Modal Analysis of Supersonic Flow Separation in Nozzles
Doktorsavhandling, 2017

Operating a convergent-divergent nozzle under overexpanded conditions can lead to supersonic flow separation in the divergent section of the nozzle. In this case, an attached oblique shock wave forms at the separation base. The sudden pressure rise across the shock wave can cause damaging lateral pressure forces, or side-loads, to act on the nozzle if the separation line is asymmetric. Such asymmetry can be caused by downstream instabilities stemming from turbulence, external excitation or periodic modes. In this thesis the applicability of applying modal decomposition methods to supersonic nozzle flows was investigated. Axisymmetric RANS and URANS simulations of nozzle flows were investigated using the Arnoldi algorithm and the Dynamic Mode Decomposition,respectively. The Arnoldi method relies on a linearized flow solver and has the advantage of being able to detect asymmetric modes on two dimensional grids. The DMD, however, is a snapshot-based algorithm which needs no explicit linearization of the flow dynamics. Results show that these methods can successfully be applied to supersonic nozzle flows with separation and strong shocks. For example, the Arnoldi method predicted a helical screeching mode with impressive accuracy and The DMD analysis on perturbed 2D URANS flow field was able to detect modes linked to transonic resonance. Finally, Detached Eddy Simulations (DES) on a separated flow inside a Truncated Ideal Contoured Nozzle were performed for two separate nozzle pressure ratios (NPR’s). The simulated sideload were lower than experimentally measured values but within uncertainty range. A three dimensional DMD analysis was performed on the DES data and revealed a strong ovalization mode at the lower NPR and a helical mode which could be linked to a peak in side-load spectrum at the higher NPR.

Separated Nozzle Flow

Dynamic Mode Decomposition



Modal Analysis


Virtual Development Laboratory, M-huset.
Opponent: Professor Abdellah Hadjadj, Department of Mechanical Engineering, National Institute for Applied Sciences, France


Ragnar Larusson

Chalmers, Tillämpad mekanik, Strömningslära

Investigation of Screech in Supersonic Jets Using Modal Decomposition

Proceedings of NSCM-27: the 27th Nordic Seminar on Computational Mechanics,; (2014)p. 25-28

Övrigt konferensbidrag

Hybrid RANS-LES Simulation of Separated Nozzle Flow

52nd AIAA/SAE/ASEE Joint Propulsion Conference, 2016,; (2016)

Paper i proceeding

Comparison of Eigenmode Extraction Techniques for Separated Nozzle Flows

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and exhibit 2014; Cleveland; United States; 28 July 2014 through 30 July 2014,; (2014)

Paper i proceeding

Linear Stability Analysis Using the Arnoldi Eigenmode Extraction Technique Applied to Separated Nozzle Flow

49TH AIAA/ASME/SAE/ASEE JOINT PROPULSION CONFERENCE, July 14 - 17, 2013. San Jose, CA, USA,; Vol. 1(2013)

Paper i proceeding



Rymd- och flygteknik

Strömningsmekanik och akustik





Grundläggande vetenskaper



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4223



Virtual Development Laboratory, M-huset.

Opponent: Professor Abdellah Hadjadj, Department of Mechanical Engineering, National Institute for Applied Sciences, France

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