William D. (William Duane) Ennis.

Applied thermodynamics for engineers online

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2225
0.08581 X 15.92



= 0.000839; at u.



= 0.000989; at J5,



= 0.000903; at r.



0.08581 X 32.24

2299
0.02002 X 53.92

1330
0.02002x162.62



= 0.001205;
= 0.000809;



= 0.00144.



1507 2271

Completing the computation as to the last set of nozzles only, the throat
area is 0.000809 sq. ft., that at the outlet being 0.00144 sq. ft. These corre-
spond to diameters of 0.385 and



T'"



1



— •.^O.IM ^



M



0.515 in. The taper may be uniform

from throat to outlet, the sides mak-'

ing an angle of 10°. This requires

a length from throat to outlet of

(0.515 - 0.385) -4- 2 tan 5° = 0.742 in.

The length from inlet to throat may

be one fourth this, or 0.186 in., the

« - . -^ ^ . , « ^. , edge of the inlet being rounded.

Fig. 257. Art. 632.— Third Stage Nozzle. * , • 1 • «? «c»t

The nozzle is shown m Fig. 257.

The diameter of the bucket wheels at mid-height is obtained from the rotative

speed and peripheral velocity. If d be the diameter,

3.1416 d X 1200 = 60 X 500, or rf = 7.98 feet



_.^



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PRESSURE TURBINE



335



The forms of bucket are derived from the Telocity diagrams. For the first
stage, we proceed as in Art. 530, using the relative angles e and /given in Fig. 255
for determining the angles of the backs of the moving blades, and the absolute
angles for determining those of the stationary blades.

533. Utilization of Pressure Enerj^y. Besides the energy of impiHse
against the wheel, unaccompanied by changes in pressure, the steam may
expand while traversing the buckets, producing work by reaction. This
involves incomplete expansion in the nozzle, and makes the velocities of
the discharged jets much less than in a pure impulse turbine. Lower
rotative speeds are therefore practicable. Loss of efficiency is avoided by
carrying the ultimate expansion down to the condenser pressure. In the
pure pressure turbine of Parsons, there are no expanding nozzles ; aU of
the expansion occurs in the buckets (Art. 524). (See Fig. 247.) Here
the whole useful effort is produced by the reaction of the expanding steam
as it emerges from the working blades to the guide blades. No velocity is
given up during the passage of the steam ; the velocity is, in fact, increasing,
hence the name reaction turbine. The impulse turbine, on the contrary,
performs work solely because of the force with which the swiftly moving
jet strikes the vane. It is sometimes called the velocity turbine. Turbines
are further classified as horizontal or vertical, according to the position of
the shaft, and as radial flow or axial flow, according to the location of the
successive rows of buckets. Most pressure turbines are of the axial flow
type.

534* Design of Pressure Turbine. The number of stages is now large. The
heat drop in any stage is so small that the entering velocity is no longer negligible.
The velocities which determine the rate of conversion of heat into work will vary
during the passage of steam, being reduced by friction and increased by expansion :
the latter being provided by appropriately shaping the buckets. We may assume

A a reduction of heat drop by friction
g — say 25 per cent — and plot the ex-
% pansive path as in Fig. 240. This
permits of determining the pressure,
volume, and quality at any tempera-
ture.

In Fig. 259, let the turbine have
four drums, FC, CD, DB, BO. .The
peripheral speeds of these drums may
vary from 130 to 350 feet per second.
We will now assume absolute veloci-
ties for the steam entering each set of moving blades, as along EA. It is cus-
tomary to allow these velocities to range fro?n 1^ to 3} times the peripheral speed
of the drums ; they should increase quite rapidly toward the' last stages of ex-
pansion. Knowing the steam velocity and peripheral velocity for any state like




Fig. 259.



