Filtered chorochronic interface as a capability for 3-D unsteady throughflow analysis of multistage turbomachinery

Abstract

This note reviews the widely used phased-lagged [Erdos, J. L., E. Alzner, and W. McNally. 1977. AIAA Journal 15: 1559–68.] approach and corresponding chorochronic interface relations [Gerolymos G. A., G. J. Michon, and J. Neubauer. 2002. Journal of Propulsion and Power 18: 1139–52.] and explores its potential extension to the approximate unsteady throughflow analysis of multistage turbomachinery. The basic relations pertaining to the binary blade-row interaction case, for which chorochronic periodicity is exact in a phase-averaged rans framework, are briefly formulated, and selected computational examples illustrate the application of the method. Then, the filtered chorochronic interface is defined as the unsteady counterpart of the well-known mixing-plane concept. This interface takes into account only those tθ-waves which are compatible with the interaction of the immediately upstream and downstream blade-rows. The concept, which is similar to the decomposition-and-superposition method [Li, H. D., and L. He. 2005. ASME J ournal of Turbomachinery 127: 589–98.], is illustrated by 3-D computations of a ½-stage transonic compressor.

Keywords:

• turbomachinery
• blade-row interaction
• multistage
• chorochronic periodicity
• filtered blade-row interface

Acknowledgements

The author wishes to thank several former doctoral students (V. Chapin, R. Haugeard, D. Vinteler, G. Tsanga, C. Hanisch, V.C. Sharma, V. Valentin, J. Neubauer, I. Noussis, N. Ben Nasr) who worked on the turbo_3D project of the Laboratory for Energetics (lemfi) at upmc, and ran the computations used to illustrate the methodology described in the present work. Funding from the European Community, the French Ministry of Research, snecma and edf is gratefully acknowledged. Computations were performed using hpc resources from genci–idris, under various grants.

Notes

1. Notice that since pitchwise-periodicity and chorochronic interface conditions are both applied (Gerolymos et al. 2002a) by harmonics-based reconstruction of phantom nodes, the exchange of nonlocal (in time and/or space) information is not done in the time-domain. For this reason, in principle, it should be possible to apply different physical time-steps in each blade-row, but this has not been tested yet.

2. As shown in He (2010), the moving-averages technique (Gerolymos et al. 2002a) leads to the same converged solution as the shape-correction technique of He (1992), the generating equations being identical. The difference between the two methods lies in the choice of the updating frequency. He (1992, 2010) updates the harmonics at the end of each period, while Gerolymos et al. (2002a) update the harmonics at every physical time-step simulated by the flow solver. A quantitative evaluation of the rate-of-convergence of the two variants would be interesting, especially in relation to the slow convergence of the harmonics problem discussed by He (2010).