The Study of the Existence of Transition Velocity and the Hydrodynamics of Turbulent Fluidized Beds

摘要 關於氣-固流體化床由氣泡床到快速床間之流態轉變，以及紊流床是否存在之問題，至今尚無定論。根據Rhodes (1996)對文獻上各研究者所得之結果分析比較，發現目前有關流態之轉變及移轉速度之探討，仍莫衷一是。因此吾人提出利用結合反射型光纖探針、熱傳探針、壓力探針來探討氣固流體化床在流態改變時床中空隙度、床-壁間傳熱係數、壓力擾動振幅三者的變化及其相關性，以了解床中之變化及其對流態之影響，並試圖證明移轉速度之存在。 本實驗裝置為內徑0.108m、高5.7m，頂端接有高1.5m擴大管的流體化床及其他形式之床體，使用數種不同粒徑Group A及Group B粒子為研究對象，分別以反射型光纖探針量測床中粒子局部空隙度及其軸向變化；以熱傳探針量測床-壁間傳熱係數及其軸向變化；以壓力探針量測床中擾動振幅大小及其軸向變化，藉由不同型式探針量測之結果，及不同統計方式之分析比較，以作為判斷移轉速度存在之指標，並了解紊流流體化床之動力行為。Abstract The transition from bubbling bed to fast fluidization bed will be investigated by using (1) optical fiber to measure the local bed voidage distribution, (2) pressure probe to measure the pressure fluctuations and (3) heat transfer probe to measure the bed-to-wall heat transfer coefficient. This transition region from bubbling bed to fast fluidized bed is now widely referred to the turbulent fluidized bed, the structure of this bed and the mechanism for the transition are still unclear. Experimental study will be carried out in a 0.108 m i.d., 5.76m high with expanded-top fluidized bed, and other type of bed. Several different sizes of Group A and B particles will be used as the fluidized particles. The local bed voidage will be measured by reflection type optical fiber probe. With the addition of mean amplitude of pressure fluctuations and bed-to-wall heat transfer coefficient measurements, hopefully the transition mechanism and the bed structure could be understood in more detailed way, and the existence of “turbulent fluidized bed” could be explained in a logical sense. Above all, by wavelet analysis, the existence of transition velocity could be identified and the hydrodynamics of turbulent fluidized bed could be characterized.目 錄 中文摘要-------------------------------- I 英文摘要--------------------------------II 圖目錄---------------------------------VII 表目錄--------------------------------XVII 第一章 緒論 1.1 研究背景與動機---------------------------1 1.2 研究方法與目的-------------------------- 2 1.3 論文架構-------------------------------- 3 第二章 文獻回顧 2.1 紊流流化床的定義------------------- 4 2.2 從氣泡床到紊流床的流態改變--------- 5 2.3 移轉區的探討----------------------- 6 2.4 移轉速度的探討----------------------- 7 2.4.1 移轉速度存在性的爭議---------------- 7 2.4.2 影響移轉速度的變因------------------ 9 第三章紊流流化床的空隙度 3.1 文獻回顧----------------------------- 11 3.1.1 空隙度擾動的量測------------------- 11 3.1.2 光纖探針量測粒子濃度之校正方法----- 13 3.2 實驗裝置與步驟---------------------- 17 3.2.1 實驗裝置與設備--------------------- 18 3.2.2 細部說明--------------------------- 19 3.2.3 實驗步驟------------------------- 21 3.2.4 固體粒子性質--------------------- 23 3.2.5 改變操作變數--------------------- 24 3.2.6 光纖探針之校正------------------- 24 3.3 統計分析----------------------------- 26 3.3.1 平均值與標準偏差------------------ 26 3.3.2 數位信號之處理------------------- 29 3.3.3 壓力擾動信號的處理--------------- 31 3.4 結果與討論--------------------------- 32 3.4.1 移轉速度之探討------------------- 32 3.4.2 床空隙度之徑向分佈--------------- 34 3.5 結論---------------------------------- 57 第四章 紊流流化床之壓力擾動對流力行為之影響 4.1 文獻回顧----------------------------- 59 4.1.1 壓力擾動的形成------------------- 59 4.1.2 壓力擾動的分析方式--------------- 60 4.1.3 壓力擾動與參數之改變------------ 61 4.1.4 壓力擾動與流態變化--------------- 61 4.2 實驗---------------------------------- 62 4.2.1 裝置與儀器----------------------- 