Turbines

Contents

i. Introduction ii. Power From Water

iii. Impulse Turbines: The Pelton Wheel iv. Reaction Turbines: The Lawn Sprinkler v. Energy Relations

vi. Steam Turbines vii. Gas Turbines

viii. References

Introduction

The word turbine was coined in 1828 by Claude Burdin (1788-1873) to describe the subject of an 1826 engineering competition for a water power source. It comes from Latin turbo, turbinis, meaning a "whirling" or a "vortex," and by extension a child's top or a spindle. Defining a turbine as a rotating machine for deriving power from water is not quite exact. The precise definition is a machine in which the water moves relatively to the surfaces of the machine, as distinguished from machines in which such motion is secondary, as with a cylinder and piston. The common overshot water wheel is a rotating machine, but not a turbine, while an undershot wheel is an impulse turbine, but not generally considered as one. We shall discuss many types of water-driven prime movers in this article, but mainly turbines, for which we will explain the fundamental theory. We shall also discuss steam turbines and gas turbines and their applications. Wind turbines are treated in another article.

Water in nature is a useful source of energy. It comes directly in mechanical form, without the losses involved in heat engines and fuel cells, and no fuels are necessary. Solar heat evaporates water, mostly from the oceans, where it is mixed into the lower atmosphere by turbulence, and moved by the winds. Through meteorological processes, it falls on the earth as precipitation, on the oceans, but also on high ground, where it makes its way downhill to the sea, with evaporative and other losses. A cubic metre of water can give 9800 J of mechanical energy for every metre it descends, and a flow of a cubic metre per second in a fall of 1 m can provide 9800 W, or 13 hp. The efficiency of hydraulic machines can be made close to 1, so that all this energy is available, and it can be converted to electrical energy with an efficiency of over 95%.

The disadvantage of energy from water is that it is strictly limited, and widely distributed in small amounts that are difficult to exploit. Only where a lot of water is gathered in a large river, or where descent is rapid, is it possible to take economic advantage. Most of these possibilities are quite small, as are the hydropower sites along the Fall Line on the Atlantic coast of the United States, or on the slopes of the Pennines in England. These were developed in the early days of the Industrial Revolution, but are now abandoned because their scale is not the scale of modern industry. Each site provided a strictly limited horsepower, and in the autumns the water often failed. For expansion and reliability, all were rapidly replaced by steam engines fueled by coal, which were expandable and reliable. Today, hydropower

usually means a large project on a major river, with extensive environmental damage. The fall in head is provided by a dam, which creates a lake that will be of limited life, since geological processes hate lakes and destroy them as rapidly as possible.

Niagara Falls is an excellent example of a hydropower site. It is unique; there is only one, and hardly anything else similar. The Niagara River carries the entire discharge of the Great Lakes, about 5520 m3/s, and the concentrated elevation difference is about 50 m. The visible falls carry nothing like this much water today; most is used for power. Hydropower could destroy the falls as a sublime view; we are lucky it has not. The power available from this discharge and drop is 3.6 x 106 hp. The figures given in the encyclopedia for the power available from the Canadian and U.S. power projects on each side add up to considerably more than this. Perhaps they use more drop, or perhaps they are just optimistic. The first large-scale hydropower development here was in 1896. This was also the site of Nikola Tesla's two-phase plant that pioneered polyphase power in the U.S.

For comparison, the more than 190 million registered motor vehicles in the U.S. probably have an aggregate power capability of neary 2 x 1010 hp, equivalent to 5000 Niagaras. Hydropower and increasing population cannot coexist; the limits of hydropower are fixed and obvious. It is really too bad that small-scale hydropower projects are no longer economically viable. In 1920, about 40% of electric power in the U.S. came from hydropower; in 1989 that percentage had dropped to 9.5%. It was not that hydropower had decreased in absolute terms, but had remained roughly constant while the total market had expanded greatly.

Power From Water

To get power from water, it must be extracted as the water is lowered in elevation. That there is a current in a stream is obvious; it comes from the open-channel flow of the water under the influence of gravity. If you hold a paddle-wheel in the stream, it will be rotated and you can extract power from it. This is an elementary impulse turbine, a rotating machine acted upon by the force of moving water. This is not a copious source of power, but at least it does not involve the disturbance of the stream, which was always of intererest to the neighbors. Wheels like this are called undershot, and were very common at all dates, because they can be used without disturbing the stream. These were the typical Roman water mills, described in Vitruvius. There are, however, very few relics remaining from these mills, and their history is often seriously misrepresented. The wheels drove horizontal millstones through gearing, usually by a face and a lantern gear. All parts of a mill were made of wood, except for small pieces of metal where desirable.

Roman water mills were suggested by the irrigation machinery that had been long used in the arid Near East to raise water. The Egyptian shaduf, a counterweighted pot, was millennia old, raising water by about 2 m, and sometimes arranged in cascade. This was not, of course, a source of energy but a consumer of it, though it made the most of human effort. A much later development was the chain of pots, saqiya or Persian wheel, that rotated to raise pots of water to a height, where they were automatically emptied into an aqueduct as they rotated. This could be operated by man or beast, but some ingenious person fitted the rim of the wheel with vanes or paddles. When dipped into the current, they rotated the wheel with sufficient force to raise the pots with no assistance. This was the remarkable noria, probably the first application of water power, developed in the fourth century BCE at an unknown location. The Syrian city of Hama, 75 km inland from the Mediterranean, received its water from aqueducts filled by norias on the River Orontes. Famous norias also were built in Portugal.

An outstanding water-raising project that should be more widely known was the Artificio of Juanelo Turriano (? - 1585) at Toledo. Toledo is 600 m above the Rio Tajo, and for centuries water had been laboriously carried up in leather bags on the backs of mules. Turriano built an undershot wheel on the river that was equipped as a noria, filling a basin on the bank. By means of reciprocating rods, a bucket filled from this basin was rocked about an axis, tipping its water down a pipe into a following bucket. This was continued up the slope to the city, each bucket rocking and alternately filling and tipping into the next, in a mechanical bucket brigade to the top, doing the work of 600 mules.

These undershot mills were very sensitive to water level. To remedy this difficulty where water level varied, wheels were mounted on pontoons that were moored in the stream. Usually, the wheel was set between two boats, where the bearings would be satisfactory and the water velocity the greatest. Mill boats were used on the Guadalquivir at Córdoba, since the river level was quite variable with the season. Mill boats were also used on the Thames in London, and beneath the Grand Pont in Paris, as well as at Cologne on the Rhine. If they were moored in the arches of a bridge they could take advantage of the higher current there. The openings in medieval bridges were usually small and inadequate, favoring this application. The invention of the floating mill is traditionally ascribed to an emergency measure of the Roman general Belisarius in 537, while defending Rome from an Ostrogothic siege.

If you were permitted to construct a weir, and usually this involved an extended legal wrangle over navigation rights, you could make available a few feet of drop all in one place. If you made a spillway, you would have some rapid water at its base to put a paddle wheel in. An alternative was to make the wheel move in a closely-fitting shroud, or to provide it with buckets, so that the water would by its weight press down the paddles. This is a completely different principle than the impulse machine, though many machines derived energy from both sources. With care, most of the energy of the descending water could be gathered, a distinctly more efficient operation than any available type of impulse machine. Later, well-designed wheels with the water applied at some height less than the wheel diameter were called breast-shot wheels because the water entered part way up the diameter. A wheel of large diameter was usually necessary to provide sufficient power at the desired slow speed. Breast wheels were the most common type of mill wheel, even into the 20th century, since they were both efficient and well suited to moderate heads.

The great weir on the River Dee at Chester supplied a head for the city's mills for many years. Despite many orders for its destruction, it has lasted to the present. At Exeter in Devon, there was great opposition to Countess Wear (an alternative spelling) built across the Exe by the Countess of Devon that facilitated the collection of traditional tolls on river traffic, as well as head for a mill. There were other weirs on this small river, each supplying a mill, and a very early navigation canal was built to bypass the weirs. Boats were often dragged upstream past a weir on water temporarily released by a flash gate. Locks were a more recent affair, and now permit easy passage without a waste of water.

