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Les diagrammes suivants illustrent la mithode. 1 2 3 1 2 3 4 5 6 Note,— This paper is sent to you ihat you may examine it in aavimce of tha meeting, and piepurc any discust^ion ui' it wiucii you may witsii to piesent. It is issued to the membursliip in conlidenee, and witii tlie distinct understand- ing tliat it IS not to be given to the press or to tlie [lubiic until after it inis boea presented at the meeting, As there will be no supply of extra copies there, and papers are liable to be reau by abstract only, prt.-erve tliis copy lor your use, and BRINQ THIS COPY WITH YOU TO THE MEETING. (Siibh'ct to hevision "* DCII.* THE SATVUATION CURVE AS A REFER EXCE LINE FOR IM)fCA TOR DIA GRAMS. liV 11. 0. ( AHI'KNTKl!, ITAIKA, NEW YOHK. (MoiuIht of llie Society.) The followin*^ p.aper is intended to describe a }T;rapliical system which the writer has employed for giving more complete informa- tion regarding the heat interchanges which occur in the steam engine than obtained by the itsnal method of reduc'.i,.^ the data of an engine test. During the past year, the students in labora- tory practice of steam engineering at Sibley College, have all l)een required to make a graphical tiiermal analysis based on the use of the saturation curve as explained in the following article. The article is intended simply to give information show- ing the use of the method and some examples are given which show the character of the resiilts which can rejulily be obtaineil. No attem]>t is made to show by these examjdes any results which have a general application and it is not expected tliat any conclusions except stich as relate to the method itself will Ije drawn from the tests presented. In apology for the elementary way in which the very simple system is described, I may say that the article is intended principally for students in technical schools. Tiiis system cannot be considered as new in its general fratures, as I find that it has been used in a somewhat similar way both by Professor Uuwin and Professor Cottorell, but there it has been helpful in many ways as a rapid and graphical method of determining the quality and thermal condition of the steam during expansion, and in some respects the method presents novel features. It seems to have been used very little, possibly * Presented at the Montreal meeting, June, 1894, of the American Society of Mechanical p]ngineers and forminji: part of volume XV\ of the Tv(irt» the clearance line, and A" 7?' represents the line of no pressure or vacuum line, oh represents the volume of clearance and ^V.V represents the volume corres- ponding to piston displacement. From the end of the compres- sion curve an hyperbola is produced backward an upward, ar,a, to the line, he, which latter corresponds to the boiler pressure .J,. 1. of steam. The volume of steam filling the clearance space cor- responds with very little error to the distance ah on the same scale as the volume of piston displacement. To use this method, the weight of steam used per stroke is required. This is to be found by an ordinary efficiency test of the engine, either by con- densing' the steam, or from a boiler test. The data then which we are supjjosed to possess, gives us data from which we can comi)ute the weight of steam per stroke of the engine. By con- sulting steam tables the volume corresponding to the weight delivered for tlie given pressure can be ascertained. This volume is then laid off to the same scale as the diagram in a horizontal direction from the point which corresponds to the volume of THE SATURATION CURVE AS A REFERENCE LINE. steam filling the clearance at boiler pressure. In the (lini c„ then the ratio of bi r?,, to />, <;„ is the quality at the point (/| ; in the same manner h.