V_i = .96 [root](2g(.5646H)) = 0.721 [root](2gH).
_Angle of Guide-Blades._
Sin [gamma] = u_i/v_i = 0.125/0.721 = 0.173;
[gamma] = 10° nearly.
_Tangential Velocity of Water entering Wheel._
w_i = v_i cos [gamma] = 0.7101 [root](2gH).
_Angle of Vanes at Inlet Surface._
Cot [theta] = (w_i - V_i)/u_i = (.7101 - .66)/.125 = .4008;
[theta] = 68° nearly.
_Hydraulic Efficiency of Wheel._
[eta] = w_iV_i/gH = .7101 × .66 × 2
= 0.9373.
This, however, neglects the friction of wheel covers and leakage. The
efficiency from experiment has been found to be 0.75 to 0.80.
_Impulse and Partial Admission Turbines._
§ 197. The principal defect of most turbines with complete admission is
the imperfection of the arrangements for working with less than the
normal supply. With many forms of reaction turbine the efficiency is
considerably reduced when the regulating sluices are partially
closed, but it is exactly when the supply of water is deficient that it
is most important to get out of it the greatest possible amount of work.
The imperfection of the regulating arrangements is therefore, from the
practical point of view, a serious defect. All turbine makers have
sought by various methods to improve the regulating mechanism. B.
Fourneyron, by dividing his wheel by horizontal diaphragms, virtually
obtained three or more separate radial flow turbines, which could be
successively set in action at their full power, but the arrangement is
not altogether successful, because of the spreading of the water in the
space between the wheel and guide-blades. Fontaine similarly employed
two concentric axial flow turbines formed in the same casing. One was
worked at full power, the other regulated. By this arrangement the loss
of efficiency due to the action of the regulating sluice affected only
half the water power. Many makers have adopted the expedient of erecting
two or three separate turbines on the same waterfall. Then one or more
could be put out of action and the others worked at full power. All
these methods are rather palliatives than remedies. The movable
guide-blades of Professor James Thomson meet the difficulty directly,
but they are not applicable to every form of turbine.
[Illustration: FIG. 197.]
C. Callon, in 1840, patented an arrangement of sluices for axial or
outward flow turbines, which were to be closed successively as the water
supply diminished. By preference the sluices were closed by pairs, two
diametrically opposite sluices forming a pair. The water was thus
admitted to opposite but equal arcs of the wheel, and the forces driving
the turbine were symmetrically placed. As soon as this arrangement was
adopted, a modification of the mode of action of the water in the
turbine became necessary. If the turbine wheel passages remain full of
water during the whole rotation, the water contained in each passage
must be put into motion each time it passes an open portion of the
sluice, and stopped each time it passes a closed portion of the sluice.
It is thus put into motion and stopped twice in each rotation. This
gives rise to violent eddying motions and great loss of energy in shock.
To prevent this, the turbine wheel with partial admission must be placed
above the tail water, and the wheel passages be allowed to clear
themselves of water, while passing from one open portion of the sluices
to the next.
But if the wheel passages are free of water when they arrive at the open
guide passages, then there can be no pressure other than atmospheric
pressure in the clearance space between guides and wheel. The water must
issue from the sluices with the whole velocity due to the head; received
on the curved vanes of the wheel, the jets must be gradually deviated
and discharged with a small final velocity only, precisely in the same
way as when a single jet strikes a curved vane in the free air. Turbines
of this kind are therefore termed turbines of free deviation. There is
no variation of pressure in the jet during the whole time of its action
on the wheel, and the whole energy of the jet is imparted to the wheel,
simply by the impulse due to its gradual change of momentum. It is clear
that the water may be admitted in exactly the same way to any fraction
of the circumference at pleasure, without altering the efficiency of the
wheel. The diameter of the wheel may be made as large as convenient, and
the water admitted to a small fraction of the circumference only. Then
the number of revolutions is independent of the water velocity, and may
be kept down to a manageable value.
[Illustration: FIG. 198.]
[Illustration: FIG. 199.]
§ 198. _General Description of an Impulse Turbine or Turbine with Free
Deviation._--Fig. 197 shows a general sectional elevation of a Girard
turbine, in which the flow is axial. The water, admitted above a
horizontal floor, passes down through the annular wheel containing the
guide-blades G, G, and thence into the revolving wheel WW. The
revolving wheel is fixed to a hollow shaft suspended from the pivot p.
The solid internal shaft ss is merely a fixed column supporting the
pivot. The advantage of this is that the pivot is accessible for
lubrication and adjustment. B is the mortise bevel wheel by which the
power of the turbine is given off. The sluices are worked by the hand
wheel h, which raises them successively, in a way to be described
presently. d, d are the sluice rods. Figs. 198, 199 show the sectional
form of the guide-blade chamber and wheel and the curves of the wheel
vanes and guide-blades, when drawn on a plane development of the
cylindrical section of the wheel; a, a, a are the sluices for cutting
off the water; b, b, b are apertures by which the entrance or exit of
air is facilitated as the buckets empty and fill. Figs. 200, 201 show
the guide-blade gear. a, a, a are the sluice rods as before. At the
top of each sluice rod is a small block c, having a projecting tongue,
which slides in the groove of the circular cam plate d, d. This
circular plate is supported on the frame e, and revolves on it by
means of the flanged rollers f. Inside, at the top, the cam plate is
toothed, and gears into a spur pinion connected with the hand wheel h.
At gg is an inclined groove or shunt. When the tongues of the blocks
c, c arrive at g, they slide up to a second groove, or the reverse,
according as the cam plate is revolved in one direction or in the
other. As this operation takes place with each sluice successively,
any number of sluices can be opened or closed as desired. The turbine
is of 48 horse power on 5.12 ft. fall, and the supply of water varies
from 35 to 112 cub. ft. per second. The efficiency in normal working
is given as 73%. The mean diameter of the wheel is 6 ft., and the
speed 27.4 revolutions per minute.
[Illustration: FIG. 200.]
[Illustration: FIG. 201.]
[Illustration: FIG. 202.]
As an example of a partial admission radial flow impulse turbine, a
100 h.p. turbine at Immenstadt may be taken. The fall varies from 538
to 570 ft. The external diameter of the wheel is 4½ ft., and its
internal diameter 3 ft. 10 in. Normal speed 400 revs. per minute.
Water is discharged into the wheel by a single nozzle, shown in fig.
202 with its regulating apparatus and some of the vanes. The water
enters the wheel at an angle of 22° with the direction of motion, and
the final angle of the wheel vanes is 20°. The efficiency on trial was
from 75 to 78%.
§ 199. _Theory of the Impulse Turbine._--The theory of the impulse
turbine does not essentially differ from that of the reaction turbine,
except that there is no pressure in the wheel opposing the discharge
from the guide-blades. Hence the velocity with which the water enters
the wheel is simply
v_i = 0.96 [root]{2g(H - [h])},
where [heta] is the height of the top of the wheel above the tail
water. If the hydropneumatic system is used, then [h] = 0. Let
Q_m be the maximum supply of water, r1, r2 the internal and external
radii of the wheel at the inlet surface; then
u_i = Q_m/{[pi](r2² - r1²)}.
The value of u_i may be about 0.45 [root]{2g(H - [eta][h])},
whence r1, r2 can be determined.