Tidal mills were also built in favorable locations. Sometimes the rising and falling tidal streams in an estuary could work an undershot wheel. More commonly, a tidal basin was filled at high tide and then emptied past the wheel at low tide, giving two periods of power a day for several hours in most places. The times of day were variable, but were at least predictable. Tidal mills were on a much smaller scale than today's tidal power schemes.

If the water was available at a sufficiently high level, perhaps through a canal or flume from an upstream point, it could be introduced near the top of the wheel. These were overshot wheels and, like breast wheels, used the weight of the water only, and were quite efficient. Overshot wheels were used by the Romans wherever sufficient head was available. At Barbegal, near Arles in southern France, a double row of 16 overshot wheels, each 9 ft in diameter and 3 ft wide, was applied to flour milling. This installation could provide flour for 80,000 people. At Laxey, on the Isle of Man, an overshot wheel of 70 ft diameter, rotating at 2.5 rpm and developing 175 hp, was fed by water under pressure that rose in a masonry column and was then led to the top of the wheel in a wooden flume. The output of the wheel was used for pumping a lead mine. This "Lady Isabella" wheel was built in 1854 or 1856, and served until the mine was abandoned in 1929.

The water for an overshot wheel was often applied beyond the centre line, so that the wheel rotated in the same sense as the water approached. If the water below the wheel became too high, it would retard the wheel, an effect known as back watering. It was easy to cure this by admitting the water on the other side of the centre, so the wheel revolved in the opposite direction and the water below would aid the rotation, not hinder it. The Laxey wheel was of this type, called a pitch-back wheel. Another help was ventilating buckets that had openings to aid the discharge of water.

John Smeaton (1724-1792), one of the first modern Civil Engineers, and a very successful one, founder of the Smeatonian Society that later became the Institution of Civl Engineers, took great interest in improving water wheels, and in introducing cast iron in their construction, just at the time when the rotary steam engine was coming into being. Improvements in water wheels continued in the 19th century, by such engineers as Robert Fairbairn, and were brought to a high state of excellence with metal replacing most of the wood in both wheel and gearing. Since the wood around waterwheels is alternately wet and dry, it is very subject to rotting, and this was a persistent problem.

The vanes, blades or buckets on a waterwheel were called floats, sometimes rungs. Water was carried to and from the wheel in a mill race. The water arrived in a head race, and left in a tail race. A head race was locally called a lade or a launder. A mill race could be called a flume in the United States, or a leat in Britain. The water was controlled by means of a sluice, sometimes redundantly called a "sluice gate." A sluice is a vertically sliding gate, often operated by rack and pinion. A penstock may be a sluice, but is also a closed channel through which water is delivered under pressure.

Water wheels can be run in reverse--driven, for example, by windmills, and function as pumps. The most common water-lifting machine in Holland was the scoop wheel, very much like a breast-shot wheel run in reverse. These were sometimes cascaded to give a greater lift. For lesser discharges, an Archimedean screw rotated by a small four-sailed windmill could be used, called a tjasker.

The Norse mill or Greek mill, was completely different, with a horizontal wheel and vertical shaft called a tirl, that turned the millstone directly, without gearing. A stream of water from a penstock was directed on the wheel, turning it by impulse. This was a very primitive mill, but a quite practical one, which appeared in about 0 CE. It was not displaced by the more elaborate Roman mill, with vertical wheel and horizontal shaft with gearing, in many places. It is really not Greek nor Norse particularly, but widely distributed in early communities. An later example was the Provençal mill from southern France. Poncelet derived a design for an

impulse turbine from this model, with a horizontal metal wheel with curiously shaped floats fed by a penstock. These horizontal mills were all impulse turbines, ancestors of the Pelton wheel. Although they may bear a resemblance to Francis turbines, the resemblance is only superficial.

The uncertainty of water supply could be ameliorated by a mill pond, which stored water to even out variable flows. Many mills had a weir or dam, a mill pond, and a flume to supply the wheel, making a very pleasant establishment. However, protracted drought or winter frosts could bring the mill to a halt. In some cases, when a steam engine was installed, it was used to pump water up to the mill pond, instead of being applied directly to the machinery. This, of course, involved the least disturbance to the existing machinery and allowed the steam engine to be immediately applied. When renovation occurred, the opportunity was used to remove the wheel and connect the steam engine directly to the machinery.

An alternative to turbines is the positive-displacement engine, in which a piston reciprocates in a cylinder, valves admitting and releasing the water. This is especially adaptable to high heads. One double stroke of the piston in effect lowers an amount of water equal to the cylinder displacement from the high reservoir to the low, extracting its potential energy. Care must be taken to cushion the shock of sudden opening and closing of valves by air chambers and other means. These column-of-water engines were extremely rare. The best known was built by Georg von Reichenbach of Bavaria to power reciprocating brine pumps. A positive displacement rotary engine like the Roots blower could easily be run in reverse on water pressure, and would, moreover, function smoothly without shock. I do not know if this has been done. Reciprocating engines have the advantage of being able to work at different speeds, which turbines can do only with difficulty. Reciprocating pumps are much more common than reciprocating engines.

Impulse Turbines: The Pelton Wheel

The impulse turbine is very easy to understand. A nozzle transforms water under a high head into a powerful jet. The momentum of this jet is destroyed by striking the runner, which absorbs the resulting force. If the velocity of the water leaving the runner is nearly zero, all of the kinetic energy of the jet has been transformed into mechanical energy, so the efficiency is high.

A practical impulse turbine was invented by Lester A. Pelton (1829-1908) in California around 1870. There were high-pressure jets there used in placer mining, and a primitive turbine called the hurdy-gurdy, a mere rotating platform with vanes, had been used since the '60's, driven by such jets. Pelton also invented the split bucket, now universally used, in 1880. Pelton is a trade name for the products of the company he originated, but the term is now used generically for all similar impulse turbines.

A diagram of a Pelton wheel is shown at the right. The wheel of pitch diameter D has buckets around its periphery, so spaced that the jet always strikes more than one at a time. The buckets have the form shown at the upper left, where the water enters at a splitter and is diverted to each side, where the velocity is smoothly reversed. Bucket sizes are from 2.5 to 4 times the jet diameter. The total head supplying the nozzle is h, the sum of the pressure head and the

approach velocity head. The theoretical jet velocity is V = √(2gh). Let's analyze an ideal wheel, and assume that this is actually the jet velocity. The peripheral velocity of the runner is u.

The vector diagrams at the left show how the velocity is transformed by the runner. For simplicity, we assume that all velocities are in the same straight line. The relative velocity of approach to the runner is V - u. We assume that this velocity is reversed, so that the final velocity is V - 2u. The force F on the runner is the rate of momentum change, or F = ρ[V + (V - 2u)]Q = 2ρ(V - u)Q, where ρ is the density and Q the volume rate of flow of water. The torque on the runner is T = FD/2 = ρD(V - u)Q. When the runner is stopped, the torque has its greatest value, ρDVQ. When the peripheral velocity of the runner is

equal to V, the torque is zero. The torque curve is a straight line between these points.

The power P = Fu or Tω. In terms of u, P = 2ρu(V - u)Q. By taking the derivative of P with respect to u and setting it equal to zero, we find that maximum power occurs when u = V/2, and this power is ρV2Q/2, or ρghQ. This is the energy content of the water from the jet, so the efficiency is unity, with all the energy of the jet turned into shaft output. For any velocity u, the efficiency is η = 4u(V-u)/V2. It is zero for u = 0 and for u = V. This analysis should have been clear and easy to follow. It illustrates the princple of the Pelton wheel very well, and actual wheels are not too far from ideal. When a Pelton wheel is working close to maximum efficiency, the water drops easily from the wheel, with a little turmoil, but not much velocity.