62 4.2.2 細部說明------------------------- 62 4.2.3 實驗方法與步驟------------------- 65 4.2.4 壓力擾動訊號的量測與處理--------- 65 4.3 平均擾動振幅的計算方式------------- 66 4.4 結果與討論--------------------------- 66 4.4.1由氣泡流體化到紊流流體化的流態轉變65 4.4.2 壓力擾動振幅與流態轉變---------- 67 4.4.2.1 絶對壓力擾動結果-------------- 67 4.4.2.2 相對壓力擾動結果--------------- 94 4.5 結論--------------------------------- 103 第五章 紊流流體化床的床－壁間熱傳現象 5.1 文獻回顧---------------------------- 104 5.2 實驗-------------------------------- 105 5.2.1 裝置與儀器---------------------- 105 5.2.2 細部說明------------------------ 107 5.2.3 實驗步驟------------------------ 108 5.2.4 熱傳探針溫度分佈的量測---------- 109 5.3 床－壁間熱傳係數------------------- 109 5.4 結果與討論-------------------------- 111 5.4.1 床-壁(bed-to-wall)間熱傳係數和氣體表面速度之關係--------------------- 111 5.4.2 床-壁(bed-to-wall)間熱傳係數和靜床高之關係------------------------ 119 5.4.3 床-壁(bed-to-wall)間熱傳係數和探針位置之關係---------------------- 131 5.4.4 床-壁(bed-to-wall)間熱傳係數和粒徑之關係--------------------------- 131 5.5 結論-------------------------------- 136 第六章 小波分析與流態變化 6.1 實驗方法與實驗步驟----------------- 137 6.2 文獻回顧---------------------------- 138 6.2.1 小波變換的定義及特點------------ 138 6.2.2 小波分析與傅立葉變換的比較------ 140 6.2.3 小波分析和信號的處理------------ 142 6.2.3.1 信號的分類-------------------- 142 6.2.3.2 小波分析對信號的處理---------- 143 6.3 統計分析方式----------------------- 1441016-1626-2340-9597-7761-7163 6.3.1 時域分析------------------------ 145 6.3.2 頻域分析------------------------ 145 6.3.3 小波分析函數-------------------- 145 6.4 結果與討論------------------------- 147 6.4.1 標準偏差分析-------------------- 147 6.4.2 冪次頻譜密度函數(PSDF)---------- 149 6.4.3 PSDF的能量強度------------------ 154 6.4.4 小波分析------------------------ 159 6.4.5 數位信號能量-------------------- 168 6.5 結論-------------------------------- 181 第七章 總結------------------------------- 183 符號說明----------------------------------- 187 參考文獻----------------------------------- 190 圖 目 錄 Fig. 3-1. Experimental setup of expanded-top fluidized bed. 18 Fig. 3-2. Calibration curve for FCC particles. 28 Fig. 3-3. Transition velocities by absolute and differential pressure fluctuations. 33 Fig. 3-4. Instantaneous local voidage fluctuation signals for FCC particles measured at 35 cm above the distributor with Ug = 0.51 m/s. (Hs = 50 cm) 35 Fig. 3-5. Instantaneous local voidage fluctuation signals for FCC particles measured at 35 cm above the distributor with Ug = 1.09 m/s. (Hs = 50 cm) 36 Fig. 3-6. Instantaneous local voidage fluctuation signals for FCC particles measured at 35 cm above the distributor with Ug = 1.72 m/s. (Hs = 50 cm) 37 Fig. 3-7. Instantaneous local voidage fluctuation signals forFCC particles measured at 35 cm above the distributor with Ug = 2.17 m/s. (Hs = 50 cm) 38 Fig. 3-8. Probability density distributions of the time series corresponding to cumulative distribution functions with Ug = 0.51 m/s. (Hs = 50 cm) 40 Fig. 3-9. Probability density distributions of the time series corresponding to cumulative distribution functions with Ug = 1.09 m/s. (Hs = 50 cm) 41 Fig. 3-10. Probability density distributions of the time series corresponding to cumulative distribution functions with Ug = 1.72 m/s. (Hs = 50 cm). 