Mathematical Modeling of the Rotational Motion of the Air Flow to Optimize the Parameters of a Vortex Wind Turbine

The relevance of the study consists in the development of a new direction of wind devices with a vertical axis of rotation without mechanisms of pointing to the wind. The main purpose of the research was to develop a mathematical model to describe the new design of the wind turbine, the distinctive feature of which is the use of the vortex effect and the concentration of the flow at its direct supply to the blades of the wind wheel. The studied design consists of a flow concentrator, inside which is a wind wheel. A vertical pipe mounted on the concentrator is used to extract the flow. The research methods are numerical calculation and mathematical modeling of air flow. In the course of the study, a literary review and analysis of mathematical methods and existing designs of wind farms were carried out. The calculation results show that the narrowing channels of the concentrator are curvilinear in plan and are described by logarithmic dependence, which creates a stable vortex motion inside the structure and the vertical pipe. Based on the results of computational and laboratory experiments, a semi-industrial sample of a 5-kW vortex wind turbine was developed.