INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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72 4. Results and Discussion 160 140 DQMOM DDM Experiment Sauter mean diameter [µm] 120 100 80 60 40 20 0 -120 -80 -40 0 40 80 120 Radial position [mm] Fig. 4.20: Experimental and numerical profiles of the Sauter mean diameter at the cross section of 0.16 m distance from the nozzle exit for 120 kg/h. profiles of Sauter mean diameter at cross sections of 0.12 m and 0.16 m away from the nozzle exit are shown in Figs. 4.19 and 4.20. An increased liquid flow rate causes a somewhat decreased droplet size: For a given liquid, increased mass flow rate leads to higher pressure drop in the atomizer, which decreases liquid sheet size and breakup length to yield smaller particles as can be seen when compared with Fig. 4.18. At the cross section of 0.12 m, it can be seen that DQMOM performs better than the DDM results as DDM overpredicts the experimental values. The scattering behavior of DQMOM simulation results near the centerline is observed in this case, too. As the droplets move to the next cross section, a decrease in large size droplets is evident, which is predicted by both DQMOM and DDM. The results show that the DQMOM shows better agreement with experiment, while DDM predicts somewhat higher values than the experiment at corresponding radial positions [205]. The overall shape of a hollow cone spray is captured quite nicely by both methods, although some deviations are observed, particularly in DQMOM as compared to experimental profile. This is possibly due to the post-processing of the experimental data as explained in Subsection 4.2.2, which is done to correct the number frequency at every measuring position to rule out the fluctuations in the effective cross sectional area of the measuring volume for the larger droplet sizes [207]. This correction of experimental data is position dependent, whereas DQMOM and DDM results account for these corrections for the initial condition but not at positions further downstream. Another reason for the discrepancies in the DQMOM results may be due to the fact that the spray equations are not yet fully coupled to the gas phase.
4.2. Two-dimensional Evaporating Water Spray in Air 73 Comparing the maximum values of the Sauter mean diameter at the two cross sections displayed in Figs. 4.18, 4.19 and 4.20, a decrease in large size droplets is observed as the droplets move away from the nozzle. Even though the process of evaporation is consi<strong>der</strong>ed in the present models, the major reason for the decrease in droplet size may be attributed to the influence of drag force applied by the surrounding gas, because significant evaporation may not occur at the present room temperature condition. This decrease is more evident in the large droplet size region, where the dynamic interaction of droplet with surrounding gas dominates, as observed in profiles of mean droplet velocity (see Figs. 4.23 and 4.24). Besides the Sauter mean diameter, in many technical applications such as particle size analysis of pow<strong>der</strong> sampling in food and pharmaceutical industries, the mean droplet diameter is an important physical quantity [201]. Radial profiles of the mean droplet diameter compared with experiment are shown in Fig. 4.21 for 80 kg/h at 0.12 m (left) and 0.16 m (right) distance away from nozzle. DDM results are in very good agreement with the experiment. A slight decrease in the mean droplet diameter is observed as the droplets move away from nozzle indicating some mass transfer from liquid to gas, which is attributable to gas–liquid interactions. The DQMOM results are in excellent agreement with experiment at the cross section of 0.12 m near the centerline, and DQMOM results show better agreement than DDM results (see left part of Fig. 4.21). At 75 mm radial position, the DQMOM results are below experimental values, which may stem from the explicit finite difference technique. At the cross section of 0.16 m, a good agreement is observed between DQMOM and experiment near the axis of symmetry, even though some scattering behavior is found (see right 100 100 Mean droplet diameter [µm] 80 60 40 20 DQMOM DDM Experiment Mean droplet diameter [µm] 80 60 40 20 DQMOM DDM Experiment 0 -100 -50 0 50 100 Radial position [mm] 0 -100 -50 0 50 100 Radial Position [mm] Fig. 4.21: Experimental and numerical profiles of the mean droplet diameter of water spray with 80 kg/h liquid flow rate at the cross section of 0.12 m (left) and 0.16 m (right) distance from the nozzle exit.
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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
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
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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
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,
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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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