PRESSURE FLUCTUATIONS IN TURBULENT FLUIDIZED BEDS

Transcription

1 00 close-packed reduced solid total UNIQUAC infinite dilution solution (Superscripts) E = excess 0 = pure component p = close-packed solution sat = saturated Literature Cited 1) Abrams, D. S. and J. M. Prausnitz: AIChEJ., 21, 1, 116 (1975). 2) API Project: "API Technical Data Book-Petroleum Refining," American Petroleum Institute (1976). 3) Bulter, A. V., D. W. Thomson and W. N. McLennan: /. Chem. Soc, (London), 674 (1933). Choudhury, M. K. D.: Indian J. Chem., 14A, 553 (1976). Dobson, H. J. E.: J. Chem. Soc, 2866 (1925). Eyring, H. and R. P. Marchi: J. Chem. Educ, 40, 562 (1963). Eyring, H. and M. S. Jhon: "Significant Liquid Structures," John Wiley and Sons (1969). Flory, P. J.: /. Chem. Phys., 9, 660 (1941). Flory, P. J.: J. Chem. Phys., 10, 51 (1942). Guggenheim, E. A.: "Mixtures," Clarendon Press (1952). ll) Huggins, M. L.: J. Chem. Phys., 9, 440 (1941). 12) Huggins, M. L.: J. Phys. Chem., 46, 151 (1942). 13) Iguchi, A.: Kagaku Sochi, 20, 66 (1978). 14) Lu, B. C.-Y.: Chem. Eng., 66, 9, 137 (1959). 15) Mertl, I.: Collection. Czec. Chem. Commun., 37, 366 (1972). 16) Murti, P. S. and M. VanWinkle: Chem. Eng. Data Ser., 3, 72 (1958). 17) Nakayama, T., H. Sagara, K. Arai and S. Saito: FluidPhase Equilibria, 38, 109 (1987). 18) Nakayama, T., H. Sagara, K. Araiand S. Saito: J. Chem. Eng. Japan, 21, 129 (1988). 19) Neindre, B. L. and B. Vodar: "Experimental Thermodynamics, Volume II," p. 57, International Union of Pure and Applied Chemistry, London (1975). 20) Rackett, H. G.: J. Chem. Eng. Data, 15, 4, 514 (1970). 21) Smith, V. C. and R. L. RobinsonJr.: J. Chem. Eng. Data, 15, 391 (1970). 22) Sorensen, J. M., T. Magnussen, P: Rasmussen and A. Fredenslund: Fluid Phase Equilibria, 3, 47 (1979). 23) Sorensen, J. M. and W. Arlt: "Liquid-Liquid Data Collection," DECHEMA(1980). Equilibrium 24) Vrevsky, M. S.: Zh. Russ. Fiz. Khim. Obshch., 42, 25) Wilson, G. M.: J. Am. Chem. Soc, 86, 127 (1964). 1 (1910). (A part of this work was presented at the 51st Annual Meeting of The Society of Chemical Engineers, Japan, at Osaka, 1986 and at the GunmaMeeting of The Society of Chemical Engineers, Japan, at Minakami, July, 1986.) PRESSURE FLUCTUATIONS IN TURBULENT FLUIDIZED BEDS Geun S. LEE and SangD. KIM Department of Chemical Engineering, Seoul , Korea Korea Advanced Institute of Science and Technology, Key Words : Pressure Fluctuations, Turbulent Fluidized Bed, Statistical Analysis, Fluctuation Intervals From the statistical analysis of pressure fluctuations, the hydrodynamic properties in a turbulent fluidized bed of glass beads (dp: 0.362mm) have been determined in a 0.1 m-id x 3m high Plexiglas column. The statistical properties such as mean amplitude, fluctuation interval, standard deviation, skewness and flatness of pressure fluctuations have been utilized to determine the transition velocity from the bubbling to turbulent flow regimes in a fluidized bed. The obtained transition velocities from these methods were found to have very similar values. In the turbulent flow regime, the meanamplitude, fluctuation interval, standard deviation and flatness of pressure fluctuations decreased with an increase in gas velocity. By contrast, the skewness of pressure fluctuations increased with gas velocity. The data of the present and previous studies on transition velocity from bubbling to turbulent flow regimes in terms of Reynolds numberhave been correlated with Archimedesnumber. Introduction The turbulent fluidized regime in a fluidized bed operation has received considerable attention in recent years due to the great contacting capability Received December 10, Correspondence concerning this addressed to S. D. Kim. rticle should be VOL 21 NO between the gas and solid phases without bubble formation in the catalytic and non-catalytic reaction systems. Transition from the bubbling to the turbulent flow regimes in a fluidized bed is marked by the breakdown of larger bubbles into smaller ones.19) The transition to the turbulent flow regime in terms of the amplitude of pressure fluctuation with gas velocity 515

