Absolute and convective instabilities of heated coaxial jet flow

Abstract

This study investigates the inviscid, linear spatio-temporal stability of heated, compressible and incompressible coaxial jet flows. The influence of the temperature ratio and the velocity ratio between the core jet and the bypass stream on the transition from convectively to absolutely unstable flows is studied numerically. The investigation shows that for coaxial jets absolute instability can occur for considerably lower core-stream temperatures than for single jets. The reason for this modified stability character is the appearance of an additional unstable mode as a result of the outer velocity shear layer between the bypass stream and the ambient flow. The presence of two shear layers enables the interaction between otherwise free waves to give rise to new instabilities. When the bypass-stream velocity is increased, the classical absolute mode known from single jets (inner mode) is first stabilized and then destabilized for high bypass-stream velocities, whereas the outer mode reaches maximum spatiotemporal growth rates when the core-stream velocity is approximately equal to twice the bypass-stream velocity. Additionally, it is demonstrated that the spatio-temporal character of the modes is very sensitive to the shear-layer thickness and to the distance separating the two layers. Increasing the Mach number strongly dampens the onset of an absolute instability for both modes. a) gioele.balestra@epfl.ch

Local analysis of absolute instability in plasma jets

“…This behaviour seems to be linked with the apparent decrease of the group velocity at the velocity perturbations maximum. Similar results have also been observed by Balestra et al (2015) in co-axial jets. Furthermore, Nichols et al (2007) observed that absolute instabilities intensified when the maximum shear aligns with the density shear in heated round jets.…”

“…Velocity profiles at the chamber inlet exhibit two streams and shear layers, similarly to coaxial jets studied in the literature (Balestra et al. 2015). The main stream is caused by the heating at the jet centreline, while the secondary stream originates from the annular inlet.…”

“…In contrast, the shear-layer mode associated with saddle S 2 is barely affected by the changes in m, in agreement with results of for single top-hat jets. However, similar results for coaxial jets were not included in the work of Balestra et al (2015) which was restricted to axisymmetric perturbations. One can note that no valid saddle was found to lie on the upper α i > 0 half-plane in the results presented.…”

“…The effect of confinement on round and planar jets and wakes was investigated by Juniper (2006Juniper ( , 2008, revealing that confinement effect on absolute instabilities is non-negligible, yet depends on the confinement parameter. More recently, these analyses were extended to co-axial jet flows by Balestra, Gloor & Kleiser (2015), revealing more complex absolute modes than the traditional jet-column and shear-layer modes identified, among others, by .…”

Convective and absolute instability of viscoelastic liquid jets in the presence of gravity

“…Following Bassi 7 and Balestra, Gloor, and Kleiser, 48 we use the saddle point method to find solutions of the dispersion relation, i.e., D(ω, k) = 0, for the complex pair (ω 0 , k 0 ), where D(ω 0 , k 0 ) = ∂D(ω 0 , k 0 )/∂k = 0 and ∂ 2 D(ω 0 , k 0 )/∂k 2 ≠ 0. In order to investigate the behavior of changing dimensionless parameters, we consider a reference state, where We = 2, F = 4, Re = 800, α = 3 and De = 10 at z = 0.…”