42 Fig. 3-11. Probability density distributions of the time series corresponding to cumulative distribution functions with Ug = 2.17 m/s. (Hs = 50 cm) 43 Fig. 3-12. Radial voidage profiles at sex superficial gas velocities for Hs = 50 cm. 48 Fig. 3-13 (a). (a) Radial profiles of standard deviation of local voidage at different superficial gas velocities for Hs = 50 cm. (Ug =0.36 m/s(◇), Ug = 0.51 m/s (○), Ug = 0.76 m/s (△), Ug = 0.91 (☆) ) 49 Fig. 3-13 (b). Radial profiles of standard deviation of local voidage at different superficial gas velocities for Hs = 50 cm. (Ug =1.09 m/s(◇), Ug = 1.34 m/s (○), Ug = 1.52 m/s (△), Ug = 1.72 m/s (☆)) 50 Fig. 3-13 (c). Radial profiles of standard deviation of local voidage at different superficial gas velocities for Hs = 50 cm. (Ug = 1.88 m/s(◇), Ug = 2.03 m/s (○), Ug = 2.17 m/s (△), Ug = 2.36 m/s (☆) ) 51 Fig. 3-14. Normalized radial solids fraction profiles at the static bed height, 36 cm, in different regimes. (Ug = 0.31 m/s(◇), Ug = 0.91 m/s (○), Ug = 1.88 m/s (△) ) 52 Fig. 3-15. Normalized radial solids fraction profiles at the static bed height, 50 cm, in different regimes. (Ug = 0.31 m/s(◇), Ug = 0.91 m/s (○), Ug = 1.88 m/s (△)) 53 Fig. 3-16. Normalized radial solids fraction profiles at the static bed height, 60 cm, in different regimes. (Ug = 0.31 m/s(◇), Ug = 0.91 m/s (○), Ug = 1.88 m/s (△) ) 54 Fig. 3-17. Normalized radial solids fraction profiles at the static bed height, 70 cm, in different regimes. (Ug = 0.31 m/s(◇), Ug = 0.91 m/s (○), Ug = 1.88 m/s (△)) 55 Fig. 3-18. Normalized radial solids fraction profiles in different regimes compared with the result of Zhang et al. (1997), Zhang et al. (Ug = 0.13 m/s(◆), Ug = 0.15 m/s(●),Ug = 0.52 m/s(▲)) 56 Fig. 4-1. Experimental apparatus of expanded-top fluidized bed. 64 Fig. 4-2. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, +14 cm, 30 cm, 45 cm. (FCC, Hs = 35 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 69 Fig. 4-3. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, +14 cm, 30 cm, 45 cm. (FCC, H s = 50 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 70 Fig. 4-4. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (FCC, Hs = 60 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 71 Fig. 4-5. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4cm, 14 cm, 30 cm, 45 cm. (FCC, Hs = 70 cm) 72 Fig. 4-6. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm. (Sand 163 , Hs = 35 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 77 Fig. 4-7. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm. (Sand 163 , Hs = 50 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△)) 78 Fig. 4-8. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (Sand 163 , Hs = 60 cm) 79 Fig. 4-9. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (Sand 163 , Hs = 70 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 80 Fig. 4-10. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm. (Sand 230 , Hs = 35 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△)) 81 Fig. 4-11. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm. (Sand 230 , Hs = 50 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△)) 82 Fig. 4-12. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm. (Sand 230 , Hs = 70 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△)) 83 Fig. 4-13. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm. (Sand 273 , Hs = 35 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△)) 84 Fig. 4-14. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (Sand 323 , Hs = 35 cm) 85 Fig. 4-15. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (Sand 323 , Hs = 50 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 86 Fig. 4-16. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (Sand 323 , Hs = 60 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 87 Fig. 4-17. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (Sand 323 , Hs = 70 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 88 Fig. 4-18. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4cm, 14 cm, 30 cm, 45cm. (Sand 460 , Hs = 35 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 89 Fig. 4-19. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (Sand 460 , Hs = 50 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 90 Fig. 4-20. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4 cm, 14 cm, 30 cm, 45 cm. (Sand 460 , Hs = 60 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 91 Fig. 4-21. Mean amplitude of absolute pressure fluctuations vs. superficial gas velocity: probe position = -4cm, 14 cm, 30 cm, 45 cm. (Sand 460 , Hs = 70 cm, Probe position：-4 cm (◇), 14 cm (○), 30 cm (△), 45 cm (☆)) 92 Fig. 4-22. Mean amplitude of differential pressure fluctuations vs. superficial gas velocity: probe position = 5 ~ 10 cm, 10 ~14 cm. (Sand 163 , Hs = 60 cm, Probe position：5 ~10 cm (◇), 10 ~ 14 cm (○)) 96 Fig. 4-23. Mean amplitude of differential pressure fluctuations vs. superficial gas velocity: probe position = 5 ~ 10 cm, 10 ~14 cm. (Sand 163 , Hs = 70 cm, Probe position：5 ~10 cm (◇), 10 ~ 14 cm (○)) 97 Fig. 4-24. Mean amplitude of differential pressure fluctuations vs. superficial gas velocity: probe position = 5 ~ 10 cm, 10 ~14 cm, 14 ~ 27 cm, 20 ~30 cm. (Sand 460 , Hs = 60 cm, Probe position：5 ~10 cm (◇), 10 ~ 20 cm (○), 14~ 27 cm (△), 20 ~ 30 cm (☆)) 98 Fig. 4-25. Mean amplitude of differential pressure fluctuations vs. superficial gas velocity: probe position = 5 ~ 10 cm, 10 ~14 cm. (Sand 460 , Hs = 70 cm,) 99 Fig. 4-26. Mean amplitude of differential pressure fluctuations vs. superficial gas velocity: probe position = 14 ~ 30 cm, 14 ~ 40 cm, 14 ~ 45cm. (Sand 163 , Hs = 35 cm, Probe position：14 ~30 cm (◇), 14 ~ 40 cm (○), 14~ 45 cm (△)) 100 Fig. 4-27. Mean amplitude of differential pressure fluctuations vs. superficial gas velocity: probe position =14 ~ 30 cm, 14 ~ 40 cm, 14 ~ 45 cm. (Sand 273 , Hs = 35 cm, Probe position：14 ~30 cm (◇), 14 ~ 40 cm (○), 14~ 45 cm (△)) 101 Fig. 5-1. Experimental apparatus of expanded-top fluidized bed. 106 Fig. 5-2. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the heater position of 35 cm. (FCC, = 71 , Heater Probe：35 cm (◇)) 113 Fig. 5-3. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the heater position of 35 cm. (Sand, = 163 , Heater Probe：35 cm (◇)) 114 Fig. 5-4. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the heater position of 35 cm. (Sand, = 230 , Heater Probe：35 cm (◇)) 115 Fig. 5-5. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the heater position of 35 cm. (Sand, = 273 , Heater Probe：35 cm (◇)) 116 Fig. 5-6. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the heater position of 35 cm. (Sand, = 323 , Heater Probe：35 cm (◇)) 117 Fig. 5-7. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the heater position of 35 cm. (Sand, = 460 , Heater Probe：35 cm (◇)) 118 Fig. 5-8. Amplitude of pressure fluctuation and bed-to-wall heat transfer coefficient vs. superficial gas velocity. (FCC, = 71 , Pressure probe：-4 cm (◇), Heater Probe：35 cm(◆)) 120 Fig. 5-9. Amplitude of pressure fluctuation and bed-to-wall heat transfer coefficient vs. superficial gas velocity. (Sand, = 163 , Pressure probe：-4 cm (◇), Heater Probe：35 cm(◆)) 121 Fig. 5-10. Amplitude of pressure fluctuation and bed-to-wall heat transfer coefficient vs. superficial gas velocity. (Sand, = 230 , Pressure probe：-4 cm (◇), Heater Probe：35 cm(◆)) 122 Fig. 5-11. Amplitude of pressure fluctuation and bed-to-wall heat transfer coefficient vs. superficial gas velocity. (Sand, = 273 , Pressure probe：-4 cm (◇), Heater Probe：35 cm(◆) ) 123 Fig. 5-12. Amplitude of pressure fluctuation and bed-to-wall heat transfer coefficient vs. superficial gas velocity. (Sand, = 323 , Pressure probe：-4 cm (◇), 14 cm (○), 30 cm (△), Heater Probe：35 cm(◆)) 124 Fig. 5-13. Amplitude of pressure fluctuation and bed-to-wall heat transfer coefficient vs. superficial gas velocity. (Sand, = 460 , Pressure probe：-4 cm (◇), 35 cm (○), (△), Heater Probe：35 cm(◆)) 125 Fig. 5-14. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the static bed height： 35 cm, 50 cm, 60 cm, 70 cm. (FCC, = 71 , Hs = 36 cm (◇), Hs = 50 cm (○), Hs = 60 cm (△), Hs = 70 cm (☆)) 126 Fig. 5-15. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the static bed height： 35 cm, 50 cm, 70 cm. (Sand, = 230 , Hs = 36 cm (◇), Hs = 50 cm (○), Hs = 70 cm (△)) 127 Fig. 5-16. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the static bed height： 35 cm, 50 cm, 60 cm, 70 cm. (Sand, = 323 , Hs = 36 cm (◇), Hs = 50 cm (○), Hs = 60 cm (△), Hs = 70 cm (☆)) 129 Fig. 5-17. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the static bed height： 35 cm, 50 cm, 60 cm, 70 cm. (Sand, = 460 , Hs = 36 cm (◇), Hs = 50 cm (○), Hs = 60 cm (△), Hs = 70 cm (☆)) 130 Fig. 5-18. Bed-to-wall heat transfer coefficient vs. superficial gas velocity with the heater position： 35 cm, 50 cm, 70 cm. (Sand, = 230 , Heater Probe：35 cm (◇), 50 cm (○), 70 cm (△) ) 132 Fig. 5-19. Bed-to-wall heat transfer coefficient of Group B particles. (Hs = 35, Heater probe = 35 cm, ：163 (◇), 230 (○), 323 (△), 460 (☆)) 133 Fig. 5-20. Bed-to-wall heat transfer coefficient of Group B particles. (Hs = 35, Heater probe = 35 cm, ：163 (◇), 230 (○), 323 (△), 460 (☆)) 135 Fig. 6-1. Standard deviation of absolute pressure fluctuations obtained at the different measurement positions 14, 30, and 50 cm above the distributor. (Pressure probe：14 cm (◇), 30 cm (○), 50 cm (△)) 148 Fig. 6-2. Standard deviation of differential pressure fluctuations obtained at the different measurement positions 30 ~ 40, 30 ~ 50, and 30 ~ 60 cm above the distributor. (Pressure probe：30 ~ 40 cm (◇), 30 ~ 50 cm (○), 30 ~ 60 cm (△)) 150 Fig. 6-3. The power spectral density function (Pa^2/Hz) of the absolute pressure fluctuations obtained at the measurement position 14 cm above the distributor. 