C iG

Art. 534, Prob. 17.— Design
Pressure Turbine.



of



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336



APPLIED THERMODYNAMICS



Z, we construct a velocity diagram aa in Fig. 249, choosing appropriate angles of
entrance and exit In ordinary practice, the expansion in the buckets is sufficient,

notwithstanding friction, to make the rela-
tive exit and absolute entrance angles and
velocities about equal. In such case, we
have the simple graphical construction of
Fig. 260.

Since ah z=bc, db = be, and ad = ec, we
obtain

work = **(«^ + ^^) ^ (id(hc -f hd)
32.2 32.2

Drop the perpendicular bh, and with h
as a center describe the arc aj. Draw
dg perpendicular to ac. Then

dg^ = ad X dc = ad{dh + Ac), and




Fia. 260. Art. 534, Prob. 18. — Velocity
Diagram, Pressure Turbine.



work = -^ foot-pounds, or i-^^-X B. t. u.
32.2 ^ \ 158.3/

In the general case, the work may be computed as in Art. 532. This result
represents the heat converted into work at a stage located vertically in line with
the point Z, Fig. 259. Let this heat be laid oflf to some convenient scale, as GH.
Similar determinations for other states give the heat drop curve IJKHLMNOP.
The average ordinate of this cur>'e is the average heat drop or work done per
stage. If we divide the total heat drop obtained by the average drop per stage,
we have the nutnber of stages, the nearest whole number being taken.* The
diameter of any drum at mid-height of buckets is computed from the peripheral
velocity and number of revolutions per minute.

535. Details. The bucket spacing and heights must be such as to give room
for the passage of the necessary volume of steam, which depends upon the turbine
output and varies with the stage of expansion attained. The blade heights should
be at least 3 per cent of the drum diameter, to avoid excessive leakage over their
tips. The clearance over tips in inches should be from 0.01 d to 0.008 d, where d
is the drum diameter in feet. Blade widths vary from } to 1^ in., with center to
center spacing of from 1^ to 4 in. Blade angles are obtained from the velocity
diagram.

If A is the angle made between the steam leaving the guide vanes and the
plane of the wheel, and c is the absolute velocity of the stream, the axial com-
ponent of this velocity is c sin A. Let the number of buckets on a wheel (stage)
be n, their height /, and their spacing e. Without allowance for thickness of
buckets, the area for passage of steam would be nel; the usual thickness of
buckets will reduce this to j nel. Tha volume of steam discharged per second will
then be | nelc sin A = Gw, in which G is the weight of flow per second and w the
specific volume, which varies while the steam is traversing a single row of buckets.

* Dividing the total heat drop at a state in a vertical line through C by the average
drop per stage from FXjo C,yre have the number of stages on the first drum.



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PRESSURE TURBINE 337

Since ne is the circumference of the wheel = irJ, where d is the diameter, we have
j irdlc sin A = Gw,

The successive drum diameters frequently have the ratio V2 : 1 (21).

Specimen Case

To determine the general characteristics of a pressure turbine operating be-
tween pressures of 100 and 3.5 lb., with an initial superheat of 300° F., the heat
drop being reduced 25 per cent by friction. There are to be 3 drums, and the heat
drop is to be equally divided between the drums. The peripheral speeds of the
successive drums are 160, 240, 320 ft per second. The relative entrance and
absolute exit velocities and atigles are equal : the absolute entrance angle is 20°.
The turbine makes 300 r. p. m. and develops 2500 kw. with losses between buckets
and generator output of 65 per cent



FiQ. 260 a. An. 535. — Expansion Path, Pressure Turbine.



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338



APPUED THERMODYNAMICS



In Fig. 260 a, the expansive path is plotted on a portion of the total heat-
entropy diagram. The total heat drop is shown to be 1342 - 1130 = 212 B. t. u.,
and the heat drop per drum is 212 -j- 3 = 70i B. t. u. In Fig. 260 b, lay off to any
scale the equal distances ab, be, cdy and the vertical distances oc, bg^ ci, rep-
resenting the drum speeds. Lay off also ak, bm, co, equal respectively to
IJ X (ae, bgj ci), and al, 6n, cp^ equal respectively




e

Fig. 260 b. Art. 535. ~ Elements of Pressure Turbine.



