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FSP-56-10

Leaving-Velocity and Exhaust Loss in

Steam Turbines

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

T h i s p a p e r g iv e s a n e x p o s i t io n o f t h e v a r i o u s i t e m s w h i c h

g o t o m a k e u p t h e l e a v i n g v e lo c i ty a n d e x h a u s t l o ss o f a

s t e a m t u r b i n e . T h e i m p o r t a n c e o f t h i s l os s a n d t h e r a

p id it y w ith 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 se i t to b e a

d e t e r m i n i n g i n f lu e n c e i n f i xi ng t h e e c o n o m i c r a t i n g o f a

m a c h i n e . T h e s e v e ra l e l e m e n t s n e c e s s a r y f o r a n a n a l y s i s

a r e e a c h e v a lu a t e d i n a f a i rl y d i r e c t, a l t h o u g h s o m e t im e s

a p p r o x i m a t e , m a n n e r . M o r e d e t a i le d a n d p r e c is e e s t i

m a t e s m i g h t b e m a d e b u t a r e b e y o n d th e i n t e n t o f t h i s

p a p er.

T h e l o ss in q u e s t io n o c c u r s i n t h e e x h a u s t h o o d b e t w e e n

t h e l a s t w h e e l ex i t a n d t h e e x h a u s t f la n g e t o t h e c o n d e n s e r .

I t i s m a d e u p b o t h o f k i n e t ic e n e r g y l o ss a n d o f p r e s su r el os s t h r o u g h t h e h o o d a n d e a c h e f f e ct v a r ie s w i t h l o a d a n d

w i t h l o c a t io n a ro u n d t h e w h e e l a n n u l u s . M o i s tu r e is

a ll o w e d f o r ; s u p e r s a t u r a t i o n n e g l e c t e d .

T h e t o t a l lo s s ma y b e e x p r e ss e d i n B t u p e r p o u n d f lo w

t o 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 i a b a t i c h e a t d r o p o r

THE most important single loss in a condensing steamturbine is the leaving loss, exhaust loss, orleaving-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 asto the items properly included under the heading nor asto the manner in which the loss is to be evaluated forcomparative purposes.

The importance of this loss and the rapidity withwhich it increases at high loads cause it to be a determining influence in fixing the economic rating of a machine (seeFig. 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 steamturbine may be likened to the tailrace loss of a water wheel.If the tailrace runs downhill, there is a correspondingloss of headthe wheel setting should have been lower.If the tailrace runs level there is the loss of velocity headonly, which may be small if the cross-sectional area is generous. If the tailrace runs smoothly uphill into quietwater, the leaving velocity is recovered because the wheel

operates under a gross static head greater than its net head bythe velocity head converted in its tailrace.

1T urbine Engineering De partm ent, General Electric Co. Mem.A.S.M.E. Mr. Robinson was grad uated from the St. LawrenceUniversity in 1911 and from the H arv ard G radu ate School of AppliedScience 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 w ar he served in the Oise-Aisne offensive as first Lie utenant with th e 302nd Engineers, U. S. A., and later as C aptain andAd jutant of the 2nd Engineer Training Regiment. For the pastfifteen years he has been employed by the General Electric Compa ny in its Tu rb ine Engineering Dep ar tm en t.

Contributed by the Power Division and presented at the AnnualMeeting, New York, N. Y., December4 to 8 , 1933 , ofT h e A m e r i ca nS o c i e ty 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 : Statements and opinions advanced in papers are to beunderstood as individual expressions of their a uthors, a nd no t those ofthe Society.

p re fe ra b ly a s a p e r c e n t o f t o ta l e n e rg y th e o r e t ic a l ly a v a il

a b l e f o r c o n v e r s i o n t o s w i t c h b o a r d p o w e r .

W i th 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 f ix ed s te a m c o n

d i t i o n s , t h e 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 i n c r e a s e s

r o u g h l y a s t h e s q u a r e o f t h e l o a d ( p a r a b o li c r u le ) .

W i th a p a r t i c u l a r e x h a u s t p a s s i n g a f ix ed fl ow , in c r e a s i n g

t h e t o t a l a v a i la b l e e n e r g y i n t h e h i g h e r s ta g e s o f t h e t u r

b in e by im p ro v e d s t e a m c o n d it 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 t a g e l o ss i n t h e e x h a u s t ( h y p e rb o l ic r u le ) .

W i th a f i xe d p e r c e n ta g e l os s 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-powero f t h e t o t a l a v a i l ab l e e n e rg y b y i n c r e a s in g t h e

f lo w t o t h e c o n d e n s e r .B a s e - lo a d o p e r a t i o n j u s ti f ie s m o r e l i b e r a l e x h a u s t a r e a s

t h a n p e a k -l o a d se rv ic e 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 -

l o a d c u r ve i s th e c h a r a c t e r i s ti c w h i c h i s o f m o s t i m p o r

t a n c e t o t h e o p e r a t o r a n d s e c o n d o n ly t o t h e r e l ia b i l it y 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 i c R a t i n g

(S t ruc t u ra l c ons i de ra ti ons l i m i t t he m a x i m u m a nnu l us a re a a t a ny s pe e d t o s l i gh t l yl e ss t ha n i n i nve r s e p ropor t i on t o t he s qua re o f t he s pe e d . T hus a s i ng le e xha us to f li m i t i ng s i ze a t 3600 rpm m a y be e xpe c t e d t o ha nd l e no t qu i t e one -qu a r t e r

a s m uc h c a pa c i t y a s a s i ng le e xha us t a t 1800 rpm . )

In the water wheel one deals with low velocities but a heavyfluid. With steam one deals with an exceedingly rarefied fluid

but with velocities which are correspondingly high and with akinetic energy content which varies with the square of thevelocity.