> d, -^ h. c. is the quality at d^, etc. The variation in quality from point to point as obtained in that manner is shown for difterent positions in the stroke by the curve below the diagram, from which it is seen that the quality during the early periods of expansion rapidly diminished then gradually increased so that just before the period of exhaust opening, the quality increased considerable above that at the be- ginning. From a study of the conditions the same method could be applied during the period of compression, the only difficulty being this, that the quality of steam at any point in the cylinder during compression is not positively known, and an assumption must be made which is perhaps no better than to assume that during compression the curve is hyperbolic. The weight of steam imprisioned in the clearance spaces is always a very small percentage of the total, hence any error which is made in assum- ing hyperbolic compression cannot affect the results seriously, in fact it becomes of very little moment. There is very much in this graphic analysis which brings out thermal properties in a way better calculated to make an impression upon the mind than the analytic and more difficult methods of Hirn's analysis. I have employed this method in the Sibley College tests as supple- mentary to the analytical method devised by Hirii. So far as * There is a slight error in this assumption, due to the volume of the entrained water. The error is in general less than can be measured. A table for correc- tion is given at the end of the article. THE SATURATION CUUVE AS A REFERENCE LIKE. the quality shown clitring expansion, the two methods have always given substantially the same results. The difference in in fact depending simply upon the accuracy with which either the computation or the drawing was made. In the test for Hirn's analysis, tJie total heat discharged from the engine is always measured or computed so that the (juality of the exhaust steam can be determined. The same data could be used in con- junction with the graphical method described, in which case the lieat interchanges could be very readily and quickly computed, using the diagrams t(j obtain thg quality at any given poini thus, if from an ordinary test the weight of steam at any point is given and the (piality is shown by tlie graphical method which has been explained, the total heat is computed from a simple formula which is no doul)t familiar to all. Thus, let X = the quality as determined from the diagram, o the internal latent heat, q the sensible heat, for the given pres- sures. The latter being obtained from a steam tiible. Then the total heat in one pound of steam will be xu + q, which can be computed from the data at hand. If /• is the total latent heat, the total heat availal)le after condensation would be xr + q. While the graphical method will not replace the more tedious and exact analytical one for all purposes, yet it is believed that it will give all the practical results which can be obtained from the analytical method with miich less work and in general, in a manner Avliich is more readily understood by the student in technical schools and I think will on the whole prove of some value to practical engineers. This, I believe, has not been the case with the analytical method of determining the heat losses. As another illustration of the method of using saturation curves, reference is made to Figs. 2 and 8 in which case we have the same engine working with tlie same brake load and prac- tically the same I. H. P. The load was very light ; and in the one case, the engine was worked Avitli very little compression and in the other, ( see Fig 3 ), with a great deal of compression. The dis- cussion here is merely to show the method of obtaining the results by a graphical process and no reference is made to the relative economy in the two trials for the reason that it will probably form the subject of a paper before the society by one of my colleagues in Sibley College. In these figures " A " Fig 2 is an exact co])y of the diagram as obtained from the indicator. In Fig. 2, diagram " B," the line AB represents the expansion THE SATUHATION CURVE AS A REFEIIENCE LINE. curve drawn to an enlar repre- sented by K L is drawn to the same scale of volumes. The 3. *< ,-- 1 i -"TT ! 