Combustion front, velocity

In the overdriven state, the observed propagation velocity of the combustion front was found to be much higher than the steady-state velocity of spherical detonation. The overdriven state exists for only a short time, and the combustion front velocity then drops rapidly to the steady-state value. The rate at which this exceedingly high velocity decreases was found by experiment to be inversely proportional to the induction distance... 

Progress is being made toward a theory of combustion synthesis. Much of the development to date has been based on classical combustion theory, where the emphasis is on the prediction of macroscopic characteristics, such as combustion front velocity and stability nature. Using this approach, a large number of impressive results have been obtained. However, the principal issues concerning the mi-crostructural aspects of the process have not been resolved. In this section, we present a variety of theoretical results, as well as some remaining problems and possible ways to approach them. 

The dependence of combustion temperature and velocity for the Si-N2 system as a function of dilution with /3-Si3N4 powder is shown in Fig. 38. In this case, at constant gas pressure, remains constant and is equal to the dissociation temperature of silicon nitride, for dilutions up to 60 wt %. However, with increasing dilution, the combustion front velocity increases. Also, increasing the overall heat evolution, smaller dilution by nonmelted nitride powder promotes coalescence of liquid Si particles, leading to an increase in the average reactant particle size, as well as to formation of thin liquid Si films, which blocks nitrogen infiltration to the reaction zone (Mukasyan et al, 1986). The same effects were also observed for the AI-N2 and B-N2 systems (Mukasyan, 1994), which are characterized by dissociation of the final product in the combustion wave. 

For a wide range of systems, the combustion front velocity and temperature decrease with increasing dilution. 

Average combustion front velocity for duration of experiment... 

Dispersion of combustion front shape (see Table XXII) Dispersion of combustion front velocities (see Table XXII) Time step see Eq. (39)... 

A detonation is usually modelled as a one dimensional shock wave (vid. [5, 23, 24]). For this purpose a coordinate system is used which moves with the combustion front (velocity Vg = —wi in the coordinate system of an outside observer, also called laboratory system, vid. Figure 2.8). The following relations are used in the model in order to relate the state after the detonation (subscript 2) with that before the detonation (subscript 1) ... 

Figure 2.6 Dependence of combustion front velocity as a function of dilution by BN (/) at initial gas pressure 2000 atm and initial sample porosity Bg=0.6.

The conditions in the reaction zone determine the release rate of the N-precursors HCN and NH3 [11], Among these conditions are the properties of the fuel (e.g., N-content and particle size), parameters related to the combustion front (temperature and propagation velocity) and the gas composition in and directly above the combustion front. As the prediction of the mass fractions of the N-precursors is important for the final goal of this research, i.e., the prediction of NO formation of the complete furnace, a model is needed in which all these conditions are represented. 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

The detonation wave is a combination of a shock and combustion front, and has a constant width on the time-distance plot. Passage thru the intermediate state would require the attainment of extremely high peak pressure, and of wave-front velocities above the CJ value. Oppenheim quotes (Ref 3, p 476) some exptl evidence of these phenomena... 

Detonotion, Reaction Front in. It is generally agreed that a detonation is a combination of a shock front and a combustion front (Ref 1, p 126 Ref 2). Where combustion is the detonation reaction, the combustion front can also be called the reaction front. The two fronts do not always have the same velocity. At an interesting stage of the DDT (Deflagration to Detonation Transition), the shock front is still faster than the reaction front behind it (See under Detona-... 

The high flame front velocities prior to attainment of the steady state probably result from the transient conditions between the combustion front and shock front. Sufficient data were lacking to show whether the shock-heated gas ignited spontaneously, immediately behind the shock front, or whether the flame front overtook the shock front. In any event, the combustion wave finally moves along with the shock wave, thus forming a detonation wave... 

This expression, together with the boundary conditions at the flame front [Eqs. (12)—(16)] and Eq. (6) for the flame surface shape, determines the combustion front propagation velocity U as a function of the normal flame... 

The velocity of the combustion front is determined by the volatile matter content of the raw coal, Wv. If the volatile matter content of the coal is high the frontal velocity will be slowed. With low volatility coals the frontal velocity will be relatively fast for the same excess energy production in the com-bustion/gasification regions of the bed. The velocity vc is set by the requirement that the volatiles content of the coal ahead of the devolatilization zone be essentially that of the raw coal. From an analysis of the energy balance in the region near the front of the devolatilization zone, it can be shown that a particular root of the relation below establishes v (3) ... 

The main characteristics of the green mixture used to control the CS process include mean reactant particle sizes, size distribution of the reactant particles reactant stoichiometry, j, initial density, po size of the sample, D initial temperature, Tq dilution, b, that is, fraction of the inert diluent in the initial mixture and reactant or inert gas pressure, p. In general, the combustion front propagation velocity, U, and the temperature-time profile of the synthesis process, T(t), depend on all of these parameters. The most commonly used characteristic of the temperature history is the maximum combustion temperature, T -In the case of negligible heat losses and complete conversion of reactants, this temperature equals the thermodynamically determined adiabatic temperature (see also Section V,A). However, heat losses can be significant and the reaction may be incomplete. In these cases, the maximum combustion temperature also depends on the experimental parameters noted earlier. 

According to the theory of Zeldovich (1941) developed for premixed gas flames, the velocity of the combustion front just before the wave ceases to propagate (e.g., by addition of inert dUent of mole fraction, b) is lower, compared to the maximum value (i.e., with no diluent added), by a factor of Ve. It was shown experimentally that this conclusion can also be applied to gasless systems with a narrow reaction zone (Maksimov et ai, 1965). Based on this idea and using Eq. 

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