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APPENDIX E
457
APPENDIXE Some knowledge of reversed centrifugal pumps, known as water turbines, is essential for a complete understanding of centrifugal pumps and vice versa.
Historical The forerunner of the modern water turbine was the water wheel or millers' wheel, some of which are still to be seen in operation. One or two hundred years ago every river of any size had several of these wheels and to this day the old weirs, lades and ruined mills are a familiar sight in our countryside. The weir wheel was generally arranged with a horizontal shaft and a rim carrying several buckets to which the water was admitted at the top (over shot wheels) half way up (breast wheels), or near the bottom (under shot wheels). Work is done on the wheel by the weight of the water falling from the head race to the rail race. It will be seen therefore that only a part of the wheel circumference receives water and that the water enters the wheel at atmospheric pressure.
Increase of Power When consideration was given to increasing the power output of the wheel such increase could occur in two ways: (i) The water could be contained in a pressure pipe so as to take advantage of a head race above the wheel.
(ii) The water could be admitted to the whole circumference of the wheel. In the above cases: (i) The energy of the water due to pressure and quantity would be converted into velocity so that the water issuing from the penstock strikes the wheel at a very high speed.
(ii) The wheel would be enclosed in a casing under pressure. The containing of the water and conversion of its mass times pressure energy to velocity
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CENTRIFUGAL PUMPS
energy so that it could strikes the blades at a greater force produced the Pelton Wheel or Impulse Turbines. The increasing of the admission to the whole circumference and the fitting of a pressure casing around the wheel produced the Francis Turbine and as a later development the Kaplan Turbine for very low heads. It will be seen, therefore, that the three major types of turbines - Pelton, Francis and Kaplan - have grown out of the original water wheel.
Development of Turbines The original Francis turbine had a runner whose inlet diameter was greater than the outlet diameter and was suitable for medium heads. When the need for higher speeds to suit electric generators arose, particularly in connection with lower heads, it was necessary to reduce the inlet diameter of the turbine until it was less than the outlet diameter. This produced the high specific speed Francis turbine which was further developed for low heads until the axial flow portion only remained, which became a propeller turbine, and with moving blades became the Kaplan turbine.
Modern Turbines Modern turbines range in head from a few cm to 2 000 m and in power from fractional kW on oil servo duties to the largest prime movers yet made. Several units of 700 MW one million HP have been made.
Specific Speed The specific Speed N s of a turbine is a convenient number to represent the shape of a turbine and indicate into which of the above three main groups (Pelton, Francis, Kaplan) the machine will fall. The number is derived as follows: Specific speed Ns
= rev/min x
Square root of Power Head 5/4
Operating Head The operating heads for the various types of water turbines are as follows:_ Large Pelton or Impulse Wheels N s 1 to 10 - 300 to 2 000 m. For small sizes Pelton wheels are suitable for heads below 300m. Francis Turbines N s 20 to 100 - 30 to 300 m. Kaplan Turbines N s 100 to 200 - up to 50 m The aforementioned limits are very approximate and naturally are affected by progress in technique, particularly in metallurgical fields, where better metals permit operation at high heads and speeds without undue risk of damage by high water velocities.
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459
Choice of Turbine For a given duty the diameter of the runner depends upon the head and the speed; the width of the runner depends upon the quantity of water; and the combination of head and quantity of water determines the power generated by the turbine. If we reduce the quantity of water and the power for the same head, a narrower runner will be required. Obviously a narrow runner is more difficult to cast and beyond the limit of narrow casting, that is the lowest specific speed of a Francis wheel, further reduction of power and specific speed can only be obtained by admitting the water at one point instead of around the circumference of the wheel. It is here that the change takes place from Francis to Pelton turbine. There is a considerable gap between the Francis (lowest - N s 20) and the Pelton (highest - N s 10) which is made up by the introduction of double jet and four jet Pelton, where a compromise is obtained between the single admission of the pelton and the full circumferential admission of the Francis. The jets are arranged in equal steps around the wheel (N s for a four jet pelton is ~ 4 or twice the N s of a single jet) 3, 5 or 6 jets are also used but are less usual. A special form of Pelton wheel with side entrance so as to permit a larger jet and a much greater quantity of water for a given wheel diameter iscalled the Turgo and competes with the two jet and four jet Pelton wheels.
