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MECH7350 Rotating Machinery 10. Hydraulic Turbines

10-1

10. HYDRAULIC TURBINES (This section is taken mainly from White)

10.1 Introduction

Hydraulic turbines extract energy from water which has a high head. There are basically two

types, reaction and impulse, the difference being in the manner of head conversion. In

reaction turbines the water fills the blade passages and the head change or pressure drop

occurs within the impeller. They can be of radial, axial or mixed flow types. In impulse

turbines the high head is first converted through a nozzle into a high velocity jet which strikes

the blades at one position as they pass by. Reaction turbines are smaller because water fills

all the blades at one time.

10.2 Reaction Turbines

Reaction turbines are low-head, high-flow devices. The flow is opposite to that in a pump

(from volute to eye of impeller after transferring most of the energy of the water to the

impeller) but a difference is the important role stationary guide vanes play. Purely radial and

mixed flow designs are called Francis turbines. At even lower heads an axial flow, propeller

turbine is more compact. It can be fixed bladed but better efficiency is obtained over an

operating range by using adjustable vanes, in the Kaplan turbine. Various impeller

configurations are shown in Fig. 10.1.

Fig. 10.1 Reaction turbines: (a) Francis, radial type; (b) Francis, mixed-flow; (c) propeller axial-flow; (d) performance curves for a Francis turbine, n = 600 rpm, D = 0.686 m, Nsp = 29 (from White).

MECH7350 Rotating Machinery 10. Hydraulic Turbines

10-2

10.3 Simple Radial Turbine Theory

The Euler turbomachine equations derived in Chapter 9 for pumps also apply to turbines if

we reverse the flow direction and reshape the blades. Fig. 10.2 shows a radial turbine runner.

Again assume one-dimensional frictionless flow through the blades. Adjustable inlet guide

vanes are essential for good efficiency. They bring the inlet flow to the blades at angle α and

absolute velocity V2 for minimum ‘shock’ or directional miss-match loss. After vectorially

adding in the runner tip speed u2 = ωr2, the outer blade angle should be set at β2 to

accommodate the relative velocity w2.

Consideration of angular momentum as for pumps (Chapter 9) gives an idealised formula for

the power P extracted by the runner:

( ) ( )2 2 1 1 2 2 2 1 1 1cos cost tP T Q r V rV Q u V u Vω ρω ρ α α= = − = −

where Vt2 and Vt1 are the absolute inlet and outlet circumferential velocity components of the

flow.

The absolute inlet flow normal velocity Vn2 = V2sinα2 is proportional to the flow rate Q. If

the flow rate changes and the runner speed u2 is constant, the vanes must be adjusted to a new

angle α2 so that w2 still follows the blade surface.

Fig. 10.2 Inlet and outlet velocity diagrams for an idealised radial-flow reaction turbine runner (from White).

MECH7350 Rotating Machinery 10. Hydraulic Turbines

10-3

10.4 Power Specific Speed

Turbine parameters are similar to those of a pump, but the dependent variable is the output

brake horsepower which depends on the inlet flow rate Q, available head H, impeller speed n

and diameter D. The efficiency is the output brake horsepower divided by the available water

horsepower ρgQH. The dimensionless forms are CQ, CH and CP defined as for a pump

(Chapter 9 in Module A). If we neglect viscous and roughness effects, the functional

relationships are written with CP as the independent variable:

( ) ( ) ( )2 2 3H H P Q Q P P

gH Q bhpC C C C C C C

n D nD gQHη η

ρ= = = = = = (10.1)

Fig. 10.1 shows typical performance curves for a Francis radial turbine. The maximum

efficiency point is called normal power.

A parameter that compares the output power with the available head, independent of size, is

found by eliminating the diameter between CH and CP. It is called the power specific speed

spN′ .

( )( )

1/ 21/ 2

5/ 45/4 1/ 2

Psp

H

n bhpCN

C gHρ′ = = (10.2)

In lazy but common form this is written as:

( ) ( )( )

1/ 2

5/ 4sp

rpm bhpN

H ft=

(10.3)

Like pumps, turbines of large size are generally more efficient.

10.5 Impulse Turbines

For high head (typically above 250 m) and relatively low power (i.e. low Nsp from (10.2)) not

only would a reaction turbine require too high a speed but also the high pressure in the runner

would require a massive casing thickness. The impulse turbine in Fig. 10.3 is ideal for this

situation. Since Nsp is low, n will be low and the high pressure is confined to the small

nozzle which converts the head to an atmospheric pressure jet of high velocity Vj. The jet

strikes the buckets and imparts a momentum change. The buckets have an elliptic split-cup

shape and are called Pelton wheels.

MECH7350 Rotating Machinery 10. Hydraulic Turbines

10-4

A simple analysis uses the Euler turbomachinery equation in Chapter 9, i.e.;

( )2 12 1w t tP T Q u V u Vω ρ= = −

( )2 12 1

1wt t

PH u V u V

gQ gρ= = −

together with the velocity diagram in Fig. 10.3. Noting that u1 = u2 = u, we substitute the

absolute exit and inlet tangential velocities into the turbine power relation:

( ) ( ){ }1 1 2 2 cost t j jP Q u V u V Q uV u u V uρ ρ β = − = − + −

or

( ) ( )1 cosjP Qu V uρ β= − − (10.4)

where u = 2πnr is the bucket linear velocity and r is the pitch radius, or distance to the jet

centreline. A bucket angle β = 180o gives maximum power but is physically impossible

because water must clear the next bucket. In practice, 165oβ ≈ and 1 – cosβ ≈ 1.966 or only

2 percent less than maximum power.

