FSP-56-10

Leaving-Velocity and E x h au st Loss in S team T urb ines

B y E R N E S T L. R O B IN S O N ,1 S C H E N E C T A D Y , N . Y.

T h is p a p e r g ives a n e x p o s i tio n o f t h e v a r io u s i te m s w h ic h go to m a k e u p th e le a v in g v e lo c ity a n d e x h a u s t lo ss o f a s te a m tu r b in e . T h e im p o r ta n c e o f t h i s lo ss a n d th e r a ­p id ity w i th w h ic h i t in c re a s e s a t h ig h lo a d s c a u s e i t t o b e a d e te r m in in g in f lu e n c e in fix ing th e e c o n o m ic r a t i n g o f a m a c h in e . T h e sev e ra l e le m e n ts n e c e s sa ry fo r a n a n a ly s is a re e a c h e v a lu a te d in a f a ir ly d i r e c t , a l t h o u g h s o m e tim e s a p p ro x im a te , m a n n e r . M o re d e ta i le d a n d p re c is e e s t i ­m a te s m ig h t b e m a d e b u t a r e b e y o n d t h e i n t e n t o f t h i s p a p e r .

T h e lo ss in q u e s t io n o c c u rs i n t h e e x h a u s t h o o d b e tw e e n th e la s t w h ee l e x it a n d th e e x h a u s t flan g e to t h e c o n d e n s e r . I t is m a d e u p b o th o f k in e t ic e n e rg y lo ss a n d o f p re s s u re lo ss th r o u g h t h e h o o d a n d e a c h e ffe c t v a r ie s w i th lo a d a n d w ith lo c a t io n a ro u n d th e w h ee l a n n u lu s . M o is tu re is a llo w ed fo r ; s u p e r s a tu r a t io n n e g le c te d .

T h e to ta l lo ss m a y be e x p re ssed in B tu p e r p o u n d flow to c o n d e n s e r o r a s a p e r c e n t o f a d ia b a t ic h e a t d ro p o r

THE most important single loss in a condensing steam turbine is the “leaving loss,” “exhaust loss,” or “leaving-velocity loss” as it is variously called. There

is a very general understanding of the magnitude and im­portance of this loss. But there is no set standard as to the items properly included under the heading nor as to the manner in which the loss is to be evaluated for comparative purposes.

The importance of this loss and the rapidity with which it increases at high loads cause it to be a determin­ing influence in fixing the economic rating of a machine (see Fig. 1).

H y d r a u l i c A n a l o g y

The leaving velocity and exhaust loss from a steam turbine may be likened to the tailrace loss of a water wheel.If the tailrace runs downhill, there is a corresponding loss of head—the wheel setting should have been lower.If the tailrace runs level there is the loss of velocity head only, which may be small if the cross-sectional area is gen­erous. If the tailrace runs smoothly uphill into quiet water, the leaving velocity is recovered because the wheel operates under a gross static head greater than its net head by the velocity head converted in its tailrace.

1 Turbine Engineering D epartm ent, General Electric Co. Mem.A.S.M.E. Mr. Robinson was graduated from the St. Lawrence University in 1911 and from the H arvard G raduate School of Applied Science in 1914 (M .C.E.). For three years he was engaged in con­struction work and the design of steel and reinforced-concrete struc­tures in New York and in water-power engineering in New England. During the war he served in the Oise-Aisne offensive as first Lieuten­an t with the 302nd Engineers, U. S. A., and later as Captain and A djutant of the 2nd Engineer Training Regiment. For the past fifteen years he has been employed by the General Electric Com­pany in its Turbine Engineering Departm ent.

Contributed by the Power Division and presented a t the Annual Meeting, New York, N. Y., December 4 to 8 , 19 3 3 , of T h e A m e r i c a n S o c i e t y o f M e c h a n i c a l E n g i n e e r s .

N o t e : Statem ents and opinions advanced in papers are to be understood as individual expressions of their authors, and no t those of the Society.

p re fe ra b ly a s a p e r c e n t o f t o t a l e n e rg y th e o r e t ic a l ly a v a i l ­a b le fo r c o n v e rs io n to s w itc h b o a rd p o w e r.

W ith a p a r t i c u l a r e x h a u s t o p e r a t in g a t fixed s t e a m c o n ­d i t io n s , t h e le a v in g v e lo c ity a n d e x h a u s t lo ss in c re a s e s ro u g h ly a s t h e s q u a r e o f t h e lo a d (p a ra b o lic ru le ) .

W ith a p a r t i c u l a r e x h a u s t p a s s in g a fixed flow , in c re a s in g t h e t o t a l a v a i la b le e n e rg y in t h e h ig h e r s ta g e s o f t h e t u r ­b in e b y im p ro v e d s te a m c o n d i t io n s c o r re s p o n d in g ly r e ­d u c e s t h e p e r c e n ta g e lo ss i n t h e e x h a u s t (h y p e rb o lic ru le ) .

W ith a fixed p e rc e n ta g e lo ss i n a p a r t i c u l a r e x h a u s t t h e p o w e r m a y b e in c re a s e d by im p ro v e d s t e a m c o n d it io n s a s t h e !/i-power o f t h e t o t a l a v a ila b le e n e rg y b y in c r e a s in g th e flow to t h e c o n d e n s e r .

B a se - lo a d o p e r a t io n ju s t if ie s m o re l ib e ra l e x h a u s t a r e a s t h a n p e a k - lo a d se rv ice b u t i n t h e u l t i m a t e t h e h e a t - r a t e - lo a d c u rv e is t h e c h a r a c te r i s t i c w h ic h is o f m o s t im p o r ­ta n c e to t h e o p e r a to r a n d s e c o n d o n ly to t h e r e l ia b i l i ty o f p e r fo rm a n c e .

F i g . 1 R a n g e s o f E c o n o m ic R a t in g (S t ru c tu ra l c o n s id e ra tio n s l im it th e m a x im u m an n u lu s a re a a t a n y sp eed to s lig h tly less th a n in in v e rse p ro p o rtio n to th e s q u a re of th e speed . T h u s a s ing le ex h a u s t of lim itin g size a t 3600 rp m m a y be e x p e c ted to h an d le n o t q u ite o n e -q u a rte r

as m uch c a p a c ity as a s ing le e x h a u s t a t 1800 rp m .)

In the water wheel one deals with low velocities but a heavy fluid. With steam one deals with an exceedingly rarefied fluid but with velocities which are correspondingly high and with a kinetic energy content which varies with the square of the velocity.

M a n u f a c t u r e r ’s V i e w p o i n t

It is the intention of this article to discuss the more important items contributing to the leaving-velocity and exhaust loss of the steam turbine from the manufacturer’s point of view. Typical curves will be given for a 35,000-kw turbine by way of illustration, ■but there is no intention of going into the finesse of design or of giving detailed formulas or test data. For reasons which will appear, it does not seem desirable to standardize any calculations or to recommend any set expressions or formulas. This does not mean that suitable comparisons among designs should not be

515

516 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

made. The idea is that each comparison should be made on its own merits.

R f e u M ^ o f I t e m s

The several items of the leaving velocity and exhaust loss may be listed as follows; this list being intended to cover all losses

W E IG H T F LO W TO C O fiP E /iS E F ' LB./SEC.

F i g . 2 C o n d e n s e r F l o w (35,000-kw exfcraction-feed-heating tu rb in e o p e ra tin g a t 250 lb p e r sq in .

gage , 700 F , a n d 1 in . H g .)

In evaluating these items it is necessary to consider the follow­ing:

(5) Moisture content of the steam(6) Possibility of supersaturated expansion.

