Vortex ring

The relation between matter and ether was rendered clearer by Lord Kelvin s vortex-atom theory, which assumed that material atoms are vortex rings in the ether. The properties of electrical and magnetic systems have been included by regarding the atom as a structure of electrons, and an electron as a nucleus of permanent strain in the ether— a place at which the continuity of the medium has been broken and cemented together again without fitting the parts, so that there is a residual strain all round the place (Larmor). 

Further measurements on the flame speed have been obtained with the use of a rotating tube [11] and vortex ring combustion [12]. Figure 4.2.4 shows the flame speed in vortex rings [12]. The values of slope in the V( -plane is nearly equal to unity for the near stoichiometric methane/air mixtures. Thus, this value is much lower than the predictions of JPi/P, and flPn/P >. 

Relation between flame speed V and maximum tangential velocity Vg in the vortex ring combustion. (From Ishizuka, S., Murakami, T., Hamasaki, T., Koumura, K., and Hasegawa, R., Combust. Flame, 113, 542,1998.)... 

Before discussing about the flame speed along a vortex core, it is first necessary to be familiar with the flames in various vortex flows. To date, four types of vortex flows have been used to study the flame behaviors. They are (1) a swirl flow in a tube [1,10], (2) vortex ring [2,3,12,13,16], (3) a forced vortex flow in a rotating tube [11], and (4) line vortex [22]. 

The existence of the vortex core can be observed in a very special case. Figure 4.2.9 exhibits a Schlieren sequence of vortex ring combustion of pure fuel. In this case, propane fuel was ejected through an orifice into an open air, and the vortex ring was ignited by an electric spark at the bottom. Although the boundary... 

Vector profiles of (a) cold vortex ring and (b) burning vortex ring (Dq = 60mm, P = 0.6MPa, stoichiometric mixture). Insets show the relative position of the PIV laser sheet to (a) the vortex ring and (b) the flame. 

Vector profile of vortex ring combustion, showing induced velocities along the vortex core. (Lean propane/air mixture, equivalence ratio O = 0.8, Do = 60 mm, P= 0.6 MPa, dotted lines show the flame front taken with the ICCD camera. The right inset shows the relative position of the PIV laser sheet relative to the flame.)... 

Thus, the same mixture atmosphere may give pure results of vortex ring combustion. 

Figure 4.2.13 shows the variation of the flame speed with the maximum tangential velocity obtained with vortex ring combustion in the same mixture atmosphere [29]. The cylinder diameter was 100 mm and various lean, stoichiometric, and rich methane/ air and propane/air mixtures were examined. The diameter of the propagating flame was also determined and the ratio of the flame diameter to the core diameter was also plotted against the maximum tangential velocity. 

U is the translational velocity of the vortex ring r is the circulation D is the ring diameter d is the core diameter... 

It can be seen that the prediction 6a underestimates any results. This is because axial expansion is unrealistic, as indicated in Figure 4.2.8. On the other hand, prediction 5a covers almost all the results, except when the value of Vg is smaller than lOm/s. This is probably because of the usage of the mean pressure averaged over twice the radius of the vortex core in the model by Asato et al. [16], which is in quantitative agreement with the present vortex ring whose core diameter is about 25% the ring diameter. 

Thus, it should be noted that the flame propagation in combustible vortex rings is not steady, but "quasi-steady" in the strict sense of the word. This may explain why prediction 9, based on the momentum flux conservation can better describe the flame speed for large values of Vg than prediction 4, which adopts the Bernoulli s equation on the axis of rotation. 

Finally, we come to the effects of the Lewis number. Figure 4.2.14 shows the intensified images of vortex ring combustion of lean and rich propane/air mixtures. Since the flame is curved and stretched at the head region, the mass and heat is transferred through a stream tube. 

McCormack, R D., Combustible vortex rings. Proceedings of the Royal Irish Academy, 71, Section A(6) 73-83, 1971. 

Sullivan, J. R, Windnall, S. E., and Ezekiel, S., Study of vortex rings using a laser Doppler velocimeter, AIAA Journal, 11, 1384-1389, 1973. 

Maxworthy, T., Turbulent vortex rings. Journal of Fluids Mechanics, 64,227-239,1974. 

Choi, H. J., Ko, Y. S., and Chung, S. H., Flame propagation along a nonpremixed vortex ring combustion. Combustion Science and Technology, 139, 277-292, 1998. 

Maekawa, T., Ikeda, M., Morimoto, Y, Ishizuka, S., and Taki, S., Flame speeds in vortex rings of combustible gases (4th Report), Proceedings of the 37th Japanese Symposium on Combustion, pp. 37-38, 1999 (in Japanese). 

J. J. Thomson, The Electron in Chemistry (London Chapham and Hall, 1923) preface. His earliest applications of physics to chemistry included Treatise on the Motion of Vortex Rings (1883) and Applications of Dynamics to Physics and Chemistry (1888). 

Thomson, Joseph John. A Treatise on the Motion of Vortex Rings. London Macmillan, 1883. 

---