of entrance absolute velocities is now assumed, so as to lie wholly within the area
kisntpuvowmx. Figure 260 c shows the essential parts of the velocity diagram
for the stages on the first drum. Here ab represents aq in Fig. 260 6, ad represents

ae, the angle bad is 20°, and f-^y= {^^Y = ZA2 B.t.u. is the heat drop
^ ' \ 158.3/ \ 158.3/ ^

for the first stage in the turbine. Making ac represent by and drawing dcy ch, q/*,

we find (jif—y= f 52i:Zy = 3.70 B. t. u. as the heat drop for the last stage on
\lo8.3/ \li)8.3/

the first drum. For intermediate stages between these two, we find,



IlCITIAL AbBOLITTK


Obdinatk rHOM


Hkat Prop,


Vklocity


d


B. T. u.


ab = 350


de = 279.7


3.12


356i


282.8


3.20


362i


285.9


3.26


368}


289.0


3.34


375


292.1


3.40


381 i


295.3


3.48


3871


298.4


3.56


393i


301.5


3.63


ac = 400


d/= 304.7


3.70



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PRESSURE TURBINE



339



In Fig. 260 5, we now divide the distance ab into 8 equal parts and lay off to
any convenient vertical scale the heat drops just found, obtaining the heat drop
curve zA. The average ordinate of this curve is 3.41 and the number of stages on
the first drum is 70| -t- 3.41 = 21 (nearest whole number). The number of stages




FiQ. 260 c. Art. 535. — Velocity Diagram, Pressure Turbine.



on the other drums is found in the same way, the peripheral velocity ad, Fig.
260 c, being different for the different drums. The diameter d of the first drum is
given by the expression

300 TTrf = 60 X 160 or rf = ff/ ^^^ = 10.2 ft.
3.1416 X 300

The weight of steam flowing per second is
2500 X 1.34 X 2545



0.65 X 212 X 3600



- = 17.1 lb.



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340 APPLIED THERMODYNAMICS

In the first stage of the first drum, the condition of the steam at entrance to
the guide blades is ( Fig. 260 a) // = 1342, p = 100 ; at exit from the moving
blades, it is H = 1338.59, p = 98. From the total heat-pressure diagram, or by
computation, the corresponding specific volumes are 6.5 and 6.6. The volumes of
steam flowing are then 6.5 x 17.1 = 111 and 6.6 x 17.1 = 113 cu. ft. per second.
The absolute steam velocities are (Fig. 260 b) 350 and 356} ft. per second. The
axial components of these velocities (entrance angle 20°) are 0.34202 x 350 = 120,
and 0.:J4202 x 356} = 122. The drum periphery is 10.2 x 3.1416 = 32 f t If the
blade thicknesses occupy } this periphery and the width for steam passage between
the buckets is constant, the width for passage of steam is} x 32 = 21.33 ft. and

the necessary height of fixed buckets is = 0.434 ft. or 5.2 in. at the

^ '^ 21.33 X 120

beginning of the stage and —— — -^ = 0.434 ft. or 5.2 in. at the end. The

Jl.o3 X 122 •

fixed blade angles are determined by the velocities be and ab. Fig. 260: those of

the moving blades by bd and be. There is no serious error involved in taking the

velocity and specific volume as constant throughout a Btage. The height of the

moving buckets should of course not be. less than that of the guide blades; this

may be accomplished by increasing the thickness of the former.

It should be noted that the velocities indicated by the curve ^r, Fig. 2605, are

those of the steam at exit from the fixed blades and entrance to the moving blades.

The diagram of Fig. 260 gives the absolute velocity of the steam entering the next

$et of fixed blades.



Commercial Forms of Turbine.