As an example of an actual Pelton wheel, one worked for a time generating electricity in Southern California with the following specifications. Pitch diameter, 162" (2.06 m); operating speed, 250 rpm (26.18 rad/s); head, 2200' (670.6 m). The theoretical V is √(2gh) = 114.6 m/s, while the peripheral velocity u = 53.86 m/s. Then, 2u = 108 m/s, very close to V and probably closer to the actual jet velocity. This wheel probably developed about 60,000 hp on a flow of around 7 m3/s. The ratio of the runner velocity u to the ideal jet velocity √(2gh) is usually denoted φ. For a Pelton wheel working at maximum efficiency, φ is about 0.5.

The conduit bringing high-pressure water to the impulse wheel is called the penstock. This was strictly just the name of the valve, but the term has been extended to the conduit and its appurtenances as well, and is a general term for a water passage and control that is under pressure, whether it serves an impulse turbine or not.

Reaction Turbines: The Lawn Sprinkler

By contrast with the impulse turbine, reaction turbines are difficult to understand and analyze, especially the ones usually met with in practice. The modest lawn sprinkler comes to our aid, since it is both a reaction turbine, and easy to understand. It will be our introduction to reaction turbines. In the impulse turbine, the pressure change occurred in the nozzle, where pressure head was converted into kinetic energy. There was no pressure change in the runner, which had the sole duty of turning momentum change into torque. In the reaction turbine, the pressure change occurs in the runner itself at the same time that the force is exerted. The force still comes from rate of change of momentum, but not as obviously as in the impulse turbine. Many turbines combine impulse and reaction, so that it is difficult to separate them conceptually.

The duty of the lawn sprinkler is to spread water; its energy output as a turbine serves only to move the sprinkler head. It is a descendant of Hero's aeolipile, the rotating globe with two bent jets that was quite a sensation in ancient times, though this worked with steam, not water. The lawn sprinkler seems directly descended from Rev. Robert Barker's proposed mill of 1740, or the probably better-known Segner's wheel of about the same time, which was quite similar. These used two jets at right angles to the radius. A later improvement fed water from below to balance the weight of the runner and reduce friction. Barker's mills only appeared as models, and were never commercially offered. The flow of water in a lawn sprinkler is radially outward. Water under pressure is introduced at the centre, and jets of water that can cover the area necessary issue from the ends of the arms at zero gauge pressure. The pressure decrease occurs in the sprinkler arms. Though the water is projected at an angle to the radius, the water from an operating sprinkler moves almost along a radius. If you have such a sprinkler, by all means observe it in action. The jets do not impinge on a runner; in fact, they are leaving the runner, so their momentum is not converted into force as in the impulse turbine. The force on the runner must act in reaction to the creation of the momentum instead, which is, of course, the origin of the name of the reaction turbine.

The engineering competition for a water mill in which Claude Burdin coined the word "turbine" and submitted a design was won by his young student Benoît Fourneyron (1802-1867) in 1827. Water entered on the axis of a horizontal ring of stationary forwardly-curved guide blades and flowed outwardly into the horizontal turbine wheel with backwardly-curved blades to exit at the circumference. The efficiency of the final improved version was over 80%. This turbine was widely applied to replace the much less capable undershot wheels that were so common, beginning around 1837.

A two-armed runner of a rotating lawn sprinkler is shown at the right. Conditions at the ends of the two arms are the same. The jet at the end of an arm is projected at an angle β with a perpendicular normal to the radius from the centre of rotation, in the direction of the rotational velocity u2 = ωr. The space velocity V2 is the vector sum of v2 and u2, which makes an angle α with u2. When the runner is stopped, V2 = v2. As the runner speeds up, V2 moves closer to a radial direction. When it reaches the radial direction, there is no longer a component normal to the radius and, therefore, no accelerating torque. It is easy to see that the torque will be a maximum when the runner is stalled.

To find v2 in terms of p1, we shall use Bernoulli's theorem. However, energy is not conserved between the axial point 1 and point 2 at the end of the arm, since the water does work in passing from one point to the other. There is a reaction force of magnitude ρV2 in the opposite direction to V2. The movement of point 2 is in the direction of u2, so the rate of doing work is ρV2u2cos α. Dividing by ρg to express this work as head, we find that a head of V2u2cos α/g must be subtracted from the difference of the heads at points 2 and 1. Since z2 = z1, and V1 = 0 at point 1, and p = 0 at point 2 (we are using gauge pressures), we get V2

2/2g = p1/ρg - V2u2cos α/g.

From the vector triangles, we find that (dropping the subscript 2 for the moment) V2 = u2 + v2 - 2uv cos(180° - β) = u2 + v2 + 2uv cos β, and also that V cosα = v cos β + u. Substituting for

V2 and V2cosα in the above equation, we find that (v2 - u2)/2g = p1/ρg = h, which simplifies to v2 = 2gh + u2. In this equation, h is the supply head, which may include approach velocity if it is to be considered.

Now we can find everything we need as a function of u2, or of the angular velocity ω. In particular the component of V perpendicular to the radius is V' = V cos α = v cos β + u. The corresponding reaction force is obtained by multiplying by ρ, and by the total discharge Av, where A is the total area of the jets on all arms. The torque, then, is T = -ρAvr(v cos β + u), where v = √(2gh + u2) and u = ωr.

A lawn sprinkler I have at hand has r = 75 mm, β = 110° and A = 8 mm2. Let us first find the free-running speed for a supply head of 300 cm. The free-running speed corresponds to zero torque, when V is radial, or when v cos β + u = 0. Here, this condition is u = 0.342v, or v2 = 8.549u2. Since v2 = 2gh + u2, we have 7.549u2 = (2)(980)(300), or u = 279 cm/s. Since r = 7.5 cm, ω = 37.2 rad/s, or n = 355 rpm (n is the usual symbol for angular velocity in rpm). This value will not be reached, of course, due to friction, but it is very reasonable. Under a tenth of the head, the free-running speed would be 112 rpm.

Let us assume that the actual speed under 300 cm head is 200 rpm, and find the corresponding torque. For this runner, T = 0.60v(0.342v - u) cm-dyne. 200 rpm is 20.94 rad/s, so u = 157 cm/s. Then, we find that v = 783 cm/s, from which T = 5.17 x 104 cm-dyne, or 53 cm-gm, as it is usually stated. This will be the torque required to turn the runner at that speed. The discharge Q = Av = (0.08)(783) = 62.6 cm3/s, or 3.76 liters/min. At stall, v = 767 cm/s, and the stall torque will be 12.07 x 104 cm-dyne, or 123 cm-gm. Note that the rotation of the runner causes v to be larger than it would be without the rotation; the runner is acting as a centrifugal pump.

The water is projected with a radial velocity of V sin α = v sin β = 0.940v. Let's assume that it is projected horizontally, although in the actual sprinkler the jets are aimed upwards a little. Then the radial velocity will be 736 cm/s. If the height of the runner is 1 m above the ground, it is easy to calculate that the water will be projected to a radius of 3.3 m. If the water were spread uniformly over this disc, the watering rate would be 6.6 mm per hour.

If we were more interested in power than in watering, β could be made 180°, and the area of the jets could be increased, partly by multiplying the number of jets. If the angular velocity of the runner could be such that v = u, the water would drop directly down, and the efficiency of the turbine would be a maximum. However, we must have v2 = 2gh + u2, so this condition cannot exist. All that can be done is to make u as large as possible, but this is not very satisfactory. This is the reason Barker's mills are not often seen these days.

An interesting related problem is the "reverse sprinkler," also known as Feynman's sprinkler, though he did not originate the problem or give a solution (see Reference). Imagine a sprinkler like the one described above immersed in water and suppose the water is sucked out of it. There is a slight impulse towards the side where the water enters when flow begins, and an equal reverse impulse when the flow stops, but for an ideal fluid there is no steady torque. It is interesting to analyze this problem. The momentum given to the fluid on entry is the same that is given up when the fluid turns and moves into the supply pipe, so there is no net torque. There was a considerable amount of argument concerning this problem in the 1980's, but the confusion over it is much older.

