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integration of cfd and low-order models for combustion ... - IWR

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|<br />

2.84 x 104<br />

mean momentum flux<br />

2.835<br />

2.83<br />

2.825<br />

2.82<br />

2.815<br />

2.81<br />

1D analysis<br />

CFD result<br />

mean velocity<br />

65<br />

60<br />

55<br />

50<br />

45<br />

40<br />

1D analysis<br />

CFD result<br />

2.805<br />

35<br />

2.8<br />

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2<br />

axial coordinate x(m)<br />

Figure 9. The mean momentum flux, where the solid lines indicate<br />

the result from a one-dimensional analysis <strong>and</strong> dash lines indicate<br />

that from the CFD calculation.<br />

8 x 106<br />

30<br />

25<br />

Figure 12.<br />

20<br />

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22<br />

axial coordinate x(m)<br />

Mean velocity, where the solid lines indicate the result<br />

from a one-dimensional analysis <strong>and</strong> dash lines indicate that from<br />

the CFD calculation.<br />

7<br />

6<br />

1D analysis<br />

CFD result<br />

mean energy flux<br />

5<br />

4<br />

1.8<br />

1.6<br />

3<br />

1.4<br />

2<br />

1.2<br />

1<br />

Figure 10.<br />

1<br />

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2<br />

axial coordinate x(m)<br />

The mean energy flux, where the solid lines indicate the<br />

result from a one-dimensional analysis <strong>and</strong> dash lines indicate that<br />

from the CFD calculation.<br />

| J 1<br />

′<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

0<br />

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22<br />

850<br />

800<br />

1D analysis<br />

CFD result<br />

0<br />

−20<br />

750<br />

−40<br />

700<br />

] deg.<br />

−60<br />

mean temperature<br />

650<br />

600<br />

angle [ J 1<br />

′<br />

−80<br />

−100<br />

550<br />

−120<br />

500<br />

−140<br />

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22<br />

450<br />

Figure 11.<br />

400<br />

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22<br />

axial coordinate x(m)<br />

Mean temperature, where the solid lines indicate the<br />

result from a one-dimensional analysis <strong>and</strong> dash lines indicate that<br />

from the CFD calculation.<br />

Figure 13. Magnitude <strong>and</strong> phase <strong>of</strong> the transfer function between<br />

shape factor J 1 <strong>and</strong> air f<strong>low</strong> rate through the atomizer at a<br />

frequency 50 Hz.

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