The Impulse Steam Turbine

The Rateau steam turbine is a typical modern multistage impulse turbine. Fig. 4 shows a longitudinal section through a machine of this type constructed in 1919 by the Metropolitan Vickers Electrical Co. for the Dalmarnock power station, the machine in question having a maximum continuous rating of 18,750 K.W. at a speed of 1,500 revs. per minute. The shaft carries altogether 15 wheels keyed upon it, each wheel running in a separate compartment. The diaphragms dividing the compartments from each other are fitted with nozzles, in which the steam undergoes successive partial expansions in its progress through the turbine, and from which it emerges with a velocity due to the drop in pressure which it has undergone. This velocity is abstracted by the action of the blading which the steam enters after issuing from each set of nozzles, the steam being brought more or less to rest and the energy due to its partial expansion appearing as useful mechanical work on the shaft.

In all large machines of this type, especially when they are working with a high vacuum, the volume of the steam at the low-pressure end becomes so great that the length of the turbine blades at this part tends to become excessive. In the machine in question a part of the steam, after having passed through io wheels, being then at a pressure of about 4 lb. abs. is passed out of the casing and used to heat the boiler feed water, the feed heater for this purpose being shown in section in the illustration. This practice diminishes, FlG.2 to a certain extent, the volume of the steam which passes through the remaining wheels, but in the machine illustrated, the makers have employed a special device to permit a reduction of the length of the last row of blades. The steam which enters the last wheel but one, is divided into two parts, that which acts on the outer annulus of the blade ring passing away directly to the condenser, and only that which acts on the inner annulus being afterwards conducted to the final wheel. The blading on the last wheel therefore only deals with about half the weight of steam which passes through the preceding wheel, and it can handle this amount at a very reduced pressure.

A rigid coupling is fitted to connect the turbine shaft with the shaft of the alternator, and the turbine shaft is located axially by means of an adjustable thrust block of the Michell type which takes care of any unbalanced end pressure along the shaft.

The mean diameter of the blading of this machine is 84 in. and the length of the last row of blades is 24 inches. The mean circumferential velocity of the blading is 550 ft. per second, the tip velocity of the longest blades being 708 ft. per second. The turbine is designed to work with a stop-valve pressure of 250 lb. per sq. in., a temperature of 650° F. and a vacuum of 0.9 in. of mercury, thus having an available heat drop of 455.2 B.Th.U. per lb. of steam. Under these conditions the guaranteed steam consumpion is 10.2 lb. per K.W.H., this figure being the same for both 15,000-K.W. and 18,750-K.W. load.

The Ljungstrom Steam Turbine

In the early days of the reaction turbine, a number of machines were built by the Hon. C. A. Parsons in which the steam passed radially outwards between two discs carrying rings of blades projecting axially from their opposed faces, one disc being stationary and the other driving the shaft of an electric generator. Mechanical difficulties were experienced, principally due to the distortion of the discs by uneven heating, and the design was soon completely abandoned in favour of the axial flow type. In the year 1910 Messrs. Birger and Frederic Ljungstrom of Stockholm built an entirely new type of radial flow reaction machine which was conspicuous not only for its mechanical merits but for its great efficiency. The Ljungstrom turbine is now being developed in sizes up to 30,000 K.W. capacity, and is manufactured in Great Britain by the Brush Electrical Engineering Co. and in the United States by the General Electric Company. The steam is admitted between two discs and in its passage from their center to their circumference it passes through concentric blading rings mounted alternately on the faces of the discs. The discs revolve at equal speeds in opposite directions, so that the relative blade speed is twice as great as in an ordinary machine of the same revolutions and diameter, with the consequence that for equal efficiency the number of blade rings is only one quarter as great. Each disc is fastened to the end of a separate alternator shaft, and as the turbine comes up to speed, the alternators come automatically into synchronism and operate in parallel so that they act virtually as a single machine.

F I C. 8 The mechanical construction of the Ljungstrom turbine is unique. Fig. 5 shows a section through a machine to develop 5,000 K.W. at 3,000 revs. per minute, the illustration including the two ends of the alternator shafts, upon which the turbine discs are mounted. The construction will be better understood by reference to figs. 610 which show the most important details to a larger scale. The steam enters the turbine through the branched pipe shown in fig. 5 and thence passes to the centre of each disc through the holes marked 2 in figs. 6 and 7, which illustrate the disc alone. It will be seen that the face of the disc contains a number of circumferential grooves. Each groove carries a blade ring, shown to a larger scale in fig. 8, in which i represents the disc; 2 a seating ring; 3 a caulking strip; 4 an expansion ring; 5 and 6 rolling edges; 7 steam packing strips; 8 caulking strips; 9 strengthening ring; io dovetail profile ring; 11 the blade itself. These blade rings are interleaved as they project alternately from the discs, and steam leakage is checked by the thin fins 7. The blades are made from drawn steel strip and are welded solidly into the strengthening rings io.

