Steam Turbines - Encyclopedia

7/30/2019 Steam Turbines - Encyclopedia

1/21


www.theodora.com/encyclopedia/t/steam_turbines.html

GEOGRAPHICAL NAMES

"STEAM TURBINES (see 25.823 and 842). - The progress of the steam turbine during 1910-21 was very marked both as regards size andefficiency. The pure Curtis type, in which velocitycompounding exists at every pressure stage,hasbeen abandoned, except possibly for verysmall powers, and the design of impulse turbines now follows generally along the lines first laiddown by Rateau, and developed principally by Rateau and Zoelly. A single Curtis wheel isfrequently used to absorb the velocity due to the expansion of the steam in the first stage, asthis practice permits of a greater heat drop in that stage, so that the pressure and superheatare considerably reduced before the steam is admitted to the body of the turbine. Velocitycompounding is recognized as less efficient than the abstraction of the energy of the steam bysingle impulse blading, but the practical advantage of obtaining a large heat drop in the firststage is often considered to outweigh a slight loss of efficiency. The typical impulse turbine ofto-day consists of a horizontal shaft carrying a number of disc wheels, each furnished with asingle row of blades around its circumference, and running in its own separate compartment.The diaphragms which separate the compartments contain nozzles which are so proportionedthat the steam expanding in them from the pressure which exists in one compartment to that inthe next acquires just the velocity which can be efficiently absorbed by the wheel in the secondcompartment. The description later of a modern impulse turbine will make clear its constructionand principles of action.

The reaction machine still maintains its position as regards efficiency and, like the impulsemachine, is employed for very large powers. In modern machines, although the thermodynamicprinciples are identical with those of the earlier machines, there has been a considerablechange in details of construction. The modern reaction turbine is frequently fitted with a velocitycompounded impulse wheel, upon which the steam acts before passing to the reaction blading,the reason for this being the advantage of reducing the temperature and pressure of the steambefore i t is admitted to the body casing. It is not unusual to design the impulse wheel so that itabsorbs about one quarter of the available energy of the steam, with the result that the drummay be materially shortened, the number of rows of reaction blading greatly reduced, and the

cost of the turbine lessened. Other features which are typical of modern reaction machines arethe great care taken to eliminate causes of distortion in the casing, by avoiding ports andirregularities of the metal. The casing is always made as symmetrical as possible.

The Reaction Steam Turbine. - Enormous progress has been. made with the reaction turbineinvented by Sir Charles Parsons, both as regards size and efficiency, and correspondingmechanical developments have taken place in the design. Land turbines of more than about10,000 I.W. capacity are usually constructed in two or more parts, each part being a completeturbine, but utilizing only a portion of the total pressure drop of the steam. Sometimes the partsare placed side by side, each driving an independent electric generator, but otherwise they arearranged in tandem on a continuation of the same shaft.

This latter arrangement is illustrated in fig. 1, which shows a section through a large moderntwo-cylinder machine constructed by Messrs. C. A. Parsons & Co. Ltd. The steam passes fromleft to right through the blading of the high-pressure cylinder, and is then conducted by means of

the circular external pipe to the centre of the low-pressure cylinder. Here it divides, flowing

Search

Encyclopedia AlphabeticallyA * B * C * D * E * F * G ** I * J * K * L * M * N * O ** Q * R * S * T * U * V * WX *Y * Z

Advertise Here

. Feedback

TweetTweet 0

| JOBS | DRUGS |ANATOMY| DIAMONDS | HEALTH TOPICS | DISEASES | ENERGY| GEOLOGY|AIRPORTS | COUNTRIES | FLAGS |

Steam Turbines

Share
http://www.theodora.com/dot.htmlhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Xhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Yhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Zhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Qhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Rhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Shttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Thttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Uhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Vhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Whttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Ahttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Bhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Chttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Dhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Ehttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Ghttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Hhttp://www.theodora.com/dot.htmlhttp://www.theodora.com/dot.htmlhttp://www.theodora.com/dot.htmlhttp://www.theodora.com/dot.htmlhttp://www.theodora.com/dot.htmlhttp://www.theodora.com/dot.htmlhttp://www.theodora.com/dot.htmlhttp://www.theodora.com/dot.htmlhttps://www.facebook.com/sharer.php?app_id=309437425817038&sdk=joey&u=http%3A%2F%2Fwww.theodora.com%2Fencyclopedia%2Ft%2Fsteam_turbines.html&display=popuphttp://www.theodora.com/encyclopediahttp://www.theodora.com/flagshttp://www.theodora.com/wfbhttp://www.photius.com/wfb2001/airport_codes.htmlhttp://www.theodora.com/geologyhttp://www.photius.com/energyhttp://www.theodora.com/diseaseshttp://www.allcountries.org/healthhttp://www.photius.com/diamondshttp://www.theodora.com/anatomyhttp://www.theodora.com/drugshttp://www.occupationalinfo.org/http://www.theodora.com/encyclopedia/tell_a_friend.phphttp://www.theodora.com/theodora_feedback.htmlhttp://www.theodora.com/wwwads.htmlhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Zhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Yhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Xhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Whttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Vhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Uhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Thttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Shttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Rhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Qhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Ohttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Nhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Mhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Lhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Khttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Jhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Ihttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Hhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Ghttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Fhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Ehttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Dhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Chttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Bhttp://www.theodora.com/encyclopedia/t/encyclopedia/index.html#Ahttp://translate.google.com/translate?u=http://www.theodora.com/encyclopedia/t/steam_turbines.html&sl=en&tl=pt&ie=UTF-8&oe=UTF-8http://translate.google.com/translate?u=http://www.theodora.com/encyclopedia/t/steam_turbines.html&sl=en&tl=ar&ie=UTF-8&oe=UTF-8http://translate.google.com/translate?u=http://www.theodora.com/encyclopedia/t/steam_turbines.html&sl=en&tl=hi&ie=UTF-8&oe=UTF-8http://translate.google.com/translate?u=http://www.theodora.com/encyclopedia/t/steam_turbines.html&sl=en&tl=ru&ie=UTF-8&oe=UTF-8http://translate.google.com/translate?u=http://www.theodora.com/encyclopedia/t/steam_turbines.html&sl=en&tl=de&ie=UTF-8&oe=UTF-8http://translate.google.com/translate?u=http://www.theodora.com/encyclopedia/t/steam_turbines.html&sl=en&tl=fr&ie=UTF-8&oe=UTF-8http://translate.google.com/translate?u=http://www.theodora.com/encyclopedia/t/steam_turbines.html&sl=en&tl=zh-CN&ie=UTF-8&oe=UTF-8http://translate.google.com/translate?u=http://www.theodora.com/encyclopedia/t/steam_turbines.html&sl=en&tl=es&ie=UTF-8&oe=UTF-8http://www.geographic.org/geographic_names/http://www.theodora.com/dot.htmlhttp://twitter.com/search?q=http%3A%2F%2Fwww.theodora.com%2Fencyclopedia%2Ft%2Fsteam_turbines.htmlhttps://twitter.com/intent/tweet?original_referer=http%3A%2F%2Fwww.theodora.com%2Fencyclopedia%2Ft%2Fsteam_turbines.html&text=Steam%20Turbines%20-%20Encyclopedia&tw_p=tweetbutton&url=http%3A%2F%2Fwww.theodora.com%2Fencyclopedia%2Ft%2Fsteam_turbines.html


