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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- Beginner's Guide to Propulsion
- Beginner's Guide to Model Rockets
- Beginner's Guide to Kites
- Beginner's Guide to Aeronautics

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*byTom
Benson
Please send suggestions/corrections to: benson@grc.nasa.gov *