Grate-surface. The amount of grate-surface required per horse power, and the proper ratio of heating-surface to grate-surface are extremely variable, depending chiefly upon the character of the coal and upon the rate of draught. With good coal, low in ash, approximately equal results may be obtained with large grate-surface and light draught and with small grate-surface and strong draught, the total amount of coal burned per hour being the same in both cases. With good bituminous coal, like Pittsburgh, low in ash, the best results apparently are obtained with strong draught and high rates of combustion, provided the grate-surfaces are cut down so that the total coal burned per hour is not too great for the capacity of the heating-surface to absorb the heat produced.

With coals high in ash, especially if the ash is easily fusible, tending to choke the grates, large grate-surface and a slow rate of combustion are required, unless means, such as shaking grates, are provided to get rid of the ash as fast as it is made.

The amount of grate-surface required per horse-power under various conditions may be estimated from the following table:

In designing a boiler for a given set of conditions, the grate-surface should be made as liberal as possible, say sufficient for a rate of combustion of 10 lbs. per square foot of grate for anthracite, and 15 lbs. per square foot for bituminous coal, and in practice a portion of the grate-surface may be bricked over if it is found that the draught, fuel, or other conditions render it advisable.

Proportions of Areas of Flues and other Gas-passages. -Rules are usually given making the area of gas-passages bear a certain ratio to the area of the grate-surface; thus a common rule for horizontal tubular boilers is to make the area over the bridge wall 1/7 of the gratesurface, the flue area 1/8, and the chimney area 1/9.

For average conditions with anthracite coal and moderate draught, say a rate of combustion of 12 lbs. coal per square foot of grate per hour, and a ratio of heating to grate surface of 30 to 1, this rule is as good as any, but it is evident that if the draught were increased so as to cause a rate of combustion of 24 lbs., requiring the grate-surface to be cut down to a ratio of 60 to 1, the areas of gas-passages should not be reduced in proportion. The amount of coal burned per hour being the same under the changed conditions, and there being no reason why the gases should travel at a higher velocity, the actual areas of the passages should remain as before, but the ratio of the area to the grate-surface would in that case be doubled.

Mr. Barrus states that the highest efficiency with anthracite coal is obtained when the tube area is 1/9 to 1/10 of the grate-surface, and with bituminous coal when it is 1/6 to 1/7, for the conditions of medium rates of combustion, such as 10 to 12 lbs. per square foot of grate per hour, and 12 square feet of heating-surface allowed to the horse-power.

The tube area should be made large enough not to choke the draught, and so lessen the capacity of the boiler; if made too large the gases are apt to select the passages of least resistance and escape from them at a high velocity and high temperature.

This condition is very commonly found in horizontal tubular boilers where

the gases go chiefly through the upper rows of tubes; sometimes also in vertical tubular boilers, where the gases are apt to pass most rapidly through the tubes nearest to the centre.

Air-passages through Grate-bars.-The usual practice is, airopening 30% to 50% of area of the grate; the larger the better, to avoid stoppage of the air-supply by clinker; but with coal free from clinker much smaller air-space may be used without detriment. See paper by F. A. Scheffler, Trans. A. S. M. E., vol. xv. p. 503.

PERFORMANCE OF BOILERS.

The performance of a steam-boiler comprises both its capacity for generating steam and its economy of fuel. Capacity depends upon size, both of grate-surface and of heating-surface, upon the kind of coal burned, upon the draft, and also upon the economy. Economy of fuel depends upon the completeness with which the coal is burned in the furnace, on the proper regulation of the air-supply to the amount of coal burned, and upon the thoroughness with which the boiler absorbs the heat generated in the furnace. The absorption of heat depends on the extent of beating-surface in relation to the amount of coal burned or of water evaporated, upon the arrangement of the gas-passages, and upon the cleanness of the surfaces. The capacity of a boiler may increase with increase of economy when this is due to more thorough combustion of the coal or to better regulation of the air-supply, or it may increase at the expense of economy when the increased capacity is due to overdriving, causing an increased loss of heat in the chimney gases. The relation of capacity to economy is therefore a complex one, depending on many variable conditions.

