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Show 8.3. Application of the strong-jet/weak-jet predictions to the C G R I burner 8.3.1. Introduction Suppose, for the moment, that the multijet effects noted above are of minor importance, so flame length and the entrainments by the fuel and air jets up to confluence can be reasonably well predicted by the simple strong-jet/weak-jet model. W e shall now examine typical resulting calculations. In the X B M 2 burner, the centres-of-exit of the fuel and air ports are on the same circle, of radius r\ = r2 = 86 m m , Table 1. There are seven ports of each kind, N = 7, so the angular separation between adjacent fuel and air ports is S\2 = 360/2/V = 25.7°. The linear separation is d\2 = 2rj sin(<5i2/2) = 38.3 m m , where r} - r\ = r2. Adjacent fuel and air port axes are not coplanar, so we estimate ji\2 as the angle between these axes at infinite distance (x » d\2, at which limit d\2 is effectively zero): P\2 = acos(l + tan 6\ tan <% cos £i2)(cos 6\ cos Oz). (14) On assuming virtual equality of the dynamic and kinematic stream-average velocities Uj = Gj I rhj and 0'} - Am} I np} D] and applying the ideal gas law, the fuel/air momentum flux ratio can be expressed in the convenient form yl2=Gl/G2.= Wyf(MJMf)(Tf/Ta)(D2/Dl)2, (15) where Wj is the stoichiometric mass fuel/air ratio, 0.0608 for our natural gas, and <pf equivalence ratio, related to the excess air fraction by cp~f ] = 1 + e. 8.3.2. Prediction of flame length For an example, consider the Series 1-XBM2-F, Set C, single-burner, full-furnace trials, Table 6, where 0\ = 35°, b\ = 10°, if/n = 0.0197, Te= 1459 °C and Lf= 1650 m m . Equation (14) gives P\2 = 26.3°. The flame length, (13), is then estimated to be Lf = 1130 m m . While the experimental value is nearly 50 % greater, this can be considered, in view of the simplicity of the model, to be a very good absolute prediction. Table 6 also shows the predictions of Z/for Sets A and B of the Series 1-XBM2-F trials. There is evidently an effect of temperature that is missed by the theory. Assuming, as seems most likely, that this may be largely attributable to the state of the recirculating product gases, we look for an association with the exhaust gas temperature and find that I/«2500Z/,theory/7;,K-1. (16) 8.3.3. Entrainment by the jets up to the point of confluence Taking the exhaust-gas density pe as the measure of the density, /?w in the theory, of the recirculating products and applying the ideal gas law, (11) and (12) give (m-mf)/mf=032(xc/Dt)^MJMf)(Tf/Te) (17) 17 |