THE EXPANSION OF STEAM.
[Illustration:
_Fig. 30._
Scale ²⁄₃ in. = 1 foot.]
[Illustration:
_Fig. 31._
Scale ¹⁄₄ in. = 1 inch.]
QUESTION 55. _How can we determine by experiment the pressure of the
steam in the cylinder at all points of the stroke?_
_Answer._ By the use of an instrument made for that purpose, called an
_indicator_. Its action can be best explained by supposing that we have
a small cylinder and piston, _T_, fig. 30, (shown on an enlarged scale
in fig. 31) attached by a pipe _U_ to one end of the cylinder _A_, so
that when steam is admitted to the latter it will be conducted to the
small cylinder _T_ through the pipe _U_. Over the small piston and
attached to it is a spiral spring, _s s_, fig. 31, which is compressed
when the piston rises and extended when it falls. To the top of the
piston-rod, _V_, a pencil, _W_, is attached. Behind this pencil we
will suppose there is a card, _a b c d_, and that this card is so
arranged that we can slide it horizontally and in contact with the
pencil point. With only the pressure of the atmosphere above and below
the piston _T_, the spring would be neither compressed nor extended,
and the piston would then stand in the position shown in fig. 31. If
now we move card horizontally, the pencil will draw a line, _g_, _h_,
called the _atmospheric line_. We will now suppose that the tension of
the spring is such that a pressure of 10 lbs. per square inch above or
below the piston will either extend or compress the spring ¹⁄₄ inch. In
other words, every pound of pressure per square inch in the piston will
move it ¹⁄₄₀ of an inch. If we could produce a vacuum under the piston,
it would be pressed down by the atmosphere above it ¹⁵⁄₄₀, or ³⁄₈ of
an inch. If, when it is thus depressed, we again slide the card along
in contact with the pencil-point, it will draw another line, _e_, _f_,
called the _vacuum-line_. Assuming that we have drawn these two lines,
and that the piston and card are in the position shown in figs. 30 and
31, we will then suppose that a reciprocating motion can be given to
the card by the lever _L_, _M_, _N_, fig. 30, which is pivoted at _M_
and attached at _N_ to the piston-rod by a short connecting-rod. It is
obvious that by connecting the upper end _L_ of the lever with a rod,
_L c_, to the card, the latter will be moved backwards and forwards
by the motion of the piston _B_, and that the motion of the card will
be simultaneous with that of the piston _B_, but of course of shorter
stroke. We will assume that the stroke of the card is equal to the
length of the atmospheric and vacuum lines _g h_ and _e f_, fig. 31.
If now, the piston being at the beginning of the stroke as shown in
fig. 30, we admit steam of 85 lbs. effective pressure per square inch
(which is equal to 100 lbs. absolute pressure) into the cylinder _A_,
it will be conveyed through the pipe _U_ to the cylinder _T_, and will
force up the piston ⁸⁵⁄₄₀ or 2¹⁄₈ inches above the atmospheric line, or
¹⁰⁰⁄₄₀ or 2¹⁄₂ inches above the vacuum line, as shown in fig. 32, and
the pencil will draw a vertical line, _g i_, on the card, (represented
by a dotted line in fig. 32.) We will suppose that steam is admitted
during 8 inches of the stroke, and is then cut off. When the piston
_B_, fig. 30, has moved that distance, which is one-third of its
stroke, the card will also have moved one-third of its stroke, and will
stand in relation to the pencil in the position represented in fig. 33,
and as the absolute steam pressure in the cylinder was maintained at
100 lbs. while the card was moving that distance, the pencil will have
drawn a horizontal line, _i j_. The steam is now cut off and begins to
expand, and its pressure is thereby reduced. When the piston of the
engine is at half-stroke, the card will also be at half-stroke, and
the steam will be expanded from 8 to 12 inches of the stroke. By the
rule given in the answer to question 20, its absolute pressure would
then be 66²⁄₃ lbs., and the indicator-piston will then be pressed down
by the spring, so that the pencil will stand in the position shown in
fig. 34, or 66²⁄₃ fortieths of an inch above the atmospheric line. The
pencil meanwhile will have drawn the curved line _j k_. When the piston
has moved 16 inches, the steam will be expanded to double its volume
and its absolute pressure will therefore be 50 lbs., and consequently
the pencil will stand 50 fortieths or 1¹⁄₄ inch above the atmospheric
line as shown in fig. 35, and the pencil will have continued the
curve _j k_ to _l_. At 20 inches the steam will have 40 lbs., and at
the completion of the stroke 33²⁄₃ lbs. absolute pressure, and the
pencil will have completed the curve _j k l m n_, as shown in figs.
