Flow characteristics in a bubbling fluidized bed at elevated temperature

Transcription

1 Chemical Engineering and Processing 42 (2003) 439/447 Flow characteristics in a bubbling fluidized bed at elevated temperature Qingjie Guo a, *, Guangxi Yue b, Toshiyuki Suda c, Junichi Sato c a Department of Chemical Engineering I, Technical University Hamburg-Harburg, D Hamburg, Germany b Department of Thermal Engineering, Tsinghua University, Beijing , People s Republic of China c Ishikawajima-Harima Heavy Industries Co. Ltd., Tokyo , Japan Received 24 January 2002; received in revised form 21 April 2002; accepted 27 May 2002 Abstract A bubbling fluidized bed with m in diameter and 1.5 m in height was employed to investigate the minimum fluidization velocity and flow dynamics at bed temperature up to C. Ashes of three sizes (Geldart B) from pressurized fluidized bed boiler were used as fluidization materials. Experiments show that the minimum fluidization velocity decreases with increasing bed temperature. Pressure fluctuation signals were analyzed by using power spectral density function (PSDF), chaos, and wavelet analysis. The major frequency of pressure fluctuation signals is in the range from 1 to 4 Hz in the fluidized state. It demonstrates that a bubbling fluidized bed at high temperature is a deterministic chaos system since all the largest Lyapunov exponents are positive. The correlation dimension and Kolmogorov entropy increase with an increase in the fluidization number, and then they vary little with increasing fluidization gas velocity. By the wavelet transform, the fluctuating pressure signals in the bed can be decomposed into its approximations and details at different resolutions. The number of peaks in the scale six detail signal represents the number of bubbles passing through pressure probe measurement region over the sampling time, which agrees with the major frequency obtained from PSDF analysis of pressure fluctuation signals. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Fluidized bed; High temperature; Minimum fluidization velocity; Power spectrum density function; Chaos; Wavelet analysis 1. Introduction Gas /solid fluidized beds are extensively employed in chemical, petrochemical and metallurgic industries, in the production of fine powder, and in the combustion and gasification of solid fuels. An understanding of dynamic characteristics for such reactors is a challenge due to the complex and hardly predicted dynamics of fluidized beds. However, the local time-dependent variables, including pressure fluctuation signals, voidage, and instantaneous heat transfer coefficient, can be used to analyze and describe the dynamic characteristics. Many investigators [1 /4] have measured pressure fluctuations to describe the dynamic behaviors of the bed using classical statistical analyses such as the probability * Corresponding author. Tel.: / ; fax: / address: q.guo@tu-harburg.de (Q. Guo). density function, autocorrelation function, fast Fourier transformation and power spectrum, and then identified a periodic component of the pressure fluctuations in the bed. In the last decade, some researchers [5 /8] applied chaos theory to analyze pressure fluctuation in the gas / solid fluidized beds and confirmed the chaotic nature of the bed. Based on correlation structure of pressure signal, He et al. [9] demonstrated that pressure fluctuations in a gas/solid fluidized bed were decomposed into fractional Brownian motion (FBM) and Gaussian white noise (GWN). It should be pointed out that all above studies were performed in the fluidized beds at ambient temperature. In comparison with investigations at ambient temperature, only a few papers reported on dynamic characteristics of bubbling fluidized beds at elevated temperature. Saxena et al. [10,11] calculated probability density function, autocorrelation function, and power spectral function of pressure and temperature signals to characterize the fluidization quality of the /02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S ( 0 2 ) 转载

