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MAYERS—FLOW PROCESSES IN U N D ERFEED STOKERS 481 p o s i t i o n n o . F i g . 5 C o n t o u r s o f C o n s t a n t T e m p e r a t u r e i n F u e l B e d o f a M u l t i p l e - R e t o r t U n d e r f e e d S t o k e r (1 4 ) P O SIT IO N NO. 2 P O S IT IO N NO. I F i g . 6 C o n t o u r s o f C o n s t a n t O x y g e n C o n c e n t r a t i o n i n F u e l B e d o f a M u l t i p l e - R e t o r t U n d e r f e e d S t o k e r (1 4 ) G a s a n d A i r F l o w As mentioned, the main part of the primary-air stream flows from the tuyeres up through the bed of broken coke at the bottom of the burning lane. During this passage it is consumed by the burning of the coke so that its oxygen content usually drops practically to zero at distances of 3 to 5 in. above the tuyeres. If the bed in the lane is much deeper than that, considerable percentages of carbon monoxide may appear in the gases leaving the lane. On the other hand, there may be places within the lane where the coke bed has not been replenished at the proper rate, so that unconsumed oxygen may, at these points, pass entirely through the bed and out into the furnace. In general, the oxygen concentration at any level may vary within rather wide limits, as shown in Fig. 7, depending upon the stream velocity of the filament of flow from which the sample is taken, and the proximity of coke surfaces, but the average analysis tends to follow the pattern just described. A relatively small portion of the primary-air stream passes under the bottom of the coke wall, which defines the burning lane, into the retort, and flows through it at low velocity because of the high resistance to flow caused by the dense packing of the small coal in this region. This air may return to the main stream passing up through the burning lane near the top, or it may pass out through the top surface of the coal in the retort into the furnace. In either case, it will carry with it the tar vapor and gases released by the coal being carbonized in the walls F i g . 7 G a s C o m p o s i t i o n i n F u e l B e d P l o t t e d A g a i n s t D i s t a n c e A b o v e T u y e r e s [The two lines show lim its within which 50 per cent of the analyses lie (14). of the lane. T hat this air has been within the combustion zone for only 1 in. or so is shown by the analysis of gas from the re-
482 TRANSACTIONS OF TH E A.S.M.E. AUGUST, 1941 torts at points inside the envelope of semicoke. It contains small concentrations of carbon dioxide, corresponding to that at levels of V* to 1 in. above the tuyeres, and increasing concentrations of hydrogen and methane as the coking zone is approached. At yet higher levels in the retort, the carbon dioxide and monoxide also increase, while the oxygen decreases, until the skin of coke at the top of the retort is penetrated, when, in many cases the oxygen concentration again increases while the combustible constituents tend to disappear. This indicates that there may be a layer of comparatively cold stagnant air lying on top of the retorts, which is only slowly aspirated into the main gas stream rising from the burning lanes. Additional evidence of the existence of this phenomenon will be apparent later. Some of the air, carrying products of combustion from the retort, may pass into the burning lane at levels below the top of the retort through shrinkage cracks in the coke and semicoke walls. Such shrinkage cracks are likely to be much deeper and more open in these walls than they are in coke formed in a byproduct-oven, because of the higher temperatures to which the walls are exposed, and the agitating action of the feeding mechanism. Thus, there may be quite free passage, at some levels, from the retorts out to the open space in the top of the burning lane. The entrance of this gas mixture into the burning lane is marked by the appearance of an increase in the concentration of the constituents hydrogen and methane in the gas, and a simultaneous increase in the concentration of oxygen. The combustible gases, both those brought by the air from the retort, and the carbon monoxide from the gasification that took place in the lower parts of the burning lane where a continuous fuel bed existed, combine rapidly with the available oxygen. The resulting gas flame, in the protection of the burning-lane walls, results in the highest temperatures observed in the bed, observations of 3000 F and even higher being not uncommon. In general, even with the air entering from the retort, there is insufficient oxygen completely to burn out the combustible gases issuing from the top of the burning lane. But, as the gases leave the lane, the oxygen concentration again increases, as shown in Fig. 7 for levels 9 to 11 in. above the tuyeres. This also supports the conclusion that there is a rather stagnant layer of relatively cool unconsumed air above the retorts which is slowly aspirated into the jets rising from the burning lanes. Visual evidence of the existence of this stagnant zone above the retorts appeared during tests of high-volatile coal in the work (14) referred to. During some of the preliminary runs with this coal, the boiler was brought off bank to a comparatively high load rather rapidly, so that about 50 per cent of the maximum rating (75 per cent of the test rating) was obtained before the furnace walls reached their normal temperature. At this time, clouds of smoke came out of the top of the retorts, but did not ignite as they did later on when