36 and 37. This curve is called the _expansion curve_, and its form
is that which mathematicians call a hyperbolic curve. If the steam is
exhausted, the indicator-piston will descend and carry the pencil down
to the atmospheric line, and the vertical line _n h_, fig. 38, will
be drawn. On the return stroke, after the steam is exhausted from the
main cylinder _A_, fig. 30, the pencil would draw the atmospheric line
_g h_, fig. 38, thus showing that there is no steam pressure under
the piston. Such a diagram is called an _indicator diagram_.[16] In
practice there are a great many influences which modify it, such as
condensation, performance of work, imperfection of valve gear, etc.,
but for the present these are disregarded.
[16] The indicator used in practice, to show the action of the
steam in the cylinders of steam engines, differs essentially in
its construction from that which we have described. The principles
of operation are, however, the same in both. We will explain the
construction of the Richard’s indicator, the one which is now most
generally used, hereafter.
[Illustration:
_Fig. 32._
_Fig. 33._
_Fig. 34._
_Fig. 35._
_Fig. 36._
_Fig. 37._
_Fig. 38._
Scale ¹⁄₄ in. = 1 inch.]
QUESTION 56. _How can we ascertain the pressure of the steam for any
point of the stroke from such a diagram?_
_Answer._ By measuring the vertical distance by the expansion curve
(fig. 38) from the vacuum or the atmospheric line, as for example 8
_j_, 12 _k_, 16 _l_, 20 _m_. As the indicator spring is extended or
compressed one-fortieth of an inch[17] from every pound of pressure
per square inch, either above or below the indicator piston, if we
construct a scale _S_, _S_, fig. 38, with division of one-fortieth of
an inch each, one of them will represent one pound of pressure per
square inch if measured vertically from the atmospheric or vacuum
line. If we sub-divide the vacuum line with the same number of parts
as there are inches in the stroke of the piston (see fig. 39) we can
draw vertical lines from these points and thus determine the pressure
by comparing the length of such lines with the scale _S_, _S_. Thus
the line 8 _j_ measures 100 fortieths of an inch, thus showing that
the absolute steam pressure at 8 inches of the stroke was 100 lbs. per
square inch; the line 12 _k_ measures 66²⁄₃ fortieths of an inch, thus
showing that at 12 inches of the stroke the steam pressure was 66²⁄₃
lbs. At 16, 20 and 24 inches of the stroke the vertical lines measure
50, 40 and 33²⁄₃ fortieths; and therefore there were that number of
pounds of steam pressure when the piston was at the point of the stroke
named. Similar measurements could be made from other points, such as 2,
6, 10, or any other number of inches of the stroke. Of course, if we
measure from the vacuum line we will have the absolute steam pressure,
or the pressure _above a vacuum_, as it is sometimes called; if we
measure from the atmospheric line we will have the effective pressure,
or the _pressure above the atmosphere_.
[17] Indicator springs are used of various degrees of tension, in
proportion to the steam pressure to be indicated.
[Illustration: _Fig. 39._
Scale ¹⁄₄ in. = 1 inch.]
QUESTION 57. _How can we determine the average pressure during the
whole stroke of steam which works expansively?_
_Answer._ This can be determined approximately by the following method:
In the first place, divide the vacuum line (fig. 39) into any number
of equal divisions, say six. From the points of division, 4, 8, 12, 16
and 20, which in this case correspond with the points which represent
inches of the stroke, draw perpendicular lines, which will divide the
indicator diagram into six divisions. It is obvious that during the
time the steam is working full stroke the pressure is uniformly 100
lbs. absolute. While the piston is moving from 8 to 12 inches the
pressure falls from 100 to 66²⁄₃ lbs., so that at 10 inches we have
very nearly the average pressure during the period named. So from 12
to 16, 16 to 20 and 20 to 24 the average is nearly 57.1, 44.4 and
36.3 lbs., respectively. Now, BY ADDING TOGETHER THE PRESSURES IN THE
MIDDLE OF EACH ONE OF A NUMBER OF EQUAL DIVISIONS OF THE STROKE AND
DIVIDING BY THE NUMBER OF DIVISIONS, WE WILL OBTAIN APPROXIMATELY THE
AVERAGE ABSOLUTE PRESSURE DURING THE WHOLE STROKE. TO GET THE AVERAGE
EFFECTIVE PRESSURE, DEDUCT THE ATMOSPHERIC PRESSURE FROM THE RESULT.