536. De Layal; Strnnpf. Figure 235 illustrates the principle of the De I^aval
machine, the working parts of which are shown in Fig. 261. Entering through
divergent nozzles, the steam strikes the buckets around the j>eriphery of the wheel
6. The shaft c transmits power through the helical pinions <i, a, which drive the
gears «, «, «, e, on the working shafts/,/. The wheel is housed with the iron cas-
ing g. This is a horizontal single-stage impulse turbine, with a single wheel.
Its rotative speed is consequently high ; in small units, it reaches 30,000 r. p. m.
It is built principally in small sizes, from 5 to 300 h. p. The nozzles make angles
of 20^ with the plane of the wheel ; the buckets are symmetrical, and their angles
range from 32° to 36°, increasing with the size of the unit. For these proportions,
the most efficient values of u would be about 950 and 2100 for absolute steam veloci-
ties of 2000 and 4400 feet per second, respectively ; in practice, these speeds are
not attained, u ranging from 500 to 1400 feet per second, according to the size.
The high rotative speeds require the use of gearing for most application?. The
helical gears used are quiet, and being cut right- and left-hand i-espectively they
practically eliminate end thrust on the shaft. The speed is usually reduced in the
proportion of 1 to 10. The high rotative speeds also prevent satisfactory balanc-
ing, and the shaft is, therefore, made flexible ; for a 5-hp. turbine, it is only }
inch in diameter. The bearinj^s A, 7 are also arranged so as to permit of some
movement. The pressure of steam in the wheel case is that of the atmosphere or
condenser, all expansion occurring in the nozzle. A centrifugal governor controls



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DE LAVAL TURBINE 341



a



H

>



<



I



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342



APPUED THERMODYNAMICS



the speed by throttling the steam supply and by opening conimunication between
the wheel case and atmosphere when necessary.

The nozzles of the De Laval turbine are located as in Fig. 235. Those of the
Stumpf, another turbine of this class, are tangential, while the buckets are of the
Peltou form (Fig. 252), and are milled in the periphery of the wheel. A very
large wheel is employed, the rotative speeds being thus reduced. In a late form
of the Stumpf machine, a second stage is added. The reversals of direction are so
extreme that the fluid friction must be excessive.

537. Curtis Turbine. This is a multi-stage impulse turbine, the principle of
operation having been shown in Fig. 245. In most cases, it is vertical ; for marine

applieations, it is necessarily made
horizontal. Figure 262 illustrates
the stationary and moving blades
and nozzles. Steam enters through
the nozzle A, strikes a row of mov-
ing vanes at a, passes from them
through stationary vanes B to
another row of moving vanes at e,
then passes through a second set
of expanding nozzles at A to the
next pressure stage. This particu-
lar machine has four pressure
stages with two sets of moving
buckets in each stage. The direc-
tion of flow is axial. The number
of pressure stages may range froni
two to seven. From two to four
velocity stages (rows of moving
buckets) are used in each pressure
stage. In the two-stage machine,
the second stage is disconnected
when the turbine runs non-con-
densing, the exhaust from the first
stage being discharged to the at-
mosphere. Governing is effected
by automatically varying the number of nozzles in use for admitting steam to the
first stage. A step bearing carries the whole weight of the machine, and must be
supplied with lubricant under heavy pressure ; an hydraulic accumulator system is
commonly employed.

538. Rateau Turbine. This is a horizontal, axial flow, multi-stage impulse
turbine. The number of pressure stages is very large — from twenty-five upward.
There is one velocity stage in each pressure stage. Very low speeds are, therefore,
possible. Figure 203 shows the general arrangement; the tranverse partitions 6, e
form cells, in which revolve the wheels/,/; the nozzles are merely slots in the
partitions. The blades are pressed out of sheet steel and riveted to the wheel.
The wheels themselves are of thin pressed steel.




Fig. 262. Art. 537. — Curtis Turbine.



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APPLICATIONS OF TURBINES 343



Fig. 263. Art. 538. - Rateau Turbine.

