2013 1(12)

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Aktershev S.P.1,2, Kuybin P.A.1,2

1 Institute of Thermophysics SB RAS, Novosibirsk, Russia
2 Novosibirsk State University, Novosibirsk, Russia


Aktershev, S.P. and Kuybin, P.A., (2013) Stability of vortex flow in a cylindrical tube, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(12), PP. 265 - 269.


hydrodynamical instability; swirl flow; vortices; numerical method


The instability development in apparatuses using flow swirling can generate oscillations with frequencies close to the eigen mechanical or acoustic ones, i.e. lead to resonance. Thus, evaluation of the eigen frequencies of unstable disturbances in swirl flow looks as an actual problem. A new method for solution of the problem on stability of vortex flow of viscous incompressible fluid in a cylindrical tube is presented in this paper. The method is based on decomposition of the velocity field of non-disturbed flow as well as its disturbances into series on the radial coordinate. This allows one to avoid difficulties caused by the numerical integration of the system of differential equation with singular point. Recurrent formulae are derived for search the series coefficients. The problem on eigen values is reduced to solution of the system of two equations with two unknowns. The method was applied for wide enough class of the axisymmetrical vortex flows of incompressible fluid.


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