Energy Relations

To analyze power turbines, we'll use Bernoulli's theorem in the form derived for the water sprinkler, written between the inlet and outlet of the turbine runner. This is (p1/ρg + z1 + V1

2/2g) - (p2/ρg + z2 + V22/2g) = hL + (V1u1cosα1 - V2u2cosα2)/g. The terms on the right are the

head loss in the supply piping, hL, and the utilized head h" which depends on conditions at inlet and outlet. There is a velocity triangle at inlet and outlet relating V, u and v, as in the case of the lawn sprinkler. There, we could use it to eliminate V from this equation in order to find v.

Practical turbines cannot be well described by a single streamline, but we can still think of average values of V1 and V2, u1 and u2, and the other quantities, and find out how they vary with the size of the turbine, the rotational speed, the developed horsepower, and the applied head. In fact, the theory of practical turbines is difficult, so tests are actually used to determine the variables under study. Experiments are made on models, and scaled up to full size, so understanding the relation between model parameters and full-size parameters is important.

The principle of a power turbine is to direct the incoming water tangentially by stationary vanes, and then to have it pass to the moving runner where it exerts forces on the runner vanes while its pressure decreases from the input head to zero. Since the pressure varies, the turbine must flow full. The exit velocity is not zero, but most of the kinetic energy can be recovered in a draft tube where the water is decelerated. In 1826, Bénoit Fourneyron (1802-1867) developed an outward-flow turbine that was efficient, but the mechanical arrangements were poor, since the runner was on the outside. Jean V. Poncelet (1788-1867) designed an inward-flow turbine in about 1820. S. B. Howd took the design to the U.S. and patented it in 1838 (I do not know if he made any improvments, or just filched the idea). In 1849, James B. Francis (1815-1892) improved Howd's turbine, where the water entered horizontally through guide vanes that gave them a whirl, then passed into the runner and was diverted downwards. His hydraulic experiments on turbines at Lowell, Massachusetts, are famous. James Thomson of Belfast, brother of Lord Kelvin, made important improvements to the inward radial flow turbine, in the shape of the vanes, control, and other matters. Practical reaction turbines are now all inward-flow machines. The water enters through a snail-like scroll case, and exits below near the axis.

The runner of a Francis turbine is illustrated at the left. Its basic dimension is the diameter D. The shape of the vanes cannot be well represented, but they are designed for smooth flow at the design speed and head of the turbine. The plan view at the right shows how the guide vanes in the stator direct the water onto the moving runner, acting like nozzles.

The water follows the dotted path in space from the inlet at 1 to the outlet at 2. Relative to the runner, it flows parallel to the vanes, exerting the force that creates the output torque. In this diagram, it is easy to imagine the velocity triangles at input and output, which will be similar to those for the lawn sprinkler.

The vertical section at the left shows that the flow is not completely radial, as it was in the earliest Francis turbines. During its passage through the runner, the water is diverted axially, and exits at the bottom of the runner. This, of course, complicates our analysis, but nothing is really fundamentally changed. The mixed flow allows a more efficient turbine by making the exit smoother. The interested reader should try to find illustrations of actual Francis runners to appreciate their complex shape. It is clear that a single streamline is not sufficient to describe their action!

The distinction between radial and axial flow has a great effect on the appearance of the turbine, but it does not affect its fundamental behavior. Hydraulic turbines can be made that are almost completely axial flow, the runner taking the form of vanes perpendicular to the axis, well-described by the term propeller turbines. An example is the Kaplan turbine, invented by Victor Kaplan (1876-1934) and first put into service in 1912-13, with movable blades that rotate, or "feather," to handle different conditions, the key to making an efficient propeller turbine. In fact, the guide vanes of a Francis turbine are usually movable for the same purpose. A turbine without such adjustments will work efficiently only at its design speed and head. The water is given a swirl at the top of a Kaplan turbine that is taken out by the propeller.

Torque is the rate of change of angular momentum, just as force is the rate of change of linear momentum. When a fluid exerts a torque on a turbine runner, the reaction is a change in angular momentum of the fluid. Fluid is given angular momentum by the guide vanes which, ideally, is destroyed by the torque exerted on the runner. With some machines, however, the water at the exit may still have considerable angular momentum, and the energy in this motion is energy that does not appear at the shaft. Where velocity in the exit fluid is part of the desired output (as with a fan), vanes to straighten out the flow help to recover some of the energy that would otherwise be lost.

When a draft tube at the outlet of a turbine is filled with water, the pressure is less than atmospheric at the turbine outlet. This, of course, is a desired effect so that advantage can be taken of the whole drop in head even when the turbine is above the level of the tail water. In a Kaplan turbine, the effect of the runner was to reduce the pressure even more, below the vapor pressure of water at that temperature. Small bubbles of vapor were produced, and when they reached higher pressure collapsed explosively, damaging the runner. This is called cavitation and is a hazard in all hydraulic machinery where the pressure may drop sufficiently. This almost caused the failure of the Kaplan turbine, but the problem was eventually solved by taking care with the turbine setting and other details.

The power developed by a turbine is P = ρgQh", where Q is the flow through the runner. The power in the inlet water is P' = ρgQh, so the efficiency of the turbine is e = h"/h. Strictly speaking, this is the hydraulic efficiency eh. The mechanical efficiency em is the fraction of the runner power that is delivered at the shaft, lessened because of friction. Hydraulic machines have a mechanical efficiency of 0.95 to 0.98 for large machines, usually closer to the higher figure. Some of the supplied water may leak by the runner and do no work. The volumetric efficiency is ev = (Q - QL)/Q, where QL is the leakage. This is also quite high in practical machines. The overall efficiency is e = P/ρgQh, where P is the shaft power output. P is usually expressed in hp (550 ft-lb/s) or watt. 746 W = 1 hp.

If f is the fraction of the runner inlet that is open, then the inlet area is A = fπDB = fπmD2, where m = B/D. The radial velocity at inlet is written Vr = V1cosα1 = C1√(2gh). Therefore, Q

= AVr = KqD2√h, which shows how Q depends on the size of the machine and the head. The power output will be P = eρgQh = eρgKqD2h3/2 = KpD2h3/2. The constant Kp will be the same for machines of the same design.

We have already mentioned the parameter φ with relation to the Pelton wheel. Using it, we can express the rotational speed in rpm by n = 60u/πD = (60φ√(2g)/π) h1/2/D. We note that n√(P) = const. x h5/4, so that the combination n√P/h5/4 will be a constant for a particular machine, or machines similar to it. This relation between speed, power and head for a turbine is very useful. The value of the expression is called the specific speed ns, but it is not really a speed, and it should be noted that the expression is not a dimensionless number. Also, the speed and power used in it should be the speed and power for maximum efficiency, so that the constants are really constant. Even with these cautions, it is a valuable way to classify turbines.

In United States practice, P is in hp and h is in feet, and ns is quoted assuming these units. In metric practice, P is in kW and h is in metre. This gives a larger ns, which can be reduced to the U.S. practice by multiplying by 0.2626.

Impulse turbines have low ns, from 1 to 10. A typical value for a Pelton wheel might be 4. Francis turbines have a specific speed of from 10 to 100, while Kaplan turbines give from 100 up. These are values for well-designed, efficient machines. Of course, monsters could be made with very different specific speeds but they would not be satisfactory. If you know the head, speed and power desired, it is easy to find the general type of turbine that would prove satisfactory.

