A time-marching meanline analysis method of axial compressor based on fifth-level averaging aerodynamic theory

The one-dimensional meanline analysis tool constitutes a fundamental component in the preliminary design phase of axial turbomachine but is always facing the challenge to improve the prediction accuracy. One potential way to tackle this issue is to retain sufficient physical information within the underlying mathematical equations to reduce dependence on empirical models. In this study, the fifth-level averaging aerodynamic theory is developed for a rigorous derivation of the primitive one-dimensional meanline flow equations of axial turbomachine, by performing a radial averaging procedure to the circumferentially averaged two-dimensional Navier-Stokes equations. A time-marching meanline analysis method is developed to facilitate the solution of meanline equations for axial compressor analysis, in which the end wall forces arising from radial averaging procedure are newly modeled based on dimensional zooming technique. The effectiveness of developed meanline analysis method with modeled end wall forces is demonstrated by numerical simulations of three test cases with a well-verified computational fluid dynamics solver. For the ideal inviscid cascade flow, the relative error of mass flow rate per throughflow area is 0.08%. For the subsonic viscous cascade flow, the absolute error of turning angle is 0.4 degrees and the relative error of drag coefficient is 2.5% under near-design condition. For the transonic axial compressor rotor flow, the maximum relative error of adiabatic efficiency is 2.4% under near-peak-efficiency conditions at various rotational speeds. This work is the first attempt to rigorously derive the primitive one-dimensional meanline flow equations and is of certain significance to provide an accurate and rapid tool for the performance analysis of axial compressor.