1 T 1 1 ==■ - J^. ^ -4-4 -- _i - in sl-i- — t i r ^^ ^ ^ ^ ♦- — r 44- \ - — ~:^ 1 ( ■ ..^W^ -„!?? 1 -.1....; - ~^\ 1 ,1 .°!J3<%^ Ou L- j.. ^ 1 I A %' 1 "SJ^ iif^o; H^ 1 - M — « f— s r" __^ _^ _1- r" " -" \ - 40 5^ —1 K.4 3. Ti ~~" It.v — ■ v — ~ "^ 110 - V - - — \ HO 1 1 — t v _^_^ -\ \ 11 1 «.' B-1 ' h— -V" AVEVlAbE .DUqRAM ._ 70 "1 — — A -1 "~ " ROM TEST - / t 1 — 1 — r ^ ~ 80|8P;hi>0 -V — a 1 «0 SI Ll.-l t "~ N I 1 1 /^ J < < -J o z a u "^ — ~~ "^^ 1 i «V 4.^ — — A S. 1 b _ 1 1 - — !^ ^ 1 — i — — V —\ % 1-7 A TM lOS'PHER \ 1 lU — A — ''s S- -^44.SN — ~ """ "< l* ,1 — j — 30 1 ■~ — "v; s ~~ V N i 1 — 1 — — — ^ \ ~ ■^v V. - ^ ^- VU i 2 r~~ w _ 6 iil ".<; J •^ ^^ ::; - ~t-t- " r ^ ^ 10 O [-4- _ _ _. .77^^ <% ~ tr Tw v— _^ ^ -_ — ~ ^' " -— .^ T7-3 - - U n. i- 1 - — AC RA ME t — — — — VJ — npt M" B ■ ~— ~ V 1 L lii 14- 1 I 1 1 _ i „ 1 _ 1. — — -..^ L Mil Fio. ',>. Fig. 3. d THE 8ATUHATI0N CURVE A8 A IlEFERICNCE LINE. (jUdlity at varif) points on tlu> ex])ansion line denoted l)y fif^- un's juid al.so re])r(»s(^nte(l by tiio (tiirvc, diuf^riini " C " at tiie tci]) of thu tit^mc. In Fi^. '.\ is shown tho diii^nun, actual and onlavf^ed in di)i<^raniH ''A " and " H" roHpoctivrly, tlio saturation curve correspond i 11}^ to the weight of steam imprisoned in the cdearance spaces, is drav/n on the supposition that this steanj is dry at the beginning of compr«>ssion. Tlie ipiality at dift'erent points in the compression curve and at different points in the expansion line, is denoted by figures on the enlarged diagram. The ecome more nearly vertical, and the intersection of the hori- zontal line becomes better defined, and is much moie accurate. It has been our custom to treat each diagram from a compound or triple expansion engine, as already explained for the simple engine, and to obtain the positions of the saturation curve before the combined diagram showing all the cards to the same scale were constructed. In making the combined diagram, we have tried various plans in order to have a continuous curve of reference to which they might be referred. To do this it is necessary to represent the diagrams as drawn from different clearance lines. Even then, because of the different weights of steam caught in the clearance spaces, the saturation curve would not be continuous, or, if adjusted, so as to be continuous it would have a diffei'ent curva- ture for the pfirt corresponding to each cylinder in each case. This later objection will not hold when the hyperbola is used as a reference line, however. The result of various experi- ments in combining diagrams has been to satisfy me that the Ij THE SATURATION CURVK AS A ItKFKllKNCE LINK. 7 niptliod of (Irawiiifj; tlie vr, j^'ivt's us a lunkuii saturation curve, as will be seen by rofenin^' to Fi^^ 4 which gives the cond)infd diagranis from the Si1)ley College experimental engine, yet, on the wlude, it seems to be the only method of Fici. 4. representing the diagrams which is general in its nature. It is true that very much smoother expansion curves are obtained for the combined diagrams which, for some cases, may more fairly represent the condition of the engine by combining the diaf^rams in such a manner that continuous reference curves are obtained either hyperbolic or in the form ot the saturation 8 THE HATURATION CUllVE A8 A KEFEUKNCF, LINK. liuo. IJut, it is bulioved, that on tlie whnlo no injustit'o in done bv tlu» (listoi lions which Hoiiu'tiiiMi occur in the iipplicution of th»> method ot applying iinit'roni scah^ <»t' prcHsuic and volume. In Vi^. 