2 440 Q. Guo et al. / Chemical Engineering and Processing 42 (2003) 439/447 fluidized beds. Svoboda et al. [12] noted that the spectrum analysis of pressure fluctuations was a sensitive, instrumental method for identification of the regimes in the bed at elevated temperature. However, there is little knowledge regarding dynamics of the bubbling fluidized beds at high temperature obtained by using chaos analysis and wavelet analysis. Furthermore, it is important for design and development of fluidized bed boilers to gain knowledge on bed dynamics. In this study, pressure fluctuation signals are sampled in an 82-mm diameter bed using various size ashes as fluidization materials (from pressurized fluidized bed boiler). Dynamic behavior of a bubbling fluidized bed at high temperature up to C is characterized by resorting to power spectral analysis, chaos analysis, and wavelet analysis. 2. Theoretical analysis 2.1. Power spectrum density function The time series of pressure fluctuations can be analyzed by using the power spectrum density function. The power spectrum illustrates how the energy is distributed over the frequency. To decrease the calculation error, the average of a number of sub-spectra [13/ 15] is used to estimate the power spectrum. Consequently, the pressure fluctuation time series are divided into k segments of each individual length L, which are represented as: p i p(nil) n1; 2; 3;...; L; i1; 2;...; k: (1) The average power spectrum is P x 1 X k klu j i1 XL n1 j2pnk=nj 2 p i (n)w(n)e ; (2) where U is the normalized power in the window function, w(n), U 1 L X L n1 [w(n) 2 ]: (3) A Hamming window applied in this study is a smooth one with a continuous first derivative; the window and its derivative are zero at the endpoints. That is, w(n) (1=T)(0:540:46cos(pt i=t)) 05½t i ½5T (4) 0 ½t i ½T The mean amplitude of the pressure fluctuations can be calculated by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 1 X n Dp t (p i p) 2 : (5) n 1 i1 The average pressure is P 1 n X n i1 p i : (6) 2.2. Wavelet transform Wavelet transformations play an important role in the investigation of self-similar signals and system [16,17]. Wavelet transform can provide information of a random signal with time and space. For practical application, Discrete Wavelet Transform (DWT) is used to perform easily wavelet transformation of self-similar signals. Generally, the wavelet transform of a continuous signal x i (t i ) can be defined as W f (a; b) 1 g ti b pffiffiffiffiffi x i (t i )8 dt; (7) ½a½ a where W f (a, b) is the wavelet coefficient, 8* is the basic wavelet function, a and b are the continuous dilation and translation parameters, respectively; they take values in the range of the amplitude function /B/ a, b B/, a "/0. Wavelet functions are a family of functions with high frequency and small duration, which are all normalized dilations and translations of a prototype wavelet base function 8 a;b (t i ) 1 ti b pffiffiffiffiffi 8 : (8) ½a½ a An original signal is decomposed into its approximations and details with different frequency bands by means of wavelet transform. The orthogonal wavelet series approximates to a continuous signal, x(t i ), expressed as x(t):a j (t i )D j (t i )D j1 (t i )D j (t i ); (9) where D 1 (t i ), D 2 (t i ),..., D j (t i ) represent detail signals of multiresolution decomposition at different resolution 2 j, and A j (t i ) is the approximation signal of multiresolution decomposition at resolution 2 j. Daubechies wavelet (db7) is utilized to calculate pressure fluctuation signals in the present investigation. 3. Experiments 3.1. Experimental set up The experiments were conducted in a bubbling fluidized bed schematically depicted in Fig. 1. The experimental set up mainly consists of a fluidized bed,

3 Q. Guo et al. / Chemical Engineering and Processing 42 (2003) 439/ Fig. 1. Experimental apparatus: (1) computer; (2) A/D; (3) pressure sensor; (4) pre-heater; (5) thermocouple; (6) cyclone; (7) fluidized bed; (8) primary heater (six silicon carbon rods); (9) insulation brick; (10) pressure probe. a cyclone, a plenum chamber, a pre-heater, a primary heater, a temperature measurement system, a pressure signal sampling system, and a gas supply system. Fluidization is carried out in a chamber made of a stainless steel pipe 1.5 m in height and m I.D. The gas distributor plate has 1% free area formed of 18 holes, 2 mm in diameter, and spaced 19 mm between centers. To guarantee gas uniform distribution, two layers of a 200-mesh stainless steel screen were mounted above the distributor. The static bed height remained m for all experiments. Solid particles escaped from the bed were collected by a cyclone, and then returned to the bed bottom through a standpipe. Six pressure probes (4 mm I.D. and 400 mm in length), made of stainless steel, were installed into the bed horizontally at 10, 25, 40, 55, 70, and 115 mm above the gas distributor. To prevent blockage by fine ashes, each probe was covered