A graphical version of this slide is 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, / denotes division, and ^ denotes exponentiation. The subscripts (last letter) 4 denotes the turbine entrance, and 5 denotes the turbine exit (nozzle entrance) The flow variables will be denoted by letters: Tt is the total temperature, pt is the total pressure, ht is the specific total enthalpy.

Most modern passenger and military aircraft are powered by gas turbine engines, which are also called jet engines. There are several different types of jet engines. But all jet engines have some parts in common. All jet engines have a turbine to drive the compressor. The job of the turbine is to extract energy from the heated flow exiting the burner. The turbine is connected to the shaft, which is also connected to the compressor. As the flow passes through the turbine, the total pressure and temperature decrease. We measure the decrease in pressure by the turbine pressure ration (TPR), which is the ratio of the air pressure exiting the turbine to the air pressure entering the turbine. This number is always less than 1.0.

Turbine Pressure Ratio: TPR = pt5 / pt4 <= 1.0

In the axial turbine, cascades of small airfoils are mounted on a shaft that turns at a high rate of speed. Since no external heat is being added to or extracted from the turbine during this process, the process is isentropic. The temperature ratio across the turbine is related to the pressure ratio by the isentropic flow equations.

Turbine Temperature Ratio: Tt5 / Tt4 = (pt5 / pt4) ^((gam -1) / gam)

Work is done by the flow to turn the turbine and the shaft. From the conservation of energy, the turbine work per mass of airflow (TW) is equal to the change in the specific enthalpy of the flow from the entrance to the exit of the turbine.

Turbine Work: TW = ht4 - ht5

The term "specific" means per mass of airflow. The enthalpy at the entrance and exit is related to the total temperature and specific heat coefficient at constant pressure (cp) at those stations.

TW = (cp * Tt)4 - (cp * Tt)5

Using algebra, we can relate the work done by the turbine to the turbine pressure ratio:

TW = (nt * cp * Tt)4 * [1 - TPR ^((gam -1) / gam)]

The efficiency factor (nt) is included to account for the actual performance of the turbine as opposed to the ideal, isentropic performance. In an ideal world, the value of the efficiency would be 1.0. In reality, it is always less than 1.0. Because of mechanical inefficiencies, you cannot get 100% of the available work from the turbine.

The turbine blades exist in a much more hostile environment than compressor blades. Sitting just downstream of the burner, the blades experience flow temperatures of more than a thousand degrees Fahrenheit. Turbine blades must, therefore, be made of special materials (http://www.ueet.nasa.gov/parts.htm). that can withstand the heat, or they must be actively cooled.

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