Turbomachinery: calculating compressible flows

This summary covers methods for numerically simulating the flow behavior of turbomachinery (fixed and moving parts of compressors and axial and centrifugal turbines). Only the aerodynamic aspect will be studied, to the exclusion of all reactive phenomena. It should also be noted that :

• only single-phase compressible fluids (gases) are considered here;

• the applications envisaged involve the compressibility of the fluid, thus excluding low-speed regimes;

• the most advanced calculation methods are mainly developed in the aeronautical field.

Flow in a turbomachine is characterized by four essential aspects: three-dimensionality, viscosity, unsteadiness (even in steady state) and heat transfer.

While the first two occur naturally, the third must be taken into account as soon as we are interested in the movement of one or more moving wheels in relation to one or more fixed wheels, a more common configuration than that of an isolated moving wheel. Unsteadiness can also be due to problems of distortion or intrinsic heterogeneities. In addition, all transient regimes are also sources of unsteady effects.

Taking heat transfer into account is essential for determining the mechanical characteristics of various fixed or moving components - compressors, turbines, disks, casings - and consequently their service life, as well as for predicting their geometric dimensions and controlling the various clearances. There are two particular areas of application for aerothermodynamics that are specific to turbomachinery. The first is the so-called internal flow, which concerns the inter-disk cavities and cooling channels inside fixed and moving turbine blades. The actual geometries are complex, with deliberate discontinuities to enhance convective exchanges. Finally, the calculation of the so-called external flow around the blades must take into account the presence of cooling flows that exit the blade either through slots, especially at the trailing edge, or through multiperforations. The same applies to internal and/or external casings. The complexity of the flow is thus increased, and these effects must be taken into account in the overall aerodynamic calculation.

Clearly, it will be impossible for some time to rigorously take all these aspects into account simultaneously when calculating a complete machine, for two main reasons in particular:

• the first is linked to memory capacity and calculation times, which are incompatible with the most powerful computers currently on the market;

• the second, more crucial, stems from the observation...