Many attempts have been made to construct a formula expressing the relation between capacity, rate of driving, or evaporation per square foot of heating-surface, to the economy, or evaporation per pound of combustible, but none of them can be considered satisfactory, since they make the economy depend only on the rate of driving (a few so-called "constants," however, being introduced in some of them for different classes of boilers, kinds of fuel, or kind of draft), and fail to take into consideration the numerous other conditions upon which economy depends. Such formulæ are Rankine's, Clark's, Emery's, Isherwood's, Carpenter's, and Hale's. A discussion of them all may be found in Mr. R. S. Hale's paper on "Efficiency of Boiler Heating Surface," in Trans. A. S. M. E., vol. xviii. p. 328. Mr. Hale's formula takes into account the effect of radiation, which reduces the economy considerably when the rate of driving is less than 3 lbs. per square foot of heating-surface per hour.

Selecting the highest results obtained at different rates of driving obtained with anthracite coal in the Centennial tests (see p. 685), and the highest results with anthracite reported by Mr. Barrus in his book on Boiler Tests, the author has plotted two curves showing the maximum results which may be expected with anthracite coal, the first under exceptional conditions such as obtained in the Centennial tests, and the second under the best conditions of ordinary practice. (Trans. A. S. M. E., xviii. 354). From these curves the following figures are obtained.

Lbs. water evaporated from and at 212° per sq. ft. heating-surface per hour: 1.6 1.7 2 2.6 3 3.5 4.5 5 6 7 8

4

Lbs. water evaporated from and at 212° per lb. combustible: Centennial. 11.8 11.9 12.0 12.1 12.05 12 11.85 11.7 11.5 10.85 9.8 8.5 Barrus..... 11.4 11.5 11.55 11.6 11.6 11.5 11.2 10.9 10.6 9.9 9.2 8.5 Avg. Cent'l 12.0 11.6 11.2 10.8 10.4 10.0 9.6 8.8 8.0 7.2

....

.....

The figures in the last line are taken from a straight line drawn as nearly as possible through the average of the plotting of all the Centennial tests. The poorest results are far below these figures. It is evident that no formula can be constructed that will express the relation of economy to rate of driving as well as do the three lines of figures given above.

For semi-bituminous and bituminous coals the relation of economy to the rate of driving no doubt follows the same general law that it does with anthracite, i.e., that beyond a rate of evaporation of 3 or 4 lbs. per sq. ft. of heating-surface per hour there is a decrease of economy, but the figures obtained in different tests will show a wider range between maximum and average results on account of the fact that it is more difficult with bituminous than with anthracite coal to secure complete combustion in the furnace.

The amount of the decrease in economy due to driving at rates exceeding 4 lbs. of water evaporated per square foot of heating-surface per hour differs greatly with different boilers, and with the same boiler it may differ with different settings and with different coal. The arrangement and size of the gas-passages seem to have an important effect upon the relation of economy to rate of driving. There is a large field for future research to determine the causes which influence this relation.

General Conditions which secure Economy of Steamboilers.-In general, the highest results are produced where the temperature of the escaping gases is the least. An examination of this question is made by Mr. G. H. Barrus in his book on "Boiler Tests," by selecting those tests made by him, six in number, in which the temperature exceeds the average, that is, 375° F., and comparing with five tests in which the temperature is less than 375° The boilers are all of the common horizontal type, and all use anthracite coal of either egg or broken size. The average flue temperatures in the two series was 444° and 343° respectively, and the difference was 101°. The average evaporations are 10.40 lbs. and 11.02 lbs. respectively, and the lowest result corresponds to the case of the highest flue temperature. In these tests it appears, therefore, that a reduction of 101° in the temperature of the waste gases secured an increase in the evaporation of 6%. This result corresponds quite closely to the effect of lowering the temperature of the gases by means of a flue-heater where a reduction of 107° was attended by an increase of 7% in the evaporation per pound of coal. A similar comparison was made on horizontal tubular boilers using Cumberland coal. The average flue temperature in four tests is 450° and the average evaporation is 11.34 lbs. Six boilers have temperatures below 415°, the average of which is 383°, and these give an average evaporation of 11.75 lbs. With 67° less temperature of the escaping gases the evaporation is higher by about 4%.

The wasteful effect of a high flue temperature is exhibited by other boilers than those of the horizontal tubular class. This source of waste was shown to be the main cause of the low economy produced in those vertical boilers which are deficient in heating-surface.