2/21

Steam Turbine Generator

Gas Turbine

Compounding
http://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-7437757543052749&output=html&h=90&slotname=4136856148&w=200&lmt=1302367477&flash=11.8.800&url=http%3A%2F%2Fwww.theodora.com%2Fencyclopedia%2Ft%2Fsteam_turbines.html&dt=1375637378817&bpp=4&bdt=566&shv=r20130730&cbv=r20130206&saldr=sa&prev_slotnames=0911851065%2C7011523576&correlator=1375637378846&frm=20&adk=2162107012&ga_vid=622792566.1375637379&ga_sid=1375637379&ga_hid=929234398&ga_fc=0&u_tz=330&u_his=1&u_java=1&u_h=768&u_w=1366&u_ah=728&u_aw=1366&u_cd=32&u_nplug=18&u_nmime=66&dff=arial&dfs=16&adx=0&ady=1587&biw=1349&bih=643&eid=86860101&oid=3&ref=http%3A%2F%2Fwww.google.co.in%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Drecent%2520development%2520in%2520compounding%2520of%2520steam%2520turbine%26source%3Dweb%26cd%3D9%26cad%3Drja%26ved%3D0CF8QFjAI%26url%3Dhttp%253A%252F%252Fwww.theodora.com%252Fencyclopedia%252Ft%252Fsteam_turbines.html%26ei%3DcYv-UeaFCMXGrAekvIDwCw%26usg%3DAFQjCNF2awTH41nXPud5hSO-ZV9zE4Q-gg%26bvm%3Dbv.50165853%2Cd.bmk&vis=2&fu=0&ifi=3&dtd=2853&xpc=olB2hXjH6J&p=http%3A//www.theodora.com&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&height=90&width=200&format=fpkc_al_lp&kw_type=radlink&prev_fmts=200x90_0ads_al&rt=ChBR_o-GAAKMqwripgH5AHAwEgtDb21wb3VuZGluZxoIC0pppfEZDikoAVITCOnD7cuo5LgCFWam4godXXcA7g&hl=en&kw0=Steam+Turbine+Generators&kw1=Gas+Turbine&kw2=Compounding&okw=Compoundinghttp://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-7437757543052749&output=html&h=90&slotname=4136856148&w=200&lmt=1302367477&flash=11.8.800&url=http%3A%2F%2Fwww.theodora.com%2Fencyclopedia%2Ft%2Fsteam_turbines.html&dt=1375637378817&bpp=4&bdt=566&shv=r20130730&cbv=r20130206&saldr=sa&prev_slotnames=0911851065%2C7011523576&correlator=1375637378846&frm=20&adk=2162107012&ga_vid=622792566.1375637379&ga_sid=1375637379&ga_hid=929234398&ga_fc=0&u_tz=330&u_his=1&u_java=1&u_h=768&u_w=1366&u_ah=728&u_aw=1366&u_cd=32&u_nplug=18&u_nmime=66&dff=arial&dfs=16&adx=0&ady=1587&biw=1349&bih=643&eid=86860101&oid=3&ref=http%3A%2F%2Fwww.google.co.in%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Drecent%2520development%2520in%2520compounding%2520of%2520steam%2520turbine%26source%3Dweb%26cd%3D9%26cad%3Drja%26ved%3D0CF8QFjAI%26url%3Dhttp%253A%252F%252Fwww.theodora.com%252Fencyclopedia%252Ft%252Fsteam_turbines.html%26ei%3DcYv-UeaFCMXGrAekvIDwCw%26usg%3DAFQjCNF2awTH41nXPud5hSO-ZV9zE4Q-gg%26bvm%3Dbv.50165853%2Cd.bmk&vis=2&fu=0&ifi=3&dtd=2853&xpc=olB2hXjH6J&p=http%3A//www.theodora.com&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&height=90&width=200&format=fpkc_al_lp&kw_type=radlink&prev_fmts=200x90_0ads_al&rt=ChBR_o-GAAKMqAripgH5AHAwEgtHYXMgVHVyYmluZRoIUE2sdy3S-UAoAVITCOnD7cuo5LgCFWam4godXXcA7g&hl=en&kw0=Steam+Turbine+Generators&kw1=Gas+Turbine&kw2=Compounding&okw=Gas+Turbinehttp://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-7437757543052749&output=html&h=90&slotname=4136856148&w=200&lmt=1302367477&flash=11.8.800&url=http%3A%2F%2Fwww.theodora.com%2Fencyclopedia%2Ft%2Fsteam_turbines.html&dt=1375637378817&bpp=4&bdt=566&shv=r20130730&cbv=r20130206&saldr=sa&prev_slotnames=0911851065%2C7011523576&correlator=1375637378846&frm=20&adk=2162107012&ga_vid=622792566.1375637379&ga_sid=1375637379&ga_hid=929234398&ga_fc=0&u_tz=330&u_his=1&u_java=1&u_h=768&u_w=1366&u_ah=728&u_aw=1366&u_cd=32&u_nplug=18&u_nmime=66&dff=arial&dfs=16&adx=0&ady=1587&biw=1349&bih=643&eid=86860101&oid=3&ref=http%3A%2F%2Fwww.google.co.in%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Drecent%2520development%2520in%2520compounding%2520of%2520steam%2520turbine%26source%3Dweb%26cd%3D9%26cad%3Drja%26ved%3D0CF8QFjAI%26url%3Dhttp%253A%252F%252Fwww.theodora.com%252Fencyclopedia%252Ft%252Fsteam_turbines.html%26ei%3DcYv-UeaFCMXGrAekvIDwCw%26usg%3DAFQjCNF2awTH41nXPud5hSO-ZV9zE4Q-gg%26bvm%3Dbv.50165853%2Cd.bmk&vis=2&fu=0&ifi=3&dtd=2853&xpc=olB2hXjH6J&p=http%3A//www.theodora.com&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&height=90&width=200&format=fpkc_al_lp&kw_type=radlink&prev_fmts=200x90_0ads_al&rt=ChBR_o-GAAKMngripgH5AHAwEhhTdGVhbSBUdXJiaW5lIEdlbmVyYXRvcnMaCHAvacRPyhVQKAFSEwjpw-3LqOS4AhVmpuIKHV13AO4&hl=en&kw0=Steam+Turbine+Generators&kw1=Gas+Turbine&kw2=Compounding&okw=Steam+Turbine+Generatorshttp://www.google.com/url?ct=abg&q=https://www.google.com/adsense/support/bin/request.py%3Fcontact%3Dabg_afc%26url%3Dhttp://www.theodora.com/encyclopedia/t/steam_turbines.html%26gl%3DIN%26hl%3Den%26client%3Dca-pub-7437757543052749&usg=AFQjCNEO6tLuzJI93OjNzUdpIsggOwAudg


3/21


www.theodora.com/encyclopedia/t/steam_turbines.html 3

Table of contents

1 Number of pressure stages in a practicable turbine.2 Blade height of a practicable turbine in in.

The Impulse Steam Turbine

The Rateau steam turbine is a typical modern multistage impulse turbine. Fig. 4 shows alongitudinal section through a machine of this type constructed in 1919 by the MetropolitanVickers Electrical Co. for the Dalmarnock power station, the machine in question having amaximum 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 thesteam undergoes successive partial expansions in its progress through the turbine, and fromwhich it emerges with a velocity due to the drop in pressure which it has undergone. Thisvelocity is abstracted by the action of the blading which the steam enters after issuing fromeach set of nozzles, the steam being brought more or less to rest and the energy due to itspartial 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, thevolume of the steam at the low-pressure end becomes so great that the length of the turbineblades 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 passedout of the casing and used to heat the boi ler feed water, the feed heater for this purpose beingshown in section in the illustration. This practice diminishes, FlG.2 to a certain extent, thevolume of the steam which passes through the remaining wheels, but in the machine i llustrated,

the makers have employed a special device to permit a reduction of the length of the last row ofblades. The steam which enters the last wheel but one, is divided into two parts, that which actson the outer annulus of the blade ring passing away directly to the condenser, and only thatwhich acts on the inner annulus being afterwards conducted to the final wheel. The blading onthe last wheel therefore only deals with about half the weight of steam which passes through thepreceding 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 theturbine shaft is located axially by means of an adjustable thrust block of the Michell type whichtakes 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 ofblades is 24 inches. The mean circumferential velocity of the blading is 550 ft. per second, thetip velocity of the longest blades being 708 ft. per second. The turbine is designed to work witha 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 theseconditions the guaranteed steam consumpion is 10.2 lb. per K.W.H., this figure being the samefor 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 ofblades projecting axially from their opposed faces, one disc being stationary and the otherdriving the shaft of an electric generator. Mechanical di fficulties were experienced, principallydue to the distortion of the discs by uneven heating, and the design was soon completelyabandoned in favour of the axial flow type. In the year 1910 Messrs. Birger and FredericLjungstrom of Stockholm built an entirely new type of radial flow reaction machine which wasconspicuous not only for its mechanical merits but for its great efficiency. The Ljungstromturbine is now being developed in sizes up to 30,000 K.W. capacity, and is manufactured inGreat Britain by the Brush Electrical Engineering Co. and in the United States by the GeneralElectric Company. The steam is admitted between two discs and in its passage from theircenter to their circumference it passes through concentric blading rings mounted alternately onthe faces of the discs. The discs revolve at equal speeds in opposite directions, so that therelative blade speed is twice as great as in an ordinary machine of the same revolutions anddiameter, with the consequence that for equal efficiency the number of blade rings is only onequarter as great. Each disc is fastened to the end of a separate alternator shaft, and as theturbine comes up to speed, the alternators come automatically into synchronism and operate inparallel so that they act virtually as a single machine.