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 importantitems contributing to the leaving-velocity and exhaust loss of thesteam turbine from the manufacturers point of view. Typicalcurves 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 ofgiving detailed formulas or test data. For reasons which willappear, it does not seem desirable to standardize any calculationsor to recommend any set expressions or formulas. This does notmean that suitable comparisons among designs should not be

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made. The idea is th at each comparison should be made on itsown merits.

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

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

W EIGH T FLOW TO C O f iPE / iSE F ' LB./SEC.

F i g . 2 C o n d e n s e r F l o w (35,000-kw exfcract ion-feed-heat ing tu rbine operat ing a t 250 lb per sq in .

gage, 700 F, and 1 in. Hg.)

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 bucketefficiency and the stream is supposed to have healed into a cylindrical jet on emerging from the wheel annulus. This latterruling is, of course, arbitrary. The N.E.L.A. Prime MoversCommittee Report on Turbines, No. 234, July, 1932, recommendedcorrecting 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 twiceand 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 operatingat 250 lb per sq in. gage pressure, 700 F temperature, and 1 in.

Hg abs back pressure with two stages of extraction for feedwaterheating.

F i g . 3 Sp 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 i n g 1 I n .

Ab s P r e s s u r e a n d 10 P e r C e n t M o i s t u r e

(35,000-kw turbine.)

If1Ss8*

I

H g

w e i g h t f l o w t o cond e n s e/? l b/sec.

F i g . 5 R e l a t i o 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 i g h t

F l o w t o r 1 I n . H g Ab 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 dotted lines A, B,_C, and D for con stant annulus volume flows correspond to the velocity diagrams in Fig. 4 and show th e relation between an

nulus pressure an d w eight flow for varying ex haust flange pressures.)

F i g . 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 in gF 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 a re velocities in ft per sec exc ept for the he at equivalents in B tupe r l b of th e ki net ic en er gy of ab so lu te ex hau st ve lo ci ty . E ach diagra m re presents a partic ular annulus volume flow, as indicated. The volume ma y bemade u p of a larger we ight of denser steam or a smaller weight of more rarefied

steam. See Fig. 5.)

existing in the exhaust hood between the exit from the wheelannulus 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 moisture moves at very low speed. For 1 in. Hg abs pressure at theexha ust flange and the exhaust-hood drop shown in Fig. 5, the points A,B, C, and D correspond to the actua l kinetic energy leaving loss and also

to the several diagrams in Fig. 4.)

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FUELS AND STEAM POWER FSP-56-10 517

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

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

By way of identifying the conditions of operation to whichthese diagrams apply, it should be noted that each represents adefinite volume flow, and Fig. 5 gives the corresponding linesfor 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 severalweight flows corresponding to the different loads of Fig. 2.

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

It is necessary to bear in mind that the annulus pressure is notuniform and Fig. 7 shows how it varies around the circumferencefor two flows approximating full load and half load, in each casefor a pressure at the exhaust flange of 1 inch Hg abs.

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

haust ve loc i ty. )

F i g . 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 Loss P e r Lb o fS t ea m a t S p e ed i n t h e A n n u l u s o f a 35 ,0 00 -K w T u r b i n e

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

A V A I L A B LE E H E / ? $ Y L O S S B T U/ LB T O T AL F L O V J T O C OM D E H S E F ?

F i g . 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 pT h r o u g h t h e E x h a u s t H o od F ro 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 to 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 ia t io 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 rc 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 oS 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 internalbracing. 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 te am a t S p e ed A r o u n d t h e P i tc 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 00 -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 , 85 L b

p e r S e c a n d 4 5 L b p e r S e c

(The weight flow i s prac t ica l ly uni form aroun d the a nnu l us . The vo l um eflow varies in inverse re la t ion to the pressure and consequent ly the ve loc i tyand kine t ic energy Vary as shown.)

F ig . 11 V a r i a t io 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 ss 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 00 -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 , 85 L b p e r S e c a n d 4 5

L b p e r S e c

(This variation is due to the variation 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) tangentialcomponent, and (3) non-uniformity of flow. It remains to

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518 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEER S

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

Fig. 10 shows the relation to be nearly linear so that Fig. 11,which illustrates the distribution around the annulus, is notabsolutely essential for a satisfactory preparation of Fig. 12which shows the available energy loss plotted against the variousloads in kw.

Ab 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 o o d

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

F i g . 12 T o t a l I n t e g r a t e d 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

(This is the average for the entire annu lus and applies to the total weighflow.)

efficiency of 75 per cent has been assumed, whereas more accurateestimates use true efficiency curves, or true integrated availableenergy.