The calculation would in the above case be as follows:
100 lbs.
100 „
80 „
57.1
44.4
36.3
-----
6)417.8
-----
69.6 = Average absolute pressure.
15
-----
54.6 = Average effective pressure.
A more accurate way of calculating the average or mean pressure, as it
is called, when steam is used expansively, and the one which is usually
employed, is to DIVIDE THE LENGTH OF THE PISTON’S STROKE IN INCHES
BY THE NUMBER OF INCHES AT WHICH THE STEAM IS CUT OFF: THE QUOTIENT
IS THE RATIO OF EXPANSION. GET THE HYPERBOLIC LOGARITHM OF THE RATIO
OF EXPANSION FROM THE TABLE OF LOGARITHMS IN THE APPENDIX, ADD 1 TO
IT, AND DIVIDE THE SUM BY THE RATIO OF EXPANSION AND MULTIPLY THE
QUOTIENT BY THE MEAN ABSOLUTE STEAM PRESSURE IN THE CYLINDER DURING ITS
ADMISSION. THE RESULT WILL BE THE MEAN ABSOLUTE PRESSURE DURING THE
STROKE. TO GET THE MEAN EFFECTIVE PRESSURE, DEDUCT THE ATMOSPHERIC
PRESSURE.
The calculation for the above example would be as follows:
24
-- = 3 = Ratio of expansion.
8
1.0986 + 1
---------- × 100 = 69.95 = Mean absolute pressure.
3
69.95 - 15 = 54.95 = Mean effective pressure.
The table of hyperbolic logarithms given in the appendix will be needed
in calculating the mean pressure of steam used expansively:
QUESTION 58. _What advantages result from using steam expansively?_
_Answer._ There is a very important saving in the amount of steam
required to do a given amount of work, and the strains and shocks which
are produced by the rapid motion of the piston and other reciprocating
and revolving parts of the engine are very much diminished by allowing
the steam to expand, and thus become reduced in pressure during the
latter part of the stroke.
QUESTION 59. _How is steam saved by using it expansively?_
_Answer._ Less steam is required when it is used expansively:
1. Because when steam of a high pressure is introduced into the
cylinder, and allowed to expand until its pressure is comparatively
low, it escapes at a lower pressure than the average pressure during
the whole stroke. If steam of a pressure equal to the _average_
pressure is worked full stroke, it would exert exactly the same force
on the piston as the steam of higher pressure did when working
expansively, but the pressure in the latter case, when the piston
reaches the end of the stroke, or the _final pressure_, as it is
called, would be considerably lower than in the other. The pressure of
steam represents _energy_, or _capacity for doing work_, and therefore
if we allow it to escape with a comparatively high pressure without
doing work, it is a waste of energy. To illustrate this, we will take
the same conditions which were used in the answer to Question 57,
in calculating the average pressure. In that case the mean absolute
pressure of the steam was 69.95 pounds per square inch, but the
pressure at the end of the stroke, when the steam escaped, was only
33²⁄₃ pounds absolute. If, therefore, steam had been used of the
average pressure through the whole stroke, it would have escaped with
a pressure of 69.95 pounds, or more than twice that of the expanded
steam, and the work done in both cases would have been the same.
2. There is also another incidental advantage in this, because
low-pressure steam can be exhausted more quickly from a cylinder than
steam of a high pressure, and consequently there is less resistance, or
_back pressure_, as it is called, in the exhausted end of the cylinder
to the movement of the piston.