2 has been studied by Canada et al.,7) and Yerushalmi and Cankurt.35) The onset of the turbulent flow regime has been determined from a point at which the mean amplitude of pressure fluctuations with gas velocity begins to level-off. However, according to the equipment size and the properties of particles, the mean amplitude of pressure fluctuations with gas velocity did not exhibit a sharp drop but a rather continuous decrease from the transition to turbulent flow regime.12) Therefore, the transition point between the bubbling and turbulent flow regimes can not be easily determined. Since pressure fluctuations observed in fluidized beds are random in nature, the statistical analysis on pressure fluctuations in the bed can be utilized for diagnosing the fluidizing behavior. Statistical properties of pressure fluctuations in the bubbling flow regime have been observed by previous investigators,ll 16'22' ) and these properties have been used to determine the transition from the dilute to the dense phase flows.27) By contrast, studies on the hydrodynamic characteristics in the turbulent flow regime by means of statistical analysis of the pressure fluctuations in the bed are relatively sparse. Therefore, in this study, the transition from the bubbling to the turbulent flow regimes has been determined from a point at which the mean amplitude of pressure fluctuations with gas velocity begins leveloff35* and the statistical properties of pressure fluctuations in the bed and the effect of the flow regimes on these statistical properties has been examined. 1. Experimental Experiments were carried out in a Plexiglas column of0.1 m-id x 3m high as shown schematically in Fig. 1. Glass beads with a weight mean diameter of 0.362mm ( mm) and density of 2500kg/ m3 were fluidized by compressor air. The minimum fluidizing velocity of the particles was found to be 0.105m/s. The soild particles were supported on a bubble cap distributor plate which contained 7 bubble caps in which 6x3.0mm in diameter holes were drilled around each bubble cap. The distributor was situated between the main column and 0.1 m-id x 0.2m high air box into which air was fed to the column through a pressure regulator, oil filter and a calibrated rotameter. Pressure taps were mounted flush with the wall of the column at 10cm height intervals from the distributor. The pressure drop across the gas distributor was ranged kPa at the gas velocity employed in this study. The entrained solid particles from the bed were collected by the first and the second cyclones in series and were recycled to the main bed simultaneously. The column was initially loaded with 10kg of glass beads giving static bed height of 1m. The pressure probe was made of 0.78cm-ID stainless steel pipe which can be moved 516 Fig. 1. Schematic diagram of experimental apparatus radially across the bed width through the pressure tap hole. One end of the probe was covered with a 200 mesh screen to prevent solid particles flowing out from the bed and the other end was connected to a differential pressure transducer (Fisher Controls Co., 1151). The pressure transducer connected to a D.C. power supplier which has two input channels and the output voltages were calibrated against the pressure difference between two channels in the linear response range of kPa. Twochannels of the pressure transducer were connected to the two vertically sepa-.rated pressure probe for measuring the pressure fluctuations between the two locations (33 and 53cm) in the bed. For measuring the pressure fluctuations, one channel of the pressure transducer was connected to the pressure probe in the bed and the other one was exposed to the atmosphere. A continuous pressure signal from the pressure transducer was amplified and sent it via an A/D converter to a personal computer (Apple He) for recording. The sampling interval of the fluctuation was selected at 10ms and 8192 samples were collected for each experimental condition. In order to determine the effect of bed height on pressure fluctuations, pressure gradients were measured along the bed height above the distributor. The measured pressure gradients remained almost constant above the bed level of 13cm from the distributor in the given ranges of gas velocity employed in this study. Therefore, the measuring points were selected above this level (33 and 53cm) throughout this study. The measured pressure fluctuation signals were analyzed in terms of meanamplitude, fluctuation interval, standard deviation, and dominant frequency. Also, the skewness and flatness of the probability density function in pressure fluctuations have been determined.5a1) In analyzing the signals with respect to the dominant frequency, an estimated smooth power spectral density function was obtained by the Hanning Windowfunction6) procedure. 2. Results and Discussion 2.1 Mean amplitude of pressure fluctuations The mean amplitude of pressure fluctuations with gas velocity between the two measuring locations (33 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

