L Combustion Instability

Low-frequency oscillation in a rocket motor depends on the pressure exponent of propellant burning rate and the free volume of the chamber.I - l When a double-base propellant composed of Nc(0-510), ng(0-355), and dep(0-120), with p 3Sa(0.015) as a platonizing catalyst, burns in a strand burner, the burning rate characteristics may be divided into four zones, as shown in Fig. 13.14. The pressure exponent varies between the pressure zones n = 0.44 in zone 1 above 3.7 MPa, n = 1.1 in zone 11 between 3.7 MPa and 2.1 MPa, n = 0.77 in zone 111 between 2.1 MPa and 1.1 MPa, and n = 1.4 in zone IV below 1.1 MPa. 

Assuming that the gas in the chamber behaves as an ideal gas and neglecting the density of the gas compared to that of the propellant, the mass balance for a rocket motor is given by 

In general, the amplitude of the pressure oscillation is much smaller than the mean pressure as cji/p 1, and thus the burning rate is given by 

Since the pressure exponent of burning rate is less than unity for conventional propellants, a becomes negative, and the burning becomes stable. In the case of n being greater than unity, a becomes positive, and increasingly oscillatory burning may occur. When n is very close to unity, a becomes approximately zero, and co can be determined from the approximation 

This predicted trend is consistent with the observed oscillatory burning behavior in zone II. Since a in zone II is determined to be of the order of 1 s or less, co may be calculated from Eq. (13.38). Eor example, the calculated co is 46 rad s when x h is 0.01 s (I 4 m) atp,.= 3.5 MPa. Eurthermore, thetermcox,.(,/nisoftheorderof 

When the propellant grain burns in an end-burning type of rocket motor in which L changes from 4 m to 20 m during burning, typical pressure-time records are as shown in Fig. 9-18. In zone I, pressures above 3.7 MPa, the burning is very stable as expected. In zone II, where the pressure exponent is approximately unity, a 

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