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

Abstract

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.