The conical steel expansion ring, 4, is a particularly important feature of the blading system, and similar rings will be seen at 1 in fig. 7, where they serve to connect the three parts of which the disc is composed. The ring of holes shown at 3 in fig. 7 is to admit the extra steam necessary for overload conditions, the inner rings of blading being then short circuited. The pressure of steam in the blading naturally tends to thrust the discs apart. It is therefore balanced by an arrangement of " dummies," or labyrinth discs, as shown in fig. 5. A detail of the labyrinth, to a larger scale, is given in fig. 9. To prevent the high-pressure steam leaking along the shafts, these are fitted with labyrinth packings, a portion of one of these packings being illustrated in fig. io. The whole packing consists of a number of rings keyed alternately to the shaft and to the housing and having deep grooves turned circumferentially in the sides. The rings interleave in the manner shown, the edges of the grooves being bent down so as practically to make contact with the walls of the grooves in the adjacent rings. An extremely effective and compact labyrinth is thus formed.

The efficiency of the Ljungstrom turbine is remarkably high for machines of moderate capacity. Independent tests of a 1,500-K.W. machine, after 15 months' service, have shown a steam consumption of 11.95 lb. per K.W.H., with steam at 208 lb. per sq. in. abs. and 569°F. temperature, and a vacuum of 1.29 in. Hg. The no-load consumption of the same machine was only 1340 lb. per hour, or 7.5% of the full-load consumption.

The appearance of a complete Brush-Ljungstrom turbo-alternator is shown in fig. i 1.

and vacua as high as 29.1 in., with the barometer at 30 inches. No commercial reciprocating engine could work under such steam conditions with anything like the efficiency a turbine would show in similar circumstances.

Speeds of Turbines

The principal use of steam turbines on land being to drive electric generators, the speed at which these can be run controls to a large extent the speeds for which turbines can be designed. Continuous current turbo generators are comparatively small in size and few in numbers, and as these are almost exclusively driven through reduction gearing on account of the diffioilties of commutation at high speeds. their characteristics do not materially affect the design of the turbines. All large land type turbines are directly coupled to alternators and as the frequency of alternation is wry  ?

'? ' Steam Conditions in Turbines. - The steam consumption of a turbine depends not only upon the excellence of its mechanical design but upon the amount of heat in every pound of steam delivered to the turbine which is available for conversion into work. The available heat may be increased by increasing the pressure and temperature of the entering steam and by lowering the pressure at which it is exhausted. Progress in these directions is limited by constructional difficulties, but nevertheless striking advances have been made. The best practice of the time may be exemplified by the io,000-K.W. machine installed in 1910 at the Carville station of the Newcastle Electric Supply Co., which operated with steam at 190 lb. per sq. in. gauge pressure and a superheat of 150° F. at the stop valve, and a vacuum of one in. of mercury. Under these conditions there was an available heat drop of 407.2 B.Th.U. per lb. of steam. In 1916 a machine of 11,000-K.W. was installed in the same station with a stop-valve pressure of 250 lb. gauge, a superheat of 244°F. and a vacuum of one in. of mercury. This change in steam conditions increased the heat drop to 450.2 B.Th.U. per lb. of steam. In 1921, a machine having an economical rating of 25,000 K.W., installed at Manchester, utilized a stop-valve pressure of 350 lb. gauge, a superheat of 264° F. and a vacuum of 0.9 in. of mercury, thus working with an available heat drop of 484.7 B.Th.U. per lb. of steam. It may be taken that modern practice sanctions steam pressures up to 350 lb. per sq. in., temperatures up to 700 F.

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.? ?' ? ? ?? ? ?? 4 ' 'r % ,l i ' " .//," %i standardized in Great Britain at 50 and 25 cycles per second, and in the United States and Canada at 60 cycles per second, the speeds of turbines have to be correspondingly standardized. If F denotes the frequency, and N the number of pairs of poles of the alternator, then F N 60 denotes the only possible speed, in revolutions per minute, at which the turbine can be run. In Great Britain the standard turbine speeds are therefore 3,000, 1,500, 1,000 and 750 revs. per minute, while for 60 cycles they are 3,600, 1,800, 1,200 and 900 revs. per minute. It is naturally desirable to build any turbine for the highest speed at which the desired output can be economically obtained. Considerations of stress limit the dimensions for a given speed, and the dimensions limit the volume of steam which can be ?,..,? j/.,,./, efficiently utilized, so that in practice a fairly definite limit of power corresponding to each speed is obtained.

Turbo alternators have been satisfactorily built, having a maximum continuous rating of over 6,000 K.W. at 3,600 revs., the limit of economical rating for this speed being at the present time about 5,000 K.W. At 3,000 revs. per minute the maximum continuous rating is about 13 ,750K.W., the economical output being 12,500 K.W., the machine built in 1921 for the Liverpool corporation being of this size. There are several turbines with a maximum continuous rating of 30,000 K.W. running at 1,800 revs. per minute, and at 1,500 revs. per minute, a continuous rating of 35,000 K.W. appears to be about the present limit, both for impulse and reaction machines. Machines of this size and speed were installed in Chicago in 1918, and in Paris in 1921. In machines of 30,000 K.W., and over it is not uncommonly the practice to use two or more generators, the whole unit really consisting of mechanically independent highand low-pressure turbines. Certain units built by the Westinghouse Co. in the United States have a maximum rated output of even 60,000 K.W., but these in fact consist of three independent turbo generators, through which the steam passes in series. This multiplication of cylinders and shafts is of course the usual custom in connexion with marine turbines.