F IC. 8 The mechanical construction of the Ljungstrom turbine is unique. Fig. 5 shows a sectionthrough a machine to develop 5,000 K.W. at 3,000 revs. per minute, the illustration including thetwo ends of the alternator shafts, upon which the turbine discs are mounted. The constructionwill be better understood by reference to figs. 610 which show the most important details to a


4/21



arger sca e. e s eam eners e ur ne roug e ranc e p pe s own n g. an encepasses to the centre of each disc through the holes marked 2 in figs. 6 and 7, which illustratethe disc alone. It will be seen that the face of the disc contains a number of circumferentialgrooves. Each groove carries a blade ring, shown to a larger scale in fig. 8, in which irepresents the disc; 2 a seating ring; 3 a caulking strip; 4 an expansion ring; 5 and 6 rollingedges; 7 steam packing strips; 8 caulking strips; 9 strengthening ring; io dovetail profile ring;11 the blade i tself. 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 stripand 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 steamnecessary for overload conditions, the inner rings of blading being then short circuited. Thepressure of steam in the blading naturally tends to thrust the discs apart. It is therefore balancedby 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 infig. io. The whole packing consists of a number of rings keyed alternately to the shaft and to thehousing and having deep grooves turned circumferentially in the sides. The rings interleave inthe manner shown, the edges of the grooves being bent down so as practically to make contactwith 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 steamconsumption of 11.95 lb. per K.W.H., with steam at 208 lb. per sq. in. abs. and 569F.temperature, and a vacuum of 1.29 in. Hg. The no-load consumption of the same machine wasonly 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 reciprocatingengine could work under such steam conditions with anything like the efficiency a turbine wouldshow in similar circumstances.

Speeds of Turbines

The principal use of steam turbines on land being to drive electric generators, the speed atwhich these can be run controls to a large extent the speeds for which turbines can bedesigned. 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 ofthe diffioilties of commutation at high speeds. their characteristics do not materially affect thedesign of the turbines. All large land type turbines are directly coupled to alternators and as thefrequency of alternation is wry ?

'? ' Steam Conditions in Turbines. - The steam consumption of a turbine depends not onlyupon the excellence of its mechanical design but upon the amount of heat in every pound ofsteam delivered to the turbine which is available for conversion into work. The available heatmay be increased by increasing the pressure and temperature of the entering steam and bylowering the pressure at which it is exhausted. Progress in these directions is limited byconstructional difficulties, but nevertheless striking advances have been made. The bestpractice of the time may be exemplified by the io,000-K.W. machine installed in 1910 at theCarville station of the Newcastle Electric Supply Co., which operated with steam at 190 lb. persq. 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. ofsteam. In 1916 a machine of 11,000-K.W. was installed in the same station with a stop-valvepressure of 250 lb. gauge, a superheat of 244F. and a vacuum of one in. of mercury. Thischange 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 thatmodern practice sanctions steam pressures up to 350 lb. per sq. in., temperatures up to 700 F.

NNINNItw? ' ??I 'IM' ????.v... 'Mil e ".? < ?? ?i ? ' /? I?II r........??..? .? ?I? ? ?.?%., ,??

...?. ? ??- :' .. ,?.?I?/`,?? , i ? ? .6////h., 'I ' ?. .???...? ? ?. ,,:?, ? !11 ??..????

'/' L... O a ? ????Q 1. NS a-. ? N. ? ? ?. ? ?? ? ?

.? ?' ? ? ?? ? ?? 4 ' 'r% ,l i ' " .//," %i standardized in Great Britain at 50 and 25 cycles persecond, and in the United States and Canada at 60 cycles per second, the speeds of turbines


5/21



have to be correspondingly standardized. If F denotes the frequency, and N the number of pairsof poles of the alternator, then F N 60 denotes the only possible speed, in revolutions perminute, at which the turbine can be run. In Great Britain the standard turbine speeds aretherefore 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 thehighest speed at which the desired output can be economically obtained. Considerations ofstress limit the dimensions for a given speed, and the dimensions limit the volume of steamwhich can be ?,..,? j/.,,./, efficiently utilized, so that in practice a fairly definite limit of powercorresponding to each speed is obtained.

Turbo alternators have been satisfactorily built, having a maximum continuous rating of over6,000 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 theLiverpool corporation being of this size. There are several turbines with a maximum continuousrating of 30,000 K.W. running at 1,800 revs. per minute, and at 1,500 revs. per minute, acontinuous rating of 35,000 K.W. appears to be about the present limit, both for impulse andreaction machines. Machines of this size and speed were installed in Chicago in 1918, and inParis in 1921. In machines of 30,000 K.W., and over it is not uncommonly the practice to usetwo or more generators, the whole unit really consisting of mechanically independent highandlow-pressure turbines. Certain units built by the Westinghouse Co. in the United States have amaximum rated output of even 60,000 K.W., but these in fact consist of three independent turbogenerators, through which the steam passes in series. This multiplication of cylinders andshafts 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 cylinderarranged 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 theseparate 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, therequisite 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 ofexpansion of the steam may be over 800.1. Fig. 1 shows a section through a two-cylindertandem turbine as constructed by the Parsons Co., and fig. 12 i llustrates the appearance of atwo-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 gearingfrom the main shaft, which acts in the case of all reaction machines by controlling the pressureat which steam is admitted to the casing. In machines constructed ei ther wholly or partially onthe 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 aresometimes provided for by admitting steam to the turbine at some intermediate point, thusraising 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 purposemay be hand operated, but as a rule they are under the control of the governor and are thusautomatically opened when the extra steam is required to maintain the speed. In view of theclose governing required on turbo generators and of the size and weight of the valves whichhave to be operated, it is the universal practice to employ a relay arrangement on all but thesmallest machines, the governor merely controlling the position of a small balanced pistonvalve which admits oi l under pressure to one side or the other of a piston which does the actualwork of operating the valves. The pressure oil is supplied from the lubrication system of theturbine.

Bearings and Lubrication

The old sleeve bearing, originally devised by Sir Charles Parsons and employed on his earliermachines, has been entirely superseded and turbine bearings are now constructed on ordinarylines, differing only from slow-speed bearings in their proportions and in the provisionnecessary 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 " whichare of cast iron or bronze. These are usually fitted with shimplates to provide a fine vertical andlateral adjustment, and are frequently supported in spherical seatings to permit of a certainamount of self-alignment. Safety strips, often of bronze, which normally lie slightly below thesurface of the white bearing metal, are usually provided. These are intended to carry the weightof the shaft safely in the event of the white metal being melted out, and thus prevent injury to theblading until the machine can be stopped. In all turbine bearings the important thing is to insurea copious supply of lubricating oil, not so much for lubrication as to carry off the heat generatedby friction and to maintain the bearings at a reasonable working temperature. Water-cooledbearings have been used by some makers, but the most approved practice is to rely on the


6/21



ow o o t roug t e ear ng to eep ts temperature own. s usua y e vere to t ebearings at a pressure of about 15 lb. per sq. in., a gauge being provided on each bearing toindicate whether the pressure is being maintained. On modern turbines an automatic deviceoperated by the oil pressure is fitted, which shuts the machine down in case of any failure of theoil supply.

