Flame wave propagation model

The DDT mechanism for this case Is similar but not identical to that of Case B. A convective flame front propagates ahead of the compressive waves which are necessary to form a precursor shock front. In modeling DDT the convective front (and its consequences) must be included because of its influence on dp/dt in the ignition region... 

In a stationary detonation wave, the shock front is followed by a zone of chemical reaction which can be considered as an ordinary stationary-state combustion wave propagating through the denser and hotter gases behind the shock front (Fig. XIV.7). Such a combustion wave is characterized by a pressure decrease and a temperature increase across the flame front. Because of this and because, in the stationary state, the flame front must follow the shock front at a fixed distance, the model of the moving surface is not quite adequate to describe a stationary detonation/ A further difference between the two is that, whereas in the mechanical shock the surface velocity Vb was an independent parameter at the disposal of the experimenter, in the detonation the chemical composition of the reacting gases is the collective parameter which replaces vt and is the means by which the experimenter can control the detonation velocity. 

The second factor, as mentioned in the previous section, refers to the propagation pattern of the flame front. In the model experiments, due to the geometry applied, the pressure waves propagated as planar waves which induce the highest related pressure amplitudes. In real structures, two- or three-dimensional flame fronts will occur, with lower pressure peak values at the same flame propagation velocities. 

For risk assessment, the prediction of the pressure wave load upon buildings and industrial structures is very important. This requires the detailed knowledge of the factors influencing the flame propagation process. However, detailed and systematic investigations cannot be performed in real industrial structures. For this reason it is desirable to perform experiments in a model system with the possibility of varying many parameters systematically. The scale-up of the results to real structures must be undertaken on the basis of similarity laws. 

For safety considerations the amplitude of the pressure wave induced by those fast propagating flames is a direct measure of the strains impacting buildings and industrial facilities in case of an accident. The maximum overpressure values measured at the channel side walls in the model experiments are presented in Fig. 17 as a function of the local propagation velocity. 

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