We shall rule out from this discussion:(7) Consideration of radial velocity in an axial-flow annulus(8) Eddy loss associated with edge thickness of buckets.

This last is properly chargeable to the nozzle and bucket efficiency and the stream is supposed to have healed into a cylin­drical jet on emerging from the wheel annulus. This latter ruling is, of course, arbitrary. The N.E.L.A. Prime Movers Committee Report on Turbines, No. 234, July, 1932, recommended correcting for bucket-edge thickness, thus in effect charging the bucket-edge loss to the exhaust loss rather than to the bucket. Suffice it to say that in any case it should not be charged twice and the manner used should be clear in any particular case.

T y p i c a l C u r v e s

Fig. 2 is the load-flow curve for a 35,000-kw turbine operating at 250 lb per sq in. gage pressure, 700 F temperature, and 1 in. Hg abs back pressure with two stages of extraction for feedwater heating.

F i g . 3 S p e c i f i c V o l u m e o r S t e a m A p p r o a c h in g 1 I n . A b s P r e s s u r e a n d 10 P e r C e n t M o is t u r e

(35,000-kw tu rb in e .)

If1Ss8*§

I

H gweight flow to con dense/? lb/ sec.

F i g . 5 R e l a t io n B e t w e e n A n n u l u s P r e s s u r e a n d W e ig h t F l o w t o r 1 I n . H g A b s P r e s s u r e a t t h e F l a n g e f o r a 3 5 ,0 0 0 -K w

T u r b i n e

(The do tted lines A, B,_C, and D for constan t annulus volum e flows corre­spond to the velocity diagram s in Fig. 4 and show the relation between an­

nulus pressure and weight flow for varying exhaust flange pressures.)

F ig . 4 V e l o c i t y D i a g r a m s A , B , C , a n d D f o r S t e a m E m e r g i n g F r o m L a s t B u c k e t o f a 3 5 ,0 0 0 -K w T u r b i n e

(Figures are velocities in f t per sec except for the heat equivalents in B tu per lb of the kinetic energy of absolute exhaust velocity. E ach diagram rep­resents a particu lar annulus volum e flow, as indicated. The volum e m ay be m ade up of a larger weight of denser steam or a sm aller weight of more rarefied

steam . See Fig. 5.)

existing in the exhaust hood between the exit from the wheel annulus and the exhaust flange:

(1) Normal velocity loss(2) Loss due to tangential component, or whirl loss(3) Eddy losses, associated with non-uniformity of flow(4) Pressure drop through the hood itself.

A n n u L u s v o m r i E f l o w , c u f t . p e r s e c .

F i g . 6 K i n e t i c - E n e r g y L o s s i n T h a t F r a c t i o n o f t h e S t e a m W h i c h C r o s s e s t h e A n n u l u s o f a 3 5 , 0 0 0 - K w T u r b i n e a t S p e e d (The m oisture moves a t very low speed. For 1 in. H g abs pressure a t the exhaust flange and the exhaust-hood drop shown in Fig. 5, the points A,B, C, and D correspond to the actual kinetic energy leaving loss and also

to the several diagram s in Fig. 4.)

FUELS AND STEAM POWER FSP-56-10 517

Fig. 3 gives the pressure-volume line for the exhaust of this turbine for an average moisture content. The variation from this line does not exceed approximately 1 per cent and is neg­lected.

Fig. 4 is a series of velocity diagrams characteristic of the last bucket exit in which we are interested only in the absolute exit velocity through the wheel annulus.

By way of identifying the conditions of operation to which these diagrams apply, it should be noted that each represents a definite volume flow, and Fig. 5 gives the corresponding lines for various weight flows and absolute pressures at the annulus. The heavy line shows, for a pressure of 1 inch Hg abs at the ex­haust flange, what the annulus pressure will be at the several weight flows corresponding to the different loads of Fig. 2.

By associating each annulus pressure with a corresponding velocity diagram, it is possible to plot Fig. 6 showing the kinetic energy of the exhaust steam in Btu per lb of steam at speed.

It is necessary to bear in mind that the annulus pressure is not uniform and Fig. 7 shows how it varies around the circumference for two flows approximating full load and half load, in each case for a pressure at the exhaust flange of 1 inch Hg abs.

The kinetic-energy content in Btu per lb of steam at speed around the annulus is shown by Fig. 8 for the same two flows as

h a u s t ve lo c ity .)

F ig . 9 T o t a l I n t e g r a t e d K i n e t i c - E n e r g y L oss P e r Lb o f S t e a m a t S p e e d i n t h e A n n u l u s o f a 3 5 ,0 0 0 -K w T u r b i n e

(This is the average for the entire annulus area and applies to the dry portion of the steam only since the moisture moves at very low velocity.)

A V A IL A B L E E H E / ? $ Y L O S S BTU/LB TO T A L F L O V J

T O C O M D E H S E F ?

F ig . 10 A v a i l a b l e E n e r g y L o s s D u e t o P r e s s u r e D r o p T h r o u g h t h e E x h a u s t H o o d F r o m t h e W h e e l A n n u l u s o f a

35,000-Kw T u r b i n e t o t h e E x h a u s t F l a n g e (If the wheel annulus could exhaust directly at 1 in. Hg abs pressure, the adiabatic energy available ahead of the last wheel exit would be increased

by the amount shown.)

F ig . 7 V a r i a t i o n o f A n n u l u s P r e s s u r e A r o u n d t h e P i t c h C i r c l e o f t h e A n n u l u s o f a 35,000-Kw T u r b i n e f o r T w o

S p e c i a l W e i g h t F l o w s , 85 Lb p e r S e c a n d 45 Lb p e r S e c (The irregularity is due to the quarter turn of the hood and its internal bracing. Lack of symmetry is due to the tangential component in the ex-

F ig . 8 V a r i a t i o n o f K i n e t i c - E n e r g y L o s s p e r P o u n d o f S t e a m a t S p e e d A r o u n d t h e P i t c h C i r c l e o f t h e A n n u l u s o f a 3 5 ,0 0 0 -K w T u r b i n e f o r t h e S p e c i a l W e i g h t F l o w s , 8 5 L b

p e r S e c a n d 4 5 L b p e r S e c (The w eigh t flow is p ra c tic a lly u n ifo rm a ro u n d the an n u lu s . The vo lum e flow v aries in inverse re la tio n to th e p ressu re a n d co n seq u en tly th e v e lo c ity

a n d k in e tic en e rg y V ary as show n.)

F ig . 11 V a r i a t i o n A r o u n d t h e A n n u l u s o f A v a i l a b l e E n e r g y L o s s D u e t o P r e s s u r e D r o p T h r o u g h t h e E x h a u s t H o o d o f a 3 5 ,0 0 0 -K w T u r b i n e f o r T w o W e i g h t F l o w s , 8 5 L b p e r S e c a n d 4 5

L b p e r S e c(This va ria tion is due to the va ria tion of pressure shown in Fig. 7.)

Fig. 7. We arrive finally at Fig. 9 which shows the kinetic- energy loss plotted against the various loads in kw.

Returning to the r&um6 of items, the method of arriving at Fig. 9 has taken care of (1) normal velocity, (2) tangential component, and (3) non-uniformity of flow. It remains to

518 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

evaluate the loss of available energy due to pressure drop through the exhaust hood itself.

Fig. 10 shows the relation to be nearly linear so that Fig. 11, which illustrates the distribution around the annulus, is not absolutely essential for a satisfactory preparation of Fig. 12 which shows the available energy loss plotted against the various loads in kw.

