Nozzle expansion process

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 ... 

A Study of Combustion and Recombination Reactions During the Nozzle Expansion Process of a Liquid Propellent Rocket Engine , Ibid, pp 366-74 F2) W.E. Johnson W. 

Procedures for calculating the theoretical flame, or product temperature and product composition of a propellant mixture were discussed in the previous section. What remains to be analyzed is the nozzle expansion process. Since most thermochemical performance calculations are made in order to compare various propellants or propellant combinations, certain.ideal assumptions as discussed in Section n. A. are made. These ideal assumptions, however, only relate to the physical processes which actually occur in the rocket motor. As explained, normal dissipative losses such as friction and heat transfer are ignored. The gasses are assumed to enter the nozzle at zero velocity at the temperature and product composition calculated theoretically for the given mixture ratio of the propellant combination. 

With the assumptions thus stated, and following the approach of (15), the theoretical calculation of the specific impulse, c, c, and cF then proceeds from the isentropic statement of the nozzle expansion process ... 

For the nozzle expansion process the energy equation becomes ... 

Since Cp indicates the efficiency of the expansion process in the nozzle flow and c indicates the efficiency of the combustion process in the chamber, gives an indication of the overall efficiency of a rocket motor. 

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. 

The air-intake used to induce air from the flight-altitude atmosphere plays an important role in determining the overall efficiency of ducted rockets. The air pressure built up by the shock wave determines the pressure in the ramburner. The temperature of the compressed air is also increased by the heating effect of the shock wave. The fuel-rich gaseous products formed in the gas generator burn with the pressurized and shock-wave heated air in the ramburner. The nozzle attached to the rear-end of the ramburner increases the flow velocity of the combustion products through an adiabatic expansion process. This adiabatic expansion process is equivalent to the expansion process of a rocket nozzle described in Section 1.2. 

A predissociation, which may or may not be related to the one just discussed, is observed in hot flames147 and in cool atomic flames148. For rotationless states the predissociating curve appears to cross the bound 2E+ state very near v = 2. The corresponding inverse predissociation has been proposed149,150 as an explanation for the observed overpopulation of the first and second vibrational levels of OH(2E+) in flames where there is a considerable excess population (over thermodynamic equilibrium) of O and H atoms. This process may produce a population inversion in nozzle expansion of a dissociated gas 15 x. 

If the reaction times taking place in the reacting mixture are extremely fast compared to the expansion time, then chemical equilibrium will be maintained at all instances during the expansion process this flow process is referred to as eauili- brium flow. However, expansion in the nozzle may occur so rapidly that the reactions may not be fast enough to maintain equilibrium. In fact the expansion can be... 

Approximate procedures have been evolved which permit one to determine the state of the expansion process for a given system. In fact these procedures permit the performance to be calculated when the chemical rates are finite and thus do not correspond to frozen, essentially zero chemical rate or equilibrium, essentially infinite chemical rate,flow. As one would expect intuitively, the results of these finite rate determinations show that the flow remains nearly in chemical equilibrium at the beginning of the expansion process, and at a given temperature or point in the nozzle the composition becomes frozen and remains so throughout the expansion process. Finite rate performance calculations are very complex and are presently limited to only a few systems due to lack of kinetic data at the temperatures of concern. Thus most performance calculations are made for either or both equilibrium and frozen flow and it is kept in mind that the actual results must lie somewhere between the two. For most systems equilibrium calculations are very satisfactory. 

Most, if not all, solutions of the nozzle expansion problem have used equilibrium composition chamber conditions as the initial condition for nozzle solution. The feature is common to all of the nozzle flow solutions that is, the equilibrium composition expansion, frozen composition expansion, Bray freezing model, and kinetic rate solutions have all invoked the assumption of equilibrium composition at the beginning of the expansion process. While the failure to obtain equilibrium composition predicted performance, in terms of experimental characteristic velocities, has suggested a departure from equilibrium in the combustion chamber, only recently have non-equilibrium compositions been measured directly (31). 

The existence of non-equilibrium combustion products is important to at least two considerations. Firstly, the observed propellant performance may depart substantially from the predicted level. This departure may result in performance either less than or greater than the equilibrium predicted level. A striking example of greater than equilibrium performance is that of hydrazine monopropellant decomposition, table m-A-1. Another is that of ethylene oxide monopropellant, as mentioned in section n. B. 4., in which the equilibrium quantities of condensed carbon never are formed. Secondly, the non-equilibrium composition may have significant effects on the expansion process. In particular, nozzle kinetic calculations based on an assumed equilibrium composition initial condition may diverge significantly from expansions occurring from non-equilibrium initial conditions. 

An additional advantageous possibility in heat transfer rockets is the use of a diabatic nozzle in which propellant heating continues during the expansion process. While difficult to achieve in practice, such heating extends the potential propellant performance beyond the limitation associated with a maximum, pre-expansion temperature. 

Turbines (Expanders) High-velocity streams from nozzles impinging on blades attached to a rotating shaft form a turbine (or expander) through which vapor or gas flows in a steady-state expansion process which converts internal energy of a high-pressure stream into shaft work. The motive force may be provided by steam (turbine) or by a high-pressure gas (expander). 

The flow expansion process at the exit of the tube may be more gradual with the addition of a nozzle than that observed in the current simulations where the tube opens abruptly into the ambient atmosphere. This observation is consistent... 

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