Calculation of the averaged three-dimensional boundary layer at the axisymmetrical boundaries of the interblade channels of turbine machines

The article discusses the flow of a gas at the blade rim of an axial turbine, consisting of an external steady-state continuous flow of an ideal compressible liquid and a three-dimensional turbulent boundary layer of a compressible liquid at the end surfaces of the rim, averaged in a peripheral direction. It presents an example of a calculation of flow in fixed blades, with a different form of the meridional cross section. In a flow through the rim of a turbine machine between the convex and concave surfaces of adjacent blades there arises a transverse gradient of the static pressure. At the end surface in the boundary layer the lines of the flow are shifted toward the convex side of the profile, and a secondary transverse flow of the liquid arises 1–3]. The article discusses the following: an external two-dimensional steady-state adiabatic flow of an ideal compressible liquid at the surface S₂, which can be taken as the mean surface of the interblade channel, with boundary lines at the peripheral and root end surfaces of the rim; a two-dimensional steady-state adiabatic flow of an ideal compressible liquid at the end surfaces of the rim between the convex and concave sides of the profiles 3, 4]; and a three-dimensional turbulent boundary layer, averaged in a peripheral direction at the end surfaces of the blade rim. The averaged boundary layer is calculated along one coordinate line s, and a simplified model of the quasi-three-dimensional flow is used. The coefficients of friction and heat transfer, and the inclination of the bottom flow lines are averaged.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–31, May–June, 1975.The author thanks G. Yu. Stepanov for posing the problem and evaluating the results.