Dynamic flow parameters in natural curvilinear coordinates for a current line in a rotating channel

A special interest in the topic of mathematical analysis of the flow of heat transfer processes is determined by the scientific significance and practical application in the development, design and production of rocket and space vehicles and installations. Substantiation of the developed techniques and modeling of the data obtained during the experiment using 3D process technologies gives an advantage. The accuracy and reliability of the calculation results play a key role in ensuring the safety and reliability of rocket and space systems. Regular verification and verification of the results are also necessary to ensure a high degree of reliability and safety. The comprehensive analysis of the fluid flow in the inter-vane channel of the impeller of a low-flow centrifugal pump presented in the article, with the construction of the energy characteristics of the impeller, can be used to clarify the number of vanes. The developed calculation method consists of four parts: firstly, an expression is obtained to determine the projection of the pressure gradient on the longitudinal axis φ, secondly, an expression is obtained to determine the projection of the pressure gradient on the transverse axis ψ, thirdly, the derivative of the longitudinal velocity in the transverse direction is determined, and fourthly, the results are presented numerical and experimental visualization: the power balance, the dependence of the pressure and the coefficient of influence of a finite number of vanes on the flow rate of a low-flow centrifugal pump. Based on the results of theoretical research, an algorithm and a calculation program were developed that allows calculating local values. The considered approach is confirmed by verification of the results of mathematical modeling by graphical visualization of the flow and measurement of the power balance of a low-flow centrifugal pump. The obtained expressions for pressure gradient projections, determination of the derivative of the longitudinal velocity and experimental visualization play an important role in the calculation and analysis of the operation of centrifugal pumps. However, there is a need for further elaboration of the method to bring it to a form that allows calculating the three-dimensional flow of the working fluid in an arbitrary channel.