Turbomachines: incompressible flow calculation - Modeling

The purpose of this document is to summarize the methods available for the numerical simulation of incompressible fluid flows through the various fixed or moving components of a turbomachine, whether generating (turbine) or receiving (pumps, fans), which are generally shrouded. Only internal flows will be considered, i.e. those linked to energy transfer mechanisms between the fluid and the machine shaft, to the exclusion of ancillary flows (external flows: leaks, cavities, bearings, balancing flows, etc.).

A special section will be devoted to modeling the phenomenon of cavitation which, under certain conditions, can occur within the flow and is very specific to the case of incompressible fluids.

The physical mechanisms governing flow in turbomachinery are complex, multiple and partially explained. Flow conditions are essentially three-dimensional, viscous, unsteady and, in the case of flows with cavitation, phase changes must be taken into account.

The unsteady nature of flows is natural when we take into account the movement of fixed and moving parts between them. It is less natural and more difficult to apprehend when it comes from heterogeneities initiated by supply distortions, or when it comes from so-called intrinsic heterogeneities such as those appearing outside the operating point or in cavitating regimes. Moreover, all transient regimes are the source of unsteady effects.

In-depth knowledge and assessment of these physical mechanisms are becoming increasingly important, especially as users and designers compete to ensure substantial performance improvements, or to guarantee ever wider operating areas while imposing ever more stringent geometric constraints.

Identifying and analyzing in depth the mechanisms that govern flows helps to improve performance. This requires a combination of theoretical investigations, the development of more or less simplified models and increasingly advanced experimental studies.

Clearly, the time is still far off when all these different aspects can be simultaneously and rigorously taken into account when calculating a complete machine with its environment.

However, methods for predicting fluid flows in turbomachinery have improved significantly over the last few decades. This is due to a combination of advances in mathematical models, numerical techniques and computing power, whose rapid annual growth has enabled us to reduce the number of simplifying assumptions. However, it is not possible to directly solve the Navier-Stokes equations in the complex geometries of industrial applications.

That's why, faced with the problems raised by the determination of these complex flows,...