A b s o l u t e V a l u e o f L o s s e s I n s i d e E x h a u s t H oo d

When it comes to expressing the total effect it is necessary to take account of the quantities involved. The kinetic-energy loss, Fig. 9, affects only the steam at speed, and since in this case 10 per cent of the condenser flow is in the form of moisture moving at low velocity, this is to be applied to 90 per cent of the eon-

F i g . 1 2 T o t a l I n t e g r a t e d A v a il a b l e E n e r g y L o s s D u e t o P r e s s u r e D r o p T h r o u g h t h e E x h a u s t H o o d o f a 3 5 ,0 0 0 - K w

T u r b i n e

(This is the average for the entire annulus and applies to the to ta l weighflow.)

efficiency of 75 per cent has been assumed, whereas more accurate estimates use true efficiency curves, or true integrated available energy.

The total loss might be divided up in another way by defining the net exhaust-hood loss as the extra loss occasioned by having the specified exhaust or condenser pressure occur at the hood flange instead of at the wheel annulus. This viewpoint has a certain merit in setting up a standard for comparison of no pressure drop through the hood. The net hood loss viewed this way is less than the actual loss due to the pressure because the pressure drop reduces the kinetic-energy loss at the annulus. In order to divide the total loss in this way it is necessary to compute the leaving velocity loss at the annulus with the specified exhaust pressure occurring at that location. The balance be­tween this and the total may be thought of as the net amount due to the presence of the exhaust hood. This is not the same as the approximate computation suggested below, because true per­formance (as nearly as can be estimated) under the supposed conditions is computed. The result especially depends on both the relation between the size of annulus and the hood and the load, and the method of computation employed for estimating what would happen under the assumed conditions. Thus a heavily loaded annulus discharging into a liberal hood will suffer very little additional loss because of pressure drop through the hood as compared with free discharge without any hood. On

F ig . 13 T o t a l L e a v i n g V e l o c i t y a n d E x h a u s t L o s s o f a 35,000-Kw T u r b i n e E x p r e s s e d a s a P e r c e n t a g e o f T o t a l T h e o ­r e t i c a l l y A v a i l a b l e E n e r g y i n A l l S t e a m , B o t h t o C o n d e n ­

s e r a n d t o E x t r a c t i o n H e a t e r s (The lower full line curve shows the subdivision betw een tru e velocity loss and pressure loss as they actually occur. The do tted line shows the approxi­m ate leaving velocity and exhaust loss based on com puted norm al annulus velocity, assuming exhaust flange pressure a t the annulus and expressed as a

per cent of the adiabatic heat drop in the turbine.)

denser flow. It should not be necessary to explain the difference in velocity between the moisture and the steam, further than to refer to the article “Supersaturation—The Flow of Wet Steam,” by the late Prof. G. A. Goodenough,2 describing steam-flow tests conducted at the General Electric Works by Prof. J. H. Keenan. The available-energy loss is expressed per pound total flow. Bearing in mind these relations, reference to Figs. 2, 9, and 12 leads to Fig. 13, the total leaving velocity and exhaust-loss curve for this turbine. For simplicity an average over-all “engine”

* Power, Sept. 27 and Oct. 4,1927.

F ig . 14 T o t a l L e a v i n g - V e l o c i t y a n d E x h a u s t Loss o f a 3 5 ,0 0 0 - K w T u b b i n e , E x p r e s s e d a s a P e r c e n t a g e o f T o t a l T h e o ­r e t i c a l l y A v a i l a b l e E n e r g y i n A l l S t e a m , D i v i d e d So a s t o S h o w t h e N e t L o s s C h a r g e a b l e t o t h e P r e s s u r e D r o p

T h b o u g h t h e H o o d (In this case the velocity loss is th a t which would occur with exhaust pres­

sure a t the wheel itself.)

the other hand, a liberal sized or lightly loaded annulus dis­charging into a more restricted hood may easily have a net loss chargeable to the presence of the hood equal to the velocity loss with no hood present thus doubling the theoretical leaving loss.

I t can be seen by reference to Fig. 14 that the net loss charge­able to the presence of the hood is really much less than would be inferred by looking at Fig. 13. The example here given has a rather high net hood loss.

A p p r o x im a t e E s t im a t e s

For comparative purposes the dotted line in Fig. 13 has been prepared in a very simple manner by multiplying the weight flow to the condenser by the specific volume at the exhaust flange and dividing by the annulus area. This gives an average annulus velocity which has been converted to a kinetic energy heat con­tent in Btu per lb and divided by the adiabatic heat drop, without regard to extraction. This curve may be compared with the more accurate estimate which is given in full lines. The appar­ent inconsistency of using exhaust flange volume as if present at

FUELS AND STEAM POWER FSP-56-10 519

the annulus goes part way to compensate for the neglect of pressure drop through the hood with its corresponding loss of available energy.

S u p e r s a t u r a t io n

In dealing with the results so far set down no account has been taken of any effects which may be caused by supersaturated expansion, that is, by expansion of the steam without condensa­tion to a momentarily cooler, denser condition. In considering Fig. 13 as representing absolute values, this reservation has to be kept in mind in addition to the minor inaccuracies purposely assumed for simplicity.

It has been noted in comparing Fig. 14 with Fig. 13 that the true loss through the exhaust hood is accompanied by a reduc­tion of velocity loss in the denser medium at the annulus. The two effects are, to a certain extent, compensating.

Similarly supersaturation, if present, results both in a reduc­tion of energy made available for conversion and in a reduction of the leaving-velocity loss. With the amount of moisture present there is not likely to be any high degree of supersaturation in this particular case. However, in a different case with, say only 2 or 3 per cent of moisture theoretically present, supersaturated expansion should be allowed for.

C o m p a r is o n o f T u r b in e s

While it is legitimate to express the leaving velocity and exhaust loss in a variety of ways, it is always well to bear in mind the significance of the type of expression used. For instance, the difference between the approximate calculation dotted in Fig. 13 and the more exact one in full lines may be quite different for another design. There are a number of tur­bines in sizes over 50,000 kw in which, under favorable load con­ditions, the hoods are diffusing and produce a lower pressure at the annulus than exists at the exhaust flange.

Thus it is correct to speak of a loss of 30 Btu per lb flow to the condenser. But such a statement is not very significant. If the adiabatic heat drop is 500 Btu, the loss may be said to be 6 per cent of the adiabatic heat drop. But there is still an un­certainty as to the effect on the power generated since the 6 per cent loss applies only to the steam going all the way through the turbine. If 6/ 6 of the power generated comes from steam which goes all the way through the turbine, then the true loss

F ig . 15 P e r C e n t L e a v i n g - V e l o c i t y a n d E x h a u s t L o s s W i t h V a r i o u s S t e a m C y c l e s , i n E a c h C a s e W i t h 3 0 - B t u L o s s p e r

L b T o t a l F l o w t o C o n d e n s e r

(If the same turbine exhaust is used for the same kw capacity while sub­s titu ting m odern steam conditions for lower pressures and older cycles, the percentage leaving loss will be greatly reduced and the ex haunt will

appear wastefully generous in size for the b e tte r steam conditions.)

Correct values of the loss may be expressed in terms of heat equivalent in Btu per lb flow to the condenser, or as a per cent of the adiabatic heat drop, or as a per cent of the total theoretical energy available within the flowing steam between throttle inlet and the several extraction and exhaust flanges, for conversion to switchboard power.

F i g . 16 A p p r o x i m a t e I n c r e a s e i n K w C a p a c it y M a d e A v a il ­a b l e b y M o d e r n C y c l e s W i t h S a m e T u r b i n e E x h a u s t

is 5 per cent of the theoretically available power which, for the reasons discussed, fails to appear on the switchboard.