The total loss might be divided up in another way by definingthe net exhaust-hood loss as the extra loss occasioned by havingthe specified exhaust or condenser pressure occur at the hoodflange instead of at the wheel annulus. This viewpoint has acertain merit in setting up a standard for comparison of no

pressure drop through the hood. The net hood loss viewed thisway is less than the actual loss due to the pressure because thepressure drop reduces the kinetic-energy loss at the annulus.In order to divide the total loss in this way it is necessary tocompute the leaving velocity loss at the annulus with the specifiedexhaust pressure occurring at th at location. The balance between this and the total may be thought of as the net amount dueto the presence of the exhaust hood. This is not the same as theapproximate computation suggested below, because true performance (as nearly as can be estimated) under the supposedconditions is computed. The result especially depends on boththe relation between the size of annulus and the hood and theload, and the method of computation employed for estimatingwhat would happen under the assumed conditions. Thus aheavily loaded annulus discharging into a liberal hood will suffervery little additional loss because of pressure drop through thehood as compared with free discharge without any hood. On

F i g . 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 la b l e E n e r g y in A l l S te 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 betwe en true velocity lossand pressure loss as they ac tually occur. The dotte d line shows the appro ximate leaving veloci ty and exhaust loss based on computed normal annulusvelocity, assuming exhaust flange pressure at the annulus and expressed as a

pe r cen t of th e adia ba tic heat dr op in th e tu rb in e. )

denser flow. It should not be necessary to explain the differencein velocity between the moisture and the steam, further than torefer to the article SupersaturationThe Flow of Wet Steam,by the late Prof. G. A. Goodenough,2describing steam-flow testsconducted 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 12leads to Fig. 13, the total leaving velocity and exhaust-loss curvefor this turbine. For simplicity an average over-all engine

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

F i g . 14 T o t a l L e a v in g - V e l o c i t y a n d E x h a u s t Loss o f a3 5,0 00 -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 la b l e E n e r g y i n A l l S te a m , D i v id e d So a s t oS 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 th e velocity loss is tha t which would occur with exhau st p ressure at the wheel itself.)

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

It 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 beinferred by looking at Fig. 13. The example here given has arather high net hood loss.

Ap p r o x i m a t e E s t i m a t e s

For comparative purposes the dotted line in Fig. 13 has beenprepared in a very simple manner by multiplying the weight flowto the condenser by the specific volume at the exhaust flange anddividing by the annulus area. This gives an average annulusvelocity which has been converted to a kinetic energy heat conten t in Btu per lb and divided by the adiabatic heat drop, without

regard to extraction. This curve may be compared with themore accurate estimate which is given in full lines. The apparent inconsistency of using exhaust flange volume as if present at

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FUELS AND STEAM POWER FSP-56-10 519

the annulus goes part way to compensate for the neglect ofpressure drop through the hood with its corresponding loss ofavailable energy.

S u p e r s a t u r a t i o n

In dealing with the results so far set down no account has beentaken 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 consideringFig. 13 as representing absolute values, this reservation has to bekept in mind in addition to the minor inaccuracies purposelyassumed for simplicity.

It has been noted in comparing Fig. 14 with Fig. 13 that thetrue loss through the exhaust hood is accompanied by a reduction of velocity loss in the denser medium at the annulus. Thetwo 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 ofthe leaving-velocity loss. With the amount of moisture presentthere is not likely to be any high degree of supersaturation inthis particular case. However, in a different case with, say only

2 or 3 per cent of moisture theoretically present, supersaturatedexpansion should be allowed for.

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

While it is legitimate to express the leaving velocity andexhaust loss in a variety of ways, it is always well to bearin mind the significance of the type of expression used. Forinstance, the difference between the approximate calculationdotted in Fig. 13 and the more exact one in full lines may bequite different for another design. There are a number of tur

bines in sizes over 50,000 kw in which, under favorable load conditions, the hoods are diffusing and produce a lower pressure atthe annulus than exists at the exhaust flange.

Thus it is correct to speak of a loss of 30 Btu per lb flow to thecondenser. But such a statement is not very significant. Ifthe adiabatic heat drop is 500 Btu, the loss may be said to be 6per 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 throughthe 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 ty a n d E x h a u s t L o s s W i th

V a r io u s S t e am C y c l e s , i n E a c h C a s e W i th 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 substituting modern steam conditions for lower pressures and older cycles,the percen tage leaving loss will be greatly reduced and the ex haunt will

appear wastefully generous in size for the better steam conditions.)

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

F i g . 16 Ap 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 i t y M a d e A v a i l

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 thereasons 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 thecondenser (see Fig. 15). Such a loss amounts to 10 per centof the adiabatic heat drop of an ancient low pressure turbinewith 300 Btu available energy while it is only 5 per cent of theadiabatic heat drop of a modern high pressure resuperheatingturbine with 600 Btu available. Similarly a full use of stageextraction for feed heating so increases the power generated froma particular exhaust that the importance of a fixed leaving-velocity and exhaust loss may be decreased as much as 20 percent in this manner; an effect which is not shown at all by expressing the loss in terms of adiabatic heat drop, which does notchange with extraction.

The use of the mercury turbine in conjunction with the steamturbine still further reduces the percentage importance of a fixedsize loss.

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

I n c r e a s e d C a p a c i t y

Fig. 16 is the counterpart of Fig. 15 showing how the capacityobtainable from the steam entering a given exhaust may beincreased by the use of modern cycles. The relative capacitiesfor 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

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

C o n d i t i o n s o f Op e r a t i o n

The type of service and conditions of operation also are veryimportant 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 mostof 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 runningat maximum capacity only a short part of the year.

