INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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94 4. Results and Discussion 0.15 0.12 Experiment DQMOM NDF [(µm) 1 ] 0.09 0.06 0.03 0 0 20 40 60 80 100 120 Droplet radius [µm] Fig. 4.45: Experimental and DQMOM approximation of droplet number density for PVP/water spray. same sub-models as employed in water spray are applied here, see Subsection 2.4. In Fig. 4.46, computed and experimental profiles of Sauter mean diameter (left) and mean droplet diameter (right) of PVP/water spray for a mass inflow rate of 112 kg/h at 0.12 m away from the nozzle exit are shown. Similar to the water spray, the spray distribution assumes a hollow-cone shape, and it is nicely predicted by DQMOM. In both the figures, a closer look reveals that across all the radial positions, the DQMOM Sauter mean diameter [µm] 140 120 100 80 60 40 DQMOM Experiment Mean droplet diameter [µm] 80 70 60 50 40 30 20 10 DQMOM Experiment 20 -75 -60 -45 -30 -15 0 15 30 45 60 75 Radial position [mm] 0 -75 -60 -45 -30 -15 0 15 30 45 60 75 Radial position [mm] Fig. 4.46: Experimental and numerical profiles of the Sauter mean diameter (left) and mean droplet diameter (right) of PVP/water spray in air at the cross section of 0.12 m distance from the nozzle exit.
4.4. Two-dimensional Evaporating PVP/Water Spray in Air 95 Sauter mean diameter [µm] 140 120 100 80 60 40 DQMOM Experiment Mean droplet diameter [µm] 100 80 60 40 20 DQMOM Experiment 20 -100 -80 -60 -40 -20 0 20 40 60 80 100 Radial position [mm] 0 -100 -80 -60 -40 -20 0 20 40 60 80 100 Radial position [mm] Fig. 4.47: Experimental and numerical profiles of the Sauter mean diameter (left) and mean droplet diameter (right) of PVP/water spray in air at the cross section of 0.16 m distance from the nozzle exit. un<strong>der</strong>predicts the experimental results and towards the periphery of the spray some deviation is observed particularly in profiles of Sauter mean diameter as compared to the experiment. This can possibly be explained by the fact that the DQMOM predicts the global droplet distribution, but there could be local discrepancies induced by the gas phase, which is not resolved in the present study. Coupling of DQMOM with the gas phase would eventually improve the simulation results. Figure 4.47 displays the Sauter mean diameter (left) and mean droplet diameter (right) at further downstream the nozzle exit, i.e., at the cross section 0.16 m. Comparing the maxima in Fig. 4.46 and 4.47 reveals that there is an increase in the Sauter mean diameter and mean droplet diameter, which is converse to the the water spray where decrease in droplet size is found. At a given temperature, the evaporation rate of water from pure water droplets is higher than from the droplets containing PVP dissolved in water due to the non-ideality effect (see Fig. 4.25). An analysis of droplet coalescence reveals that it occurs 1.5 times more often in PVP/water spray compared to water spray, which also contributes to an increased droplet size in the PVP/water spray. The elevated viscosity of PVP leading to higher viscous PVP/water droplets compared to pure water droplets influences the droplet coalescence. The present model is suitable to capture these effects, and a good agreement between the experiment and simulation is found [209]. The mean droplet velocity of PVP/water spray with 112 kg/h liquid inflow rate at 0.12 m away from the nozzle is shown in Fig. 4.48. Increased liquid flow rate leads to higher droplet velocity (compare Figs. 4.23 and 4.48), which increases the chances of
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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
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2.3. Euler - Euler Approach 23 Will
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2.3. Euler - Euler Approach 25 of t
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2.3. Euler - Euler Approach 27 With
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2.4. Single Droplet Modeling 29 col
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2.4. Single Droplet Modeling 31 the
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2.4. Single Droplet Modeling 33 pol
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2.4. Single Droplet Modeling 35 gra
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2.4. Single Droplet Modeling 37 thr
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2.4. Single Droplet Modeling 39 whe
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2.4. Single Droplet Modeling 41 (a)
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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
Page 97 and 98: 4.3. Single Bi-component Droplet Ev
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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
Page 144 and 145: BIBLIOGRAPHY xiii [142] R. Clift, J
Page 146 and 147: BIBLIOGRAPHY xv [170] G. Brenn, L.
Page 148 and 149: BIBLIOGRAPHY xvii [197] M. Stieß:
Page 150: BIBLIOGRAPHY xix [222] I. S. Grigor
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