__8:
TURBOPROP ENGINE__

The
turboprop engine uses a propeller with a large disk area to accelerate a large
mass flow rate of air through a small _{}. Thus it has high propulsive efficiency. Twin-spool designs
enable operation of the propeller shaft and the main high-pressure compressor
shaft at different rotation speeds. Such engines have better performance at
take-off and at low Mach number than turbofans and turbojets.

The propeller rotation speed is limited to about 2000 to 3000 rpm because of the need to keep the tip Mach number below 1. The turbine shaft speed may be in the range of 4000 to 10000. Thus a gear is needed to reduce the rpm. This adds a considerable amount of weight to the engine.

**IDEAL TURBINE
WORK FRACTION: AN OPTIMIZATION PROBLEM**

Engine design involves many decisions based on trade-offs between various factors. An example is the decision on the best division of the available power between the propeller and the exhaust nozzle. There may be many other constraints in practice, such as low noise, low weight, etc. For this example, let us define "best" as the division which produces maximum thrust. This division will depend on the efficiency of the nozzle, propeller, turbine, and on the flight velocity.

Let

_{} be the enthalpy drop
available, after taking out enough work to run the
turbine which runs the compressor and other auxiliary devices.

_{} is the fraction of the enthalpy drop used
to run the power turbine. This is
what we want to optimize.

_{} be the efficiencies
of the power turbine, nozzle, gear,
and propeller respectively.

Energy Balance for the propeller:

_{}

Energy balance for the exhaust nozzle:

_{}, where

_{}

Thus, total thrust is

_{} so that

_{}Differentiate with respect to _{}and equate to zero to
solve for the optimum value _{}:

_{}

Note:

1) As u increases, it pays to exhaust more kinetic energy through the nozzle.

2)
At very low u, (e.g., helicopters, tanks), the optimum value _{}is very close to 1,
so that all available power should be taken out through the shaft.