1. Hydraulic Turbines

3. Turbines are devices that extract energy from a flowing fluid.
The geometry of turbines is such that the fluid exerts a torque on the rotor in the direction of its rotation.
The shaft power generated is available to drive generators or other devices.

4. The two basic types of hydraulic turbines(dynamic type) are impulse and reaction.
For hydraulic impulse turbines, the pressure drop across the rotor is zero; all of the pressure drop across the turbine stage occurs in the nozzle row.
Both the pressure drop across the bucket and the change in relative speed (i.e., fluid speed relative to the moving bucket) of the fluid across the bucket are negligible. The space surrounding the rotor is not completely filled with fluid. It is the impulse of the individual jets of fluid striking the buckets that generates the torque. Suitable for high heads & low flow rates.
Example: Pelton wheel
Reaction is related to the ratio of static pressure drop that occurs across the rotor to static pressure drop across the turbine stage, with larger rotor pressure drop corresponding to larger reaction.
For reaction turbines the rotor is surrounded by a casing (or volute), which is completely filled with the working fluid. There is both a pressure drop and a fluid relative speed change across the rotor. As for example in the radial-inflow turbine guide vanes act as nozzles to accelerate the flow and turn it in the appropriate direction as the fluid enters the rotor. Thus, part of the pressure drop occurs across the guide vanes and part occurs across the rotor. Suitable for low head & large flow rates.
Example: Francis(radial or mixed flow), Kaplan(axial flow adjustable blade), propeller turbine(axial flow fixed blade)

5. Pelton Wheel(impulse Turbine)

6. Francis turbine(Reaction turbine)

7. Pelton wheel Turbine
Usually the shaft of a Pelton wheel is horizontal, and then not more than two jets are used. If the wheel is mounted on a vertical shaft a larger number of jets (up to six) is possible.
The nozzles, however, must never be spaced so closely that the spent fluid from one jet interferes with another jet.
Because of the symmetry of the buckets, the side thrusts produced by the fluid in each half should balance – although it is usual for small thrust bearings to be fitted on the shaft to cope with lapses from this ideal.
The absolute velocity of the jet is determined by the head available at the nozzle, that is, the gross head Hgr minus the head loss hf due to friction in the pipe-line.
The jet velocity V1 is given by where H represents the net head(H= Hgr- hf).
The relative velocity W2 with which the fluid leaves the bucket is somewhat less than the initial relative velocity W1. There are two reasons for this. First, although the inner surfaces
of the buckets are polished so as to minimize frictional losses as the fluid flows over them, such losses cannot be entirely eliminated. Second, some additional loss is inevitable as the fluid strikes the splitter ridge, because the ridge cannot have zero thickness. These losses of mechanical energy reduce the relative velocity between fluid and bucket. We therefore write W2 = kW1 where k is a fraction slightly less than unity.

8. Pelton wheel Turbine
Pelton wheel turbines operate most efficiently with a larger head and lower flow rates.

9. Considering k=1, W1=W2

10. Theoretically maximum power can be extracted when jet deflection angle β is 180 deg.
In practice, however, the deflection is limited to about 165◦ if the fluid leaving one bucket is not to strike the back of the following one.
Results in a relatively small reduction in power(less than 2%).
The torque is maximum when the wheel is stopped there is no power under this condition.
On the other hand, the power output is a maximum when

11. The energy arriving at the wheel is in the form of kinetic energy of the jet,
and its rate of arrival is given by Therefore, the wheel efficiency,
Peak efficiency occurs at
For an actual Pelton wheel turbine, there are other losses besides that of above equation mechanical friction(mechanical losses), aerodynamic drag on the buckets (windage losses),friction along the inside walls of the buckets, nonalignment of the jet and bucket as the bucket turns, back splashing, and nozzle losses. Even so, the efficiency of a well-designed Pelton wheel turbine can approach 90 percent.
Moreover, as the losses due to bearing friction and windage increase rapidly with speed, the peak of overall efficiency occurs when the ratio u/v1 (often termed the speed ratio) is slightly less than the value of 0.5; the figure usually obtained in practice is about 0.46.

