FIGURE 11-7. Measured burning rate characteristics of a double-base (DB) propellant and three composite-modified double-base (CMDB) propellants which contain an increasing percentage of small diameter (159 ^m) particles of ammonium perchlorate (AP). When the size of the AP particles is reduced or the percentage of AP is increased, an increase in burning rate is observed. None of these data form straight lines. (Reproduced with permission of the AIAA from Chapter 1 of Ref. 11-3.)
become very sensitive to one another and disastrous rises in chamber pressure can occur in a few milliseconds. When the n value is low and comes closer to zero, burning can become unstable and may even extinguish itself. Some propellants display a negative n which is important for "restartable" motors or gas generators. A propellant having a pressure exponent of zero displays essentially zero change in burning rate over a wide pressure range. Plateau propellants are those that exhibit a nearly constant burning rate over a limited pressure range. One is shown with a dashed line in Fig. 11-6; they are relatively insensitive to major changes in chamber pressure for a limited range of pressures. Several double base propellants and a few composite propellants have this desirable plateau characteristic. Table 12-1 lists the nominal burning rate r and the pressure exponent n for several operational (production) propellants.
Temperature affects chemical reaction rates and the initial ambient temperature of a propellant grain prior to combustion influences burning rate, as shown in Figs. 11-6 and 11-8. Common practice in developing and testing larger rocket motors is to "condition" the motor for many hours at a particular temperature before firing to insure that the propellant grain is uniformly at the desired temperature. The motor performance characteristics must stay within specified acceptable limits. For air-launched missile motors the extremes are usually 219 K (—65°F) and 344 K (160°F). Motors using typical composite propellant experience a 20 to 35% variation in chamber pressure and a 20 to 30% variation in operating time over such a range of propellant temperatures (see Fig. 11-8). In large rocket motors an uneven heating of the grain (e.g., by the sun heating one side) can cause a sufficiently large difference in burning rate so that a slight thrust misalignment can be caused (see Ref. 11-4).
The sensitivity of burning rate to propellant temperature can be expressed in the form of temperature coefficients, the two most common being with ap, known as the temperature sensitivity of burning rate, expressed as percent change of burning rate per degree change in propellant temperature at a particular value of chamber pressure, and tck as the temperature sensitivity of pressure expressed as percent change of chamber pressure per degree change in propellant temperature at a particular value of K. Here K is a geometric function, namely the ratio of the burning surface Ab to nozzle throat area A,.
The coefficient ap for a new propellant is usually calculated from strand-burner test data, and nK from small-scale or full-scale motors. Mathematically,
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