Page 62 - Fluid Mechanics and Thermodynamics of Turbomachinery

Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency 43
theoretical kinetic energy per unit mass obtained by an isentropic expansion to the
same back pressure, i.e.
1 2 1 2
N D . c //. c / D .h 01 h 2 //.h 01 h 2s /. (2.40)
2 2 2 2s
Nozzle efficiency is sometimes expressed in terms of various loss or other coeffi-
cients. An enthalpy loss coefficient for the nozzle can be defined as

1 2
N D .h 2 h 2s //. c /, (2.41)
2 2
and, also, a velocity coefficient for the nozzle,
K N D c 2 /c 2s . (2.42)

It is easy to show that these definitions are related to one another by
2
N D 1/.1 C N / D K . (2.43)
N
EXAMPLE 2.2. Gas enters the nozzles of a turbine stage at a stagnation pressure
and temperature of 4.0 bar and 1200 K and leaves with a velocity of 572 m/s and
at a static pressure of 2.36 bar. Determine the nozzle efficiency assuming the gas
has the average properties over the temperature range of the expansion of C p D
1.160 kJ/kg K and
D 1.33.
Solution. From eqns. (2.40) and (2.35) the nozzle efficiency becomes

1 T 2 /T 01 1 T 2 /T 01
N D D .
1 T 2s /T 01 1 .p 2 /p 01 / .
1//
Assuming adiabatic flow .T 02 D T 01 /:
1 2 1 2
T 2 D T 02 c /C p D 1200 ð 572 /1160 D 1059 K,
2 2 2
and thus
1 1059/1200 0.1175
N D D D 0.9576.
1 .2.36/4/ 0.33/1.33 0.12271

Diffusers

A diffuser is a component of a fluid flow system designed to reduce the flow
velocity and thereby increase the fluid pressure. All turbomachines and many other
flow systems incorporate a diffuser (e.g. closed circuit wind tunnels, the duct
between the compressor and burner of a gas turbine engine, the duct at exit from a
gas turbine connected to the jet pipe, the duct following the impeller of a centrifugal
compressor, etc.). Turbomachinery flows are, in general, subsonic (M< 1) and the
diffuser can be represented as a channel diverging in the direction of flow (see
Figure 2.13).
The basic diffuser is a geometrically simple device with a rather long history of
investigation by many researchers. The long timespan of the research is an indicator
that the fluid mechanical processes within it are complex, the research rather more