Bearings up to 8-in. diameter are usually bored larger than the shaft to the extent of about0.004 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 offresh cool oi l. The shaft, when running, is kept out of metallic contact with the bearing by a thinfilm of oi l continually dragged underneath it by i ts rotation. It is this fi lm 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, themore effectively is the film established, and the greater therefore the permissible load on thebearing. But the fact that bearings have to start from rest, when the film is imperfect, imposes apractical 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 ofsurface of shaft in ft. per second. This is said to be applicable to bearings of normal design inwhich 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, andprobably has a considerable margin of safety when the speeds are high and when there is novibration. One large manufacturing firm is said to take the permissible pressure per sq. in. ofprojected area as ranging from 167 to 235 when the velocity ranges from 20 to 73.5 ft. persecond. Modern practice is to give P a value not exceeding 150 lb. in bearings where thevelocity 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. Thebearings of land turbines usually work at temperatures from 120 F. to 160 F., but the lattertemperature should not be exceeded, as not only is the oi l injured, but its viscosity is so low thatthe 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 vin which l and dare respectively the length and diameter of the bearing expressed in in., visthe velocity of the surface of the shaft in ft. per second, and tis the temperature on theFahrenheit scale. The same authority quotes the following formula as often used in slow-speedmarine practice: B.Th.U. per hour = lXdXv 1 ' 38 . Treating the heat which escapes by radiationand conduction as negligible, these formulae give the heat which has to be carried away by theoil and extracted by the oi l cooler. This heat of course is the equivalent of the work lost byfriction in the bearing. The increase of temperature of the oil passing through the bearingshould not exceed 10 to 20F., and if the specific heat of oi l be taken at 0.31 the minimumquantity 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 alongthe shaft and other contingencies.

Mechanical Gearing of Turbines

The De Laval steam turbine, consisting of a single impulse wheel running at a speed of 30,000to 1 0,000 revolutions per minute according to the size, has always contained reductiongearing as an integral part of the machine because such speeds are far too high for drivingordinary machinery. Turbines of this type have, however, only been built for powers up to a fewhundred horse-power, and although the use of reduction gear may be dated from theintroduction of the Laval turbine in 1886, it never became a recognized practice for largepowers until it was developed by Sir Charles A. Parsons as the solution of the problem ofmarine propulsion. De Laval had shown that it was possible to transmit power satisfactorilythrough 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. Thereduction 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 havebeen found necessary to the successful performance of modern gears transmitting severalthousand horse-power through a single pinion. The double helical form of tooth ofcomparatively fine pitch has been retained, as this design eliminated end thrust and insuredsilent running by reason of the number of teeth simultaneously in contact. Ample lubrication ofthe teeth by means of oi l jets was also employed by De Laval, who succeeded in producingdurable and satisfactory gears which had an efficiency of about 97 per cent. These gears areused up to about 600 H.P. which is the commercial limit of the type of turbine for which they aredesigned.

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


7/21



ur ne, ere ore, rec y o a prope er s a nvo ves a compromse n esgn, n w c espeed is greater than desirable for the propeller yet so low as to require the turbine to be ofgreater 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 ofturbine 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 therecognized driving power. But ordinary cargo vessels and tramp steamers, with an averagespeed of 10 or 12 knots, were outside the practical field of the steam turbine until speedreduction gearing was available to couple a high-speed turbine with a slow moving propeller. Itwas really the problem of the slow speed ship which brought about the development of marineturbine gearing, and now that the mechanical difficulties have been overcome, the directcoupled 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, inconnexion 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 turbinesdriving a single propeller. This vessel had previously been equipped with triple expansionreciprocating engines of the usual type, and before these were removed they were put intoperfect order, and very careful tests were made to determine the efficiency and performance ofthe vessel. The geared turbines drove the same shaft and propeller as the engines had doneand were supplied with steam from the same boilers. The power developed was about 1,000H.P. and the shaft ran at 70 revs. per minute, the gear reduction ratio being 19.9:1. Theinstallation of the turbines resulted in an increase of about one knot in speed for the same coalconsumption, 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 inperfect 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 Bri tish Admiraltyadopted gearing, the torpedo boats " Badger " and " Beaver " being the first warships to beequipped with geared turbines. In these vessels each L.P. turbine drove its shaft directly, butthe H.P. and cruising turbines were geared to a forward extension of the turbine spindles. At fullload about 3,000 H.P. were transmitted through each set of gearing. Six years later completegear drives had become the standard practice for British war vessels of all types and by 1920some 652 gears, transmitting an aggregate of 7,280,000 shaft H.P., were fitted, or on order forthe royal navy (Tostevin, Trans. I.N.A. 1920).

The appended particulars of H.M. battle cruiser " Hood," of 144,000 shaft H.P., which wascompleted in 1920, will indicate the development of gearing for turbines and will at the sametime 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. . 1.1533Normal 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


8/21



Gearing H.M.S. "Hood."The earliest practice with regard to marine gearing was to use ahelical angle of 23' in conjunction with a normal pitch of 0.75 inches. Subsequently a helicalangle of 45 which had been found successful in the De Laval gears was adopted with theidea of securing quieter running, but modern practice favours an angle of about 30', as teeth cutat this angle will run silently, while their less inclination to the axis of the shaft results inincreased efficiency and greater effective strength. The usual angle of obliquity is 141', and thenormal pitch except for the very largest gears is nearly always 0'583 inches. The permissiblepressure in lb. per in. of axial length of the pinion is determined by the formula P = KI DD inwhich D is the pi tch diameter of the pinion in in. and K is a constant which has a value usuallybetween 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. Acircumferential 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-hardenednickel steel, containing not less than 3.5% of nickel and from 0.30 to 0.35% of carbon, with anultimate tensile strength of 40 to 45 tons. The gear wheels are to be of steel of 31 to 35 tonsultimate tensile strength with 26% elongation in two inches.

It is essential that the teeth of turbine gearing shall be very effectively lubricated, and to insurethis, oil under a pressure of from 5 to 10 lb. per sq. in. issues in jets which flood the teethimmediately before they come into engagement. A further point of primary importance is thatthe fitting and alignment of the gears must be as perfect as possible and great care must betaken to maintain and insure these conditions. In America the practice has been adopted ofcarrying 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 theadvantages of the system are doubted by many engineers.

Gearing of British naval turbines is exclusively of the single reduction type, but double reductiongearing has been largely introduced into cargo vessels during recent years, with the object ofefficiently using turbine machinery for ships of comparatively low speed without involving toolarge a reduction ratio for a single pair of gears. The general design follows - mutatis mutandis- thatof single reduction gear.

Numerous tests have been carried out to determine the mechanical efficiency of gears of thekind described. The mechanical efficiency of a single reduction gear at full load should be over98%, 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 orelectrical methods has yet been devised which will approach the efficiency obtainable withmechanical gearing.

Fig. 12 gives a good idea of the shafts of the Cunard liner " Transylvania." built by ScottsShipbuilding & Engineering Co. Ltd. An exactly similar set of machinery was fitted to drive theother shaft. The " Transylvania " was the first Atlantic liner to be fitted with geared turbines. Thevessel had a length of 548 ft. and a gross tonnage of 14,500. Each set of turbines and gearingwas designed to develop and transmit 5,500 shaft H.P. and they drove the vessel at 16.75knots. The turbines ran at 1,500 revs. per minute and drove the propellers at 120 revs. perminute, the ratio of the gearing being therefore 12.5:1. In the illustration the pinion in theforeground 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 animpulse wheel followed by a comparatively few rows of reaction blading, is seen on the forwardend of the low-pressure turbine. The size of the machinery is indicated by the fact that the gearwheel is to ft. in diameter and 5 ft. wide.

Theory Of The Steam Turbine Throughout the ensuing section, heat is expressed in foot poundcentigrade units, and the symbols employed have the following meanings: H =Total heat in onelb. 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 steamin cub. ft. after an isentropic expansion.

p = Absolute pressure in lb. per sq. in.

t, =Saturation temperature (centigrade).

