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) 2 denotes the compressor entrance, and 3 denotes the compressor exit (burner 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, also called jet engines. All types of jet engines have some parts in common. All jet engines have a compressor to increase the pressure of the incoming air. There are currently two principal compressor designs found on jet engines: the axial compressor, in which the air flows parallel to the axis of rotation, and the centrifugal compressor, in which the air is turned perpendicular to the axis of rotation. In either design, the job of the compressor is to increase the pressure of the flow. We measure the increase by the compressor pressure ratio (CPR), which is the ratio of the air total pressure (pt) exiting the compressor to the air pressure entering the compressor. This number is always greater than 1.0.
Compressor Pressure Ratio: CPR = pt3 / pt2 >= 1.0
To produce the increase in pressure, the compressor must perform work on the flow. In the axial compressor, cascades of small airfoils are mounted on a shaft that turns at a high rate of speed. Several rows, or stages, are usually used to produce a high CPR, with each stage producing a small pressure increase. In the centrifugal compressor, an additional pressure increase results from turning the flow radially (radiating from or converging to a common center). Since no external heat is being added to the compressor during the pressure increase, the process is isentropic. The temperature ratio across the compressor is related to the pressure ratio by the isentropic flow equations.
Compressor Temperature Ratio: Tt3 / Tt2 = (pt3 / pt2) ^((gam -1) / gam)
Where "gam" is the ratio of specific heats. Work must be done to turn the shaft on which the compressor is mounted. From the conservation of energy, the compressor work per mass of airflow (CW) is equal to the change in the specific enthalpy of the flow from the entrance to the exit of the compressor.
Compressor Work: CW = ht3 - ht2
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.
CW = (cp * Tt)3 - (cp * Tt)2
Performing a little algebra, we can relate the compressor work to the compressor pressure ratio:
CW = (cp * Tt)2 * (CPR ^((gam -1) / gam) - 1) / nc
The efficiency factor (nc) is included to account for the actual performance of the compressor 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. So additional work is needed to overcome the inefficiency of the compressor to produce a desired CPR. The work is provided by the power turbine, which is connected to the compressor by the central shaft.
Notice that the CPR is also related to the total temperature ratio across the compressor. Since the CPR is always greater than 1.0 and the value of gamma (the ratio of specific heats) is about 1.4 for air, the total temperature ratio is also greater than 1.0. The air heats up as it passes through the compressor. There are material limits (http://www.ueet.nasa.gov/parts.htm) on the temperature of the compressor. On some engines, the temperature at the exit of the compressor becomes a design constraint (a factor limiting the engine performance).
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