A Numerical Study of the Global Instability in Counter-Current Homogeneous Density Incompressible Round Jets

Abstract

The paper focuses on a global instability phenomenon in counter-current round jets issuing from co-axial nozzles. Three different configurations that differ in a way of the counter flow generation are investigated. Besides typical configurations used in experimental and numerical research performed so far, in which suction applied in an annular nozzle is a driving force for the counterflow, a novel set-up is proposed where the annular nozzle is oriented in the opposite direction and placed above the main one. Such a configuration eliminates the suction of fluid from the main jet, which in previous research was found to have a destructive impact on the occurrence of the global flow instability. The research is performed using a large eddy simulation (LES) method and the computations are carried out applying a high-order numerical code, the accuracy of which has been proven in previous works and also in the present research through comparisons with available experimental data. The research is complemented by the linear stability analysis which supports the LES results and formulated conclusions. In agreement with a number of the previous works it has been shown that the global modes can be triggered only when the velocity ratio (I) between the main jet velocity and the velocity of the jet issuing from the annular nozzle is above a certain threshold level ($$I_{\text {cr}}$$ I cr ). It has been shown that in the classical configurations of the co-axial nozzles the range of $$I\ge I_{\text {cr}}$$ I ≥ I cr for which the global instability phenomenon exists is very narrow and it disappears for larger velocity ratios. Reasons for that have been identified through detailed scrutiny of instantaneous flow pictures. In the new set-up of the nozzles the global instability persists for a significantly wider range of I. It has been shown that $$I_{\text {cr}}$$ I cr depends on both the momentum thickness of the mixing layer formed between the counter-current streams and the applied configuration of the nozzles. The LES results univocally showed that the latter factor decides on the type of the instability mode (Mode I or Mode II) that emerges in the flow, as it directly influences on a length of the region where the counter-current streams are parallel allowing the growth of short or long wave disturbances characteristic for Mode I and Mode II, respectively.