Wu and Faeth [28] showed experimentally that aerodynamic phenomena for turbulent primary breakup are largely controlled by the liquid/gas density ra-tio. When this ratio is less than 500, aerodynamic phenomena affect the onset
𝑢
", L
𝑈
&Gas Liquid
Lift
Figure 5.4: Liquid jet atomization
location of breakup, droplet sizes and velocities just after breakup. Figure 5.4 il-lustrates how lift enhances interfacial distruption and creating smaller droplets.
In Figure 5.4, L is the turbulent eddy size, u0the turbulent eddy velocity, and it is assumed that the liquid structure moves at the bulk jet velocity U0. Therefore, the followings scalings can be written:
- Kinetic energy of the liquid structure : EK∼ ρlu02 - Energy through aerodynamic lift: EL∼ ρgU02 - Energy associated with surface tension: EST∼ σ/L
ELand EK need to overcome EST in order to lead to breakup. If the den-sity ratio (ρl/ρg) is large, then it is justified to neglect aerodynamic lift. The important effects are then the turbulent kinetic energy and surface tension. For EK>ESt, the interface is expected to deform. If the density ratio is small, then ELwill contribute to destabilizing the interface, enabling the creation of smaller droplets.
In this work, simulations with high liquid/gas density ratio, (ρl/ρg>500, were limited to water injection into still air. Simulations were performed for the turbulent planar jet with jet exit liquid Weber numbers in the range We = 102− 107and for bulk Reynolds numbers of Rebulk= 11500, 23000, 46000 and 92000. The simulation conditions are summerized in Table 5.2. Results were compared with Wu and Faeth [42] and Sallam et al. [14, 39].
Parameter Value
Baseline Variations
µl 8.94 × 10−4 kg/ms [4.47 − 17.88] × 10−4 kg/ms µg 18.5 × 10−5kg/ms 9.25 × 10−5− 37 × 10−5 kg/ms
D 10.2 mm 10.2 mm
ubulk 2 m/s [1,2,4,8] m/s
ρl/ρg 860 16 − 860
Rebulk 23000 11500,23000,46000,92000
We 107 102− 107
Oh 0.0138 0.0034 − 0.0138
Table 5.1: Summary of simulation conditions for the liquid jet
The main results of this study are summerized in a breakup regime map, Figure 5.5. The plotted model results correspond to the baseline conditions shown in Table 5.1 except for We and Rebulk, which vary as indicated in the plot. The vertical axis shows the axial position x normalized by the jet diameter (x/D). Onset, and column length refer to the location of the onset of breakup, i.e. the axial position of the first multiphase eddy, and the length of the liquid core respectively. Wu et al. [36] and Sallam et al. [14] suggested correlations for the onset and the length of the liquid core in terms of the liquid Weber number We =ρlDu20/σ, where ρl is the liquid density, u0is the average liquid veloc-ity at the jet exit, andσ is the surface tension of the liquid. Three modes of liquid-column breakup were identified by Sallam et al. [14] for turbulent round liquid jets. As described in section 5.3, these modes are a weakly turbulent Rayleigh-like breakup mode observed at low jet exit Weber number, a turbulent breakup mode observed at moderate jet exit Weber number, and an aerodynamic bag/shear breakup mode observed at high jet exit Weber number. The breakup-length correlation shown by Sallam et al. [14] for each of these mechanisms is illustrated in Figure 5.5. ODT model simulation results are shown for both the median and the most probable location based on an ensemble of 1000 realiza-tions for each Weber and Reynolds number, indicated in Figure 5.5 by solid and dashed lines, respectively. Since there is no clear indication that the correlations suggested by Sallam et al. [14] are based on the mean, most probable, or other locations statistic, both statistics are presented.
The results and validations compared to experiments including liquid breakup
102 103 104 105 106 107 10−2
10−1 100 101 102 103
We
x/D
Onset−Sallam,Dai&Faeth(2002) Last−Sallam,Dai&Faeth(2002)
Column Length Rayleigh−Sallam,Dai&Faeth(2002) Column Length Turbulent−Sallam,Dai&Faeth(2002) Column Length Bag/Shear−Sallam,Dai&Faeth(2002) Surface Breakup Wu et al.(1995)
Reynolds 46000 Median Reynolds 23000 Median Reynolds 11500 Median Reynolds 46000 Most Probable Reynolds 23000 Most Probable Reynolds 11500 Most Probable
Figure 5.5: Breakup regime map.
lengths and turbulent breakup properties are presented in papers I and III.
The major conclusions of this study follows:
• After parameter adjustments, column-breakup results reported formerly by Sallam et al. [14] and Wu et al. [36] encompassing the weakly turbu-lent Rayleigh-like breakup, turbuturbu-lent breakup, and aerodynamic bag/shear breakup regimes. ODT model simulations reproduced the behaviors of experiments and correlations reported in the literature.
• Results for the onset of droplet breakup based on both ensemble averag-ing and most probable locations agree well with experiments in the range of Weber numbers [104- 106].
Droplet statistics To further elucidate the parameter dependences of droplet sizes and velocities, scatter plots of normalized droplet axial velocity against di-ameter from ODT model simulations and experiments are shown in Figure 5.6.
0 0.5 1 1.5 2 Droplets diameter/SMD [-]
0.2 0.4 0.6 0.8 1 1.2 1.4
Ud/Ufavre [-]
0 2 4 6 8 10 12 14 16 18 20 X/D Sallam et al. (1999)
Figure 5.6: Scatter plot of droplet axial velocity, normalized by the favre veloc-ity, versus diameter. The color indicates the distance from the jet inlet.
The velocities in this plot are normalized by the mass-weighted (Favre) aver-aged droplet velocities, UFavre, while the drop diameters are normalized by the SMD. Color is used to indicate the axial location at the instant of droplet for-mation in the ODT simulation.
Values of Ud are seen to increase in magnitude with increasing d initially and then remain nearly unity in both ODT model simulations and experiments.
The scatter plot Figure 5.6 shows that droplets close to the jet inlet have lower axial velocities than droplets farther downstream. This can be explained by the influence of the flow profile of the jet at the jet inlet plane: in the near field the velocities inside the liquid jet near the liquid-gas interface are still dominated by the boundary layer profile leading to low velocities in the droplet-generating region near the interface. Further downstream, radial turbulent transport within the jet tends to homogenize the lateral profile of the axial velocity, thereby in-creasing it near the liquid-gas interface.