539. Westinghoose-Parsoiis Turbine. This is of the axial flow pressure type,
and horizontal. The steam expands through a large number of successive fixed
and moving blades. In Fig. 264, the steam enters at A and passes along the vari-
ous blades toward the left ; the movable buckets are mounted on the three drums,
and the fixed buckets project inward from the casings. The diameters of the
drums increase by steps ; the increasing volume of the steam within any section is
accommodated by varying the bucket heights. The balance pistons P, P, P are
used to counteract end thrust. The speed is fairly high, and special provision
must be made for it in the design of the bearings. Governing is effected by inter-
mittently opening the valve V; this valve is wide open whenever open at all.

The length of this machine is sometimes too great for convenience. To oveiv
come this, the " double-flow " turbine receives steam near its center, through
expanding nozzles which supply a simple Pelton impulse wheel. This utilizes
a large proportion of the energy, and the steam then flows in both directions
axially, through a series of fixed and moving expanding buckets. Besides reduc-
ing the length, this arrangement practically eliminates end thrust and the neces-
sity for balance pistons.

540. Applications of Turbines. Turbo-locomotives have been experimented
with in Grennany; the direct connection of the steam turbine to high-pressure
rotary air compressors has been accomplished. In stationary work, the direct
driving of generators by turbines is common, and the high rotative speeds of the
latter have cheapened the former. At high speeds, difficulties may be experi-
enced with commutation ; so that the turbine is most successful with alternating-
current machines. When driving pumps, turbines permit of exceptionally high
lifts with good efficiencies for the centrifugal type, and low first costs. For low-
pressure, high-speed blow^ers, the turbine is an ideal motor. The outlook for a gas
turbine is not promising, any gas cycle involving combustion at constant pressure
being both practically and thermodynamically inefficient.

The objections to the turbine in marine application have arisen from the high



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344 APPLIED THERMODYNAMICS






o









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EXHAUST STEAM TURBINES 345

speed and the difficulty of reversing. A separate reversing wheel may be em-
ployed, and graduation of si)eed is generally attained by installing turbines in
pairs. A small reciprocating engine is sometimes employed for maneuvering at
or near docks. Since turbines are not well adapted to low rotative speeds, they
are not recommended for vessels rated under 15 or IH knots. The advantages of
turboK)peration, in decreased vibration, greater simplicity, smaller and more deeply
immersed propellers, lower center of gravity of engine-room machinery, decreased
size, lower first cost, and greater unit capacity without excessive size, have led to
extended marine application. The most conspicuous examples are in the Cunard
liners Lusitania and Mauretania. The former has two high-pressure and two low-
pressure main turbines, and two astern turbines, all of the Parsons type (22).
The drum diameters are respectively 96, 140, and 104 in. An output of 70,000 lip.
is attained at full speed.

541. The Exhaust-steam Turbine. From the heat chart. Fig. 177, it is
obvious that steam expanding adiabatically from 150 lb. absolute pressure and
600° F. to 1.0 lb. absolute pressure transforms into work 365 B. t. u. It has been
shown that in the ordinary reciprocating engine such complete expansion is unde-
sirable, on account of condensation losses. The final pressure is rarely below 7 lb.
absolute, at which the heat converted into work in the above illustration is only
252 B. t. u. The turbine is particularly fitted to utilize the remaining 113 B. t. u.
of available heat. The use of low-pressure turbines to receive the exhaust steam
from reciprocating engines, has, therefore, been suggested. Some progress has
been made in applying this principle in plants where the engine load is intermit-
tent and condensation of the exhaust would scarcely pay. With steel mill en-
gines, steam hammers, and similar equipment, the introduction of a low-pressure
turbine is decidedly profitable. The variations in supply of steam to the turbine
are offset by the use of a regenerator or accumulator, a cast-iron, water-sprayed
chamber having a large storage capacity, constituting a " fly wheel for heat," and
by admitting live steam to the turbine through a reducing valve. When a sur-
plus of steam reaches the accumulator, tiie pressure rises; as soon as this falls,
some of the water is evaporated. The maximum pressure is kept low to avoid
back pressure at the engines. A steam consumption by the turbine as low as
35 lb. per brake hp.-hr. has been claimed, with 15 lb. initial absolute pressure and
a final vacuum of 26 in. Other good results have been shown in various trials
(23). Wait (24) has described a plant at South Chicago, 111., in which a 42 by
60 double cylinder, reversible rolling-mill engine exhausts to an accumulator at a
pressure 2 or 3 lb. above that of the atmosphere. This delivers steam at about
atmospheric pressure to a 500 kw. Rateau turbine oi>erated with a 28-in. vacuum.
The steam consumption of the turbine was about 35 lb. per electrical hp.-hr.,
delivered at the switchboard.

