Novak P. Developments in hydraulic engineering - Vol. 5
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Earlier also radial-inflow turbines were frequently installed in low-head plants, though
under certain conditions the use of high-speed Francis machines is still justifiable.
Similarly the Dériaz turbine (diagonal-inflow wheel) has been developed for application
as a reversible machine (pump-
FIG. 41. Turbine types.
turbine), but it is suitable for utilization in the higher part of the low-head range only. Up
to the present only a few Dériaz machines have been constructed. In mini and micro
stations, besides the above mentioned types, also cross-flow turbines are frequently
installed.
7.2 Typical Low-Head Generating Aggregates
The low-head sets can be categorized according to the following main types:
(1) Conventional (i.e. vertical-axis) propeller or Kaplan unit. Inflow from the spiral
case into the wicket gate is radial; thereafter the flow is diverted and passes the runner in
an axial direction; finally the ‘used’ water passes through an elbow-type expanding draft
tube connecting the wheel with the tailwater. The typical set (conventional Kaplan unit)
usually comprises a directly driven vertical-axis generator (Figs 11, 13–16, 21, 24, 25).
Figure 42 shows a simplified cross-sectional drawing of a conventional axial wheel and
in Fig. 43 the photograph of a large Kaplan runner can be seen. Application head range:
up to 50–60 m, exceptionally even higher (e.g. Orlik, Czechoslovakia, H=71 m). The unit
capacity exceeds 100 MW at several plants (Ligga, Sweden, 182 MW).
In earlier low-head plants equipped with axial or radial turbines shafts were built
instead of spiral cases, and the water was conveyed from the wheel through vertical,
diffuser-shaped draft tubes into free-surface tail-water pits. Similar arrangements are still
chosen in small projects.
Water power development: low-head Hydropower utilization 59
(2) The bulb-generator set comprises an axial (propeller or Kaplan) wheel installed
into a horizontal or slightly inclined passage (tube) and a directly coupled or gear-driven
generator housed in a steel bulb (bulb unit) (Figs 17, 23, 26). The inflow to the wheel is
symmetrical around the bulb and the outflow is effected through the expanding straight
draft tube.
FIG. 42. Cross-section of a
conventional axial (Kaplan or
propeller) turbine.
FIG. 43. View of a conventional
Kaplan runner; mounting in the
workshop. (From issue No. 20, Voith
Forschung und Konstruktion.)
Developments in hydraulic engineering–5 60
(During the last decades, as mentioned in Section 4.1.2, the bulb set penetrated into the
lower head field of the conventional unit.) Figure 44 illustrates the cross-section of a bulb
unit and Fig. 45 the wicket gate of a bulb turbine. Unit capacities of 20–40 MW are no
longer rare (e.g. Shingo No. 2 plant, Japan, H=22·5 m, 41 MW; Péage-de-Rousillon,
France, H=12·5 m, 40 MW; Altenwörth, Austria, H=14 m, 40 MW). In the case of very
low heads it may be necessary to insert a gear drive (e.g. Mosel plants in the Federal
Republic of Germany).
(3) In the rim-generator aggregate the poles of the generator rotor are bolted to a ring
which is fixed to the turbine runner and rotates in a slot of the tubular passage. The
generator stator encircles this slot. The delicate sealing problems have been solved. Its
first application (based on an early patent of L.F.Harza) was restricted to small units
operating under very low heads in submersible plants (Fig. 22). Its improved version, the
so-called STRAFLO machine, is designed for higher heads and for larger capacities as
well, being applicable in any type of plant (see Fig. 18 where a block powerhouse
accommodates two sets, each of 8MW). Most of the rim-generator turbines are single-
regulated (propeller type). A considerable progress in this field is manifested by the
STRAFLO propeller-type units of 20 MW already in operation in the Annapolis pilot
tidal plant
FIG. 44. Cross-section view of a large-
size bulb aggregate; Racine plant, Ohio
river, USA, H=7 m, P
25 MW, D=7·7
m.
