Liquid Propellant Rocket Engines¶
Liquid propellant rocket engines are a critical piece of a launch vehicle. Many rockets destined for low Earth orbit and beyond are launched from the surface of the Earth using liquid propellant-fueled rockets.
As we discussed previously, liquid propellant rockets have two big advantages over solid-propellant rockets:
They can be turned on and off
They can be throttled to adjust the thrust level
Both of these characteristics are due to the use of liquid propellants, and in particular, the ability of liquid propellants to be pumped into a combustion chamber. Controlling the flow rate through the pump(s), or turning them off, provides both of the functions described above.
The most common liquid propellant combinations for launch vehicles are LH2/LOX, RP-1/LOX, and LCH4/LOX. The L indicates the propellants are in a liquid state, and OX means oxygen in this case. RP-1 is a kerosene-based fuel similar to jet fuel. These combinations are bipropellants, or binary propellants, because they require both a fuel and an oxidizer to function.
Other common fuels include monopropellants such as hydrazine, which are able to react by themselves or with the help of a catalyst.
Note
For an hilarious and insightful read about the early history of rocket fuel development, check out Ignition by John D. Clark. You can buy a new printing of it, but it’s old enough that it’s in the public domain and you can find PDFs and epubs of Ignition online. Sample quote:
If, however, this coat is melted or scrubbed off, and has no chance to reform, the operator is confronted with the problem of coping with a metal-fluorine fire. For dealing with this situation, I have always recommended a good pair of running shoes. John D. Clark, Ignition, pg. 74. [Cla72]
Rocket Motor Components¶
Fig. 8 A schematic of a simple rocket engine, showing the injector, combustion chamber, and nozzle.¶
The rocket motor has three primary components, as shown in Fig. 8:
The injector
The combustion chamber
The nozzle
Propellants are injected into the combustion chamber, where they react at nearly zero velocity. After reacting, the propellants enter the converging-diverging nozzle, which accelerates them to supersonic speed at the exit.
There are a few important dimensions on the nozzle we should be aware of. In general, rocket motors are axisymmetric, as shown by the centerline drawn on Fig. 8:
\(r_c\) - the radius of the combustion chamber
\(r_t\) - the radius of the nozzle throat, the smallest radius in the nozzle
\(r_e\) - the radius of the nozzle exit
\(\alpha\) - the expansion angle of the nozzle at the exit
The converging section of the nozzle accelerates the flow to \(M = 1\). At the throat, the Mach number is exactly equal to one, and the flow is said to be choked. This means that changing the pressure at the nozzle exit will not change the mass flow rate. After the throat, the nozzle diverges. This further accelerates the flow into supersonic speeds.
Ideally, the flow will leave the nozzle parallel to the axis. However, this often requires additional length of the nozzle, translating to additional mass that must be carried. There is a significant penalty for any additional mass on a rocket, so the nozzle may be cut short, and the flow may leave at some angle relative to the axis, given by \(\alpha\).