E f f e c t o f M o d e r n S t e a m C y c l e s

For instance, take the same loss of 30 Btu per pound flow to the condenser (see Fig. 15). Such a loss amounts to 10 per cent of the adiabatic heat drop of an ancient low pressure turbine with 300 Btu available energy while it is only 5 per cent of the adiabatic heat drop of a modern high pressure resuperheating turbine with 600 Btu available. Similarly a full use of stage extraction for feed heating so increases the power generated from a particular exhaust that the importance of a fixed leaving- velocity and exhaust loss may be decreased as much as 20 per cent in this manner; an effect which is not shown at all by ex­pressing the loss in terms of adiabatic heat drop, which does not change with extraction.

The use of the mercury turbine in conjunction with the steam turbine still further reduces the percentage importance of a fixed size loss.

In other words, modern cycles warrant the use of much higher absolute losses per pound of steam exhausted to conden­ser, because much less steam is being exhausted per kw hour generated.

I n c r e a s e d C a p a c it y

Fig. 16 is the counterpart of Fig. 15 showing how the capacity obtainable from the steam entering a given exhaust may be increased by the use of modern cycles. The relative capacities for constant percentage loss are based on the approximate rela­tion that, for a given cycle, the absolute value of the leaving- velocity and exhaust loss increases as the square of the flow. This leads directly to the conclusion that relative capacity for a

520 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

constant percentage loss increases as the 3/ V p o w e r 0f the total energy theoretically available.

C o n d it io n s o f O p e r a t i o n

The type of service and conditions of operation also are very important in evaluating the amount of leaving velocity and ex­haust loss that is acceptable. This is because of the rapid change at high loads. Thus a base load machine which is to run most of the time at its maximum rated capacity requires a more

liberal exhaust with smaller absolute loss than a machine de­signed for a broad range of service and the expectation of running at maximum capacity only a short part of the year.

Roughly speaking, the higher the annual capacity factor the lower should be the fixed loss in the exhaust but this is just an­other way of saying the more you run a machine the more ef­ficient it should be. For careful comparison actual load re­quirements should be analyzed. For instance, Fig. 17 illustrates two types of service, the total energy generated being the same in each case, but Station A is taking the swings and does the bulk of its operation at half and three-quarters load while Station B is on base-load service and operates mostly around three-quarters to full load. If these two stations were each equipped with a single turbine of the type represented by Fig. 13, the integrated loss due to hood effects in Station B would be 50 per cent more than in Station A, the difference amounting to approximately1 per cent of fuel requirements. From this it may be inferred that with medium coal prices a purchaser could afford to pay some 10 per cent more in the case of Station B for a turbine with more liberal exhaust and a different load curve from that which would be suitable for Station A.

This brings attention directly to the load curve as being con­sidered a most important feature by operators in the selection of a turbine. It is second only to reliability of operation and with turbines as dependable as they have been of late years, attention (perhaps too often) is likely to be concentrated en­tirely on the load curve. Together with throttle loss at light loads, which dwindles out at full load, the leaving-velocity and exhaust loss, which increases from very little at light loads, is one of the most effective tools the turbine designer has at his disposal in producing the type of machine suited to the operating conditions.

DiscussionW. E. C a l d w e l l .* The paper presents a comprehensive

method of calculating the exit loss in a condensing turbine. How-• Efficiency Engineer, The New York Edison Co., New York,

N. Y. Mem. A.S.M.E.

ever, this method is somewhat difficult to apply and if a simpler method could be devised for comparing turbines it would be helpful in evaluation procedure. It would be interesting if the author could indicate the probable error which might be intro­duced in comparing the exhaust end of a variety of turbines on the basis referred to in the N.E.L.A. Prime Movers Committee Report No. 234 on Turbines.

The author speaks of load curves and conditions for which a turbine is chosen but these conditions are so subject to change

that it is difficult to predict conditions far in advance. In case of doubt as to the future it may be wise to lean in the direction of capital savings at the expense of economy. Until quite recently growth of load through­out the country was rapid and new units were in­stalled at fairly frequent intervals. Each succeeding installation carried design improvements rendered pos­sible by the advance in the art. With new units of superior economy added to the system, the capacity fac­tor of the earlier machines dropped and they are op­erated only at peak loads. For example, on one system new machines purchased some years ago were operated at 58 per cent capacity factor for about 6 years and after this period the use of these machines diminished almost annually until it finally reached a capacity factor in the neighborhood of 5 per cent in about 20 years. Experiences of this kind cannot be safely taken as a basis for purchase of new machines since it

presupposes a continuation of load growth such as we have had in the past.

In the absence of continued load growth, the capacity factor and use factor of the more recent machines will increase materially above that which might be anticipated from earlier experience. Under such conditions machines evaluated for a relatively low capacity and use factor may ultimately become base-load units of the system. This is a situation which cannot always be foreseen and should not be lost sight of in the purchase of new units, es­pecially as it influences exhaust areas.

Another important consideration in the choice of exhaust areas in the turbine is the cost of steam-generating capacity to meet full-load requirements. With a lower exit loss less steam-generat­ing capacity is required and this should be carefully considered in evaluating turbine performance. Whether the value of the additional boiler-plant capacity required by a less efficient turbine is taken on a pro-rata base or increment cost base is largely a matter of judgment, but it is an important consideration if the highest economy in the use of capital is to be achieved.

Summarizing, the influences to be considered in the design of the turbine-exhaust end are the capacity factor, cost of boiler and condenser capacity, cost of steam, and quality, quantity and temperature-duration curves of circulating water available. The design is influenced also by the relation of the system de­mand period to the circulating water temperature, and if the period of maximum demand of the system coincides with the period of minimum circulating water temperatures, the condi­tions are favorable for a design with relatively low exit loss.

The paper clearly brings out the influence of higher initial steam conditions and other improvements in reducing the per­centage exit loss, nevertheless there is often potential capacity available which might have been purchased at an attractive price. In latitudes favored with an abundance of cold condens­ing water during the period of maximum demand, it is probable that there are cases where available capacity might have been purchased in the last wheel and condenser well below the unit cost of the plant.

As the art advances progress in improving efficiencies will diminish as the more attractive possibilities have been exhausted

F ig . 17 T y p i c a l A n n u a l - L o a d C u b v e s (Since the leaving-velocity and exhaust loss increases roughly in a parabolic m anner with the load, a base load sta tion such as B will experience a greater in teg ra ted loss th an a s ta tion like A which shares light loads. Turbines for base load service w arran t

more liberal exhaust areas.)

FUELS AND STEAM POWER FSP-56-10 521

and we may find it profitable in the future to resort to more liberally designed exhaust areas in steam turbines, as well as more liberal condensers and auxiliaries. With each successive installation closer cooperation is developed between the engineers of the manufacturers and those of the power producers and it is through the mutual understanding of the common problems in­volved that the greatest progress may be made in achieving a well-balanced design in the ultimate plant.

A. G. C h r i s t i e .4 As the author states in his opening para­graph, the combined leaving-velocity and exhaust loss constitute the most important single loss in condensing steam turbines. These losses have attracted the serious attention of the plant- designing and operating engineers only in the last few years.