80
Water power development: low-head Hydropower utilization 61
FIG. 45. Assembly of wicket gate of a
bulb turbine in the workshop; Parki
plant, Sweden, H=13 m, Q=172 m
3
/s,
P=20 MW, runner diameter 4·9 m.
(After a prospectus of the KWM
turbine factory.)
FIG. 46. Sketch of the STRAFLO
aggregate: 1, bearings; 2, runner; 3,
Developments in hydraulic engineering–5 62
sealings; 4, generator stator; 5,
generator rotor; 6, guide vane. (After a
publication of the STRAFLO Group.)
(Nova Scotia, Canada). Figure 46 explains the STRAFLO arrangement. The STRAFLO
turbines in the Weinzödl plant (Fig. 18) are double regulated, i.e. they have to be termed
STRAFLO-Kaplan machines.
(4) The S-arrangement (see Fig. 19) contains an axial (propeller or Kaplan) wheel
accommodated in an S-shaped tubular passage and a generator coupled to it directly or by
speed-increasing gear. Vertical-axis S-machines can sometimes be found installed in
adequately formed passages. The head range extends from very low heads up to about
15–20 m. Usually the unit capacity does not exceed 5–10 MW. The designs of the Allis-
Chalmers Corporation (USA) are termed TUBE turbines. The largest TUBE aggregates
are the five approximately 50MW units of the Ozark plant, Arkansas (H=9·8 m). The S-
installation is a preferred solution for mini and micro plants.
(5) The various types of cross-flow turbines (Banki, Michell, Ossberger) are
exclusively used in small-size development. As the name indicates, the jet passes the
wheel twice (Fig. 47). The cross-flow turbine can efficiently be used for heads from the
lowest up to about 200 m, though utilizing low discharges only, so that its capacity is
limited to about 1 MW.
(6) Under adequate hydrological and load conditions high-speed vertical-axis Francis
machines, even large ones, can still be competitive with axial turbines; however, because
of their lower specific speed they are
FIG. 47. Cross-flow turbines: (a)
schematic drawing of the Banki
turbine; (b) cross-section of an
Ossberger wheel with vertical
inflow.
81–83
being considered mainly within the upper low-head domain, i.e. at about 40 m or higher
(Itaparica, Brazil, H=53 m, three machines each 264 MW; Inga II, Zaire, H=63 m, four
178 MW units; Noxon Rapids, USA, H=46 m, one 128 MW turbine).
Water power development: low-head Hydropower utilization 63
7.3 Hydromechanical Principles and Operational Characteristics of
Axial Turbines
7.3.1 Basic Principles of Operation
In the conventional set the spiral (scroll) case provides for uniformly distributed inflow
along the outer periphery of the wicket gate (guide vane assembly) (Fig. 15) whilst the
adjustable guide vanes regulate the discharge (Fig. 42). The scroll case forces the water to
move along spiral traces, inducing the formation of an almost ideal irrotational vortex,
which promotes the development of a tangential (whirl) component of the flow; the
tangential component of the velocity necessary for the proper entrance of the water into
the runner is formed along the curved guide vanes.
Water under pressure entering the runner is deviated by its blades, thus exerting
impulse forces on them. The rotational components of these blade forces develop a torque
revolving the runner and the generator rotor. The pressure part of the entire energy (equal
to the net head) is first converted into kinetic energy and then used to a large extent at the
exit of the runner. Nevertheless the water leaves the runner with a fairly high velocity.
