System analysis of rotodynamic machines

This article deals with the operation of rotodynamic fluid machines (or turbomachines). It aims to show how this operation is dependent, not only on design parameters (sizing of the rotor and stator components) and the machine's rotation speed, but also on the characteristics of the system in which the machine is installed for the user's needs (sizing of circuits, pressure losses associated with flows circulating in the installation). The various analyses are carried out primarily for machines with very low fluid compressibility (pumps, fans and hydraulic turbines), but many of the conclusions can be extended to machines handling more compressible fluids, even if aspects specific to this higher compressibility are not dealt with (in particular all aspects concerning sonic blocking and shock waves). The consequences of coupling between machine and system are first analyzed from a "static" point of view, i.e. assuming continuous operation on average. The notion of operating point is thus defined, and the questions of its uniqueness and stability are addressed. The transient behaviors associated with start-up, shutdown and flow regulation phases are then analyzed. A number of basic concepts are introduced, based on a straight pipe of constant cross-sectional area. Phenomena characteristic of longitudinal wave propagation are introduced. Examples of turbine and hydraulic pump transients are then described. Finally, the special case of the propagation of small pressure and flow disturbances during permanent averaging operation is discussed. A frequency approach using assemblies of hydroacoustic transfer matrices and "source" terms is presented. The various concepts developed in this article provide a basis for dialogue between machine manufacturers and users.