with a 200-mesh stainless steel screen. To avoid heat conduction, a 70-mm quartz pipe with 7.0-mm I.D. is connected with each probe, with connection points sealed by asbestos lines. The opposite end of each quartz pipe was connected with a rubber pipe and a pressure sensor, as shown in Fig. 2. Three Pt/Rh10 Pt thermocouples, located at 10, 25, and 40 mm above the gas distributor, were inserted into the bed for measurement of bed temperature. A pre-heater and a primary heater heated the bed. Insulation bricks were applied to the bed to avoid heat loss. Fluidization air is measured by a flow meter, and heated by an electric pre-heater before entering the bed. The maximum heating powers of the pre-heater and the primary heater are 1.41 and 6.5 kw, respectively. The thermocouples are connected to a SR71 PID and a PACO3B voltage adjustor, which controls the bed temperature up to C with an accuracy of 9/5 8C. Ashes of three sizes from the pressurized fluidized bed boiler of Ishikawajima-Harima Heavy Industries Co. Ltd., Japan, were utilized as fluidization material and their physical properties are summarized in Table 1. Table 2 provides ash composition. The surface/volume average particle diameter is calculated by using Eq. (10). 1 d p Pi (X i =d pi ) ; (10) Table 1 Physical properties of solid particles Solid particle /d p (mm) r p (kg/m 3 ) Fig. 2. Schematic diagram of pressure probe: (1) stainless steel pipe; (2) asbestos; (3) quartz pipe; (4) rubber pipe. IHI ash IHI ash IHI ash

4 442 Q. Guo et al. / Chemical Engineering and Processing 42 (2003) 439/447 Table 2 IHI ash composition Composition Combustion loss SiO 2 Al 2 O 3 Fe 2 O 3 CaO MgO wt.% MnO TiO 2 P 2 O 5 Na 2 O K 2 O Other wt.% where X i is the weight fraction of particles of diameter d pi. Densities of ashes were determined by means of mercury displacement. For each 5-min-interval, ash sample was taken from the bed to check whether particle agglomeration occurred Measuring instrument The pressure measurement system includes six probes, six differential pressure sensors (Setra 264 Series Low Pressure Transducers), an A/D converter, and a computer. To meet experimental requirements, the sampling rate can be changed and the sampling rate for this test is 200 Hz. The full scale of pressure sensors is 5.0 kpa. During the experiments, the signals at 0.04 m above the gas distributor are employed to analyze dynamic behavior of the bed. 4. Results and discussion 4.1. Effect of bed temperature on minimum fluidization velocity The minimum fluidization velocity for polydisperse particles is a subjective parameter, which is obtained experimentally. At different bed temperatures, the minimum fluidization velocity for three ashes was presented by measuring the bed pressure drop for decreasing values of the air velocity. A typical plot for 0.85 mm ash at bed temperatures of 600, 800, and C is shown in Fig. 3. Fig. 4 shows that the minimum fluidization velocity for each size ash is a function of the bed temperature. Obviously, increasing bed temperature leads to decreasing minimum fluidization velocity as the bed temperature varies from ambient temperature to C. Similar trends can also be found from the experimental results of Flamant et al. [18] and Svoboda and Hartman [19]. Based on Geldart s classification, ashes with three sizes belong to the Geldart B Group. During all experiments, the Reynolds number of ashes is less than 10 because of gas velocity less than 3 m/s; thus the flow of gas around ashes is laminar. Based on Ergun Equation, the fluid /particle interaction force is dominated by the gas viscosity and Galileo number under the laminar flow conditions. Since gas viscosity increases with increasing bed temperature, the minimum fluidization velocity decreases with increasing bed temperature Statistical analysis Fig. 5 illustrates the effect of the superficial gas velocity on standard deviation of pressure fluctuations (SDPFs) at various bed temperatures. The fluidization number is defined as the ratio of the superficial gas velocity to the minimum fluidization velocity. At an axial height of 0.04 m, increasing fluidization number increases SDPF due to the fact that increasing superficial gas velocity results in the larger bubble diameter and larger number of bubbles as well as greater probability of bubbles coalescence. The bed temperature also influences the SDPF. Obviously, an increase in bed Fig. 3. Typical fluidization curve. Fig. 4. Effect of bed temperature on the minimum fluidization velocity.