Suppose you have a head of 2200 ft available, and want a 250 rpm machine delivering 60,000 hp. The specific speed will then be (250)√(60,000)/22005/4 = 4.06. This points to a Pelton wheel, and, in fact, one was used under these conditions. If you have a head of 89 ft available on the Susquehanna at Conowingo, PA, and want 54,000 hp at 81.8 rpm, then the specific speed is 69.5, clearly pointing to a Francis turbine. In the machine used, D = 18 ft. At Rock River, IL, a head of only 7 ft is available. 800 hp at 80 rpm is required. The specific speed is 199, clearly indicating a Kaplan turbine, which was installed. The maximum horsepower that can be developed can be estimated by the discharge Q and the available head. In engineering units, Pmax = 3.65Qh hp, where Q is in cfs and h is in feet. The speed often depends on the speed for a directly-coupled alternator. If N is the number of poles and f the frequency, then n = 60f/(P/2) = 120(f/P). For f = 60 Hz and N = 24, n = 300 rpm. Alternators have from 12 to 96 poles, usually, so rotational speeds will range from 600 rpm to 75 rpm.

Steam Turbines

It is possible to obtain large quantities of gaseous water at considerable pressure simply by heating it in a closed container, the boiler. As this vapour expands to a lower pressure, it can transform its internal energy to kinetic energy, which can be converted to shaft work in a turbine, exactly like water falling under gravity. Unlike water, steam is compressible and its density depends on its pressure. Also, steam is much less dense than liquid water so high velocities are necessary for significant energy transfer. This was recognized by James Watt, who deemed turbines impractical for steam power under the engineering limitations of the time. At the present time, however, steam turbines provide over 80% of electric power.

Although practical steam turbines were not developed until after about 1875, turbines of both principal types--impulse and reaction--were known in antiquity as curiosities or toys. Very well-known is Hero's Aeolipile, described by Hero of Alexandria in the 1st century CE but probably originating with Ctesibus in the 3rd century BCE. Less well-known are the impulse wheels described by Giovanni Branca (1571-1645) or the Ottoman scientist Taqi ad-Din (1526-1585). Neither seems to have claimed to have invented the device and merely described it, but ancient references have not been found. The Aeolipile is an example of a pure reaction turbine, just like the lawn sprinkler but using steam. Branca's Wheel is an example of a pure impulse turbine, analogous to the Pelton Wheel.

It is not difficult to apply either device to do useful work. Karl Gustaf Patrik de Laval (1845-1913), a Swedish engineer working in the milk industry, applied a 2-armed reaction turbine very much like the Aeolipile to drive a centrifugal cream separator around 1875. In 1882 he created an impulse turbine with two or more nozzles and a single rotor wheel, that was improved with the converging-diverging nozzle that carries his name that could accelerate the steam to supersonic speeds. A very high rotative velocity was necessary to achieve reasonable efficiency, and de Laval experimented with shafts and bearings that would be serviceable.

A turbine that could be conveniently used for naval propulsion and electric generation was devised by Charles Algernon Parsons (1854-1931), youngest son of the Earl of Rosse, in 1884. His idea was the division of the expansion into a large number of steps. In each step, the steam would be expanded in a fixed ring of blades and the velocity created used in the following ring of moving blades. The diameter of the ring or the height of the blades would be increased to accommodate the expansion. 50 or 100 stages of expansion were not unusual. The rotational speed was still large, but quite practical using herringbone reduction gears to drive the propeller shafts of ships. Elecrical generators could be driven directly.

The turbine ship Turbinia was launched in 1894 and appeared in the Spithead naval review in 1897, where it amazed the spectators with its speed of over 34 knots, faster than anything else at the show. The turbine supplied 2000 hp to two outer shafts, each with three propellers. Later, three turbines powered three shafts, each with three propellers in tandem. In testing this ship, the phenomenon of cavitation was observed and methods were devised to limit its damage. This ship is on display in the discovery Museum at Newcastle on Tyne, while its power plant is in the Science Museum in London. In 1906, the battleship HMS Dreadnought was launched with a 75,000 hp turbine. Turbine power became standard on warships, though its application to cargo ships was not as extensive, since large powers were not required. The Liberty ships of 1941-1945 still had triple-expansion reciprocating engines of 2500 hp, and diesel ships are still common.

Charles Gordon Curtis (1860-1953), winner of the 1910 Rumford Prize, designed small electric motors before he turned to steam turbines in 1895. He devised a way, patented in 1896, to apply the principle of the de Laval impulse turbine at much lower rotational speeds. The steam is expanded in a stationary ring of nozzles through a large pressure difference, and then the high velocity is reduced to a small value in a series of fixed and rotating blades at constant pressure. Two stages is very common, but up to 10 stages have been used. This is

called velocity compounding. in contrast to the pressure compounding of a Parsons turbine. The combination of the stationary nozzle plate and two rotor rings separated by a fixed ring of blades is called a Curtis wheel, and one or two of these can be used as the initial stages of a large turbine with a high steam pressure input. Curtis wheels reduce the losses in the clearance space of the Parsons turbine, since the pressure is rapidly reduced. The steam velocity is reduced by about 400 fps on each moving ring, with an inital speed of 2000 fps.

Curtis turbines were licensed to General Electric Company in the U.S. and to the John Brown Company in the U.K., where they were used on many large ships. General Electric supplied its first turbogenerator, a 500kW unit with two stages of pressure compounding (two Curtis wheels) and a vertical shaft, in 1903. The vertical shaft was abandoned for a horizontal shaft by 1913, and the speed was raised from 500 to 1800 rpm. Curtis turbines are widely used on ships because of the lower shaft velocity. They may be used as the astern turbine beside the main ahead turbine (turbines cannot be reversed). Westinghouse and Allis-Chalmers appear to have employed Parsons turbines.

Because random molecular motion, heat, is involved in the operation of a steam turbine, thermodynamics must be used to analyze the energy relationships. One important consequence of this is that all the energy supplied to the steam cannot be recovered by the turbine: a certain fraction must be rejected at a lower temperature. The processes involved as the water is heated, evaporated, expanded and returned to its original state can be represented by the Rankine cycle, illustrated at the left. The

coordinates are the enthalpy h and the entropy s per unit mass. Starting with water at the pressure of the boiler, point a, it is heated at this constant pressure until it vaporizes completely and even hotter at point d (the difference between the final temperature and the temperature where the water is completely vaporized is called the superheat. The heat source is generally at a much higher temperature than the water or steam, so it is not difficult to provide superheat. Then the steam is expanded adiabatically--that is, without heat transfer--until its pressure reaches the lower pressure of the cycle at point e, which may be in a condenser cooled in some way. This is usually the case in a reciprocating engine or a turbine since the steam passes through very rapidly. Now the steam is compressed at constant pressure until it is completely liquefied at point f. Heat is rejected during this process. Finally, the water is pumped adiabatically up to the pressure of the boiler at point a, closing the cycle.

The heat absorbed in a reversible process at constant pressure is equal to the increase in enthalpy of the working substance. The enthalpy is the sum of the internal energy and the product of the pressure and the volume, H = U + PV, and is given as a function of temperature and pressure in steam tables. The heat transferred during the two isobaric processes can be calculated from the difference in enthalpy. The net work done is the difference in these two values, and the thermodynamic efficiency of the cycle is the ratio of the net work to the heat input.

The heat absorbed is H(d) - H(a), the heat rejected is H(e) - H(f), so the work done is W = H(d) - H(a) - H(e) + H(f) and the efficiency is W/[H(d) - H(a)]. As an example, suppose the boiler pressure is 200 psi (1379 kPa), the condenser pressure is 15 psi (103.4 kPa), and the superheat is 100°F (55.6 °C). From the steam tables, H(d) = 1258 Btu/lb, H(e) = 1054 Btu/lb, H(a) = 181.8 Btu/lb, H(f) = 181.2 Btu/lb. The heat absorbed is 1076 Btu/lb (2503 kJ/kg), the

heat rejected is 873 Btu/lb (1952 kJ/kg), so the work done is 203 Btu/lb (472 kJ/kg) and the thermal efficiency is 0.19.

Note that point e is just within the saturation curve, so there will be little condensed water at this point and so during the expansion. One of the important benefits of superheating is eliminating this condensed moisture, which can harm the turbine, as we see here. Also, more work can be obtained in the same quantity of steam. The effect on the efficiency is not very great, however.

