INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

More documents

Recommendations

Info

82 4. Results and Discussion Droplet mass [µg] 1.6 1.4 1.2 1 0.8 0.6 0.4 Mass [ U g = 0.65 m/s ] Mass [ U g = 10 m/s ] T [ U g = 0.65 m/s ] T [ U g = 10 m/s ] 120 100 80 60 40 Droplet temperature [°C] 0.2 0 0.5 1 1.5 2 20 2.5 Time [s] Fig. 4.30: Effect of gas velocity on the evolution of mass and temperature of a mannitol/water droplet. thereby the water evaporation, hence there is quicker development of the solid layer. The solid layer forms in about 1.7 s with U g = 0.65 m/s, whereas with U g = 10 m/s, the solid layer forms in about 0.75 s. A closer look reveals that there is higher droplet mass at any given time after solid layer formation when compared with lower gas velocity situation, which means that increased gas velocity would lead to larger particle and the porosity, defined as the ratio of the volume occupied by water at the instance of 1 0.9 0.8 U g = 0.65 m/s T g = 67°C T g = 100°C T g = 160°C (d/d 0 ) 2 [-] 0.7 0.6 0.5 0.4 0.3 0 0.5 1 1.5 2 2.5 3 3.5 Time [s] Fig. 4.31: Effect of elevated gas temperature on the surface area of a mannitol/water droplet.
4.3. Single Bi-component Droplet Evaporation and Solid Layer Formation 83 solid layer formation over that of the whole particle volume, would be higher in case of increased gas velocity (see Fig. 4.33). Figure 4.31 shows the effect of initial gas temperature on the temporal change of the dimensionless surface area of a mannitol/water droplet. Elevated gas temperature leads to higher energy transfer from the gas to the droplet, and thereby, an increase in the rate of droplet evaporation and drying. The surface area continuously decreases due to water evaporation until the beginning of solid layer formation whereupon particle size remains constant, which is reflected in Fig. 4.31. The higher the gas temperature the quicker the time taken for the solid layer formation: In case of 67 ◦ C the solid layer develops in about 2.9 s and with 100 ◦ C the solid layer forms in 1.7 s, whereas with 160 ◦ C, the same is observed in about 0.9 s. There is larger surface area at the time of solid layer formation with higher gas temperature, which means that elevated gas temperature would give larger particles towards the end of the drying process (see Fig. 4.33). The effect of gas temperature on the development of mannitol mass fraction profiles inside the droplet of initial radius 70 µm subjected to dry air with 0.5% R.H., flowing at 0.65 m/s with temperatures of 67, 100 and 160 ◦ C is shown in Fig. 4.32 at 0.5 s (left) and at 0.9 s (right), respectively. Initially, the droplet interior has a homogenous mannitol mass fraction distribution of 0.15 (not shown here) and with time, there is development of mannitol mass fraction gradients inside the droplet, and the droplet size reduces due to continuous water evaporation. For 100 ◦ C initial gas temperature, the droplet radius is 62 µm at 0.5 s whereas at 0.9 s it reduces to 56 µm, which is seen in Fig. 4.32, respectively. The increased initial gas temperature yields higher mass fraction gradients inside the droplet mainly due to the decreased activity coefficient of 0.35 Time = 0.5 s 0.8 Mannitol mass fraction [] 0.3 0.25 0.2 T g = 67°C T g = 100°C T g = 160°C Mannitol mass fraction [] 0.7 0.6 0.5 0.4 0.3 Time = 0.9 s T g = 67°C T g = 100°C T g = 160°C 0.15 0 10 20 30 40 50 60 70 Radial position inside the droplet [µm] 0.2 0 10 20 30 40 50 60 70 Radial position inside the droplet [µm] Fig. 4.32: Effect of gas temperature on the temporal development of mannitol mass fraction inside the droplet at 0.5 s (left) and 0.9 s (right).
Page 1:
INAUGURAL-DISSERTATION zur Erlangun
Page 5:
Dreams can never become a reality w
Page 8 and 9:
II ial direction). Earlier studies
Page 10 and 11:
IV DQMOM wird die Tropfengrößen-
Page 13 and 14:
Contents Abstract . . . . . . . . .
Page 15 and 16:
List of Tables 4.1 Initial weights
Page 17 and 18:
List of Figures 1.1 A schematic dia
Page 19 and 20:
List of Figures XIII 4.27 Effect of
Page 21 and 22:
1. Introduction Drying has found ap
Page 23 and 24:
3 Fig. 1.2: Chemical structure of p
Page 25 and 26:
5 via inhalation aerosols. Dry powd
Page 27 and 28:
7 equations are written in terms of
Page 29 and 30:
9 for through appropriate sub-model
Page 31 and 32:
2. Mathematical Modeling Spray cons
Page 33 and 34:
2.1. State of the Art 13 the govern
Page 35 and 36:
2.1. State of the Art 15 and if the
Page 37 and 38:
2.2. Euler - Lagrangian Approach 17
Page 39 and 40:
2.2. Euler - Lagrangian Approach 19
Page 41 and 42:
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
Page 97 and 98: 4.3. Single Bi-component Droplet Ev
Page 101: 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
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
show all

INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?