On this slide we have gathered together all of the equations
necessary to compute the theoretical thrust for a
turbojet engine.
The general thrust
equation is given just below the graphic in the specific
thrust form.
Fs = F / m = (1 + mf) * Ve  V0
where Fs is the specific thrust, F is the net thrust,
m is the air flow rate through the
engine, mf is the fuelair ratio,
Ve is the nozzle exit velocity, and V0 is the free
stream velocity. The
equation for the exit velocity was developed on the nozzle
performance slide:
Ve = sqrt( 2 * Cp * Tt8 * n8 * [1  {1 / NPR} ^((gam  1) / gam) ] )
where Cp is the specific heat at constant pressure,
Tt8 is the total temperature in the nozzle, n8 is an efficiency factor,
NPR is the nozzle pressure ratio, and gam is the ratio of specific heats.
The NPR is simply the ratio of the total pressure in the
nozzle pt8 to the free stream static pressure p0.
NPR = pt8 / p0
The nozzle total pressure pt8
and the total temperature Tt8 depend on the engine
pressure ratio EPR and temperature ratio. ETR.
Tt8 = Tt2 * ETR
pt8 = pt2 * EPR
The equations for these ratios are given on separate
slides and depend on the pressure and temperature ratio across each
of the engine components. The engine
pressure and temperature ratios are referenced to conditions at the
compressor face, station 2.
Compressor face conditions depend on free stream
conditions and inlet performance, IPR:
Tt2 = Tt0
pt2 = pt0 * IPR
The equations at the bottom of the slide are
compressible forms
for determining the total pressure and temperature conditions from the
corresponding static conditions and the free stream velocity.
Tt0 = T0 * (1 + .5 * [gam 1] * V0 ^2 / a0 ^2)
pt0 = p0 * (Tt0 / T0) ^ ( gam / ( gam 1))
where a0 is the free stream speed of
sound.
a0 = sqrt (gam * R * T0)
where R is the gas constant from the
equation of state.
With the set of equations, knowing the free stream temperature, pressure and velocity,
one can calculate the thrust generated by a engine design.
These calculations are performed in the
EngineSim engine simulator. A
technical paper
describing the details of the method used in EngineSim is also
available.
Activities:
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EngineSim  Engine Simulator:

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