Valery L. Okulov

Experiments were carried out in a water-filled elongated cup of a “kitchen scale,” where motion was created by a rotating disk with various micro- and nano-roughness in the top of the cup. The obtained results have shown that for some patterns of nanostructures, there is a noticeable growth of a vortex, generated by the disk, while other roughnesses do not make visible changes in the flow structure. The results are of interest in assessing the efficiency of surfaces with nanoscale roughnesses. Indeed, the first type of nano-roughness may become useful for enhancing soft mixing in chemical and bio-reactors, including in the preparation of special food delicacies. On the other hand, the use of nanostructured surfaces that do not affect the main flow can help to solve some industrial problems of water and ice erosion, for example, in wind turbines or any other objects where disturbances of the main flow are undesirable.

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.

The results of analytical modeling of a system of helical vortices detached from the ends of the rotating blades of an NEJ rotor (proposed by N.E. Joukowsky) are presented. An analytical solution for determining the decreasing flow velocity on the blade, induced by the vortex wake, is constructed. For the first time, the wake vortex system was simulated using a model with a uniform vorticity distribution in the core of each tip vortex detached from the NEJ rotor blades. The solution was obtained by extending the Dyson method, which was previously used only for a separate helical vortex, to a multivortex system of blade vortices. This result can be used to construct theoretical and numerical models to assess the optimal performance of rotors and predict the occurrence of erosion and icing on their blades. The results of this work are of interest for a fundamental understanding and description of the behavior of flows with a system of helical vortices in rotor aerodynamics and other studies, where multivortex helical structures arise in swirling flows, e.g., in tornado cores, in vortex devices and cyclonic separators, in combustion chambers, etc.

The review reflects physical solutions for de-icing, one of the main problems that impedes the efficient use of wind turbines for autonomous energy resources in cold regions. This topic is currently very relevant for ensuring the dynamic development of wind energy in the Arctic. The review discusses an effective anti-icing strategy for wind turbine blades, including various passive and active physical de-icing techniques using superhydrophobic coatings, thermal heaters, ultrasonic and vibration devices, operating control to determine the optimal methods and their combinations. After a brief description of the active methods, the energy consumption required for their realization is estimated. Passive methods do not involve extra costs, so the review focuses on the most promising solutions with superhydrophobic coatings. Among them, special attention is paid to plastic coatings with a lithographic method of applying micro and nanostructures. This review is of interest to researchers who develop new effective solutions for protection against icing, in particular, when choosing systems for protecting wind turbines.

The development of wind-power engineering in the Arctic has led to increasing wind turbines in cold climatic zones. A problem operating wind turbines in cold conditions is the icing of blades. The icing of the blades leads to a change in rotor aerodynamics, a decrease in energy production, the additional weight of blades, and load on the rotor, which increase wear and reduce the lifetime of the turbines. The growth of icing on the blades threatens the uncontrollable separation of ice pieces from the blade edges, and the operation is unsafe. Non-contact methods for detecting icing on the blades need to prevent critical operating modes with ice formation on the blades. This review analyzes methods for detecting icing. The advantages and disadvantages of various optical methods are presented to give valuable insights on ice prevention for wind turbines operating in cold regions.

The accuracy of numerical calculations of the dynamics of vortex filaments is estimated via the cutoff method using the example of the motion of helical vortices. In the case of helical vortices with uniform vorticity distribution of a Rankine core, there are two analytical approaches to solving the problem. These approaches are used to determine the minimum admissible distance between vortex filaments or their elements to ensure the accuracy of calculations when using the cutoff method. There is an established error that occurs in the calculations based on the cutoff method in the case of convergence of the rounds of a helical vortex.

The effect of nanoroughnesses on the structure of a closed vortex flow generated in a motionless vertical cylindrical container by an upper rotating disk with various roughnesses deposited on its surface is investigated. An increase in the Reynolds number is found in the presence of roughnesses on a rotating disk, which leads to an increase in the length along the axis of the vortex cell with circulating motion leading to the intensification of mixing and mass transfer. It is shown for the first time that, for the case of the Wenzel interaction of fluid with a surface (without an “air” interlayer between them), a 5–11% increase in the size of the vortex cell is observed for nanoroughnesses simulating the superhydrophobic surface of a lotus leaf. The results obtained are of interest for the further development of the vortex apparatus and reactors providing the complex vortex motion of ingredients, the optimization of the operation of existing installations, and the designing of new devices.

The motion of a helical vortex and the movement of the fluid particles along its axis are analyzed. The same form of the helical axis of the vortex and the trajectory of the particles sometimes leads to a false assumption of equality of these two different motions. The correct identification of both motions, however, is essential when considering the helical vortices in the wakes of rotors, or the displacement of the core of helicoidal tornado, etc. Only the same helical shape is the vortex axis and the streamline of the fluid particles can mistakenly merge these two different motions as the identical travel. We describe an experiment that clearly separates these two motions for the case of a stationary helical vortex, along the axis of which the fluid particles intensively move. The result shows that the absolute velocity of fluid particles does not coincide with the motion of the helical vortex as a whole.

The paper presents an analytical solution for helical vortices with a Gaussian vorticity distribution in the core, which is confirmed by experimental and numerical simulations. This result is obtained by extending the Dyson method to the Biot–Savart law. Previously, analytical solutions were found and studied only for vortices with constant vorticity distribution in the core (a Rankine-type vortex core). One of the important issues raised during the discussion is the difference between self-induced movements of helical structures with both types of vortex core. The proposed solutions are important for the fundamental understanding and description of the behavior of helical eddy flows in various fields of industry and in nature. Examples include tip vortices behind the rotors of wind or hydro turbines, tornadoes, or axial vortices in aerodynamic devices such as vortex apparatuses and generators; cyclone separators, combustion chambers, etc.