TY - JOUR

T1 - Review of Analytical Approaches for Simulating Motions of Helical Vortex

AU - Okulov, V. L.

AU - Fukumoto, Y.

N1 - Funding Information: The simulation of helical vortices using the Dyson method and the regularization of the Kapteyn series was carried out with the financial support of the Bilateral Joint Program JSPS (Grant No. JPJSBP120214812) and the RFBR (Grant No. 21-58-50003); the approximation and data analysis of the cutoff methods was carried out by VLO under a contract with the Ministry of Education and Science of the Russian Federation (Contract No. 075-15-2019-1923). Funding Information: The authors would like to acknowledge the support from the Department of Wind Energy, Technical University of Denmark and Institute of Mathematics for Industry, Kyushu University. Publisher Copyright: Copyright © 2022 Okulov and Fukumoto.

PY - 2022/2/15

Y1 - 2022/2/15

N2 - 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.

AB - 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.

KW - helical vortex

KW - near wake

KW - tip vortex

KW - tornadoes

KW - wind turbine

UR - http://www.scopus.com/inward/record.url?scp=85125621648&partnerID=8YFLogxK

U2 - 10.3389/fenrg.2022.817941

DO - 10.3389/fenrg.2022.817941

M3 - Article

AN - SCOPUS:85125621648

VL - 10

JO - Frontiers in Energy Research

JF - Frontiers in Energy Research

SN - 2296-598X

M1 - 817941

ER -