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Show structures augmenting gradient diffusion transport processes. Figure 7 shows radial and axial profiles for the axial velocity variance. The numerical simulations tend to underpredict peak axial velocity fluctuations throughout the jet, though the general trends are consistent with measurements. Without more detailed information concerning the turbulent flow at the nozzle exit, it is typical to prescribe an inlet turbulence intensity (5-6% for fully developed turbulent flow) and hydraulic diameter. The intensity (5%) used here severely underspecified the velocity fluctuations measured at the fuel nozzle exit, but this difference should not significantly effect simulation results for velocity variance beyond the neighborhood of the nozzle exit (less than 5-10 diameters). Mean mixture fraction profiles are examined in Figure 8. The same general trends that are seen for mean axial velocities are observed for f mean as well, with strong overall agreement seen, especially for the R K E and R S M models. Mixture fraction profiles demonstrate excessive jet spreading from 5 to 40 diameters downstream. Simulation results improve at 60 and 80 diameters, with the RKE model slightly underpredicting axial mixture fraction decay. Not surprisingly, the region from 0 to 40 diameters coincides with the observed "momentum dominated" regime in buoyant, turbulent jet flames. The increasing influence of buoyancy in the transition region beyond 40 diameters augments turbulent transport, and subsequently, leads to better predictions. Predictions of mixture fraction fluctuations are shown in Figure 9. All models perform similarly. Fluctuations are generally underpredicted, particularly in the upstream portion of the flame (less than 40 diameters). Improved predictions are seen for locations further downstream. Figure 10 provides comparisons of mean temperature profiles. The overprediction of mixture fraction decay on the centerline leads to a flame that is slightly shorter and broader than seen experimentally. Though the peak temperature is significantly underpredicted at x/d agreement is good. = 5, the overall Agreement of the numerical simulations and experimental data with observed similarity scaling law for jet spreading rate can also be examined. Analysis has shown [2,5,6] that for momentum dominated jets and flames W ~ constant / x where b is the half-width radius of the jet, and x is the distance from the nozzle exit. This linear spreading rate is observed, as well, beyond the transition to buoyancy dominated flow (up to E, = 5.5) [6]. Figure 11 is a plot of spreading rate versus x/d for the experimental data and numerical simulations. A linear rate of jet growth is clearly seen. Rate constants of 0.07 [6] and 0.08 [5] have been reported. These agree well with the data and predicted results. At 5 diameters, the flow has not yet reached a fully turbulent nature indicative of the jet far field. A similar analysis can be performed by examining the centerline Momentum Flux Density (MFD), given by [6] MFD = (n , \^ fraf*7*.J where M0 is the initial momentum rate issuing from the fuel nozzle. In the limit of momentum dominated flow, the M F D is conserved with downstream location. f n _ _ \K - pcu2 cx2JMQ I If the effects of buoyancy are considered within the flame zone, it can be shown that the M F D varies linearly with downstream distance 4 -4 A plot of M F D versus \ for the experimental data and numerical results is shown in Figure 12. Becker & Yamazaki [6] found the M F D to be approximately 3.3 in the |