Leaving losses were considered a few years ago by the Prime Movers Committee of N.E.L.A. Data on various turbines were collected and referred to the writer for analysis. In many cases arbitrary assumptions had to be made regarding the amount of steam to exhaust and other items. Certain of these such as the allowance for blade-outlet thickness on the last set of blades are, as pointed out by Mr. Robinson, open to question. Manu­facturers at that time were somewhat reluctant to discuss leaving losses. There appeared to be no standard or other method of expressing leaving losses. The writer therefore proposed as a tentative measure the expression of leaving loss as the equivalent of the absolute velocity from the last row of blades assuming axial flow and found by assuming the exhaust pressure and volume at the blade annulus instead of at the exhaust nozzle. In other words the losses in the exhaust hood were not con­sidered. The Prime Movers Committee then considered the question of a standard method of expressing leaving loss. How­ever, differences of opinion developed and a suggestion was made that a leading authority on turbine design be asked to discuss this whole subject in a paper before A.S.M.E. Mr. Robinson’s concise and enlightening paper is the result of this suggestion. A careful analysis of its contents will aid plant designers and op­erators to give intelligent consideration of these losses and to their influence on plant economy.

Mr. Robinson shows very clearly that the leaving-velocity loss and the pressure loss in the hood are interdependent and both should be considered. The method of indicating leaving loss used in the N.E.L.A. report does not give all the facts.

In Fig. 13 Mr. Robinson shows that the total leaving-velocity and exhaust-hood loss at 28,000 kw, the most efficient load on the 35,000-kw turbine under consideration, exceeds the loss cal­culated by the N.E.L.A. method by 0.6 per cent but he also points out that this may not be true for turbines with diffuser exhausts. Few of the turbines in the N.E.L.A. report have diffuser exhaust hoods so that the computed losses are probably not as large as the sum of the true leaving loss and hood loss. However, it is apparent that the computed figures published by the writer in the N.E.L.A. report can only be used with reser­vations.

Leaving loss depends upon the length of the last row of tur­bine blades and the quantity of steam flowing to the condenser. Hence the amount of this loss when the maximum length of blades is used, depends upon the output rating of a given casing as fully discussed in the writer’s paper before the World Power Conference a few years ago.

Losses through the hood will also be dependent upon the out­put of a given casing but as Mr. Robinson states these will also depend upon exhaust outlet design. Certain exhaust hoods exert a diffuser effect so that the leaving velocity of the steam is partly converted into pressure head to overcome hood losses.

4 Professor of Mechanical Engineering, Johns Hopkins University, Baltimore, Md. Mem. A.S.M.E.

The question arises as to whether it would be desirable and economic to incorporate diffuser designs in the exhaust hoods of all turbines. Some savings would result from such an ideal design.

Regarding supersaturation, Mr. Robinson indicates that this only needs consideration when moisture contents of 2 to 3 per cent occur at exhaust. Generally the moisture content ranges from 8 to 11 per cent. Can any supersaturation exist at the last row of blades under these conditions? The late Professor Callendar and H. M. Martin, both of England, have advanced the opinion that supersaturation will persist even to exhaust. R. Colburn and the writer concluded two years ago that supersaturation might exist at high moisture contents for there appear to be indications that this was a contributing factor in blade erosion from moisture. But the question is by no means settled.

One of the Power Test Code Committees should consider a standard definition for the combined leaving and hood loss. Mr. Robinson indicates the different ways in which the loss can be expressed but has not given any method preference over the others. It is highly desirable that the expression of this loss be standardized so that all engineers can refer to it in the same terms.

A further comment may be made. These losses are fixed by the original design of the turbine and are inherent in its con­struction. They cannot be increased or decreased for given operating conditions by any efforts of the station operators. It is therefore incumbent upon the plant designer to give the fullest consideration to the economics of these losses in the initial selection of the turbine equipment. Mr. Robinson points out certain factors such as the character of load, etc., which influence the economic effect of leaving losses.

There are differences of opinion in regard to the allowance for leaving losses in determining the true end-point of the condition curve. In some cases, the whole of the leaving loss has been deducted from the total heat to exhaust to find the end-point of the condition curve. Others estimate the probable stage ef­ficiency of the last stage and only deduct from the heat to exhaust, the product of this stage efficiency and the leaving losses. Ob­viously the latter method gives the higher end-point. Can Mr. Robinson indicate which method more nearly approaches the true end-point?

This paper will prove valuable to designing and operating engi­neers as it discusses a hitherto little understood subject in a clear and comprehensive manner.

S a b i n C r o c k e r .6 Mr. Robinson’s paper presents valuable information on turbine-exhaust loss as seen by a turbine designer. As such, the presentation of these data is an excellent and timely work. The writer would like to present the turbine user’s view of these data as they may be applied to turbines in power plants.

As power-plant heat rates have been improved through the development of more efficient equipment and the adoption of more favorable heat-utilization cycles, it has become necessary for engineers charged with the design and operation of power plants to go progressively to greater refinements in order to continue an improvement of thermal efficiency within the eco­nomic limitations of the case. Consequently in order to obtain further improvements at the present time it is necessary to con­sider comparatively small differences and quantities, such, for instance, as are involved in the return of low-grade heat through the turbine feedheating circuit, in changes in condensing equip­ment to obtain better vacuum, or other changes which may affect the exhaust loss in different ways.

5 Engineer, Engrg. D iv., Detroit Edison Co., Detroit, Mioh. Mem. A.S.M.E.

522 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

Operating companies make many such studies in which the exhaust loss becomes an important item. Under present prac­tise it is necessary to obtain specific data from the manufacturer for each case considered. This results in great expense to both parties, loss of time in correspondence, and a restriction in the number of comparisons that can be made in a given study. In consequence, while the manufacturer usually shows a willing­ness to cooperate in such matters, the results are not always satisfactory.

The present paper is a notable beginning toward clearing up these difficulties in that it enumerates all the items involved in the exhaust loss of a steam turbine. A detailed statement of the turbine-user’s need for data of this type should likewise help the situation. Briefly, he should be able to determine the exhaust loss on his turbines for any possible operating condition. In this regard Figs. 4 and 7 from which can be determined the magnitude of the loss for a given turbine are of particular interest. It would seem that such information should be made available to a turbine owner in either of two different ways: (a) on request furnish him curves similar to Figs. 4 and 7 applying to his particular tur­bine and (b) make available to him the methods for computing such curves from the basic data for his type and size of turbine. Such material is indispensible to the turbine operator for an in­telligent solution to his problems in power-plant design. Ap­parently Fig. 4 can readily be used for any desired operating condition but it appears that Fig. 7 would have to be given for a series of different condenser pressures and exhaust flows before it would be of much use to a plant designer. This would entail a large amount of detailed work on the part of the manufacturer, which it would seem he could eliminate by making more general­ized computation methods available to the turbine user.

The writer is quite aware that many variables are involved in computing exhaust losses, and that turbine manufacturers and their designers prefer to pass out information piecemeal rather than to give an operating company’s engineers sufficient informa­tion about a given turbine for them to compute the necessary correction factors for that turbine themselves. Nevertheless, it would seem that the author could well afford to give the user’s requirements further consideration in closing an otherwise com­mendable paper.

C. C. F r a n c k . 6 In discussing the actual loss due to the pres­sure drop through the exhaust load, the author places consider­able stress on the size of the cylinder-exhaust area, without a great deal of concern for the flow area of the last row of blades.

For a turbine of equal exhaust dimensions to that presented by the author, the loss resulting directly from the increase in exhaust pressure caused by crowding the exhaust hood, consti­tutes only a small part of the actual loss in heat converted into work.

Zu2By virtue of the consideration o f----for not only the last row,A u

but for the last three stages, which are affected by the change in vacuum, it may be pointed out that the reduction in adiabatic heat available, Au, results in an increase in the operating ef­ficiency of the group and partially offsets the reduction in avail­able heat. Another important point to be considered is the so- called “explosion loss” or loss occurring when the volumetric flow through the last row of blading is of such magnitude that a portion of the expansion actually occurs outside of the last-row- blade passage. This results in an uncontrolled expansion which destroys a greater part of the energy liberated.

