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

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.

The calculation basis for a four-component jet mixer for fertilizer and water

This article covers calculation basis for a four-component jet mixer for fertilizer and water. The calculation for a four-component jet mixer for fertilizer consists in determining the basic geometric and hydrau-lic parameters of a four-component jet mixer for fertilizer and water and supplying the mixture to irrigated areas, with fertilizing irrigation, which will allow supplying all types of fertilizers and changing the concentration of mixture in the required proportions. All geometric relative parameters are calculated on the basis of the need to scale the mixer dimensions and are taken as the ratio of the diameters of the mixer elements to the cylindri-cal part of the mixing chamber. The above calculation bases determine the main parameter of the mixer necessary for determining all the elements – the cross-sectional area of the annular nozzle. It was founded that when calculating the geometric characteristic, you should be guided by the desire to accept the value of the geometric characteristic m=2.5 ÷ 8.0, corre-sponding to the maximum value of the efficiency up to 40% and higher.

Design method of a two-phase annular nozzle in cryogenic liquid expander

The two-phase annular nozzle is a critical component of liquid expanders. It matches the outlet of the first stage and the inlet of the second stage. A design method of two-phase annular nozzle involving a two-step process is proposed. Nonequilibrium effects are introduced by the area factor during the second process. The flashing in two-phase annular nozzle is simulated through the cavitation method and validated by the experimental results of Brookhaven National Laboratory’s nozzle and Hord’s hydrofoil. A forward flashing two-phase annular nozzle and a backward flashing two-phase nozzle are designed with different centerline angle distributions where they show a good agreement with the design. Forward flashing two-phase annular nozzle exhibits high curvature and nonuniformity. Backward flashing two-phase nozzle exhibits lower nonuniformity and a slightly higher boundary layer ratio, which shows a better performance in terms of the nonequilibrium effects.