INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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100 5. Conclusions and Future Work system is also modeled using DDM. In DQMOM, the source terms are computed same as done in the one-dimensional case, and the evolution of droplet size and velocity distributions are analyzed with both DDM and DQMOM. Droplet collisions are included in DQMOM by modeling the droplet coalescence. The DDM does not include droplet collisions due to computational complexity such as redistribution of droplet classes and increased computational effort. For initialization and validation of the simulation results, experimental data is used, which was provided by Prof. G. Brenn TU Graz, measured using PDA. The experimental data contains droplet size and velocity in axial and radial direction and this data is post-processed in order to eliminate errors in the large size droplets region. The experimental data at the cross section closest to the nozzle exit are used for the generation of initial conditions for the simulations, and the numerical results of DQMOM are compared with experimental data at the later cross sections, and with DDM. Overall, both the methods i.e., DQMOM and DDM show good agreement with the experiment. Some deviations between DQMOM and experiment are observed that might result from the present DQMOM formulation, which is not yet fully coupled with the gas phase equations. Concerning the experimental data, a post-processing of the raw data has been performed in order to correct the number density of large size droplets with respect to the effective cross section area, leading to different correction factors for different axial positions in experimental data away from the nozzle exit, which may also lead to discrepancy between numerical and experimental results. The DDM performs somewhat better in the periphery of the spray and DQMOM near the centerline. However, DQMOM shows an excellent numerical performance, and droplet coalescence is included with relative ease compared to DDM. Therefore, the DQMOM is further extended to simulate PVP/water sprays in air. Before simulating the PVP/water spray in air using DQMOM, a model to describe the bi-component droplet evaporation and solid layer formation is developed. The system under consideration is governed by the continuity (diffusion) and energy equations. Brenn’s model is modified to include the resistance from the solid layer, and this extended formulation is used to compute the evaporation rate of water from the bi-component droplet. The temperature inside the droplet appears to be uniform, and the change in droplet temperature due to heat exchange between the droplet surface and the surrounding gas is calculated with similar modifications used for mass evaporation rate to account for the resistance from the solid layer. The variable physical and thermal properties and the volume fraction based radius are introduced based on Brenn’s model. The predictability and efficiency of the developed single droplet model is first verified by simulating PVP/water and mannitol/water droplets. The liquid mixture is treated as non-ideal with the activity coefficient calculation using the im-
101 proved UNIFAC-vdW-FV method for PVP in water and ASOG contribution method for mannitol/water solution. The effect of various drying conditions on the evolution of single droplet characteristics is analyzed and the results are compared with experimental data. These drying conditions include the effect of gas temperature, gas velocity, initial solute (PVP or mannitol) mass fraction and relative humidity, which are found to have significant effect on the evaporation and drying characteristics of PVP/water as well as mannitol/water droplet. The study reveals that an increase in gas velocity and temperature cause earlier formation of the solid layer and faster drying, leading to larger particles with higher porosity. Humidity in air leads to smaller size particles with less porosity. The lower initial solute (PVP or mannitol) mass fraction implies that there is more water to evaporate resulting in smaller size particle with longer drying time. The variation of the activity coefficient of water with PVP mass fraction is much higher than that of mannitol, causing a stronger retardation of water evaporation rate from the PVP/water droplet compared to mannitol/water, which results in a faster solid layer formation for mannitol/water droplets. The present model successfully predicts the first three stages of droplet evaporation and drying, i.e., until solid layer formation at the droplet surface, which can readily be incorporated into an overall model of spray drying. The developed bi-component single droplet evaporation and drying model is then included in the DQMOM to simulate evaporating PVP/water spray flows in air in two-dimensional, axisymmetric configuration. Even though the developed spray model is equally applicable to simulate PVP/water and mannitol/water spray flows but only computations of PVP/water spray flows are performed as mannitol/water spray flow experimental data is not available. The physical processes of the spray such as drag and coalescence are included through the appropriate sub-models. Numerical results are compared with experimental data at different cross sections, and results are found to be in good agreement with experiment. Some deviations between DQMOM and experiment in case of mean droplet diameter are observed that might have originated from the present DQMOM formulation, which is not yet fully coupled with the gas phase equations. Moreover, the employed numerical technique uses an explicit finite difference method to solve the DQMOM transport equations – an implicit scheme may lead to considerable improvement. Additionally, the Schiller–Naumann correlation for drag coefficient may need revision. In conclusion, mono- and bi-component evaporating spray flows and preliminary stages of spray drying are successfully modeled and simulated using DQMOM. During spray drying, elevated gas temperature enhances droplet heating and evaporation thus advanced formulation of DQMOM is required in order to model spray
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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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2.4. Single Droplet Modeling 43 not
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3. Numerical Methods In the numeric
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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 113 and 114: 4.4. Two-dimensional Evaporating PV
Page 119: 5. Conclusions and Future Work The
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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