4 are shown the coinhinecl diiif^rams tVom the hij^h, intornuMliate, and h)w prenHnn^ cylin(h*rH of the triple ex])iMiHion enj^ino at Sii)loy (JoHef^e. The satiration curve drawn as already, i^xphiiued for each dia^'ram Keparathicall_\ to the ii<^ht of tht* diaj^ram. Th(> engine, in this case, »vas st»?am jacktitt'd with liigh j)r(!SHure steam on all the (!ylinders and in both receivers. The eti'ect of t'H> jacket steam on tlie quality is very niarked as is shown by reference to the expansion curve of the low pres^^ure cylinder. It will be noted in this case that the figures indicate in some stages a qualit}' exceeding one hundred. T "s nundjer should be con- sidered in its true signilicanco as representing the ratio of heat to that in the same; wtdght of dry and saturated steam rather than as representing the per c(;nt of dry steam. This can be takfui merely as r(>])resenting a su})erheated condition withcmt a specific statement oi the degree of superheat. I am well awar(! that there may be some objections to the use of the word " qualit}' ," as cover this case, but its convenience is cer- tainly very great as it saves a laborious ca.lculaticm, which is of no value when conq)h'ted. The ])eculiar form of the quality curves shown in the tigures as pertaining to the high and intermediate cylinders seems very generally true for the usual conditions of the steam engine. In a great many trials that we have considered, the curves have the form shown in each case, The point of contratiexure in these curves usually occurs some little distance .after the cut-oli' and indicates, of course, the position in the cylinder where the quality has become constant and condensation has ceased and re-evaporation has begun. The peculiar curvature occuring after re-evaporation begins is no doubt largely due to the rapid motion of the piston when near the centre of the stroke and to i: very slov/ motion near the end. These few remarks serve to show in a general way the charac- ter of the analysis and the results which may be obtained by using a saturated curve a& explained. I think it will be con- TFIK HATnUTiON ClTliVF, AS A IlKKKKKM"!.; UNR. 9 codrtl tli.'t iiH •! inctliixl, it is ccrtiiiirv worth cim^ftil <'(iiiHira- tioii. Tlic iiifi»iniatii>ii i'('},'iir(liiij^' tlic int«^'''liaiij4(>H of liciit cnii \\(A lie ohtaMicd so it'iuKly l>v iiiiy otlnu' iiitlhod t!iat Ih known to tlif \vi-if«M, while I Itclicvc it will no found to ('oin[)aro wnll with ;iiiy for coniph'tonoHrt and acciiracv of infoi-ination. A|>|>lifations of the nicth-xls which havo Immmi hou) deHcrihcd have alread*- l)»'('n i)j(^s«!nttHl to the Hocit'tv in fcho diHcusaion of the tt>sts of tlu> IMihvnnkoo cn^'ino !)v Dr. Thnrston, r»ad at tiie fall incotin;^', and, also, a |)a|)(>r at th<» present nieetinf^ on the snlijet^t oi 7'//i Slmin Jiuhl, also by Dr. Thnrston. In presmtinj^' the drawir,<^'H for this paper thn writer is under (»l)li;j;ation to Mr. Thomas Hall, a ^aadiiate student in Sibloy Collep;o. A DD END UM— (!A U I ' EN TEH— No. 60S ERllATA. The proofs of the writer's article were not seen by him, and correction for several errors which are quite apparent could not be made. In one place, however, the construction is such as to give a meaning quite contrary to that which the writer in- tended. It is believed that the privilege of correction under these circumstances will be freely accorded. Aside from simple errors of construction, of which no correc- tion need be made at this place, the principal misinterpretation is likely to occur with reference to the remarks on page 8 made respecting the combined diagram shown in Fig. 4. Without DIAGRAM SHOWING RELATION or PRCSSURC, VOLUME AND ABSOLUTE TEMPERA- TURE OF SATURATED AND SUPERHEATCD STEAM. ^ I I I ^ I I I Slips''''"'"'!"'! 8tSn77Iir--«o.f. T Fig. 4. attempting to point out specificially the change of construction which is required, I will merely say that tlie substitution of the Avord "heat" for "volume" is responsible for a great portion of the difficulty. The Avriter wishes to state as a substitution for these remarks that the term "quality" was not intended to be used with reference to tlie low-pressure cylinder. For this case the numbers on the expansion curve represent ratio of volumes of equal weights of steam in saturated and superheated condi- tions ; it is somewliat doubtful if the degree of superhejit can be computed. See following note. Note. — Error