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Show for the mass entrainment by the fuel jet up to confluence, kg recirculating products entrained per kg fuel, and (m-ma)lma = 0.32(xc / D2)J(Mt I Ma)(Ta I Te) (18) for that by the air jet, kg recirculating products entrained per kg air. For the trials in Series 1-XBM2-F, w e obtain the predictions shown in Table 6. It is seen that the fuel jet entrains around 17 kg of products per kg of fuel up to confluence, and the air jet entrains around 6 kg per kg of air. There is clearly a high level of dilution of both fuel and air with products before they begin to mix with each other. 8.3.4. Effects of scaleup and changes in design and operating parameters The predictions of the strong-jet/weak-jet model give clear indications of effects of scaleup, changes in burner design parameters, and changes in burner operating parameters. The factor yr in (13) is fairly weak, so let us approximate it as (0.02)°A = 0.676. In addition, introduce (15) and (16), giving Lf= 22000 dl2T;] Qxp[0M25/32 nWf<pf(D2/D^(MJMf)(Tf/Ta)], (19) where as before, j3\2 is in degrees and Te is in kelvins. It appears that: 1. Scaleup is geometric in effect: a change in scale of all important burner dimensions (d\2, r\, r2, D\ and D2) by the same factor, without change of the essential geometry (thus, holding 0\, 02. and N constant), proportionately changes the flame dimensions. 2. Changing the limit angle fi\2 between adjacent fuel and air ports from 20° to 40° at ¥n=[Wf(pf{D2IDx)^Mal Mf){TfITa)f =0.02 increases the flame length by a factor of 8.3. Obviously, fi\2 very strongly affects the flame dimensions, and is a key design factor for obtaining flames of appropriate size. Since the flame length, according to the model, is proportional to the distance xc to confluence of the fuel and air jets, and, from (17) and (18), the amount of recirculating product gas entrained up to confluence is also proportional to xc, the 8.3-fold increase in flame length is accompanied by an increase in the said entrainment, and thus of the dilution of fuel and air with products, by the same factor 3. Changing y/\2 from 0.02 to 0.03 by a 22.5 % increase in D2ID\ at /3\2 = 20° increases the flame length L/ by 17.3 %, so Lj is roughly proportional to D2ID\. It is also evident that manipulation of D2ID\ is normally the only practical way of significantly changing the fuel/air momentum flux ratio y/\2. If the change is made by increasing D2 while holding D\ constant (and always, of course, holding the firing rate and excess air constant), then, according to (18), the entrainment of recirculating products by the air jet up to confluence, x = xc oc L/, is practically unchanged, because L/D2 is nearly the same. The entrainment by the fuel jet up to confluence, on the other hand, from (17), increases in proportion to L/.. If, however, the change in D2ID\ is made by decreasing D\ while holding D2 constant, then the entrainment by the air jet increases in proportion to Lf. but that by the fuel jet increases in proportion to Lj/D\ or, approximately, to L2 f , an interesting asymmetry of effects.. 18 |