Limiting Speed The speed of water flow through the wheel and the speed of blades relati ve to the water imposes a limit on the revolutions per minute and consequently upon the head against which the wheel may operate, since excessive speeds give rise to cavitation with consequent damage to the wheel element. In the case of aFrancis wheel if the power is very small the runner may be of an awkward shape for casting and may require to run at a speed inconvenient to the generator. It is for this reason that on low powers the Pelton is used for heads as low as 30 m.
Application of Water Turbines Water turbines provide power for all purposes. In the larger sizes the power produces is almost invariably used for generating electricity for the national grid or for industry. There are certain pump schemes particularly in the chemical field for cooling or scrubbing duties, where the return main has a greater height or pressure than can be recovered by a syphon. In many cases the water, after having passed through the process, enters a turbine so as to recover as much power as possible. These turbines are very often arranged in tandem with the pump so that the motor power necessary is reduced by the contribution made by the turbine.
Problems in the Operation of Turbines A steam turbine is governed by stop valves controlled by a speed governor and itis possible to close this stop valve quickly. In the case of a water turbine, however, there is in the penstock a large mass of water approaching at a relatively high speed.
460
CENTRIFUGAL PUMPS
Pipeline Inertia. To close the turbine gates too quickly would give rise to a considerable increase ofpressure since the long column of water would suddenly be brought to rest. In order to avoid a pipe fracture, therefore, it is necessary to bring this column of water slowly to rest. Water turbo alternators differ from some other prime movers in that they load, in this case the alternator torque, can vanish instantly without any warning. If an electric storm strikes the grid, the circuit breakers may disconnect the generating station from its load within a fraction of a second. At this time, however, the turbine is being fed with water and generating full power, and until the water column can be brought to rest, power is still being fed to the turbine. As a result, its speed increases and in the limit may reach the runaway speed, which is nearly twice the normal running speed.
Rotor Inertia The only way in which this rate of increase of speed can be regulated is by building a greater flywheel effect or inertia into the rotor of the electric generator. This is a particularly difficult problem for the electrical designers, since on the one hand they must build as much metal into their rotor as possible, and on the other hand this rotor should be capable of running at nearly twice normal speed without bursting (this is vital in case of governor failure). To this end the shortening of the penstock to the minimum possible length is essential and therefore on any power scheme it is usual to provide a horizontal canal or tunnel from the upper lake to a point as near the power house as possible, followed by a very short pipeline. At top of this pipeline is erected a surge tank with an open top, so that the water flowing in the horizontal tunnel or canal can escape and the turbine designer need only consider the amount of water in the length of the relatively short penstock approaching the turbine. It will be seen that this problem resol ves itself into the balancing of the water inertia in the pipe against the inertia of the rotating parts of the turbo alternator. A further means of helping this problem is to provide a by-pass so that as soon as the governor starts to close the gates beyond a certain speed the by-pass is opened, permitting the penstock water to run to waste instead of through the turbine. This by-pass or relief valve is only opened if the speed of governor movement exceeds a certain valve. On the other hand, even with a pressure relief valve on certain turbines, the incidence of over speed causes in itself a reduction of quantity which in turn gives rise to a further pressure increase, the cumulative effect of which on lowest specific speed of Francis turbines is extremely difficult to forecast. In the case of a Pelton wheel, by-passing can be carried out more conveniently with a deflector which removes the jet entirely from the wheel. The deflectors have the advantage that no pressure rise whatever occurs, since the water is not deflected until it is passed out of the nozzle into the atmosphere.
Construction of Turbines The Francis turbine usually comprises a scroll casing which leads the water from a pipe into the periphery of the runner. Before entering the runner the water passes through a
APPENDIX E
461
series of gates which are controlled by the governor, thus admitting a larger or smaller quantity of water into the turbine. A Kaplan turbine is similar, but has in addition the problem of moving the rotating blades by a servo motor in the shaft. The blades and the gates normally move in unison. With a Kaplan turbine there is, furthermore, a risk of exceptionally high overspeed should the correct phasing of blades and gates accidentally get out of order. In addition, constructional features such as the shaft for supporting the runner bearings, gland, casing, gate mechanism, etc, are involved. The casing may be of concrete up to 90 ft head or of steel for higher heads. The Pelton wheel is rather more simple, comprising only the wheel and the nozzle at the end of the penstock, which is controlled by a needle valve arranged so as to reduce the size of the jet without altering its speed or causing any undue frictional loss. The Pelton wheel is contained in a light casing so as to prevent undue splashing. The buckets are of double hemispherical shape. The wheel runs at half the jet speed and the jet is turned through nearly 180 0 in the bucket. The water speed when leaving the bucket is theoretically zero, all its energy being given to the wheel.
