Chapter 28
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]