The first attempts to apply the steam turbine to railway locomotives usually tried to include the components that led to high efficiency in static applications, which were high=pressure water-tube boilers and condensers, and this was the main reason for early failure. Water-tube boilers were complicated, delicate and lacked reserve steam capacity. Condensers were not only large and required cooling, but also made some form of artifical draft necessary for the fire. These were not drawbacks for static service, where there was ample room, no vibration and steady operating conditions, but were very troublesome in railway applications. Turbine rotational speeds were also too high for convenience.

In marine and turbogenerator service, the moving parts had low inertia and could be started easily. In railway service, the turbine had to accelerate the whole train from rest. When turbine velocity is zero, the steam still rushes through the passages and provides a large impulsive force, just as a reciprocating engine does. In fact, the force is twice that exerted at full speed. However, since no work is done at rest, the steam is not decelerated and exits at full velocity. The reciprocating engine uses little steam at rest or when moving slowly, while the turbine prodigiously wastes steam. This is a problem that was never satisfactorily solved for direct-drive turbines

In Sweden, Frederik Ljungström (1875-1964) worked to develop a turbine that would be suitable for locomotive service. His first experiments, after 1921, included a condenser, as did the experimental locomotive he built in England in association with Beyer-Peacock in 1926-1928. These engines developed 2000 hp at a turbine speed of 10,500 rpm through triple reduction gears at a ratio of 25.2 to 1. In 1932 he built three very successful 2-8-0 locomotives with standard boilers and no condenser, driven through a jackshaft geared to the turbine under the smokebox, that served until the line was electrified in 1950. These engines were an inspiration to William Stanier in designing his Turbomotive of 1935.

In 1935, Sir William Stanier (1876-1965), Chief Mechanical Engineer of the London, Midland and Scottish Railway, created a steam turbine locomotive from an existing Princess Royal class 4-6-2 passenger locomotive by using a Ljungströ&m turbine with a transverse axis placed below the smokebox and driving the leading driving axle through double reduction spur gears and a quill drive. The main forward turbine had 18 rows of blades fed by 6 steam inputs to 6 Curtis-type units, supplying 2400 hp at 7060 rpm from the boiler pressure of 250 psi. The boiler was a standard fire-tube boiler. The smaller reverse turbine had 4 rows of blades. To start a train, opening the first set of nozzles would supply sufficient impulse force, and as the locomotive accelerated the steam would be decelerated in several stages of velocity compounding. When the locomotive was up to speed, the turbine would be rotating fast enough to decelerate the steam from all the nozzles. That is, the turbine was to some degree a variable-speed machine, which suited it much better to railway service. Exhaust steam supplied the draft as in a normal locomotive. This locomotive, 6202 (46202 in Bristish Rail days), was completely satisfactory in service, but it was not duplicated. When there were

troubles with the main turbine in 1949, the engine was withdrawn from service. Since Sir William was no longer around to fix things, the locomotive was rebuilt as a standard reciprocating engine in 1952. It was damaged beyond repair the same year in the Harrow and Wealdstone disaster.

In 1938, General Electric in the U.S. built two steam-turbine electric locomotives for the Union Pacific. These were 2500 hp 2-C+C-2 engines for passenger service intended for operation coupled or singly. These units had Babcock and Wilcox water-tube boilers supplying steam at 1500 psi and air-cooled condensers. They burned Bunker C oil, which was then very cheap. They had two 12-pole DC generators and 6 traction motors. The compound HP and LP turbines operated at 12,500 rpm, reduced by gearing to 1200 rpm for the generators. They were the only condensing locomotives ever used in the United States. The UP returned them to GE as unsatisfactory, although they seem to have operated successfully during a power shortage on the Great Northern Railway in 1943. They were broken up at the end of World War II.

In 1947, the Chesapeake and Ohio received three steam-turbine electric locomotives from Baldwin-Westinghouse, numbers 500, 501 and 502. These had normal coal-fired boilers delivering steam at 310 psi, no condensers, developing 6000 hp. They were very troublesome for a variety of reasons, including coal dust in the electrical equipment, and were scrapped by 1950.

Baldwin tried again in 1954 with a 4500 hp C+C-C+C freight locomotive for the Norfolk and Western, numbered 2300. The Babcock and Wilcox water-tube boiler worked at 900 psi, fired with powdered coal. The DC generator supplied 12 traction motors. This locomotive was used in pusher service, and probably gave no improvement in fuel economy. It was withdrawn in 1958.

In 1944, the Pennsylvania Railroad produced a locomotive very similar in principle, but much larger. This was the Class S2, number 6200, with wheel arrangement 6-8-6 and a turbine shaft between the 2nd and 3rd driving axles, with double reduction gears and quill drive between the frames. This engine weighed 290 tons in comparison to the 6202's 112 tons. The forward turbine produced 6900 hp, and the reverse turbine, usable up to 22 mph, 1500 hp. Westinghouse supplied the turbine, and Baldwin Locomotive Works the rest of the machine. As in the 6202, the boiler was of a standard type and the exhaust was used for the draft. This locomotive did well in service, but used a great amount of steam in starting. There were some troubles with the boiler; one engineer claimed that the steady draft from the turbine exhaust did not shake up the fire the way the pulsations of a reciprocating engine did, and this was the cause of the problem. This locomotive was withdrawn from service in 1949 and scrapped in 1953.

Gas Turbines

The working fluid in a gas turbine is a permanent gas, in contrast with a condensable vapour in the steam turbine, produced in a gas generator at high presure by continuous combustion in a combustion chamber. The combustion chamber is supplied with air for combustion by a compressor, normally driven by a turbine using the gas produced. This gas contains much more energy than is required for the compressor. A gas turbine requires neither a boiler nor a condenser, so it can be made very compact and light. The thermodynamic cycle is called a Brayton cycle in this case, which like the Rankine cycle has two isobars and two isentropes.

If the gas produced in the combustion chamber is expanded to a low pressure, it acquires a large velocity and, therefore, momentum. The reaction to the creation of this momentum is the output of the machine in the turbojet. If the turbine following the combustion chamber is increased in output, it can drive a larger ducted fan on the same shaft as the compressor, increasing the mass of fluid so the same momentum is created at a lower fluid velocity when it mixes with the gas from the gas generator. This is a fanjet. Most large aircraft now use fanjets because the smaller exhaust velocity produces less noise. The turbojet was introduced by Frank Whittle in 1930, and first used in 1937, but it was not widely applied until after World War II.

A gas turbine can also be designed to deliver power to a rotating shaft, instead of, or in addition to, the reaction force of its exhaust. It is then called a turboshaft engine. If the shaft power is used to turn a propeller, it is called a turboprop engine, frequently used on cargo planes and small airliners. The output shaft may be an extension of the shaft rotating the compressor and turbine, as in early turboprop engines. However, most turboshaft engines now consist of two parts, the gas generator and the free turbine, where the free turbine drives the output shaft. The gas generator need not be a rotary compressor. A diesel engine or a free-piston engine, designed only to produce gas, may be used instead. Diesel engines often use turbochargers driven by exhaust gases, in fact.

The turboshaft engine has found its widest application in helicopters because of its high power to weight ratio. For example, a Rolls Royce Gnome H1200 Mk660 turboshaft machine develops 1350 hp and weighs 314 lb. An EMD 16-567 medium speed diesel developing the same power weighs 30,000 lb. The first turboshaft machine was applied to a helicopter in 1951, and presently all but the smallest helicopters use them. These machines generally operate at a constant full power, which maximizes their efficiency.

An advantage of a turboshaft machine, in addition to its large power to weight ratio, is its large starting torque, similarly to a steam turbine, which adapts it to vehicular propulsion. Its disadvantages are a lower fuel efficiency, which at best is somewhat less than a diesel engine and even lower when operated below full design power, and an inconveniently high rotational speed, rarely less than 10,000 rpm, which is not easily applied. Although there have been many experiments, gas turbines are not currently widely applied outside of aeronautics, where their characteristics are optimum. The greatest competition to the turboshaft machine is the diesel engine, which by comparison is more fuel efficient and much more easily controlled. The recent increase in prices of liquid fuels has rendered gas turbines even less desirable.

