Reaction rate in the combustion wave

When the same chemical compositions of the reactants are used to generate both types of flame, the chemical reaction rate is considered to be the same in both cases. However, the reaction surface area of the turbulent flame is increased due to the nature of eddies and the overall reaction rate at the combustion wave appears to be much higher than that in the case of the laminar flame. Furthermore, the heat transfer process from the burned gas to the unburned gas in the combustion wave is different because of the thermophysical properties specifically, the thermal diffu-sivity is higher for the turbulent flame than for the laminar flame. Thus, the flame speed of a turbulent flame appears to be much higher than that of a laminar flame. 

Fig. 11.13 shows the temperature profiles in the combustion waves of AP py-rolants with and without B parhcles at 1 MPa. It is evident that the temperature gradient above the burning surface is increased by the addition of B particles. Thus, the heat flux transferred back from the gas phase to the propellant is increased, and hence the burning rate is increased. The heat of reaction is also increased as the mass frachon of B particles is increased, as shown in Fig. 11.14. The results indicate that the B particles act as a fuel component in the gas phase, undergoing oxidation just above the burning surface.

Since NC is a fuel-rich nitrate ester, a nitropolymer propellant with a high NC content generates black smoke as a combustion product. In addition, the combustion of nitropolymer propellants becomes incomplete at low pressures below about 3 MPa and black smoke composed of solid carbon particles is formed. This incomplete combustion is caused by the slow rates of the reactions of NO with aldehydes and CO in the combustion wave. Thus, the nitropolymer propellants are no longer smokeless propellants under low-pressure burning conditions. 

Fig. B-1 presents a steady-state flow in a combustion wave, showing mass, momentum, and energy transfers, including chemical species, in the one-dimensional space of Ax between Xj and %2- The viscous forces and kinetic energy of the flow are assumed to be neglected in the combustion wave. The rate of heat production in the space is represented by coQ, where ai is the reaction rate and Qis the heat release by chemical reaction per unit mass.

In order to clarify the combustion wave structure of AP composite propellants, photographic observations of the gas phase at low pressure are very informative. The reaction rate is lowered and the thickness of the reaction zone is increased at low pressure. Fig. 7.3 shows the reduced burning rates of three AP-HTPB composite propellants at low pressures below 0.1 MPa.FI The chemical compositions of the propellants are shown in Table 7.1. The burning rate of the propellant with the composition ap(0-86) is higher than that of the one with ap(0-80) at constant pressure. However, the pressure exponents are 0.62 and 0.65 for the ap(0-86) and Iap(0.80) propellants, respectively that is, the burning rate is represented by r for the p(0.86) propellant and by r for the p(0.80) propellant. 

No theoretical criterion for flammability limits is obtained from the steady-state equation of the combustion wave. On the basis of a model of the thermally propagating combustion wave it is shown that the limit is due to instability of the wave toward perturbation of the temperature profile. Such perturbation causes a transient increase of the volume of the medium reacting per unit wave area and decrease of the temperature levels throughout the wave. If the gain in over-all reaction rate due to this increase in volume exceeds the decrease in over-all reaction rate due to temperature decrease, the wave is stable otherwise, it degenerates to a temperature wave. Above some critical dilution of the mixture, the latter condition is always fulfilled. It is concluded that the existence of excess enthalpy in the wave is a prerequisite of all aspects of combustion wave propagation. 

A combustion wave is established in an explosive medium by application of a local source of ignition. As heat and, possibly, chain carriers of various kinds flow from the source into the adjacent medium, reaction is initiated in the layer next to the source which in turn becomes a source for igniting the next layer, and so on. Let us consider a mass element of the unburned mixture being overrun by the combustion wave. The reaction rate is virtually zero at the initial temperature but increases with temperature at... 

The pressure and temperature change in a compression wave corresponding to a change in the combustion rate occurs extraordinarily rapidly. If this change were the cause of the flame acceleration, the transition from combustion to detonation would occur at a distance which exceeds the width of the reaction zone in the flame by only a few times, i.e., at a distance of not more than a few millimeters. 

In a gas the combustion rate falls with the combustion temperature—if the lower combustion temperature occurs for a given initial state as a result of incomplete combustion. The combustion rate, however, again increases when the combustion temperature does not exceed TB so that the reaction is limited to the liquid phase the reasons for the increase are indicated above. However, it is better here to speak not of the combustion rate, but of the propagation rate of the heating wave of the liquid due to reaction in the liquid phase. The maximum temperature achievable in a liquid is limited by the quantity TB, just as the combustion temperature, in the strict sense, is limited by the quantity Tc. Calculation of the velocity of the heating wave in a liquid is not difficult [see formulas (3.32), (3.34)] if the kinetics of the chemical reaction in the liquid phase are known. 

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