Relation between the Heating-surface and Grate-surface to obtain the Highest Efficiency. A comparison of three tests of horizontal tubular boilers with anthracite coal, the ratio of heating-surface to grate-surface being 36.4 to 1, with three other tests of similar boilers, in which the ratio was 48 to 1, showed practically no difference in the results. The evidence shows that a ratio of 36 to 1 provides a sufficient quantity of heating-surface to secure the full efficiency of anthracite coal where the rate of combustion is not more than 12 lbs. per sq. ft. of grate per hour.

In tests with bituminous coal an increase in the ratio from 36.8 to 42.8 secured a small improvement in the evaporation per pound of coal, and a high temperature of the escaping gases indicated that a still further increase would be beneficial. Among the high results produced on common horizontal tubular boilers using bituminous coal, the highest occurs where the ratio is 53.1 to 1. This boiler gave an evaporation of 12.47 lbs. A double-deck boiler furnishes another example of high performance, an evaporation of 12.42 lbs. having been obtained with bituminous coal, and in this case the ratio is 65 to 1. These examples indicate that a much larger amount of beating-surface is required for obtaining the full efficiency of bituminous coal than for boilers using anthracite coal. The temperature of the escaping gases in the same boiler is invariably higher when bituminous coal is used than when anthracite coal is used. The deposit of soot on the surfaces when bituminous coal is used interferes with the full efficiency of the surface, and an increased area is demanded as an offset to the loss which this deposit occasions. It would seem, then, that if a ratio of 36 to 1 is sufficient for anthracite coal, from 45 to 50 should be provided when bituminous coal is burned, especially in cases where the rate of combustion is above 10 or 12 lbs. per sq. ft. of grate per hour.

The number of tubes controls the ratio between the area of grate-surface and area of tube opening. A certain minimum amount of tube-opening is required for efficient work.

The best results obtained with anthracite coal in the common horizontal boiler are in cases where the ratio of area of grate-surface to area of tubeopening is larger than 9 to 1. The conclusion is drawn that the highest efficiency with anthracite coal is obtained when the tube-opening is from 1/9 to 1/10 of the grate-surface.

When bituminous coal is burned the requirements appear to be different. The effect of a large tube opening does not seem to make the extra tubes inefficient when bituminous coal is used. The highest result on any boiler of the horizontal tubular class, fired with bituminous coal, was obtained where the tube-opening was the largest. This gave an evaporation of 12.47 lbs., the ratio of grate-surface to tube-opening being 5.4 to 1. The next highest result was 12.42 lbs., the ratio being 5.2 to 1. Three high results, averaging 12.01 lbs., were obtained when the average ratio was 7.1 to 1. Without going to extremes, the ratio to be desired when bituminous coal is used is that which gives a tube-opening having an area of from 1/6 to 1/7 of the grate surface. This applies to medium rates of combustion of, say, 10 to 12 lbs. per sq. ft. of grate per hour, 12 sq. ft. of water-heating surface being allowed per horse-power.

A comparison of results obtained from different types of boilers leads to the general conclusion that the economy with which different types of boilers operate depends much more upon their proportions and the conditions under which they work, than upon their type; and, moreover, that when these proportions are suitably carried out, and when the conditions are favorable, the various types of boilers give substantially the same economic result.

Efficiency of a Steam-boiler.-The efficiency of a boiler is the percentage of the total heat generated by the combustion of the fuel which is utilized in heating the water and in raising steam. With anthracite coal the heating-value of the combustible portion is very nearly 14,500 B. T. U. per lb., equal to an evaporation from and at 2120 of 14,500 - 966 = 15 lbs. of water. A boiler which when tested with anthracite coal shows an evaporation of 12 lbs. of water per lb. of combustible, has an efficiency of 1215 80%, a figure which is approximated, but scarcely ever quite reached, in the best practice. With bituminous coal it is necessary to have a determination of its heating-power made by a coal calorimeter before the efficiency of the boiler using it can be determined, but a close estimate may be made from the chemical analysis of the coal. (See Coal.)

The difference between the efficiency obtained by test and 100% is the sum of the numerous wastes of heat, the chief of which is the necessary loss due to the temperature of the chimney-gases. If we have an analysis and a calorimetric determination of the heating-power of the coal (properly sampled), and an average analysis of the chimney-gases, the amounts of the several losses may be determined with approximate accuracy by the method described below.

Heating-value of the coal by Dulong's formula, 14,243 heat-units. The gases being collected over water, the moisture in them is not determined.

3. Ash and refuse as determined by boiler-test, 10.25, or 2% more than that found by analysis, the difference representing carbon in the ashes obtained in the boiler-test.

4. Temperature of external atmosphere, 60° F.

5. Relative humidity of air, 60%, corresponding (see air tables) to .007 lb. of vapor in each lb. of air.

6. Temperature of chimney-gases, 560° F.

Calculated results:

The carbon in the chimney-gases being 3.8% of their weight, the total weight of dry gases per lb. of carbon burned is 100+ 3.8 26.32 lbs. Since the carbon burned is 80.55 - 2 = 78.55% of the weight of the coal, the weight of the dry gases per lb. of coal is 26.32 × 78.55 100 = 20.67 lbs.

Each pound of coal furnishes to the dry chimney-gases.7855 lb. C, .0108N,

and (270 - 4.50)- 100.0214 lb. O; a total of .8177, say .82 lb. This sub

tracted from 20.67 lbs. leaves 19.85 lbs. as the quantity of dry air (not includ ing moisture) which enters the furnace per pound of coal, not counting the air required to burn the available hydrogen, that is, the hydrogen minus one eighth of the oxygen chemically combined in the coal. Each lb. of coal burned contained .045 lb. H, which requires .045 × 8.36 lb. O for its combustion. Of this, .027 lb. is furnished by the coal itself, leaving .333 lb. to come from the air. The quantity of air needed to supply this oxygen (air containing 23% by weight of oxygen) is .333 .23 = 1.45 lb., which added to the 19.85 lbs. already found gives 21.30 lbs. as the quantity of dry air supplied to the furnace per lb. of coal burned.

The air carried in as vapor is .0071 lb. for each lb. of dry air, or 21.3 X .0071 0.15 lb. for each lb. of coal. Each lb. of coal contained .029 lb. of moisture, which was evaporated and carried into the chimney-gases. The .045 lb. of H per lb. of coal when burned formed .045 X 9 = .405 lb. of H2O. From the analysis of the chimney-gas it appears that .09 3.80 = 2.37% of the carbon in the coal was burned to CO instead of to CO,. We now have the data for calculating the various losses of heat, as follows, for each pound of coal burned:

66

20.67 lbs. dry gas X (560° - 60°) × sp. heat 0.24
.15 lb. vapor in air × (560° - 60°) X sp. heat .48
.029 lb. moisture in coal heated from 60° to 212°
évaporated from and at 212°; .029 × 966
steam (heated from 212° to 560°) X 348 X.48 =
.405 lb. H2O from H in coal × (152+966 +348 × .48) =
.0237 lb. C burned to CO; loss by incomplete com-
bustion, .0237 × (14544 - 4451)

.02 lb. coal lost in ashes; .02 × 14544 Radiation and unaccounted for, by difference

Utilized in making steam, equivalent evaporation 10.37 lbs. from and at 212° per lb. of coal

= 10,014.9 70.32 14,243.0 100.00

The heat lost by radiation from the boiler and furnace is not easily determined directly, especially if the boiler is enclosed in brickwork, or is protected by non-conducting covering. It is customary to estimate the heat lost by radiation by difference, that is, to charge radiation with all the heat lost which is not otherwise accounted for.

One method of determining the loss by radiation is to block off a portion of the grate-surface and build a small fire on the remainder, and drive this fire with just enough draught to keep up the steam-pressure and supply the heat lost by radiation without allowing any steam to be discharged, weighing the coal consumed for this purpose during a test of several hours' duration.

Estimates of radiation by difference are apt to be greatly in error, as in this difference are accumulated all the errors of the analyses of the coal and of the gases. An average value of the heat lost by radiation from a boiler set in brickwork is about 4 per cent. When several boilers are in a battery and enclosed in a boiler-house the loss by radiation may be very much less, since much of the heat radiated from the boiler is returned to it in the air supplied to the furnace, which is taken from the boiler-room.

An important source of error in making a "heat balance" such as the one above given, especially when highly bituminous coal is used, may be due to the non-combustion of part of the hydrocarbon gases distilled from the coal immediately after firing, when the temperature of the furnace may be reduced below the point of ignition of the gases. Each pound of hydrogen which escapes burning is equivalent to a loss of heat in the furnace of 62,500 heat-units.

In analyzing the chimney gases by the usual method the percentages of the constituent gases are obtained by volume instead of by weight. To reduce percentages by volume to percentages by weight, multiply the percentage by volume of each gas by its specific gravity as compared with air, and divide each product by the sum of the products.