The effect of the diameter ratio on the absolute and convective instability of free coflowing jets

Abstract

The stability of two coflowing streams with finite cross stream extent has been studied in both axisymmetric as well as plane geometries. Transition curves from convective to absolute instability have been obtained in terms of the control parameters, namely, the density ratio, S, the velocity ratio, Λ, and, more importantly, the diameter ratio, a. A new mode of instability caused by the external shear layer included in the velocity profile has been identified. It has also been found that this mode is responsible for triggering the absolute instability of configurations considered convectively unstable in the limit a→∞. Moreover, in the present study it has been shown that, when Λ=1, the critical density ratio necessary to sustain absolute instability in axisymmetric jets decreases with the diameter ratio as Sc∝a−4, while it decreases as Sc∝a−6/5 in plane jets. In more general situations, where Λ≠1, two modes of instability associated, respectively, with the inner and the outer shear layers coexist. The analysis reveals that the outer shear layer has a significant effect on the stability of the internal interface, especially for light jets, corresponding to S<1, when a is sufficiently close to unity. Furthermore, a new region of absolute instability has been described in the a–Λ–S parameter space.