Absolute instability of an annular jet: local stability analysis
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ORIGINAL PAPERS
Absolute instability of an annular jet: local stability analysis A. Boguslawski
. K. Wawrzak
Received: 2 October 2019 / Accepted: 14 September 2020 Ó The Author(s) 2020
Abstract The paper presents parametric studies of the first and second azimuthal absolute modes in annular non-swirling and swirling jets. The spatiotemporal linear stability analysis is applied to investigate an influence of governing parameters including axial velocity gradients in inner and outer shear layers, back-flow velocity, swirl number and shape of the azimuthal velocity. A new base flow is formulated allowing a flexible variation of the shape of axial and azimuthal velocity profiles. It is shown that the first helical absolute mode is governed mainly by the backflow velocity and swirl intensity. A steepness of the inner shear layer can control the absolute mode frequency. The velocity gradient in the outer shear layer and the shape of the azimuthal velocity have rather limited impact on the absolute mode characteristics. Finally, it is shown that the second helical absolute mode can dominate the flow with a stronger swirl intensity. Keywords Annular jet Swirling jet Absolute instability Linear stability theory
A. Boguslawski (&) K. Wawrzak Department of Thermal Machinery, Czestochowa University of Technology, al. Armii Krajowej 21, 42-201 Czestochowa, Poland e-mail: [email protected]
1 Introduction Annular swirling jets are met in many technical applications. Gas turbines and aeroengines are examples where annular nozzles are utilised to deliver fuel and oxidiser with a swirl stabilising the flame. In the case of non-premixed combustors mixing processes of the fuel and oxidiser in annular jets are of primary importance for the combustion efficiency and safety. Naturally formed vortical structures in such flows could enhance or deteriorate a mixing intensity. Hence, improved understanding of the annular jets instability could help in the development of new combustion technologies. The swirling jets undergo a vortex breakdown process characterised by spiralshaped structures. Despite that this phenomenon has been known for many years a mechanism leading to helical structures formation has not been fully understood so far [1]. Theories formulated for the vortex breakdown were categorised into the following underlying concepts: 1. The phenomenon is associated with the concept of critical state or, more generally, with wave phenomena [2–4]. 2. The phenomenon is analogous to boundary layer separation or flow stagnation [5, 6]. 3. The phenomenon is a consequence of the hydrodynamic instability [7–10].
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Meccanica
As was mentioned in [1] the vortex breakdown is highly time dependent phenomenon and the spiralshaped structures start to precess about the axis of symmetry thus forming the so called precessing vortex core (PVC) [11]. There are many more recent advanced approaches to the vortex breakdown in swirling jets like a sensitivity analysis of Quadri et al. [12] s
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