5 Q. Guo et al. / Chemical Engineering and Processing 42 (2003) 439/ Fig. 5. Effect of the superficial gas velocity on SDPF. temperature leads to lower SDPF at a given fluidization number. The reason is that the minimum fluidization velocity of the particles decrease with increasing bed temperature, and decreasing superficial gas velocity causes fewer number of bubbles, lower coalescence probability of bubbles, and smaller bubble diameter. The above findings agree with the conclusions drawn by Svoboda et al. [12], and Saxena et al. [10,11]. It should be pointed out that no particle agglomeration occurs at bed temperature up to C. As shown in Fig. 5, SDPF varies little with fluidization number at an axial height of m because the bubble diameter is small at such height. Power spectra for four superficial gas velocities are plotted in Fig. 6. At higher fluidization number, the power spectra are characterized by the lower major frequency with larger fluctuation scale. At lower fluidization number, the pressure fluctuations are featured by the higher major frequency with smaller fluctuation scale. The variation of major frequency with fluidization number for various bed temperatures can be visualized in Fig. 7. It can be seen from this figure that major frequency decreases with increasing fluidization number and tends to level off at higher gas velocities. This can be explained that an increase in the superficial gas velocity can cause both increasing bubble size and increasing the number of bubbles, but primarily increasing bubble size. These trends fit well with those reported by Saxena et al. [10,11] and by Svoboda et al. [12] who analyzed pressure signal in bubbling fluidized beds at high temperature, by Fan et al. [1] and Bai et al. [5,6] who analyzed pressure signals in bubbling fluidized beds at ambient temperature Chaos analysis A sufficient number of time series is a necessary parameter to ensure the estimation accuracy of chaos exponents. For bubbling fluidized beds, Hay et al. [20] evaluated 5000 points to be sufficient, and Bai et al. [5] estimated 4000 points to be sufficient. The present calculations indicate that points are sufficient to reach precise evaluation for correlation dimension, Kolmogorov entropy, and the largest positive Lyapunov exponent. The calculation methods of correlation dimension and Kolmogorov entropy has been reported elsewhere [15,20]. The Lyapunov exponent providing a qualitative and quantitative characterization of dynamical behavior represents the exponentially fast divergence of nearby orbits in the phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. The calculation method proposed by Wolf et al. [21] was adopted in the present study. A series of calculations indicate that the estimate of Lyapunov exponent tends to become constant as evolution time rises. Fig. 8 illustrates the largest Lyapunov exponents for various fluidization numbers at temperatures of 700 and C. Although the data are scattered, all largest Lyapunov exponents are positive, demonstrating that a bubbling fluidized bed at high temperature is also a deterministic chaos system. The effect of fluidization gas velocity on correlation dimension and on Kolmogorov entropy at temperatures of 700 and C is shown in Figs. 9 and 10. At the minimum fluidization velocity, some reorganization takes place during the transition from fixed state to fully fluidized state, indicating that both the correlation dimension and the Kolmogorov entropy increase with an increase in the fluidization velocity. When the bed is in bubbling fluidization with the fluidization number greater than 1.5, both the correlation dimension