Stability Criteria for a Rocket Motor

Let us consider a propellant burning in a rocket motor as shown in Fig. 14.8. The mass generation rate in the chamber, ntg, is given by 

One assumes that and are constant and that the burning rate is expressed by Eq. (3.68) during the pressure transient in the rocket motor Eq. (14.6) is then represented byhl 

Substituting Eq. (3.68) into Eq. (14.9), one gets the chamber pressure at a steady-state condihon as 

As shown in Fig. 14.9, the chamber pressure is given by the crossover point of thg and in a plot of these parameters versus pressure. It is evident that stable combustion occurs only under the condition of 

Based on Eq. (14.8), the characteristic time in the combustion chamber, x,., is defined as 

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