=


9/21



.

n = Hydraulic efficiency.

u =Thermodynamichead expended in isentropic expansion.

U =Thermodynamic head expended in a practicable expansion. y = Index for adiabaticexpansion.

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 apracticable 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 turbineand one operated by water. An essential feature in both cases is that the potential energywhich a fluid possesses in virtue of its pressure is utilized to maintain a flow through a set ofnozzles or guide vanes. In the ideal case of frictionless flow the energy possessed by unit massof the fluid is the same whether it be at rest in the reservoir or whether it forms part of the jetand has accordingly a kinetic energy due to its velocity. The theoretical velocity of efflux of agas can accordingly be determined by equating the kinetic energy to the work which the samemass 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 takesplace. In thus expanding behind a piston, W, the theoretical work done per lb. of the fluid isgiven by the equation 11 - I W=144 y ylpo V. 1 - (o ly 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 ofadiabatic expansion, on the assumption that the relationship between the volume and thepressure during such an expansion can be represented by the formula Ip}'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 asp ibecomes smaller and smallerbecomes greater and greater. When, however, the velocity of efflux becomes equal to thevelocity of sound in the escaping fluid, any further reduction in p i occasions no increase in theweight discharged from the nozzle per second. This follows because the velocity at which anyimpulse 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 isprogressively reduced, " news " of each successive reduction is transmitted back along the jetinto the reservoir at the speed of sound, and as a consequence the pressure gradients thereundergo a readjustment and the flow into the nozzle is increased. Once, however, the speed ofissue exceeds that of sound, no " news " as to any further reduction in the external pressure canreach the interior of the reservoir. The pressure gradients therein consequently remainunaltered, 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 inthe case of a liquid such as water it has no practical significance, as the head necessary togenerate 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 theratio of the lower pressurep ito the upper pressure is equal to 0.5457. No further reduction ofthe lower pressure will increase the weight of steam flowing per second, but final velocities ofefflux greatly exceeding the velocity of sound can be attained by making use of a nozzleconverging first to the throat and then slowly diverging again. The theoretical velocities undersuch 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


10/21



. -divergent nozzle is fixed by the area of the throat. In the case of steam, for each sq. in. of throatarea the maximum weight which can be passed per second is wmax=0.3155? (Vo) wheredenotes the absolute pressure of supply in lb. per sq. in. and V. the corresponding specificvolume of the steam in cub. ft. per lb. This equation holds whether the steam is superheated orwet.

In equation (I) above, the work due from one lb. weight of steam under pressurepc, isexpressed in ft. lb., but in steam turbine prac tice i t is generally more conveniently expressed inheat units, and the convenience is the greater because the equation p 1 V = constant, is aninexact representation of the relationship between pressure and volume in the adiabaticexpansion 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 Mollierchart. of which many have been published. A diagrammatic chart of this kind is reproduced infig. 13, in which the ordinates represent entropy, and the abscissa are total heats of steam25.827). The curves drawn on the chart represent lines of constant pressure, constanttemperature or constant wetness. The use of the chart is best i llustrated by an example. To findthe velocity of efflux from a nozzle supplied with steam at an absolute pressure of 200 lb. persq. in. and at a temperature of 300 C., which is discharging into a' receiver maintained at anabsolute pressure of 120 lb. per sq. in., the point A is marked on the chart at a positioncorresponding to the initial conditions and a straight line is drawn horizontally (i.e. with constantentropy) to cut the 120-lb. pressure line at B. The length AB, as measured by the scale of totalheats, represents 30.6 lb. centigrade heat units. The theoretical velocity is therefore300.2,130.6 =1,660 ft. per second nearly.

Owing to nozzle friction the actual velocity will be less than this figure, which has accordingly tobe 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 animpulse turbine is to convert the kinetic energy of the jet into useful work on the shaft. Themethod of drawing a velocity diagram and estimating therefrom the probable efficiency ofconversion is explained in the earlier article on Steam Engine (25.843). With impulse steamturbines a stage efficiency of about o. 80 can be realized if the blade velocity be sufficientlyhigh. To obtain such an efficiency the ratio of blade speed to steam speed should be about o47. For commercial reasons this figure is seldom obtained, but if represents the actual ratio ofblade speed to steam speed, and S i the ratio corresponding to maximum efficiency then theefficiency, 7 corresponding to can be obtained from the equation 23 S' i=ni Si a12 A steamimpulse 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 expandsthe steam from a pressure of say 200 lb. per sq. in. and a temperature of 300 C. to apressure of 120 lb. per sq. inch. Then, as shown above, in the absence of frictional losses, thestate of the steam as delivered to the next elementary turbine would be represented by thepoint B on the chart, fig. 13, where the pressure is 120 lb. per sq. in. and the total heat 698.2 lb.


11/21



. .conditions to a final pressure of 120 lb. per sq. in., would in the assumed case of a perfectturbine be converted into useful work on the shaft. In practice, however, only a part of thisadiabatic heat drop will be usefully converted, the remainder being wasted in friction andadded as heat to the steam, before it is delivered to the next elementary turbine, or stage. If theefficiency of conversion is 0.7, the heat which would be added to the steam in the aboveexample will be o 3 X30.6, or 9.18 lb. centigrade units, thus making the total heat of the steamon 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., theadiabatic heat drop will be found as before by drawing a horizontal line from C to cut the curvefor 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 usefulwork, the remainder being added to the steam as heat, the total heat of the steam as deliveredto 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 JK us the point E on the chart as representing the condition of the steam as supplied to the thirdstage. Proceeding in this way, a series of ' t state points " can be marked on the chart, each ofwhich represents the condition of the steam as supplied to the next elementary turbine of theseries.

So long as the steam is superheated or supersaturated its volume can be determined, whenthe 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 - oo16) _ 1.0706 T - 0.4213 p (373'01 in which T denotes the absolute temperature on thecentigrade scale. With wet steam expanding in a condition of thermal equilibrium the volume ofthe steam is equal to the volume of dry saturated steam at the same pressure, multiplied by thedryness 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 secondstage, 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 theaggregate to the value of u obtained when the whole of the expansion is effected in a singlestage, is known as the " reheat factor " R. In the case of a reaction turbine the number of stagesis so great that the expansion may, for practical purposes, be considered as effectedcontinuously instead of in a series of steps. In this case the reheat factor for superheated orsupersaturated steam can be read off from the diagram fig. 14, which is reproduced fromMartin'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 thatwhich would be performed by a turbine of unit efficiency, so that W = eu. The hydraulicefficiency, denoted by n, is defined as the ratio of the work done to the total effectivethermodynamic 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 = iRu, so that R =767.

The hydraulic efficiency ii of a turbine is a much more fundamental property than the efficiencyratio e, and remains unaltered whatever the number of elementary turbines or stages, intowhich the whole turbine is divided, or whatever be the total ratio of expansion. In the ideallimiting case in which the expansion is carried down to zero pressure the efficiency ratio isalways unity, whatever the hydraulic efficiency may be.

Where the heat drop per stage of a turbine is small, it cannot be measured with accuracy froma chart but must be calculated from formulas or derived from steam tables, of which Callendar'sare the most reliable and self-consistent, and accord best with the most trustworthyexperimental data. Callendar's formula for the adiabatic expansion of superheated orsupersaturated 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 hydraulicefficiency n, the relation between volume and pressure during the expansion is representedaccurately 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)p13 = constant (3).

In practice - A in equation (2) may be taken as unity without I.3 involving serious error; andsince, along the saturation line, the relation between pressure and volume is represented veryapproximately by the equation 0.9406 log p + log (V - o. o16) =2.5252, the point at which thesaturation line is crossed in a continuous expansion, effected with an efficiency i, can be foundapproximately 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 singleadditional point representing the state of the steam at some intermediate pressure gives the "


12/21



condition line " in the superheated field with sufficient accuracy as the curvature of this line isalways very slight. The condition line for wet steam expanding in thermal equilibrium is bestobtained from the chart. To this end a horizontal line is drawn from M to cut the exhaustpressure line at S. The length MS then represents, on the scale of total heats, the adiabaticheat drop for an expansion from M in a condition of thermal equilibrium. Denoting this by u sthe corresponding useful work done is eu s and the heat wasted in friction is (I - e)us. If we addthis wasted energy to the total heat corresponding to the point S we get J as the state pointrepresenting the condition of the steam as finally discharged. A similar procedure gives us thestate point K at some intermediate pressure, and the three points M, K, J suffice to fix withpractical accuracy the condition line for wet steam expanding from M to S in thermalequilibrium.