the walls were hot. These clouds did not flow rapidly; they appeared to ooze out, and to roll slowly downward along the top of the retort. The ends gradually approached the stream rising from the burning lane, into which they were sucked and dispersed. Thus, the flow above the retorts must have been very slow; it had a negligible upward component, but was mainly along the top of the retort, lengthwise of the stoker. Evidently, the gas velocity distribution in the vertical direction shows marked discontinuities in the furnace just above the fuel bed; high values exist in the jets rising from the burning lanes, with relatively small upward velocities in the spaces between. A vector plot of gas velocities at the level of the top of the bed would look like a comb, with teeth pointing upward above each burning lane. The jets spread, as has been shown for other types of jet, with increasing distance from the level of the bed, and gradually entrain the gases from the space above the retorts. If cold secondary air is admitted to the furnace at low velocity, it will fall down on the retorts because of its high density and blanket them, only slowly being drawn into the main stream of combustion gases where it is needed. Thus, the need for very high pressures in the secondary-air jets is demonstrated, for only if sufficient velocity is supplied will the jets carry through the furnace and produce adequate mixing of the highvelocity streams from the burning lanes and the relatively stagnant gas above the retorts. In its passage through the fuel bed at the bottom of the burning lane, the air and combustion gas obey laws similar to those observed for flow of cold gas through beds of broken solids (15, 16). The pressure drop of the gas is proportional to the height of the bed traversed, i.e., the pressure gradient is practically constant over a considerable portion of the height of the bed. This is the normal behavior of a stream of fluid passing through a uniformly packed passage of constant cross section. Moreover, the pressure gradient is proportional to a power of the rate of gas flow slightly greater than 2. While the exponent observed in the Hell Gate tests 2.1 is somewhat greater than has been observed in closely controlled experiments at normal temperatures, this discrepancy may be accounted for by the relatively few data from which it was determined, by probable inaccuracies in the data inseparable from plant-scale testing, by a possible temperature effect on turbulent flow through such beds not now recognized because of the lack of data for such high-temperature zones, or, by an effect due to the expansion and contraction of the gas caused by the violent changes in temperature during its passage through the burning zone. Since the gas flow appears to obey the laws previously found by investigations on cool fluids not undergoing reaction, it is probably permissible to turn to these investigations for other information concerning flow phenomena in fuel beds. These experiments show that for small flow velocities, a bed of broken solids acts like a pipe, tube, or other resistance to flow. For very small flows, the streaming is viscous, and the resistance to flow increases as the first power of the mass velocity. Beyond a rather well-defined critical point, flow enters the turbulent regime, when the resistance increases with a power of the velocity (15) somewhat less than 2., This continues up to the point when the pressure gradient through the bed approaches in value the bulk density of the bed reduced to the same element of volume. That is, for a bed of coke, whose bulk density may be 36 lb per cu ft, the limiting pressure gradient will be —— 36 = 0.0209 psi per in. of 1728 36 bed depth, or expressed differently X 12 = 7 in. of water column per ft of bed depth. When this critical flow is reached, the bed is, on the average, supported by a force equal to its own weight, so that it becomes loose, almost fluid, and the interlocking of neighboring pieces, which gave it its character as a pure resistance, is reduced (16). If the air-flow rate is increased slightly beyond this point, the bed maintains its general form, but becomes capable of great extension in the direction of flow; any slight disturbance, however, or a slight further increase in flow is sufficient to disrupt it entirely so that the bed is completely blown away. The last phenomenon is, of course, known to every fuel engineer; it has not, however, been generally recognized that the point at which it occurs is so definitely fixed by the fundamental properties of the bed as an interlocking aggregate of particles. Carman (15) has shown that the resistance to flow through a bed of broken solids can be estimated if the void volume and the specific surface of the bed are known. These properties can be measured (17, 18) or estimated from the size analysis (19). Fig. 8 shows the resistance to air flow in the turbulent regime for
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ate of change will be n = T J L . I
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Bulb temperature B ath ✓---------
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The Bureau of Standards paper2 give
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Discussion M. F. Behar.4 This paper
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The differential equations for the
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Filling it with mercury reduces the
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