For example, assume that Au for the last three stages at full6 Turbine A pparatus Div., Engrg. Dept., Westinghouse Elec.

and Mfg. Co., South Philadelphia Works, Philadelphia, Pa. Jun. A.S.M.E.

capacity including reheat, is 160 Btu/lb at 29 in. vacuum of which 105 Btu/lb can be converted into useful work. Then by virtue of limited exhaust dimensions the pressure at the exit of the last row of blades is reduced 0.5 in. vacuum to 28.5 in. Then the reduction in available energy will be (from Fig. 10) 21.6 Btu/lb and the resulting Ai, will be 139.4 Btu/lb at 28.5- in. vacuum of which 100 Btu/lb can be converted into useful work.

Consequently from this consideration the actual reduction in heat to work will be 5.0 Btu/lb, not corrected for moisture losses which, for such small changes, could be neglected.

Carrying this example to a conclusion by adding the effect of moisture, we see on the i-s diagram that the average moisture for the expansion to 29-in. vacuum is 9.25 per cent while the average moisture for the expansion to 28.5-in. vacuum is 9.0 per cent. Assuming no moisture removal and applying a correction

of 1 per cent loss in efficiency for 1 per cent average moisture content to the heat converted into work for the two expansions, we see that the heat converted to work for the 29-in. expansion is 95.3 Btu/lb and 90.5 for the 28.5-in. expansion. Hence the reduction in heat to work is 4.8 Btu/lb resulting from a reduction in available energy of 21.6 Btu/lb.

This points out that even with great care exercised in the design of the low-pressure exhaust load, a restricted last-row blade annulus may tend greatly to reduce the expected gain.

Another point of importance to be considered at this time is the possibility of correlating the design of the turbine and condenser in order to produce an approximately constant volu­metric flow through the exhaust end for the normal range of operating loads. This could be obtained by controlling the condenser circulating water to produce the desired vacuum with changes in steam flow. In this manner the design consideration of the turbine with regards to exhaust dimensions could be simplified.

With such a system of variable vacuum the discussion on re­duction in available work would have to be continued with lower flows. With such conditions of reduced volumetric flow, i.e., half load flow at 29 in. vacuum, the effect of explosion is en­tirely eliminated and the actual operating vacuum could be increased to 29.25 or 29.5 in. and at the same time the extra

FUELS AND STEAM POWER FSP-56-10 523

available energy converted into work at approximately the same efficiency as in the case of the 29-in. expansion.

In regard to the question of designating leaving losses it appears that the most rational method of evaluating them would be to consider the loss in kw. By the use of kw an ab­solute loss is immediately determined and its magnitude is left without question.

Another point which should be considered is the method of carrying peak loads. Some installations carry peak loads with the bleeder heaters cut out of service and this condition lends itself to separate consideration by virtue of the added flow passed through an already crowded exhaust.

Fig. 18 shows a typical “leaving-loss” curve for a reaction ma­chine of 35,000 kw.

H. G. Hiebelek.7 We are pleased to see such a thorough definition and explanation of a subject which has caused much comment by power engineers within the past few years.

We feel that it is a function of the turbine designers to define what should be understood by such losses and to show their rela­tive magnitude.

From a strictly operating viewpoint, once the selection of a machine has been made, these losses are beyond control except to a limited degree by the plant men. In southern stations, such as thq Deepwater (Houston) plant, the high circulating-water temperatures which prevail throughout most of the year limit the vacuum obtainable. In the north, however, with colder water conditions, particularly in the winter time, absolute pres­sures between 0.50 to 0.75 in. Hg abs may prevail for several weeks in extreme cases. In some instances, due to the pressure from operating departments together with the natural conser­vatism of designers, condensers are purchased for summer condi­tions. With such installations undoubtedly the magnitude of these leaving velocities and exhaust losses is very great. From the operating viewpoint, attention should be called therefore to the fact that many units are unable to use such high vacua effec­tively or that there is a limit beyond which it is not economical to go. This would suggest reduced speeds of the circulating pumps, resulting in a saving in auxiliary power. Further, on some types of condensers, refrigeration losses of the condensate are increased under high vacuum conditions.

The author’s paper considers the performance of the unit as­suming a constant back pressure of 1 in. Hg abs at the flange. We believe it would be of interest to call attention to the variation in the performance of modern condensers with variations in load and with variations in circulating-water temperatures, such as occur from season to season. The following will illustrate the typical performance of a condensing unit for a 35,000-kw machine under the conditions prevailing at Houston:

T em peratu re of in let circ. w ater

50 deg F 65 deg F 80 deg F 95 deg F

•----- Steam condensed, lb per b r------ -360,000 315,000 235,00 170,000/------Back pressure, in. H g abs----- -

0 .8 6 0 .7 8 0 .6 4 0 .59 1 .30 1 .20 1.02 0 .9 42 .0 0 1 .85 1 .60 1 .44 3 .0 4 2 .82 2 .4 8 2 .21

In the tabulation above, the flows which correspond to maxi­mum load (40,000 kw), full load (35,000 kw), three-fourths and half load happen to correspond very closely to the flows assumed by the author. This tabulation will show a variation of approxi­mately 25 per cent in the specific volume of the steam to the condenser between half load and maximum load for the same water conditions and a change of approximately 300 per cent for the same load between summer and winter conditions. This of course neglects the consideration of moisture.

’ Assistant Superintendent of Power, Houston Lighting and Power Co., Houston, Tex. Mein. A.S.M.E.

The use of these factors would considerably alter the author’s Fig. 13 and also call attention to the necessity of using weighted averages over the entire year in connection with the author’s Fig. 17, showing typical annual load curves, in order to compute the total annual losses from this source.

P. H. Knowlton.8 This paper is an excellent presentation of the calculation of the total exhaust loss from a turbine. It appears worth while to supplement this work by a statement as to the background of the method and the reasons for believing that such calculations are adequate.

In the first place, for any particular turbine the characteristics of the last stage wheel and buckets are, of course, known to the designer. The calculations necessary for Fig. 4 are fairly simple, involving the aforesaid characteristics together with the laws of flow for wet steam as they are understood.

Fig. 7, however, requires something more than well-known rules. The flow of steam through the ordinary downward exhaust type of hood is rather complicated and resource must be had to tests to determine the characteristics of various types. Two ways of testing are open, namely, by means of models or by testing hoods on actual turbines in operation. In either case, the test consists of measurements of the annulus static pressure together with the steam flow through the last stage wheel.

Of the two means, the model tests are easier and more in­structive. We are able to make models from Ve to V12 size or smaller, depending upon the size of the actual hood in question. We test these models using air as the flowing fluid, and are able to observe very closely the flow characteristics. This can, of course, be done in advance of the construction of the full-sized hood in the factory.

Any model tests should be checked if possible on the actual full-sized apparatus and we have been able to check in this case by making annulus pressure measurements in actual turbines operating in some of the power stations in the country. The agreement between model and full-sized hood is very good and justifies the model tests.

