Chapter XII: Part 12

With the exception of the small amount of carbon in combination with hydrogen as methane, and a very small percentage of free hydrogen, ordinarily less than 0.1 per cent, the calorific value of blast furnace gas is due to the CO content which when united with sufficient oxygen when burned under a boiler, burns further to CO_{2}. The heat value of such gas will vary in most cases from 85 to 100 B. t. u. per cubic foot under standard conditions. In modern practice, where the blast is heated by hot blast stoves, approximately 15 per cent of the total amount of gas is used for this purpose, leaving 85 per cent of the total for use under boilers or in gas engines, that is, approximately 8500 pounds of gas per ton of pig iron produced. In a modern blast furnace plant, the gas serves ordinarily as the only fuel required. Table 49 gives the analyses of several samples of blast furnace gas.

TABLE 49

TYPICAL ANALYSES OF BLAST FURNACE GAS

+----------------------------------------------------------------+ |+-----------------------+------+----+-----+----+------+--------+| || |CO_{2}| O | CO | H |CH_{4}| N || |+-----------------------+------+----+-----+----+------+--------+| ||Bessemer Furnace | 9.85|0.36|32.73|3.14| .. |53.92 || ||Bessemer Furnace | 11.4 | .. |27.7 |1.9 | 0.3 |58.7 || ||Bessemer Furnace | 10.0 | .. |26.2 |3.1 | 0.2 |60.5 || ||Bessemer Furnace | 9.1 | .. |28.7 |2.7 | 0.2 |59.3 || ||Bessemer Furnace | 13.5 | .. |25.2 |1.43| .. |59.87 || ||Bessemer Furnace[47] | 10.9 | .. |27.8 |2.8 | 0.2 |58.3 || ||Ferro Manganese Furnace| 7.1 | .. |30.1 | .. | .. |62.8[48]|| ||Basic Ore Furnace | 16.0 |0.2 |23.6 | .. | .. |60.2[48]|| |+-----------------------+------+----+-----+----+------+--------+| +----------------------------------------------------------------+

Until recently, the important consideration in the burning of blast furnace gas has been the capacity that can be developed with practically no attention given to the aspect of efficiency. This phase of the question is now drawing attention and furnaces especially designed for good efficiency with this class of fuel are demanded. The essential feature is ample combustion space, in which the combustion of gases may be practically completed before striking the heating surfaces. The gases have the power of burning out completely after striking the heating surfaces, provided the initial temperature is sufficiently high, but where the combustion is completed before such time, the results secured are more satisfactory. A furnace volume of approximately 1 to 1.5 cubic feet per rated boiler horse power will give a combustion space that is ample.

Where there is the possibility of a failure of the gas supply, or where steam is required when the blast furnace is shut down, coal fired grates of sufficient size to get the required capacity should be installed. Where grates of full size are not required, ignition grates should be installed, which need be only large enough to carry a fire for igniting the gas or for generating a small quantity of steam when the blast furnace is shut down. The area of such grates has no direct bearing on the size of the boiler. The grates may be placed directly under the gas burners in a standard position or may be placed between two bridge walls back of the gas furnace and fired from the side of the boiler. An advantage is claimed for the standard grate position that it minimizes the danger of explosion on the re-ignition of gas after a temporary stoppage of the supply and also that a considerable amount of dirt, of which there is a good deal with this class of fuel and which is difficult to remove, deposits on the fire and is taken out when the fires are cleaned. In any event, regardless of the location of the grates, ample provision should be made for removing this dust, not only from the furnace but from the setting as a whole.

Blast furnace gas burners are of two general types: Those in which the air for combustion is admitted around the burner proper, and those in which this air is admitted through the burner. Whatever the design of burner, provision should be made for the regulation of both the air and the gas supply independently. A gas opening of .8 square inch per rated horse power will enable a boiler to develop its nominal rating with a gas pressure in the main of about 2 inches. This pressure is ordinarily from 6 to 8 inches and in this way openings of the above size will be good for ordinary overloads. The air openings should be from .75 to .85 square inch per rated horse power. Good results are secured by inclining the gas burners slightly downward toward the rear of the furnace. Where the burners are introduced over coal fired grates, they should be set high enough to give headroom for hand firing.

Ordinarily, individual stacks of 130 feet high with diameters as given in Kent's table for corresponding horse power are large enough for this class of work. Such a stack will give a draft sufficient to allow a boiler to be operated at 175 per cent of its rated capacity, and beyond this point the capacity will not increase proportionately with the draft. When more than one boiler is connected with a stack, the draft available at the damper should be equivalent to that which an individual stack of 130 feet high would give. The draft from such a stack is necessary to maintain a suction under all conditions throughout all parts of the setting. If the draft is increased above that which such a stack will give, difficulties arise from excess air for combustion with consequent loss in efficiency.

A poor mixing or laneing action in the furnace may result in a pulsating effect of the gases in the setting. This action may at times be remedied by admitting more air to the furnace. On account of the possibility of a pulsating action of the gases under certain conditions and the puffs or explosions, settings for this class of work should be carefully constructed and thoroughly buckstayed and tied.

Natural Gas--Natural gas from different localities varies considerably in composition and heating value. In Table 50 there is given a number of analyses and heat values for natural gas from various localities.

This fuel is used for steam generating purposes to a considerable extent in some localities, though such use is apparently decreasing. It is best burned by employing a large number of small burners, each being capable of handling 30 nominal rated horse power. The use of a large number of burners obviates the danger of any laneing or blowpipe action, which might be present where large burners are used. Ordinarily, such a gas, as it enters the burners, is under a pressure of about 8 ounces. For the purpose of comparison, all observations should be based on gas reduced to the standard conditions of temperature and pressure, namely 32 degrees Fahrenheit and 14.7 pounds per square inch. When the temperature and pressure corresponding to meter readings are known, the volume of gas under standard conditions may be obtained by multiplying the meter readings in cubic feet by 33.54 P/T, in which P equals the absolute pressure in pounds per square inch and T equals the absolute temperature of the gas at the meter. In boiler testing work, the evaporation should always be reduced to that per cubic foot of gas under standard conditions.

TABLE 50

TYPICAL ANALYSES (BY VOLUME) AND CALORIFIC VALUES OF NATURAL
GAS FROM VARIOUS LOCALITIES

+----------------+-----+-----+-----+-----+-----+----+-------+------+--------+ |Locality of Well| H |CH_{4}| CO |CO_{2}| N | O | Heavy |H_{2}S|B. t. u.| | | | | | | | |Hydro- | | per | | | | | | | | |carbons| | Cubic | | | | | | | | | | | Foot | | | | | | | | | | |Calcul- | | | | | | | | | | |ated[49]| |----------------+-----+-----+-----+-----+-----+----+-------+------+--------+ |Anderson, Ind. | 1.86|93.07| 0.73| 0.26| 3.02|0.42| 0.47 | 0.15 | 1017 | |Marion, Ind. | 1.20|93.16| 0.60| 0.30| 3.43|0.55| 0.15 | 0.20 | 1009 | |Muncie, Ind. | 2.35|92.67| 0.45| 0.25| 3.53|0.35| 0.25 | 0.15 | 1004 | |Olean, N. Y. | |96.50| 0.50| | |2.00| 1.00 | | 1018 | |Findlay, O. | 1.64|93.35| 0.41| 0.25| 3.41|0.39| 0.35 | 0.20 | 1011 | |St. Ive, Pa. | 6.10|75.54|Trace| 0.34| | | 18.12 | | 1117 | |Cherry Tree, Pa.|22.50|60.27| | 2.28| 7.32|0.83| 6.80 | | 842 | |Grapeville, Pa. |24.56|14.93|Trace|Trace|18.69|1.22| 40.60 | | 925 | |Harvey Well, | | | | | | | | | | | Butler Co., Pa.|13.50|80.00|Trace| 0.66| | | 5.72 | | 998 | |Pittsburgh, Pa. | 9.64|57.85| 1.00| |23.41|2.10| 6.00 | | 748 | |Pittsburgh, Pa. |20.02|72.18| 1.00| 0.80| |1.10| 4.30 | | 917 | |Pittsburgh, Pa. |26.16|65.25| 0.80| 0.60| |0.80| 6.30 | | 899 | +----------------+-----+-----+-----+-----+-----+----+-------+------+--------+

When natural gas is the only fuel, the burners should be evenly distributed over the lower portion of the boiler front. If the fuel is used as an auxiliary to coal, the burners may be placed through the fire front. A large combustion space is essential and a volume of .75 cubic feet per rated horse power will be found to give good results. The burners should be of a design which give the gas and air a rotary motion to insure a proper mixture. A checkerwork wall is sometimes placed in the furnace about 3 feet from the burners to break up the flame, but with a good design of burner this is unnecessary. Where the gas is burned alone and no grates are furnished, good results are secured by inclining the burner downward to the rear at a slight angle.

By-product Coke Oven Gas--By-product coke oven gas is a product of the destructive distillation of coal in a distilling or by-product coke oven. In this class of apparatus the gases, instead of being burned at the point of their origin, as in a beehive or retort coke oven, are taken from the oven through an uptake pipe, cooled and yield as by-products tar, ammonia, illuminating and fuel gas. A certain portion of the gas product is burned in the ovens and the remainder used or sold for illuminating or fuel purposes, the methods of utilizing the gas varying with plant operation and locality.

Table 51 gives the analyses and heat value of certain samples of by-product coke oven gas utilized for fuel purposes.

This gas is nearer to natural gas in its heat value than is blast furnace gas, and in general the remarks as to the proper methods of burning natural gas and the features to be followed in furnace design hold as well for by-product coke oven gas.

TABLE 51

TYPICAL ANALYSES OF BY-PRODUCT
COKE OVEN GAS

+----------------------------------------------+ |+------+-------------------------------------+| ||CO_{2}| O |CO |CH_{4}| H | N |B.t.u. per|| || | | | | | |Cubic Foot|| |+------+-----+---+------+----+----+----------+| || 0.75 |Trace|6.0|28.15 |53.0|12.1| 505 || || 2.00 |Trace|3.2|18.80 |57.2|18.0| 399 || || 3.20 | 0.4 |6.3|29.60 |41.6|16.1| 551 || || 0.80 | 1.6 |4.9|28.40 |54.2|10.1| 460 || |+------+-----+---+------+----+----+----------+| +----------------------------------------------+

The essential difference in burning the two fuels is the pressure under which it reaches the gas burner. Where this is ordinarily from 4 to 8 ounces in the case of natural gas, it is approximately 4 inches of water in the case of by-product coke oven gas. This necessitates the use of larger gas openings in the burners for the latter class of fuel than for the former.

By-product coke oven gas comes to the burners saturated with moisture and provision should be made for the blowing out of water of condensation. This gas too, carries a large proportion of tar and hydrocarbons which form a deposit in the burners and provision should be made for cleaning this out. This is best accomplished by an attachment which permits the blowing out of the burners by steam.

UTILIZATION OF WASTE HEAT

While it has been long recognized that the reclamation of heat from the waste gases of various industrial processes would lead to a great saving in fuel and labor, the problem has, until recently, never been given the attention that its importance merits. It is true that installations have been made for the utilization of such gases, but in general they have consisted simply in the placing of a given amount of boiler heating surface in the path of the gases and those making the installations have been satisfied with whatever power has been generated, no attention being given to the proportioning of either the heating surface or the gas passages to meet the peculiar characteristics of the particular class of waste gas available. The Babcock & Wilcox Co. has recently gone into the question of the utilization of what has been known as waste heat with great thoroughness, and the results secured by their installations with practically all operations yielding such gases are eminently successful.

TABLE 52

TEMPERATURE OF WASTE GASES FROM
VARIOUS INDUSTRIAL PROCESSES

+-----------------------------------------------------+ |+-----------------------------------+---------------+| ||Waste Heat From |Temperature[50]|| || | Degrees || |+-----------------------------------+---------------+| ||Brick Kilns | 2000-2300 || ||Zinc Furnaces | 2000-2300 || ||Copper Matte Reverberatory Furnaces| 2000-2200 || ||Beehive Coke Ovens | 1800-2000 || ||Cement Kilns | 1200-1600[51]|| ||Nickel Refining Furnaces | 1500-1750 || ||Open Hearth Steel Furnaces | 1100-1400 || |+-----------------------------------+---------------+| +-----------------------------------------------------+

The power that can be obtained from waste gases depends upon their temperature and weight, and both of these factors vary widely in different commercial operations. Table 52 gives a list of certain processes yielding waste gases the heat of which is available for the generation of steam and the approximate temperature of such gases. It should be understood that the temperatures in the table are the average of the range of a complete cycle of the operation and that the minimum and maximum temperatures may vary largely from the figures given.

The maximum available horse power that may be secured from such gases is represented by the formula:

W(T-t)s
H. P. = ------- (23)
33,479

Where W = the weight of gases passing per hour,
T = temperature of gases entering heating surface,
t = temperature leaving heating surface,
s = specific heat of gases.

The initial temperature and the weight or volume of gas will depend, as stated, upon the process involved. The exit temperature will depend, to a certain extent, upon the temperature of the entering gases, but will be governed mainly by the efficiency of the heating surfaces installed for the absorption of the heat.

Where the temperature of the gas available is high, approaching that found in direct fired boiler practice, the problem is simple and the question of design of boiler becomes one of adapting the proper amount of heating surface to the volume of gas to be handled. With such temperatures, and a volume of gas available approximately in accordance with that found in direct fired boiler practice, a standard boiler or one but slightly modified from the standard will serve the purpose satisfactorily. As the temperatures become lower, however, the problem is more difficult and the departure from standard practice more radical. With low temperature gases, to obtain a heat transfer rate at all comparable with that found in ordinary boiler practice, the lack of temperature must be offset by an added velocity of the gases in their passage over the heating surfaces. In securing the velocity necessary to give a heat transfer rate with low temperature gases sufficient to make the installation of waste heat boilers show a reasonable return on the investment, the frictional resistance to the gases through the boiler becomes greatly in excess of what would be considered good practice in direct fired boilers. Practically all operations yielding waste gases require that nothing be done in the way of impairing the draft at the furnace outlet, as this might interfere with the operation of the primary furnace. The installation of a waste heat boiler, therefore, very frequently necessitates providing sufficient mechanical draft to overcome the frictional resistance of the gases through the heating surfaces and still leave ample draft available to meet the maximum requirements of the primary furnace.

Where the temperature and volume of the gases are in line with what are found in ordinary direct fired practice, the area of the gas passages may be practically standard. With the volume of gas known, the draft loss through the heating surfaces may be obtained from experimental data and this additional draft requirement met by the installation of a stack sufficient to take care of this draft loss and still leave draft enough for operating the furnace at its maximum capacity.

Where the temperatures are low, the added frictional resistance will ordinarily be too great to allow the draft required to be secured by additional stack height and the installation of a fan is necessary. Such a fan should be capable of handling the maximum volume of gas that the furnace may produce, and of maintaining a suction equivalent to the maximum frictional resistance of such volume through the boiler plus the maximum draft requirement at the furnace outlet. Stacks and fans for this class of work should be figured on the safe side. Where a fan installation is necessary, the loss of draft in the fan connections should be considered, and in figuring conservatively it should be remembered that a fan of ample size may be run as economically as a smaller fan, whereas the smaller fan, if overloaded, is operated with a large loss in efficiency. In practically any installation where low temperature gas requires a fan to give the proper heat transfer from the gases, the cost of the fan and of the energy to drive it will be more than offset by the added power from the boiler secured by its use. Furthermore, the installation of such a fan will frequently increase the capacity of the industrial furnace, in connection with which the waste heat boilers are installed.

In proportioning heating surfaces and gas passages for waste heat work there are so many factors bearing directly on what constitutes the proper installation that it is impossible to set any fixed rules. Each individual installation must be considered by itself as well as the particular characteristics of the gases available, such as their temperature and volume, and the presence of dust or tar-like substances, and all must be given the proper weight in the determination of the design of the heating surfaces and gas passages for the specific set of conditions.

[Graph: Per Cent of Water Heating Surface passed over by Gases/Per Cent of the Total Amount of Steam Generated in the Boiler against Temperature in Degrees Fahrenheit of Hot Gases Sweeping Heating Surface

Fig. 31. Curve Showing Relation Between Gas Temperature, Heating Surface passed over, and Amount of Steam Generated. Ten Square Feet of Heating Surface are Assumed as Equivalent to One Boiler Horse Power]

Fig. 31 shows the relation of gas temperatures, heating surface passed over and work done by such surface for use in cases where the temperatures approach those found in direct fired practice and where the volume of gas available is approximately that with which one horse power may be developed on 10 square feet of heating surface. The curve assumes what may be considered standard gas passage areas, and further, that there is no heat absorbed by direct radiation from the fire.

Experiments have shown that this curve is very nearly correct for the conditions assumed. Such being the case, its application in waste heat work is clear. Decreasing or increasing the velocity of the gases over the heating surfaces from what might be considered normal direct fired practice, that is, decreasing or increasing the frictional loss through the boiler will increase or decrease the amount of heating surface necessary to develop one boiler horse power. The application of Fig. 31 to such use may best be seen by an example:

Assume the entering gas temperatures to be 1470 degrees and that the gases are cooled to 570 degrees. From the curve, under what are assumed to be standard conditions, the gases have passed over 19 per cent of the heating surface by the time they have been cooled 1470 degrees. When cooled to 570 degrees, 78 per cent of the heating surface has been passed over. The work done in relation to the standard of the curve is represented by (1470 - 570) ÷ (2500 - 500) = 45 per cent. (These figures may also be read from the curve in terms of the per cent of the work done by different parts of the heating surfaces.) That is, 78 per cent - 19 per cent = 59 per cent of the standard heating surface has done 45 per cent of the standard amount of work. 59 ÷ 45 = 1.31, which is the ratio of surface of the assumed case to the standard case of the curve. Expressed differently, there will be required 13.1 square feet of heating surface in the assumed case to develop a horse power as against 10 square feet in the standard case.

The gases available for this class of work are almost invariably very dirty. It is essential for the successful operation of waste-heat boilers that ample provision be made for cleaning by the installation of access doors through which all parts of the setting may be reached. In many instances, such as waste-heat boilers set in connection with cement kilns, settling chambers are provided for the dust before the gases reach the boiler.

By-passes for the gases should in all cases be provided to enable the boiler to be shut down for cleaning and repairs without interfering with the operation of the primary furnace. All connections from furnace to boilers should be kept tight to prevent the infiltration of air, with the consequent lowering of gas temperatures.

Auxiliary gas or coal fired grates must be installed to insure continuity in the operation of the boiler where the operation of the furnace is intermittent or where it may be desired to run the boiler with the primary furnace not in operation. Such grates are sometimes used continuously where the gases available are not sufficient to develop the required horse power from a given amount of heating surface.

Fear has at times been expressed that certain waste gases, such as those containing sulphur fumes, will have a deleterious action on the heating surface of the boiler. This feature has been carefully watched, however, and from plants in operation it would appear that in the absence of water or steam leaks within the setting, there is no such harmful action.

CHIMNEYS AND DRAFT

The height and diameter of a properly designed chimney depend upon the amount of fuel to be burned, its nature, the design of the flue, with its arrangement relative to the boiler or boilers, and the altitude of the plant above sea level. There are so many factors involved that as yet there has been produced no formula which is satisfactory in taking them all into consideration, and the methods used for determining stack sizes are largely empirical. In this chapter a method sufficiently comprehensive and accurate to cover all practical cases will be developed and illustrated.

Draft is the difference in pressure available for producing a flow of the gases. If the gases within a stack be heated, each cubic foot will expand, and the weight of the expanded gas per cubic foot will be less than that of a cubic foot of the cold air outside the chimney. Therefore, the unit pressure at the stack base due to the weight of the column of heated gas will be less than that due to a column of cold air. This difference in pressure, like the difference in head of water, will cause a flow of the gases into the base of the stack. In its passage to the stack the cold air must pass through the furnace or furnaces of the boilers connected to it, and it in turn becomes heated. This newly heated gas will also rise in the stack and the action will be continuous.

The intensity of the draft, or difference in pressure, is usually measured in inches of water. Assuming an atmospheric temperature of 62 degrees Fahrenheit and the temperature of the gases in the chimney as 500 degrees Fahrenheit, and, neglecting for the moment the difference in density between the chimney gases and the air, the difference between the weights of the external air and the internal flue gases per cubic foot is .0347 pound, obtained as follows:

Weight of a cubic foot of air at 62 degrees Fahrenheit = .0761 pound
Weight of a cubic foot of air at 500 degrees Fahrenheit = .0414 pound
------------------------
Difference = .0347 pound

Therefore, a chimney 100 feet high, assumed for the purpose of illustration to be suspended in the air, would have a pressure exerted on each square foot of its cross sectional area at its base of .0347 × 100 = 3.47 pounds. As a cubic foot of water at 62 degrees Fahrenheit weighs 62.32 pounds, an inch of water would exert a pressure of 62.32 ÷ 12 = 5.193 pounds per square foot. The 100-foot stack would, therefore, under the above temperature conditions, show a draft of 3.47 ÷ 5.193 or approximately 0.67 inches of water.

The method best suited for determining the proper proportion of stacks and flues is dependent upon the principle that if the cross sectional area of the stack is sufficiently large for the volume of gases to be handled, the intensity of the draft will depend directly upon the height; therefore, the method of procedure is as follows:

1st. Select a stack of such height as will produce the draft required by the particular character of the fuel and the amount to be burned per square foot of grate surface.

2nd. Determine the cross sectional area necessary to handle the gases without undue frictional losses.

The application of these rules follows:

Draft Formula--The force or intensity of the draft, not allowing for the difference in the density of the air and of the flue gases, is given by the formula:

/ 1 1 \
D = 0.52 H × P |--- - -----| (24)
\ T T_{1}/

in which

D = draft produced, measured in inches of water,
H = height of top of stack above grate bars in feet,
P = atmospheric pressure in pounds per square inch,
T = absolute atmospheric temperature,
T_{1} = absolute temperature of stack gases.

In this formula no account is taken of the density of the flue gases, it being assumed that it is the same as that of air. Any error arising from this assumption is negligible in practice as a factor of correction is applied in using the formula to cover the difference between the theoretical figures and those corresponding to actual operating conditions.

The force of draft at sea level (which corresponds to an atmospheric pressure of 14.7 pounds per square inch) produced by a chimney 100 feet high with the temperature of the air at 60 degrees Fahrenheit and that of the flue gases at 500 degrees Fahrenheit is,

/ 1 1 \
D = 0.52 × 100 × 14.7 | --- - --- | = 0.67
\ 521 961 /

Under the same temperature conditions this chimney at an atmospheric pressure of 10 pounds per square inch (which corresponds to an altitude of about 10,000 feet above sea level) would produce a draft of,

/ 1 1 \
D = 0.52 × 100 × 10 | --- - --- | = 0.45
\ 521 961 /

For use in applying this formula it is convenient to tabulate values of the product

/ 1 1 \
0.52 × 14.7|--- - -----|
\ T T_{1}/

which we will call K, for various values of T_{1}. With these values calculated for assumed atmospheric temperature and pressure (24) becomes

D = KH. (25)

For average conditions the atmospheric pressure may be considered 14.7 pounds per square inch, and the temperature 60 degrees Fahrenheit. For these values and various stack temperatures K becomes:

_Temperature Stack Gases_ _Constant K_
750 .0084
700 .0081
650 .0078
600 .0075
550 .0071
500 .0067
450 .0063
400 .0058
350 .0053

Draft Losses--The intensity of the draft as determined by the above formula is theoretical and can never be observed with a draft gauge or any recording device. However, if the ashpit doors of the boiler are closed and there is no perceptible leakage of air through the boiler setting or flue, the draft measured at the stack base will be approximately the same as the theoretical draft. The difference existing at other times represents the pressure necessary to force the gases through the stack against their own inertia and the friction against the sides. This difference will increase with the velocity of the gases. With the ashpit doors closed the volume of gases passing to the stack are a minimum and the maximum force of draft will be shown by a gauge.

As draft measurements are taken along the path of the gases, the readings grow less as the points at which they are taken are farther from the stack, until in the boiler ashpit, with the ashpit doors open for freely admitting the air, there is little or no perceptible rise in the water of the gauge. The breeching, the boiler damper, the baffles and the tubes, and the coal on the grates all retard the passage of the gases, and the draft from the chimney is required to overcome the resistance offered by the various factors. The draft at the rear of the boiler setting where connection is made to the stack or flue may be 0.5 inch, while in the furnace directly over the fire it may not be over, say, 0.15 inch, the difference being the draft required to overcome the resistance offered in forcing the gases through the tubes and around the baffling.

One of the most important factors to be considered in designing a stack is the pressure required to force the air for combustion through the bed of fuel on the grates. This pressure will vary with the nature of the fuel used, and in many instances will be a large percentage of the total draft. In the case of natural draft, its measure is found directly by noting the draft in the furnace, for with properly designed ashpit doors it is evident that the pressure under the grates will not differ sensibly from atmospheric pressure.

Loss in Stack--The difference between the theoretical draft as determined by formula (24) and the amount lost by friction in the stack proper is the available draft, or that which the draft gauge indicates when connected to the base of the stack. The sum of the losses of draft in the flue, boiler and furnace must be equivalent to the available draft, and as these quantities can be determined from record of experiments, the problem of designing a stack becomes one of proportioning it to produce a certain available draft.

The loss in the stack due to friction of the gases can be calculated from the following formula:

f W² C H
[Delta]D = -------- (26)
A³

in which

[Delta]D = draft loss in inches of water,
W = weight of gas in pounds passing per second,
C = perimeter of stack in feet,
H = height of stack in feet,
f = a constant with the following values at sea level:
.0015 for steel stacks, temperature of gases 600 degrees
Fahrenheit.
.0011 for steel stacks, temperature of gases 350 degrees
Fahrenheit.
.0020 for brick or brick-lined stacks, temperature of gases
600 degrees Fahrenheit.
.0015 for brick or brick-lined stacks, temperature of gases
350 degrees Fahrenheit.
A = Area of stack in square feet.

This formula can also be used for calculating the frictional losses for flues, in which case, C = the perimeter of the flue in feet, H = the length of the flue in feet, the other values being the same as for stacks.

The available draft is equal to the difference between the theoretical draft from formula (25) and the loss from formula (26), hence:

f W² C H
d^{1} = available draft = KH - -------- (27)
A³

Table 53 gives the available draft in inches that a stack 100 feet high will produce when serving different horse powers of boilers with the methods of calculation for other heights.

TABLE 53

AVAILABLE DRAFT

CALCULATED FOR 100-FOOT STACK OF DIFFERENT DIAMETERS ASSUMING STACK
TEMPERATURE OF 500 DEGREES FAHRENHEIT AND 100 POUNDS OF GAS PER HORSE POWER

FOR OTHER HEIGHTS OF STACK MULTIPLY DRAFT BY HEIGHT ÷ 100

+-----+-------------------------------------------------------------------+ |Horse| | |Power| Diameter of Stack in Inches | +-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | |36 |42 |48 |54 |60 |66 |72 |78 |84 |90 |96 |102|108|114|120|132|144| +-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 100 |.64| | | | | | | | | | | | | | | | | | 200 |.55|.62| | | | | | | | | | | | | | | | | 300 |.41|.55|.61| | | | | | | | | | | | | | | | 400 |.21|.46|.56|.61| | | | | | | | | | | | | | | 500 | |.34|.50|.57|.61| | | | | | | | | | | | | | 600 | |.19|.42|.53|.59| | | | | | | | | | | | | | 700 | | |.34|.48|.56|.60|.63| | | | | | | | | | | | 800 | | |.23|.43|.52|.58|.61|.63| | | | | | | | | | | 900 | | | |.36|.49|.56|.60|.62|.64| | | | | | | | | |1000 | | | |.29|.45|.53|.58|.61|.63|.64| | | | | | | | |1100 | | | | |.40|.50|.56|.60|.62|.63|.64| | | | | | | |1200 | | | | |.35|.47|.54|.58|.61|.63|.64|.65| | | | | | |1300 | | | | |.29|.44|.52|.57|.60|.62|.63|.64|.65| | | | | |1400 | | | | | |.40|.49|.55|.59|.61|.63|.64|.65|.65| | | | |1500 | | | | | |.36|.47|.53|.58|.60|.62|.63|.64|.65|.65| | | |1600 | | | | | |.31|.43|.52|.56|.59|.62|.63|.64|.65|.65| | | |1700 | | | | | | |.41|.50|.55|.58|.61|.62|.64|.64|.65| | | |1800 | | | | | | |.37|.47|.54|.57|.60|.62|.63|.64|.65| | | |1900 | | | | | | |.34|.45|.52|.56|.59|.61|.63|.64|.64| | | |2000 | | | | | | | |.43|.50|.55|.59|.61|.62|.63|.64| | | |2100 | | | | | | | |.40|.49|.54|.58|.60|.62|.63|.64| | | |2200 | | | | | | | |.38|.47|.53|.57|.59|.61|.62|.64| | | |2300 | | | | | | | |.35|.45|.52|.56|.59|.61|.62|.63| | | |2400 | | | | | | | |.32|.43|.50|.55|.58|.60|.62|.63| | | |2500 | | | | | | | | |.41|.49|.54|.57|.60|.61|.63| | | |2600 | | | | | | | | | |.47|.53|.56|.59|.61|.62|.64|.65| |2700 | | | | | | | | | |.45|.52|.55|.58|.60|.62|.64|.65| |2800 | | | | | | | | | |.44|.59|.55|.58|.60|.61|.64|.65| |2900 | | | | | | | | | |.42|.49|.54|.57|.59|.61|.63|.65| |3000 | | | | | | | | | |.40|.48|.53|.56|.59|.61|.63|.64| |3100 | | | | | | | | | |.38|.47|.52|.56|.58|.60|.63|.64| |3200 | | | | | | | | | | |.45|.51|.55|.58|.60|.63|.64| |3300 | | | | | | | | | | |.44|.50|.54|.57|.59|.62|.64| |3400 | | | | | | | | | | |.42|.49|.53|.56|.59|.62|.64| |3500 | | | | | | | | | | |.40|.48|.52|.56|.58|.62|.64| |3600 | | | | | | | | | | | |.47|.52|.55|.58|.61|.63| |3700 | | | | | | | | | | | |.45|.51|.55|.57|.61|.63| |3800 | | | | | | | | | | | |.44|.50|.54|.57|.61|.63| |3900 | | | | | | | | | | | |.43|.49|.53|.56|.60|.63| |4000 | | | | | | | | | | | |.42|.48|.52|.56|.60|.62| |4100 | | | | | | | | | | | |.40|.47|.52|.55|.60|.62| |4200 | | | | | | | | | | | |.39|.46|.51|.55|.59|.62| |4300 | | | | | | | | | | | | |.45|.50|.54|.59|.62| |4400 | | | | | | | | | | | | |.44|.49|.53|.59|.62| |4500 | | | | | | | | | | | | |.43|.49|.53|.58|.61| |4600 | | | | | | | | | | | | |.42|.48|.52|.58|.61| |4700 | | | | | | | | | | | | |.41|.47|.51|.57|.61| |4800 | | | | | | | | | | | | |.40|.46|.51|.57|.60| |4900 | | | | | | | | | | | | | |.45|.50|.57|.60| |5000 | | | | | | | | | | | | | |.44|.49|.56|.60| +-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

FOR OTHER STACK TEMPERATURES ADD OR DEDUCT BEFORE MULTIPLYING BY HEIGHT ÷ 100 AS FOLLOWS[52]

For 750 Degrees F. Add .17 inch. For 700 Degrees F. Add .14 inch. For 650 Degrees F. Add .11 inch. For 600 Degrees F. Add .08 inch. For 550 Degrees F. Add .04 inch. For 450 Degrees F. Deduct .04 inch. For 400 Degrees F. Deduct .09 inch. For 350 Degrees F. Deduct .14 inch.

[Graph: Horse Power of Boilers against Diameter of Stack in Inches

Fig. 33. Diameter of Stacks and Horse Power they will Serve

Computed from Formula (28). For brick or brick-lined stacks, increase the diameter 6 per cent]

Height and Diameter of Stacks--From this formula (27) it becomes evident that a stack of certain diameter, if it be increased in height, will produce the same available draft as one of larger diameter, the additional height being required to overcome the added frictional loss. It follows that among the various stacks that would meet the requirements of a particular case there must be one which can be constructed more cheaply than the others. It has been determined from the relation of the cost of stacks to their diameters and heights, in connection with the formula for available draft, that the minimum cost stack has a diameter dependent solely upon the horse power of the boilers it serves, and a height proportional to the available draft required.

Assuming 120 pounds of flue gas per hour for each boiler horse power, which provides for ordinary overloads and the use of poor coal, the method above stated gives:

For an unlined steel stack--

diameter in inches = 4.68 (H. P.)^{2/5} (28)

For a stack lined with masonry--

diameter in inches = 4.92 (H. P.)^{2/5} (29)

In both of these formulae H. P. = the rated horse power of the boiler.

From this formula the curve, Fig. 33, has been calculated and from it the stack diameter for any boiler horse power can be selected.

For stoker practice where a large stack serves a number of boilers, the area is usually made about one-third more than the above rules call for, which allows for leakage of air through the setting of any idle boilers, irregularities in operating conditions, etc.

Stacks with diameters determined as above will give an available draft which bears a constant ratio of the theoretical draft, and allowing for the cooling of the gases in their passage upward through the stack, this ratio is 8. Using this factor in formula (25), and transposing, the height of the chimney becomes,

d^{1}
H = ----- (30)
.8 K

Where H = height of stack in feet above the level of the grates,
d^{1} = available draft required,
K = constant as in formula.

Losses in Flues--The loss of draft in straight flues due to friction and inertia can be calculated approximately from formula (26), which was given for loss in stacks. It is to be borne in mind that C in this formula is the actual perimeter of the flue and is least, relative to the cross sectional area, when the section is a circle, is greater for a square section, and greatest for a rectangular section. The retarding effect of a square flue is 12 per cent greater than that of a circular flue of the same area and that of a rectangular with sides as 1 and 1½, 15 per cent greater. The greater resistance of the more or less uneven brick or concrete flue is provided for in the value of the constants given for formula (26). Both steel and brick flues should be short and should have as near a circular or square cross section as possible. Abrupt turns are to be avoided, but as long easy sweeps require valuable space, it is often desirable to increase the height of the stack rather than to take up added space in the boiler room. Short right-angle turns reduce the draft by an amount which can be roughly approximated as equal to 0.05 inch for each turn. The turns which the gases make in leaving the damper box of a boiler, in entering a horizontal flue and in turning up into a stack should always be considered. The cross sectional areas of the passages leading from the boilers to the stack should be of ample size to provide against undue frictional loss. It is poor economy to restrict the size of the flue and thus make additional stack height necessary to overcome the added friction. The general practice is to make flue areas the same or slightly larger than that of the stack; these should be, preferably, at least 20 per cent greater, and a safe rule to follow in figuring flue areas is to allow 35 square feet per 1000 horse power. It is unnecessary to maintain the same size of flue the entire distance behind a row of boilers, and the areas at any point may be made proportional to the volume of gases that will pass that point. That is, the areas may be reduced as connections to various boilers are passed.

With circular steel flues of approximately the same size as the stacks, or reduced proportionally to the volume of gases they will handle, a convenient rule is to allow 0.1 inch draft loss per 100 feet of flue length and 0.05 inch for each right-angle turn. These figures are also good for square or rectangular steel flues with areas sufficiently large to provide against excessive frictional loss. For losses in brick or concrete flues, these figures should be doubled.

Underground flues are less desirable than overhead or rear flues for the reason that in most instances the gases will have to make more turns where underground flues are used and because the cross sectional area of such flues will oftentimes be decreased on account of an accumulation of dirt or water which it may be impossible to remove.

In tall buildings, such as office buildings, it is frequently necessary in order to carry spent gases above the roofs, to install a stack the height of which is out of all proportion to the requirements of the boilers. In such cases it is permissible to decrease the diameter of a stack, but care must be taken that this decrease is not sufficient to cause a frictional loss in the stack as great as the added draft intensity due to the increase in height, which local conditions make necessary.

In such cases also the fact that the stack diameter is permissibly decreased is no reason why flue sizes connecting to the stack should be decreased. These should still be figured in proportion to the area of the stack that would be furnished under ordinary conditions or with an allowance of 35 square feet per 1000 horse power, even though the cross sectional area appears out of proportion to the stack area.

Loss in Boiler--In calculating the available draft of a chimney 120 pounds per hour has been used as the weight of the gases per boiler horse power. This covers an overload of the boiler to an extent of 50 per cent and provides for the use of poor coal. The loss in draft through a boiler proper will depend upon its type and baffling and will increase with the per cent of rating at which it is run. No figures can be given which will cover all conditions, but for approximate use in figuring the available draft necessary it may be assumed that the loss through a boiler will be 0.25 inch where the boiler is run at rating, 0.40 inch where it is run at 150 per cent of its rated capacity, and 0.70 inch where it is run at 200 per cent of its rated capacity.

Loss in Furnace--The draft loss in the furnace or through the fuel bed varies between wide limits. The air necessary for combustion must pass through the interstices of the coal on the grate. Where these are large, as is the case with broken coal, but little pressure is required to force the air through the bed; but if they are small, as with bituminous slack or small sizes of anthracite, a much greater pressure is needed. If the draft is insufficient the coal will accumulate on the grates and a dead smoky fire will result with the accompanying poor combustion; if the draft is too great, the coal may be rapidly consumed on certain portions of the grate, leaving the fire thin in spots and a portion of the grates uncovered with the resulting losses due to an excessive amount of air.

[Graph: Force of Draft between Furnace and Ash Pit--Inches of Water against Pounds of Coal burned per Square Foot of Grate Surface per Hour

Fig. 34. Draft Required at Different Combustion Rates for Various Kinds of Coal]

Draft Required for Different Fuels--For every kind of fuel and rate of combustion there is a certain draft with which the best general results are obtained. A comparatively light draft is best with the free burning bituminous coals and the amount to use increases as the percentage of volatile matter diminishes and the fixed carbon increases, being highest for the small sizes of anthracites. Numerous other factors such as the thickness of fires, the percentage of ash and the air spaces in the grates bear directly on this question of the draft best suited to a given combustion rate. The effect of these factors can only be found by experiment. It is almost impossible to show by one set of curves the furnace draft required at various rates of combustion for all of the different conditions of fuel, etc., that may be met. The curves in Fig. 34, however, give the furnace draft necessary to burn various kinds of coal at the combustion rates indicated by the abscissae, for a general set of conditions. These curves have been plotted from the records of numerous tests and allow a safe margin for economically burning coals of the kinds noted.

Rate of Combustion--The amount of coal which can be burned per hour per square foot of grate surface is governed by the character of the coal and the draft available. When the boiler and grate are properly proportioned, the efficiency will be practically the same, within reasonable limits, for different rates of combustion. The area of the grate, and the ratio of this area to the boiler heating surface will depend upon the nature of the fuel to be burned, and the stack should be so designed as to give a draft sufficient to burn the maximum amount of fuel per square foot of grate surface corresponding to the maximum evaporative requirements of the boiler.

Solution of a Problem--The stack diameter can be determined from the curve, Fig. 33. The height can be determined by adding the draft losses in the furnace, through the boiler and flues, and computing from formula (30) the height necessary to give this draft.

Example: Proportion a stack for boilers rated at 2000 horse power, equipped with stokers, and burning bituminous coal that will evaporate 8 pounds of water from and at 212 degrees Fahrenheit per pound of fuel; the ratio of boiler heating surface to grate surface being 50:1; the flues being 100 feet long and containing two right-angle turns; the stack to be able to handle overloads of 50 per cent; and the rated horse power of the boilers based on 10 square feet of heating surface per horse power.

The atmospheric temperature may be assumed as 60 degrees Fahrenheit and the flue temperatures at the maximum overload as 550 degrees Fahrenheit. The grate surface equals 400 square feet.

2000 × 34½
The total coal burned at rating = ---------- = 8624 pounds.
8

The coal per square foot of grate surface per hour at rating =

8624 ---- = 22 pounds. 400

For 50 per cent overload the combustion rate will be approximately 60 per cent greater than this or 1.60 × 22 = 35 pounds per square foot of grate surface per hour. The furnace draft required for the combustion rate, from the curve, Fig. 34, is 0.6 inch. The loss in the boiler will be 0.4 inch, in the flue 0.1 inch, and in the turns 2 × 0.05 = 0.1 inch. The available draft required at the base of the stack is, therefore,

_Inches_ Boiler 0.4 Furnace 0.6 Flues 0.1 Turns 0.1 --- Total 1.2

Since the available draft is 80 per cent of the theoretical draft, this draft due to the height required is 1.2 ÷ .8 = 1.5 inch.

The chimney constant for temperatures of 60 degrees Fahrenheit and 550 degrees Fahrenheit is .0071 and from formula (30),

1.5
H = ----- = 211 feet.
.0071

Its diameter from curve in Fig. 33 is 96 inches if unlined, and 102 inches inside if lined with masonry. The cross sectional area of the flue should be approximately 70 square feet at the point where the total amount of gas is to be handled, tapering to the boiler farthest from the stack to a size which will depend upon the size of the boiler units used.

Correction in Stack Sizes for Altitudes--It has ordinarily been assumed that a stack height for altitude will be increased inversely as the ratio of the barometric pressure at the altitude to that at sea level, and that the stack diameter will increase inversely as the two-fifths power of this ratio. Such a relation has been based on the assumption of constant draft measured in inches of water at the base of the stack for a given rate of operation of the boilers, regardless of altitude.

If the assumption be made that boilers, flues and furnace remain the same, and further that the increased velocity of a given weight of air passing through the furnace at a higher altitude would have no effect on the combustion, the theory has been advanced[53] that a different law applies.

Under the above assumptions, whenever a stack is working at its maximum capacity at any altitude, the entire draft is utilized in overcoming the various resistances, each of which is proportional to the square of the velocity of the gases. Since boiler areas are fixed, all velocities may be related to a common velocity, say, that within the stack, and all resistances may, therefore, be expressed as proportional to the square of the chimney velocity. The total resistance to flow, in terms of velocity head, may be expressed in terms of weight of a column of external air, the numerical value of such head being independent of the barometric pressure. Likewise the draft of a stack, expressed in height of column of external air, will be numerically independent of the barometric pressure. It is evident, therefore, that if a given boiler plant, with its stack operated with a fixed fuel, be transplanted from sea level to an altitude, assuming the temperatures remain constant, the total draft head measured in height of column of external air will be numerically constant. The velocity of chimney gases will, therefore, remain the same at altitude as at sea level and the weight of gases flowing per second with a fixed velocity will be proportional to the atmospheric density or inversely proportional to the normal barometric pressure.

To develop a given horse power requires a constant weight of chimney gas and air for combustion. Hence, as the altitude is increased, the density is decreased and, for the assumptions given above, the velocity through the furnace, the boiler passes, breeching and flues must be correspondingly greater at altitude than at sea level. The mean velocity, therefore, for a given boiler horse power and constant weight of gases will be inversely proportional to the barometric pressure and the velocity head measured in column of external air will be inversely proportional to the square of the barometric pressure.

For stacks operating at altitude it is necessary not only to increase the height but also the diameter, as there is an added resistance within the stack due to the added friction from the additional height. This frictional loss can be compensated by a suitable increase in the diameter and when so compensated, it is evident that on the assumptions as given, the chimney height would have to be increased at a ratio inversely proportional to the square of the normal barometric pressure.