Handbook of Turbomachinery Second Edition Revised - Ventech!

The approximation of Eq. (1) is adequate for turbines operating on air and
other common gases at moderate pressures and temperatures. Total
conditions are normally used for both temperature and pressure at the
inlet to the turbine, so that the inlet pressure is correctly referred to as p 0 in in
Eq. (1).
As discussed earlier, the actual energy transfer in a turbine is smaller
than the isentropic value due to irreversibilities in the flow. The actual
process is marked by an increase in entropy and is represented in the h–s
diagram of Fig. 6(b) by adotted line. The actual path is uncertain, as the
detailsoftheentropychangeswithintheturbineareusuallynotknown.Due
to the curvature of the isobars, the enthalpy change associated with an
entropy increase is less than that for an isentropic process. The degree of
entropy rise is usually described indirectly by the ratio of the actual enthalpy
drop to the isentropic enthalpy drop. This quantity is referred to as the
isentropic (sometimes adiabatic) efficiency, Z, and is calculated from
Z OA ¼ hin hdis
Dhisentropic
The subscript OA indicates the overall efficiency, since the enthalpy drop is
taken across the entire turbine. The efficiency is one of the critical
parameters that describe turbine performance.
So far we have not specified whether the total or static pressure should
be used at the turbine exit for calculating the isentropic enthalpy drop.
(Note that this does not affect the actual enthalpy drop, just the ideal
enthalpy drop.) Usage depends on application. For applications where the
kinetic energy leaving the turbine rotor is useful, total pressure is used. Such
cases include all but the last stage in a multistage turbine (the kinetic energy
of the exhaust can be converted into useful work by the following stage) and
cases where the turbine exhaust is used to generate thrust, such as in a
turbojet. For most power-generating applications, the turbine is rated using
static exit pressure, since the exit kinetic energy is usually dissipated in the
atmosphere. Note that the total-to-static efficiency will be lower than the
total-to-total efficiency since the static exit pressure is lower than the total.
With the energy available to the turbine established by the inlet and
exit conditions, let’s take a closer look at the actual mechanism of energy
transfer within theturbine.Figure7shows ageneralized turbine rotor.Flow
enters the upstream side of the rotor at point 1 with velocity V ! 1 and exits
from the downstream side at point 2 with velocity V ! 2. The rotor spins about
its centerline coincident with the x-axis with rotational velocity o. The
location of points 1 and 2 is arbitrary (as long as they are on the rotor), as
are the two velocity vectors. The velocity vectors are assumed to represent
Copyright © 2003 Marcel Dekker, Inc.
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