The practice of dividing a turbine into two parts, namely a highand a low-pressure cylinder arranged in tandem, was first introduced many years ago and the design has been standardized for the larger machines of the reaction type. It has the advantage that the separate casings are shorter and less liable to distortion than an equivalent single casing, while by making the low-pressure drum of larger diameter and of the double flow type, the requisite area for the enormous volume of the low-pressure steam is conveniently provided for. The importance of this will be realized from the fact that in a modern turbine the ratio of expansion of the steam may be over 800.1. Fig. 1 shows a section through a two-cylinder tandem turbine as constructed by the Parsons Co., and fig. 12 illustrates the appearance of a two-cylinder side by side arrangement as used with gearing for marine purposes.

Governing of Steam Turbines

The speed regulation of turbines is effected by a centrifugal governor driven by worm gearing from the main shaft, which acts in the case of all reaction machines by controlling the pressure at which steam is admitted to the casing. In machines constructed either wholly or partially on the impulse principle, the governor may open up successively extra nozzles or groups of nozzles as the load increases. Loads in excess of the maximum economical load are sometimes provided for by admitting steam to the turbine at some intermediate point, thus raising the pressure there above the normal full load pressure and enabling the turbine to do more work, although at a somewhat reduced efficiency. The by-pass valves for this purpose may be hand operated, but as a rule they are under the control of the governor and are thus automatically opened when the extra steam is required to maintain the speed. In view of the close governing required on turbo generators and of the size and weight of the valves which have to be operated, it is the universal practice to employ a relay arrangement on all but the smallest machines, the governor merely controlling the position of a small balanced piston valve which admits oil under pressure to one side or the other of a piston which does the actual work of operating the valves. The pressure oil is supplied from the lubrication system of the turbine.

Bearings and Lubrication

The old sleeve bearing, originally devised by Sir Charles Parsons and employed on his earlier machines, has been entirely superseded and turbine bearings are now constructed on ordinary lines, differing only from slow-speed bearings in their proportions and in the provision necessary for their proper lubrication. The bearings are made in two halves, split horizontally, the interior working surfaces being of white metal cast and anchored into the " steps " which are of cast iron or bronze. These are usually fitted with shimplates to provide a fine vertical and lateral adjustment, and are frequently supported in spherical seatings to permit of a certain amount of self-alignment. Safety strips, often of bronze, which normally lie slightly below the surface of the white bearing metal, are usually provided. These are intended to carry the weight of the shaft safely in the event of the white metal being melted out, and thus prevent injury to the blading until the machine can be stopped. In all turbine bearings the important thing is to insure a copious supply of lubricating oil, not so much for lubrication as to carry off the heat generated by friction and to maintain the bearings at a reasonable working temperature. Water-cooled bearings have been used by some makers, but the most approved practice is to rely on the flow of oil through the bearing to keep its temperature down. Oil is usually delivered to the bearings at a pressure of about 15 lb. per sq. in., a gauge being provided on each bearing to indicate whether the pressure is being maintained. On modern turbines an automatic device operated by the oil pressure is fitted, which shuts the machine down in case of any failure of the oil supply.

Bearings up to 8-in. diameter are usually bored larger than the shaft to the extent of about 0.004 in. for every in. of shaft diameter. In larger bearings the clearance is proportionately less. This somewhat large clearance enables the heat to be carried away by the continuous wash of fresh cool oil. The shaft, when running, is kept out of metallic contact with the bearing by a thin film of oil continually dragged underneath it by its rotation. It is this film which supports the shaft, and the pressure of the latter on the bearing must therefore not be greater than the film can stand. Theory and experiment both indicate that the greater the surface velocity of the shaft, the more effectively is the film established, and the greater therefore the permissible load on the bearing. But the fact that bearings have to start from rest, when the film is imperfect, imposes a practical limit to the load which can be imposed.

A formula connecting permissible pressure with velocity, given by Mr. F. H. Clough, is P =17 1,/ V, in which P denotes the pressure in pounds per sq. in. of projected area, and V = velocity of surface of shaft in ft. per second. This is said to be applicable to bearings of normal design in which the length is from twice to three times the diameter. Many designers, however, use the rule that P X V must not exceed 5,600, a simple rule which gives good results in practice, and probably has a considerable margin of safety when the speeds are high and when there is no vibration. One large manufacturing firm is said to take the permissible pressure per sq. in. of projected area as ranging from 167 to 235 when the velocity ranges from 20 to 73.5 ft. per second. Modern practice is to give P a value not exceeding 150 lb. in bearings where the velocity is not greater than 30 to 35 ft. per second, and the temperature comparatively low, say, moo° to m mo° F. Such conditions would apply to low speed marine turbine bearings. The bearings of land turbines usually work at temperatures from 120° F. to 160° F., but the latter temperature should not be exceeded, as not only is the oil injured, but its viscosity is so low that the supporting film is thinned and the margin of safety becomes low.

