Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

32 Fluid Mechanics, Thermodynamics of Turbomachinery
Comparing the above definitions it is easily deduced that the mechanical efficiency h m,
which is simply the ratio of shaft power to rotor power, is
In the following paragraphs the various definitions of hydraulic and adiabatic efficiency
are discussed in more detail.
For an incremental change of state through a turbomachine the steady flow energy
equation, eqn. (2.5), can be written
From the second law of thermodynamics
Eliminating dQ between these two equations and rearranging
(2.19)
For a turbine expansion, noting W . x = W . t > 0, integrate eqn. (2.19) from the initial state
1 to the final state 2,
(2.20)
For a reversible adiabatic process, Tds = 0 = dh - dp/r. The incremental maximum
work output is then
Hence, the overall maximum work output between initial state 1 and final state 2 is
(2.20a)
where the subscript s in eqn. (2.20a) denotes that the change of state between 1 and 2
is isentropic.
For an incompressible fluid, in the absence of friction, the maximum work output
from the turbine (ignoring frictional losses) is
where gH = p/r + 1 – 2 c 2 + gz
Steam and gas turbines
(2.20b)
Figure 2.5a shows a Mollier diagram representing the expansion process through an
adiabatic turbine. Line 1–2 represents the actual expansion and line 1–2s the ideal or
reversible expansion. The fluid velocities at entry to and at exit from a turbine may be