The curve marked “total loss” in Figs. 13 and 14 can be checked as to shape by still another means which is open to us. A tur­bine can be operated under test conditions so that the weight flow through the last stage buckets is at a constant rate. Then the turbine condenser pressure can be varied by bleeding air to the condenser, or by other means, and the variation of turbine output can be measured. This variation of output is really a difference between the change in available energy due to the change in exhaust pressure and the change in exhaust loss oc­casioned by the change in exhaust volume flow. The change in available energy is readily calculated from the steam chart, leaving a change in exhaust loss determined. Whenever pos­sible, therefore, we obtain these variable vacuum curves at constant flow, as valuable aids and checks on our calculation methods. It is not always possible, since turbines of moderate and large capacities must be tested, if tested at all, in the operator’s power station and operating conditions or other factors may make extended tests impracticable.

It is evident from the foregoing that means of testing have been developed and are used for checking and substantiating the methods of exhaust loss calculation as presented by Mr. Robin-

H. V. Rasmussen.9 The author has written a very interesting paper which is of vital interest to the turbine designer, as the

8 Turbine Engineering Department, General Electric Co., Schenec­tady, N. Y. Jun. A.S.M.E.

• Westinghouse Electric and Manufacturing Co., South Phila­delphia Works, Philadelphia, Pa. Mem. A.S.M.E.

524 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

dimensioning of the last spindle row and the turbine-exhaust casing has a deciding influence on both the turbine performance and the manufacturing cost.

If a turbine element in the high-pressure end of a turbine is not very efficient, up to one-half the losses may be recovered in the rest of the turbine due to reduced moisture and increased heat drop, but losses in the exhaust end of a turbine are irretrievably lost to useful work. Any improvement obtainable in the ex­haust end will have a direct bearing on the over-all performance of the turbine.

While the performance of a turbine is improved by a large last-row annulus with a correspondingly low kinetic leaving loss, the manufacturing cost of a turbine goes up rapidly with the increase of the dimensions of the last row. Also, blade and spindle stresses place a definite limitation on the physical dimen­sions involved. A proper compromise between these various factors must, therefore, be established in practical turbine design.

The present tendency toward large single-cylinder turbines makes it necessary to employ high peripheral blade speed in the last row, with a resulting high steam speed and a large kinetic leaving loss. The place for improvement, consequently, is in the exhaust casing which should be designed to offer the smallest possible resistance to flow from the last-row annulus to the exhaust opening.

It would be interesting to know how the author arrived at the annulus pressure drop shown on Figs. 5 and 7, and also how it was established that some exhaust casings are actually diffusing. Measurements on actual turbines are very difficult to obtain as they involve measurements of static pressure in the high velocity jet. Some attempts were made to measure the pressure drop in an exhaust casing of a large Westinghouse turbine by tapping the cylinder casing at various points in the cover and base. No conclusive results were obtained from this investigation as it was obvious that a velocity head created by the steam impinging against the measuring hole obscured the results and, at the very best, these measurements would only record the pressure exist­ing at the periphery of the casing. They could not disclose the pressure distribution in the middle of the casing. Measurements with pressure-measuring tubes, such as the Fechheimer tube, were given up as impracticable, as the moisture in the steam would partly fill the passages and cause incorrect readings.

Another approach to this problem is to conduct tests with small-scale models. A number of exhaust model experiments for various exhaust-cylinder designs were run by the Westinghouse Company. Wooden models of the exhaust casing were made to Vs of full size and air was blown through the models. A rotating blade row, mounted on a disk and driven by a motor, represented the last spindle row. Pressure measurements were taken with a Fechheimer tube at a number of points around the blade annulus and the velocity distribution over the exhaust opening was recorded with a Prandtl impact tube.

These experiments disclosed a number of interesting facts. First of all, it was found that steam is distributed most unevenly throughout the casing and the exhaust opening. The steam clings to the generator side of the exhaust casing and also crowds this side of the exhaust opening, while the part of the exhaust opening that is nearest to the turbine is hardly filled. If a part of the exhaust opening is located under the bladed part of the cylinder, the pressure drop through the casing will increase con­siderably.

The tests also showed that ribs and steam deflectors in an exhaust cylinder might improve the distribution of the steam over the exhaust end, but generally accomplishes this at a cost of an increased pressure drop from the last row to the exhaust opening. The older exhaust-cylinder design with a number of separate passages from the last row to the exhaust opening had thus a

and the low-pressure end losses AR become zero. This inter­change of energy is contrived through a completely reversible process and while it represents the ideal in achievement it is, in the light of our present knowledge of the physical laws, quite beyond the realm of possibility.

The next possible solution to Equation [1] lies in the recon­version of a portion of the kinetic energy of discharge by a diffusor- shaped exhaust chamber. It is represented physically by the boundary condition > pi and by (i2 — ii) > A f vdp. Prac­tically, this solution is the aim of all good designs since the total low-pressure end losses become less than the leaving-velocity loss at the blade annulus. Unfortunately, mechanical restric­tions, imposed largely by the purchaser, have prevented many exhaust-end designs of this type in the United States, although in Europe the practise is used frequently to advantage.

A solution almost akin to the one just described lies in a partial reconversion into pressure which is subsequently lost through wall friction in the exhaust chamber. In this case pi = p2, and the low-pressure end loss is equal to the kinetic energy of the fluid from the last-blade annulus. This assumption was widely used in turbine design up to the past few years but increasing demands for economy have necessitated a solution more in keeping with the actual condition. This solution usually consists not only in a complete loss of the kinetic energy of discharge but in an addi­tional pressure drop as well (p2 < pi). In this case the a J^2 vdp is negative. This is the condition to which the author devotes himself, and while far from the ideal it is at present the most common. The real problem in this design lies in the determina­tion of the pressure drop. Since measurements on actual ma­chines are practically impossible, models are usually prepared. However, the requirements of similarity are not wholly satisfied in the model due to the extreme velocity and pressure conditions that exist in the usual exhaust end.

10 Experim ental Engrg. Dept., Westinghouae Elec. and Mfg. Co., South Philadelphia Works, Philadelphia, Pa. Jun. A.S.M.E.

considerably larger pressure drop through the casing than the bare exhaust cylinder. However it was found possible to design a deflector that was shaped as part of a rotative body and that reduced the pressure drop as it diminished the concentra­tion of flow at the condenser side of the exhaust opening.

The pressure measurements around the periphery showed a somewhat similar distribution to that shown on Fig. 7 of the author’s paper.

R o n a l d B. S m i t h . 10 Low-pressure end losses consist of fric­tion due to wall resistance and curvature losses in the exhaust hood, and eddy friction resulting from the attempt to convert kinetic energy at the blade annulus to potential energy at the condenser flange. Physically these losses are an evaluation of the well-known relation

in which R is the total low-pressure end loss, i the enthalpy of the steam, A the Joule conversion factor, with the subscripts 1 and 2 referring to conditions at the exhaust annulus and the exhaust flange, respectively. In the design of the exhaust we are faced with four characteristic solutions of the relation ex­pressed by Equation [1], First, there may be complete recon­version of the kinetic energy at the exhaust annulus into poten­tial energy. In this case we have an isentropic change in which

FUELS AND STEAM POWER FSP-56-10 525

As the author has already pointed out an expression for the low-pressure losses in per cent of the adiabatic enthalpy change means little unless one is familiar with the type of cycle. A term more closely representing the efficiency of the low-pressure end design proper would be the ratio of the average kinetic energy at the exhaust flange to the total frictional loss.

Equation [2] is a m*'.« ire of the designer’s skill, and for the perfect diffusor has ■ value of

TJexh = 100 per cent.