For the heat generated in a turbine bearing Stoney gives the formula B.Th.U. per hour - 19l 32 v in which l and d are respectively the length and diameter of the bearing expressed in in., v is the velocity of the surface of the shaft in ft. per second, and t is the temperature on the Fahrenheit scale. The same authority quotes the following formula as often used in slow-speed marine practice: B.Th.U. per hour = lXdXv 1 ' 38 . Treating the heat which escapes by radiation and conduction as negligible, these formulae give the heat which has to be carried away by the oil and extracted by the oil cooler. This heat of course is the equivalent of the work lost by friction in the bearing. The increase of temperature of the oil passing through the bearing should not exceed 10° to 20°F., and if the specific heat of oil be taken at 0.31 the minimum quantity of oil required for each bearing may be readily calculated. In practice it is advisable to increase this calculated fig. by from 30 to 50%, to allow a margin for steam heat travelling along the shaft and other contingencies.

Mechanical Gearing of Turbines

The De Laval steam turbine, consisting of a single impulse wheel running at a speed of 30,000 to 1 0,000 revolutions per minute according to the size, has always contained reduction gearing as an integral part of the machine because such speeds are far too high for driving ordinary machinery. Turbines of this type have, however, only been built for powers up to a few hundred horse-power, and although the use of reduction gear may be dated from the introduction of the Laval turbine in 1886, it never became a recognized practice for large powers until it was developed by Sir Charles A. Parsons as the solution of the problem of marine propulsion. De Laval had shown that it was possible to transmit power satisfactorily through mechanical gearing running with a circumferential velocity of over moo ft. per second. The gears he used were of the double helical type with a spiral angle of 45 degrees. The reduction ratio was usually about 10:1, and the pitch of the teeth varied from 0.15 in. to o

26 in., according to the power of the turbine. The De Laval gear embodied all the features which have been found necessary to the successful performance of modern gears transmitting several thousand horse-power through a single pinion. The double helical form of tooth of comparatively fine pitch has been retained, as this design eliminated end thrust and insured silent running by reason of the number of teeth simultaneously in contact. Ample lubrication of the teeth by means of oil jets was also employed by De Laval, who succeeded in producing durable and satisfactory gears which had an efficiency of about 97 per cent. These gears are used up to about 600 H.P. which is the commercial limit of the type of turbine for which they are designed.

Steam turbines of any type, designed with due regard to efficiency and cost of manufacture, require to run at a far higher speed of revolution than is practicable for screw propellers, especially when the latter are employed to drive ships of moderate speed. The coupling of a turbine, therefore, directly to a propeller shaft involves a compromise in design, in which the speed is greater than desirable for the propeller yet so low as to require the turbine to be of greater size and weight and of lower efficiency than it would otherwise be. In the case of high-speed vessels direct coupling afforded a commercially acceptable solution of the problem of turbine propulsion, and for vessels of eighteen knots speed and over, such as warships, passenger liners and cross-channel boats, the direct coupled turbine soon became the recognized driving power. But ordinary cargo vessels and tramp steamers, with an average speed of 10 or 12 knots, were outside the practical field of the steam turbine until speed reduction gearing was available to couple a high-speed turbine with a slow moving propeller. It was really the problem of the slow speed ship which brought about the development of marine turbine gearing, and now that the mechanical difficulties have been overcome, the direct coupled marine turbine is likely to be largely displaced by the geared turbine in all classes of vessels.

The first example of marine turbine reduction gearing appears to have been in 1897, in connexion with a twin screw launch, in which the Parsons Marine Steam Turbine Co. fitted a to-H.P. turbine driving the two shafts by means of helical gearing having a speed ratio of 14:1. The result appears to have been entirel y satisfactory. Other experiments followed, and in 1909, the "JVespasian," a cargo vessel of 4,350 tons displacement, was fitted with geared turbines driving a single propeller. This vessel had previously been equipped with triple expansion reciprocating engines of the usual type, and before these were removed they were put into perfect order, and very careful tests were made to determine the efficiency and performance of the vessel. The geared turbines drove the same shaft and propeller as the engines had done and were supplied with steam from the same boilers. The power developed was about 1,000 H.P. and the shaft ran at 70 revs. per minute, the gear reduction ratio being 19.9:1. The installation of the turbines resulted in an increase of about one knot in speed for the same coal consumption, and the results of the trials were highly satisfactory in every respect, and convincing as to the advantages of geared turbines over reciprocating engines. After the " Vespasian " had run 18,00o m. in regular service, the pinion was examined and found to be in perfect condition, the wear not exceeding 0.002 inches. (See Trans. I.N.A. 1910 and 1911.) The success of the " Vespasian " led to rapid developments. In 1910 the British Admiralty adopted gearing, the torpedo boats " Badger " and " Beaver " being the first warships to be equipped with geared turbines. In these vessels each L.P. turbine drove its shaft directly, but the H.P. and cruising turbines were geared to a forward extension of the turbine spindles. At full load about 3,000 H.P. were transmitted through each set of gearing. Six years later complete gear drives had become the standard practice for British war vessels of all types and by 1920 some 652 gears, transmitting an aggregate of 7,280,000 shaft H.P., were fitted, or on order for the royal navy (Tostevin, Trans. I.N.A. 1920).