From a condition line the total heat of the steam corres ponding to any pressure can be readoff, and the corresponding volume then obtained as already described. The condition line forsteam expanding beyond the saturation line in a con dition of thermal equilibrium, has, asalready mentioned, no practical significance in steam turbine work. Once the sat uration line ispassed the expansion never proceeds in thermal equilibrium. This discovery renders obsoletethe theory of the steam turbine working with non-superheated steam, as un derstood up to theend of 1912, at which time attention was directed anew to certain remarkable anomaliesobserved in experiments on the discharge of non-superheated steam from nozzles. Numerouscareful experiments had shown that the weight discharged was often in excess of what the thenac cepted theory declared to be possible. In discussing these re sults in Engineering, Jan. io1913, Martin pointed out that the experiments of Aitken and Wilson on the sudden expansion ofdust free vapour afforded conclusive evidence that in expanding through a nozzle, the steammust be in the supersaturated condition and not in thermal equilibrium, so that the acceptedtheory was based on a fundamental error. Stodola succeeded in confirming this conclusion bydirect 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 condensationoccurring 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 anexhaustive study of the whole question and showed that the anomalies observed in nozzleexperiments entirely disappeared if the steam were considered to remain in a supersaturatedcondition up to a point beyond the throat of the nozzles. Moreover, under such an assumption,the computed frictional losses became in good accord with those observed in experiments withair. There is however, of course, a point beyond which steam cannot be expanded withoutcondensation occurring. From experiments of C. T. R. Wilson, H. M. Martin calculated thefollowing table giving the properties of steam at the supersaturation limit, or the" Wilson line "as he called i t (" A New Theory of the Steam Turbine," Engineering1913): - r .n ??

_?Z??? :7:11G1? -_ ?_?? ????_???? ? ? ?? -??? ??? ' '1?_'?:111 ?S?:::!???????1111 MA. ???????

Z Merino r09? ???? ?`Z` ' ?? y Nt???? ???

'Moms . ?? ??

? ? ?.??

? ??.???????????iI'_'ONO ????i??i _-- ' UM. ' Noon ' 'Minim - ?

d ,-

F.'

.,.,a.

H'

?

o

a J

,-:

s.?

'

?

o o

>5

?,:,

?.a

a?

? o

?

H?

z

.9 12.

o

??

wr

5

? ?

E

? ?

'??

w

?

?.o

-,,z,..

c o

w ?

tw P. Vu, IIw ts yVs i'w

lb. per cub. ft. cub. ft.

deg. C. sq. in. per lb. F.P.C. deg. C. per lb.

0 0 '9888 295'30 593.79 38.52 325'85 1 9098

10 1'739 1 73'33 598 28 49'41 191.50 I 8641

20 2.935 106.11 602.64 60 33 116.91 1.8220

3 o 4'764 6 7.339 606.85 71.19 74' 21 8 1.7825

4 0 7'478 44.091 610.90 82.13 48'474 1.7476

50 11.39 2 9.73 2 61 4.75 93' 00 32.666 1 7141


13/21



60 16.86 20 566 618.36 103'89 22.575 1 6830

70 24.36 14.5 31 621 70 1 14.80 1 5'957 1.6537

80 34.41 10.506 624.56 125.66 11 537 1.6261

9 0 47'6 0 7.720 627'47 136.57 8.638 1.5998

Ioo 64.64 5'778 630 01 1 47.4 8 6'353 1 5748

IIO 86.28 4 389 632.10 158.40 4.832 1.5 508

120 113'37 3'376 6 33.89 169.48 3.713 1.5278

FIC.14 3 a T TABLE I.Properties of Steam at the Wilson Line.Along the Wilson line the

relation between pressure and volume is given with considerable accuracy by the equation0.9401 log pi + log (V -0.016) = 2.4651.

At the supersaturation limit moisture is formed and settles out in the form of minute droplets.

To proportion rationally the blading of a steam turbine it is necessary to know the relationshipbetween the pressure and the volume, or between the pressure and the total heat of the steamduring the expansion. The discovery that wet steam does not expand through a turbine in acondition of thermal equilibrium, whilst affording an explanation of certain anomaliesexperienced in practice, has raised new difficulties, since we are no longer in a position todetermine with certainty the volume of wet steam at different points of the expansion. So longas the expansion is not carried beyond the supersaturation limit, or the " Wilson line," thebehaviour of the steam is in accord with the equations given above. At the supersaturation limit,however, an overdue change abruptly occurs, and it is a matter of general experience that whena condition of unstable equilibrium is suddenly upset the subsequent phenomena arecommonly incalculable. In such cases there is frequently found to be a period of transition

during which " repeat " experiments fail to give consistent results. Once, however, the transitionis fairly effected, a new steady state is generally established. In the case of steam, this steadystate appears to be obtained if the expansion is continued considerably beyond thesupersaturation limit. In this steady state, such evidence as is available goes to show that thewater of condensation which remains suspended in the steam in the form of minute droplets,has a temperature approximating to that of saturated steam of the same pressure, whilst thegaseous portion of the steam has a temperature corresponding to that of steam just on thepoint of condensing at the supersaturation limit. The dryness fraction of the exhaust steam froma turbine is therefore given approximately by the relation H e - ts YH11.-ts where H e denotesthe total heat in one lb. of the exhaust steam, i s the temperature corresponding to saturation atthe same pressure while Hw is the total heat of one lb. of dry steam at the exhaust pressure butat the limit of supersaturation, as given in table above for various pressures. The volume V e ofthe exhaust steam is equal to yVw where Vw is taken from a table similar to table I.

In general, engineers express exhaust pressures as so many in. of mercury. The standardbarometric height is taken as 30 in. of mercury, and a vacuum of 29 in. of mercury, correspondstherefore to an absolute pressure of one in. of mercury, or 0.491 lbs. per sq. inch. Values of Hw,Vw, and twfor different vacua are tabulated below: Table 2.

Vacuum tw Hw Vw ^

(in. of mercury). (C).lb. centigrade

units.

cub. ft.

per lb.

29 - 11 37 588.59 569.3

28 - 0.15 593'67 296.3

27 + 6.9 8 596.92 202.5

26 +12.21 599.22 154'5

It will be seen that the determination of V e depends' upon a knowledge of H e, whilst H e =H i -indicated work done.

The indicated work done in the expansion of wet steam can only (as matters stand to-day) befound as the result of experience with actual turbines, and our knowledge is accordinglyempirical in character. If we take steam expanding from the saturation line to ordinary exhaustpressures, the following rule for the effective thermodynamic head Us engendered is in goodaccord with experience U s =,,tu s. Where u 3 denotes the adiabatic heat drop, assuming theexpansion from the initial to the final pressure to be effected under condition of thermalequilibrium, whilst = 1.1070+ 0.02212 100 - n(0.1638+ 0.0286 100) In this expression xdenotes the ratio of the initial pressure to the exhaust pressure and n is the hydraulic efficiency,which is taken to be the same as if the turbine were operated with steam in a superheatedcondition throughout the whole range of expansion.

The coefficients in this formula for4, have been selected so as to make the indicated work

'


14/21



. . . ,small amount of work done by expansion below the saturation line is attributed to the effectivethermodynamic head being less than if the expansion had been effected under conditions ofthermal equilibrium. Baumann's empirical rule on the other hand assumes that the efficiencydecreases by I % for every I % of moisture in the steam, the latter being assumed to expand inthermal equilibrium.