3 and 53cm) above the distributor is shown in Fig. 2. As can be seen, the mean amplitude of pressure fluctuations initially increases with an increase in gas velocity, though it went to a maximumvalue at a gas velocity, and then it sharply decreases with an increase in gas velocity. The sharp decrease in the mean amplitude of pressure fluctuations at a given gas velocity may be attributed to the breakdown of slugs into smaller bubbles, and this maximumpoint has been regarded as the onset to the turbulent flow regime in the bed.7 35) From the figure, the transition velocity to the turbulent flow regime is found to be 0.85m/s. This value gives a ratio of transition to particle terminal velocities of0.313 which is similar to those in the bed of coarse particles.7'26) 2.2 Pressure fluctuation intervals The probability distribution function which is a cummulation of the probability density function for pressure fluctuations. The 80 and 90%fluctuation intervals of pressure fluctuation have been determined from the former. These values can be used to describe the extent of large bubbles present in the bed. A sample calculation of these fluctuation intervals is shown in Fig. 3. The variation of 80 and 90% fluctuation intervals with gas velocity is shown in Fig. 4. The trends of these fluctuation intervals are similar in nature to those of the mean amplitude as shown in Fig. 2. However, the 80%fluctuation interval exhibits a more sharp decrease with gas velocity than that of the 90% fluctuation interval at around the transition region to the turbulent flow regime. It mayindicate that the larger bubbles produce higher pressure fluctuation intervals in the bed at the transition region from bubbling to turbulent flow regime. Therefore, the variation of the pressure fluctuation interval with gas velocity maybe utilized to determine the transition velocity to the turbulent flow regime in the bed. The variation of the 80%pressure fluctuation interval with gas velocity has been used to determine the malfunction of the gas distributor in fluidized beds by Song et al29) 2.3 Standard deviation of pressure fluctuations The standard deviation of pressure fluctuations with gas velocity measured at 0.53m above the distributor in the bed is shown in Fig. 5. As can be seen, the standard deviation initially increases with gas velocity up to around 0.4m/s. However, it remains almost constant until the transition region of the turbulent flow regime is reached. Thereafter, it decreases with further increase in gas velocity in the turbulent flow regime. The increase of standard deviation in pressure fluctuations maybe attributed to the increase in bubble size with gas velocity in the bubbling flow regime. In the slugging flow regime, three types of slugs have been observed, name- VOL 21 NO Fig. 2. Meanamplitude of pressure-drop fluctuations with gas velocity Fig. 3. Sample calculation for fluctuation intervals of pressure-drop fluctuations at a gas velocity of 1.05 m/s Fig. 4. Variation of 90% and 80%fluctuation intervals of pressure-drop fluctuations with gas velocity A:90% B:80% Fig. 5. Standard deviation of pressure fluctuations vs. gas velocity ly, axisymmetric, asymmetric and square-nosed slugs.3'4>30'33) In general, the square-nosed slug can be observed in the bed of coarse particles as used in the present study. Therefore, the standard deviation of 517

