Parametric Description of the Stationary Helical Vortex in a Hydrodynamic Vortex Chamber
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PARAMETRIC DESCRIPTION OF THE STATIONARY HELICAL VORTEX IN A HYDRODYNAMIC VORTEX CHAMBER S. I. Shtorka,b , E. S. Geshevaa , P. A. Kuibina,b,∗,
UDC 532.5.01
V. L. Okulovb,c , and S. V. Alekseenkoa
Abstract: A swirling flow in a tangential-type hydrodynamic chamber with stationary vortex structures is experimentally investigated. The main attention is paid to determining the geometric and kinematic parameters necessary for a correct description of helical vortices and their spatial structure, in particular, to testing the possibility of a theoretical description of the limiting case where the vortex becomes stationary, i.e., its rotation frequency (or precession frequency) vanishes. It is shown that the theory of helical vortices ensures a sufficiently accurate prediction of conditions for the appearance of their stationary (motionless) states. Keywords: vortex dynamics, helical vortex, vortex chamber, parametric description. DOI: 10.1134/S0021894420030062 INTRODUCTION Swirling motion of the medium is the basis of operation of many power engineering facilities, including combustion chambers of coal dust boilers [1–3], gas-turbine combustors [4, 5], wind turbines [6], water turbines [7–9], vortex reactors with a centrifugal fluidized bed [10], vortex heat exchangers [11], etc. Vortex flows are frequently encountered in nature, e.g., in the form of intense atmospheric vortices [12, 13], which are rather hazardous for people. The interest to studying vortex flows is inspired not only by various applications, but also by complex physical phenomena arising in these flows: laminar–turbulent transition [14], instability and waves [15, 16], vortex breakdown and vortex core precession [17, 18]. A typical feature of the vortex filament is the helical shape of its rotation axis [15, 19]. Self-induced shifting of the rotation axis, which occurs due to filament curvature, has to be taken into account in the description of motion of helical vortices [20, 21]. A commonly accepted approach formulated at the beginning of the 20th century by Joukowsky [22] is the allowance for only the binormal component of velocity in the analysis of self-induced motion of the helical filament. However, erroneous ideas disproving the classical concept still appear (see the discussion on this issue in [23]). A physical experiment [23] was performed to test these hypotheses. In this experiment, a stationary (motionless) helical vortex generated in a hydrodynamic vortex chamber with tangential swirling of the flow was studied in order to provide experimental justification for the difference between the binormal motion of the helical vortex and the motion of particles along the axis of this vortex [1, 2]. The choice of a stationary vortex as an object of the study offers some advantages for experimental investigations. In particular, visualization can
a Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia; [email protected]; gesheva [email protected]; ∗ [email protected]; [email protected]. b Novosibirsk State U
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