Roughly speaking, the higher the annual capacity factor thelower 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 samein each case, but Station A is taking the swings and does the bulkof its operation at half and three-quarters load while Station B ison base-load service and operates mostly around three-quartersto full load. If these two stations were each equipped with asingle turbine of the type represented by Fig. 13, the integratedloss due to hood effects in Station B would be 50 per cent morethan in Station A, the difference amounting to approximately1 per cent of fuel requirements. From this it may be inferredthat with medium coal prices a purchaser could afford to paysome 10 per cent more in the case of Station B for a turbine withmore liberal exhaust and a different load curve from that whichwould be suitable for Station A.

This brings attention directly to the load curve as being con

sidered a most important feature by operators in the selectionof a turbine. It is second only to reliability of operation andwith 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 thro ttle loss at lightloads, which dwindles out at full load, the leaving-velocity andexhaust loss, which increases from very little at light loads, isone of the most effective tools the turbine designer has at hisdisposal in producing the type of machine suited to the operatingconditions.

Discussion

W. 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 simplermethod could be devised for comparing turbines it would behelpful in evaluation procedure. It would be interesting if theauthor could indicate the probable error which might be introduced in comparing the exhaust end of a variety of turbineson the basis referred to in the N.E.L.A. Prime Movers CommitteeReport No. 234 on Turbines.

The author speaks of load curves and conditions for which aturbine is chosen but these conditions are so subject to changethat it is difficult to predict conditions far in advance.In case of doubt as to the future it may be wise to leanin the direction of capital savings at the expense ofeconomy. Until quite recently growth of load throughout the country was rapid and new units were installed at fairly frequent intervals. Each succeedinginstallation carried design improvements rendered possible by the advance in the art. With new units ofsuperior 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 systemnew machines purchased some years ago were operated

at 58 per cent capacity factor for about 6 years andafter this period the use of these machines diminishedalmost annually until it finally reached a capacityfactor in the neighborhood of 5 per cent in about 20years. Experiences of this kind cannot be safely takenas a basis for purchase of new machines since it

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

In the absence of continued load growth, the capacity factorand use factor of the more recent machines will increase materiallyabove that which might be anticipated from earlier experience.Under such conditions machines evaluated for a relatively lowcapacity and use factor may ultimately become base-load units ofthe 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 areasin the turbine is the cost of steam-generating capacity to meetfull-load requirements. With a lower exit loss less steam-generating capacity is required and this should be carefully consideredin evaluating turbine performance. Whether the value of theadditional boiler-plant capacity required by a less efficient turbineis taken on a pro-rata base or increment cost base is largely amatter of judgment, but it is an important consideration if thehighest economy in the use of capital is to be achieved.

Summarizing, the influences to be considered in the design ofthe turbine-exhaust end are the capacity factor, cost of boiler andcondenser 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 theperiod of maximum demand of the system coincides with theperiod 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 initialsteam conditions and other improvements in reducing the percentage exit loss, nevertheless there is often potential capacityavailable which might have been purchased at an attractiveprice. In latitudes favored with an abundance of cold condensing water during the period of maximum demand, it is probablethat there are cases where available capacity might have beenpurchased 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 i g . 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 mannerwith the load, a base load station such as B will experience a greater integrated lossthan a s tat ion l ike A which shares light loads. Turbines for base load service w arrant

more liberal exhaust areas.)

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and we may find it profitable in the future to resort to moreliberally designed exhaust areas in steam turbines, as well asmore liberal condensers and auxiliaries. With each successiveinstallation closer cooperation is developed between the engineersof the manufacturers and those of the power producers and it is through the mutual understanding of the common problems in

volved 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 para

graph, the combined leaving-velocity and exhaust loss constitutethe 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 PrimeMovers Committee of N.E.L.A. Data on various turbines werecollected and referred to the writer for analysis. In many casesarbitrary assumptions had to be made regarding the amount ofsteam to exhaust and other items. Certain of these such as theallowance for blade-outlet thickness on the last set of blades are,as pointed out by Mr. Robinson, open to question. Manu

facturers at that time were somewhat reluctant to discuss leavinglosses. There appeared to be no standard or other method ofexpressing leaving losses. The writer therefore proposed as atentative measure the expression of leaving loss as the equivalentof the absolute velocity from the last row of blades assumingaxial flow and found by assuming the exhaust pressure andvolume at the blade annulus instead of at the exhaust nozzle.In other words the losses in the exhaust hood were not con

sidered. The Prime Movers Committee then considered thequestion of a standard method of expressing leaving loss. How

ever, differences of opinion developed and a suggestion was madethat a leading authority on turbine design be asked to discuss

this whole subject in a paper before A.S.M.E. Mr. Robinsonsconcise 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 totheir influence on plant economy.

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

In Fig. 13 Mr. Robinson shows that the total leaving-velocityand exhaust-hood loss at 28,000 kw, the most efficient load on the35,000-kw turbine under consideration, exceeds the loss cal

culated by the N.E.L.A. method by 0.6 per cent but he alsopoints out that this may not be true for turbines with diffuser exhausts. Few of the turbines in the N.E.L.A. report havediffuser exhaust hoods so that the computed losses are probablynot as large as the sum of the true leaving loss and hood loss. However, it is apparent that the computed figures publishedby 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 tur

bine blades and the quantity of steam flowing to the condenser.Hence the amount of this loss when the maximum length ofblades is used, depends upon the output rating of a given casingas fully discussed in the writers paper before the World Power Conference a few years ago.

