A graphical version of this slide is also available. The interactive Java applet EngineSim is also available. This program solves these equations and displays the thrust and fuel flow values for a variety of turbine engines. In the text only version presented here, * denotes multiplication, and / denotes division The subscripts (last letter) 3 denotes the compressor exit (burner entrance), and 4 denotes the burner exit (turbine entrance) The flow variables will be denoted by letters: Tt is the total temperature.
The propulsion system of an aircraft must perform two important roles:
On this page we show the thermodynamic equations which relate the the temperature ratio in the burner to the fuel mass flow rate. The fuel mass flow rate is denoted by (mdot f) and is given in units of mass per time (kg/sec). The fuel mass flow rate is related to the total engine air flow rate (mdot a) by the fuel to air ratio (f). The energy equation for the burner can be solved for the temperature ratio across the burner:
Burner Temperature Ratio: Tt4 / Tt3 = (1 + f * nb * Q / (cp * Tt3)) / (1 + f)
Where Tt4 is the burner exit temperature, Tt3 is the burner entrance temperature, Q is the fuel heating value, cp is the specific heat coefficient of air at constant pressure and nb is an efficiency factor to account for losses in the burner.
Using the temperature equation, and a little algebra, it is possible to solve for the fuel to air ratio (f).
Fuel to Air Ratio: f = [ (Tt4 / TT3) - 1] / [nb * Q / (cp * Tt3) - (Tt4 /Tt3) ]
From the fuel to air ratio, we can obtain the fuel mass flow rate by a simple multiplication.
Fuel Mass Flow Rate: mdot f = f * mdot a
The engine air flow rate is normally set by conditions in the nozzle. We can use the value of fuel to air ratio to determine the engine's specific fuel consumption. As explained in another section of the Beginner's Guide to Aerodynamics, the specific fuel consumption and the aircraft fuel load determine the maximum flight time and the maximum range of an aircraft.
It would appear that we can make the temperature ratio (and resulting thrust) as large as we want by just increasing the fuel flow rate (and the fuel/air ratio). However, the details of the combustion process sets some limits on values of the fuel/air ratio. And in engine operation, there is a maximum burner exit temperature (Tt4) which is determined by materials limits (http://www.ueet.nasa.gov/parts.htm). If we try to run the engine hotter than this maximum temperature, the burner and the turbine will be damaged.
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