3. The causes which produce the greatest economy when steam is used
expansively cannot be fully explained without discussing principles of
science more abstruse than it is desirable to introduce here. They can,
however, with the aid of the table of the “Properties of Steam,”[18] in
the appendix, be illustrated by a few simple calculations, so that the
economy of using steam expansively will be apparent.
[18] This table is copied from Colburn’s Treatise on the Locomotive
Engine.
For the basis of the calculations the same data and dimensions will
be employed that were used in the previous illustration; that is, a
cylinder of 16 in. diameter and piston with 24 in. stroke and steam
of 100 lbs. absolute pressure cut off at 8 in. of the stroke. We will
suppose, further, that the steam used is generated from water of a
temperature of 60 degrees, and we will then calculate the total number
of units of heat in the steam used for each stroke of the piston.
The area of a piston 16 in. in diameter is 201 square inches; and as
the steam is admitted until the piston moves 8 inches of its stroke,
therefore the quantity of steam would be 8 times 201 cubic inches, or
1608
201 × 8 = 1608 cubic in. = ---- cubic ft.
1728
From the table it will be seen that one cubic foot of steam of 100 lbs.
pressure weighs .2307 lbs.; therefore the weight of the fraction of a
cubic foot given above would be calculated as follows:
.2307 × 1608
------------ = .2146 lb. =
1728
weight of 1608 cubic in. of steam of 100 lbs. absolute pressure.
From the table it will be seen that the total heat above zero of steam
of 100 lbs. absolute pressure is 1213.4 degrees. That is, as was
explained in answer to Question 40,[19] in order to boil water under
a pressure of 100 lbs. per square inch we must first heat water up to
327.9 degrees, and then, to convert it into steam, 885.5 degrees more
must be added. It was also explained in the answer to Question 35 that
one pound of water heated one degree is the standard of measurement or
_unit of heat_. Now if we have 1 lb. of water with a temperature of
zero, evidently it will take 1213.4 _units of heat_ to convert it into
steam of 100 lbs. absolute pressure. But as the water from which our
steam was generated had a temperature of 60 degrees, we must deduct
that much from 1213.4: 1213.4 - 60 = 1153.4 = units of heat in one
pound of steam of 100 lbs. absolute pressure generated from water of 60
degrees temperature.
[19] In the illustration used in answer to Question 40, steam of 100
lbs. _effective_ pressure was used, whereas in the above case it is
_absolute_ pressure.
If now one pound of steam has 1153.4 units of heat, the following
calculation will give the units of heat in .2146 lbs.: 1153.4 × .2146 =
247.51 = units of heat in .2146 lbs., or 1608 cubic in. of steam of 100
lbs. absolute pressure.
It was shown in answer to Question 57 that the average pressure of
steam of 100 lbs. cut off at 8 in. of the stroke was 69.95 lbs. per
square inch. Disregarding the small fraction, we will call it 70 lbs.
Now if we admit steam of this pressure through the _whole stroke_ of
the piston, we will use 4,824 cubic inches. It will be found by a
calculation similar to the above, that to generate this quantity of
steam of 70 lbs. pressure from water of a temperature of 60 degrees
would require 527 units of heat, or more than twice as many as were
required to do the same work with steam of 100 lbs. pressure cut off
at 8 inches when using it expansively during the rest of the stroke.
The actual difference in practice is not so great as this, because the
loss of heat from radiation and condensation in the cylinder and other
causes is greater when steam of a high pressure is expanded than when
lower pressure steam is admitted through the whole stroke. But after
allowance is made for all such sources of loss and waste, there is
still an enormous gain from using steam expansively.
QUESTION 60. _What is meant by wire-drawn steam?_
_Answer._ It is the fall which the pressure of the steam undergoes
during its passage from the boiler to the cylinder,[20] and which is
due to the contracted opening of the steam pipes or valves.
[20] Rankine.
QUESTION 61. _What is the economical effect of reducing the pressure,
or of wire-drawing it, by partly closing the valve by which it is
admitted to the cylinders?_
_Answer._ By reducing the pressure of steam in this or any other way,
it is necessary in doing the same amount of work to admit steam to the
cylinder for a longer period, and therefore to reduce the degree of
expansion. To illustrate the effect of this, we will estimate the total
heat required to exert a pressure of 70 lbs. on the piston described
above. It will be assumed that the steam pressure in the boiler is 100
lbs. absolute, and that this is wire-drawn down to 70 lbs. and admitted
to the cylinder through the whole stroke. As was shown in the preceding
answer, 4,824 cubic inches of steam are required to fill the cylinder.
Now 3,376.8 cubic inches of steam of 100 lbs. pressure, if expanded
to 70 lbs. pressure, will make 4,824 cubic inches. The total heat
required to generate 3,376.8 cubic inches of steam of 100 lbs. absolute
pressure from water of 60 degrees is 519.9 units, so that to do the
same work by using steam of _high pressure cut off at one-third of the
stroke_, using steam of _low boiler pressure full stroke_, and using
_wire-drawn steam full stroke_, would, in the example we have selected,
require 247.5, 527 and 519.9 units of heat respectively.
QUESTION 62. _To what extent can we work steam expansively, with
advantage and economy?_
_Answer._ The theoretical economy of using steam increases with the
degree of expansion and the pressure. This is shown very clearly in the
following table, in the first column of which the number of inches of
the piston stroke is given during which steam is admitted to a cylinder
16 in. in diameter and 24 in. stroke. In the second column is given the
pressure of the steam, or _initial pressure_, as it is called, which
must be admitted into the cylinder in order to produce a mean pressure
of 70 lbs. per square inch when it is cut off at the point indicated
in the first column. In the third column is given the total heat which
is required to generate the steam required in each case, and in the
last column the percentage of saving is given which results from the
different degrees of expansion and a mean pressure of 70 lbs. per
square inch in each case.
RESULTS OF USING STEAM EXPANSIVELY.
+======================================+==========+=========+========+
| | | | Per- |
| | | | centage|
| | Initial | | of |
| | Pressure | Total | saving |
| | of steam | heat of |compared|
| | in pounds| steam | with |
| Period of admission or point of |per square| used, | full |
| cut-off. | inch. |in units.| stroke.|
+--------------------------------------+----------+---------+--------+
|Full stroke | 70. | 527. | |
|18 in. = Three-quarters of the stroke,| 72.5 | 408.7 | 22¹⁄₂ |
|12 in. = One-half „ „ | 82.7 | 309.5 | 41¹⁄₄ |
| 8 in. = One-third „ „ | 100. | 247.5 | 53 |
| 6 in. = One-quarter „ „ | 117.4 | 215.9 | 58 |
| 4 in. = One-sixth „ „ | 150.5 | 186.5 | 64¹⁄₂ |
| 3 in. = One-eighth „ „ | 181.8 | 165.8 | 68¹⁄₂ |
| 2 in. = One-twelfth „ „ | 241.4 | 144.8 | 72¹⁄₂ |
+--------------------------------------+----------+---------+--------+
From this table it will be seen that theoretically 22¹⁄₂ per cent. of
heat is saved by cutting off at ³⁄₄ of the stroke and using steam of
72.5 lbs. pressure instead of steam of 70 lbs. worked full stroke.
Cutting off at half stroke and using steam of 82.7 lbs., 41¹⁄₄ per
cent. of heat is saved, and cutting off at quarter stroke with steam
of 117.4 lbs. saves 58 per cent. of heat; and at one-twelfth of the
stroke, or expanding steam of 241.4 lbs. pressure to twelve times its
volume, saves 72¹⁄₂ per cent. of heat.
As stated before, the above is the _theoretical_ advantage of using
steam expansively. There are, however, practical difficulties in
the way of using some of these high degrees of expansion. It has
already been explained that if steam is cut off early in the stroke
and the degree of expansion increased, the pressure and consequently
the temperature of the steam must also be increased. The danger of
explosion is greater with the higher pressures, and stronger and more
expensive boilers and machinery are therefore needed. With steam of
very high temperature the metal of the cylinders, pistons and valves
becomes so much heated that they soften, and then the friction of the
one on the other causes them to cut or scratch each other. The high
temperature at the same time destroys the oil or other lubricant used
in contact with the steam. It is also impossible to admit and cut off
steam very early in the stroke with the ordinary mechanical appliances
used for moving slide-valves of locomotives. This latter difficulty
will be more fully explained hereafter.