| OCR Text |
Show suggested in the literature. None of the literature techniques shown in Figure 4 satisfactorily predicted the data of this study. However, the prediction technique recommended by Hottel and Hawthorne (26) predicted the proper trend, and correlated the lengths of large flames from this and other studies. Figure 5 shows the ability of the API 521 correlation (based on Hottel and Hawthorne (26)) to correlate the flame length of this study. Half filled symbols are data from other studies (except for £j which represent lengths of air-assisted flares from this study). The solid symbols represent the flare lengths of simple open pipe flares 3 through 12 inches in diameter from this study: open symbols are flame lengths from specially designed flare and nozzles smaller than three inches in diameter. The API 521 or modified correlation represents most of the data over a wide range of throughputs. However, scatter and deviation of the data from the correlation is typically 50-100 percent. Deviations in flame lengths are expected for altered mixing conditions as exist for most pressure, coanda-injection, and air-assisted heads. However, a better correlation is expected for simple large open pipe flares. Such a correlation was developed in this study based in the Richardson number corrected for expansion due to combustion of the flared gas. The empirical correlation developed is: / q x F \ °*60 L/d = 7.41 - I RI- 0.216 d) \Cp.Too (l+26x)/ where L = flame length, ft d = flare head diameter q = 2,350 Btu/ft^, propane gas lower heating value x = mole fraction of propane F = fraction of heat lost by radiation from the flame Cgoo = constant pressure heat capacity of the air, Btu/ft^R Too = ambient temperature, R 2 6 = factor to account for the change in moles as a result of stoichiometric combustion of propane Ri = Richardson Number based on conditions at flare head (gd/v^) The factor F was not measured in this study, but its relative value was obtained from a single set of data with different mole fractions of propane and a constant Richardson number of 2.0 as shown in Figure 6. This relation was then applied to all other flames. The absolute value of F does not matter for a correlation with a single fuel. However, F factors are available in the literature and will be required for correlations of flames burning different gases. Comparison of the flame lengths measured in this study for simple 3, 6, and 12 inch pipe flares shows that equation (1) correlates the measured flame lengths within 20 percent. Inspection of the literature shows that similar correlations, in slightly different form have successfully correlated the lengths of jet flames, pool fires, and crib fires. Physical reasoning, dimensionless 9 |
