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Long-wave instabilities of two interlaced helical vortices
Airbus Helicopters, Aerodynamics Department, Marignane, France. (CNRS, Aix-Marseille Universit ́e, Centrale Marseille, IRPHE, Marseille, France)
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9446-7477
CNRS, Aix-Marseille Universit ́e, Centrale Marseille, IRPHE, Marseille, France.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
2017 (English)Manuscript (preprint) (Other academic)
Abstract [en]

We investigate theoretically and experimentally the stability of two interlaced helical vortices with respect to displacement perturbations having wavelengths that are large compared to the size of the vortex cores. First, existing theoretical results are recalled and applied to the present configuration. Various modes of unstable perturbations, involving different phase relationships between the two vortices, are identified and their growth rates are calculated. They lead to a local pairing of neighbouring helix loops, or to a uniform pairing with one helix expanding and the other one contracting. A relation is established between this instability and the three-dimensional pairing of arrays of straight parallel vortices, and a striking quantitative agreement concerning the growth rates is found, showing that the local pairing of vortices is the driving mechanism behind the instability of the helix system. Second, an experimental study designed to observe these instabilities in a real flow is presented. Two helical vortices are generated by a two-bladed rotor in a water channel and characterised through dye visualisations and PIV measurements. Unstable displacement modes are triggered individually, either by varying the rotation frequency of the rotor, or by imposing a small rotor eccentricity. The observed unstable mode structure, and the corresponding growth rates obtained from advanced processing of visualisation sequences, are in good agreement with theoretical predictions. The non-linear late stages of the instability are also documented experimentally. Whereas local pairing leads to strong deformations and subsequent break-up of the vortices, uniform pairing results in a leapfrogging phenomenon, which intermittently restores the initial double-helix geometry, in agreement with recent observations from numerical simulations.

Place, publisher, year, edition, pages
2017. , p. 34
Keywords [en]
vortex flows, vortex instability, vortex interactions
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-218170OAI: oai:DiVA.org:kth-218170DiVA, id: diva2:1159843
Note

QC 20171124

Available from: 2017-11-23 Created: 2017-11-23 Last updated: 2017-11-24Bibliographically approved
In thesis
1. Studies on instability and optimal forcing of incompressible flows
Open this publication in new window or tab >>Studies on instability and optimal forcing of incompressible flows
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis considers the hydrodynamic instability and optimal forcing of a number of incompressible flow cases. In the first part, the instabilities of three problems that are of great interest in energy and aerospace applications are studied, namely a Blasius boundary layer subject to localized wall-suction, a Falkner–Skan–Cooke boundary layer with a localized surface roughness, and a pair of helical vortices. The two boundary layer flows are studied through spectral element simulations and eigenvalue computations, which enable their long-term behavior as well as the mechanisms causing transition to be determined. The emergence of transition in these cases is found to originate from a linear flow instability, but whereas the onset of this instability in the Blasius flow can be associated with a localized region in the vicinity of the suction orifice, the instability in the Falkner–Skan–Cooke flow involves the entire flow field. Due to this difference, the results of the eigenvalue analysis in the former case are found to be robust with respect to numerical parameters and domain size, whereas the results in the latter case exhibit an extreme sensitivity that prevents domain independent critical parameters from being determined. The instability of the two helices is primarily addressed through experiments and analytic theory. It is shown that the well known pairing instability of neighboring vortex filaments is responsible for transition, and careful measurements enable growth rates of the instabilities to be obtained that are in close agreement with theoretical predictions. Using the experimental baseflow data, a successful attempt is subsequently also made to reproduce this experiment numerically.

In the second part of the thesis, a novel method for computing the optimal forcing of a dynamical system is developed. The method is based on an application of the inverse power method preconditioned by the Laplace preconditioner to the direct and adjoint resolvent operators. The method is analyzed for the Ginzburg–Landau equation and afterwards the Navier–Stokes equations, where it is implemented in the spectral element method and validated on the two-dimensional lid-driven cavity flow and the flow around a cylinder.

Place, publisher, year, edition, pages
Stockholm, Sweden: KTH Royal Institute of Technology, 2017. p. 47
Series
TRITA-MEK, ISSN 0348-467X ; 2017:19
Keywords
hydrodynamic stability, optimal forcing, resolvent operator, Laplace preconditioner, spectral element method, eigenvalue problems, inverse power method, direct numerical simulations, Falkner–Skan–Cooke boundary layer, localized roughness, crossflow vortices, Blasius boundary layer, localized suction, helical vortices, lid-driven cavity, cylinder flow
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-218172 (URN)978-91-7729-622-5 (ISBN)
Public defence
2017-12-14, D3, Lindstedtsvägen 5, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20171124

Available from: 2017-11-24 Created: 2017-11-23 Last updated: 2017-11-27Bibliographically approved

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