid,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 4, 89–100 (2003).
S. K. Betyaev and A. M. Gaifullin, Helical Vortices [in Russian], Central Aerohydrodynamic Inst., Moscow (2001).
M. Van-Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, New York-London (1964).
G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge University Press, Cambridge (1996).
M. E. Goldshtein, Aeroacoustics [in Russian], Mashinostroenie, Moscow (1981).
P. G. Saffman, Vortex Dynamics, Cambridge University Press, Cambridge (1992).
S. V. Alexeenko, P. A. Kuibin, and V. L. Okulov, Introduction into the Theory of Concentrated Vortices [in Russian], Inst. Computer Research, Izhevsk, Moscow (2002).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 57–65, March–April, 2007.
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Betyaev, S.K. Ideal incompressible flow around a wedge tip. J Appl Mech Tech Phys 48, 192–199 (2007). https://doi.org/10.1007/s10808-007-0025-8
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DOI: https://doi.org/10.1007/s10808-007-0025-8