4 pressure fluctuations remains almost constant with an increase in gas velocity in slugging flow regime due to the formation of square-nosed slugs which were observed in the present system. The standard deviation sharply decreases at the transition region to the turbulent flow regime and it decreases with gas velocity because of the breakdown of square-nosed slugs into small bubbles or voids. Consequently, the changes in standard deviation of the pressure fluctuations may be used to indicate the onset of the turbulent flow regime in the bed. 2.4 Skewness and flatness of pressure fluctuations The nondimensionalized third central moment, skewness, is a measure of the lack of symmetry in probability density function about the mean value. The nondimensionalized fourth central moment, flatness, is a measure of the extent of sharpness in probability density function about the mean value. These values are defined as *4 "4 - oo (1) (x - x)3f(x)dx +oo {x - xff(x)dx where x is the random signal value, x is the mean value of random signals, a is the standard deviation, and/(x) is the probability density function ofx. When the probability density function lies in the normal distribution, the skewness and the flatness have the values of 0 and 3, respectively. The variations of these values from the normal distribution having the same value of standard deviation in the random signals are shown in Fig. 6. As can be seen, the skewness has the values of positive or negative sign to the direction of asymmetry in probability density function about the mean value. The value of flatness is larger or smaller than 3 of the normal distribution depending on the extent of sharpness in probability density function about the mean value. The skewness of pressure fluctuation with the variation of gas velocity in the bed is shown in Fig. 7. The skewness decreases with an increase in gas velocity in the bubbling flow regime, it remains almost constant in the slugging flow regime and it increases with further increase in gas velocity in the turbulent flow regime. These trends have been observed in all the radial positions of the bed. The skewness obtained from the signals of the capacitance probe1} also increases with an increase in gas velocity at all the radial positions of the bed in the turbulent flow regime. As can be seen in the figure, the transition to the turbulent flow regime takes place at the very same gas velocity as observed previously. Moreover, the change in the value of the skewness is nearly opposite 518 (2) Pressure Fig. 6. Variations of skewness and flatness from normal distribution with the same value of standard deviation in randomsignals Fig. 7. Skewness of pressure fluctuations vs. gas velocity to that of the standard deviation with gas velocity as shown in Fig. 5. In the slugging flow regime, the skewness remains almost constant regardless of the increase in gas velocity because of the nearly constant standard deviation prevailing in pressure fluctuations. The decrease in skewness in the bubbling flow regime maybe attributed to the increase in small fluctuations which occurs at the upper half of pressure fluctuations which were caused by the raining of solid particles through the slugs.1n The increase of skewness with gas velocity in the turbulent flow regime results from the increase in small fluctuations in the lower half of the pressure fluctuations due to the breakdown of the slugs into smaller bubbles. The typical small fluctuations superimposed on the major fluctuations which occur in the upper half and in the lower half of pressure fluctuations in the slugging and turbulent flow regimes can be seen in Fig.8. Typical probability density functions of pressure fluctuations in the slugging and turbulent flow regimes are compared with the normal distribution as shown in Fig. 9. As can be seen, the shape in the probability density function of pressure fluctuations in the turbulent flow regime is different from that in the slugging flow regime. The probability density function of the major fluctuations is skewed to the positive side of its mean in the slugging flow regime and it is skewed slightly to the negative side in the JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