From the above expression for U s we can find H e from the general relation He=Hi-nU; andfrom this we can calculate Vo as already explained.

To determine the volume of the steam at other points of the expansion it is perhaps sufficient inthe present state of our knowledge to use an interpolation formula which shall give correctly theinitial and final volumes at the saturation line and at the exhaust, and which shall also give

correctly the work done between these two limits. No doubt there is force in the argument thatas we know accurately the relation between the volume and the pressure of the steam inexpanding down to the Wilson line, it would be more logical not to make use of an interpolationformula until the necessity actually arose by this line being crossed, but in the present state of

our knowledge the simpler procedure seems adequate for practical needs. It is certainly nearerthe truth than the assumption hitherto adopted, that the steam expands in thermal equilibrium.

Callendar has devised a very simple and easily applied interpolation formula which satisfiesthe required conditions. It may be written as log (H-C) = log A + u logp. The value of theconstants are determined by writing H 1 -C Pint!. p?

H2 - C u. p 2V2 - Cpl In practice it is seldom necessary to determine either A or u, whilst C ismost easily obtained by writing (H1-H2) p?V1 H1-C= p1V1 -p2V2 The use of the formula willbe made clearer by taking a practical example. Thus, suppose dry saturated steam at a

pressure of 20 lb. per sq. in. to be expanded down to a vacuum of 29 in. with an hydraulicefficiency of 0.7. (This efficiency is low for a modern turbine but the method is of courseapplicable whatever the value of n.) Then from Callendar's steam tables it will be found that H,=642.82 centigrade heat units; V 1 =20.08 cub. ft. per lb., whilst u 8 =125.46 units. In this caseoo = 49 0 = 0.4 0 75, so that I = 0.993 2 and U s =124.61 centigrade heat units. The " indicated" work done is therefore o 7X124.61=87.23 and hence He= H2=H1 - 8 7.2 3 = 555'59. Thedryness fraction at exhaust is therefore 555'5926'09 - _ given by y = 588.592609 0.94 1 3, sothat Ve =yVw = 0.94 1 3 X 5 6 9.3 = 535.9 cub. ft. per lb.

Had the steam expanded in thermal equilibrium and an equal amount of work been taken out ofit, its volume on exhaust would have been 594.4 cub. ft. per lb. Hence at high vacua the volumeof steam to be provided for at exhaust is some Io % less than on the old theory in which it wasassumed to expand in thermal equilibrium.

The requisi te data for constituting Callendar's interpolation formula are now available. Thus wehave p i V i =401.6; p 2 V 2 =263 I; whilst H 1 -11 2 =87.23. Hence H1C= 401.6X87.23 253.0.

3 8 '5 - 53' Thus C=389.8 and H2-C=165.8.

We therefore get log (H i -C)-log (H 2 -C) =0.1835 and logpi-logP2 = I. 6099.

We divide each of these differences by 10 (say) and can then calculate corresponding valuesof log (H-C) and logp by repeated subtraction of these dividends, giving the figures tabulatedin columns 2 and 3 in table 3 below. To determine corresponding values of log V we proceed inan exactly similar manner, determining the difference between log V 1 and log V2 andrepeatedly adding one tenth of this difference until the value of log V2 is obtained. This latterprocedure is based upon the general relation H 1 -H =77U, so that - dH = ndU = I J 4 nVdp andthus V =144 n dBut on differentiating Callendar's relationship above, we get dH (H- Cl dp p lwhich gives us V= J H - C 144n Since by hypothesis n is constant we may write this as vlog V=log (H - C) - logp. But logp is a linear function of log (H-C) and therefore so also is log V. Itmay be noted that log V is accordingly also a linear function of logp, so that this interpolation

formula gives betweenp and V a relationship of the type pV A =constant. But the value of theintegral ofVdp is adjusted so as to bring the total work done into accord with the data. Theformulas for V and H-C are, in short, empirical interpolation formulas and must be regarded assuch. They are not absolutely consistent with each other but the discrepancy is small enough tobe negligible in practice.

TA 3.

Sec-

tion.

log

(H -C)l o gp lo V

lo H - C

U Vg n n

A 2.40310 I 30100 I 30280 2 55800 361 4 0 20 08

B 2.38475 1 14001 1.44543 2 '539 6 5 34 6 '5 1 4'9 27.89


15/21



. . . .

D 2.3 4805 0.81803 1.7 3069 2.502 95 318.4 43.0 53'79

E 2.32970 0.6 57 0 4 1.87332 2.48460 3 0 5 2 56'2 74'7 0

F 2.311 35 0.49 605 2.0159 5 2.46625 292.6 68.8 103.8

G 2.29300 0.33506 2.15858 2.4479 0 280.5 80.9 1 44.1

H 2.2 74 65 0.17 4 07 2.30121 2.4 2 955 268.9 92.5 200 I

I 2.25630 0 01308 2.44384 2.41120 2 57.8 103.6 2 77.8

J 2.23795 i 85209 2.586 4 7 2.39 285 2 47.1 11 4'3 385.9

K 2.21960 i 691 I O 2.72910 2'37450 236.8 124.6 535.9

To avoid an accumulation of errors and to facilitate checking the values of the intermediatelogarithms in the above table are tabulated to five figures but only four of these are significant.When the additions and subtractions are accurately carried out the values in the last line of thetable must be the values at the exhaust with which the calculation was started. The convenienceof this check is so great that it is advisable (even at the expense of the slight inaccuraciesinvolved) to use this type of interpolation formula even in the case of steam superheatedthroughout its expansion, although in this case exact relationships between the di fferentfunctions can be stated.

Knowing U, the general characteristics of a turbine intended to operate with a given hydraulicefficiency can be very readily determined.

Thus if we define Kas K- (d 12(R.P.M.12 I O 100) where ddenotes the mean diameter in in.of a moving row of blades, and the summation includes the moving rows only; the efficiency ofthe turbine is a function of ------ as will be readily understood from, the obvious consideration

that Kis proportional to the mean square of the blade speed, whilst U is proportional to themean square of the steam speed. If the hydraulic efficiency be plotted against the resultantcurve is an ellipse, but this ellipse is not symmetrical about the axis along which K u ismeasured. The equation to this ellipse is (n KU i l 2 KUl n 1T U K>.) -4 U Kl where m denotesthe maximum value of n, and U - is the corresponding value of U.

The relation between n and U as determined by the collation, of actual test figures is given infigures 15 and 16. In both cases the expansion is assumed to be continuous in characterinstead of being effected in finite steps, a ci rcumstance which slightly lowers the apparenthydraulic efficiency of the impulse machine, but the error is small and moreover cancels outwhen the curve is used for purposes of design.

When the steam is initially superheated the value of U to be used in the formula is given by U=U

1 -}-US where U l represents the thermodynamic head expended down to the saturation lineand U 3 =1Gu3 as explained above.

FIG.15

a

Lin Indicatea

Effective

I?o

the

8/ode

-F;(

P712?a

00

Hydrauiic

Path

in

Thermodynamic

where

Ellie/cagy cicagy

3'

Inches

of

Head

is

the

impulse

in lb

mean

Turbines

Cent

dia

o U- Units

a K= of

Values o 'r

Indicated

Turbines

Hydraulic Efficiency f Reaction

(no t cerrectedfor Ti r o Leakage)

U- Effective Thermodynamic Head

ff d y

K`24/2/-2?

Values ge


16/21



Suppose that an impulse turbine which is to operate with dry saturated steam supplied at apressure of 20 lb. absolute and exhausted at a vacuum of 29 in. mercury is to run at a speed of1,500 revs. per minute, the mean diameter of all the blade rows being 44a in. whilst thedesigned hydraulic efficiency is o 7. Then from fig. 15 it will be seen that U = 43 6. Hence asfrom table 3 the total thermodynamic head is 124.6, the value ofKmust be 124.6 X 43 6=54,330.

Section. .

U.. .

A

0

B

1 4'9

C

29.3

D

43' 0

E

56.2

F

68.8

v o 1.435 2 82 4' 1 4 5'4 1 6 63

log p. . 1.3010 1.1400 0.9 790 0.8180 0.6 5 70 0.49 61Section. . G H I J K ...