and the Kolmogorov entropy vary little with the fluidization number. Apparently, the trends of both chaotic exponents with fluidization number are consistent with conclusions obtained by van den Bleek and coworkers [22] in a bubbling fluidized bed at ambient temperature. Pence et al. [8] calculated signals of a platinum film heat flux probe to present the Kolmogorov entropy ranging from 20 to 43 bits/s, having the same order with our findings. A positive, nonfinite estimate of the Kolmogorov entropy provides further evidence that pressure fluctuation signals at high temperature behave chaotically. Moreover, both our study and previous investigations [5,8,20,22] have confirmed that correlation dimension has the same range from 1 to 4 in bubbling fluidized beds, suggesting the bubbling fluidized beds have the similar flow structure Wavelet analysis of pressure fluctuation signal The typical coefficients of DWT of pressure fluctuations (u/u mf /1.88) are plotted in Fig. 11. The similar decomposition figures can be obtained from the pressure signals at other superficial gas velocities. On the basis of wavelet analysis, the wavelet transform can separate an original signal into various scales (multiresolution levels). Fine scale detail components D1, D2, and D3

6 444 Q. Guo et al. / Chemical Engineering and Processing 42 (2003) 439/447 Fig. 6. Power spectra for four superficial gas velocities. (the fine scale) mainly describe the high frequency oscillations. High frequency scale coefficients (D1, D2, D3) indicate GWN brought about jetting action above the distributor. The coarse scale components D8 and A8 correspond to lower frequency oscillations. Fig. 11 also exhibits that the dominant scale over sampling time is the D6 scale, which represents the main pressure fluctuations in a bubbling fluidized bed. Schaaf et al. [23] found that the upward propagation of pressure fluctuation wave of a gas pulse includes three phases: the first phase is a homogenous oscillation representing bubble formation, the second represents a bubble rising along a fluidized bed, and the third corresponds to a bubble eruption on the bed surface. The pressure

7 Q. Guo et al. / Chemical Engineering and Processing 42 (2003) 439/ Fig. 7. Effect of fluidization number on the major frequency. Fig. 11. Plot of discrete wavelet coefficient of a pressure fluctuation signal (t/800 8C, d p /0.85 mm, u/u mf /1.88). Fig. 8. The largest Lyapunov exponent is a function of fluidization number. Fig. 9. Effect of fluidization number on correlation dimension. fluctuations are the comprehensive results of the pressure wave travelling upward and downward, in which the first phase leads to the maximum pressure fluctuation. Therefore, the larger pressure fluctuations can be attributed to the bubble formation. By means of Origin 5.0 software, the number of peaks for 20 s (4000 points) in scale 6-detail signal is 49, as shown in Fig. 11, which fits into the major frequency of power spectral density function (PSDF) (2.44 Hz) of pressure fluctuation signals. It can be concluded that each peak in scale 6-detail signal should correspond to a bubble. Therefore, the number of peaks in the scale 6- detail signal represents the number of bubbles passing through pressure probe measurement region over the sampling time. An excellent agreement between original pressure signal and reconstructed pressure signal, Fig. 12, exhibits that the above wavelet decomposing process is reasonable. Fig. 10. Effect of fluidization number on Kolmogorov entropy. Fig. 12. Comparison between original pressure signal and reconstructed pressure signal (t/800 8C, d p /0.85 mm, u/u mf /1.88).