5 Fig. 8. Pressure fluctuation signals in slugging and turbulent flow regimes A: slugging B: turbulent Fig. 10. Flatness of pressure fluctuations vs. gas velocity Table 1. Transition velocities from the bubbling to the turbulent flow regime by the statistical properties of pressure fluctuations Statistical properties Uc [m/s] Mean amplitude % fluctuation interval % fluctuation interval 0.87 Standard deviation 0.84 Skewness 0.80 Flatness 0.83 Fig. 9. Probability density function of pressure fluctuations compared to normal distribution in slugging and turbulent flow regimes A: slugging B: turbulent turbulent flow regime. This trend is in agreement with that of the probability density function obtained from the signals of capacitance probe in the bed of FCC particles with a meansize of0.06mm.8)as can be seen in Fig. 7, the skewness of pressure fluctuations with gas velocity can be also used to determine the transition velocity to the turbulent flow regime in the bed. The flatness of pressure fluctuations with gas velocity at the wall and the center of the bed are shown in Fig. 10. As can be seen, the value offlatness exhibits a maximumvalue with an increase in gas velocity. The maximumpoint may be used to indicate the transition point to turbulent flow regime. The major probability densities of the fluctuations with gas velocity can be observed where the pressure fluctuations are highly deviated from the mean value due to the larger bubble size in the slugging flow regime. However, the standard deviation of pressure fluctuations is nearly constant in the bubbling flow regime as can be seen in VOL. 21 NO Fig. 5. However, in the turbulent flow regime, the deviation decreases with an increase in gas velocity since the major probability densities of pressure fluctuations are located at around the mean value (Fig. 9) which can be attributed to the homogeneous phase resulting from the breakdown of larger bubbles in the bed. Evidently, the variation of the flatness in the fluctuation signals with gas velocity can be utilized to determine the transition region from the bubbling to turbulent flow regimes in fluidized beds. The flatness of pressure fluctuations at the center of the bed is greater to some extent than that at the wall of the bed. The difference between these values decreases with gas velocity in the turbulent flow regime. It indicates that the pressure fluctuation characteristics in the radial direction gradually become similar with an increase in gas velocity in the turbulent flow regime. The transition velocities between the bubbling and turbulent flow regimes obtained from the statistically treated values of pressure fluctuation signals are summarized in Table 1. As expected, the values obtained indicate quite similar values of the transition velocity and consequently, the transition velocity from the bubbling to the turbulent flow regime can be easily determined from these statistical properties. The power spectral density function of pressure fluctuations with gas velocity of 1.17m/s is shown in Fig. ll. The dominant frequency of a pressure fluc- 519

6 Fig. ll. Power spectral density function of pressure fluctuations at a gas velocity of 1.17m/s tuation signal can be determined from the peak of its power spectral density function of 0.56Hz as can tx found in the figure. In the present study, the dominani frequencies are found to be insensitive to the in crease in gas velocity in the turbulent flow regime within the frequency range of Hz. The data of the present and the previous studiesl,2,7-10,13,15,17-21,23,24,26,28,31,33,35) for ^ ^ sition velocity to the turbulent flow regime are correlated in terms of the Reynolds number with the Archimedes number as where 7tec = r0-485 (3; Rr _p9ucdp Ar_d3Ppd(Ps-pg)g Horio14) presented the value of the exponent on th< Archimedes number in Eq. (3) as of which is very similar to the present value. The goodness of fit between the measured anc calculated values of Reynolds number at the transition velocity to the turbulent flow regime is shown ir Fig. 12. Conclusions The statistical properties of pressure fluctuations with gas velocity such as mean amplitude, fluctuatior interval, standard deviation, skewness and flatness can be utilized to determine the transition velocit} from the bubbling to the turbulent flow regime ir fluidized beds. The values obtained from the statistical properties are found to have very similar values In the turbulent flow regime, the mean amplitude, fluctuation interval, standard deviation and flatness of pressure fluctuations decrease with an increase in gas velocity. By contrast, the skewness of the pressure fluctuations increases with an increase in gas velocity, The transition velocity to the turbulent flow regime is correlated in terms of Reynoldsnumberwith the Archimedes Acknowledgment number. The authors wish to acknowledge a Grant-in-Aid for research from the Korea Science and Engineering Foundation. 