Engineering Software
Thrust Analysis
Thrust
Introduction
This section provides an isentropic thrust analysis when the working fluid is air.
Analysis
In the presented thrust analysis, only air is considered as the working fluid behaving as a perfect gas -- specific heat has a constant value. Ideal gas state equation is valid -- pv = RT.
Air enters a nozzle at point 1 and it exits the nozzle at point 2. Isentropic expansion is considered with no entropy change.
Figure 1 contains a thrust schematic layout.
Figure 1 - Thrust Schematic Layout
Figure 2 presents a thrust temperature vs entropy diagram.
Figure 2 - Thrust Temperature vs Entropy Diagram
Figure 3 presents thrust performance as a function of the nozzle inlet stagnation temperature and pressure values for a few fixed values such as: working fluid mass flow rate, nozzle outlet Mach Number and ambient pressure. Only subsonic nozzle operation is considered.
Figure 3 - Thrust Performance
One can notice that thrust increases with an increase in the inlet stagnation temperature and pressure values.
Assumptions
Working fluid is air. There is no friction and heat transfer. Expansion is isentropic -- there is no entropy change. Ideal gas state equation is valid -- pv = RT. Air behaves as a perfect gas -- specific heat has a constant value.
Governing Equations
Tt/T = (1 + M^2(ϰ - 1)/2)
pt/p = (1 + M^2(k - 1)/2)^ϰ/(ϰ-1)
Tt/T = (pt/p)^(ϰ-1)/ϰ
v = (2cp(Tt - T))^1/2
vs = (ϰRT)^1/2
M = v/vs
ϰ = cp/cv
cp - cv = R
pv = RT
Thrust = vm + (p - pa)A
Input Data
T1 = 900, 1,200 and 1,500 [K]
p1 = 5, 10 and 15 [atm]
R = 0.2867 [kJ/kg*K]
cp = 1.004 [kJ/kg*K]
ϰ = 1.4 [/]
m = 1 [kg/s]
M = 0.85 [/]
pa = 1 [atm]
Results
Thrust Performance vs Nozzle Inlet Stagnation Temperature and Pressure
Outlet Mach Number = 0.85 [/] and Ambient Pressure = 1 [atm]
Working Fluid Mass Flow Rate = 1 [kg/s]
Thrust
[N]
Inlet Stagnation Temperature
[K]
Inlet Stagnation Pressure
[atm]
5
10
15
900
797.7
873.5
898.7
1,200
922.3
1,009.3
1,038.7
1,500
1,031.1
1,128.6
1,161.3
Conclusions
Thrust increases with an increase in the inlet stagnation temperature and pressure values.
References
JANAF Thermochemical Data - Tables, 1970