Approximation of blades of radial machines with multiparameter family of smooth surfaces

Purpose. Development of a mathematical model for creating the spatial forms of blade devices of rotating radial dynamic blade machines. Methodology. An approach to the development of a mathematical model of blade profiling of radial dynamic blade machines, as parts of power plants, air-jet engines and fuel component supply systems of rocket engines, has been suggested. The approach is based on a physical model of the working body flow over helical surfaces. Findings. A system of equations for describing the blade of a radial dynamic blade machine of any purpose as a family of smooth surfaces has been obtained. A multi-parameter correction of the shape of the smooth surface of the blade, accounting for the change in geometric data, based on input and output parameters of the blade, has been developed. Based on a review of modern technology samples, possible configurations of the spatial shape of the blade of the radial and radial-axial type, geometric factors affecting the surface of the blade being created are taken into account. The possibility of obtaining a multi-level blade apparatus by changing the conditions of the geometric parameters at the entrance is shown. Originality. As part of the developed approach, in relation to the conditions for ensuring the calculated geometric parameters and the working process conditions of the blade machine, blade machines operating on compressible and non-compressible working bodies are considered. In particular, the possibility is shown of ensuring the construction of the spatial surface of the blade of the impellers of radial blade machines with a wide range of angles of the blades at the entrance and exit using smooth surfaces. Practical value. The use of a developed mathematical method allows you to perform the profile of rotating vane devices for radial vane dynamic machines of various purposes, such as centrifugal pumps and compressors, centrifugal radial turbines, as well as diagonal type vane machines. The practical significance of the obtained results is determined by the use of dynamic radial vane machines in aviation and rocket technology, aggregates of the mining industry, and technological devices of chemical industry enterprises.