APPENDIXE Some knowledge of reversed centrifugal pumps, known as water turbines, is essential for a complete understanding of centrifugal pumps and vice versa.
Historical The forerunner of the modern water turbine was the water wheel or millers' wheel, some of which are still to be seen in operation. One or two hundred years ago every river of any size had several of these wheels and to this day the old weirs, lades and ruined mills are a familiar sight in our countryside. The weir wheel was generally arranged with a horizontal shaft and a rim carrying several buckets to which the water was admitted at the top (over shot wheels) half way up (breast wheels), or near the bottom (under shot wheels). Work is done on the wheel by the weight of the water falling from the head race to the rail race. It will be seen therefore that only a part of the wheel circumference receives water and that the water enters the wheel at atmospheric pressure.
Increase of Power When consideration was given to increasing the power output of the wheel such increase could occur in two ways: (i) The water could be contained in a pressure pipe so as to take advantage of a head race above the wheel.
(ii) The water could be admitted to the whole circumference of the wheel. In the above cases: (i) The energy of the water due to pressure and quantity would be converted into velocity so that the water issuing from the penstock strikes the wheel at a very high speed.
(ii) The wheel would be enclosed in a casing under pressure. The containing of the water and conversion of its mass times pressure energy to velocity
458
CENTRIFUGAL PUMPS
energy so that it could strikes the blades at a greater force produced the Pelton Wheel or Impulse Turbines. The increasing of the admission to the whole circumference and the fitting of a pressure casing around the wheel produced the Francis Turbine and as a later development the Kaplan Turbine for very low heads. It will be seen, therefore, that the three major types of turbines - Pelton, Francis and Kaplan - have grown out of the original water wheel.
Development of Turbines The original Francis turbine had a runner whose inlet diameter was greater than the outlet diameter and was suitable for medium heads. When the need for higher speeds to suit electric generators arose, particularly in connection with lower heads, it was necessary to reduce the inlet diameter of the turbine until it was less than the outlet diameter. This produced the high specific speed Francis turbine which was further developed for low heads until the axial flow portion only remained, which became a propeller turbine, and with moving blades became the Kaplan turbine.
Modern Turbines Modern turbines range in head from a few cm to 2 000 m and in power from fractional kW on oil servo duties to the largest prime movers yet made. Several units of 700 MW one million HP have been made.
Specific Speed The specific Speed N s of a turbine is a convenient number to represent the shape of a turbine and indicate into which of the above three main groups (Pelton, Francis, Kaplan) the machine will fall. The number is derived as follows: Specific speed Ns
= rev/min x
Square root of Power Head 5/4
Operating Head The operating heads for the various types of water turbines are as follows:_ Large Pelton or Impulse Wheels N s 1 to 10 - 300 to 2 000 m. For small sizes Pelton wheels are suitable for heads below 300m. Francis Turbines N s 20 to 100 - 30 to 300 m. Kaplan Turbines N s 100 to 200 - up to 50 m The aforementioned limits are very approximate and naturally are affected by progress in technique, particularly in metallurgical fields, where better metals permit operation at high heads and speeds without undue risk of damage by high water velocities.
APPENDIX E
459
Choice of Turbine For a given duty the diameter of the runner depends upon the head and the speed; the width of the runner depends upon the quantity of water; and the combination of head and quantity of water determines the power generated by the turbine. If we reduce the quantity of water and the power for the same head, a narrower runner will be required. Obviously a narrow runner is more difficult to cast and beyond the limit of narrow casting, that is the lowest specific speed of a Francis wheel, further reduction of power and specific speed can only be obtained by admitting the water at one point instead of around the circumference of the wheel. It is here that the change takes place from Francis to Pelton turbine. There is a considerable gap between the Francis (lowest - N s 20) and the Pelton (highest - N s 10) which is made up by the introduction of double jet and four jet Pelton, where a compromise is obtained between the single admission of the pelton and the full circumferential admission of the Francis. The jets are arranged in equal steps around the wheel (N s for a four jet pelton is ~ 4 or twice the N s of a single jet) 3, 5 or 6 jets are also used but are less usual. A special form of Pelton wheel with side entrance so as to permit a larger jet and a much greater quantity of water for a given wheel diameter iscalled the Turgo and competes with the two jet and four jet Pelton wheels.
