Vortex breakdown

He considered that the rapid flame propagation could be achieved with the same mechanism as vortex breakdown. Figure 4.2.2 schematically shows his vortex bursting mechanism [4,5]. When a combustible mixture rotates, Ihe pressure on the axis of rotation becomes lower than the ambient pressure. The amount of pressure decrease is equal to max in Rankine s combined vor-fex, in which p denotes fhe unburned gas density and Vg denotes the maximum tangential velocity of the vortex. However, when combustion occurs, the pressure on the axis of rofafion increases in the burned gas owing to the decrease in the density, and becomes close to the ambient pressure. Thus, there appears a pressure jump AP across the flame on fhe axis of rotation. This pressure jump may cause a rapid movement of the hot burned gas. By considering the momentum flux conservation across the flame, fhe following expression for the burned gas speed was derived ... 

Umemura, A. and Tomita, K., Rapid flame propagation in a vortex tube in perspective of vortex breakdown phenomena. Combustion and Flame, 125,820-838, 2001. 

P. Billant, J.-M. Chomaz, and P. Huerre. Experimental study of vortex breakdown in swirling jets. J. Fluid Mech., 376 183-219, 1998. 

O. Lucca-Negro and T. O Doherty. Vortex breakdown a review. Prog. Energy Comb. Sci., 27 431-481, 2001. 

Later Mayle, 1970 [400] continued their research by performing measurements of velocity and pressure within the fire whirl. He found that the behavior of the plume was governed by dimensionless plume Froude, Rossby, second Damkohler Mixing Coefficient and Reaction Rate numbers. For plumes with a Rossby number less than one the plume is found to have a rapid rate of plume expansion with height. This phenomenon is sometimes called vortex breakdown , and it is a hydraulic jump like phenomena caused by the movement of surface waves up the surface of the fire plume that are greater than the speed of the fluid velocity. Unfortunately, even improved entrainment rate type models do not predict these phenomena very well. 

Observations show that about 25% of the observed mid-latitude ozone column depletion occurs above about 25 km, in the altitude range where gas-phase photochemistry is rapid and it is difficult for dynamics to compete (see e.g., SPARC, 1998). A further contribution due to PSC processing and to vortex breakdown is highly likely. Thus, a substantial chemical contribution of at least half of the trend in the column seems difficult to dispute even if locally-driven chemical ozone depletion in the mid-latitude lower stratosphere were to be substantially smaller than suggested by modelling studies and by the post-Pinatubo measurements described above. Thus, the evidence suggests that chlorine chemistry has played an important and very likely dominant role in the observed trends in mid-latitude ozone over the past two decades (for a recent review, see WMO/UNEP, 2003). 

Sarpkaya, T. 1971. Vortex breakdown in conical flows. AIAA J. 9 1792-99. 

Faler, J.H., and S. Leibovich. 1977. Disrupted states of vortex flow and vortex breakdown. Physics Fluids 20 1385-400. 

Brucker, C., and Althaus, W., Study of vortex breakdown by particle tracking velocimetry (PTV) Part 1 Bubble-type vortex breakdown, Exps. in Fluids, 12, 339-349 (1992). 

Just upstream of the vortex finder entry vortex breakdown occurs, similar to the breakdown structures observed by Escudier et al. (2005) slightly upstream or inside a contraction. 

Obviously the vortex tube shown in Fig. 7.3.4 is very similar to a cyclone, and the exit tube very similar to the vortex finder in a cyclone. One very interesting feature found by Derksen is a vortex breakdown of type 0 , according to the classification of types of vortex breakdown by Faler and Leibovich (1977), in the exit tube at certain flowrates and in certain geometrical configurations. In a type 0 breakdown, a gas bubble with recirculatory flow is formed at the point where the vortex breaks down, and the flow downstream is much more turbulent, and less intensely swirling. Derksen s simulations are shown in Fig. 7.3.5. 

Fig. 7.3.5. CFD simulations of Derksen showing type 0 vortex breakdown in the gas outlet of a swirl-tube-like geometry, reprinted from Derksen (2005), copyright 2004, with permission from Elsevier...

Obviously the existence of such a vortex breakdown in the vortex finder will have significant impact on our understanding of the very high pressure drop in the vortex finder (see Chap. 4), and the working of pressure-recovery vanes (see Hoffmann et al., 2005, Sect. 15.1.5). 

One is that the end of the vortex is an axisymmetric phenomenon, that the end represents a sort of recirculating gas bubble . Such a vortex end is observed in the research field of vortex breakdown in vortex tubes , tubes in which a flowing liquid is caused to swirl with swirl vanes. A difference between a vortex tube and a cyclone or swirl tube is that the flow reverses in the latter, while in the vortex tube it continues past the vortex end, and discharges from the bottom of the tube. Another difference is that this type of experiment is usually (but not always, see Sarpkaya, 1995) performed under laminar flow conditions, while the flow in a cyclone is turbulent. 

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