OCR Text |
Show measurement is expected to give an estimate of the location of the boundary between the near and ~ fields, the surface represented by the horizontal line approximately one-third of the way up t e furnace in Figure 4. An example of the response of the hot wire probe at the furnace exit after stopping the helium flow t~ the burner is shown in Figure lOa. The signal exhibits the characteristic time dependence ? well-mixed and plug-flow reactors in series. The first derivative of the response to a step cha~ge m tracer concentration is the residence time distribution (probability density function for resIdence times), shown in idealized form in Figure lOb for values of the parameters derived fro~ t~e measurement in Figure lOa. The mean residence time of gas in the furnace is the residence tIme m the plug flow plus the time for decay of the exponential portion of the distribution to lie of its peak value, 5.25 s in the example shown in Figure 10. The mean residence time in a reactor is equal to the mass of gas in the vessel divided by the steady mass flowrate into and out from the enclosure. For the low velocity flows under consideration here, calculation of the mass of gas requires only integration of the gas density over an experimentally determined temperature distribution (changes in average molecular weight are small except in the fuel jets, which are a very small fraction of the furnace volume). However, measurement of the temperature distribution at a sufficient level of detail is time-consuming even under the favorable conditions of the research furnace; in a full scale boiler or process heater it would be a major and costly undertaking. A very rough estimate of the average furnace temperature is given by the exit gas temperature. This is possible because gas temperature changes slowly in the post-flame region and the gas near the end of the flame is a principal source of the gas in the external recirculation zone, which occupies a large portion of the lower furnace, as shown in Figure 4. The mean residence times for all of the conditions investigated are shown in Figure 11 as a function of the volumetric flowrate of furnace exit gas. The measured mean residence times are in good agreement with the ratio of furnace volume to volumetric flowrate when the mean furnace gas density is estimated using the furnace exit gas temperature, except at the two highest flowrates, 0.7 and 0.9 m3/s. The measured times at the highest flowrates are longer than the calculated times, which is opposite to the relationship which would result from an overestimate of the mean gas density using the furnace exit gas temperature. A better estimate of the mean furnace gas temperature can be obtained using the correlation of Hottel and Sarofim (1967). Prediction of the residence times in the well-mixed and plug-flow portions of the furnace flow is not so simple. The minimum (plug flow) residence times are shown as a function of the mass flowrate of fuel plus air in Figure 12. One approach to estimating the minimum residence time is to calculate the time required for gas to travel from the burner to the furnace exit along the highest velocity streamlines. Measurements of gas velocity at various heights in the furnace are shown in Figure 13 and the highest velocities at each height are shown as a function of height in Figure 14. Scaling of this relation in direct proportion to the total mass flowrate and integration over the velocity profile give the dependence of residence time on mass flowrate shown by the curve in Figure 12, which underestimates the minimum residence time over most of the range of flowrates investigated. In th absence of a known relationship of the plug-flow residence time to input or output conditions e three-dimensional numerical calculation of the flow, direct measurement of the residence t~~: 7 |