Part 28
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.
[Illustration: 24,420 Horse-power Installation of Babcock & Wilcox Boilers and Superheaters, Equipped with Babcock & Wilcox Chain Grate Stokers in the Quarry Street Station of the Commonwealth Edison Co., Chicago, Ill.]
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.
[Illustration: 6000 Horse-power Installation of Babcock & Wilcox Boilers at the United States Navy Yard, Washington, D. C.]
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.