Abstracts - KTH Mechanics

44
Axisymmetric absolute instability of swirling jets
J. J. Healey ∗
The linearized stability, and propagation characteristics, of disturbances to a family
of simple models for swirling jet flow will be presented. Although non-axisymmetric
waves are known to produce absolute instability (AI), and have been successfully related
to helical modes of vortex breakdown, a difficulty in the application of Briggs’
method to axisymmetric waves in swirling jets has been noted by several authors.
The ‘pinch-point’ can cross the imaginary axis of the complex wavenumber plane,
leading to the appearance of eigenfunctions that grow, instead of decay, with distance
outside the shear layer. The same problematic behaviour of the pinch-point was recently
found by the author in the rotating disk boundary layer, and the physical
consequences were studied in detail in that context.
Our understanding of this behaviour in the rotating disk problem has been used to
help us to calculate for the first time AI of inviscid axisymmetric waves in swirling jets.
It is found that these waves can grow with distance in the radial direction outside the
jet, and that the addition of a bounding cylinder far from the jet converts this spatial
growth into an AI. As the distance from the jet to the outer cylinder reduces, the AI
increases, and less swirl is needed to produce AI, see figure 1(a). It is interesting to
note that many experiments on axisymmetric vortex breakdown involve swirling flows
in pipes, and it may be that the presence of the pipe is instrumental in creating the
AI, which perhaps leads in turn to vortex breakdown. Following previous studies, the
model profiles have uniform axial flow, and constant angular velocity, within the jet
and both velocity components drop discontinuously to zero outside the jet. A more
realistic family of profiles with finite thickness smooth shear layers at the jet edge has
also been studied. It is found that increasing the shear layer thickness produces AI,
even in the unconfined jet, via an enhancement of the centrifugal instability, see figure
1(b). For a given swirl, the shear layer at the jet’s edge thickens with downstream
distance, causing the flow to change from CI to AI at a critical distance from the jet
nozzle, possibly providing the location for axisymmetric vortex breakdown.
∗ Department of Mathematics, Keele University, Keele, Staffs. ST5 5BG, UK
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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Figure 1: Neutral curves for axisymmetric AI. (a) Confined jets: swirl vs. outer
cylinder radius (dashed line is limit as h →∞). (b) Smooth jets: swirl vs. shear layer
thickness (dashed lines are non-pinching saddles).