The appended particulars of H.M. battle cruiser " Hood," of 144,000 shaft H.P., which was completed in 1920, will indicate the development of gearing for turbines and will at the same time indicate the proportions which have been adopted.

Horse-power of H.P. turbine .	17,500
Horse-power of L.P. turbine. .	18,500
Revs. per minute H.P. turbine	1,497
Revs. per minute L.P. turbine .	1,098
Revs. per minute propellers .	210
Diameter of pitch circle, in H.P. pinion	20.174
Diameter of pitch circle, in L.P. pinion	27.51
Diameter of pitch circle, in gear wheel	143.787
Number of teeth H.P. pinion	55
Number of teeth L.P. pinion.	75
Number of teeth gear wheel .	392
Circular pitch, in. .	1.1533
Normal pitch, in. .	0.9985
Helical angle of teeth .	29'57'
Effective width of pinion face, in.. .	73.25
Number of teeth engaging .	36.6
Total length of tooth contact, in H.P. pinion	128.8
Total length of tooth contact, in L.P. pinion	132'9
Load in lb. per in. on total H.P. .	965
Width of tooth face (= P) L.P. .	1030
Value of K in formula P=K 'P.D.) H.P.	215
Value of K in formula P= K p D L.P.	196
Velocity of pitch line ft. per second .	132 Gearing H.M.S. "Hood." The earliest practice with regard to marine gearing was to use a helical angle of 23' in conjunction with a normal pitch of 0.75 inches. Subsequently a helical angle of 45° which had been found successful in the De Laval gears was adopted with the idea of securing quieter running, but modern practice favours an angle of about 30', as teeth cut at this angle will run silently, while their less inclination to the axis of the shaft results in increased efficiency and greater effective strength. The usual angle of obliquity is 141', and the normal pitch except for the very largest gears is nearly always 0'583 inches. The permissible pressure in lb. per in. of axial length of the pinion is determined by the formula P = KI DD in which D is the pitch diameter of the pinion in in. and K is a constant which has a value usually between the limits of 160 and 230. This formula represents the practice of the Parsons Co., who have a preponderating experience on these gears. There is reason for believing, however, that the pressure might be made more directly proportional to the pitch diameter. A circumferential velocity of 150 ft. per second on the pitch line has been successfully employed, and it is possible that this might be exceeded with safety. For turbine gearing the British Admiralty specify that the pinion shall be made of oil-hardened nickel steel, containing not less than 3.5% of nickel and from 0.30 to 0.35% of carbon, with an ultimate tensile strength of 40 to 45 tons. The gear wheels are to be of steel of 31 to 35 tons ultimate tensile strength with 26% elongation in two inches. It is essential that the teeth of turbine gearing shall be very effectively lubricated, and to insure this, oil under a pressure of from 5 to 10 lb. per sq. in. issues in jets which flood the teeth immediately before they come into engagement. A further point of primary importance is that the fitting and alignment of the gears must be as perfect as possible and great care must be taken to maintain and insure these conditions. In America the practice has been adopted of carrying the pinion on a floating frame with the object of permitting a certain amount of self-alignment, but the required correction is of such a very small order of magnitude that the advantages of the system are doubted by many engineers. Gearing of British naval turbines is exclusively of the single reduction type, but double reduction gearing has been largely introduced into cargo vessels during recent years, with the object of efficiently using turbine machinery for ships of comparatively low speed without involving too large a reduction ratio for a single pair of gears. The general design follows - mutatis mutandis - that of single reduction gear. Numerous tests have been carried out to determine the mechanical efficiency of gears of the kind described. The mechanical efficiency of a single reduction gear at full load should be over 98%, and 98.5% has been recorded. With double reduction gear the efficiency is about 97.0%. These figures include bearing friction. No method of obtaining speed reduction by hydraulic or electrical methods has yet been devised which will approach the efficiency obtainable with mechanical gearing. Fig. 12 gives a good idea of the shafts of the Cunard liner " Transylvania." built by Scotts Shipbuilding & Engineering Co. Ltd. An exactly similar set of machinery was fitted to drive the other shaft. The " Transylvania " was the first Atlantic liner to be fitted with geared turbines. The vessel had a length of 548 ft. and a gross tonnage of 14,500. Each set of turbines and gearing was designed to develop and transmit 5,500 shaft H.P. and they drove the vessel at 16.75 knots. The turbines ran at 1,500 revs. per minute and drove the propellers at 120 revs. per minute, the ratio of the gearing being therefore 12.5:1. In the illustration the pinion in the foreground is driven by the high-pressure turbine, the steam from which operates the low-pressure turbine on the other side of the gear wheel. The astern turbine, consisting of an impulse wheel followed by a comparatively few rows of reaction blading, is seen on the forward end of the low-pressure turbine. The size of the machinery is indicated by the fact that the gear wheel is to ft. in diameter and 5 ft. wide. Theory Of The Steam Turbine Throughout the ensuing section, heat is expressed in foot pound centigrade units, and the symbols employed have the following meanings: H =Total heat in one lb. of steam. H,, =Total heat in one lb. of steam at the supersaturation limit or Wilson line. H, =Total heat in one lb. of steam at the saturation line. V = Volume of one lb. of steam in cub. ft. V30 = Volume of one lb. of steam in cub. ft. at the Wilson line. V, = Volume of one lb. of steam in cub. ft. at the saturation line. V4, =Volume of one lb. of steam in cub. ft. after an isentropic expansion. p = Absolute pressure in lb. per sq. in. t, =Saturation temperature (centigrade). = Efficiency ratio. n = Hydraulic efficiency. u =Thermodynamic head expended in isentropic expansion. U =Thermodynamic head expended in a practicable expansion. y = Index for adiabatic expansion. X =Index for an expansion at constant efficiency. = Flow of steam in lb. per second. = Number of pressure stages in an ideal turbine. Number of pressure stages in a practicable turbine. Blade height of an ideal turbine, in in. Blade height of a practicable turbine in in. Mean diameter in in. of a row of blades. = Drum diameter of a reaction turbine. = Joules equivalent. (J I oo) 2 mov i ng rows only being included in the summation. From the standpoint of hydraulics there is a somewhat close analogy between a steam turbine and one operated by water. An essential feature in both cases is that the potential energy which a fluid possesses in virtue of its pressure is utilized to maintain a flow through a set of nozzles or guide vanes. In the ideal case of frictionless flow the energy possessed by unit mass of the fluid is the same whether it be at rest in the reservoir or whether it forms part of the jet and has accordingly a kinetic energy due to its velocity. The theoretical velocity of efflux of a gas can accordingly be determined by equating the kinetic energy to the work which the same mass of fluid could perform were it allowed to expand, behind the piston of an ideal engine, from the pressure of the reservoir down to that of the receiver into which the discharge takes place. In thus expanding behind a piston, W, the theoretical work done per lb. of the fluid is given by the equation 11 - I W=144 y y l po V. 1 - ( o l y where W denotes the work in foot pounds, / po and p i the initial and final pressures, respectively, expressed in lb. per sq. in., while V. represents the original volume of the fluid in cub. ft. at pressure and y is the index of adiabatic expansion, on the assumption that the relationship between the volume and the pressure during such an expansion can be represented by the formula I p}' V = constant. By the principle already stated, the theoretical velocity of efflux will be obtained by writing =W =144 y - I po From this expression it appears that as p i becomes smaller and smaller becomes greater and greater. When, however, the velocity of efflux becomes equal to the velocity of sound in the escaping fluid, any further reduction in p i occasions no increase in the weight discharged from the nozzle per second. This follows because the velocity at which any impulse is transmitted through a medium is the same as that of sound in the medium. Hence, if, starting from an equality of pressure in reservoir and receiver, the receiver pressure is progressively reduced, " news " of each successive reduction is transmitted back along the jet into the reservoir at the speed of sound, and as a consequence the pressure gradients there undergo a readjustment and the flow into the nozzle is increased. Once, however, the speed of issue exceeds that of sound, no " news " as to any further reduction in the external pressure can reach the interior of the reservoir. The pressure gradients therein consequently remain unaltered, and the weight of fluid fed to nozzle per second remains unchanged. This reasoning, which originated with Osborne Reynolds, applies to all cases of the efflux of fluids, although in the case of a liquid such as water it has no practical significance, as the head necessary to generate a velocity equal to that of sound in water would be many miles in height. In the case of superheated or supersaturated steam, the speed of sound is attained when the ratio of the lower pressure p i to the upper pressure is equal to 0.5457. No further reduction of the lower pressure will increase the weight of steam flowing per second, but final velocities of efflux greatly exceeding the velocity of sound can be attained by making use of a nozzle converging first to the throat and then slowly diverging again. The theoretical velocities under such conditions can be calculated from equation (I). In practice the actual velocity of efflux is less than the theoretical on account of losses due to nozzle friction. The maximum weight which can be discharged per second from a convergent-divergent nozzle is fixed by the area of the throat. In the case of steam, for each sq. in. of throat area the maximum weight which can be passed per second is wmax=0.3155? (Vo) where denotes the absolute pressure of supply in lb. per sq. in. and V. the corresponding specific volume of the steam in cub. ft. per lb. This equation holds whether the steam is superheated or wet. In equation (I) above, the work due from one lb. weight of steam under pressure pc, is expressed in ft. lb., but in steam turbine prac tice it is generally more conveniently expressed in heat units, and the convenience is the greater because the equation p 1 V = constant, is an inexact representation of the relationship between pressure and volume in the adiabatic expansion of steam. By working in heat units this difficulty is avoided. I 6 h` h ? ? p, 6 I, , ??6 ?6 Pns:i`? I,`?'? ? ??O? v - ,t l?- ? ???? ` ? '- ?`?°/6,^?° /6 ,` h S? - ??c' `'? ` ,?: o ea ' 4 =?, _ Q z? g t Tcta` p ? s ` ?1 0 ?? ?,?p? 0 0 ??` If lb.-centigrade heat units be adopted, the theoretical velocity of efflux given by the relation v = 300.2 ?