EngineSim - Engine Simulator:
Thrust Equation:
A graphical version of this slide is also available. In the text only version presented here, * denotes multiplication, / denotes division, ^ denotes exponentiation, ^2 means quantity squared, sqrt means square root. The subscripts (last letter) 0 denotes a free stream value, 2 denotes conditions at the compressor face of the engine, 8 (or e) is the conditions at the exit of the nozzle. The flow variables will be denoted by letters: T is the temperature, p is the pressure, V is the velocity, and m is the mass flow rate, gam is the ratio of specific heats..
On this page we have gathered together all of the equations necessary to compute the theoretical thrust for a turbojet engine. We will begin with the thrust equation and work our way back to any other equations which we need. The general thrust equation is given in the specific thrust form. Specific thrust is thrust (F) divided by the mass flow rate.
Specific Thrust (Fs) Equation: Fs = F / m = (1 + mf) * Ve - V0
The specific thrust depends only on the exit velocity (Ve) from the nozzle, the free stream velocity (V0) , and the fuel to air ratio, (mf).
The equation for the exit velocity was developed on the nozzle performance slide and depends on some thermodynamic properties, the total temperature (Tt) in the nozzle, and the nozzle pressure ration (NPR).
Nozzle Performance Equation: Ve = sqrt( 2 * Cp * Tt8 * n8 * [1 - {1 / NPR} ^((gam - 1) / gam) ] )
Where (Cp) is the specific heat capacity at constant pressure and n8 is the nozzle efficiency factor. The NPR is simply the ratio of the total pressure in the nozzle to the free stream static pressure.
Nozzle Pressure Ratio: NPR = pt8 / p8 = pt8 / p0
The total pressure (pt8) and the total temperature (Tt8) in the nozzle depend on the engine pressure ratio (EPR) and temperature ratio (ETR). The equations for these ratios are given on separate slides and depend on the pressure and temperature ratio across each of the engine components.
Nozzle Pressure and Temperature Values: Tt8 = Tt2 * ETR .... pt8 = pt2 * EPR
The engine pressure and temperature ratios are referenced to conditions at the compressor face. Compressor face conditions depend on free stream conditions and inlet performance.
Inlet Performance Equations: Tt2 = Tt0 .... pt2 = pt0 * IPR
Where IPR is the inlet pressure recovery which depends on aircraft speed and details of the inlet design. The free stream total conditions can be found from compressible equations relating the total pressure and temperature conditions to the corresponding static conditions and the free stream velocity.
Isentropic Temperature Equation: Tt0 = T0 * (1 + .5 * [gam -1] * V0 ^2 / a0 ^2)
Isentropic Pressure Equation: pt0 = p0 * (Tt0 / T0) ^ ( gam / ( gam -1))
The variable "a0" is the free stream speed of sound.Speed of Sound: a0 = sqrt (gam * R * T0)
Where R is the gas constant for air.
EngineSim - Engine Simulator:
Thrust Equation:
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byTom
Benson
Please send suggestions/corrections to: benson@grc.nasa.gov