Losses through the hood will also be dependent upon the out

put of a given casing but as Mr. Robinson states these will alsodepend upon exhaust outlet design. Certain exhaust hoodsexert 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 ofall turbines. Some savings would result from such an idealdesign.

Regarding supersaturation, Mr. Robinson indicates that thisonly needs consideration when moisture contents of 2 to 3 per centoccur at exhaust. Generally the moisture content ranges from 8

to 11 per cent. Can any supersaturation exist at the last row ofblades under these conditions? The late Professor Callendar andH. M. Martin, both of England, have advanced the opinionthat supersaturation will persist even to exhaust. R. Colburnand 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 erosionfrom moisture. But the question is by no means settled.

One of the Power Test Code Committees should consider astandard 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 bestandardized 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 con

struction. They cannot be increased or decreased for givenoperating 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 theinitial selection of the turbine equipment. Mr. Robinson pointsout certain factors such as the character of load, etc., whichinfluence 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 conditioncurve. In some cases, the whole of the leaving loss has beendeducted 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. Ob

viously 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 engi

neers as it discusses a hitherto little understood subject in a clearand comprehensive manner.

S a b i n C r o c k e r .6 Mr. Robinsons paper presents valuableinformation 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 usersview of these data as they may be applied to turbines in powerplants.

As power-plant heat rates have been improved through thedevelopment of more efficient equipment and the adoption ofmore favorable heat-utilization cycles, it has become necessaryfor engineers charged with the design and operation of powerplants to go progressively to greater refinements in order tocontinue an improvement of thermal efficiency within the eco

nomic limitations of the case. Consequently in order to obtainfurther improvements at the present time it is necessary to con

sider comparatively small differences and quantities, such, forinstance, as are involved in the return of low-grade heat throughthe turbine feedheating circuit, in changes in condensing equip

ment to obtain better vacuum, or other changes which may affectthe exhaust loss in different ways.

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

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Operating companies make many such studies in which theexhaust loss becomes an important item. Under present practise it is necessary to obtain specific data from the manufacturerfor each case considered. This results in great expense to both

parties, loss of time in correspondence, and a restriction in thenumber 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 alwayssatisfactory.

The present paper is a notable beginning toward clearing upthese difficulties in that it enumerates all the items involved in theexhaust loss of a steam turbine. A detailed statement of theturbine-users need for data of this type should likewise help thesituation. Briefly, he should be able to determine the exhaustloss on his turbines for any possible operating condition. In thisregard Figs. 4 and 7 from which can be determined the magnitudeof the loss for a given turbine are of particular interest. It wouldseem that such information should be made available to a turbineowner in either of two different ways: (a) on request furnishhim curves similar to Figs. 4 and 7 applying to his particular turbine and (b) make available to him the methods for computingsuch 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 operatingcondition but it appears that Fig. 7 would have to be given for aseries of different condenser pressures and exhaust flows before itwould be of much use to a plant designer. This would entail alarge 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 incomputing exhaust losses, and that turbine manufacturers andtheir designers prefer to pass out information piecemeal ratherthan to give an operating companys engineers sufficient information about a given turbine for them to compute the necessarycorrection factors for that turbine themselves. Nevertheless,it would seem that the author could well afford to give the usersrequirements 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 agreat deal of concern for the flow area of the last row of blades.

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

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

but for the last three stages, which are affected by the change invacuum, it may be pointed out that the reduction in adiabaticheat 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 volumetricflow through the last row of blading is of such magnitude that aportion of the expansion actually occurs outside of the last-row-blade passage. This results in an uncontrolled expansion whichdestroys a greater part of the energy liberated.

For example, assume that Au for the last three stages at full

6 Turbine Apparatus 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 ofwhich 105 Btu/lb can be converted into useful work. Thenby virtue of limited exhaust dimensions the pressure at the exitof 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 inheat to work will be 5.0 Btu/lb, not corrected for moisture losseswhich, for such small changes, could be neglected.

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

of 1 per cent loss in efficiency for 1 per cent average moisturecontent to the heat converted into work for the two expansions,we see that the heat converted to work for the 29-in. expansion is95.3 Btu/lb and 90.5 for the 28.5-in. expansion. Hence thereduction in heat to work is 4.8 Btu/lb resulting from a reductionin available energy of 21.6 Btu/lb.

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

Another point of importance to be considered at this timeis the possibility of correlating the design of the turbine andcondenser in order to produce an approximately constant volumetric flow through the exhaust end for the normal range ofoperating loads. This could be obtained by controlling thecondenser circulating water to produce the desired vacuum withchanges in steam flow. In this manner the design considerationof the turbine with regards to exhaust dimensions could besimplified.

With such a system of variable vacuum the discussion on reduction in available work would have to be continued withlower flows. With such conditions of reduced volumetric flow,i.e., half load flow at 29 in. vacuum, the effect of explosion is en

tirely eliminated and the actual operating vacuum could beincreased to 29.25 or 29.5 in. and at the same time the extra

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

In regard to the question of designating leaving losses itappears that the most rational method of evaluating themwould be to consider the loss in kw. By the use of kw an ab

solute loss is immediately determined and its magnitude is left without question.

