Investigating Circumferential Non-Uniformities in Throughflow Calculations using an Harmonic Reconstruction

The flow field in a multistage turbomachine is very complex. It is 3D, unsteady and turbulent. Even if modern simulation tools can describe most of the flow features, the computation time needed and the extraction of useful information remain severe drawbacks to systematic use of URANS codes in a design procedure. In this context the throughflow simulation proved to be more convenient. Nevertheless the need for empiricism limits the potential of throughflow solvers.
As an alternative, Admaczyck (1984) proposed three averaging operators (ensemble, time and passage) that lead to the average-passage model, linking the unsteady turbulent flow field to a steady flow field in a typical blade passage. This model involves additional terms that respectively bring back the mean effect of turbulence, deterministic unsteadiness and aperiodicity on the mean periodic flow. These terms need to be modelled; it is the closure problem. Harmonic closure, which consists in solving a linearized perturbation system in the frequency domain, revealed to be an efficient method to approximate deterministic stresses (He and Ning, 1998, Stridh, 2005, Vilmin, 2006).
A fourth averaging can be performed, a circumferential averaging, giving rise to the throughflow model. Additional terms appear: the so-called circumferential stresses. It has been proven that these terms play an important role in the description of the flow (Jennions, 1986, Perrin, 1995), being at least as considerable as deterministic stresses. Introducing these terms in a throughflow simulation allows to reproduce the averaged 3D steady flow field (Simon, 2007). The aim of the present contribution is to prove that harmonic method can potentially be used to reconstruct circumferential stresses.
The importance of circumferential stresses in a throughflow simulation is first highlighted on a single stage low speed compressor testcase, for viscous and non-viscous flow fields. The second step is the characterization of the frequency spectrum of the circumferential perturbation field. Next are compared the stresses associated to a Fourier reconstruction of the perturbation field with the real ones. Finally the approximated circumferential stresses are injected into a throughflow simulation tool to analyse and demonstrate their capability to reproduce a 3D averaged flow field.