Dynamic Mode Decomposition of a Separated Nozzle Flow with Transonic Resonance
Journal article, 2017

Operating convergent–divergent nozzles at low pressure ratios can lead to flow separation. Certain nozzle contours are known to produce a discrete acoustical tone under such conditions that are believed to be generated by a phenomenon known as transonic resonance, which involves a standing pressure wave situated between the separation shock and the nozzle exit plane. This paper reports the findings of a dynamic mode decomposition analysis of a perturbed axisymmetric unsteady Reynolds-averaged Navier–Stokes simulation of a nozzle flow known to exhibit this phenomenon. Two cases of different pressure ratios were studied in depth. The results show that the two cases differ in the shape of the standing pressure wave. The lower pressure ratio produces a standing 3/4 pressure wave, whereas the higher pressure ratio produces a 1/4 wave. In both cases, dynamic mode decomposition modes that match the standing pressure wave shape were found to be the least damped and the most energetic modes of the modes produced by the dynamic mode decomposition algorithm. The frequency of the mode for the lower pressure ratio matched the experimentally observed transonic tone frequency extraordinarily well, whereas the higher pressure ratio case was in fair agreement. The dynamic mode decomposition algorithm captured the transonic frequency for five additional pressure ratios.

Transonic resonance

Free-shock separation

Supersonic nozzle flow

Dynamic Mode Decomposition (DMD)


Ragnar Larusson

Chalmers, Applied Mechanics, Fluid Dynamics

Niklas Andersson

Chalmers, Applied Mechanics, Fluid Dynamics

Jan Östlund

GKN Aerospace

AIAA Journal

0001-1452 (ISSN) 1533-385X (eISSN)

Vol. 55 4 1295-1306

Areas of Advance


Subject Categories

Aerospace Engineering

Fluid Mechanics and Acoustics


Basic sciences


C3SE (Chalmers Centre for Computational Science and Engineering)



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