of delirmimnrj quality of the stmm. The quality ADDENDUM. of the steam can be defined as tlie percentage by weight of steam in a mixture of steam and Avater. Denote th(3 quality l)y .v , the percentage of moisture by weight, 100 — .r, the volume in cubic feet of one pound of dry and saturated steam by v, volume of one pound of water by c. the volume of one pound of the mixture by >n. Then will we have XV from which (100 - x) (' = w, X =: '"-' =. ^ - f 100 - '") C. V — C V \ V J In the above expression /" corresponds to the actual volume shown b}' the diagram for any given pressure, r that of the cor- responding volume measured to tlie saturation curve ; the quo- tient IV -^ V being the ([uantity which has been taken as the quality in the preceding discussion. From the above formula it is evident that the true quality will be less than the quantity so obtained by an amount the value of which is expressed in the second term of the second member. This last quantity is always very small. The value of c is nearly constant, and may be taken without sensible error as 0.01'!. The value of this correction does not equal 1/ until the quality has become less than 40'/, or until the amount of moisture exceeds (lO'c. The followinix table gives the percentage of correction for different, conditions with respect to volumes of the steam. Tablk fok corrkotino Values ok Quamty as obtained kuom Ratio of Volumes as explained in PArER. A. Ji •■ Porceiitngo Correction to Tnu; viiliir ol' obtiiiiKMl by bn siil)lnict,t(l. till' (jiia/if!/ y ratio of I'erci'iilMgt;. per ct'iil,. VollUlK'S V' -4- r. 100 0.000 100.00 us o.o;« 97.908 i)(5 0.0(i4 95.930 1)5 0.080 94.93 94 0.096 93.904 !J'3 (i.r.'S 91.872 90 0.10 89.84 85 0.'24 84.70 80 0.32 79.68 75 . 0.40 74.60 B I ' I'l'rcciit.'mo Corrictioii to 'I'riie value of obliiiMud liy iK'subtriictcd. tbf i/nu/i/;/ x ratio oC I'crui'ntuge. pur cent, volunieri j ''■' f- /■. 70 05 60 55 50 45 40 35 30 25 0.48 69.52 , 50 04.44 0.04 59.30 . 0.72 54.28 O.80 49.20 0.88 44.12 0.96 39.04 1.04 ;i;}.90 1.12 28.88 1.20 23.80 ADDENDUM. Application to Superheated Steam. If the volume of steam for a given pressure is greater than that obtained by measuring to the saturation curve, the steam is superheated. It is somewhat doubtful if the degree of super- heat can be determined by the increase in volume. If we could consider steam when superheated as a perfect gas, the product of pressure and volume divided by absolute temperature would be constant ; farther, for any given pressure the volume would \ary directly as the temperature. I have been unable to find much information relating to the properties of superheated steam. It seems, however, generally admitted that until the degree of superheat becomes considerable, the temperature does not increase at the same rate as the volume. After the steam is superheated considerably, it behaves like a perfect gas, of which the equation is pv = 85.5 ft. -lbs., in which p is the pressure in pounds per square foot, v the volume in cubic feet, and T the absolute temperature. The range of tem- perature required for the steam to pass from the saturated to the gaseous condition for any given pressure is given by Hirn* as 1() ' Fahr., and by Siemens as 18 Fahr. The following diagram was constructed by computing ratio of ^ from the values given in the steam table in Wood's Titer- mo'lynnmics and shows the relation between p, v, and T for differ- ent pressures with saturated steam. The straight line represents the equation as given above for superheated steam. It is to be noticed that the constant for saturated steam varies from 85.5 at 1 lb. pressure to 78.5 at 200 lbs. pressure. An application of these equations to the diagram of the low- pressure cylinder in Fig. 4 would indicate that the steam enter- ing the low-pressure cylinder was ;;4(> in temperature. As the jacket steam was only 350 , this amount seems unreasonably high. *See Thurstou'M Steam Engine, vol. i p. 771; Theory Mecanique de la Chalcur, Ency. Britaiinica, vol.