In the 35,000-kw machine described by the author the net annulus area appears to be 31 sq ft. Assuming that the exhaust- flange area is about 31/0.4 = 78 sq ft, the average kinetic energy at the. exhaust is 6.7 Btu at full load. Then the efficiency of the exhaust end proper is = 26.5 per cent. The corre­sponding loss based on the adiabatic enthalpy change is about 4.9 per cent. These two factors would appear to define fully the conditions at the low-pressure end. The exhaust efficiency repre­sented by Equation [2] is a measure of the relative merit of the exhaust hood, and to the designer it represents the internal ef­ficiency of the low-pressure end. The conventional leaving loss on the other hand shown in Figs. 13 and 14, represents the low- pressure frictional losses in respect to the total available energy; it determines whether efforts to improve the exhaust end ef­ficiency tjexh are justified from the standpoint of economy.

C. R. S o d e r b e r g . 11 Turbine designers will welcome this paper on a subject which has always represented an important question in the art. Very little of the material as presented can be regarded as controversial, and the writer will limit himself to a brief discussion of a few points.

The leaving loss is undoubtedly one of the most important single items in condensing turbines, particularly because it can be influenced to a considerable extent by modifications in design, specifically by the size of the exhaust annulus. A similar in­vestigation was made sometime ago by Prof. A. G. Christie and presented at the 2nd World Power Conference in 1930.11 This in­vestigation, as well as the one covered by the present paper, neglects another loss item which is of the same significance and which must be considered in connection with the leaving loss. This is the loss caused by the moisture in the low-pressure end of condensing turbines. Very little reliable information exists as to the magnitude of the latter loss, but some of the results ob­tained recently by the Westinghouse Company indicate that it is often greater than the leaving loss. In particular, it is in­creased rapidly with the peripheral speed. If the leaving loss is reduced by an increase in blade annulus, this reduction is accom­panied by an increase of the moisture loss which may, in certain cases, more than offset the reduction of leaving loss. With this fact in mind, it is impossible to arrive at an economical size of exhaust annulus without injecting the moisture loss. Supersaturation, on the other hand, can generally be disregarded, at least for the moisture contents now common in condensing turbines.

The author has properly emphasized the importance of in­cluding in the leaving loss the losses in the exhaust hood. The

11 Manager, Turbine Apparatus Division, Westinghouse Elec. and Mfg. Co., South Philadelphia Works, Philadelphia, Pa. Mem. A.S.M.E.

11 “Economic Considerations in the Application of Modem Steam Turbines to Power Generators” by A. G. Christie. Second World Power Conference, 1930.

benefit of a generously dimensioned exhaust annulus may be lost unless the hood is properly proportioned and dimensioned.

It would be of great interest to know by what means the pres­sure distribution shown by Fig. 7 was obtained. We have made attempts at similar measurements and have been forced to con­clude that it is exceedingly difficult to get the pressure readings inside the exhaust of an actual turbine. Fig. 7 indicates a de­gree of precision which I know is very difficult to reach.

A t jt h o r ’s C l o s u r e

In concluding this discussion, it seems necessary first to set down the distinction between the leaving-velocity and exhaust loss on the one hand and the vacuum corrections applicable to the turbine-performance curve on the other hand. This paper has confined itself entirely to the former which is supposed to occur in the exhaust hood between annulus and exhaust flange. In preparing the vacuum corrections showing the variation of turbine performance with changing back pressure at the exhaust flange, it is necessary to take account of all other contributing or interrelated effects, whether or not they are parts of the loss in question. It is, of course, true that in many cases the vacuum corrections consist almost entirely of leaving-velocity and ex­haust loss but the distinction is very real. Operators generally are interested in the vacuum correction. The leaving loss, as such, has always seemed to us a matter of interest particularly to the designer. It is one of the most important elements in­fluencing turbine performance.

Mr. Caldwell is inclined to doubt the continuance of load growth. It is true that there has been a five-year cessation in this matter but it is also true that in many areas with favorable rate structures the per capita consumption of electricity is several times what it is in some of our largest metropolitan centers. In our opinion, any system that has the courage to look ahead 15 or 20 years may expect a load growth to two or three times its present size. While the annual percentage increments may fall off, it is likely that the actual kw increments may increase. Cer­tainly the use of electricity is going to increase whether the pres­ent systems furnish the power or whether it is to be supplied in some other manner.

Professor Christie raises the question as to the desirability of incorporating diffuser exhaust hoods in all turbines and this mat­ter is also touched Upon by Mr. Smith. This question is largely an economic one and it is not easy to answer it briefly. However, this much may be said: that such diffusing hoods as are now in existence have that property as a by-product of other features of design and were not so made for that reason alone. The design is usually expensive and justified only under special conditions.

The author’s remarks on supersaturation were based on the findings of the General Electric Company as set forth by Pro­fessor Goodenough in his published report in 1927. It must be admitted that the true condition is still a matter of argument but undoubtedly more specific analyses will be available in the future. Probably we should not have said it could be “neg­lected.” When a manufacturer bases his promises on well-es­tablished past performance, it is impossible for him to neglect anything. But, on the other hand, the more specific his analy­sis, the greater are his opportunities to improve design.

Professor Christie also asks about the true end-point of the condition curve. It seems to the author that that is given by the exhaust heat and the exhaust pressure and that it is the only point definitely known except that fixed by the initial conditions. Given the initial conditions, known performance gives the end point. All intermediate points must be estimated by design technique and the better they are filled in, the better may they be used for improving design. For instance, to get back to the wheel exit, it is necessary to divide the exhaust heat between

526 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

pressure-volume energy, temperature energy, velocity energy, and if there is supersaturation, it may be necessary to include surface-tension energy. As a short cut from the true end-point to the wheel exit, one might draw a horizontal line to the left to annulus pressure and thence down the pressure line so as to de­duct the velocity energy fraction of the leaving loss. That would locate what might be called the “chart condition” of the- steam at the wheel exit, which would be useful to give the mois­ture content. This is to be distinguished from what would be the end-point of the machine if it had zero-leaving loss. The important point in this matter is to base predictions upon exactly the same conventions used in analyzing performance.

Mr. Crocker has pointed out how necessary it is for an operator to have all the essential information about his machine. Cer­tainly the manufacturer intends to furnish all such information and if it has not been done in the past, that must have been due to a misunderstanding of the needs in the particular case.

Mr. Franck has called particular attention to a number of items and rightly expresses his concern about the flow area of the last row of blades. That is usually the most important fea­ture of all, and, if the author did not show proper concern about it, that was because of its general recognition. Mr. Franck’s remarks about the effects on the preceding stages help to bring out the distinction which is necessary between the total net effect on turbine performance of a change of vacuum, and the leaving-

velocity and exhaust loss by itself. Although the distinction might be thought of as only a matter of definition, it is none the less important.

Mr. Hiebeler points out the important effects of varying cool- ing-water conditions on the vacuum and consequently on the magnitude of the leaving losses. The diagrams in the paper have been based on 1 in. Hg abs back pressure. There is a certain back pressure below which better vacuum fails to yield any more power. Refrigeration, in itself, is detrimental. In deciding how much water to pump it is necessary for an operator to bal­ance his pump requirements and refrigeration losses against the additional power shown by his vacuum corrections.

Mr. Knowlton’s discussion anticipates the questions raised by Messrs. Rasmussen and Soderberg about the pressure meaure- ments in exhaust hoods as shown in Figs. 5 and 7 and it does not seem necessary for the author to add anything further on that subject.

Mr. Soderberg also mentions the importance of proper consider­ation of moisture losses and here again it may help in clarifying the situation to point out that moisture effects have been consid­ered in the paper only in so far as they affect the leaving-velocity and exhaust loss itself. Changing degrees of moisture in pre­ceding stages affect the turbine performance and have to be con­sidered in predicting vacuum corrections but such effects are not a part of the leaving loss even though in part due to it.