Another point which should be considered is the method ofcarrying peak loads. Some installations carry peak loads withthe bleeder heaters cut out of service and this condition lendsitself to separate consideration by virtue of the added flow passedthrough an already crowded exhaust.

Fig. 18 shows a typical leaving-loss curve for a reaction ma

chine of 35,000 kw.

H. G. Hie b e l e k .7 We are pleased to see such a thoroughdefinition and explanation of a subject which has caused muchcomment 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 amachine has been made, these losses are beyond control except toa limited degree by the plant men. In southern stations, suchas thq Deepwater (Houston) plant, the high circulating-watertemperatures which prevail throughout most of the year limitthe vacuum obtainable. In the north, however, with colderwater conditions, particularly in the winter time, absolute pres

sures between 0.50 to 0.75 in. Hg abs may prevail for severalweeks in extreme cases. In some instances, due to the pressurefrom operating departments together with the natural conser

vatism of designers, condensers are purchased for summer condi

tions. With such installations undoubtedly the magnitude ofthese leaving velocities and exhaust losses is very great. Fromthe operating viewpoint, attention should be called therefore tothe fact that many units are unable to use such high vacua effec

tively or that there is a limit beyond which it is not economical togo. 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 increasedunder high vacuum conditions.

The authors paper considers the performance of the unit as

suming a constant back pressure of 1 in. Hg abs at the flange.We believe it would be of interest to call attention to the variationin the performance of modern condensers with variations in load and with variations in circulating-water temperatures, such asoccur from season to season. The following will illustrate thetypical performance of a condensing unit for a 35,000-kw machine under the conditions prevailing at Houston:

Temperature of inlet circ. water

50 deg F65 deg F80 deg F95 deg F

-----

Steam condensed, lb per br------

-360,000 315,000 235,00 170,000/------Back pressure, in. Hg abs ----- -

0.86 0 .78 0 .64 0 .591.30 1.20 1.02 0.942.00 1.85 1.60 1.443.04 2 .82 2 .48 2 .21

In the tabulation above, the flows which correspond to maxi

mum 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 approxi

mately 25 per cent in the specific volume of the steam to the condenser between half load and maximum load for the samewater conditions and a change of approximately 300 per centfor the same load between summer and winter conditions. This ofcourse neglects the consideration of moisture.

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

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

P. H. Kn o w l t o n .8 This paper is an excellent presentation of

the calculation of the total exhaust loss from a turbine. Itappears worth while to supplement this work by a statement as tothe background of the method and the reasons for believing thatsuch calculations are adequate.

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

Fig. 7, however, requires something more than well-knownrules. The flow of steam through the ordinary downwardexhaust 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 pressuretogether with the steam flow through the last stage wheel.

Of the two means, the model tests are easier and more in

structive. We are able to make models from Ve to V12 size orsmaller, 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, ofcourse, be done in advance of the construction of the full-sized hoodin 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 turbinesoperating in some of the power stations in the country. The

agreement between model and full-sized hood is very good andjustifies 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 tur

bine can be operated under test conditions so that the weight flow through the last stage buckets is at a constant rate. Thenthe 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 adifference between the change in available energy due to thechange in exhaust pressure and the change in exhaust loss oc

casioned by the change in exhaust volume flow. The change inavailable energy is readily calculated from the steam chart, leaving a change in exhaust loss determined. Whenever pos

sible, therefore, we obtain these variable vacuum curves at constant flow, as valuable aids and checks on our calculationmethods. It is not always possible, since turbines of moderate andlarge capacities must be tested, if tested at all, in the operatorspower station and operating conditions or other factors maymake extended tests impracticable.

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

H. V. Ra s m u s s e n .9 The author has written a very interestingpaper which is of vital interest to the turbine designer, as the

8 Turbine Engineering Departm ent, General Electric Co., Schenec

tady, N. Y. Jun. A.S.M.E. Westinghouse Electric and Manufacturing Co., South Phila

delphia Works, Philadelphia, Pa. Mem. A.S.M.E.

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dimensioning of the last spindle row and the turbine-exhaustcasing has a deciding influence on both the turbine performanceand 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 therest 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 ex

haust end will have a direct bearing on the over-all performance ofthe turbine.

While the performance of a turbine is improved by a largelast-row annulus with a correspondingly low kinetic leaving loss,the manufacturing cost of a turbine goes up rapidly with theincrease of the dimensions of the last row. Also, blade andspindle stresses place a definite limitation on the physical dimen

sions involved. A proper compromise between these variousfactors must, therefore, be established in practical turbine design.

The present tendency toward large single-cylinder turbinesmakes it necessary to employ high peripheral blade speed in the last row, with a resulting high steam speed and a large kineticleaving loss. The place for improvement, consequently, is in theexhaust casing which should be designed to offer the smallest

possible resistance to flow from the last-row annulus to the exhaustopening.

It would be interesting to know how the author arrived at theannulus 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 asthey involve measurements of static pressure in the high velocityjet. Some attempts were made to measure the pressure dropin an exhaust casing of a large Westinghouse turbine by tappingthe 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 impingingagainst the measuring hole obscured the results and, at the verybest, these measurements would only record the pressure exist

ing at the periphery of the casing. They could not disclose thepressure distribution in the middle of the casing. Measurementswith pressure-measuring tubes, such as the Fechheimer tube, were given up as impracticable, as the moisture in the steam wouldpartly fill the passages and cause incorrect readings.

