Pressure exponent of the flame

The flame stand-off distance, L4, defined in Eq. (3.70), decreases with increasing pressure, and the pressure exponent of the flame stand-off distance, d, ranges from -1.9 to -2.3 for RDX and HMX propellants. The overall order of the reaction in the dark zone is determined to be m = 2.5-2.8. This is approximately equal to the overall order of the reaction in the dark zone in the case of double-base propellants, m = 2.5, which would suggest close similarity of the reaction pathways in the dark zone for nitramine composite propellants and double-base propellants. 

It is often observed experimentally that if the relative concentrations of the reactants and the initial temperature of the mixture are kept fixed but the pressure p is decreased, then a limiting pressure is reached, below which flame propagation cannot be achieved. The flammable range of 0 usually narrows as the pressure is decreased, and below a critical pressure flame propagation does not occur for any value of 0. These observations are consistent with equation (24), in which the main pressure-dependent quantities are ml and L(Tf In terms of the overall order n (the pressure exponent) of the overall reaction rate, ml p . It will be seen in the following section that L(Tf) p", where m 0 for conductive or convective losses and 0 < m < 1 for radiative losses. Since n > 1 for practically all flames, the right-hand side of equation (24) decreases more rapidly than the left-hand side as p decreases, and the limiting equality may therefore be expected to be surpassed at a sufficiently low pressure. 

Since the final gas phase reaction to produce a luminous flame zone is initiated by the reaction in the dark zone, the reaction time is determined from the dark zone length Ld, i.e., the flame standoff distance. Figures 6-7 and 6-8 show the results for the dark zone length and dark zone temperature, Td, of the propellants listed in Table 6-1, respectively. The luminous flame front approaches the burning surface and the dark zone length decreases as pressure increases for the propellants. There is no clear difference between the propellants with respect to the dark zone length and the pressure exponent of the dark zone, d = n - m, defined in Eq. (3.70) is determined to be approximately -2.0. The overall order of the reaction in the dark zone is also determined to be m= 2.6 for all the propellants. However, the dark zone temperature increases as pressure increases at constant (N02) and also increases as (N02) increases at constant pressure. 

Because K/Cp is independent of pressure, for ideal gases, the density increases linearly with pressure. In hydrocarbon flames, the burning rate decreases approximately as where the exponent m is around 0.5 for methane flames. Thus, the thickness of the flame varies with pressure as... 

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