151 Fig. 6-4. The power spectral density function (Pa^2/Hz) of the differential pressure fluctuations obtained at the measurement position 30 ~ 60 cm above the distributor 153 Fig. 6-5. The normalized PSDF of absolute pressure fluctuations obtained at the measurement positions 14, 30, and 50 cm above the distributor. (Pressure probe：14 cm (◇), 30 cm (○), 50 cm (△)) 156 Fig. 6-6. The normalized PSDF of differential pressure fluctuations obtained at the measurement positions 30 ~ 40, 30 ~ 50, and 30 ~ 60 cm above the distributor. (Pressure probe：30 ~40 cm (◇), 30 ~ 50 cm (○), 30 ~ 60 cm (△)) 157 Fig. 6-7. Eight decomposed resolution detail scales of the pressure fluctuation signals. 162 Fig. 6-8 (a). Wavelet energy (%) profiles for pressure fluctuation signals. (a)Wavelet energy profiles of absolute pressure fluctuations obtained at the measurement position 14 cm above the distributor. (Ug = 0.88 m/s(◇), Ug = 1.85 m/s (○), Ug = 2.75 m/s (△)) 163 Fig. 6-8 (b). (b) Wavelet energy profiles of differential pressure fluctuations obtained at the measurement position 30 ~ 60 cm above the distributor. (Ug = 0.92 m/s(◇), Ug = 1.79 m/s (○), Ug = 2.77 m/s (△)) 164 Fig. 6-9 (a). The PSDF (Pa^2/Hz) of multi-resolution decomposition of the pressure fluctuation signals at Ug = 0.96 m/s. (a) Detail scales, ~ 169 Fig. 6-9 (b). (Continued) (b) Approximation scales, ~ 170 Fig. 6-10 (a). Standard deviation of the reconstructed absolute pressure fluctuation signals of and obtained at axial positions 14, 30, and 50 cm above the distributor. (a) (Pressure probe：14 cm (◇), 30 cm (○), 50 cm (△)) 171 Fig. 6-10 (b). (Continued) (b) (Pressure probe：14 cm (◇), 30 cm (○), 50 cm (△)) 172 Fig. 6-11 (a). Standard deviation of the reconstructed differential pressure fluctuation signals of and obtained at different positions 30 ~ 40, 30 ~ 50, 30 ~ 60 cm above the distributor. (a) (Pressure probe：30 ~ 40 cm (◇), 30 ~ 50 cm (○), 30 ~ 60 cm (△)) 173 Fig. 6-11 (b). (Continued) (b) . (Pressure probe：30 ~ 40 cm (◇), 30 ~ 50 cm (○), 30 ~ 60 cm (△)) 174 Fig. 6-12 (a). The energy of absolute pressure fluctuations obtained at the different measurement positions 14, 30, 50 cm above the distributor. (a) Original signal. (Pressure probe：14 cm (◇), 30 cm (○), 50 cm (△)) 175 Fig. 6-12 (b). (Continued) (b) . (Pressure probe：14 cm (◇), 30 cm (○), 50 cm (△)) 176 Fig. 6-12 (c). (Continued) (c) . (Pressure probe：14 cm (◇), 30 cm (○), 50 cm (△)) 177 Fig. 6-13 (a). The energy of differential pressure fluctuations obtained at the different measurement positions 30 ~ 40, 30 ~ 50, 30 ~ 60 cm above the distributor. (a) Original signal. (Pressure probe：30 ~ 40 cm (◇), 30 ~ 50 cm (○), 30 ~ 60 cm (△)) 178 Fig. 6-13 (b). (Continued) (b) . (Pressure probe：30 ~ 40 cm (◇), 30 ~ 50 cm (○), 30 ~ 60 cm (△)) 179 Fig. 6-13 (c). (Continued) (c) . (Pressure probe：30 ~ 40 cm (◇), 30 ~ 50 cm (○), 30 ~ 60 cm (△)) 180 表 目 錄 Table 3-1. Properties of solid particles 23 Table 4-1. Mean amplitude pressure fluctuations with different particles, bed heights, and probe positions 74 Table 4-2. Comparison of measured values by absolute pressure fluctuations 75 Table 4-3. Result of experimental values of absolute pressure fluctuations 76 Table 4-4. Comparison of measured values by differential pressure fluctuations 10