Comparison of Liąuid Propellcmt Rocket Engine Feed Systems - 1 - 5
where, my. Pressurizing gas mass (kg).
pp: Propellant tank instantaneous pressure (Pa). py Gas tank instantaneous pressure (Pa). py Pressurizing gas initial pressure (Pa).
T„: Pressurizing gas initial temperaturę (K).
Vy Propellant volume (m3).
Ry Pressurizing gas constant (J/kgK). yy Pressurizing gas specific heat ratio.
To foresee the scope of this analysis, the assumptions that allow deriving the previous eąuation will be enunciated:
• Adiabatic process.
• Ideał gas.
• Negligible initial mass inside the pipes and propellant tanks.
It will be assumed that the instantaneous pressure in the gas and propellants tanks is the same, that is, there are no losses in the pipes connecting them. Also, it is interesting to refer all feed system pressures to the combustion chamber pressure, which is a project parameter [3], Based on this criterion, the following constant is defined:
k
p
where pc is the combustion chamber pressure (Pa).
Not all the volume of a propellant tank is occupied by this one. A smali part is occupied by gas and that portion of the total volume of the tank is denominated ułlage. This is the necessary space to allow the propellant thermal expansion, the accumulation of gases that were originally dissolved in the propellants and to contain the reaction products of the slow reactions, which occurs during storage [1], To assess this ąuantity in the analysis, an additional constant relating both volumes will be introduced, also assuming that it is the same for both tanks:
k„
(2.1.3)
where, V,/ Fuel tank volume (m3).
V,y Oxidizer tank volume (m3).
V/ Fuel volume (m3).
V„: Oxidizer volume (m3).
Besides, the gas constant should be expressed in terms of their molar mass, thus:
Rg =
(2.1.4)
where, Ry Universal gas constant (8314.41 J/kmolK). My Pressurizing gas molar mass (kg/kmol).
Furthermore, volume and mass will be related through the following expressions: