MEAN SPECIFIC HEAT OF SUPERHEATED STEAM
CALCULATED FROM MARKS AND DAVIS TABLES
_______________________________________________________________
|Gauge | |
|Pressure | Degree of Superheat |
| |_____________________________________________________|
| | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 |
|_________|_____|_____|_____|_____|_____|_____|_____|_____|_____|
| 50 | .518| .517| .514| .513| .511| .510| .508| .507| .505|
| 60 | .528| .525| .523| .521| .519| .517| .515| .513| .512|
| 70 | .536| .534| .531| .529| .527| .524| .522| .520| .518|
| 80 | .544| .542| .539| .535| .532| .530| .528| .526| .524|
| 90 | .553| .550| .546| .543| .539| .536| .534| .532| .529|
| 100 | .562| .557| .553| .549| .544| .542| .539| .536| .533|
| 110 | .570| .565| .560| .556| .552| .548| .545| .542| .539|
| 120 | .578| .573| .567| .561| .557| .554| .550| .546| .543|
| 130 | .586| .580| .574| .569| .564| .560| .555| .552| .548|
| 140 | .594| .588| .581| .575| .570| .565| .561| .557| .553|
| 150 | .604| .595| .587| .581| .576| .570| .566| .561| .557|
| 160 | .612| .603| .596| .589| .582| .576| .571| .566| .562|
| 170 | .620| .612| .603| .595| .588| .582| .576| .571| .566|
| 180 | .628| .618| .610| .601| .593| .587| .581| .575| .570|
| 190 | .638| .627| .617| .608| .599| .592| .585| .579| .574|
| 200 | .648| .635| .624| .614| .605| .597| .590| .584| .578|
| 210 | .656| .643| .631| .620| .611| .602| .595| .588| .583|
| 220 | .664| .650| .637| .626| .616| .607| .600| .592| .586|
| 230 | .672| .658| .644| .633| .622| .613| .605| .597| .591|
| 240 | .684| .668| .653| .640| .629| .619| .610| .602| .595|
| 250 | .692| .675| .659| .645| .633| .623| .614| .606| .599|
|_________|_____|_____|_____|_____|_____|_____|_____|_____|_____|
|Gauge | |
|Pressure | Degree of Superheat |
| |-----------------------------------------------------|
| | 140 | 150 | 160 | 170 | 180 | 190 | 200 | 225 | 250 |
|---------+-----+-----+-----+-----+-----+-----+-----+-----+-----|
| 50 | .504| .503| .502| .501| .500| .500| .499| .497| .496|
| 60 | .511| .509| .508| .507| .506| .504| .504| .502| .500|
| 70 | .516| .515| .513| .512| .511| .510| .509| .506| .504|
| 80 | .522| .520| .518| .516| .515| .514| .513| .511| .508|
| 90 | .527| .525| .523| .521| .519| .518| .517| .514| .510|
| 100 | .531| .529| .527| .525| .523| .522| .521| .517| .513|
| 110 | .536| .534| .532| .529| .528| .526| .525| .520| .517|
| 120 | .540| .537| .535| .533| .531| .529| .528| .523| .519|
| 130 | .545| .542| .539| .537| .535| .533| .531| .527| .523|
| 140 | .550| .547| .544| .541| .539| .536| .534| .530| .526|
| 150 | .554| .550| .547| .544| .542| .539| .537| .533| .529|
| 160 | .558| .554| .551| .548| .545| .543| .541| .536| .531|
| 170 | .562| .558| .555| .552| .549| .546| .544| .538| .533|
| 180 | .566| .561| .558| .555| .552| .549| .546| .540| .536|
| 190 | .569| .565| .562| .558| .555| .552| .549| .543| .538|
| 200 | .574| .569| .566| .562| .558| .555| .552| .546| .541|
| 210 | .578| .573| .569| .565| .561| .558| .555| .549| .543|
| 220 | .581| .577| .572| .568| .564| .561| .558| .551| .545|
| 230 | .585| .580| .575| .572| .567| .564| .561| .554| .548|
| 240 | .589| .584| .579| .575| .571| .567| .564| .556| .550|
| 250 | .593| .587| .582| .577| .574| .570| .567| .559| .553|
|_________|_____|_____|_____|_____|_____|_____|_____|_____|_____|
Factor of Evaporation with Superheated Steam--When superheat is present
in the steam during a boiler trial, where superheated steam tables are
available, the formula for determining the factor of evaporation is that
already given, (2),[22] namely,
H - h
Factor of evaporation = -----
L
Here H = total heat in one pound of superheated steam from the table,
h and L having the same values as in (2).