/u where denotes the adiabatic heat drop and is conveniently measured from a Mollier chart. of which many have been published. A diagrammatic chart of this kind is reproduced in fig. 13, in which the ordinates represent entropy, and the abscissa are total heats of steam 25.827). The curves drawn on the chart represent lines of constant pressure, constant temperature or constant wetness. The use of the chart is best illustrated by an example. To find the velocity of efflux from a nozzle supplied with steam at an absolute pressure of 200 lb. per sq. in. and at a temperature of 300° C., which is discharging into a' receiver maintained at an absolute pressure of 120 lb. per sq. in., the point A is marked on the chart at a position corresponding to the initial conditions and a straight line is drawn horizontally (i.e. with constant entropy) to cut the 120-lb. pressure line at B. The length AB, as measured by the scale of total heats, represents 30.6 lb. centigrade heat units. The theoretical velocity is therefore 300.2,130.6 =1,660 ft. per second nearly. Owing to nozzle friction the actual velocity will be less than this figure, which has accordingly to be multiplied by a coefficient, the value of which is commonly taken to be 0.95 or o 96. With convergent-divergent nozzles the loss is much greater. The function of the moving wheel of an impulse turbine is to convert the kinetic energy of the jet into useful work on the shaft. The method of drawing a velocity diagram and estimating therefrom the probable efficiency of conversion is explained in the earlier article on Steam Engine (25.843). With impulse steam turbines a stage efficiency of about o. 80 can be realized if the blade velocity be sufficiently high. To obtain such an efficiency the ratio of blade speed to steam speed should be about o 47. For commercial reasons this figure is seldom obtained, but if represents the actual ratio of blade speed to steam speed, and S i the ratio corresponding to maximum efficiency then the efficiency, 7 corresponding to can be obtained from the equation 23 S' i=ni Si a12 A steam impulse turbine generally consists of a series of elementary turbines or stages arranged in succession on the same shaft. Suppose the first of the series has unit efficiency and expands the steam from a pressure of say 200 lb. per sq. in. and a temperature of 300° C. to a pressure of 120 lb. per sq. inch. Then, as shown above, in the absence of frictional losses, the state of the steam as delivered to the next elementary turbine would be represented by the point B on the chart, fig. 13, where the pressure is 120 lb. per sq. in. and the total heat 698.2 lb. centigrade heat units. The whole of the 30.6 units due in an adiabatic expansion from the initial conditions to a final pressure of 120 lb. per sq. in., would in the assumed case of a perfect turbine be converted into useful work on the shaft. In practice, however, only a part of this adiabatic heat drop will be usefully converted, the remainder being wasted in friction and added as heat to the steam, before it is delivered to the next elementary turbine, or stage. If the efficiency of conversion is 0.7, the heat which would be added to the steam in the above example will be o 3 X30.6, or 9.18 lb. centigrade units, thus making the total heat of the steam on delivery to the second stage 698.2 -}- 9 . 18 =707.4 nearly. This gives point Con the chart. If it be assumed that the second stage expands the steam down to 80 lb. per sq. in., the adiabatic heat drop will be found as before by drawing a horizontal line from C to cut the curve for 80-lb. pressure at D. The length of this line as measured on the scale of total heats is 22.8 lb. centigrade heat units. If, as before, we assume that but o 7 of this is converted into useful work, the remainder being added to the steam as heat, the total heat of the steam as delivered to the third stage will be 707.4-0.7 X22 8 = 691.5 heat units, giving (I) .2, 1'9 10 w v n h' h d D J K us the point E on the chart as representing the condition of the steam as supplied to the third stage. Proceeding in this way, a series of ' t state points " can be marked on the chart, each of which represents the condition of the steam as supplied to the next elementary turbine of the series. So long as the steam is superheated or supersaturated its volume can be determined, when the pressure and total heat are known, by Callendar's equation V= 2.2436 4 0.0123. The relation between the volume, pressure and temperature under the same condition is (V - o o16) _ 1.0706 T - 0.4213 p (373'01 in which T denotes the absolute temperature on the centigrade scale. With wet steam expanding in a condition of thermal equilibrium the volume of the steam is equal to the volume of dry saturated steam at the same pressure, multiplied by the dryness fraction as read from the chart. Since the steam in passing through a turbine never does expand in a condition of thermal equilibrium, this case is of no practical importance. If u l denotes the adiabatic heat drop for the first stage of the series, u 2 that for the second stage, and so on, then the aggregate of these values of u for the whole series will be greater, the greater the number of stages into which the whole turbine is divided. The ratio of the aggregate to the value of u obtained when the whole of the expansion is effected in a single stage, is known as the " reheat factor " R. In the case of a reaction turbine the number of stages is so great that the expansion may, for practical purposes, be considered as effected continuously instead of in a series of steps. In this case the reheat factor for superheated or supersaturated steam can be read off from the diagram fig. 14, which is reproduced from Martin's New Theory of the Steam Turbine. The " efficiency ratio " of a turbine is denoted by e, and is defined as the ratio which the useful work W actually