By M S Natanzon; F Culick
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Extra info for Combustion instability
But if the APFC is determined from the system of differential equations, then that requirement does not apply. “ch01” — 2008/3/14 — page 17 — #17 18 M. S. 0 a) 2 b) Re c) Fig. 8 The APFC of separate components: (a) APFC of the combustion zone (k2 ); (b) APFC of the acoustic component (kA ); (c) APFC (1) of the working process and −1 ). the inverse APFC (2) of the acoustic component (kA The AFC and PFC of this component are found from Eq. 9) describes a circle of unit radius, shown in Fig. 8a, where the dimensionless frequency ωτ is the parameter on the curve, ranging from 0 to 2π .
10) 7 The limitations for application of this theorem are not essential for the class of problems of interest in this work. 11) According to Lyapunov’s theorem, the stability condition for Eq. 10) is the same as that for Eq. 7). In accordance with its physical meaning, h will subsequently be called a dimensionless pressure difference. The value of τπ is equal to the ratio of the mass of gas in the combustion chamber to its flow rate, and hence is the residence time for gas in the combustion chamber.
A better approach to reality can be obtained after taking into account the final rate of formation of combustion products from the liquid propellant. We note also that during combustion in solid-propellant engines the dependence of the rate of formation of gas on the pressure can be such that the system will lose stability . The nature of the intersection of the curves corresponding to this case is represented in Fig. 2b. 5 Only the elementary definitions corresponding to a physical level of rigor  are given here.