A gas turbine requires considerable power to operate its compressor, and this power must be subtracted from the power output. This is the principal reason why the fuel efficiency of the gas turbine is so low, often half that of a diesel engine, and why the turbine appears most efficient at full power, since the power required to run the compressor is a smaller part of the whole in that case, not because the turbine is more efficient. Steam turbines (and reciprocating engines) do not require significant power to operate, only the work done in the feedwater pump and friction. Diesel engines require only a minor amount of work in the compression strokes. It is remarkable that gas turbine proponents did not realize that the large energy required just to operate the engine would make it very fuel inefficient compared to alternatives.

In 1940, the Great Western Railway ordered two gas-turbine-electric locomotives, one from Brown Boveri and one from Metropolitan Vickers. They were not delivered until after the war, the Brown Boveri in 1949 and the Metropolitan Vickers in 1952, to British Railways (Western Region), the successor to the GWR. The Brown Boveri locomotive was numbered 18000, the Metropolitan Vickers 18100. The 18000 was rated at 2500 hp, top speed 90 mph, and weighed 115 long tons. The turboshaft engine drove a DC generator supplying 4 traction motors, and the wheel arrangement was A1A-A1A (two three-axle bogies with the outer axles driven). The turboshaft engine had a recuperator (heat exchanger) and burned heavy fuel oil. An auxiliary diesel engine was provided to start the turbine and to move the light engine without starting the turbine. light fuel oil was used to start the turbine which had only a single shaft, unlike later turboshaft engines. Even with all the steps that had been taken towards economy, the engine still burned a great deal of fuel. It is interesting that of the total turbine output of 10,300 hp, 7800 hp was used by the compressor, leaving 2500 hp for the shaft work. Most of the fuel was used just to turn the compressor, not to do useful work.

The 18100 was rated at 3000 hp, top speed 90 mph, and weighed 129 long tons. There was no auxiliary diesel engine. The turbine burned light oil (aviation kerosene), had no recuperator, and a single shaft, as in the 18000. it drove three DC generators, each supplying two traction motors. The wheel arrangement was Co-Co with all axles driven. The generators were used to start the turbine with current from batteries. Its fuel economy was even worse than that of the 18000, and it was withdrawn first, in 1958, and converted to a 25 kV AC locomotive. The electrical systems of both locomotives were complicated, and there was at the time little expertise in electrical maintenance. The 18000 even ran with only three traction motors at the end, but still managed to do its duty. The locomotives were capable of hauling express trains, but the fuel costs were always excessive. The 18000 was withdrawn in 1960.

The only successful direct-drive turboshaft locomotive was the English Electric GT3 (the gas-turbine-electrics were considered GT1 and GT2), which underwent service tests in 1961, after a long development process in the 1950's under the engineer J. O. P. Hughes. By that time, British Railways had decided on diesel traction, so the locomotive never entered regular service and was not duplicated. This locomotive was built on a chassis like that of a steam 4-6-0, with a leading bogie and three coupled axles. The 2700 hp English Electric EM27L recuperative turboshaft engine was placed at the front, with longitudinal shafts. Air was filtered then compressed in 8 stages of axial compression and a final centrifugal stage. It passed through the recuperator, heated by the exhaust gases, and then into a combustion chamber where diesel fuel was injected and burned. The gases then passed through a 2-stage turbine driving the compressor and a 3-stage free power turbine before exhausting through the recuperator. The shaft of the power turbine drove the middle driving axle through a forward or reverse mitre gear. Spline clutches, patented by Hughes, connected one or the other gear. The mitre gear drove a transverse pinion shaft engaging a large gear on the driving axle. At the design speed of 90 mph, the 69-inch driving wheels rotated at about 88 rpm. The engine was started by an electric motor on the compressor shaft. This shaft also drove a parallel shaft with oil pumps that drove the DC generator through a belt drive. The gas generator section could idle with the locomotive stationary.

The tender contained the train heating boiler, fuel tanks and water tank (for the heating boiler). The engine and tender together weighed 123.5 long tons, the engine alone 79.8 long tons. The engine could do good work, but its fuel consumption was, as might be expected, miserably excessive.

The United Aircraft Turbo Train, which saw service in the U.S. and Canada between 1968 and 1982, was also direct-drive, using Pratt and Whitney of Canada ST6 turboshaft engines. These were a modification of the popular PT6 turboprop engines, derated to around 400 hp. The gas generator section had 3 stages of axial compression and one of centrifugal, a combustion chamber, and a single stage turbine, operating at 45,000 rpm. The power section contained a single stage turbine operating at 30,000 rpm. Two stages of planetary reduction gears reduced this to 1900-2200 rpm. There was one power unit at each end of a train set.

In 1948, the American Locomotive Company and General Electric, then associated in building diesel locomotives (Alco-GE) built a demonstrator gas-turbine-electric locomotive numbered 101. This engine was a B+B-B+B developing 4500 hp with 8 DC traction motors, weighing 250 short tons. It had a control cab at each end, unusual in the U.S. It burned No. 6 (Bunker C) heavy fuel oil, which was very cheap at the time. The Union Pacific was interested in high-horsepower locomotives to replace its large steam locomotives, and requested trials with the 101. It was repainted in UP yellow, and numbered 50, but was never owned by the UP and was returned later to Alco-GE. The trials were very successful, and the UP received 10 similar units in 1952 which had only one operating cab, numbered 51-60. All these units used a steam generator to supply steam for heating the fuel oil to 93°C to reduce its viscosity so it could be used. They also included a small diesel engine for hostling moves. These units were withdrawn in 1963-65.

15 more units were delivered in 1954, numbered 61-75, again very similar except for walkways beside a narrowed hood, and revised air intake facilities. The 7200 gallon fuel capacity was found to be inadequate, so fuel tenders carrying 24,000 gallons were added in 1955, and gradually added to all the gas-turbine locomotives. Some of these tenders were specially built, and some came from withdrawn steam locomotives. A cabless 1500 hp B-B diesel unit was generally run behind the tender to move the locomotive when the full power was not required, and to supply electricity for heating the fuel oil.

In 1958-61, 30 much larger 8500 hp gas-turbine-electrics, weighing 450 short tons and with a C-C+C-C wheel arrangement and 12 traction motors were delivered, and numbered 1-30. The turbines and generators were in the second car bodies, and fuel tenders from withdrawn steam locomotives were used. The locomotives included an 850 hp diesel engine for hostling, starting the turbine and exciting the dynamic brakes. These engines operated successfully between Omaha and Ogden, but were not allowed in Los Angeles because of the loud exhaust noise. All of these engines were withdrawn by 1970.

An experiment was made in burning pulverized coal in a gas turbine with the locomotive numbered 80 initially, then 8080, wich began tests in 1961. This strange engine consisted of an Alco-GE passenger diesel of 2000 hp, and a 5000 hp turbine in the car body of a Great Northern W1 2-D+D-2 electric locomotive. The pulverized coal was injurious to the gas turbine, so the attempt was deemed unsuccessful. The locomotive was withdrawn in 1968.

The overwhelming disadvantage of all these gas-turbine locomotives was their very poor fuel economy, since they burned about twice as much fuel as an equivalent diesel. As long as No. 6 fuel oil was very cheap, this was tolerable, but when prices began in rise in the 1960's the further use of the turbines became uneconomic. Since then, the problem has only worsened. This seems to be the problem with gas turbines in all applications as major prime movers except for turbojets and helicopters, where they have unique advantages.