Another approach to this problem is to conduct tests withsmall-scale models. A number of exhaust model experiments forvarious exhaust-cylinder designs were run by the WestinghouseCompany. Wooden models of the exhaust casing were made toVs of full size and air was blown through the models. A rotatingblade row, mounted on a disk and driven by a motor, representedthe last spindle row. Pressure measurements were taken with aFechheimer tube at a number of points around the blade annulusand 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 unevenlythroughout the casing and the exhaust opening. The steamclings to the generator side of the exhaust casing and also crowdsthis side of the exhaust opening, while the part of the exhaustopening that is nearest to the turbine is hardly filled. If a partof the exhaust opening is located under the bladed part of thecylinder, the pressure drop through the casing will increase con

siderably.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 anincreased pressure drop from the last row to the exhaust opening.

The older exhaust-cylinder design with a number of separatepassages from the last row to the exhaust opening had thus a

and the low-pressure end losses AR become zero. This inter

change of energy is contrived through a completely reversibleprocess and while it represents the ideal in achievement it is,in the light of our present knowledge of the physical laws, quitebeyond the realm of possibility.

The next possible solution to Equation [1] lies in the recon

version of a portion of the kinetic energy of discharge by a diffusor-shaped exhaust chamber. It is represented physically by theboundary condition > pi and by (i2 ii) > A f vdp. Prac

tically, this solution is the aim of all good designs since the totallow-pressure end losses become less than the leaving-velocityloss at the blade annulus. Unfortunately, mechanical restric

tions, imposed largely by the purchaser, have prevented manyexhaust-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 partialreconversion into pressure which is subsequently lost through wall friction in the exhaust chamber. In this casepi = p2, and thelow-pressure end loss is equal to the kinetic energy of the fluidfrom the last-blade annulus. This assumption was widely usedin turbine design up to the past few years but increasing demandsfor economy have necessitated a solution more in keeping withthe actual condition. This solution usually consists not only in acomplete loss of the kinetic energy of discharge but in an addi

tional pressure drop as well (p2 < pi). In this case thea J 2 vdp

is negative. This is the condition to which the author devoteshimself, and while far from the ideal it is at present the most common. The real problem in this design lies in the determina

tion of the pressure drop. Since measurements on actual ma

chines are practically impossible, models are usually prepared.However, the requirements of similarity are not wholly satisfiedin the model due to the extreme velocity and pressure conditionsthat exist in the usual exhaust end.

10 Ex perim enta l E ngrg. De pt., Westinghouae E lec. an d Mfg. Co.,South Philadelphia Works, Philadelphia, Pa. Jun. A.S.M.E.

considerably larger pressure drop through the casing than thebare exhaust cylinder. However it was found possible to designa deflector that was shaped as part of a rotative body andthat reduced the pressure drop as it diminished the concentra

tion of flow at the condenser side of the exhaust opening.

The pressure measurements around the periphery showed asomewhat similar distribution to that shown on Fig. 7 of theauthors paper.

Ro n a l d B. S m i t h . 10 Low-pressure end losses consist of fric

tion due to wall resistance and curvature losses in the exhausthood, 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 thewell-known relation

in which R is the total low-pressure end loss, i the enthalpy ofthe steam, A the Joule conversion factor, with the subscripts1 and 2 referring to conditions at the exhaust annulus and the

exhaust flange, respectively. In the design of the exhaust weare faced with four characteristic solutions of the relation ex

pressed by Equation [1], First, there may be complete recon

version of the kinetic energy at the exhaust annulus into poten

tial energy. In this case we have an isentropic change in which

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As the author has already pointed out an expression for the low-pressure losses in per cent of the adiabatic enthalpy changemeans little unless one is familiar with the type of cycle. Aterm more closely representing the efficiency of the low-pressureend 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 designers skill, and for theperfect diffusor has value of

TJexh = 100 per cent.

In the 35,000-kw machine described by the author the netannulus area appears to be 31 sq ft. Assuming that the exhaust-flange area is about 31/0 .4 = 78 sq ft, the average kineticenergy at the. exhaust is 6.7 Btu at full load. Then the efficiencyof the exhaust end proper is = 26.5 per cent. The corre

sponding loss based on the adiabatic enthalpy change is about4.9 per cent. These two factors would appear to define fully the conditions at the low-pressure end. The exhaust efficiency repre

sented by Equation [2] is a measure of the relative merit of theexhaust hood, and to the designer it represents the internal ef

ficiency of the low-pressure end. The conventional leaving losson 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 ef

ficiencytjexhare justified from the standpoint of economy.

C. R. S o d e r b e r g . 11 Turbine designers will welcome thispaper on a subject which has always represented an importantquestion in the art. Very little of the material as presented canbe regarded as controversial, and the writer will limit himself to abrief discussion of a few points.

