Specific impulse of rockets

From equation (14) a simple and explicit formula for V2 (and therefore for /gp) can be drived if a one-component gas with a constant specific heat flows through the nozzle. Since h = constant CpT in this case, /iq 2 = CpTo(l — T2/T0). In place of the parameter T2, it is generally more convenient to use P2 because the atmospheric pressure (to which P2 has been equated above) is usually specified in discussing propellant performance. For isentropic flow [equation (13)] of a one-component ideal gas with Cp — constant, it is well known and readily derived from equations (6), (7), and (1-9) that T2/T0 = (P2/PoY where the ratio of specific heats is y = Cplc (Cj, = specific heat at constant volume). Since 

Reactions in Flows with Negligible Molecular Transport 

---

Oxidizers. The characteristics of the oxidizer affect the baUistic and mechanical properties of a composite propellant as well as the processibihty. Oxidizers are selected to provide the best combination of available oxygen, high density, low heat of formation, and maximum gas volume in reaction with binders. Increases in oxidizer content increase the density, the adiabatic flame temperature, and the specific impulse of a propellant up to a maximum. The most commonly used inorganic oxidizer in both composite and nitroceUulose-based rocket propellant is ammonium perchlorate. The primary combustion products of an ammonium perchlorate propellant and a polymeric binder containing C, H, and O are CO2, H2, O2, and HCl. Ammonium nitrate has been used in slow burning propellants, and where a smokeless exhaust is requited. Nitramines such as RDX and HMX have also been used where maximum energy is essential. 

Uses. A review of its use as an oxidizer in rocket proplnts is given in Ref 6. A 50 50 mixt of N trifluoride F, with ammonia as fuel, yields a specific impulse of 295sec and a d impulse (specific impulse X d) of 340 (Ref 6). Mixts with methyl fluoride, 1,1 -difluoropropane, and 1,3-dlfluoropropane have been patented as monoptoplnts(Ref 9). AN trifluoride/H flame has been proposed as a cutting and welding torch (Ref 8)... 

It is rather interesting that the maximum specific impulse of a rocket propellant system occurs when (T2iMW2)1/2 is maximized, even though the rocket combustion process is not one of detonation [17],... 

The specific impulse of a rocket motor, I, as defined in Eq. (1.75), is dependent on both propellant combushon efficiency and nozzle performance. Since is also defined by Eq. (1.79), rocket motor performance can also be evaluated in terms of the characterishc velocity, c, defined in Eq. (1.74) and the thrust coefficient, Cp, defined in Eq. (1.70). Since c is dependent on the physicochemical parameters in the combustion chamber, the combushon performance can be evaluated in terms of c. On the other hand, Cp is dependent mainly on the nozzle expansion process, and so the nozzle performance can be evaluated in terms of Cp. Experimental values of and Cpgxp are obtained from measurements of chamber pressure, p, and thrust, F ... 

It should be noted that the gas flow process in the port is not isentropic because mass and heat addihons occur in the port. This implies that there is stagnation pressure loss and so the specific impulse is reduced for nozzleless rockets. When a convergent nozzle is attached to the rear end of port, the static pressure at the port exit, Pj, continues to decrease to the atmospheric pressure and the specific impulse of the nozzleless rocket motor is increased. The expansion process in a divergent nozzle is an isentropic process, as described in Section 1.2. 

Fig. 14.25 Specific impulse of an N204/pyrolant gas-hybrid rocket as a function of oxidizer/fuel ratio.

Though the specific impulse of a solid rocket is determined by the energetics of its propellant, the specific impulse of a ducted rocket is determined by the mixture ratio of the fuel flow rate from the gas generator and the airflow rate induced from the atmosphere. The ram pressure in the rambumer is raised by the shock wave formed at the air-intake. The combustion in the rambumer further increases the... 

Boron is one of the essential materials for obtaining high specific impulse of a ducted rocket However, the combustion efficiency of boron-containing gas-generating pyrolants is low due to incomplete combustion of the boron particles in the ramburner.[i3-i l Fig. 15.20 shows the combustion temperature ofa boron-containing pyrolant with and without boron combustion as a function of air-to-fuel ratio, 8. A typical boron-containing pyrolant is composed of mass fractions of boron particles b(0-30), ammonium perchlorate ap(0.40), and carboxy-terminated polybutadiene ctpb(0-30). If the boron particles burn completely in the ramburner, the maximum combustion temperature reaches 2310 K at 8 = 6.5 and v = Mach 2 p =... 

MPa) under conditions of sea-level flight However, if no boron combustion occurs, the temperature decreases to 1550 K under the same flight conditions. The combustion efficiency of boron particles is an important parameter for obtaining high specific impulse of ducted rockets. 

For firework rockets the most important factors include the weight of the rocket, the weight of the propellant, the specific impulse of the propellant and the shape and size of the rocket. 

Blackpowder is still used in sq ll rockets (e.g. signal or rescue rockets for carrying the rope from shore to ship or vice versa). Its limited application is due to the fact that blackpowder gives a very low specific impulse ls=from 40 to 80 sec, which is much lower than that of modern composite propellants and smokeless rocket powders which give a specific impulse of 180-200 sec. 

---