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66 4. Results and Discussion 4.2 Two-dimensional Evaporating Water Spray in Air A water spray injected into air through a hollow cone Delavan SDX-SE-90 nozzle in a vertical spray chamber, is modeled by DQMOM and DDM. The one-dimensional transport equations of DQMOM [191] are extended to two-dimensional to model the spray flow in axisymmetric configuration [202, 203]. The starting data for the simulations are taken from experimental data, where the experiments are conducted by the group of Prof. G. Brenn at TU Graz, Austria. The experimental setup is explained in the next section. The generation of initial data is discussed in the following section. The simulation results of DQMOM are compared with the results of DDM and both these model results are validated with the experiment [202, 203]. 4.2.1 Experimental Setup A series of experiments is carried out at TU Graz by the group of Prof. G. Brenn where a water spray in air is studied for different liquid mass inflow rates. The droplet sizes and velocities are recorded at various cross sections for different liquid inflow rates using phase Doppler anemometry (PDA) [204]. The present simulations concern the experimental data generated using a Delavan nozzle SDX-SE-90 having an internal diameter of 0.002 m, an outer diameter of 0.012 m at the nozzle throat and 0.016 m at the top, for liquid inflow rates of 80 kg/h and 120 kg/h. A water spray is injected into a cylindrical spray chamber of diameter 1 m. The carrier gas is air at room temperature and atmospheric pressure. Measurements are recorded at cross sections of 0.08 m, 0.12 m and 0.16 m. Figure 4.13 illustrates the schematic of the experimental Fig. 4.13: Schematic diagram of the experimental setup.
4.2. Two-dimensional Evaporating Water Spray in Air 67 setup. The data at 0.08 m are taken as starting point for initial data generation for computations, and results are compared at later cross sections [205]. 4.2.2 Initial Data Generation The experimental data at the closest position to the nozzle is used to generate initial data for the numerical computations of DQMOM. The nearest experimental position is 0.08 m from the nozzle, where the measurements are available at radial positions separated by 1.5 × 10 −3 m distance. The PDA data at every radial position consists of droplet radius, velocities in axial and radial directions, and the time elapsed for each measurement, which gives the total time carried out over a period. These data are grouped into 100 droplet size classes [206]. The effective cross sectional area of the probe volume is computed, which is done to eliminate errors in measuring volume due to nonlinearity in phase/diameter relationship in large size droplets because of the nonuniform beam intensity [207]. The result of the calculation for a water flow rate of 80 kg/h, at a position of 0.066 m from the center is shown in Fig. 4.14. The trajectory length exhibits strong fluctuations, and fluctuations increase with the droplet size. Furthermore, the number of droplets in the size classes for the larger diameters is typically much lower than in the smaller size classes. Therefore, the properties such as droplet trajectory lengths through the probe volume are statistically unreliable for drops with sizes greater than a certain threshold value [206, 207]. In particular, the decrease of the effective probe volume size with increasing droplet size such as from 0.45 Effective crosssection area [mm 2 ] 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 x x x x x xx x x xxx x x x x x x x Experiment Corrected Trend line x x x x x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x x x x x x x x x x x x x 0 0 100 200 300 400 Drop size class [µm] Fig. 4.14: Profile of effective cross-section area of the probe volume for measured droplet size.
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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
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
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Page 89 and 90: 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 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
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BIBLIOGRAPHY v [49] D. L. Marchisio
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BIBLIOGRAPHY vii [72] G. M. Faeth:
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BIBLIOGRAPHY ix [95] C. Cercignani,
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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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