fluid_mechanics

680 Chapter 12 ■ Turbomachines
U W 1
V 1
U W 1
V 1
U W 1
V 1
U W 1
V 1
Inlet
F I G U R E E12.7
If we consider the energy equation 1Eq. 5.842 for flow across
the rotor we have
(a)
(b)
(c)
(d)
p 1
g V 2 1
2g z 1 h S p 2
g V 2 2
W 2 = W 1
W 2 = W 1
U V 2 = 0
6 180°
where h S is the shaft work head. This simplifies to
2g z 2 h L
since p 1 p 2 and z 1 z 2 . Note that the impulse turbine obtains
h S V 2 2 V1
2 h
U V 2g
L
2
(2)
its energy from a reduction in the velocity head. The largest shaft
work head possible 1and therefore the largest power2 occurs
when all of the kinetic energy available is extracted by the turbine,
giving
U
V 2 0
(Ans)
V 2 W 2 = W 1
This is consistent with the maximum power condition represented
by Fig. E12.7b.
COMMENT As indicated by Eq. 1, if the exit absolute velocity
is not in the plane of the rotor 1i.e., b 6 180° 2, there is a reduction
V 2
in the power available 1by a factor of 1 cos b2. This is also
U
supported by the energy equation, Eq. 2, as follows. For b
value of V 2 to zero—there is always a component in the axial direction.
Outlet
the inlet and exit velocity triangles are as shown in Fig. E12.7d.
Regardless of the bucket speed, U, it is not possible to reduce the
Thus, according to Eq. 2, the turbine cannot extract the
entire velocity head; the exiting fluid has some kinetic energy left
in it.
W 2 = W 1
Dentist drill turbines
are usually of
the impulse class.
A second type of impulse turbine that is widely used 1most often with air as the working
fluid2 is indicated in Fig. 12.29. A circumferential series of fluid jets strikes the rotating blades
which, as with the Pelton wheel, alter both the direction and magnitude of the absolute velocity.
As with the Pelton wheel, the inlet and exit pressures 1i.e., on either side of the rotor2 are equal,
and the magnitude of the relative velocity is unchanged as the fluid slides across the blades 1if frictional
effects are negligible2.
Typical inlet and exit velocity triangles 1absolute, relative, and blade velocities2 are shown in
Fig. 12.30. As discussed in Section 12.2, in order for the absolute velocity of the fluid to be changed
Nozzles
Control
volume
T shaft
ω
Fluid jets
(a)
(b)
F I G U R E 12.29 A multinozzle, non-Pelton wheel impulse turbine commonly used with air as the
working fluid.