Burning Rate Models

The heat flux feedback from zone II to zone I by conduction heat transfer, A, is given by 

Equation (3.54) is the simplified burning rate equation. If the reaction rates in the gas phase are known, the burning rate is given in terms of gas density (pressure), burning surface temperature, initial propellant temperature, and physical properties of the energetic material. 

The burning surface temperature is related to the burning rate by an Arrhenius equation, which assumes a first-order decomposition reaction for each reaction species at the burning surface. 

Generally, the gas-phase reactions in both flame models for premixed gases and the burning of energetic materials are assumed to be bimolecular and hence of second order. Eq. (3.54) can then be expressed as 

The reaction rate constant, kg, is a function of temperature and is expressed as 

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If the fuel responds fast to the compartment changes, such a quasi-steady burning rate model will suffice to explain the expenditure of fuel mass in the compartment. The fuel heat flux is composed of flame and external (compartment) heating. The flame temperature depends on the oxygen mass fraction ( Yq2 ), and external radiant heating depends on compartment temperatures. 

Table 6.2 Physicochemical parameters used in a burning rate model for a double-base propellant.

The simplified burning-rate model given by Eq. (3.59) only represents the increased burning rate, i. e., super-rate burning, within the pressure region in which carbonaceous materials are formed on the burning surface. 

The basic assumptions in the following description of the burning rate model are... 

A number of burn rate models have been developed for MTV by Cudzilo, Kubota, Kuwahara and Koch. 

Cudzilo makes an even broader approach [22, 23] and takes into account both conductive and radiative heat flux from the gas-phase reaction and heat generated in the condensed phase (Figure 6.12 page 76). His model is based on a burn rate model that has been developed earlier for Mg/NaNOs [24, 25] ... 

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