to K it follows that if in any turbine log p when plotted against K gives a straight line, that turbine, whether of the impulse or reac- tion type, cannot be designed to operate with uniform efficiency. In the diagram fig. 17 the values of log p represent the pressure of the steam after discharge from the preceding stage, stage No. I being thus conceived as being preceded by an imaginary stage No. o. A corresponding plot of the volume would, however, give not the volume at discharge from the guide blades, but this volume as in- creased by the heat generated in the passage of the steam through the moving buckets. All stages being similar, the effective thermo- dynamic head at each stage is the same. But the apparent thermo- dynamic head, obtained by dividing the total thermodynamic head U by the number of stages, is somewhat greater than the adiabatic heat drop at each stage.
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20 In*. 10 IS 17 IS IS 14 13 12 II 10 9 8 7
a
3
4
3
2 1-0 09 0-8 07 M 0-5 04 0-3 02 01 OH 01
- 2
0-3 A
-04
According to what has been stated above, the velocity of dislarge from the_guide blades of a stage is commonly taken as
=300-2 Xo-gsVtt where u is the adiabatic heat drop. The weight
' discharged per second per sq. ft. of guide blade area is
... v__ 300-2XQ-95VM
V* \
lere V$ represents the volume of the steam after an adiabatic pansion between the pressure above and below the stage. Instead calculating these values it is more convenient to utilize the known lues of U and V and to correct the above formula by using an propriate coefficient $. As there are 12 stages in the present
se we get = ' = 10-38 =q, and the above equation may Before be written
W =
^300-2X0-95^10-38
-
i interpolation formula for / which is applicable for the ordinary ige of turbine efficiencies and for convergent guide blades is , 1+0-13 (i i))Vx i where x denotes the ratio of the pressure we and below the stage. The coefficient / is readily evaluated the ordinary slide rule with quite sufficient accuracy. In the case under consideration we note from the curve fig. 17, it when v = i , log p = I 197 so that x = I -27 and / is therefore I -025. The area available for flow through a row of guide blades is
-^ where h' denotes the blade height in in., and a is
..
" effective " angle of discharge, allowing if necessary for the
fact that the blades are of finite thickness. Hence if iv be the weight of steam flowing through the turbine per second
_
6223 /' d sin aV q
Taking sin = 0-30, 5=44!, 3 = 10-38 and w = 10-3 Ib. per second, this expression reduces to h' = -O3732V. Values of h' thus calcu- lated for the values of V given in table 3 are plotted in fig. 17 and from the curve thus obtained we read off the theoretical blade heights at the different stages. These are :
Stage No. . Theor. blade height in in. .
I
0-94
2
1-18
3 i-5i
4 1-95
5
2-48
6 '
3-24
Stage No. . Theor. blade height in in. .
7 4'3
8
fcfis
9
7-69
10 10-48
ii
14-40
12
20-0
In practice the nearest even dimensions will be substituted for the calculated heights. The calculated heights for the last three stages are inconveniently long, but they can all be reduced to say 9 in. by suitably increasing the effective angles of discharge. Some builders moreover increase the pressure drop at the exhaust end, and would accordingly combine stages II and 12 into one. These expedients decrease the efficiency but are cheaper than the alternative of con- structing the low-pressure end on the double flow principle.
The high-pressure end of a turbine can be proportioned in a man- ner exactly similar to that described, but as the steam there is com- monly superheated, the problem is correspondingly simplified and need not therefore be discussed here. It is, however, usually neces- sary to construct some of the high pressure stages as partial admis- sion stages and it is also a common practice to have a large pressure drop at the first stage with the object (at some sacrifice of efficiency) of making a large initial reduction in the temperature and pressure of the steam, so that the high pressures and temperatures are con- fined to the nozzle-boxes of the first stage. To the same end a veloc- ity compounded wheel is frequently used in the first stage. The general theory of these wheels is described in Prof. Evving's article (see 25.844), but it may be observed that in practice it has been found necessary to adopt empirical methods of designing such wheels. If designed as pure impulse wheels operated with a fluid which is " freely deviated " the results are very disappointing. One rule which has been used is to assume that only 85 % of the total heat drop of the stage is utilized in the nozzles, and of the residue that 5 % is utilized in each of the three sets of blading. The wheel there- fore works to some extent as a reaction turbine.
A -et
ts
+
V*
- :
- r
s - '--
-K f*.**r\
..til J
k- / -
FIG.I8
h- -77i
Speaking generally, the principle of " free deviation " as embodied in some water wheel designs is inadmissible in. steam turbine prac- tice, in which the moving blades should be just sufficiently long to avoid " spilling " of the steam delivered to them from the guide blades. As to the exact form of the moving blades, this does not appear to be of primary importance within reasonable limits, as,