Where no such tables are available but the specific heat of superheat is
known, the formula becomes:
H - h + Sp. Ht.(T - t)
Factor of evaporation = ----------------------
L
Where H = total heat in one pound of saturated steam at pressure
existing in trial,
h = sensible heat above 32 degrees in one pound of water at the
temperature entering the boiler,
T = temperature of superheated steam as determined in the trial,
t = temperature of saturated steam corresponding to the boiler
pressure,
Sp. Ht. = mean specific heat of superheated steam at the pressure and
temperature as found in the trial,
L = latent heat of one pound of saturated steam at atmospheric
pressure.
Advantages of the Use of Superheated Steam--In considering the saving
possible by the use of superheated steam, it is too often assumed that
there is only a saving in the prime movers, a saving which is at least
partially offset by an increase in the fuel consumption of the boilers
generating steam. This misconception is due to the fact that the fuel
consumption of the boiler is only considered in connection with a
definite weight of steam. It is true that where such a definite weight
is to be superheated, an added amount of fuel must be burned. With a
properly designed superheater where the combined efficiency of the
boiler and superheater will be at least as high as of a boiler alone,
the approximate increase in coal consumption for producing a given
weight of steam will be as follows:
_Superheat_ _Added Fuel_
_Degrees_ _Per Cent_
25 1.59
50 3.07
75 4.38
100 5.69
150 8.19
200 10.58
These figures represent the added fuel necessary for superheating a
definite weight of steam to the number of degrees as given. The standard
basis, however, of boiler evaporation is one of heat units and,
considered from such a standpoint, again providing the efficiency of the
boiler and superheater is as high, as of a boiler alone, there is no
additional fuel required to generate steam containing a definite number
of heat units whether such units be due to superheat or saturation. That
is, if 6 per cent more fuel is required to generate and superheat to 100
degrees, a definite weight of steam, over what would be required to
produce the same weight of saturated steam, that steam when superheated,
will contain 6 per cent more heat units above the fuel water temperature
than if saturated. This holds true if the efficiency of the boiler and
superheater combined is the same as of the boiler alone. As a matter of
fact, the efficiency of a boiler and superheater, where the latter is
properly designed and located, will be slightly higher for the same set
of furnace conditions than would the efficiency of a boiler in which no
superheater were installed. A superheater, properly placed within the
boiler setting in such way that products of combustion for generating
saturated steam are utilized as well for superheating that steam, will
not in any way alter furnace conditions. With a given set of such
furnace conditions for a given amount of coal burned, the fact that
additional surface, whether as boiler heating or superheating surface,
is placed in such a manner that the gases must sweep over it, will tend
to lower the temperature of the exit gases. It is such a lowering of
exit gas temperatures that is the ultimate indication of added
efficiency. Though the amount of this added efficiency is difficult to
determine by test, that there is an increase is unquestionable.
Where a properly designed superheater is installed in a boiler the
heating surface of the boiler proper, in the generation of a definite
number of heat units, is relieved of a portion of the work which would
be required were these heat units delivered in saturated steam. Such a
superheater needs practically no attention, is not subject to a large
upkeep cost or depreciation, and performs its function without in any
way interfering with the operation of the boiler. Its use, therefore
from the standpoint of the boiler room, results in a saving in wear and
tear due to the lower ratings at which the boiler may be run, or its use
will lead to the possibility of obtaining the same number of boiler
horse power from a smaller number of boilers, with the boiler heating
surface doing exactly the same amount of work as if the superheaters
were not installed. The saving due to the added boiler efficiency that
will be obtained is obvious.
Following the course of the steam in a plant, the next advantage of the
use of superheated steam is the absence of water in the steam pipes. The
thermal conductivity of superheated steam, that is, its power to give up
its heat to surrounding bodies, is much lower than that of saturated
steam and its heat, therefore, will not be transmitted so rapidly to the
walls of the pipes as when saturated steam is flowing through the pipes.
The loss of heat radiated from a steam pipe, assuming no loss in
pressure, represents the equivalent condensation when the pipe is
carrying saturated steam. In well-covered steam mains, the heat lost by
radiation when carrying superheated steam is accompanied only by a
reduction of the superheat which, if it be sufficiently high at the
boiler, will enable a considerable amount of heat to be radiated and
still deliver dry or superheated steam to the prime movers.
It is in the prime movers that the advantages of the use of superheated
steam are most clearly seen.
