To cite this version :
Weller-Calvo, Jessie and Fontane, Jérôme and
Joly, Laurent
Mode selection in swirling coaxial jets.
(2015)
In: Proceedings of Sixth International Symposium on Bifurcations
and Instabilities in Fluid Dynamics (BIFD 2015), 15 July 2015 - 17
July 2015 (Paris, France).
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MODE SELECTION IN SWIRLING COAXIAL JETS
Jessie Weller-Calvo, Jérôme Fontane & Laurent Joly
Institut Supérieur de l’Aéronautique et de l’Espace,
BP 54032, 10 Avenue Edouard Belin, 31055 Toulouse Cedex 4, France
Abstract We perform a temporal stability study of coaxial jets in the case where the inner jet is rotating (swirling jets, coaxial jets, temporal instability).
In order to improve the mixing properties of injectors, we investigate the potential synergy between decrease in circulation and axial shear. For this purpose, we examine the linear modal stability of a simplified analytical model which consists of a temporally evolving swirling jet surrounded by an annular jet with a different axial velocity. The present study extends the results of Gallaire & Chomaz [1] where a single swirling jet was considered. From an experimental point of view this set-up has been studied in particular by Ivanic et al. [2]. Their study, and others on coaxial jets, show that the mean axial velocity profiles close to the nozzle exit are characterized by a strong velocity deficit at the interface between the inner and outer jets. To account for this behaviour we considered the analytical profiles proposed by Hairoud [4] and Talamelli & Gavarini [3]. In this last study, the authors carry out a linear stability analysis of coaxial jets, linking the instability frequency to the different wake parameters. When we add swirl to the mix, the choice of shear layer thickness and minimum velocity in the wake has a strong impact on the outcome of the linear stability analysis, affecting not only the intensity of the instabilities, but also which particular azimuthal modes are most amplified. For a given wake model we then compute the maximum instability growth rate over a wide range of azimuthal and axial wavenumbers, for different values of swirl intensity and jet velocity ratio. We identify the dominant azimuthal wavenumber for each combination (Figure 1). Finally we look at the topology of the most unstable modes, identifying the respective roles of centrifugal and shear instabilities. 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 −1 −2 −3 −4 −4 −5 −6 −7 −8 −9 −10 −11
Λ
S
Figure 1. Mode selection and instability growth rates. S denotes the intensity of the swirl, Λ the velocity ratio Uout/Uin. The figure
shows growth rate isovalues, with darker tones indicating higher values, and displays the dominant azimuthal wavenumbers (which are always lower or equal to zero)
References
[1] F. Gallaire, J.-M. Chomaz, Mode selection in swirling jet experiments: a linear stability analysis, J. Fluid Mech 494, 223–253 (2003). [2] T. Ivanic, E. Foucault, J. Pecheux, Dynamics of swirling jet flows, Experiments in Fluids 35, 317–324 (2003).
[3] A. Talamelli, I. Gavarini, Linear instability characteristics of incompressible coaxial jets, Flow Turbulence Combust 76, 221–240 (2006). [4] A. Hairoud, Sur la stabilité globale des jets coaxiaux tournants, PhD Thesis, Université de Poitiers (2012).