The S.S. Tui-hinia, in 1897, was fitted with low-pressure turbines receiving the
exhaust from reciprocating engines and operating between 9 lb. and 1 lb. absolute.
One third of the total power of the vessel was developed by the turbines, although
the initial pressure was 160 lb.

542. Commercial Considerations. The best turbines, in spite of their thermo-
dynamically superior cycle, have not yet equalled in efficiency the best reciprocat-



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346 APPLIED THERMODYNAMICS

ing engines, both operating at full load. The average turbine is more economical
than the average engine ; and since the mechanical and fluid friction losses are
disproportionately large, it seems reasonable to expect improved efficiencies as
experimental knowledge accumulates.

The turbine is cheaper than the engine ; it weighs less, has no fly wheel,
requires less space and very much less foundation. It can be built in larger units
than a reciprocating cylinder. Power house buildings are cheapened by its use ; the
cost of attendance and of sundry operating supplies is reduced. It probably depre-
ciates less rapidly than the engine. The wide range of expansion makes a high
vacuum desirable ; this leads to excessive cost of condensing apparatus. Similarly,
superheat is so thoroughly beneficial in reducing steam friction losses that a con-
siderable investment in superheaters is necessaiy. The turbine must have a direct
connected balanced load ; so that the cost of generators must often be included in
the initial expense, although otherwise unnecessary. The choice as between the
turbine and the engine must be determined with reference to all of the condi-
tions, technical and commercial, including that of load factor. Turbine economy
cannot be measured by the indicator, but must be determined at the brake or
switchboard and should be expressed on the heat unit basis (B. t. u. consumed per
unit of output per minute).

(1) Trans. Inst. Engrs. and Shipbuilders in Scotland, XLVI, V. (2) Berry,
The Temperature-Entropy Diagram, 1905. (3) To show this, put the expression in

V

the brace equal to wi, and make — = ; then — = ( y "^ ) , which may be solved

dp p \ 2 I

for any given value of y. (4) Thesis, Polytechnic Institute of Brooklyn, 1906.

(6) Thomas, Steam Turbines, 1006, 89. (6) l>roc. List. Civ. Eng., CXL, 199.

(7) Zeits. Ver. Deutsch. Ing., Jan. 16, 1904. (8) Rankine, The Steam Engine, 1897,
844. (9) ETcperimental Researches on the Flow of Steam, Brydon tr. ; Thomas, op. cit.,
106. (10) Thomas, op. cit., 123. (11) Engineering, XIII (1872). (12) Trans.
A. S. M. E., XI, 187. (18) Mitteil. iiber Forschungsarb., XVIII, 47. (14) Practice
and Theory of the Injector, 1894. (16) Peabody, Thermodynamics, 1907, 443.
(16) Trans. A. S. M. E., XXVII, 081. (17) Stodola, Steam Turbines. (18) The
Steam Engine, 1906, I, 170. (19) Technical Thermodynamics, Klein tr., 1907: I,
226: II, 153. (20) Trans. A. S. M. E., XXVII, 081. (21) See H. F. Schmidt, in
The Engineer (Chicago), Dec. 16, 1907: Trans, Inst. Engrs. and Shipbuilders in
Scotland, XLXIX. (22) Power, November, 1907, 770. (23) TYans. A. S. M. E.,



Online LibraryWilliam D. (William Duane) EnnisApplied thermodynamics for engineers → online text (page 33 of 43)