INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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74 4. Results and Discussion 120 DQMOM DDM Experiment 80 DQMOM DDM Experiment 100 Mean droplet diameter [µm] 80 60 40 Mean droplet diameter [µm] 60 40 20 20 0 -120 -80 -40 0 40 80 120 Radial position [mm] 0 -120 -80 -40 0 40 80 120 Radial position [mm] Fig. 4.22: Experimental and numerical profiles of the mean droplet diameter of water spray with 120 kg/h liquid flow rate at the cross section of 0.12 m (left) and 0.16 m (right) distance from the nozzle exit. side of Fig. 4.21). In Fig. 4.21, deviations from the experiment occur in the large droplet size region, which is due to the fact that the numerical technique captures the distribution function globally, and there could be some local discrepancies as well. This may be improved by solving the gas phase equations for DQMOM, which is not yet done in the present study, where the inlet gas flow properties are used to calculate the source terms for transport equations for DQMOM [209]. Figure 4.22 shows the computed and experimental profiles of the mean droplet diameter at cross sections of 0.12 m (left) and 0.16 m (right) away from the nozzle exit for liquid inflow rate of 120 kg/h. Similar to Sauter mean diameter, elevated liquid flow rate leads to somewhat decreased droplet size (compare Fig. 4.22 with 4.21) . At 0.12 m away from the nozzle exit, both DDM and DQMOM agree well with each other near the centerline, where they show relatively higher values than the experiment. At the radial positions away from the centerline, DQMOM is in good agreement with the experiment, and it is better than the DDM results. As the droplets move away from the nozzle exit, a decrease in size can be observed at the cross section of 0.16 m away from the the nozzle exit (see right part of the Fig. 4.22), which is similar to the case of liquid flow rate of 80 kg/h. Near the centerline at 0.16 m away from the nozzle exit, both DQMOM and DDM show the same behavior and predict slightly higher values than experiment. At higher radial positions, DDM values are higher compared to DQMOM and experiment, whereas DQMOM coincides with the experimental data. In Figs. 4.23 and 4.24, the radial profiles of mean droplet velocity are displayed at different cross sections. It can be seen that the droplet velocity is higher for larger
4.2. Two-dimensional Evaporating Water Spray in Air 75 Mean droplet velocity [m/s] 6 5 4 3 DQMOM DDM Experiment 2 -100 -50 0 50 100 Radial position [mm] Fig. 4.23: Experimental and numerical profiles of the mean droplet velocity at the cross section of 0.12 m distance from the nozzle exit. droplets as anticipated. Interestingly, the small size droplets near the axis of symmetry also move at a higher velocity as observed in the experiment and thus causing the velocity profile bimodal, which is predicted quite nicely by both models. A closer look reveals that the width of the jet is captured by the DQMOM, whereas the DDM predicts somewhat broa<strong>der</strong> profiles with a lower maximum value at the centerline. At the spray edge, a judgement of the numerical methods is difficult, since the Mean droplet velocity [m/s] 6 5 4 3 DQMOM DDM Experiment 2 -100 -50 0 50 100 Radial position [mm] Fig. 4.24: Experimental and numerical profiles of the mean droplet velocity at the cross section of 0.16 m distance from the nozzle exit.
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INAUGURAL-DISSERTATION zur Erlangun
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Dreams can never become a reality w
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II ial direction). Earlier studies
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IV DQMOM wird die Tropfengrößen-
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Contents Abstract . . . . . . . . .
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List of Tables 4.1 Initial weights
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List of Figures 1.1 A schematic dia
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List of Figures XIII 4.27 Effect of
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1. Introduction Drying has found ap
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3 Fig. 1.2: Chemical structure of p
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5 via inhalation aerosols. Dry powd
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7 equations are written in terms of
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9 for through appropriate sub-model
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2. Mathematical Modeling Spray cons
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2.1. State of the Art 13 the govern
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2.1. State of the Art 15 and if the
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2.2. Euler - Lagrangian Approach 17
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2.2. Euler - Lagrangian Approach 19
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2.3. Euler - Euler Approach 21 quan
Page 43 and 44: 2.3. Euler - Euler Approach 23 Will
Page 45 and 46: 2.3. Euler - Euler Approach 25 of t
Page 47 and 48: 2.3. Euler - Euler Approach 27 With
Page 49 and 50: 2.4. Single Droplet Modeling 29 col
Page 51 and 52: 2.4. Single Droplet Modeling 31 the
Page 53 and 54: 2.4. Single Droplet Modeling 33 pol
Page 55 and 56: 2.4. Single Droplet Modeling 35 gra
Page 57 and 58: 2.4. Single Droplet Modeling 37 thr
Page 59 and 60: 2.4. Single Droplet Modeling 39 whe
Page 61 and 62: 2.4. Single Droplet Modeling 41 (a)
Page 63 and 64: 2.4. Single Droplet Modeling 43 not
Page 65 and 66: 3. Numerical Methods In the numeric
Page 67 and 68: 3.2. Spray Modeling 47 and solid la
Page 69 and 70: 3.2. Spray Modeling 49 ⎛ ⎞ ⎛
Page 71 and 72: 3.2. Spray Modeling 51 application
Page 73 and 74: 3.3. Numerical Performance 53 where
Page 75 and 76: 4. Results and Discussion Results p
Page 77 and 78: 4.1. One-dimensional Evaporating Wa
Page 87 and 88: 4.2. Two-dimensional Evaporating Wa
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Page 97 and 98: 4.3. Single Bi-component Droplet Ev
Page 113 and 114: 4.4. Two-dimensional Evaporating PV
Page 119 and 120: 5. Conclusions and Future Work The
Page 121 and 122: 101 proved UNIFAC-vdW-FV method for
Page 123: Appendix
Page 126 and 127: 106 A. Nomenclature Symbol Unit Des
Page 128 and 129: 108 A. Nomenclature S n S g S l Vec
Page 130 and 131: 110 A. Nomenclature List of Abbrevi
Page 132 and 133: Bibliography [1] K. Masters: Spray
Page 134 and 135: BIBLIOGRAPHY iii [24] K. D. Squires
Page 136 and 137: BIBLIOGRAPHY v [49] D. L. Marchisio
Page 138 and 139: BIBLIOGRAPHY vii [72] G. M. Faeth:
Page 140 and 141: BIBLIOGRAPHY ix [95] C. Cercignani,
Page 142 and 143: BIBLIOGRAPHY xi [119] R. O. Fox: Hi
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BIBLIOGRAPHY xiii [142] R. Clift, J
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BIBLIOGRAPHY xv [170] G. Brenn, L.
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BIBLIOGRAPHY xvii [197] M. Stieß:
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BIBLIOGRAPHY xix [222] I. S. Grigor
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