Ideal Ramjet Analysis
Throughout this course, we will analyze engine performance by considering one station at a time.
An ideal ramjet engine has an isentropic inlet, which decelerates incoming air at a flight Mach number of 3.0 to a low Mach number without any losses. Heat is then added by chemical reaction with a fuel whose heating value is 19,000 Btu / lbm. The altitude is 11000m. The maximum temperature in the engine is limited to 2000K. The heat addition occurs at constant pressure, and at a low Mach number. The nozzle is fully expanded, and has an exit diameter of 1 meter. Find the thrust and thrust-specific fuel consumption of the engine, assuming constant specific heats.
Here we have undisturbed air, just before entering the inlet of the engine. The stagnation temperature can be determined from the static temperature and the Mach number using the isentropic relation.
Isentropic diffuser, from Station 1 to Station 2:
Adiabatic, and no work done except that of volume change:
Isentropic (reversible, adiabatic, therefore no losses):
Constant-Pressure Heat Addition, from Station 2 to Station 3:is specified, for a given thrust setting. For maximum thrust, this value is limited by the limiting temperature of the combustor material.
To find the fuel/air ratio needed to achieve this temperature, we consider the enthalpy balance across the combustor.
Stagnation enthalpy of the air + burned products leaving the combustor = Stagnation enthalpy of the air entering the combustor + sensible enthalpy of the fuel + heat released by reaction.
We neglect the sensible enthalpy of the fuel, since it is very small compared to the heat released by reaction.
Solving for the fuel/air ratio,
Isentropic Nozzle, from Station 3 to Station 4: