Review of Analytical Approaches for Simulating Motions of Helical Vortex

V L Okulov,Y Fukumoto

doi:10.3389/fenrg.2022.817941

V L Okulov, Y Fukumoto

Open Access

https://doi.org/10.3389/fenrg.2022.817941

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Abstract

The study investigates helical vortices, which are fundamental structures in fluid dynamics, and a basic model of tip vortices behind wind turbines. In connection with the intensive development of wind energy, interest in modeling helical vortex wakes behind the rotors has increased. Therefore, the purpose of this mini-review is to compare the existing methods for calculating the induced velocities of screw vortices. The three methods for calculating the motion of helical vortices are compared. Two typical forms of vorticity with uniform (Rankine-type) and Gaussian distributions in the core of helical vortices are compared, and the minimum distance between the vortex filaments or their turns is identified with sufficient accuracy in both cases. The results presented in this mini-review can be used to model the helical vortices in the rotor wakes, central helical vortices in vortex devices, or natural phenomena such as tornadoes, dust tornadoes, and waterspouts.

Highlights

Helical vortices are fundamental objects in fluid dynamics (Alekseenko et al, 2007). These vortices have played an important role in the development of hydrodynamics as the oldest mathematical idealization of tip vortices in the wake behind a screw, propeller, or wind turbine (Okulov et al, 2015; Sørensen et al, 2013; Okulov et al, 2021) and describe one of the main states of swirling flows caused by concentrated vortices in tornadoes, six to eight vortex devices and rotating tanks, and pipes (Alekseenko et al, 2007)
In the dynamics of slender vortices, the size of their core is usually assumed to be much smaller than any other linear sizes
The results indicate that the three methods give the same solution when the vortex pitch is at least six times the diameter of the vortex core. This result is in good agreement with direct Navier–Stokes simulations (DNS) numerical simulations (Selçuk et al, 2017), which established that the cutoff method deviates from the correct solution for dimensionless helical pitches of less than 2π

Summary

Introduction

Helical vortices are fundamental objects in fluid dynamics (Alekseenko et al, 2007). These vortices have played an important role in the development of hydrodynamics as the oldest mathematical idealization of tip vortices in the wake behind a screw, propeller, or wind turbine (Okulov et al, 2015; Sørensen et al, 2013; Okulov et al, 2021) and describe one of the main states of swirling flows caused by concentrated vortices in tornadoes, six to eight vortex devices and rotating tanks, and pipes (Alekseenko et al, 2007). Unlike the theory of point vortices (White, 2015) and vortex rings (Saffman, 1992), helical vortex theory has not been systematically described in the literature and is not generally considered in textbooks and monographs on classical fluid mechanics. The concentration of the vorticity on the axis of the vortex tube reduces the integration to one direction along the axis, but this produces the new problem of calculating the self-induced velocity at points on the axis associated with singular behavior. This problem can be avoided by using various regularization methods

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