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Show ~1~~1_:-J :1 t~;;i ~ I i w is W ~ 6 5 , 3 theoor~tltal E t ~ ~ 2 ~ , \ . t'~ 0 I c:-- 0 . --r---------r-------- , Fig. 14 - Axial variation in momentum and energy fluxes: supercritical flow, il~ ... SSBR S=0.7, Uo=4.7 mis, B/A=2 (a=200), Df =<j>440mm • a. ......... • T"_U'."",,, ~ .. , '~--------------~~--------T---I-_-_ I· Fig. 15 I. 'IIWIKD arAa1l1: J . _IT_ I J. IftIKI' cn. ..... 1CAL Supercritical/subcritical transition in an expanding swirling flow, S=0.7, Df /A=1.5, B/A=1.5 o - 0 experimental point ~ - ~ inviscid calculation, eqn (4) x - x inviscid calculation, eqn (2) short quarl (Figure 15) and a high after the quarl, the agreement is with a longer quarl (Figure 14), a fraction of the initial energy is confinement good, while significant lost during expansion. This trend has been observed, in the other cases measured, that for either a high swirl number or a larger expansion, the energy loss during expansion is significant. The loss of energy during expansion is probably the driving force which reduces the strength of the IRZ from that predicted from the inviscid model. DISCUSSION In general, the use of the inviscid model to predict important features of the flow field generated by an expanding swirling flow has proven quite successful. The basic features of the flow field can be readily estimated with the inviscid model developed during the IFRF near field aerodynamics work. In reference [3], which is the Phase 2 final report, a chapter has been included which provides a summary of the practical results which can be directly used in burner design applications without performing tedious calculations with the inviscid equations. The inviscid model has also provided insight into the physics of swirling flow. The ability of the inviscid equations to predict, for simple cases, the flow pattern to a high degree of accuracy implies that the model is basically correct. In Figure 15, a comparison between measurement and the inviscid model for a case of a relatively small expansion, b/a = 1.5, and a furnace diameter equal to the quarl exit is shown. In region 1, which is contained in and just downstream of the expansion, the flow can be considered inviscid and the velocity profiles calculated from equations (4) and (5). Before the IRZ is formed, the simplified form of equations (4) and (5) (see [4]) can be used and, after the IRZ is present, the full equation must be used with the additional inviscid boundary condition that the axial velocity along the IRZ boundary is zero. In Figure 15, a comparison of the calculated and measured velocity profiles is shown, where excellent agreement can be seen. Region 2 is the regime where viscous effects dominate and cannot be handled analytically by inviscid theory. Using the supercritical/ subcritical transition theory [3], the flow, starting at region 3, can again be approximated with inviscid theory using the measured IRZ length as an input into equation (2). Again, experiment and theory fit reasonably well except in the center of the recirculation zone where an inner, very weak secondary recirculation zone was experimentally observed. 96 Also shown in Figure 15 is the measured and theoretical total energy flux as a function of the axial location. As can be seen, the supercritical/ subcritical transition theory can predict quite well the amount of energy which is lost by the expanding swirling flow. T~e measured internal recirculation rate for this case was 18 percent relative to the mass input, while the transition theory would predict 16 percent recirculation. When the quarl is longer or external recirculation occurs then deviations from the inviscid model occur. The inviscid model still provides a basis for estimating the effect of parameter changes and, with empirical corrections derived from experiments, still provides a sound basis for engineering calculations. |