Instability diffusive-thermal

Diffuse-thermal instabilities involve the relative diffusion reactants and heat within a laminar flame. These are the smaHest-scale instabilities (11). 

Kaiser, C., Liu, J.B., and Ronney, P.D., Diffusive-thermal instability of counterflow flames at low lewis number, 38th Aerospace Sciences Meeting and Exhibit, AIAA Paper 2000-0576, 2000. 

However, it should be emphasized here that the complete stability question is complex. Flame stability is the subject of the following chapter. For Lewis numbers different from unity, there are diffusive-thermal instabilities that are influenced by heat loss and that have led to various statements concerning the dependence of the stability in Figure 8.2 on the Lewis number [46]. We shall postpone any further discussion of these stability questions until the following chapter. It seems sufficient here to reemphasize that if special types of flame instabilities are not observed in an experiment, then the upper branch of Figure 8.2 may be expected to apply, with I = 1/e providing a correct extinction criterion (within about 10% accuracy since corrections of order 1/P may be anticipated). 

Instabilities arise in combustion processes in many different ways a thorough classification is difficult to present because so many different phenomena may be involved. In one approach [1], a classification is based on the components of a system (such as a motor or an industrial boiler) that participate in the instability in an essential fashion. Three major categories are identified intrinsic instabilities, which may develop irrespective of whether the combustion occurs within a combustion chamber, chamber instabilities, which are specifically associated with the occurrence of combustion within a chamber, and system instabilities, which involve an interaction of processes occurring within a combustion chamber with processes operative in at least one other part of the system. Within each of the three major categories are several subcategories selected according to the nature of the physical processes that participate in the instability. Thus intrinsic instabilities may involve chemical-kinetic instabilities, diffusive-thermal instabilities, or hydrodynamic instabilities, for example. Chamber instabilities may be caused by acoustic instabilities, shock instabilities, or fiuid-dynamic instabilities within chambers, and system instabilities may be associated with feed-system interactions or exhaust-system interactions, for example, and have been assigned different specific names in different contexts. 

The inherent oscillations that have been addressed here in fact correspond to a limiting case of the diffusive-thermal intrinsic instabilities of flames, which will be introduced in Section 9.5. At large values of the Lewis number the character of the diffusive-thermal instability is that which has been described here. It will be found in Section 9.5 that additional types of instability behavior may occur if diffusion of chemical species is not negligible. 

FIGURE 9.9 Schematic illustration of the mechanism of diffusive-thermal instability. 

For estimating when diffusive-thermal instabilities may occur, it is important to know the value of the critical Lewis number, Le. Although... 

FIGURE 9.10. Regions of diffusive-thermal instability in a Lewis-number, heat-loss plane, with dispersion relations illustrated by insets. 

The Lewis number specifies the relative significance of thermal diffusion and mass diffusion and is used as a criterion of the diffusion-thermal instability of a laminar flame. For a multi-component system the Lewis number of each component presented in Table 1.2 [16] can be calculated. 

A significant disadvantage of the burner method is the diffusion-thermal instability of the flame front in lean hydrogen-air mixtures (15% H2 and less), which leads to non-uniformities of the flame concentration and temperature. Instead of a smooth cone, the flame in such mixtures takes the shape of a polyhedron with the alternation of luminous zones and zones where luminescence is not observed. The other proof of the non-uniformity is the cone vertex break. Experimental observations of the specific features referred to in lean hydrogen-air mixtures have been made in [34-36]. In [37] a theoretical description of the cone vertex break was presented. 

Lewis number (Le) Ratio of the medium thermal diffusivity coefficient to mass transfer caused by diffusion. For light molecule diffuse transfer in a heavy carrying substance, the Le does not exceed 1. Heavy molecule transfer in a lighter mixture takes place at Le > 1. The Lewis number determines the relative role of heat diffusion and substance diffusion. It is used as a criterion of flame diffusion-thermal instability. 

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