In this chapter, the rocket engine as an energy conversion device is analyzed. A rocket engine consists of two basic components:
|combustion chamber: converts chemical energy to heat by a chemical reaction, combustion|
|nozzle: converts heat to kinetic energy of the stream of gas, or jet, that is exhausted from it.|
From the analysis, the basic constraints on engine design are derived.
3.2 Nozzle Analysis
A nozzle is a device which increases kinetic energy adiabatically. Rocket nozzles are sometimes called DeLaval nozzles, after their inventor. A nozzle consists of a converging section following the combustion chamber, a cross-section of minimum area, called the throat, followed by a diverging section, sometimes called the engine bell because of its approximate shape. Why this nozzle shape? The cross-sectional area at any point along the flow axis can be derived by application of thermodynamics. This equation for area, A, can then be used to produce the optimal nozzle shape. The derivation is as follows.
The nozzle can be diagrammed as shown below.
A control volume is constructed in the flow, with inlet and exit quantities as shown. (Quantity v is specific volume, or 1/r , where r is the gas density.) Two thermodynamic assumptions are made about the process:
|isentropic flow: D s = 0; a reversible process|
|adiabatic flow: D Q = 0; no heat transfer (loss)|
From these assumptions, it follows that
Mass conservation requires that ,, or
The flow speed of the gas from the combustion chamber (to the left) to the nozzle exit (right end) is . Eqn. (3.1-2) can be expressed as:
Expanding the differential leads to the equivalent equation,
Energy conservation (the First Law) requires that
where ek is specific kinetic energy, Ek/m:
Substituting for dek in (3.2-6),
Substituting (3.2-9) into (3.2-5),
From (3.2-9) and (3.2-8),
Substituting (3.2-11) into (3.2-10), the result is