Analyzing the rotation of an inviscid vortex tube

Authors

DOI:

https://doi.org/10.15587/1729-4061.2015.51081

Keywords:

quasi-solid core of the vortex, distribution of stresses in the wall, cross-sectional structure effect

Abstract

The study suggests a precise solution of the problem of distributing radial and circumferential stresses in the wall of the hollow cylindrical quasi-solid core of a vortex tube. The solution is based on two other well-known equations of linear elasticity theory––the Lamé problem and the problem of stress in a rotating tube.

The above equations are approached with the superposition theorem. As a result, we get two equations for determining the circumferential and radial stresses in the wall of the core of any structure. The problem simultaneously refers to two models of a continuum––a solid body without shear stresses and a fluid without convective acceleration. We have shown that stress differences at a point of the fluid are caused by the flow structure and noted similarity to the effect of stress concentration in a solid body.

We have distinguished a particular case of the obtained equations for a solid core, which coincides with the equation of the dynamics of an ideal fluid. The equation for the speed at which the core disintegrates is derived from the condition when the circumferential stress is equal to zero. We have supplied examples of the findings practical use.

Author Biography

Виталий Александрович Бударин, Odessa National Polytechnic University 1 Shevchenko str., Odessa, Ukraine, 65044

Associate professor, PhD

Department of Theoretical and general non-conventional energy

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Published

2015-10-20

How to Cite

Бударин, В. А. (2015). Analyzing the rotation of an inviscid vortex tube. Eastern-European Journal of Enterprise Technologies, 5(7(77), 20–24. https://doi.org/10.15587/1729-4061.2015.51081

Issue

Vol. 5 No. 7(77) (2015): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2015 Виталий Александрович Бударин

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