##
**Origin of transonic buffet on aerofoils.**
*(English)*
Zbl 1181.76092

Summary: Buffeting flow on transonic aerofoils serves as a model problem for the more complex three-dimensional flows responsible for aeroplane buffet. The origins of transonic aerofoil buffet are linked to a global instability, which leads to shock oscillations and dramatic lift fluctuations. The problem is analysed using the Reynolds-averaged Navier-Stokes equations, which for the foreseeable future are a necessary approximation to cover the high Reynolds numbers at which transonic buffet occurs. These equations have been shown to reproduce the key physics of transonic aerofoil flows. Results from global-stability analysis are shown to be in good agreement with experiments and numerical simulations. The stability boundary, as a function of the Mach number and angle of attack, consists of an upper and a lower branch - the lower branch shows features consistent with a supercritical bifurcation. The unstable modes provide insight into the basic character of buffeting flow at near-critical conditions and are consistent with fully nonlinear simulations. The results provide further evidence linking the transonic buffet onset to a global instability.

### MSC:

76H05 | Transonic flows |

76E09 | Stability and instability of nonparallel flows in hydrodynamic stability |

### Software:

ARPACK
Full Text:
DOI

### References:

[1] | Crouch, IUTAM Symposium on Unsteady Separated Flows and Their Control (2009) |

[2] | DOI: 10.1016/j.jcp.2006.10.035 · Zbl 1123.76018 |

[3] | DOI: 10.1016/S1270-9638(03)00061-0 · Zbl 1045.76531 |

[4] | DOI: 10.2514/3.12149 |

[5] | DOI: 10.2514/1.29332 |

[6] | Lehoucq, ARPACK User’s Guide (1998) · Zbl 0901.65021 |

[7] | DOI: 10.1016/0021-9991(81)90128-5 · Zbl 0474.65066 |

[8] | DOI: 10.2514/3.25144 |

[9] | DOI: 10.1016/j.ijheatfluidflow.2006.02.013 |

[10] | DOI: 10.1016/S0376-0421(02)00030-1 |

[11] | DOI: 10.2514/2.2071 |

[12] | DOI: 10.2514/1.9694 |

[13] | Drazin, Hydrodynamic Stability (1981) |

[14] | DOI: 10.1016/S0376-0421(01)00003-3 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.