13. Governing mechanism in Pelton wheel by flow control
A Pelton wheel is almost invariably used to drive an electrical generator mounted on the same shaft. It is designed to operate at the conditions of maximum efficiency, and the governing of the machine must be such as to allow the efficiency to be maintained even when the power demand at the shaft varies.
No variation of the angular velocity, and hence of bucket velocity u, can normally be permitted(for this would alter the frequency of the electrical output)
The control must therefore be in the volume rate of flow Q, and yet there must be no change in the jet velocity because that would alter the speed ratio u/v1 from its optimum value of about 0.46.
Since Q = A v1 it follows that the control must be effected by a variation of the cross-sectional area A of the jet. This is usually achieved by a spear valve in the nozzle. Movement of the spear along the axis of the nozzle increases or decreases the annular area between the spear and the housing.

14. A Francis turbine comprises mainly the four components:
Francis Turbine(Reaction Turbine( radial or mixed flow))
Reaction turbines are best suited for higher flow rate and lower head situations.
The principal distinguishing features of a reaction turbine, we recall, are that only part of the overall head is converted to velocity head before the runner
is reached, and that the working fluid, instead of engaging only one or two blades at a time (as in an impulse machine), completely fills all the passages
in the runner. Thus the pressure of the fluid changes gradually as it passes through the runner.
A Francis turbine comprises mainly the four components:
(i) spriral casing,
(ii) guide vanes(wicket gates) & stay vanes,
(iii) runner blades,
(iv) draft-tube
The Francis turbine is particularly suitable for medium heads (i.e. from about 15 m to 300 m) and overall efficiencies exceeding 90% have been achieved for large machines.

15. Spiral Casing : Most of these machines have vertical shafts although some smaller machines of this type have horizontal shaft. The fluid enters from the penstock (pipeline leading to the turbine from the reservoir at high altitude) to a spiral casing which completely surrounds the runner. This casing is known as scroll casing or volute. The cross-sectional area of this casing decreases uniformly along the circumference to keep the fluid velocity constant in magnitude along its path towards the guide vane. This is so because the rate of flow along the fluid path in the volute decreases due to continuous entry of the fluid to the runner through the openings of the guide vanes or stay vanes.
Stay & Guide vanes : The basic purpose of the guide vanes or stay vanes is to convert a part of pressure energy of the fluid at its entrance to the kinetic energy and then to direct the fluid on to the runner blades at the angle appropriate to the design. Moreover, the guide vanes are pivoted and can be turned by a suitable governing mechanism to regulate the flow while the load changes.
Runner blades : The flow entry in the runner of a Francis turbine may be radial or mixed. The flow is inward, i.e. from the periphery towards the centre. The height of the runner depends upon the specific speed. The height increases with the increase in the specific speed. The main direction of flow change as water passes through the runner and is finally turned into the axial direction while entering the draft tube. The shape of the blades of a Francis runner is complex. The exact shape depends on its specific speed. It is obvious from the equation of specific speed that higher specific speed means lower head. This requires that the runner should admit a comparatively large quantity of water for a given power output and at the same time the velocity of discharge at runner outlet should be small to avoid cavitation.

16. Runner cont...
In a purely radial flow runner, as developed by James B. Francis, the bulk flow is in the radial direction. To be more clear, the flow is tangential and radial at the inlet but is entirely radial with a negligible tangential component at the outlet. The flow, under the situation, has to make a 90o turn after passing through the rotor for its inlet to the draft tube. Since the flow area (area perpendicular to the radial direction) is small, there is a limit to the capacity of this type of runner in keeping a low exit velocity. This leads to the design of a mixed flow runner where water is turned from a radial to an axial direction in the rotor itself. At the outlet of this type of runner, the flow is mostly axial with negligible radial and tangential components. Because of a large discharge area (area perpendicular to the axial direction), this type of runner can pass a large amount of water with a low exit velocity from the runner. The blades for a reaction turbine are always so shaped that the tangential or whirling component of velocity at the outlet becomes zero.
The inlet blade angle    of a Francis runner varies  
and the guide vane angle from 

17. Degree of reaction
The change in pressure energy of the fluid in the rotor can be found out by subtracting the change in its kinetic energy from the total energy released. Therefore, we can write for the degree of reaction.

