Fluid mechanics and thermodynamics are the fundamental sciences used for the aerodynamic design and analysis of axial-flow compressors. This chapter highlights some fundamental concepts from fluid mechanics to complement the concepts from thermodynamics covered in Chapter 2. The governing equations will be developed in forms suitable for the various aerodynamic analyses commonly employed for axial-flow compressors. Detailed solution procedures will be covered in subsequent chapters.
Several types of fluid dynamic analysis are useful for this purpose. The through-flow analysis is widely used in both design and performance analysis. This involves solving the governing equations in the hub-to-shroud plane at stations located between blade rows. The flow is normally considered to be axisymmetric at these locations, but still three-dimensional because of the existence of a tangential velocity component. Empirical models are employed to account for the fluid turning and losses that occur when the flow passes through the blade rows. A simplification of this analysis is the “pitch-line” or “mean-line” one-dimensional flow model, which ignores the hub-to-shroud variations. These were very common for many years, but are no longer particularly relevant to the problem. Computers are sufficiently powerful today that there is really no need to simplify the problem that much. The through flow in an axial-flow compressor is strongly influenced by viscous effects near the end walls. The primary influence from these end-wall boundary layers is commonly described as end-wall blockage. An inviscid through-flow analysis ignores the low momentum fluid in the boundary layers and will overestimate the mass flow that the passage can accommodate for a given flow field solution. To compensate the common practice is to impose a blockage factor to effectively reduce the passage area. This requires consideration of boundary layer analysis to estimate the appropriate blockage factors to be used. More fundamental internal flow analyses are often useful for specific components, particularly blade rows. These include two-dimensional flow analyses in either the blade-to-blade or hub-to-shroud direction, and quasi-three-dimensional flow analyses developed by combining and interacting these two-dimensional analyses. Again, wall boundary layer analysis is often used to evaluate viscous effects. Any of these analyses may be used in a design mode as well as an analysis mode. A design mode seeks to define the gas path geometry (end-wall contours and blades) to produce the desired flow field, while an analysis mode seeks to predict the flow field from specified geometry.
Viscous computational fluid dynamics (CFD) solutions are also in use for axial-flow compressors. These are typically three-dimensional flow analyses, which consider the effects of viscosity, thermal conductivity and turbulence. In most cases, commercial viscous CFD codes are used although some in-house codes are in use within the larger companies. Most design organizations cannot commit the dedicated effort required to develop these highly sophisticated codes, particularly since viscous CFD technology is changing so rapidly that any code developed will soon be obsolete unless its development continues as an ongoing activity. Consequently, viscous CFD is not covered in this book beyond recognizing it as an essential technology and pointing out some applications for which it can be effectively used to supplement conventional aerodynamic analysis techniques.