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Computer drawing of gas turbine schematic showing the equations
 for pressure ratio, temperature ratio, and work for a turbine.

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 partsin 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 pt and temperature Tt 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. Referring to our station numbering, the turbine entrance is station 4 and the turbine exit is station 5. The TPR is equal to pt5 divided by pt4

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.

Tt5 / Tt4 = (pt5 / pt4) ^((gam -1) / gam)

where gam is the ratio of specific heats.

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 ht of the flow from the entrance to the exit of the turbine.

TW = ht4 - ht5

The term "specific" means per mass of airflow. The enthalpy at the entrance and exit is related to the total temperature Tt at those station:

TW = cp * (Tt4 - Tt5)

Using algebra, we arrive at the equation:

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

that relates the work done by the turbine to the turbine pressure ratio, the incoming total temperature, some properties of the gas, and an efficiency factor nt. The efficiency factor 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 that can withstand the heat, or they must be actively cooled. You can now use EngineSim to study the effects of different materials on engine operation.


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Editor: Nancy Hall
NASA Official: Nancy Hall
Last Updated: May 13 2021

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