520 Fig. 12. Comparison of measured and calculated values of Reynolds number at the transition velocity to turbulent flow regime Nomenclature Ar = Archimedes number, dlpg(ps - Pg)g/iu2 [-] dp = particle diameter [m] F = flatness defined in Eq. 2 [-] f(x) = probability density function of x [-] g = acceleration constant due to gravity [m/s2] Rec = Reynolds numberbased on the transition velocity to the turbulent flow regime, pjp UJli [-} S = skewness defined in Eq. 1 [-] Uc = transition velocity from bubbling to turbulent flow regime [m/s] Ug = superfical gas velocity [m/s] x = random signal values of pressure fluctuations x = mean value of random signals in pressure fluctuations p = density [kg/m3] \i = viscosity [Pa s] (Subscript) g s = gas = solid Literature Cited 1) Abed, R.: Fluidization IV, Kunii, D. and R. Toei (eds.), p. 137, Engineering Foundation, New York (1984). 2) Avidan, A. A., R. M. Gould and A. Y. Kam: Circulating Fluidized Bed Technology, Basu, P. (ed.), p. 287, Pergamon Press, Canada (1986). 3) Baeyens, J. and D. Geldart: Chem. Eng. Sci., 29, 255 (1974). 4) Baker, C. G. J. and D. Geldart: Powder TechnoL, 19, 177 (1978). 5) Bendat, J. S. and A. G. Piersol: Random Data-Analysis and Measurement Procedures, John & Wiley Interscience, New York (1971). 6) Blackman, R. B. and J. W. Tukey: The Measurement of Power Spectra, Dover Publications, New York (1968). 7) Candada, G. S., M. H. McLaughlin and F. W. Staub: AIChE Symp. Ser., 74 (176), 14 (1978). 8) Carotenuto, L., S. Crescitelli and G. Donsi: Quad. Ing. Chim. Ital., 10, 185 (1974). 9) Crescitellis, S., G. Donsi, G. Russo and R. Clift: Chisa Conf.,p. 1 (1978). 10) Fan, L. (1983). T.,T. C. HoandW. P. Walawender: AIChEJ., 29, 33 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN [Pa] [Pa]

7 Fan, L. T., T. C. Ho, S. Hiraoka and W. P. Walawender: AIChE J., 27, 67 (1980). Geldart, D. and M. J. Rhodes: Circulating Fluidized Bed Technology, Basu, P. (ed.), p. 21, Pergamon Press, Canada (1986). Han, G. Y., G. S. Lee and S. D. Kim: Korean J. Chem. Eng., 2, 141 (1985). Horio, M.: J. Soc. Powder TechnoL, 23, 80 (1986). Jin, Y., Z. Yu, Z. Wang and P. CaifFluidization V, 0stergaard, K. and A. Sorensen (eds.), p. 289, Engineering Foundation, New York (1986). Kang, W. K., J. P. Sutherland and G. L. Osberg: Ind. Eng. Chem. Fundam., 6, 499 Kehoe, W. K. and J. (1967). F. Davidson: CHEMECA'70, Inst. Chem. Eng. Symp. Ser., No.33, p. 97, Butterworths, Melbourne (1971). Kojima, T., K. Ishihara, K. Kuramoto and T. Furusawa: Proc. of World Congr. Ill of Chem. Eng., Vol. IV, p. 291, Japan (1986). Lanneau, K. P.: Trans. Instn. Chem. Engrs., 38, 125 (1960). Lee, Li, J. S. and S. D. Kim: Hwahak Konghak, 20, 207 (1982). Y. and M. Kwauk: Fluidization, Grace, R. and J. M. Matsen Lirag, (eds.), R. C. Jr. p. 537, and H. Plenum Littman: Press, New York (1980). AIChE Symp. Ser., 67 (116), ll (1971). Massimilla, L.: AIChE Symp. Ser., 69(128), ll (1973). Rhodes, M. J. and D. Geldart: Fluidization V, 0stergaard, K. and S. S0rensen, (eds.), p. 281, Engineering Foundation, New York (1986). Sadasivan, N., D. Barreteau and C. Laguerie: Powder Technol., 26, 67 (1980). Satija, S. and L. S. Fan: AIChEJ., 31, 1554 (1985). Satija, S., J. B. Young and L. S. Fan: Powder Technol., 43, 257 (1985). Shin, B. C, Y. B. Koh and S. D. Kim: Hwahak Konghak, 22, 253 (1984). Song, J. C, L. T. Fan and N. Yutani: Chem. Eng. Commun., 25, 105 (1984). Stewart, P. S. B. and J. F. Davidson: Powder Technol., 1, 61 (1967). Subbarao, D. and P. Basu: Circulating Fluidized Bed Technology, Basu, P. (ed.), p. 281, Pergamon Press, Canada (1986). Taylor, P. A., M. H. Lorenz and M. R. Sweet: Proc. of Intern. Congr. on Fluidization and its Applications, p. 90, Soc. Chim. Industrille, Toulouse (1973). Thiel, W. J. and O. E. Potter: Ind. Eng. Chem. Fundam., 16, 242 (1977). Winter, O.: AIChE J., 14, 426 (1968). Yerushalmi, J. and N. T. Cankurt: Powder Technol., 24, 187 (1979). VOL 21 NO