In an engine, steam is admitted into a space that has been cooled by the
steam exhausted during the previous stroke. The heat necessary to warm
the cylinder walls from the temperature of the exhaust to that of the
entering steam can be supplied only by the entering steam. If this steam
be saturated, such an adding of heat to the walls at the expense of the
heat of the entering steam results in the condensation of a portion.
This initial condensation is seldom less than from 20 to 30 per cent of
the total weight of steam entering the cylinder. It is obvious that if
the steam entering be superheated, it must be reduced to the temperature
of saturated steam at the corresponding pressure before any condensation
can take place. If the steam be superheated sufficiently to allow a
reduction in temperature equivalent to the quantity of heat that must be
imparted to the cylinder walls and still remain superheated, it is clear
that initial condensation is avoided. For example: assume one pound of
saturated steam at 200 pounds gauge pressure to enter a cylinder which
has been cooled by the exhaust. Assume the initial condensation to be 20
per cent. The latent heat of the steam is given up in condensation;
hence, .20 × 838 = 167.6 B. t. u. are given up by the steam. If one
pound of superheated steam enters the same cylinder, it would have to be
superheated to a point where its total heat is 1199 + 168 = 1367
B. t. u. or, at 200 pounds gauge pressure, superheated approximately 325
degrees if the heat given up to the cylinder walls were the same as for
the saturated steam. As superheated steam conducts heat less rapidly
than saturated steam, the amount of heat imparted will be less than for
the saturated steam and consequently the amount of superheat required to
prevent condensation will be less than the above figure. This, of
course, is the extreme case of a simple engine with the range of
temperature change a maximum. As cylinders are added, the range in each
is decreased and the condensation is proportionate.
The true economy of the use of superheated steam is best shown in a
comparison of the "heat consumption" of an engine. This is the number of
heat units required in developing one indicated horse power and the
measure of the relative performance of two engines is based on a
comparison of their heat consumption as the measure of a boiler is based
on its evaporation from and at 212 degrees. The water consumption of an
engine in pounds per indicated horse power is in no sense a true
indication of its efficiency. The initial pressures and corresponding
temperatures may differ widely and thus make a difference in the
temperature of the exhaust and hence in the temperature of the condensed
steam returned to the boiler. For example: suppose a certain weight of
steam at 150 pounds absolute pressure and 358 degrees be expanded to
atmospheric pressure, the temperature then being 212 degrees. If the
same weight of steam be expanded from an initial pressure of 125 pounds
absolute and 344 degrees, to enable it to do the same amount of work,
that is, to give up the same amount of heat, expansion then must be
carried to a point below atmospheric pressure to, say, 13 pounds
absolute, the final temperature of the steam then being 206 degrees. In
actual practice, it has been observed that the water consumption of a
compound piston engine running on 26-inch vacuum and returning the
condensed steam at 140 degrees was approximately the same as when
running on 28-inch vacuum and returning water at 90 degrees. With an
equal water consumption for the two sets of conditions, the economy in
the former case would be greater than in the latter, since it would be
necessary to add less heat to the water returned to the boiler to raise
it to the steam temperature.
The lower the heat consumption of an engine per indicated horse power,
the higher its economy and the less the number of heat units must be
imparted to the steam generated. This in turn leads to the lowering of
the amount of fuel that must be burned per indicated horse power.
With the saving in fuel by the reduction of heat consumption of an
engine indicated, it remains to be shown the effect of the use of
superheated steam on such heat consumption. As already explained, the
use of superheated steam reduces condensation not only in the mains but
especially in the steam cylinder, leaving a greater quantity of steam
available to do the work. Furthermore, a portion of the saturated steam
introduced into a cylinder will condense during adiabatic expansion,
this condensation increasing as expansion progresses. Since superheated
steam cannot condense until it becomes saturated, not only is initial
condensation prevented by its use but also such condensation as would
occur during expansion. When superheated sufficiently, steam delivered
by the exhaust will still be dry. In the avoidance of such condensation,
there is a direct saving in the heat consumption of an engine, the heat
given up being utilized in the developing of power and not in changing
the condition of the working fluid. That is, while the number of heat
units lost in overcoming condensation effects would be the same in
either case, when saturated steam is condensed the water of condensation
has no power to do work while the superheated steam, even after it has
lost a like number of heat units, still has the power of expansion. The
saving through the use of superheated steam in the heat consumption of
an engine decreases demands on the boiler and hence the fuel consumption
per unit of power.
Superheated Steam for Steam Turbines--Experience in using superheated
steam in connection with steam turbines has shown that it leads to
economy and that it undoubtedly pays to use superheated steam in place
of saturated steam. This is so well established that it is standard
practice to use superheated steam in connection with steam turbines.
