Laminar deflagration

Recall that we are assuming faem "C faff (°r fax, if turbulent flow). Anyone who has carefully observed a laminar diffusion flame - preferably one with little soot, e.g. burning a small amount of alcohol, say, in a whiskey glass of Sambucca - can perceive of a thin flame (sheet) of blue incandescence from CH radicals or some yellow from heated soot in the reaction zone. As in the premixed flame (laminar deflagration), this flame is of the order of 1 mm in thickness. A quenched candle flame produced by the insertion of a metal screen would also reveal this thin yellow (soot) luminous cup-shaped sheet of flame. Although wind or turbulence would distort and convolute this flame sheet, locally its structure would be preserved provided that faem fax. As a consequence of the fast chemical kinetics time, we can idealize the flame sheet as an infinitessimal sheet. The reaction then occurs at y = yf in our one dimensional model. 

Figure 25.1 Regimes of turbulent combustion 1 — offshore flares, 2 — spark-ignition engines, 3 — supersonic combustion, Kl — turbulent kinetic energy referred to laminar ratio of kinematic viscocity to chemical time, — Damkohler number based on Kolmogorov scale, Ld — integral scale referred to thickness of laminar deflagration...

With representative values for A, Cp, and po with Vq 50 cm/s, equation (4) gives S 10 cm. Therefore 5 is large compared with a molecular mean free path (about 10 cm), and the continum equations of fluid dynamics are valid within the deflagration wave but 3 is small compared with typical dimensions of experimental equipment (for example, the diameter of the burner mouth, and hence the radius of curvature of the flame cone, for experiments with Bunsen-type burners), and laminar deflagration waves may be approximated as discontinuities in many experiments. Since equations (3) and (4) imply that 3 at constant temperature, experimental... 

For decelerating flames, flames propagating downward, or burner-stabilized flames with the flow upward, the body-force effects are stabilizing. Because of other mechanisms of instability, to be discussed later, the ease with which stable laminar deflagrations are observed in the laboratory may be attributable largely to the stabilizing influence of buoyancy. Normal... 

The flame propagates in the mixture from the zone around the spark-plug at a rate of the order of 50 m s l. This is a rate of turbulent deflagration, much higher than that of a laminar deflagration, which is of the order of 50 cm s l, but very much smaller than that of a detonation, which is of the order of 2000 m s . ... 

A deflagration can best be described as a combustion mode in which the propagation rate is dominated by both molecular and turbulent transport processes. In the absence of turbulence (i.e., under laminar or near-laminar conditions), flame speeds for normal hydrocarbons are in the order of 5 to 30 meters per second. Such speeds are too low to produce any significant blast overpressure. Thus, under near-laminar-flow conditions, the vapor cloud will merely bum, and the event would simply be described as a large fiash fire. Therefore, turbulence is always present in vapor cloud explosions. Research tests have shown that turbulence will significantly enhance the combustion rate in defiagrations. 

Before the size of the flammable portion of a vapor cloud can be calculated, the flammability limits of the fuel must be known. Flanunability limits of flammable gases and vapors in air have been published elsewhere, for example, Nabert and Schon (1963), Coward and Jones (1952), Zabetakis (1965), and Kuchta (1985). A summary of results is presented in Table 3.1, which also presents autoignition temperatures and laminar burning velocities referred to during the discussion of the basic concepts of ignition and deflagration. 

Deflagration initiation. A relatively weak energy source, such as an electric spark, ignites the mixture and a laminar flame is first formed. The mechanism of laminar flame propagation is via molecular transport of energy and free radicals from the reaction zone to the unburnt mixture ahead of it. 

Turbulence is required for the flame front to accelerate to the speeds required for a VCE otherwise, a flash fire will result. This turbulence is typically formed by the interaction between the flame front and obstacles such as process structures or equipment. Turbulence also results from material released explosively or via pressure jets. The blast effects produced by VCEs can vary greatly and are strongly dependent on flame speed. In most cases, the mode of flame propagation is deflagration. Under extraordinary conditions, a detonation with more severe blast effects might occur. In the absence of turbulence, under laminar or near-laminar conditions, flame speeds are too low to produce significant blast overpressure. In such a case, the cloud will merely bum as a flash fire. 

The oxide (an intercalated laminar material) is thermally unstable and on rapid heating it will deflagrate at a temperature dependent on the method of preparation. This temperature is lowered by the presence of impurities, and dried samples of iron(III) chloride-impregnated oxide explode on heating. 

Region III (weak deflagration) encompasses the laminar flame solutions that were treated in Chapter 4. 

Rogg, B., A. Linan, and F. A. Williams. 1986. Deflagration regimes of laminar flames modeled after the ozone decomposition flame. Combustion Flame 65 79-101. 

The velocity of advance of the front is super sonic in a detonation and subsonic in a deflagration. In view of the importance of a shock process in initiating detonation, it has seemed difficult to explain how the transition to it could occur from the smooth combustion wave in laminar burning. Actually the one-dimensional steady-state combustion or deflagration wave, while convenient for discussion, is not easily achieved in practice. The familiar model in which the flame-front advances at uniform subsonic velocity (v) into the unburnt mixture, has Po> Po> an[Pg.249]

Nevertheless, the most typical general feature of a reaction is the existence of fronts of chemical transformation which are able to propagate, without being extinguished, in a hot mixture with a constant velocity at subsonic speed for a laminar flame (or deflagration front), at supersonic speed for a detonation wave (see below for a more detailed discussion of this paper). 

This chapter concerns the structures and propagation velocities of the deflagration waves defined in Chapter 2. Deflagrations, or laminar flames, constitute the central problem of combustion theory in at least two respects. First, the earliest combustion problem to require the simultaneous consideration of transport phenomena and of chemical kinetics was the deflagration problem. Second, knowledge of the concepts developed and results obtained in laminar-flame theory is essential for many other studies in combustion. Attention here is restricted to the steadily propagating, planar laminar flame. Time-dependent and multidimensional effects are considered in Chapter 9. 

In all these laminar-flame experiments, the combustion wave propagates at a definite velocity that empirically depends on the pressure, temperature, and composition of the initial combustible mixture. Our primary objective in this chapter is to predict this burning velocity. In Section 5.1.2 a simple physical picture of the deflagration wave is presented, leading to a crude estimate of the burning velocity. The discussion, which is similar to that of Landau and Lifshitz [3], illustrates the essential mechanism involved. 

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