INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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86 4. Results and Discussion 1 0.8 R.H. = 1% Simulation [ T g = 60°C ] Experiment [ T g = 60°C ] Simulation [ T g = 95°C ] Experiment [ T g = 95°C ] 1 0.8 R.H. = 30% Simulation [ T g = 60°C ] Experiment [ T g = 60°C ] Simulation [ T g = 95°C ] Experiment [ T g = 95°C ] (d/330 µm) 2 [-] 0.6 0.4 (d/360 µm) 2 [-] 0.6 0.4 0.2 0.2 0 0 10 20 30 40 50 60 70 80 Time [s] 0 0 50 100 150 200 250 Time [s] Fig. 4.35: Effect of gas temperatures of 60 ◦ C and 95 ◦ C and relative humidity of 1% R.H. (left) and 30% R.H. (right) on the droplet surface area. 30% R.H. the same observed in about 205 s, see right part of Fig. 4.35. The profiles of the normalized droplet surface, (d/d 0 ) 2 , shown in the Fig. 4.35, reveal that the droplet evaporation rate prior to solid layer formation in the present case deviates from the linear decrease with time as would be expected from the classical d 2 law, where a constant evaporation constant is assumed. These experiments are carried out with different initial droplet radius for every experiment, and Tab. 4.4 gives the initial droplet radii (R 0 ) and particle size at the time of solid layer formation (t s ) in every experiment and its corresponding computed value from simulation. The comparison between rapid mixing model (RMM) and the present model is given in Fig. 4.36, which shows the time evolution of mannitol/water droplet surface area for initial droplet radius of 70 µm at 20 ◦ C temperature and subjected to hot air of 160 ◦ C with 0.5% R.H. and flowing at 0.65 m/s. Even though there is little difference between RMM and the present approach during the initial time period, however, in the later Tab. 4.4: Experiment vs simulation T g R.H. R 0 Particle radius at t s [µm] [ ◦ C] [%] [µm] Simulation Experiment 60 1.0 330 145.1 147.9 30.0 360 155.2 155.1 95 1.0 215 95.0 109.4 30.0 280 122.5 121.4
4.3. Single Bi-component Droplet Evaporation and Solid Layer Formation 87 1 0.9 0.8 T g = 160°C, U g = 0.65 m/s RMM Present model (d/d 0 ) 2 [] 0.7 0.6 0.5 0.4 0.3 0 0.2 0.4 0.6 0.8 1 1.2 Time [s] Fig. 4.36: Time evolution of mannitol/water droplet surface area computed by present model and RMM. time period RMM overpredicts the decrease in droplet surface and thereby the time of the solid layer formation caused by the fact that the assumption of homogeneous liquid mixture within the droplet. This assumption leads to more water to be evaporated, which increases the solute mass fraction to the critical value so that the formation of solid layer begins. The effect of initial droplet temperatures of 20 ◦ C and 70 ◦ C on the evaporation 1.6 T g = 160°C 120 Droplet mass [µg] 1.4 1.2 1 0.8 0.6 0.4 Mass [ T 0 = 20°C ] T [ T 0 = 20°C ] Mass [ T 0 = 70°C ] T [ T 0 = 70°C ] 100 80 60 40 Droplet temperature [°C] 0.2 0 0.2 0.4 0.6 0.8 1 20 1.2 Time [s] Fig. 4.37: Effect of initial droplet temperature on the evaporation rate of mannitol/water droplet.
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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
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
Page 97 and 98: 4.3. Single Bi-component Droplet Ev
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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
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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INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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