Chemical front propagation, velocity

Detonation Propagation of a flame-driven shock wave at a velocity at or above the speed of sonnd in the nnreacted medinm as measnred at the flame front. The wave is snstained by chemical energy released by shock compression and ignition of the nnreacted medinm. The flame front is conpled in time and space with the shock front, and there is no pressnre increase significantly ahead of the shock-flame front. Propagation velocities in the range 1000-3500 m/s may be observed depending on the gas mixtnre, initial temperatnre and pressnre, and type of detonation. 

The autowave chemical conversion in a film was initiated by a local mechanical disturbance in the form of a puncture or scratch. Figure 14 presents the results of measuring the averaged value of the wave-front propagation velocity as a function of the irradiation dose. It is seen that for... 

All chemical waves reflect the basic features of their fronts propagation velocity and waveform are directly linked to the chemical kinetics of... 

The propagation velocity of the TM does not exceed 85-87% of the theoretical detonation velocity DT. Calculation of DT is carried out under the assumption of a chemical reaction which runs after compression by the shock wave without any thermal or hydrodynamic losses. In the case of the TM, meanwhile, the very possibility of propagation of a fast flame with the velocity of the shock wave depends on a velocity redistribution as a result of braking of the layers adjacent to the wall. In constructing the equations for the motion as a whole, braking plays the role of a loss which reduces the velocity. In fact, the velocity will be even smaller than the value cited besides the losses in the hydrodynamic preparation zone (the zone of velocity redistribution between the shock wave front and the forward point of the flame front, zone I-II in Fig. 19) we must add the losses in the combustion zone (from the forward point of the flame front to the cross-section in which combustion has ended, zone II-III in Fig. 19). 

Indeed, in normal (slow) combustion, which may propagate only due to heat conduction, the heat flux is a quantity of the same order as the combustion heat released in unit time. The width of the front should be of the same order as the product of the chemical reaction time and the flame propagation velocity. 

Theoretical analysis of gas detonation leads to the conclusion that a shock wave propagates at the detonation front, compressing and heating the gas mixture. The chemical reaction runs in the already compressed gas, and it is only after completion of the reaction that the state of the explosion products calculated in the classical theory is attained (pressure pc, velocity wc, temperature Tc). In particular, in the wave front the velocity w1 and the pressure p1 of the compressed gas are approximately twice as large as in the reaction products w1 2wc, p1 2pc. The amount of the compressed gas at the pressure px and the thickness of this layer are proportional to the chemical reaction time, r. 

All the reaction systems considered, despite being greatly different chemically, have been found to have similar dynamic characteristics of the autowave processes occurring therein. Particularly, the linear velocities of the wave-front propagation are in the range of 1 -4 cm/s for all systems. All of them have a certain critical irradiation dose below which the excitation of an autowave process becomes impossible and the system responds to a local disturbance only with local conversion incapable of self-propagating (the situation discussed above and illustrated by Fig. 5). 

The process of forming a detonation front associated with the onset of chemical reactions that eventually overruns the compaction shockfront is also illustrated in Fig. 15, where the position of these fronts is plotted as a function of time. Initially the compaction front propagates into the material with a velocity of 6.4 km/s, as indicated by the slope of the dashed line. Chemical reactions begin near 2.0 ps, and by 3.0 ps the leading edge of the reaction zone is definable. The position of this detonation front is shown as a solid line in Fig. 15. Because the detonation front is traveling faster... 

The front velocity v/ is the result of the interplay among the flow characteristics (i.e., intensity U and length scale L), the diffusivity D, and the production time scale x. In this chapter we shall study the problem of front propagation in the case of cellular flows. In particular, introducing the Damkohler number Da = L/(Ux) (the ratio of advective to reactive time scales) and the Pec let number Pe = UL/D (the ratio of diffusive to advective time scales), we shall discuss how the front speed can be expressed as a nondimensional function such as Vf/vo = < >(Da,Pe). A crucial role in determining i >(Da. Pe) is played by the renormalization of the diffusion coefficient and chemical time scale [13] induced by the advection. 

For high Da the column is dose to chemical equilibrium and behaves very similar to a non-RD column with n -n -l components. This is due to the fact that the chemical equilibrium conditions reduce the dynamic degrees of freedom by tip the number of reversible reactions in chemical equilibrium. In fact, a rigorous analysis [52] for a column model assuming an ideal mixture, chemical equilibrium and kinetically controlled mass transfer with a diagonal matrix of transport coefficients shows that there are n -rip- 1 constant pattern fronts connecting two pinches in the space of transformed coordinates [108]. The propagation velocity is computed as in the case of non-reactive systems if the physical concentrations are replaced by the transformed concentrations. In contrast to non-RD, the wave type will depend on the properties of the vapor-liquid and the reaction equilibrium as well as of the mass transfer law. 

M, and c = 5.0 x 10 M. Find the chemically acceptable stationary states of the kinetic term in (4.136) and determine their stability. Show that (4.136) has a propagating front solution connecting the stable to the unstable steady state and determine the propagation velocity v. Compare your value with the experimental... 

Following the argument by Bunde and Drager [62], front propagation is well defined in the chemical distance space. The front has to propagate with constant velocity, i.e., the front position in the chemical distance space behaves like / t. Euclidean and chemical distances are related by (6.1). The front position in real... 

A general schematic of FC is shown in Figure 2.1. The initial reaction medium consists of a porous matrix of solid reactants and inert diluents, where the pores are filled with gas-phase reactants. The combustion front propagates through the sample with a velocity, U, due to the chemical interaction between the gas- and condensed-phase reactants. Behind the front, the final product is formed, which in some cases may approach pore-free structure, since the volume of the final product grains is typically greater than that of reactant particles. 

Deflagration A propagating chemical reaction of a substance in which the reaction front advances into the unreacted substance at less than the sonic velocity in the unreacted material. Where a blast wave is produced that has the potential to cause damage, the term explosive deflagration may be used. 

Chemical explosions are uniform or propagating explosions. An explosion in a vessel tends to be a uniform explosion, while an explosion in a long pipe is a propagating explosion. Explosions are deflagrations or detonations. In a deflagration, the burn is relatively slow, for hydrocarbon air mixtures the deflagration velocity is of the order of 1 m/s. In contrast, a detonation flame shock front is followed closely by a combustion wave that releases energy to sustain the shock wave. A... 

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