In Chapter 3, simplified one-dimensional performance relations were developed. They require a knowledge of the composition of the hot rocket gas and the properties of the propellant reaction products, such as their combustion temperature Tx, average molecular mass 93?, the specific heat ratio or the enthalpy change (hx — h2). This chapter discusses several theoretical approaches to determine these thermochemical properties for a given composition of propellant, chamber pressure, nozzle shape, and nozzle exit pressure. This then allows the determination of performance parameters, such as theoretical specific impulse or exhaust velocity values for chemical rockets.
By knowing the calculated gas temperature, pressure, and gas composition (e.g., whether reducing or oxidizing species) it is possible to calculate other gas properties. This knowledge also allows a more intelligent analysis and selection of materials for chamber and nozzle structures. Heat transfer analyses require the determination of the specific heats, thermal conductivity, and specific heat ratio for the gas mixture. The calculated exhaust gas composition forms the basis for estimating environmental effects, such as the potential spreading of a toxic cloud near a launch site, as discussed in Chapter 20. The exhaust gas parameters also form the basis for the analysis of exhaust plumes (Chapter 18) or flames external to the nozzle.
With the advent of digital computers it has been possible to solve the set of equations involving mass balance, energy balance, or thermodynamic and chemical equilibria of complex systems with a variety of propellant ingredients. This chapter is intended to introduce the basic approach to this theoretical analysis, so the reader can understand the thermodynamic and chemical basis of the several computer programs that are in use today. This chapter does not describe any specific computer analysis programs. However, it discusses which of the physical phenomena or chemical reactions can or cannot be adequately simulated by computer analysis.
The reader is referred to Refs. 5-1 to 5-5 for general chemical and thermodynamic background and principles. For a detailed description of the properties of each of the possible reactant and reaction products, see Refs. 5-6 to 5-12.
All of these theoretical analyses are only approximations of what really happens in rocket combustion and nozzle flow, and they all require some simplifying assumptions. As more of the different phenomena are understood and mathematically simulated, the analysis approach and the computer implementation become more sophisticated, but also more complex. The 11 assumptions made in Section 3.1 for an ideal rocket are valid here also, but only for a quasi-one-dimensional flow. However, some of the more sophisticated analyses can make one or more of these assumptions unnecessary. The analysis is usually divided into two somewhat separate sets of calculations:
1. The combustion process is the first part. It usually occurs in the combustion chamber at essentially constant chamber pressure (isobaric) and the resulting gases follow Dalton's law. The chemical reactions or the combustions occur very rapidly. The chamber volume is assumed to be large enough and the residence time in the chamber long enough for attaining chemical equilibrium in the chamber.
2. The nozzle gas expansion process constitutes the second set of calculations. The fully reacted, equilibrated gas combustion products enter the nozzle and undergo an adiabatic expansion in the nozzle. The entropy remains constant during a reversible (isentropic) nozzle expansion, but in real nozzle flows it increases slightly.
The principal chemical reactions occur inside the combustion chamber of a liquid propellant rocket engine or inside the grain cavity of a solid propellant rocket motor, usually within a short distance from the burning surface. These chamber combustion analyses are discussed further in Chapters 9 and 13. However, some chemical reactions also occur in the nozzle as the gases expand; the composition of the reaction products can therefore change in the nozzle, as described in this chapter. A further set of chemical reactions can occur in the exhaust plume outside the nozzle, as described in Chapter 18; many of the same basic thermochemical analysis approaches described in this chapter also apply to exhaust plumes.
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