8 446 Q. Guo et al. / Chemical Engineering and Processing 42 (2003) 439/ Conclusions The investigations of the minimum fluidization velocity and flow dynamics were performed in a bubbling fluidized bed at high temperature (up to C). With ashes of Geldart B type used as bed materials, the minimum fluidization velocity decreases with increasing bed temperature. Pressure fluctuation signals were analyzed by using PSDF analysis and chaos analysis as well as wavelet analysis. The major frequency of pressure fluctuation signals decreases with an increase in fluidization number, ranging from 1 to 4 Hz in the fluidized state. Calculations reveal that all the largest Lyapunov exponents of pressure signals are positive, indicating that a bubbling fluidized bed at high temperature is a deterministic chaos system. Furthermore, the correlation dimension and Kolmogorov entropy increase with increasing fluidization number, and then they vary little with fluidization number. By means of wavelet transform, the fluctuating pressure signals in a bubble column can be decomposed into its approximations and details at different resolutions. The number of peaks in the scale 6-detail signal represents the number of bubbles passing through pressure probe measurement region over the sampling time, which agrees with the major frequency obtained from PSDF analysis of pressure signals. Acknowledgements Dr Qingjie Guo gratefully acknowledges a research scholarship awarded by Alexander von Humboldt Foundation. During his stay in Germany, the great support from Professor J. Werther is greatly appreciated. Appendix A: Nomenclature A scale parameter A j approximation of multiresolution decomposition at resolution 2 j B transition parameter Dc correlation dimension D j detail of multiresolution decomposition at resolution 2 j /d p / average particle diameter (mm) d pi average particle diameter between successive sieves (mm) f m major frequency (Hz) K Kolmogorov entropy (bits/s) k segment number in time series L individual length of each segment n length of time series P bed pressure drop across the fluidized bed (Pa) P i instantaneous pressure (Pa) /p/ average pressure in a time series (Pa) P x power spectrum density function Re particle Reynolds number t i time (s) t temperature (8C) T cycle time (s) U normalized power in the window function W f (a, b) the wavelet coefficient W(n) window function X i weight fraction of particles x i (t i ) continuous signal x(t i ) original signal Greek letters D mean pressure fluctuation standard (Pa) l the largest Lyapunov exponent (bits/s) 8 mother wavelet r p particle density (kg/m 3 ) References [1] L.T. Fan, T.Ch. Ho, S. Hiraoka, W.P. Walawender, Pressure fluctuations in a fluidized bed, Am. Inst. Chem. Eng. J. 27 (1981) 388/396. [2] R.C. Lirag, H. Littman, Statistical study of pressure fluctuations in a fluidized bed, Am. Inst. Chem. Eng. Symp. Ser. 67 (1971) 116/122. [3] N. Yutani, T.C. Ho, L.T. Fan, W.P. Walawender, J.C. Song, Statistical study of the grid zone behavior in a shallow gas/solid fluidized bed using a mini-capacitance probe, Chem. Eng. Sci. 38 (1983) 38/45. [4] S.C. Saxena, N.S. Rao, Fluidization characteristics of gasfluidized beds: air and glass beads, Energy 14 (1989) 811/821. [5] D. Bai, H.T. Bi, J.R. Grace, Chaotic behavior of fluidized beds based on pressure and voidage fluctuations, Am. Inst. Chem. Eng. J. 43 (1997) 1357/1361. [6] D. Bai, J.R. Grace, J. Zhu, Characterization of gas fluidized beds of Group C, A and B particles based on pressure fluctuations, Can. J. Chem. Eng. 77 (1999) 319/324. [7] M. Van den Bleek, J.C. Schouten, Deterministic chaos: a new tool in fluidized bed design and operation, Chem. Eng. J. 53 (1993) 75/87. [8] D.V. Pence, D.E. Beasley, J.B. Riester, Deterministic chaotic behavior of heat transfer in gas fluidized beds, J. Heat Transfer 117 (1995) 465/472. [9] Z. He, W. Zhang, K. He, B. Chen, Modeling pressure fluctuations via correlation structure in a gas/solid fluidized bed, Am. Inst. Chem. Eng. J. 43 (1997) 1914/1920. [10] S.C. Saxena, N.S. Rao, S.J. Zhou, Fluidization characteristics of gas fluidized beds at elevated temperatures, Energy 15 (1990) 1001/1014. [11] S.C. Saxena, N.S. Rao, V.N. Tanjore, Diagnostic procedures for establishing the quality of fluidization of gas/solid systems, Exp. Therm. Fluid Sci. 6 (1993) 56/73. [12] K. Svoboda, J. Cermak, M. Hartman, K. Selucky, Pressure fluctuations in gas-fluidized beds at elevated temperatures, Ind. Eng. Chem. Process Des. Dev. 22 (1993) 514/520.

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