Fluid mechanics and thermodynamics are the fundamental sciences used for turbine aerodynamic design and analysis. 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 turbines. Detailed solution procedures will be covered in subsequent chapters. The content of this chapter is quite similar to this writer's previous coverage of this topic for compressor aerodynamics [1, 2], but is specifically adapted to be more relevant to turbine aerodynamics.
Several types of fluid dynamic analysis are useful for this purpose. The through-flow analysis is widely used in axial-flow turbine performance analysis. This involves solving the governing equations for inviscid flow 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. By contrast, hub-to-shroud through-flow analysis is not very useful for the performance analysis of radial-flow turbomachines such as radial-inflow turbines and centrifugal compressors. The inviscid flow governing equations do not adequately model the flow in the curved passages of radial turbomachines to be used as a basis for performance analysis. Instead, a simplified “pitch-line” or “mean-line” one-dimensional flow model is used, which ignores the hub-to-shroud variations. These also continue to be used for axial-flow turbine performance analysis, but are no longer particularly relevant to the problem. Computers are sufficiently powerful today that there is really no longer a need to simplify the problem that much for axial-flow turbomachinery. More fundamental internal flow analyses are often useful for the aerodynamic design of specific components, particularly blade rows. These include two-dimensional flow analyses in either the blade-to-blade or hubtoshroud direction, and quasi-three-dimensional flow analyses developed by combining those two-dimensional analyses. Wall boundary layer analysis is often used to supplement these analyses with an evaluation of viscous effects.
Viscous computational fluid dynamics (CFD) solutions are also in use for turbines. 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.