Page 72 - Intro to Space Sciences Spacecraft Applications

59
Propulsion
gent-divergent nozzle, leaving with an exit velocity v, at an exhaust pres-
sure p,. The nozzle exit area is represented by A, in Figure 3-2.
Aerodynamic and thermodynamic relationships relate the conditions
between the combustion chamber and the exit area of the expansion noz-
zle. Though the derivation is beyond the scope of this introduction, the
exhaust velocity can be found to be:

An examination of this relationship tells us what is necessary to have a
high propellant exhaust velocity, and thus, higher thrust.
The term y is the ratio of the specific heats of the propellant mixture:

y=' C
C"

where: cp = specific heat (under constant pressure)
c, = specific heat (under constant volume)

The particular value for y depends on the properties of the particular
propellant, but its value is usually between 1.2 to 1.4 and for our purpos-
es can be simply considered a constant in equation 3-5.
The term R represents the specific gas constant for the particular pro-
pellant used. This term is actually the Universal Gas Constant (R = 8.314
joule/mole OK) divided by the molecular weight of the propellant (M
kg/mole). From equation 3-5 we see that a propellant with a lower mole-
cular weight will contribute to a higher exhaust velocity. This shows the
benefit of using hydrogen as a propellant, as first realized by Tsiolkovsky,
over heavier fuels like hydrocarbons.
A higher combustion temperature To increases the exhaust velocity
directly. This temperature is known as the adiabatic flame temperature
and is primarily a function of the propellants used and their combustion
properties. Practical limitations in combustion temperatures exist due to
the structural properties of the combustion chamber and rocket nozzles.
Liquid oxygen (LOX) and liquid hydrogen are kept at very low tempera-
tures, and many liquid-fueled systems circulate these propellants through