U.. . 80 9 92 5 103 6 114.3 124.6 ...

7.79 8.91 9.98 II.OI 12.0 ...

logp.. 0.3 3 51 o. 1741 0 0131 -0.1479 -0.3089 .. .

But ifvbe the number of stages (44 '8 75) 2 (1500)2 IO J IOO J whence v = 12, so that aturbine of 12 stages with wheels of 44 in. mean diameter will give the required efficiency. Ifvdoes not turn out to be an even number, it can be made so by suitably adjusting the value of d.Intermediate values ofvare directly proportional to the corresponding values of U and a seriesof such values calculated with an ordinary io-in. slide rule, which is amply accurate for thepurpose, are as follows: The values of v are fractional, but they are used merely for curveplotting, the values of the different functions corresponding to integral values of v being readfrom the curves. Thus in fig. 17 log p has been plotted against vand it should be noted that thecurve is by no means represented by a straight line. Since vis proportional '03 ' K=vto Kitfollows that if in any turbine log p when plotted against Kgives a straight line, that turbine,whether of the impulse or reaction type, cannot be designed to operate with uniform efficiency.In the diagram fig. 17 the values of log p represent the pressure of the steam after dischargefrom the preceding stage, stage No. I being thus conceived as being preceded by animaginary stage No. o.

A corresponding plot of the volume would, however, give not the volume at discharge from theguide blades, but this volume as increased by the heat generated in the passage of the steamthrough the moving buckets. All stages being similar, the effective thermodynamic head at eachstage is the same. But the apparent thermodynamic head, obtained by dividing the totalthermodynamic head U by the number of stages, is somewhat greater than the adiabatic heatdrop at each stage.

?-- i __

?

4? - ?

-?

- ? a?? ,,,,

o

,,

.

i/1 II?

__iI_-/

y

111

I

I 1

According to what has been stated above, the velocity of discharge from the guide blades of astage is commonly taken as v=30o 2 Xo 95-,/u where u is the adiabatic heat drop. The weightW discharged per second per sq. ft. of guide blade area is _ v 30o. 2 Xo 95J1 u W V,, V'where Vcb represents the volume of the steam after an adiabatic expansion between thepressure above and below the stage. Instead of calculating these values it is more convenientto utilize the known values of U and V and to correct the above formula by using an appropriate

coefficient '. As there are 12 stages in the present case we get U = 124.6 -- Io 38 =q,. and theabove equation may 12 12 therefore be written W= 30o 2Xo 951lIO.38.

Stage No..

Theor. blade heightI 2 3 4 5 6

in in... . 0.94 I.18 1.51 1.95 2'48 3'24


17/21



.

Theor. blade height

in in.4.30 5.6 5 7.6 9 10.48 14.40 20.0

V the ? 4 effective " angle of discharge, allowing if necessary for the fact that the blades are offinite thickness. Hence if w be the weight of steam flowing through the turbine per second h' =wV ' 6223 f' dsin a? q Taking sin a =0.30, d =448 i q= Io 38 and w =10-3 lb. per second, thisexpression reduces to h' _ 03732V. Values ofh'thus calculated for the values of V given intable 3 are plotted in fig. 17 and from the curve thus obtained we read off the theoretical bladeheights at the different stages. These are: - In practice the nearest even dimensions will besubstituted for the calculated heights. The calculated heights for the last three stages are

inconveniently long, but they can all be reduced to say 9 in. by suitably increasing the effectiveangles of discharge. Some builders moreover increase the pressure drop at the exhaust end,and would accordingly combine stages II and 12 into one. These expedients decrease theefficiency but are cheaper than the alternative of constructing the low-pressure end on thedouble flow principle.

The high-pressure end of a turbine can be proportioned in a manner exactly similar to thatdescribed, but as the steam there is commonly superheated, the problem is correspondinglysimplified and need not therefore be discussed here. It is, however, usually necessary toconstruct some of the high pressure stages as partial admission stages and it is also acommon practice to have a large pressure drop at the first stage with the object (at somesacrifice of efficiency) of making a large initial reduction in the temperature and pressure of thesteam, so that the high pressures and temperatures are confined to the nozzle-boxes of the firststage. To the same end a velocity compounded wheel is frequently used in the first stage. Thegeneral theor y of these wheels is described in Prof. Ewing's article (see 25.844), but it may be

observed that in practice it has been found necessary to adopt empirical methods of designingsuch wheels. If designed as pure impulse wheels operated with a fluid which is " freely deviated" the results are very disappointing. One rule which has been used is to assume that only 85%of the total heat drop of the stage is utilized in the nozzles, and of the residue that 5% is utilizedin each of the three sets of blading. The wheel therefore works to some extent as a reactionturbine.

?E -_ _IL----I h_ 7735" Speaking generally, the principle of free deviation " as embodied insome water wheel designs is inadmissible in steam turbine practice, in which the movingblades should be just sufficiently long to avoid " spilling " of the steam delivered to themfrom the guide blades. As to the exact form of the moving blades, this does not appear to beof primary importance within reasonable l imits, as, 0 0a 01 -03 -04 20 Ins. Is 14 8653 2An

interpolation formula forfwhich is applicable for the ordinary range of turbine efficiencies andfor convergent guide blades is f = I -{-o 1 3 (I - n) Nix - I where x denotes the ratio of thepressure above and below the stage. The coefficient fis readily evaluated by the ordinary sliderule with quite sufficient accuracy.

In the case under consideration we note from the curve fig. 17, that when v = 1, log p = 1.197 sothat x =1.27 and fis therefore 1.023.

The area available for flow through a row of guide blades is h' dsin a where h'denotes theblade height in in., and a is ?

?

5/93_ 7

.8437. - -d ???- ? F'IC.18 although the practice of di fferent makers varies considerably, allimpulse turbines exhibit much the same efficiency under corresponding conditions. Typical

Rateau blading is i llustrated in fig. 18. The discharge angle is commonly about 30 save atthe last row of blading where it is increased to 35.

As regards nozzle and guide blade efficiencies, generally, reliable experimental data are stilllacking. It has been assumed that the efficiency of convergent guide blades is a maximumwhen the speed of efflux is equal to the velocity of sound, and though this is not improbablefrom aprioriconsiderations no conclusive evidence in support of the view has yet beenforthcoming, and turbines which attempt to embody this theory have not shown the slightestsuperiority over competing designs. A great drawback to high steam speeds is the liability toexcessive wear of the blading, and in this respect reaction blading has a great advantage overimpulse blading in addi tion to the higher inherent efficiency of the former. This higher inherentefficiency depends upon the fact that the overall efficiency of a steam turbine depends upon itsstage efficiency, a stage being defined as the section of a turbine comprised between twosuccessive heat drops. In the case of impulse turbines for each successive heat drop, frictionallosses are experienced in two elements, namely, the nozzles or guide blades and the movingbuckets, whereas in a reaction turbine at each heat drop there is loss in one row of blading


18/21



ony.

The Design of Reaction Turbines

The proportioning of a compound reaction turbine is a somewhat intricate problem, and as apreliminary it will be convenient to discuss the flow of steam through a series of openings orstages. At each of these a certain thermodynamic head q is expended, and this is not, ingeneral, the same for each stage. If however U denote the total thermodynamic head expendedin forcing the steam through n stages we haveX14 = U dn dn. Now Laplace's theorem in thecalculus of finite differences may be written q dn + - - 2 q + 1 2 (zq - Ago) - (6, 2 q - A 2 go) +oc. 24 the terms comprising the differences we get Z 1 q= U= fq dn + q 2 q o, so that dU 1 dq

do - _ q+2 do Now d U - J44 Vdp whilst if (as it is frequently permissible to assume) thevelocity of flow at each stage is proportional to d q we may write q - - Fu', V2 S2 where F

denotes some coefficient, w is the weight of steam f

Date post:	14-Apr-2018
Category:	Documents
Upload:	divya-prakash-srivastava
View:	262 times
Download:	3 times

Steam Turbines - Encyclopedia

Documents