18. Draft tube
The draft tube is a conduit which connects the runner exit to the tail race where the water is being finally discharged from the turbine. The primary function of the draft tube is to reduce the velocity of the discharged water to minimize the loss of kinetic energy at the outlet. This permits the turbine to be set above the tail water without any appreciable drop of available head.

20. Kaplan Turbine(Reaction Turbine( axial flow adjustable blades))
Higher specific speed corresponds to a lower head. This requires that the runner should admit a comparatively large quantity of water. For a runner of given diameter, the maximum flow rate is achieved when the flow is parallel to the axis. Such a machine is known as axial flow reaction turbine. Between the guide vanes and the runner, the fluid in an axial turbine turns through a right-angle into the axial direction and then passes through the runner.

21. The function of the guide vane is same as in case of Francis turbine
The function of the guide vane is same as in case of Francis turbine. Between the guide vanes and the runner, the fluid in a propeller turbine turns through a right-angle into the axial direction and then passes through the runner. The runner usually has four or six blades and closely resembles a ship's propeller. Neglecting the frictional effects, the flow approaching the runner blades can be considered to be a free vortex with whirl velocity being inversely proportional to radius, while on the other hand, the blade velocity is directly proportional to the radius. To take care of this different relationship of the fluid velocity and the blade velocity with the changes in radius, the blades are twisted. The angle with axis is greater at the tip that at the root. The blade angles may be fixed if the available head and the load are both fairly constant, but where these quantities may vary a runner is used on which the blades may be turned about their own axes while the machine is running. When both guide-vane angle and runner-blade angle may thus be varied, a high efficiency can be maintained over a wide range of operating conditions. Such a turbine is known as a Kaplan turbine after its inventor, the Austrian engineer Viktor Kaplan (1876–1934).

23. Reaction Turbine efficiency
Hydraulic Efficiency
Hydraulic losses
Losses in scroll casing
Losses at the entry to the runner blade due to non tangential entry
Blade friction loss
Flow outlet from Runner blade deviate from tangential
Losses in the draft tube
Draft tube Exit K.E. loss
Where, H = the net head.
Mechanical efficiency
Mechanical losses
1. Mechanical frictional losses in bearings, and other solid contact points with relative velocity.
Overall efficiency

25. In an axial-flow machine the fluid does not move radially, and so for a
particular radius u1 = u2 and the term (u12−u22) is zero.
In a radial or mixed flow machine, however, each of the terms in the expression is effective. For a turbine, that is, a machine in which work is done by the fluid, the expression
above must be positive. This is most easily achieved by the inward-flow
arrangement.
Then u1 >u2 and,
since the flow passages decrease rather than increase in cross-sectional area, R2 usually exceeds R1.
The contributions of the second and third brackets to the work done by the fluid are thus positive.

26. Similarity laws and power specific speed

27. Particularly useful in showing the characteristics of turbines are results obtained under conditions of constant rotational speed and head. For a particular machine and a particular incompressible fluid, D and are constant. Then gH/ω2D2 is constant.
η is then simply a function of P, and the results may be presented in the forms shown
in Fig. below

28. For a turbine using a particular fluid the operating conditions are expressed by values of ω, P and H. It is important to know the range of these conditions which can be covered by a particular design (i.e. shape) of machine. Such information enables us to select the type of machine best suited to a particular application, and serves as a starting point in its design. We require, therefore, a parameter characteristic of all the machines of a homologous series and independent of the size represented by D. A parameter involving ω, P and H but not D is the dimensionless speed parameter Cω defined by
A particular value of the speed coefficient therefore relates all the combinations of ω, , P and H for which the flow conditions are similar in the machines of that homologous
series.
Interest naturally centres on the conditions for which the efficiency is a maximum, so, in calculating the value of the expression above, it is customary to use values of ω, P and H that correspond to maximum efficiency.
Power specific speed=

29. The value of (or NP) obtained from a set of values of ω (or N), P and H indicates the shape of a machine that meets those conditions.
The rotational speed was often expressed in non-SI units such as rev/s, denoted by the symbol N. Hence it became common practice in industry to work with values of NP1/2/H5/4.
When the site of the installation and the output required from a turbine are known, the value of may be calculated and the type of machine best suited to these conditions selected. For the principal types of turbine, experience has shown the values in Table most suitable.