The corresponding kinetic energy would, if no measures were taken, cause an
unacceptable loss of the natural resource. Therefore, in order to regain a substantial
portion of the wheel exit head, expanding draft tubes are joined to the steel housing
(discharge ring) of the runner. Owing to the significant expansion of the draft tube its exit
velocity (v in Fig. 35) is much smaller than that from the runner; thus, the difference
between the two kinetic heads (reduced by the friction losses within the tube) can be
recovered. The draft tube permits the utilization of the entire net head even when the
tailwater lies lower than the exit section of the runner (see Figs 13 and 35). The elbow-
type configuration of the conventional axial turbines also directs the outflowing water at
minimum losses into the river or canal.
The best performance efficiency of the wheel is achieved when, at a selected
revolution (rated speed), the water leaving the runner and entering the draft tube has no
tangential (whirl) component. It is obvious that only the axial (meridional) component
has a bearing on the through-flow capacity, while the kinetic energy imparted by a
possible tangential velocity component is wasted.
A detailed hydromechanical and mathematical treatment of the theory of operation of
axial turbines can be found in various reference books.
84–89
From the theory it follows
that, under a certain head and at the rated speed, efficiency varies with the opening of the
wicket gate which determines the discharge. Thus the efficiency curves can be plotted
against discharge or, since the discharge is in definite relation to power, also against
turbine output. By adequate turbine design the best efficiency can be allocated to the
maximum output or, if necessary, to lower values as well.
If the runner blades are also adjustable (Kaplan turbine) the efficiency, in comparison
with the propeller machines, remains very high over almost the entire output range. The
efficiency curve can be plotted against discharge, gateage (percentage of the full-gate
discharge), output, or percentage of the rated power. Figure 48 shows the efficiency
curves of a Kaplan and a propeller wheel assuming that the designer allocated the
maximum efficiency to 75% of the rated power. The significant difference in favour of
the Kaplan machine can be easily understood when bearing in mind that the position of
Developments in hydraulic engineering–5 64
the runner blades (setting angle β) can be adjusted to any opening of the wicket gate, i.e.
to any power output, to attain the highest possible efficiency. In other words, the
efficiency diagram of a Kaplan machine is the enveloping curve of an infinite number of
continuously adjoining efficiency curves of propeller wheels (see Fig. 49).
It follows from the above that fixed-blade (propeller) turbines are still justifiable when
head and output (load) do not significantly vary. The above is also valid for all other
types of axial machines (bulb, rim-generator, S-type), except that they do not require a
spiral case.
In order to reduce expenses several modern high-powered stations are partly or
completely equipped with normal propeller turbines, or even with turbines having the
wicket gate fixed (see Fig. 41).
FIG. 48. Comparison of efficiency
curves of axial turbines.
7.3.2 Cavitation and Static Draft (Suction) Head
The wheel can be exposed to cavitation when the absolute pressure drops below the
vapour pressure prevailing at the actual temperature. From the Bernoulli theorem it
follows that the lowest absolute pressure occurs in the exit section of the runner and,
expressed in water column, is (Fig. 50):
(36)
Water power development: low-head Hydropower utilization 65
FIG. 49. Interpretation of the
efficiency curve of Kaplan wheels.
89a
FIG. 50. Definition sketch for the static
draft (suction) head.
where B=p
0
/γ denotes the actual barometric pressure and ∆h the friction losses in the draft
tube; h
s
(the difference between the exit level of the runner and the TWL) is the section
(static draft) head. If, due to an improper setting of the unit, p/γ<p
v
/γ, where p
v
denotes
the vapour pressure, the lower tips of the runner blades, the runner hub and the lower
portion of the discharge ring are exposed to cavitation. The pitting due to cavitation can,
in extreme cases, completely destroy the blades and other parts of the wheel. Cavitation
can also cause intolerable vibration, noise and considerable decrease in efficiency.
Neglecting kinetic energy and friction in eqn (36), the simplified expression for the
suction head is
Developments in hydraulic engineering–5 66
(37)
Substituting p/γ=σH, where σ is the cavitation coefficient and H the net head, gives
(38)
Considering that p/γ must exceed the vapour pressure head by a certain safety margin, it
follows that σ must be greater than a critical value σ
c
to avoid cavitation, and thus h
s
must
not exceed the magnitude corresponding to σ
c
.