Aside from the economy secured through using superheated steam, there is
an important advantage arising through the fact that it materially
reduces the erosion of the turbine blades by the action of water that
would be carried by saturated steam. In using saturated steam in a steam
turbine or piston engine, the work done on expanding the steam causes
condensation of a portion of the steam, so that even were the steam dry
on entering the turbine, it would contain water on leaving the turbine.
By superheating the steam the water that exists in the low pressure
stages of the turbine may be reduced to an amount that will not cause
trouble.
Again, if saturated steam contains moisture, the effect of this moisture
on the economy of a steam turbine is to reduce the economy to a greater
extent than the proportion by weight of water, one per cent of water
causing approximately a falling off of 2 per cent in the economy.
The water rate of a large economical steam turbine with superheated
steam is reduced about one per cent, for every 12 degrees of superheat
up to 200 degrees Fahrenheit of superheat. To superheat one pound of
steam 12 degrees requires about 7 B. t. u. and if 1050 B. t. u. are
required at the boiler to evaporate one pound of the saturated steam
from the temperature of the feed water, the heat required for the
superheated steam would be 1057 degrees. One per cent of saving,
therefore, in the water consumption would correspond to a net saving of
about one-third of one per cent in the coal consumption. On this basis
100 degrees of superheat with an economical steam turbine would result
in somewhat over 3 per cent of saving in the coal for equal boiler
efficiencies. As a boiler with a properly designed superheater placed
within the setting is more economical for a given capacity than a boiler
without a superheater, the minimum gain in the coal consumption would
be, say, 4 or 5 per cent as compared to a plant with the same boilers
without superheaters.
The above estimates are on the basis of a thoroughly dry saturated steam
or steam just at the point of being superheated or containing a few
degrees of superheat. If the saturated steam is moist, the saving due to
superheat is more and ordinarily the gain in economy due to superheated
steam, for equal boiler efficiencies, as compared with commercially dry
steam is, say, 5 per cent for each 100 degrees of superheat. Aside from
this gain, as already stated, superheated steam prevents erosion of the
turbine buckets that would be caused by water in the steam, and for the
reasons enumerated it is standard practice to use superheated steam for
turbine work. The less economical the steam motor, the more the gain due
to superheated steam, and where there are a number of auxiliaries that
are run with superheated steam, the percentage of gain will be greater
than the figures given above, which are the minimum and are for the most
economical type of large steam turbines.
An example from actual practice will perhaps best illustrate and
emphasize the foregoing facts. In October 1909, a series of comparable
tests were conducted by The Babcock & Wilcox Co. on the steam yacht
"Idalia" to determine the steam consumption both with saturated and
superheated steam of the main engine on that yacht, including as well
the feed pump, circulating pump and air pump. These tests are more
representative than are most tests of like character in that the saving
in the steam consumption of the auxiliaries, which were much more
wasteful than the main engine, formed an important factor. A résumé of
these tests was published in the Journal of the Society of Naval
Engineers, November 1909.
The main engines of the "Idalia" are four cylinder, triple expansion,
11-1/2 × 19 inches by 22-11/16 × 18 inches stroke. Steam is supplied by
a Babcock & Wilcox marine boiler having 2500 square feet of boiler
heating surface, 340 square feet of superheating surface and 65 square
feet of grate surface.
The auxiliaries consist of a feed pump 6 × 4 × 6 inches, an independent
air pump 6 × 12 × 8 inches, and a centrifugal pump driven by a
reciprocating engine 5-7/16 × 5 inches. Under ordinary operating
conditions the superheat existing is about 100 degrees Fahrenheit.
Tests were made with various degrees of superheat, the amount being
varied by by-passing the gases and in the tests with the lower amounts
of superheat by passing a portion of the steam from the boiler to the
steam main without passing it through the superheater. Steam temperature
readings were taken at the engine throttle. In the tests with saturated
steam, the superheater was completely cut out of the system. Careful
calorimeter measurements were taken, showing that the saturated steam
delivered to the superheater was dry.
The weight of steam used was determined from the weight of the condensed
steam discharge from the surface condenser, the water being pumped from
the hot well into a tank mounted on platform scales. The same
indicators, thermometers and gauges were used in all the tests, so that
the results are directly comparable. The indicators used were of the
outside spring type so that there was no effect of the temperature of
the steam. All tests were of sufficient duration to show a uniformity of
results by hours. A summary of the results secured is given in Table 26,
which shows the water rate per indicated horse power and the heat
consumption. The latter figures are computed on the basis of the heat
imparted to the steam above the actual temperature of the feed water
and, as stated, these are the results that are directly comparable.