Tube diameter critical

Knystautas, R., J. H. Lee, and C. M. Guirao. 1982. The critical tube diameter for detonation failure in hydrocarbon-air mixtures. Combustion and Flame. 48 63-83. 

A deflagration-detonation transition was first observed in 1985 in a large-scale experiment with an acetylene-air mixture (Moen et al. 1985). More recent investigations (McKay et al. 1988 and Moen et al. 1989) showing that initiation of detonation in a fuel-air mixture by a burning, turbulent, gas jet is possible, provided the jet is large enough. Early indications are that the diameter of the jet must exceed five times the critical tube diameter, that is approximately 65 times the cell size. 

R. BCnystautas, C. Guirao, J.H.S. Lee, and A. Sulmistras, Measurements of cell size in hydrocarbon-air mixtures and prediction of critical tube diameter, critical initiation energy and detonability limits, AIAA Prog. Astronautics Aeronautics, 94, 23-37,1984. 

As in consideration of deflagration phenomena, other parameters are of import in detonation research. These parameters—detonation limits, initiation energy, critical tube diameter, quenching diameter, and thickness of the supporting reaction zone—require a knowledge of the wave structure and hence of chemical reaction rates. Lee [6] refers to these parameters as dynamic to distinguish them from the equilibrium static detonation states, which permit the calculation of the detonation velocity by C-J theory. 

The extent to which a detonation will propagate from one experimental configuration into another determines the dynamic parameter called critical tube diameter. It has been found that if a planar detonation wave propagating in a circular tube emerges suddenly into an unconfined volume containing the same mixture, the planar wave will transform into a spherical wave if the tube diameter d exceeds a certain critical value dc (i.e., d > dc). II d < d.. the expansion waves will decouple the reaction zone from the shock, and a spherical deflagration wave results [6],... 

Some analytical and experimental estimates show that the critical tube diameter is 13 times the detonation cell size (dc > 13 A) [6], This result is extremely useful in that only laboratory tube measurements are necessary to obtain an estimate of dc. It is a value, however, that could change somewhat as more measurements are made. 

Critical tube diameter is the minimum diameter of a tube that will peimit a detonation wave to continue propagating into an open volume as a spherically expanding wave. 

From a practical point of view this equation is still not very helpful as Ci depends on conversion by being proportional to the critical tube diameter. Sensitivity considerations on the influence of the safe distance between true and critical tube diameter on Cl and on the Ci dependent term of Equ.(4-148), however, show, that a further simplification is justified. These considerations are presented graphically in Fig. 4-37. 

If the true pipe diameter is only 10% smaller than the critical diameter, the Ci-dependent term of Equ.(4-148) already amoimts to 0.85, and it approaches 1 if the safety distance is made greater. If a cooling intensity is demanded for fixed-bed reactors which is determined for a fixed value of 1 for the Ci-dependent term, then this can only be advantageous for process safety, especially for a design with close proximity of true and critical tube diameter. 

Figure 10. Comparison of the critical tube diameter -with the...

Knystautas, R., Guirao, C.M., Lee, J.H.S., Sulmistras, A. "Measurements of Cell Size in Hydrocarbon-Air Mixtures and Predictions of Critical Tube Diameter Initiation Energy and Detonability Limits", 9th Int. Colloq. on Dynamics of Explosions and Reactive Systems (1983). 

Critical tube diameters have also been measured for stoi-... 

Figure k. Variation of computed induction length and critical tube diameter with degree of nitrogen dilution for stoichiometric fuel-oxidizer mixtures. The symbols are described in the text. 

The model has also been used to predict the variation of induction length with initial gas temperature Tq (33). At constant initial pressure, the induction length and critical tube diameter were found to increase slowly with Tq. The variation in initial density with Tq is therefore more important than the slight increase in elementary reaction rates with Tq. These results suggest that the detonability of cold gas mixtures, such as those which can result from spills of liquefied natural gas (LNG) or other cryogenically stored fuels, will be slightly greater than the same mixtures at normal ambient temperatures. 

Figure 5 Variation of computed induction length and experimentally measured critical tube diameter with initial pressure. Solid curves are computed results for fuel-O mixtures dashed curves for fuel-air mixtures and dotted lines with symbols represent experimental data from Matsui and Lee (33).

E, 31-2 XI, vi, II, 25-7. Later experimenters found that only in the case of the detonation wave is the flame velocity independent of the material of the tube, but Holm, Phil. Mag., 1932, xiv, 18 1933, XV, 329, thought the inability of flame to pass through narrow tubes is due to the extreme curvature of the flame-surface and consequent large heat loss from burnt to unbumt gas. The critical tube diameter is the same for glass as copper, with a thermal conductivity 400 times that of glass. The rate of heat transfer to the wall depends on the thermal conductivity of the gas, so that the assumption that the arrest of the flame is due to cooling by the wall rather than in the gas would not be satisfactory. 

Propagation From a Tube into a Large Open Space "Critical Tube Diameter"... 

Keywords Concentration limits Critical gap Critical tube diameter Flame... 

A critical tube diameter is a characteristic parameter of flame extinction. There is also a term critical gap du, i.e. a distance between two parallel plates when flame extinction occurs. It has been found empirically that the critical tube diameter is approximately 1.5 times bigger than the critical gap du [29]. 

Another example of geometrical limitation is a spherical detonation initiation in an open space by a detonation wave diffracting out of a tube or a rectangular cross section duct into the space. In [1,2] it was found that the induction zone length A in the ZND model is proportional to the transverse detonation cell size (width) a. The experiments revealed that the critical tube diameter for initiation is at least 13 transverse waves [30]. As this takes place, the critical diameter of detonation initiation can be found from ... 

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