From (10.4) the theoretical power of an impulse turbine is a maximum when dP/du = 0, or

Fig. 10.3 Impulse turbine: (a) side view of wheel and jet; (b) top view of bucket; (c) typical velocity diagram (from White).

MECH7350 Rotating Machinery 10. Hydraulic Turbines

10-5

* * 12

2 ju n r Vπ= =

For a perfect nozzle, the entire available head would be converted to jet velocity

( )1/22jV gH= . Since there are 2 to 8 percent nozzle losses, a velocity coefficient Cv is used:

( )1/22 0.92 0.98j v vV C gH C= ≤ ≤ (10.5)

By combining (10.1) and (10.5) the theoretical impulse turbine efficiency becomes:

( ) ( )2 1 cos vCη β φ φ= − − (10.6)

where

( )1/ 22

u

gHφ = = peripheral velocity factor

Maximum efficiency occurs at 1

0.47.2 vCφ = ≈

Fig. 10.4 shows (10.6) plotted for an ideal turbine (β = 180o, Cv = 1.0) and for typical

working conditions (β = 160o, Cv = 0.94). The latter case predicts ηmax = 85 percent but

windage, mechanical friction, backsplashing and nonuniform bucket flow reduce this to about

80 percent. An impulse turbine is not quite as efficient as the Francis or propeller turbines at

their BEPs.

Fig. 10.5 shows the optimum efficiency of the three types of turbines, and the importance of

the power specific speed Nsp as a selection tool for designers.

Fig. 10.4 Efficiency of an impulse turbine calculated from (10.6): solid curve = ideal, β = 180o, Cv = 1.0; dashed curve = actual, β = 160o, Cv = 0.94; open circles = data, Pelton wheel, diameter = 0.61 m (from White).

MECH7350 Rotating Machinery 10. Hydraulic Turbines

10-6

The water power available to a turbine may vary due to either head or flow rate changes, both

of which are common in hydroelectric plants. The demand for power also varies from light

to heavy, and the operating response is a change in the flow rate by adjustment of a gate

valve or needle valve (Fig. 10.3). As shown in Fig. 10.6, all three turbines achieve fairly

uniform efficiency as a function of the level of power being extracted. Especially effective is

10.6 Some Practical Considerations

Cavitation must be avoided in hydraulic turbines. It can occur at turbine outlets where the

pressure is lowest.

More detail of a Pelton wheel turbine is shown in Fig. 10.7. Rapid shutdown of the turbine,

as would be required after loss of load from the driven machine, cannot be effected by rapid

Fig. 10.5 Optimum efficiency of turbine designs (from White).

Fig. 10.6 Efficiency versus power level for various turbine designs at constant speed and head (from White).

MECH7350 Rotating Machinery 10. Hydraulic Turbines

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closure of the spear (needle valve) due to water hammer effects. Shutdown is effected by

inserting into the jet either a cut-off to destroy its kinetic energy or a deflector to direct the jet

away from the bucket. The jet is then cut off at a suitably safe rate.

Fig. 10.8 shows a typical large Francis turbine in which water is fed radially to the runner

from guide vanes which are disposed around the full circumference. The angle of these vanes

can be varied to control machine output and the water is uniformly distributed to them by a

spiral casing. The loads on the guide vanes can be very large. The guide vanes are moved by

cranks attached to the end of one of the spindles, the other end of the crank being located in a

regulating ring. The ring is rotated by hydraulic rams or servomotors. Some form of slipping

device is incorporated so that if a foreign body jams between two vanes, the remainder can be

moved normally. A warning device indicates that the slipping device is operating. Large

axial thrusts are handled by admitting some high-pressure water to the underside of the

machine and by using a thrust bearing (usually of the tilting-pad type).

Fig. 10.9 shows details of a large Kaplan turbine through which the water flow is essentially

axial. The runner resembles a ship’s propeller whose blades (typically four to six in number)

are adjustable in pitch to present the optimum angle of attack to the water flow. The blades

are most conveniently adjusted by means of a lever arm within the hub.

Fig. 10.7 Pelton wheel turbine (from MPSP).

MECH7350 Rotating Machinery 10. Hydraulic Turbines

10-8

10.7 Pumped-Storage

Pumped-storage involves operations between two lakes; water is run through a turbine when

peak electricity generation is needed, and pumped from the lower to the higher lake to store

potential energy at periods of low demand. Separate pumps and turbines can be used, or a

reversible pump-turbine. Such a machine enables both pumping and turbining to be

performed by the same runners. It is effectively a Francis turbine whose runner geometry is a

compromise between the optimum for pumping and generation. During generation, the

turbine output is absorbed by the generator; whilst pumping, the generator acts as a motor,

driving the runner in the opposite direction. An advantage of the combined unit is the

reduction of equipment and installation costs.

Fig. 10.8 A large Francis turbine (from MPSP).

MECH7350 Rotating Machinery 10. Hydraulic Turbines

10-9

Fig. 10.9 A large Kaplan turbine showing detail of the hub mechanism for varying blade angle (from MPSP).