done by the steam bears to that which would be performed by a turbine of unit efficiency, so that W = eu. The hydraulic efficiency, denoted by n, is defined as the ratio of the work done to the total effective thermodynamic head, which head, as pointed out above, is always greater than u in the case of a multistage turbine, as it is the sum of the values of u for each stage. We thus have W = nU = i Ru, so that R =767. The hydraulic efficiency ii of a turbine is a much more fundamental property than the efficiency ratio e, and remains unaltered whatever the number of elementary turbines or stages, into which the whole turbine is divided, or whatever be the total ratio of expansion. In the ideal limiting case in which the expansion is carried down to zero pressure the efficiency ratio is always unity, whatever the hydraulic efficiency may be. Where the heat drop per stage of a turbine is small, it cannot be measured with accuracy from a chart but must be calculated from formulas or derived from steam tables, of which Callendar's are the most reliable and self-consistent, and accord best with the most trustworthy experimental data. Callendar's formula for the adiabatic expansion of superheated or supersaturated steam is 13 p 3 T =constant where T denotes the absolute temperature. In a continuous expansion of superheated or supersaturated steam effected with a hydraulic efficiency n, the relation between volume and pressure during the expansion is represented accurately by the expression I A p 1 V - o o16 -) = constant (2) i 3 where - = I - 0.230773. A closely approximate expression has been given by Callendar in the form --- 3 n (H - 464) p 13 = constant (3). In practice - A in equation (2) may be taken as unity without I.3 involving serious error; and since, along the saturation line, the relation between pressure and volume is represented very approximately by the equation 0.9406 log p + log (V - o. o16) =2.5252, the point at which the saturation line is crossed in a continuous expansion, effected with an efficiency i, can be found approximately by combining this equation with (2), which gives: log p + log (V - o. o16) = log po + log (Vo - o.o16). The pressure thus obtained can be plotted on the steam chart as at 111 (fig. 13). A single additional point representing the state of the steam at some intermediate pressure gives the " condition line " in the superheated field with sufficient accuracy as the curvature of this line is always very slight. The condition line for wet steam expanding in thermal equilibrium is best obtained from the chart. To this end a horizontal line is drawn from M to cut the exhaust pressure line at S. The length MS then represents, on the scale of total heats, the adiabatic heat drop for an expansion from M in a condition of thermal equilibrium. Denoting this by u s the corresponding useful work done is eu s and the heat wasted in friction is (I - e)us. If we add this wasted energy to the total heat corresponding ° to the point S we get J as the state point representing the condition of the steam as finally discharged. A similar procedure gives us the state point K at some intermediate pressure, and the three points M, K, J suffice to fix with practical accuracy the condition line for wet steam expanding from M to S in thermal equilibrium. From a condition line the total heat of the steam corres ponding to any pressure can be read off, and the corresponding volume then obtained as already described. The condition line for steam expanding beyond the saturation line in a con dition of thermal equilibrium, has, as already mentioned, no practical significance in steam turbine work. Once the sat uration line is passed the expansion never proceeds in thermal equilibrium. This discovery renders obsolete the theory of the steam turbine working with non-superheated steam, as un derstood up to the end of 1912, at which time attention was directed anew to certain remarkable anomalies observed in experiments on the discharge of non-superheated steam from nozzles. Numerous careful experiments had shown that the weight discharged was often in excess of what the then ac cepted theory declared to be possible. In discussing these re sults in Engineering, Jan. io 1913, Martin pointed out that the experiments of Aitken and Wilson on the sudden expansion of dust free vapour afforded conclusive evidence that in expanding through a nozzle, the steam must be in the supersaturated condition and not in thermal equilibrium, so that the accepted theory was based on a fundamental error. Stodola succeeded in confirming this conclusion by direct experiment. He studied, under very strong illumination, the appearance of jets of steam discharged from a nozzle and found that the steam exhibited no signs of condensation occurring until the pressure had been reduced far below the saturation point. Finally, in 1915, Callendar, in a paper published in the Proceedings of the Inst. Mech. Engineers, gave an exhaustive study of the whole question and showed that the anomalies observed in nozzle experiments entirely disappeared if the steam were considered to remain in a supersaturated condition up to a point beyond the throat of the nozzles. Moreover, under such an assumption, Copyright Statement These files are public domain. Bibliography Information Chisholm, Hugh, General Editor. Entry for 'Steam Turbines'. 1911 Encyclopedia Britanica. https://www.studylight.org/​encyclopedias/​eng/​bri/​s/steam-turbines.html. 1910. terms of use • privacy policy • rights and permissions • contact sl • about sl • link to sl To report dead links, typos, or html errors or suggestions about making these resources more useful use the convenient contact form StudyLight.org © 2001-2022 Powered by Lightspeed Technology Ads FreeProfile