30. Figure indicates the variation of power specific speed with the shape
of the turbine runner.
For given values of H and P, ω increases with P. With the same peripheral runner velocity, a larger value of ω implies a smaller value of D and so, in general, lower cost. For this reason, where a choice lies between two machines of different power specific speeds, the designer usually prefers that with the higher value. Machines of high power specific speeds, however, are limited to low heads because of cavitation.

31. The performance characteristics of turbines
Although desirable, it is not always possible for a turbine to run at its maximum efficiency. Interest therefore attaches to its performance under conditions for which the efficiency is less than the maximum. In testing model machines it is usual for the head to be kept constant (or approximately so) while the load, and consequently the speed, are varied. If the head is constant then for each setting of the guide vane angle (or spear valve for a Pelton wheel) the power output P, the efficiency η and the flow rate Q may be plotted against the speed ω as the independent variable.
It is more useful, however, to plot dimensionless parameters
Thus one set of curves is applicable not just to the conditions of the test, but to any machine in the same homologous series, operating under any head.

32. Often the D terms are omitted also, ω is replaced by N, and the resulting ratios P/H3/2,Q/H1/2,N/H1/2 are then referred to as unit power, unit flow and unit speed. Their numerical values correspond respectively to the power, volume flow rate and speed obtainable if the machine could be operated with unchanged efficiency under one unit of head, for example, 1 m.)

33. For a reaction turbine, changes of load are dealt with by alteration of the guide vane angle. Fig shows the general effect of change of guide vane angle for a machine of the Francis type or fixed-blade propeller type. Only at the maximum efficiency point does the direction of the relative velocity at inlet conform with that of the inlet edges of the runner blades. At other conditions these directions do not conform, and so the fluid does not flow smoothly into the passages in the runner. Instead, it strikes either the front or back surfaces of the blades; considerable eddy formation ensues and the consequent dissipation of energy reduces the efficiency of the machine.
In the Kaplan turbine the runner blade angle may be altered in addition to the guide vane angle. Thus it is possible to match the directions of the relative velocity at inlet edges of the runner blades for a wide range of conditions. In consequence, the part-load efficiency of the Kaplan machine is superior to
that of other types.

34. A change of load also affects the conditions at outlet
A change of load also affects the conditions at outlet. A reduction in the rate of flow through the machine results in a decreased value of R2. Consequently, if the blade velocity u2 is unaltered, there is a departure from the ideal right-angled vector triangle at outlet (see Fig. ); the resulting whirl component of velocity causes a spiral motion in the draft tube and hence a reduction of the draft-tube efficiency. The possibility of cavitation
is also increased.

35. Cavitation in turbine
Since cavitation begins when the pressure reaches too low a value, it is likely to occur at points where the velocity or the elevation is high, and particularly at those where high velocity and high elevation are combined. In a reaction turbine the point of minimum pressure is usually at the outlet end of a runner blade, on the leading side.
For the flow between such a point and the final discharge into the tail race

36. For cavitation not to occur pe must be greater than the vapour pressure of the liquid, pv, that is
=Thoma’s cavitation parameter( )
If either z (the height of the turbine runner above the tail water surface) or H is increased, σ is reduced. To determine whether cavitation is likely in a particular installation, the value of σ may be calculated: if it is greater than the tabulated (empirical) value of σc for that design of turbine, cavitation should not be experienced.
In practice the expression is used to determine the maximum elevation zmax of the turbine above the tail water surface for cavitation to be avoided:

37. Figure shows that turbines of high power specific speed have higher values of σc and so they must be set at much lower elevations than those of smaller power specific speed. For a high net head H it might be necessary to place the turbine below the tail water surface, thus adding considerably to the difficulties of construction and maintenance. This consideration restricts the use of propeller turbines to low heads

39. Governing of reaction turbine
Governing of Reaction Turbines Governing of reaction turbines is usually done by
altering the position of the guide vanes and thus controlling the flow rate by changing
the gate openings to the runner. The guide blades of a reaction turbine (Figure )
are pivoted and connected by levers and links to the regulating ring.
Two long regulating rods, being attached to the regulating ring at their one ends, are
connected to a regulating lever at their other ends. The regulating lever is keyed to a
regulating shaft which is turned by a servomotor piston of the oil