Heat feedback phase

As is evident from experimental measurements, most kinds of nitrate esters appear to decompose to NOj and C,H,0 species with the breaking of the O-NOj bond as the initial step. A strong heat release occurs in the gas phase near the decomposing surface due to the reduction of NO2 to NO accompanied by the oxidation of C,H,0 species to HjO, CO, and COj. NO reduction, however, is slow and this reaction is not observed in the decomposition of some nitrate ester systems. Even when the reaction occurs, the heat release does not contribute to the heat feedback to the surface because the reaction occurs at a distance far from the surface. 

Model for Heat Feedback from the Cas Phase to the Condensed Phase... 

Most importantly, the presence of lead compounds results in a strong acceleration of the fizz zone reactions, i. e., those in the gas phase close to the burning surface. Acceleration of the reactions in the subsequent dark zone or in the luminous flame zone is not significant. The net result of the fizz zone reaction rate acceleration is an increased heat feedback to the surface (e. g., by as much as 100 %), which produces super-rate burning. 

The temperature in the condensed phase increases from the initial propellant temperature, Tq, to the burning surface temperature, Tj, through conductive heat feedback from the burning surface. Then, the temperature increases in the gas phase because of the exothermic reaction above the burning surface and reaches the final combustion temperature, Tg. Since the physical structure of AP composite propellants is highly heterogeneous, the temperature fluctuates from time to time and also from location to location. The temperature profile shown in Fig. 7.2 thus illustrates a time-averaged profile. This is in a clear contrast to the combustion wave... 

Physicochemical Model. In constructing the GDF model, it is assumed that gasification at the solid regressing surface is driven by conductive heat feedback from a two-stage flame occurring in the gas phase (see Figure 1). This solid-to-gas phase step is generally endo-... 

A recent study of the deflagration of RDX (Ref 107) presents the following model for the deflagration process (1) partial decompn in the liq phase (2) vaporization and gas phase decompn (3) oxidation of products (particularly HCHO) by N02. As system press increases, (1) and (3) become progressively more prominent. Although the reacting liq layer at high pressures is thin, its heat feedback into the still unreacted material increases... 

Several additional assumptions are applied to the above equations19,101 (1) no endothermic or exothermic reaction is involved within the condensed phase (below the burning surface), (2) the luminous flame zone does not contribute to the conductive heat feedback from the gas phase to the burning surface, and (3) no species diffusion occurs in the condensed phase or in the gas phase. Equations (3.39) and (3.40) are then simplified as follows ... 

The pyrolysis equations above are based on an assumed which is not generally known from condensed phase considerations alone. To proceed further and obtain a solution for mass flux requires information about the conductive heat feedback to the surface from the gas phase qc which must be supplied by the gas... 

In the limits of high and low Dg (high and low pressure) the model outlined here approaches condensed phase controlled burning regimes, independent of Eg. That is, both Eg I and Eg I models converge to the same set of equations. In the low Dg (low pressure) limit, gas conductive heat feedback becomes negligible compared with condensed phase heat release and/or radiative heat feedback, and m and Ts are given by Eqs. (11) and (15) with qc 0 (xg -> >). 

The most efficient way to illustrate the effect of various parameters (although not always the most physically insightful) is through non-dimensional parameters. A baseline case for illustrating the effect of various non-dimensional parameters on steady regression behavior is selected as shown in Table 1. The value of Dg is selected so that the mass fluxes are the same between the two cases Eg 1 and Eg 1 (the different Dg values compensate for the different Eg values), and therefore the surface temperatures and conductive heat feedback terms are the same. The temperature and volumetric heat release profiles are shown in Fig. 2. The effect of large E is to concentrate the condensed phase heat release in a narrow zone at the surface, Xg - 0. Similarly, the effect of large Eg is to... 

Fig. 4 Non-dimensional surface temperature and conductive heat feedback from gas phase to surface for benchmark case (Table 1).

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