Since the actual plant σ resulting from any combination of H and h
s
station data is
(39)
it is obvious that the design has to fulfil the condition σ
p
=σ
c
. By substituting the gross
head H
0
into eqns (38) and (39), safe values for h
s
and σ are obtained. It should be
emphasized that for high-specific-speed turbines, especially when operating in the higher
range of low-head, eqn (38) furnishes negative figures, which show how far the runner
exit has to be submerged below the minimum TWL (see Figs 17, 18, 25). σ
c
and σ
p
are in
close relation to the hydromechanical characteristics of the turbine and, in practice,
determined as a function of its specific speed.
To find the decisive setting of the turbine, the permissible maximum h
s
has to be
related to the lowest TML, assuming the simultaneously possible highest HWL. Under
some conditions, however, a sunk HWL is decisive for the setting height.
A more accurate approach for determining h
s
can be accomplished by inclusion of the
vapour pressure head
90
or also the dynamic draft head
91
(40)
in the derivation.
7.3.3 Operational, Specific, Synchronous and Runaway Speed
The speed of the revolving unit connected to a network is constant during its operation
(disregarding the extremely slight fluctuation of the grid frequency, which has no bearing
on the general design procedure and is of importance for dimensioning the governing
system only). Selection of the operational (rated, normal) speed substantially influences
the generator design, because the higher the speed the lower the number of rotor pole
pairs required to satisfy the network frequency. Thus, according to eqn (27) and assuming
f=50 Hz, the necessary number of pairs of poles at a speed n (without speed increasing
gear) is:
(41)
Water power development: low-head Hydropower utilization 67
Further (see Section 8) with higher speed the same power output can be achieved with a
lower-diameter rotor. Higher speed also entails a slightly lower turbine diameter.
Summing up, the construction and installation costs of the entire powerhouse can be
diminished by augmentation of the rated speed since, as is shown in Section 9, all main
dimensions of the powerhouse vary in direct proportion to the machine diameters (turbine
and generator rotor). Nevertheless, the scope for the selection of the rated speed is
limited, as is shown below.
The geometrical configuration of the wheel (including also the prevailing position of
the wicket gate and runner blades) defines the hydromechanical characteristics and
operational behaviour of the turbine. Accordingly, wheels of different sizes but with
geometrically similar shapes (homologous turbines), on the basis of the similarity laws,
can be identified by a single parameter. In engineering practice specific speed is most
commonly used:
(42)
where P is the rated power (full load) of the turbine in kW, H is the rated head in m, n is
the rated speed in rpm. (It can also be related to peak efficiency.) From the derivation of
this formula, the specific speed of a turbine can be formulated as the speed at which a
geometrically similar (homologous) turbine would run under a head of 1 m if its size
were selected so that it produced 1 kW power. The range of specific speeds for axial
turbines is between 350 and 950 rpm. Earlier the specific speed was allocated to 1 HP, so
the relation is
(43)
If turbine data are in the foot-pound system the following conversion applies:
(44)
At present, especially the turbine designers and manufacturers prefer dimensionless
numbers (shape factors) to characterize the turbine types. Troskolanski was the first to
introduce a dimensionless number,
92
though later various other type numbers were also
suggested.
93
In order to avoid cavitation within the runner (and also for other hydromechanical
reasons) its velocity must not exceed a certain experimentally found part of the spouting
velocity (
). Hence, it can be proved that with increasing head the permissible
specific speed has to be reduced. Several experts, manufacturers and institutions have
presented formulas and diagrams displaying, for all types of turbines, the permissible
highest n
s
against rated head.
94,95
The author suggests
96
for conventional Kaplan turbines:
(45)
which can be increased by about 7–12% for tubular machines (n
s
related to kW).
Developments in hydraulic engineering–5 68