The leaving loss is undoubtedly one of the most important single items in condensing turbines, particularly because it canbe influenced to a considerable extent by modifications in design,specifically by the size of the exhaust annulus. A similar in

vestigation was made sometime ago by Prof. A. G. Christie andpresented at the 2nd World Power Conference in 1930.11 This in

vestigation, as well as the one covered by the present paper,neglects another loss item which is of the same significance andwhich must be considered in connection with the leaving loss.This is the loss caused by the moisture in the low-pressure end ofcondensing turbines. Very little reliable information exists asto the magnitude of the latter loss, but some of the results ob

tained recently by the Westinghouse Company indicate that it isoften greater than the leaving loss. In particular, it is in

creased rapidly with the peripheral speed. If the leaving loss isreduced by an increase in blade annulus, this reduction is accom

panied by an increase of the moisture loss which may, in certaincases, more than offset the reduction of leaving loss.With this fact in mind, it is impossible to arrive at an economicalsize 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 condensingturbines.

The author has properly emphasized the importance of in

cluding 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 SteamTurbines to Power Generators by A. G. Christie. Second WorldPower 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 pres

sure distribution shown by Fig. 7 was obtained. We have madeattempts at similar measurements and have been forced to con

clude that it is exceedingly difficult to get the pressure readingsinside the exhaust of an actual turbine. Fig. 7 indicates a de

gree of precision which I know is very difficult to reach.

A t j t h o r s C l o s u r e

In concluding this discussion, it seems necessary first to setdown the distinction between the leaving-velocity and exhaustloss on the one hand and the vacuum corrections applicable tothe turbine-performance curve on the other hand. This paperhas confined itself entirely to the former which is supposed tooccur in the exhaust hood between annulus and exhaust flange.In preparing the vacuum corrections showing the variation ofturbine 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 vacuumcorrections consist almost entirely of leaving-velocity and ex

haust loss but the distinction is very real. Operators generallyare interested in the vacuum correction. The leaving loss, assuch, has always seemed to us a matter of interest particularly to the designer. It is one of the most important elements in

fluencing turbine performance.

Mr. Caldwell is inclined to doubt the continuance of load growth. It is true that there has been a five-year cessation inthis matter but it is also true that in many areas with favorablerate structures the per capita consumption of electricity is severaltimes what it is in some of our largest metropolitan centers. Inour opinion, any system that has the courage to look ahead 15or 20 years may expect a load growth to two or three times itspresent size. While the annual percentage increments may falloff, it is likely that the actual kw increments may increase. Cer

tainly the use of electricity is going to increase whether the pres

ent systems furnish the power or whether it is to be supplied insome other manner.

Professor Christie raises the question as to the desirability ofincorporating diffuser exhaust hoods in all turbines and this mat

ter is also touched Upon by Mr. Smith. This question is largelyan economic one and it is not easy to answer it briefly. However,this much may be said: that such diffusing hoods as are now inexistence have that property as a by-product of other features ofdesign and were not so made for that reason alone. The design isusually expensive and justified only under special conditions.

The authors remarks on supersaturation were based on the findings of the General Electric Company as set forth by Pro

fessor Goodenough in his published report in 1927. It must beadmitted that the true condition is still a matter of argument but undoubtedly more specific analyses will be available in thefuture. Probably we should not have said it could be neg

lected. When a manufacturer bases his promises on well-es

tablished past performance, it is impossible for him to neglect anything. But, on the other hand, the more specific his analy

sis, 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 bythe exhaust heat and the exhaust pressure and that it is the onlypoint definitely known except that fixed by the initial conditions.Given the initial conditions, known performance gives the endpoint. All intermediate points must be estimated by design

technique and the better they are filled in, the better may theybe used for improving design. For instance, to get back to thewheel exit, it is necessary to divide the exhaust heat between

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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 includesurface-tension energy. As a short cut from the true end-pointto the wheel exit, one might draw a horizontal line to the left to annulus pressure and thence down the pressure line so as to de

duct the velocity energy fraction of the leaving loss. Thatwould locate what might be called the chart condition of the-steam at the wheel exit, which would be useful to give the mois

ture content. This is to be distinguished from what would bethe end-point of the machine if it had zero-leaving loss. Theimportant 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 operatorto have all the essential information about his machine. Cer

tainly the manufacturer intends to furnish all such informationand 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 ofitems and rightly expresses his concern about the flow area ofthe last row of blades. That is usually the most important fea

ture of all, and, if the author did not show proper concern about it, that was because of its general recognition. Mr. Francksremarks about the effects on the preceding stages help to bring out the distinction which is necessary between the total net effecton turbine performance of a change of vacuum, and the leaving-

velocity and exhaust loss by itself. Although the distinctionmight 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 themagnitude of the leaving losses. The diagrams in the paper havebeen based on 1 in. Hg abs back pressure. There is a certainback pressure below which better vacuum fails to yield any more power. Refrigeration, in itself, is detrimental. In decidinghow much water to pump it is necessary for an operator to bal

ance his pump requirements and refrigeration losses against the additional power shown by his vacuum corrections.

Mr. Knowltons discussion anticipates the questions raisedby 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 thatsubject.

Mr. Soderberg also mentions the importance of proper consider

ation of moisture losses and here again it may help in clarifying the situation to point out that moisture effects have been consid

ered in the paper only in so far as they affect the leaving-velocity and exhaust loss itself. Changing degrees of moisture in pre

ceding stages affect the turbine performance and have to be con

sidered in predicting vacuum corrections but such effects arenot a part of the leaving loss even though in part due to it.