Limiting Speed The speed of water flow through the wheel and the speed of blades relati ve to the water imposes a limit on the revolutions per minute and consequently upon the head against which the wheel may operate, since excessive speeds give rise to cavitation with consequent damage to the wheel element. In the case of aFrancis wheel if the power is very small the runner may be of an awkward shape for casting and may require to run at a speed inconvenient to the generator. It is for this reason that on low powers the Pelton is used for heads as low as 30 m.
Application of Water Turbines Water turbines provide power for all purposes. In the larger sizes the power produces is almost invariably used for generating electricity for the national grid or for industry. There are certain pump schemes particularly in the chemical field for cooling or scrubbing duties, where the return main has a greater height or pressure than can be recovered by a syphon. In many cases the water, after having passed through the process, enters a turbine so as to recover as much power as possible. These turbines are very often arranged in tandem with the pump so that the motor power necessary is reduced by the contribution made by the turbine.
Problems in the Operation of Turbines A steam turbine is governed by stop valves controlled by a speed governor and itis possible to close this stop valve quickly. In the case of a water turbine, however, there is in the penstock a large mass of water approaching at a relatively high speed.
460
CENTRIFUGAL PUMPS
Pipeline Inertia. To close the turbine gates too quickly would give rise to a considerable increase ofpressure since the long column of water would suddenly be brought to rest. In order to avoid a pipe fracture, therefore, it is necessary to bring this column of water slowly to rest. Water turbo alternators differ from some other prime movers in that they load, in this case the alternator torque, can vanish instantly without any warning. If an electric storm strikes the grid, the circuit breakers may disconnect the generating station from its load within a fraction of a second. At this time, however, the turbine is being fed with water and generating full power, and until the water column can be brought to rest, power is still being fed to the turbine. As a result, its speed increases and in the limit may reach the runaway speed, which is nearly twice the normal running speed.
Rotor Inertia The only way in which this rate of increase of speed can be regulated is by building a greater flywheel effect or inertia into the rotor of the electric generator. This is a particularly difficult problem for the electrical designers, since on the one hand they must build as much metal into their rotor as possible, and on the other hand this rotor should be capable of running at nearly twice normal speed without bursting (this is vital in case of governor failure). To this end the shortening of the penstock to the minimum possible length is essential and therefore on any power scheme it is usual to provide a horizontal canal or tunnel from the upper lake to a point as near the power house as possible, followed by a very short pipeline. At top of this pipeline is erected a surge tank with an open top, so that the water flowing in the horizontal tunnel or canal can escape and the turbine designer need only consider the amount of water in the length of the relatively short penstock approaching the turbine. It will be seen that this problem resol ves itself into the balancing of the water inertia in the pipe against the inertia of the rotating parts of the turbo alternator. A further means of helping this problem is to provide a by-pass so that as soon as the governor starts to close the gates beyond a certain speed the by-pass is opened, permitting the penstock water to run to waste instead of through the turbine. This by-pass or relief valve is only opened if the speed of governor movement exceeds a certain valve. On the other hand, even with a pressure relief valve on certain turbines, the incidence of over speed causes in itself a reduction of quantity which in turn gives rise to a further pressure increase, the cumulative effect of which on lowest specific speed of Francis turbines is extremely difficult to forecast. In the case of a Pelton wheel, by-passing can be carried out more conveniently with a deflector which removes the jet entirely from the wheel. The deflectors have the advantage that no pressure rise whatever occurs, since the water is not deflected until it is passed out of the nozzle into the atmosphere.
Construction of Turbines The Francis turbine usually comprises a scroll casing which leads the water from a pipe into the periphery of the runner. Before entering the runner the water passes through a
APPENDIX E
461
series of gates which are controlled by the governor, thus admitting a larger or smaller quantity of water into the turbine. A Kaplan turbine is similar, but has in addition the problem of moving the rotating blades by a servo motor in the shaft. The blades and the gates normally move in unison. With a Kaplan turbine there is, furthermore, a risk of exceptionally high overspeed should the correct phasing of blades and gates accidentally get out of order. In addition, constructional features such as the shaft for supporting the runner bearings, gland, casing, gate mechanism, etc, are involved. The casing may be of concrete up to 90 ft head or of steel for higher heads. The Pelton wheel is rather more simple, comprising only the wheel and the nozzle at the end of the penstock, which is controlled by a needle valve arranged so as to reduce the size of the jet without altering its speed or causing any undue frictional loss. The Pelton wheel is contained in a light casing so as to prevent undue splashing. The buckets are of double hemispherical shape. The wheel runs at half the jet speed and the jet is turned through nearly 180 0 in the bucket. The water speed when leaving the bucket is theoretically zero, all its energy being given to the wheel.