Hovercraft, or air cushion vehicles, have been another application of the gas turbine, since the application is similar to that of helicopters, where high power and small weight and size are desired. The large SRN4, a car-ferry hovercraft that appeared in 1968, used four Rolls-Royce Proteus turboprop engines of 4000 hp each. Two were used for propulsion, and two for lift. The SRN5, a medium sized passenger hovercraft, used a 900 hp Rolls-Royce Gnome turboshaft, and its successor SRN6 a 1050 hp Gnome. Hovercraft are now rare in civil service, but the military use many as landing craft, since they make 70% of shorelines available instead of the 15% suitable for boats. The U.S. Navy LCAC (Landing Craft Air Cushion)-1 from 1986 uses four Lycoming TF-40B engines of 4000 hp each.

Seatrain Containers engined four ships with gas turbines in 1970. In 1982 they were re-engined with diesels because of poor fuel economy. The GTS (Gas-Turbine Ship) Finnjet, a large ferry, appeared in 1977, using two Pratt & Whitney FT4C-1 turboshaft engines, but in 1980 a diesel engine was added for use when the full turbine power was not required. It is quite common now for naval patrol boats to have a diesel engine for cruising, and a gas turbine for peak speed. There have been a few attempts to use gas turbines in cargo ships, but the overriding need for economy rules against them.

The U.S. Army M1 Abrams main battle tank, which appeared in 1980 and is still in service, uses a Honeywell AGT1500 turboshaft engine of 1500 hp. It is similar to engines used in helicopters, but weighs 2500 lb, which is no drawback in this application. The compressor has two spools (rotors) and the power turbine one. The power turbine rotates at a nominal 30,000 rmp, reduced by gears on the engine to 3,000 rpm at the output shaft, which is connected directly to the Allison automatic transmission. The engine can burn a variety of liquid fuels, including diesel, jet fuel and gasoline, with only small adjustments.

The turbine requires 10 gal. of fuel to start, burns 12 gal. an hour idling, and uses 1 gal. per mile when moving. The fuel tank holds 500 gal., and the service range is 289 mi. This is pretty much typical for such a gas turbine, and clearly shows why the gas turbine is not more widely used in vehicles. Scaling it down to a 150 hp output for a motor car, the fuel economy would not be greater than 10 miles per gallon, which is clearly unacceptable.

Chrysler Corporation, who designed the M1 Abrams tank, worked in the 1960's and 1970's to produce a turbine-powered motor car for general sale. 55 experimental 2-door coupes were produced in 1963 and tested by selected individuals. Two of these cars still exist and are operable. They had 130 hp turboshaft engines and a normal transmission. They were said to get 17 miles per gallon, but this is probably under optimum conditions, and in normal driving the economy would be much worse. At first the turbines produced too much nitric oxide for environmental regulations, but this was eventually solved. The very hot exhaust was another difficulty. The gas-turbine effort was abandoned in 1977 before any cars were manufactured for sale to the public, as a condition of a government bailout.

References

R. L. Daugherty and J. B. Franzini, Fluid Mechanics, 6th ed. (New York: McGraw-Hill, 1965). Chapters 15 and 16 deal with turbines, but the theoretical background is scattered in several previous chapters, chiefly 6 and 14. Machines are the most difficult part of engineering fluid mechanics, but the most fascinating part. It is remarkable that the conservation laws go so far to explain turbines.

J. Reynolds, Windmills and Watermills (New York: Praeger, 1970). Very well illustrated; covers all kinds of historic mills.

M. Vitruvius, De Architectura (Cambridge, MA: Harvard University Press, 1934. Loeb Classical Library #280). Vol II, Book X, Chapter V, pp. 304-307.

S. Strandh, A History of the Machine (New York: A&W Publishers, 1979). pp. 92-108. Well-illustrated.

P. N. Wilson, Water Turbines (London: HMSO, 1974). A Science Museum Booklet. Well-illustrated.

A. Jenkins, An Elementary Treatment of the Reverse Sprinkler, Am. J. Phys. 72, 1276-1282 (2004).

F. W. Sears, An Introduction to Thermodynamics, the Kinetic Theory of Gases, and Statistical Mechanics, 2nd ed. (Cambridge, MA: Addison-Wesley, 1953). Chapter 10. A good concise discussion of the Kelvin cycle.

J. H. Keenan, F. G. Keyes, P. G. Hill and J. G. Moore, Steam Tables (New York: John wiley and Sons, 1969).

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Composed by J. B. CalvertCreated 23 July 2003Last revised 11 February 2010

water turbines

Water turbines are basically fairly simple systems.  They consist of the following components:

intake shaft  - a tube that connects to the piping or penstock which brings the water into the turbine

water nozzle - a nozzle which shoots a jet of water (impulse type of turbines only) runner - a wheel which catches the water as it flows in causing the wheel to turn generator shaft - a steel shaft that connects the runner to the generator generator - a small electric generator that creates the electricity exit valve - a tube or shute that returns the water to the stream it came fro powerhouse - a small shed or enclosure to protect the water turbine and generator from the 

elements

Impulse vs. Reaction Turbines

Water turbines are also often classified as being either impulse turbines or reaction turbines.  In a reaction turbine the runners are fully immersed in water and are enclosed in a pressure

casing.  The runner blades are angled so that pressure differences across them create lift forces, like those on aircraft wings, and the lift forces cause the runner to rotate.

In an impulse turbine the runner operates in air, and is turned by one or multiple jets of water which make contract with the blade.  A nozzle converts the pressurized low velocity water into a high speed jet much like you might use with a garden hose nozzle. The nozzle is aligned so that it provides maximum force on the blades. 

Types of Turbines

There are many kinds of micro hydro turbine designs. Typical microhydro generators have outputs of 10 kilowatts (kW) or less and can generate either DC or AC current depending upon the design. You will often hear water turbines referred to as either Pelton or Turgo turbines.  These terms have to do with the structure of the water wheel inside the turbine. 

Turgo Turbines

Pictured here is a Turgo style wheel. A Turgo turbine is an impulse type of turbine in which a jet of water strikes the turbine blades.  The structure of a Turgo wheel is much like that of airplane turbine in which the hub is surrounded by a series of curved vanes. These vanes catch the water as it flows through the turbine causing the hub and  shaft to turn.  Turgo turbines are designed for higher speeds than Pelton turbines and usually have smaller diameters.

Pelton Turbines

A Pelton turbine is also an impulse turbine but in this type of turbine the hub is surrounded by a series of cups or buckets which catch the water. The buckets are split into two halves so that the central area does not act as a dead spot incapable of deflecting water away from the oncoming jet.  The cutaway on the lower lips allows the following bucket to move further before cutting off the jet propelling the bucket ahead of it.  This also permits a smoother entrance of the bucket into the water jet. 

Cross-Flow Turbines

A cross-flow turbine, also sometimes called a Michell-Banki turbine (from the name of the manufacturer) is a turbine that uses a drum shaped runner much like the wheel on an old paddle wheel steamboat.  A vertical rectangular nozzle is used with this type of turbine to drive a jet of water along the full length of the runner. One advantage of this type of turbine is that it can be used in situations where you have significant flow but not enough head pressure to use a high head turbine. 

Francis Turbine

The Francis type of turbine is a reaction type of turbine in which the entire wheel assembly is immersed in water and surrounded by a pressure casing.  In a Francis turbine the pressure casing is spiral shaped and is tapered to distribute water uniformly around the entire perimeter of the runner.  It uses guide vanes to ensure that water is fed into the runners at the correct angle.

Propeller Turbine

A propeller turbine is just what its name implies.  It uses a runner shaped just like a boat propeller to turn the generator.  The propeller usually has six vanes.  A variation of the propeller turbine is the Kaplan turbine in which the pitch of the propeller blades is adjustable.  This type of turbine is often used in large hydroelectric plants.  An advantage of propeller type of turbines is that they can be used in very low head conditions provided there is enough flow.

Selecting the Best Type of Turbine

Which type of water turbine is best for a particular situation often depends on the amount of head (water pressure) you will have in your location and whether you want to suspend the turbine in the water  (reaction) or whether you want to use jets of water (impulse).  By

looking at these factors together you can get some indication of what type of turbine design will work best: