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Real time visualisation and analysis of dense phase powder conveying1
Powder Technology 102 Ž1999. 1–13
Real time visualisation and analysis of dense phase powder conveying K. Ostrowski, S.P. Luke ) , M.A. Bennett, R.A. Williams
1
2
Camborne School of Mines, UniÕersity of Exeter, Redruth, Cornwall TR15 3SE, UK Received 29 October 1997; accepted 30 July 1998
Abstract Investigation and control of flow phenomena in the pneumatic conveying of solids requires a detailed knowledge on the flow regimes and a number of phase flow properties. Electrical capacitance tomography ŽECT. is shown here to be a robust tool for this purpose, particularly when dense phase plug flow is to be monitored. The application of ECT to dense phase powder conveying in an experimental vacuum system is demonstrated and described, including the visualisation of slug size, shape and velocity. Measured gas and solid flow rates were also analysed in an attempt to ultimately provide a basis for comprehensive on-line analysis. A number of statistical estimators were selected and used in data processing, in order to distinguish between particular types of dense flow. The results show the potential for use of the method for the on-line control of dense phase pneumatic conveyors. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Real time visualisation; Dense phase; Powder conveying
1. Introduction Pneumatic conveying offers many advantages over other methods of granular solids transport, factors such as low routine maintenance and manpower costs, dust free transportation and flexible routing. The main disadvantage is the reliance upon empirical procedures for conveyer design, which often result in an unnecessarily high or variable wear rate and power consumption. In addition, product degradation and particle size separation can be major problems. Dense phase pneumatic conveying systems have the relative attributes of a low air requirement and hence energy demand, low pipeline erosion and low product degradation. However, the control requirements of such a transportation system are clearly far more acute in respect to the maintenance of flow regime and the prevention of blockage w1x. The flow regime within a pipeline, for a given particulate material, can often be controlled by variation of the air velocity. Although some constant feed applications require low velocity, continuous dense-phase operation, the major) Corresponding author. Tel.: q44-1209-714866; Fax: q44-1209612941 1 The authors are members of the Virtual Centre for Industrial Process Tomography. 2 E-mail: [email protected].
ity of industrial scale pneumatic conveyors would be expected to operate with discontinuous dense-phase flow regimes. This may take the form of discrete plugs of material, rolling dunes or a combination of the two. In reality, a pneumatic conveying system may simultaneously exhibit several flow regimes throughout its length. If unstable flow occurs, it can result in violent pressure surges which will increase both plant wear and product degradation problems. In addition, the identification of the flow regime at critical sections of the pneumatic conveyor is fundamental to any void fraction estimate, upon which many standard measurements Žsuch as solids mass flow rate. will depend. Assuming that the particulate material in question is suitable for pneumatic conveying, blocking within such systems is normally caused by insufficient air velocity. Once blockage has occurred, it can be extremely difficult to remedy. Cross-sectional imaging of the pipeline therefore offers potential benefits in both the control and fault monitoring of pneumatic conveying systems. 2. Electrical capacitance tomography measurements and data processing system 2.1. Capacitance tomographic imaging system Electrical Capacitance Tomography ŽECT. is gaining acceptance as an on-line tool to analyse multi-phase sys-
0032-5910r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 9 8 . 0 0 2 0 1 - 0
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K. Ostrowski et al.r Powder Technology 102 (1999) 1–13
Fig. 1. Principles of capacitance imaging.
tems such as powder conveying w2x, powder fluidisation w3,4x, trickle-bed reactors w5x and oilrwaterrgas transport w6,7x. An ECT system consists of three basic units ŽFig. 1.: the sensor, the electronic panel and the host computer supported by the set of transputers as described in detail elsewhere w8x. The sensor consists of a number of sensing and guard electrodes usually placed outside or embedded within an insulating pipe. The resolution of reconstructed image and speed of frame capture strongly depend on the number of electrodes. The electronic system provides fast Žca. 6600 measurements sy1 . and accurate measurements of the capacitances for the independent electrode connections. The host computer controls the measurement process and manipulates the captured data to obtain a reconstructed cross-sectional image using an appropriate algorithm w9x. For a typical single source electrode system, the number of distinct measurements obtained is equal to N Ž N y 1.r2 where N is the number of electrodes. The reconstructed image resolution is related to the number of independent interelectrode measurements while the speed of frame capture is inversely proportional to the number of such measurements. Thus, the ECT system designed for pneumatic conveying control and monitoring has a relatively low number of electrodes Ž N s 6, 8 or 12.. The ECT system ŽProcess Tomography, Wilmslow. used here had a 12-electrode sensor and provides a data capture rate equal to about 100 frames sy1 with a resolution equal to ca. 5% Ži.e., the size of the target object should be at least 5% of pipe diameter. if its boundary is to be discerned distinctly. This is, however, assuming that there is a sufficiently large difference in dielectric constant between the object and the surrounding medium. Thus, such a system is particularly suitable for monitoring large-scale perturbations with a significant permittivity difference between phases, like the powder slugs passing through the sensor. Yang et al. w7x have discussed some critical features associated with the design of the hardware within an ECT
system, including the type of the measuring circuit: the need for high measurement resolution Žca. 0.3 f F., low noise level Žrms - 0.1 f F., low baseline drift but a wide dynamic range of measurement Žfrom 0.3 f F up to 2000 f F.. In the present paper, the practical consequences and performance of using a state-of-the-art ECT system to monitor a dense phase powder conveying system are considered. Image reconstruction algorithms used in ECT can be divided into three main groups based on methods involving linear back-projection ŽLBP. w9,10x, iterative solutions and neutral network w11x. The LBP algorithm is the simplest and the fastest method and was consequently chosen for the described experimentation, since these factors are essential in the monitoring of fast perturbations. The LBP algorithm is based on obtaining a priori capacitance sensitivity distribution maps for all possible single-electrode combinations and all pixels. The presently used software formats a single image into 1024 square pixels based on 32 = 32 Cartesian mesh. The total number of pixels placed into the sensing region is 814. Consequently, the size of each pixel is 3.15% of the inner diameter ŽID. of the sensor, which for a 12-electrode sensor gives approximately twice the resolution of the electronic system. Thus, each frame of captured data, reconstructed from 66 distinct measurements between electrodes, consists of 814 normalised dielectric constant values which represent phase distribution in the sensing region. These data may be used in further statistical and stochastical analysis. 2.2. Sensor design method The following section is intended to provide concise information on the ECT sensor used in present experimentation and the design method relating to the selection of the sensing electrode dimensions. The set of initial parameters which are taken into account consist of: D 1 , D 2 , N, ´ MIN ´ MAX and ´ PL Žsee Figs. 1 and 2 for details. which denote the pipe ID and OD, maximum and minimum dielectric constants of the phases to be monitored and pipe
Fig. 2. Cross-section of ECT sensor used in present experiment.
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liner permittivity. These parameters may be reduced to four nondimensional values, e.g., D 1rD 2 , N, ´ MIN r´ MAX and ´ PL r´ MAX . Over the past decade w2–9x, the general assembly of ECT sensors Žsizes and mounting details of the radial and guard electrodes and of the outer screen. has been developed and verified experimentally Žthey are difficult to calculate.. The basic design task reduces to the selection of two parameters: Ø the sensing electrode axial length, L, Ø the angle of the gap between sensing electrodes, a G Žor the gap width for given D 2 .. Since the range of capacitance measured by the sensor is approximately determined by the sensor calibration data, it is reasonable to consider the case when the sensing region is filled with homogeneous media having a varying dielectric constant. Then, the number of independent capacitance measurements, nominally quoted as N Ž N y 1.r2, may be reduced to Nr2, where N represents the number of electrodes. For a 12-electrode system, the six principal measurements may be exemplified by the capacitance values associated with electrode combination 1–2, 1–3, . . . ,1–7. Thus, the subject of analysis is the set of six capacitances C1J for given ´ and the set of six capacitance changes DC1J due to a change in ´ . These values should obey the following conditions: Ø DC1J should be relatively large, to provide good measurement resolution, but maximum value of C1J should not exceed ca. 2 pF to avoid the electronic system saturation w12x; Ø DC1J values should be relatively uniform, i.e., the ratio of minimum to maximum values should not be too small; Ø There should be a functional dependence of ´ Ž C1J ., i.e., each value of capacitance should correspond with one unique dielectric constant value; Ø The above dependence should be close to linear and also should be stable, i.e., small changes in DC1J should yield small changes of ´ . Since only two parameters can be adjusted, it is difficult to fulfil these four conditions exactly. However, for the gas–solid flows considered here, the variation in dielectric constant between phases does not exceed a factor of two or three. For such moderate values, the deflection of the electrostatic field due to the presence of the wall Žanalogous to the so-called ‘soft field’ problem. is small. Thus, in gas–solid systems, contrary to gas–liquid systems, the two last conditions are fulfilled almost automatically. Since the use of driven Žnot grounded. guard electrodes is used, the electrostatic field existing in the sensing area filled with homogeneous medium is close to the 2-dimensional field. To simulate it, the procedure presented by Ostrowski et al. w13x has been applied. This method, based on the conjugate harmonics application, solves the Laplace equation in two domains: the sensing region consisting of the wall of the pipe having the dielectric constant equal to ´ PL , and the pipe interior having arbitrary, but constant
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dielectric constant, ´ . Dirichlet boundary conditions were imposed on the electrodes and gap surfaces and conditions of the second kind w13x were imposed on the inner wall interface. The known distribution of stream Žcurrent. function over the electrode contour returns the straightforward method of the electrode capacitance calculation being linearly related to the stream Žcurrent. increment D c J between its two-edge points: C1J s
´ O ´ PL L V
D cJ ,
Ž 1.
where V is the voltage difference between the source and the detecting electrodes. Since the solution may be easily normalised, an algorithm can be deduced, which calculates the values of C1J and DC1J for a given set of initial parameters: D 1rD 2 , N, ´ MIN r´ MAX , ´ PLr´ MAX and ´ PL for a unit axial length of the sensing electrode. This procedure was adopted to assess the required sensor geometry for the conveying application as discussed below. In the present experiment, the ECT sensor was placed on the horizontal pipe for which D 1 s 52 mm and D 2 s 60 mm Žsee Section 3 for details.. The pipe liner permittivity was equal to ca. 2.5. The values of ´ MIN and ´ MAX correspond with 1 Žair. and about 2.4 Ždielectric constant of solid packed bed.. Experimental evaluation of several differing sensor configurations eventually led to the axial length of sensing electrode, L, and the gap width being selected as 100 and 2 mm, respectively. Generally, the capacitance increment is directly proportional to L Ž2-dimensional approach., while the influence of the electrode gap size is more significant for measurements between adjacent electrodes. Since the value of ´ MA X is, by necessity, a mean nominal value, calculations have been performed for three values of ´ MA X Ž2.2, 2.4 and 2.6. to check the stability of the results obtained. Table 1a, b, c presents the calculated values of C1J and DC1J for selected ´ MIN and ´ MAX . It should be pointed out that these data provide only a partial measurement of capacitance resulting from the ‘inner’ electrostatic field interaction. The total capacitance is larger because of additional effects such as the capacitance of the connection leads. Since these effects, however, may be assumed to be constant Ži.e., independent of the dielectric constant of the sensed medium. the DC1J values return the trial estimation of the range of expected capacitance increments. The results in Table 1 indicate satisfactory stability within this range of ´ MA X . The maximum change of DC1J is close to 20 fF Žpair 1–2. and maximum relative change Žpair 1–7. is no greater then 40%. It was therefore concluded that the proposed sensor dimensions were appropriate for the intended powder conveying application. To make the sensor movable along and around the pipe, the radial guard electrodes were not inserted into a pipe wall but their edges were placed on its outer surface. Sensing and driven electrodes were made from 50-mmthick copper foil, cut to a length of 100 and 40 mm,
K. Ostrowski et al.r Powder Technology 102 (1999) 1–13
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Table 1 Theoretical predictions of calibration data of the ECT sensor designed for present measurements; ´ PL s 2.5, ´ MIN s1.0 and ´ MAX Žsolid bulk permitivitty. s 2.2 Ža., 2.4 Žb. and 2.6 Žc.
Ø slug frequency and distribution, Ø correlation analysis of the above parameters.
Ža. Electrode number
Minimum capacitance wpFx
Maximum capacitance wpFx
Capacitance increment wpFx
1–2 1–3 1–4 1–5 1–6 1–7
1.638 0.088 0.037 0.024 0.019 0.017
1.737 0.172 0.079 0.051 0.041 0.038
0.098 0.084 0.042 0.027 0.022 0.020
1.638 0.088 0.037 0.024 0.019 0.017
1.747 0.184 0.085 0.056 0.044 0.041
0.109 0.096 0.048 0.032 0.026 0.024
1.638 0.088 0.037 0.024 0.019 0.017
1.756 0.196 0.092 0.060 0.048 0.044
0.118 0.108 0.055 0.036 0.029 0.027
Žb. 1–2 1–3 1–4 1–5 1–6 1–7 Žc. 1–2 1–3 1–4 1–5 1–6 1–7
respectively. The cylindrical outer screen, of 76-mm diameter was fabricated from 0.5-mm-thick copper sheet. 2.3. Visualisation and analysis of tomograms The captured images were reconstructed as described earlier. Image files were then transferred to a workstation for rendering in the form of a three-dimensional animation movie. For this purpose, the AVS software visualisation package was adopted as a standard. Hence, bursts of individual tomographic images could be stacked together to form a three-dimensional image against time. The information can be stored in this form and subsequently viewed in any orientation, e.g., useful two-dimensional isocontour slices can be taken in radial or axial directions. Movies viewed from inside or outside the pipe can be generated. Reconstructed images can be time-gated to enable quantitative analysis. In the context of this paper, individual images were used to deduce: Ø the average volume occupied by solids, Ø the height of the solidrgas interface Žif present., and sequences of images were used to extract Žin combination with calibration measurements using a video, see Section 3.2.: Ø slug length and distribution of slug lengths, Ø slug velocity and velocity distribution,
3. Conveying plant 3.1. General description The experimental vacuum conveying system is shown in Fig. 3. The system was designed to enable different types of powder flows to be generated in a controlled and repeatable manner. It is a closed loop system for solids and an open system for air. Solids sucked from solid tank are transferred through an standpipe 11 m in length and stored in the vacuum conveyor. Induced air is pushed through a filter and removed by the vacuum pump to atmosphere. Vacuum is achieved by using a multistage injector ŽPIAB, MLL 800 model w14x., driven by air supplied from compressor. For an air pressure in the pump inlet section equal to ca. 0.5 MPa, the possible pressure vacuum and maximum induced air flow rate are 80 kPa and 0.1 N m3 sy1 , respectively. These parameters are sufficient to generate a wide range of flow patterns, from dense slug flow up to dilute, fast flow with low solids concentration. In order to facilitate visual observations of the flow regime, a 3-m-long horizontal test section was made from transparent pipe ŽExcelon R-4000, 60 mm OD and 52 mm ID.. The rest of the pipeline was made from transparent or opaque PVC, except for two stainless steel bends used to minimise pipe wall attrition. The height difference between the bottom and upper horizontal sections of the standpipe is approximately 2.7 m. The experimental system is controlled using eleven valves, allowing adjustment of the flow parameters which correspond to particular flow regimes. The valves numbered from V1 to V6 ŽFig. 3. are Georg-Fisher w15x electrically actuated units, thus may be operated automatically. The functions of particular valves are listed briefly below, since an understanding of their operation shows how the manipulation of combinations of these valves can be used to produce differing flow regimes. Ø V1—main air inlet valve, may be actuated with different frequencies to obtain various slug patterns; Ø V2—butterfly valve dividing the vacuum conveyor and solid tank; when all the solids are transferred through the standpipe, this valve is opened to discharge vacuum conveyor, otherwise, it remains closed during the plant operation; Ø V3, V4—auxiliary valves to cut off the system from vacuum pump and equalise the pressures in vacuum conveyor and solids tank; Ø V5–injection valve to remove a solid plug from vertical part of pipeline Žsuitable for solids of low fluidity., to feed the system with solids and to generate additional pressure pulses if necessary;
K. Ostrowski et al.r Powder Technology 102 (1999) 1–13
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Fig. 3. Schematic diagram of an experimental vacuum conveying system and data acquisition equipment.
Ø V6, V9—valves controlling auxiliary bypass which enable the supply of compressed air directly to the solids tank Žsuitable for solids of low fluidity.; Ø V7, V8—ball and needle throating valves which control air flow rate; Ø V10—compressed air cut-off or throating valve; Ø V11—outlet valve to drain water from compressed air pipeline. As mentioned, the conveying plant flow parameters are adjusted mainly by valves V1, V7, and V8. If necessary, the auxiliary valves V5 and V10 may be used for this purpose Žthe latter valve to change the vacuum pump characteristics., while valves V2, V3 and V4 control the discharging process after solids transfer is completed. Since the conveying plant has been designed to examine the flow of different types of powders or plastic pellets, the plug valve ŽPV, Fig. 3. has been mounted at the solids inlet to adjust its cross-section.
section through valve V1 while the second is supplied to the top of solid tank and then drawn through the packed bed of solids within the hopper. The ratio of both streams depends on the valve V1 adjustment, on the height of solid bed in the holding tank and also on the type of particulates. The instantaneous value of total volumetric flow rate is obtained by measurements of pressure drop caused by the OPF restriction and absolute pressure to calculate the fluid density in the orifice plate assembly. These values are provided by two strain gauge pressure transducers P1 and P2 having ranges 2 kPa and 0.1 MPa, respectively. In order to cover as wide as possible a range of air flow rates, a set of four orifice plates have been fabricated with diameters of the orifice openings equal to 4, 6.2, 7.1 and 12 mm. These correspond to air flow rates equal to approximately 0.5, 1.2, 2, 5 N m3 sy1 obtained for the maximum pressure drop equal to 2 kPa. Then the air volumetric flow rate could be calculated following the known relationship:
3.2. Measurement procedure
'
QA s g A P 2 D prr , In addition to the data supplied by ECT system, two other parameters, the gas and the solid flow rates, were measured. Atmospheric air enters system through valves V7, V8 and then is drawn through an orifice plate flowmeter ŽOPF.. The air stream leaving the orifice plate flowmeter is subsequently split. One stream is directed to the inlet
Ž 2.
where QA , g , A P , D p and r are the volumetric flow rate Žat conditions in the orifice plate assembly., the discharge coefficient Žbeing a function of Reynolds number and specific geometry., the area of the orifice opening, the
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K. Ostrowski et al.r Powder Technology 102 (1999) 1–13
pressure drop and the air density. Since departures from standard geometry and installation Že.g., British Standard 1042. were unavoidable the empirical discharge coefficients were unknown. Calibration of the system was therefore required for each orifice plate. To obtain appropriate values at any other position in the standpipe or at normal conditions ŽNTP., it is necessary to calculate the actual value of air density. Air pressure reduction along the length of the pipeline, i.e., gradual decompression of the transportation media, will result in a corresponding increase in both gas velocity and volumetric flow rate. This phenomenon greatly affects the slug shapes and velocities along the length of the pipeline. Because of this effect, the slugs which enter the vacuum conveyor and cause changes of the load cell signal are different from those which were observed and monitored in the test section. This effect strongly depends on flow pattern. It has been found that for slow slug flow Žsee Section 4.1 for details. the total pressure drop in the standpipe is equal to 0.03–0.04 MPa. Thus, the outlet volumetric air flow rate is about 1.4–1.7 of its inlet value. The direct influence of this increment on slugs shape and velocity is difficult to estimate because of significant slug dispersion Žparticularly in the vertical part of pipeline. and air filtering through the slugs Žsee Section 4.1.. It has been observed however that the slugs in the upper horizontal section travel at a much higher velocity than those passing through the test section. The mass flow rate of material was estimated by means of the changes of vacuum conveyor mass measurements with time. The vacuum conveyor was suspended elastically with a Kulite strain gauge load cell ŽLC. placed at the top point of its frame, and supported at two other points. Since the vacuum conveyor was attached to the solid tank with flexible rubber bellows, calibration of the load cell and associated signal conditioning circuitry was relatively straightforward. However, minor correction of this was necessary because of an additional suction force resulting from the resistance to air flow through the solids tank. This suction force was monitored by a second pressure transducer ŽP2. and correction was achieved by multiplying the signal from this transducer by the solid tank cross-section and then subtracting the result from the total force registered by the load cell. All three analogue signals were sampled and digitised in the 12-bit analogue–digital converter and fed into a personal computer for further data processing. The sampling frequency was selected as 500 Hz. This value greatly exceeds the typical slug frequency being 0–10 sy1 and consequently the Nyquist frequency based on the slug movement observations. The reason for such a high value, however, was the registration of rapid changes of pressure drop during the slug generation process. In the present experiment, Maranyl nylon plastic pellets were used as solid phase having the following properties as specified by the manufacturer: Ø bulk densitys 750 kg my3 ,
Ø solid densitys 1120 kg my3 , Ø lengths 2–3 mm, Ø aspect ratio s 1–2. For this medium, the maximum mass transferred during a rig single run, before the charge in the solid tank ŽFigs. 2 and 3. was exhausted, was approximately 25 kg. The time needed for complete discharge strongly depended on the flow regime and varied from about 30 s for dilute flow conditions up to 100 s for the dense, slug flow pattern. A significant transient of several seconds was observed, when running the conveying system from an empty pipeline situation, before quasi-periodic Žfor slug flow. or steadystate Žfor dilute flow. conditions were achieved for all observed flow regimes. After this period the data capture system was initiated, providing the time series of data for a duration of 15–20 s. Thus the lengths of the collected digital signals varied from 7500 up to 10 000 data points, although where necessary this raw data was truncated for signal processing purposes. A video camera positioned both upstream and downstream of the tomographic sensor was used to verify the tomographic images and the analogue signals which were fed into the PC. In this way, the video camera film enabled the transfer of time coordinate into the equivalent spatial domain. The camera provided 125 frames sy1 , since the initial moments for all records have been synchronised, so it was possible to compare all recorded data with the corresponding slugs position in the test section. In particular, the slug length and velocity could be estimated, providing data verification of the ECT measurements. The experimental data obtained from the experimental conveying plant consist of three main types: Ø the set of images captured by ECT system with a capture rate of approximately 100 frames sy1 ; Ø the three analogue signals, to calculate the phase flow rates, with sampling frequency of 500 Hz; Ø the video film to estimate slug length, shape and velocity. 3.3. Data acquisition and control system The pneumatic conveyor was controlled by a PC running Windows software based on Labview. This is a program development application based on a graphical programming language Ž‘G’.. It is commonly used in data acquisition and control for creating a virtual instrument, which operates like any other instrument with numeric and graphical controls and indicators, except they are virtual in the host computer. The software regulates a data acquisition and control board ŽLABPCq .. The control PC is capable in total of outputting 24 bits of digital information or receiving 24 bits of digital information Ž0–5V., but not simultaneously in time. It is also capable of accepting four analogue input signals and outputting one analogue signal. The board was configured so that the Labview software interfaced with 12
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bits of digital output to the interfacing electronics, 12 lines of digital input from the interfacing electronics, four wires carrying analogue input and one line carrying analogue output Žnot used. at present. 4. On-line measurement results 4.1. Flow characterisation The vacuum experimental system described in Section 3.1 may operate in two general modes: one under control in which the powder slugs are generated automatically, and the other in which additional pressure pulses may be supplied to the system Že.g., by closing and opening some valves periodically.. In this case, it is possible to adjust some of the slug characteristics by manual or sequenced perturbations. Results from operating under automatic slug generation will form the basis of discussion within this paper, for which the following factors are important: Ø the characteristics of pneumatic source driving the conveyor, Ø the geometry of the system, Ø the adjustment of the set of operating valves, Ø the solid phase properties. If the solid phase is coarse enough Ži.e., the air gaps between the pellets are not very small., it is possible to obtain significant air flow through the packed bed and also through the slugs. In this case, the air averaged velocity is larger than that of solids. Thus, behaviour may be subdivided into two different types, defined as follows: Ža. Air is supplied together with solids through the common inlet from solid tank, thus valve V1 ŽFig. 3. is closed. Žb. Valve V1 is opened, thus the bulk of air is supplied through the separate inlet. Both methods enable the observation of dense, slug flow regimes having apparently similar flow parameters. Table 2 presents the set of phases flow rates and their superficial velocities. It is evident that the differences between type Ža. Žlabelled record number 1 in the table. and Žb. Žrecord numbers 2–7. are not significant as far as these basic flow parameters are concerned. However, a
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number of very different flow features are evident between the two types of behaviour. Fig. 4 shows examples of averaged values of the normalised dielectric constant in the sensing region registered by the ECT system. Fig. 5 indicates the air flow rate profiles Ž Q . against time for the corresponding data sets. System adjustment allowing operation in Ža. provides a flow pattern which may be considered as slow, slug flow ŽFigs. 4a and 5a.. It is characterised by long and slow slugs generated with relatively regular frequency. Since the low velocities of solids are compensated by higher averaged volume fraction Žsimulated by the mean value of ² ´ N : in Table 3., the solid mass flow rate, as well as solid superficial velocity may be approximately the same as for Žb. ŽFigs. 4b–d and 5b–d.. The latter generates a fast slug flow regime. It is evident that perturbations are shorter and more irregular. Moreover, the minimum solid level is also a random parameter and may vary widely during the time of data capture. Because of this effect, the definition of the ‘slug’ is of necessity arbitrary. Generally, the fast slug flow represents more disordered structure than the slow slug flow. In order to show the differences between both slug flow patterns more clearly, it is useful to calculate and plot some basic stochastic estimators. Fig. 6 shows examples of autocorrelation functions calculated for both types of flow, from which it is apparent that flow phenomena occur at different length scales being larger for slow slug flow by about one order of magnitude. Thus, calculation of autocorrelation is a simple, effective and robust tool to distinguish between particular dense flow patterns. If the slug frequencies are to be considered, it is more suitable to calculate power spectral density of the signal. Since spectral leakage is generally present, it is common practice to taper the original signal Ž² ´ N : in Fig. 4. before transformation, reducing any discontinuities at its edges. Many different windows have been recommended for this purpose. Window selection depends on the nature of the signal and on the type of information to be extracted from its spectrum. In the present analysis, it was essential to select one type of window for all signals assuming that the type of flow pattern is unknown a priori, so this information should result from previously completed calculations. The Parzen, Hanning, Hamming and Welch
Table 2 Flow parameters for seven different modes Žrecords. of operation of a pilot-plant for dense phase pneumatic conveying considered in present analysis No. of record
Air flow rate a wm3 sy1 x = 10 3
Air superficial velocity a wm sy1 x
Solid flow rate wkg hy1 x
Solid superficial velocity wm sy1 x
1 2 3 4 5 6 7
0.89 0.48 0.70 0.79 0.87 0.89 0.93
0.42 0.23 0.33 0.37 0.41 0.42 0.44
1370 1210 1320 1370 1410 1440 1480
0.16 0.14 0.15 0.16 0.16 0.17 0.17
a
The given values refer to normal conditions ŽNTP..
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Fig. 4. Registered averaged in ECT sensor volume value of normalised constant ² ´ N : as powder slugs pass through the sensor vs. time wsx, for flow conditions corresponding with Table 2 ŽŽa. No. 1, Žb. No. 2, Žc. No. 5 and Žd. No. 7.. Tomographic visualizations of the powder slugs are shown beneath each graph for the time increment indicated by the arrow.
windows were taken into account Žsee, e.g., Ref. w16x for details.. From these, the Hanning window was chosen as the best in this sense that returns a narrow main spectral lobe to prevent ‘local’ spreading of the spectrum, and also low side-lobe levels to reduce ‘distant’ spectral leakage Žit should be pointed out that usually these two requirements are in conflict.. The examples of power spectrum densities calculated using above data tapering and then Fast Fourier Transform are shown in Fig. 7. Slow slug flow is characterised by small power spread with distinctive strong peak at about 0.3 Hz. Frequency components above 1 Hz may be neglected. Fast slug flow represents the wider spread, up to 3 Hz, with a few maximas. All power spectral densities calculated for this flow regime Žnot shown in the paper. are similar to each other and there is no clear dependence
of their shape on the phase flow rates within the test ranges utilised during present experimentation. Generally, it should be pointed out that the fast and slow notation of flow regimes are rather qualitative and used to distinguish between two types of phenomena, presently under consideration, which are however fundamentally slow. In fact, the rate of frame capture provided by ECT system Žsee Section 2.1. of about 100 sy1 exceeds many times the Nyquist frequency that is required for the accurate observation of ² ´ N :Ž t . signals. On the other hand, a total data capture time of 18 s Ž1800 data points in discrete series., enables the capture of images corresponding to 5–10 slugs passing through the sensor. Since the signals shown in Fig. 4 suggest the ² ´ N : distributions are close to bimodal Ži.e., representing the minimum and maximum solid levels., the histogram esti-
K. Ostrowski et al.r Powder Technology 102 (1999) 1–13
mators were calculated as an initial statistical test. The associated bar-graphs are shown in Fig. 8. The range of ² ´ N :, which lies within the range ²0, 1:, was subdivided into one hundred quantisation levels. It is seen that slow flow represents more symmetrical distribution than the fast flow. For the former, the maximum probability occurs from relatively high values of ² ´ N :, while from the latter, low solid levels are more probable. In Table 3, the mean value, standard deviation and median for all, seven recorded ² ´ N :Ž t . signals are presented. It is clear from this data, that standard deviation it is not a robust tool for distinguishing between the two types of slug flows Žall values are close to each other.. More promising indicators are the mean value and, particularly, the median. It is possible to extend the number of estimators and include, e.g., higher order moments: skewness and kurtosis as the additional tests. It has been found, however, that neither provide a clearer method of flow pattern recogni-
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Table 3 The basic statistical estimators of averaged dielectric constant signals ² ´ N :Žt. for seven records having flow parameters presented in Table 2 No. of record
Mean value of ² ´ N :
Standard deviation of ² ´ N :
Median of ² ´ N :
1 2 3 4 5 6 7
0.51 0.17 0.17 0.20 0.18 0.17 0.24
0.26 0.24 0.23 0.23 0.24 0.23 0.24
0.53 0.06 0.08 0.13 0.12 0.06 0.10
tion and, because of that, they have not been deployed in this analysis. 4.2. Slug size and shape The design of pneumatic conveying systems is notoriously difficult. The fragility of an apparently viable design
Fig. 5. Registered air flow rates Q wlrsx Žunder NTP conditions. plotted vs. time wsx. Flow parameters correspond with the numbers in Table 2: Ža. No. 1, Žb. No. 2, Žc. No. 5 and Žd. No. 7.
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Fig. 6. Comparison of autocorrelation functions of ² ´ N :Ž t . signals for slow slug flow ŽNo. 1., left, with fast slug flow ŽNo. 5., right.
has often been shown by relatively minor rerouting of the pipeline, a change in material to be transported, or natural variations in environmental conditions Žparticularly humidity.. In virtually all industrial situations, plugging of the conveying pipeline must be avoided. The conveying properties of some particulate materials are predictable and repeatable, in which case, provided the pipeline diameter, the air volume and the conveying capacity have been correctly selected, pneumatic conveying can be performed in a stable range without a tendency to plug. Other materials, particularly those which have been ground to very fine powders, or are brittle or ‘sticky’ by nature, tend to plug very easily. A well-established technique for dealing with these materials is to use a secondary air valve, which is opened intermittently, in order to artificially produce discrete moving slugs of a manageable length. Clearly, under these circumstances, the ability to visualise on-line, the size and shape of individual slugs would form an invaluable tool in terms of: Ø determination of the conveying properties of sample materials, through standard test sections;
Ø the commissioning of industrial systems designed by standard empirical methods; Ø the adaptive control of the secondary air valve. On-line visualisation of powder flow is now possible for different flow conditions, by means of time-stacking ECT cross-sectional images. Fig. 9 shows such a pseudo three-dimensional image obtained from the experimental rig described in Section 3. This serves to demonstrate how ECT can be used to visualise the size and shape of plugs, which is a valuable tool for process diagnosis and in the validation and development of fundamental slug-flow models. 4.3. Implication for on-line process control It has already been illustrated how the ECT data together with additional standard measurements provides the possibility of flow regime identification by analysing a number of statistical estimators. So far, this analysis has been performed off-line and could be easily enhanced by
Fig. 7. Comparison of power spectral densities of ² ´ N :Ž t . signals forslow slug flow ŽNo. 1., left, with fast slug flow ŽNo. 5., right.
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Fig. 8. Comparison of ² ´ N :Ž t . signals histograms for slow slug flow ŽNo. 1., left, with fast slug flow ŽNo. 5., right.
increasing the number of statistical tests applied to the data set. However, the constraints imposed by the need to progress to on-line analysis are somewhat more rigorous, since it is necessary to carefully select the estimators to be used to fulfil two basic requirements: Ø These estimators should be robust, i.e., should provide enough information to the control system to make up decision by a simple set of logical operations. Ø The number of estimators as well as time needed to complete their calculations have to be limited since the answer of the control system should be fast. It is difficult to precisely quantify the above constraints, since these are not only dependent on the action of a particular control system, but also on the parameters of the pneumatic conveying system itself. With respect to dense phase conveying, a typical control system should realise following main functions: Ø The phase velocities should be kept low to avoid significant attrition, but
Ø These velocities should not be too low to avoid choking of the standpipe, also Ø The supplied mechanical energy per unit mass of transferred solid should be minimised. The comprehensive analysis of such control systems and a general set of data used within them, is beyond the scope of this paper. However, we will suggest two simple estimators which can be used if control is based on the data obtained from ECT system only. Adjustment of the individual phase velocities is in effect equivalent to an adjustment of the flow regime. The boundaries between particular regimes are of necessity arbitrary. According to results presented in Section 4.1, however, it is possible to direct the simple system towards two main aims: Ø to distinguish between slug Ždense. flow and other flow patterns which are expected to occur Ždilute flow, stratified flow, dune flow.; and Ø to distinguish between slow Žvery dense. slug flow and fast Žless dense. slug flow.
Fig. 9. Three-dimensional visualisation of slug traveling at approximately 0.25 m sy1 .
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Assuming that the time required to complete these flow recognition is too short to calculate and analyse autocorrelations, power spectra or histograms the selection of estimators should be based on only a few values obtained. The data presented in Table 3 suggest one of several possible solutions, viz.: Condition A: Calculate the standard deviation of the ² ´ N :Ž t . signal Žits length depends on particular requirements. and follow the instruction: If standard deviation) critical value A, then slug flow occurs, otherwise there is another Ždilute flow, stratified flow, dune flow. flow pattern in the standpipe. Condition B: Calculate the median of the ² ´ N :Ž t . signal and follow the instruction: If median) critical value B, then slow slug flow occurs, Žotherwise fast slug flow.. The nature of selected signals resulting from the final response depends on the pneumatic system parameters and its equipment. Also, the values of critical values A and B above strongly depend on the geometry of the system and type of the transferred solids thus should be selected in each, individual case.
Voltage Time
Greek
aG g D ´ ´0 ´ MA X ´ MIN ´N ²´ N : ´ PL r C
Gap angle ŽFig. 2. Discharge coefficient ŽEq. Ž2.. Increment or difference Dielectric constant Permittivity of free space, 8.85 = 10y1 2 F my1 Maximum dielectric constant Minimum dielectric constant Normalised dielectric constant Normalised dielectric constant averaged spatially in the sensing region Pipe liner dielectric constant Air density Stream Žcurrent. function
Subscripts I J
Source electrode Detecting electrode
Acknowledgements
5. Conclusions The visualisation capability of ECT systems shows great potential for both increasing our understanding the flow dynamics of particulate, and in the further development of empirical design methodologies for the conveying systems themselves. In addition, the use of statistical analysis of the pixel values within ECT images would appear to be a reliable method for the identification of both slow and fast slug flow regimes within dense phase conveying. This strategy can be incorporated as part of a control scheme for industrial conveyors to enable their efficient operation for various feedstocks, under conditions where attrition or power consumption can be minimised.
6. Nomenclature A AP C D D1 D2 D3 fS L N p Re Q
V t
Area of cross-section Area of the orifice opening ŽEq. Ž2.. Capacitance Diameter Pipe ID Pipe OD Diameter of outer shield ŽFig. 2. Frequency of capacitance measurements Length of sensing electrode Number of electrodes Pressure Reynolds number Air flow rate
The authors acknowledge financial support from the CSM Trust and the Engineering and Physical Science Research Council.
References w1x G.E. Klinzing, R.D. Marcus, F. Rizk, L.S. Leung, Pneumatic Conveying of Solids—A Theoretical and Practical Approach, 2nd edn., Chapman & Hall, 1997. w2x S.L. McKee, R.A. Williams, T. Dyakowski, T. Bell, T. Allen, Solid flow imaging and attrition studies in a pneumatic conveyor, Powder Technology 82 Ž1995. 105–113. w3x S.J. Wang, T. Dyakowski, C.G. Xie, R.A. Williams, M.S. Beck, Real time capacitance imaging of bubble formation at the distributor of a fluidized bed, Chem. Eng. J. 56 Ž1995. 95–100. w4x T. Dyakowski, R.B. Edwards, C.G. Xie, R.A. Williams, Application of capacitance tomography to gas–solid flows, Chem. Eng. Sci. 52 Ž13. Ž1997. 2099–2110. w5x N. Reiecke, D. Mewes, Investigation of the two-phase flow in trickle-bed reactors using capacitance tomography, Chem. Eng. Sci. 52 Ž13. Ž1997. 2111–2127. w6x C.G. Xie, N. Reinecke, M.S. Beck, R.A. Williams, Electric tomography techniques for process engineering applications, in: M.S. Beck et al. ŽEds.., Process Tomography—A Strategy for Industrial Exploitation, UMISTrECAPTrEU Brite Euram, Manchester, 1994, pp. 25–32. w7x W.Q. Yang, M.S. Beck, M. Byars M, Electrical capacitance tomography—from design to applications, Meas. Control 28 Ž1995. 261– 266. w8x R.A. Williams, M.S. Beck Žed.., Process Tomography—Principles, Techniques and Applications, Butterworth-Heinemann, Oxford, 1995. w9x C.G. Xie, S.M. Huang, B.S. Hoyle, R. Thorn, C. Lenn, D. Snowden
K. Ostrowski et al.r Powder Technology 102 (1999) 1–13 D, M.S. Beck, Electrical capacitance tomography for flow imaging: system model for development of image reconstruction algorithms and design of primary sensors, IEE Proc. I 139 Ž1992. 89–98. w10x P.J. Oakley, M.S. Bair, A low cost quantitative reconstruction algorithm for ECT and EIT, in: M.S. Beck et al. ŽEds.., Process Tomography—Implementation for Industrial Processes, UMISTr ECAPTrEU, Manchester, 1995, pp. 393–400. w11x W.Q. Yang, J.C. Gamio, M.S. Beck, A fast iterative image reconstruction algorithm for capacitance tomography, Žaccepted by Sensors and their Applications VIII, 7–10 Sept., 1997, Glasgow, UK..
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w12x M. Byars, Process Tomography, Cheshire, personal communication, 1996. w13x K.L. Ostrowski, S.P. Luke, R.A. Williams, Application of conjugate harmonics to electrical process tomography, Meas. Sci. Technol. 7 Ž1996. 316–324. w14x Vacuum Conveying—PIAB Catalogue No. 2, 1994. w15x Instruction Manual, Georg-Fischer Rohrleitungssysteme, 1994. w16x W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Verrerling, Numerical Recipes—The Art of Scientific Computing, Cambridge Univ. Press, Cambridge, 1986.
Real time visualisation and analysis of dense phase powder conveying K. Ostrowski, S.P. Luke ) , M.A. Bennett, R.A. Williams
1
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Camborne School of Mines, UniÕersity of Exeter, Redruth, Cornwall TR15 3SE, UK Received 29 October 1997; accepted 30 July 1998
Abstract Investigation and control of flow phenomena in the pneumatic conveying of solids requires a detailed knowledge on the flow regimes and a number of phase flow properties. Electrical capacitance tomography ŽECT. is shown here to be a robust tool for this purpose, particularly when dense phase plug flow is to be monitored. The application of ECT to dense phase powder conveying in an experimental vacuum system is demonstrated and described, including the visualisation of slug size, shape and velocity. Measured gas and solid flow rates were also analysed in an attempt to ultimately provide a basis for comprehensive on-line analysis. A number of statistical estimators were selected and used in data processing, in order to distinguish between particular types of dense flow. The results show the potential for use of the method for the on-line control of dense phase pneumatic conveyors. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Real time visualisation; Dense phase; Powder conveying
1. Introduction Pneumatic conveying offers many advantages over other methods of granular solids transport, factors such as low routine maintenance and manpower costs, dust free transportation and flexible routing. The main disadvantage is the reliance upon empirical procedures for conveyer design, which often result in an unnecessarily high or variable wear rate and power consumption. In addition, product degradation and particle size separation can be major problems. Dense phase pneumatic conveying systems have the relative attributes of a low air requirement and hence energy demand, low pipeline erosion and low product degradation. However, the control requirements of such a transportation system are clearly far more acute in respect to the maintenance of flow regime and the prevention of blockage w1x. The flow regime within a pipeline, for a given particulate material, can often be controlled by variation of the air velocity. Although some constant feed applications require low velocity, continuous dense-phase operation, the major) Corresponding author. Tel.: q44-1209-714866; Fax: q44-1209612941 1 The authors are members of the Virtual Centre for Industrial Process Tomography. 2 E-mail: [email protected].
ity of industrial scale pneumatic conveyors would be expected to operate with discontinuous dense-phase flow regimes. This may take the form of discrete plugs of material, rolling dunes or a combination of the two. In reality, a pneumatic conveying system may simultaneously exhibit several flow regimes throughout its length. If unstable flow occurs, it can result in violent pressure surges which will increase both plant wear and product degradation problems. In addition, the identification of the flow regime at critical sections of the pneumatic conveyor is fundamental to any void fraction estimate, upon which many standard measurements Žsuch as solids mass flow rate. will depend. Assuming that the particulate material in question is suitable for pneumatic conveying, blocking within such systems is normally caused by insufficient air velocity. Once blockage has occurred, it can be extremely difficult to remedy. Cross-sectional imaging of the pipeline therefore offers potential benefits in both the control and fault monitoring of pneumatic conveying systems. 2. Electrical capacitance tomography measurements and data processing system 2.1. Capacitance tomographic imaging system Electrical Capacitance Tomography ŽECT. is gaining acceptance as an on-line tool to analyse multi-phase sys-
0032-5910r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 9 8 . 0 0 2 0 1 - 0
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Fig. 1. Principles of capacitance imaging.
tems such as powder conveying w2x, powder fluidisation w3,4x, trickle-bed reactors w5x and oilrwaterrgas transport w6,7x. An ECT system consists of three basic units ŽFig. 1.: the sensor, the electronic panel and the host computer supported by the set of transputers as described in detail elsewhere w8x. The sensor consists of a number of sensing and guard electrodes usually placed outside or embedded within an insulating pipe. The resolution of reconstructed image and speed of frame capture strongly depend on the number of electrodes. The electronic system provides fast Žca. 6600 measurements sy1 . and accurate measurements of the capacitances for the independent electrode connections. The host computer controls the measurement process and manipulates the captured data to obtain a reconstructed cross-sectional image using an appropriate algorithm w9x. For a typical single source electrode system, the number of distinct measurements obtained is equal to N Ž N y 1.r2 where N is the number of electrodes. The reconstructed image resolution is related to the number of independent interelectrode measurements while the speed of frame capture is inversely proportional to the number of such measurements. Thus, the ECT system designed for pneumatic conveying control and monitoring has a relatively low number of electrodes Ž N s 6, 8 or 12.. The ECT system ŽProcess Tomography, Wilmslow. used here had a 12-electrode sensor and provides a data capture rate equal to about 100 frames sy1 with a resolution equal to ca. 5% Ži.e., the size of the target object should be at least 5% of pipe diameter. if its boundary is to be discerned distinctly. This is, however, assuming that there is a sufficiently large difference in dielectric constant between the object and the surrounding medium. Thus, such a system is particularly suitable for monitoring large-scale perturbations with a significant permittivity difference between phases, like the powder slugs passing through the sensor. Yang et al. w7x have discussed some critical features associated with the design of the hardware within an ECT
system, including the type of the measuring circuit: the need for high measurement resolution Žca. 0.3 f F., low noise level Žrms - 0.1 f F., low baseline drift but a wide dynamic range of measurement Žfrom 0.3 f F up to 2000 f F.. In the present paper, the practical consequences and performance of using a state-of-the-art ECT system to monitor a dense phase powder conveying system are considered. Image reconstruction algorithms used in ECT can be divided into three main groups based on methods involving linear back-projection ŽLBP. w9,10x, iterative solutions and neutral network w11x. The LBP algorithm is the simplest and the fastest method and was consequently chosen for the described experimentation, since these factors are essential in the monitoring of fast perturbations. The LBP algorithm is based on obtaining a priori capacitance sensitivity distribution maps for all possible single-electrode combinations and all pixels. The presently used software formats a single image into 1024 square pixels based on 32 = 32 Cartesian mesh. The total number of pixels placed into the sensing region is 814. Consequently, the size of each pixel is 3.15% of the inner diameter ŽID. of the sensor, which for a 12-electrode sensor gives approximately twice the resolution of the electronic system. Thus, each frame of captured data, reconstructed from 66 distinct measurements between electrodes, consists of 814 normalised dielectric constant values which represent phase distribution in the sensing region. These data may be used in further statistical and stochastical analysis. 2.2. Sensor design method The following section is intended to provide concise information on the ECT sensor used in present experimentation and the design method relating to the selection of the sensing electrode dimensions. The set of initial parameters which are taken into account consist of: D 1 , D 2 , N, ´ MIN ´ MAX and ´ PL Žsee Figs. 1 and 2 for details. which denote the pipe ID and OD, maximum and minimum dielectric constants of the phases to be monitored and pipe
Fig. 2. Cross-section of ECT sensor used in present experiment.
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liner permittivity. These parameters may be reduced to four nondimensional values, e.g., D 1rD 2 , N, ´ MIN r´ MAX and ´ PL r´ MAX . Over the past decade w2–9x, the general assembly of ECT sensors Žsizes and mounting details of the radial and guard electrodes and of the outer screen. has been developed and verified experimentally Žthey are difficult to calculate.. The basic design task reduces to the selection of two parameters: Ø the sensing electrode axial length, L, Ø the angle of the gap between sensing electrodes, a G Žor the gap width for given D 2 .. Since the range of capacitance measured by the sensor is approximately determined by the sensor calibration data, it is reasonable to consider the case when the sensing region is filled with homogeneous media having a varying dielectric constant. Then, the number of independent capacitance measurements, nominally quoted as N Ž N y 1.r2, may be reduced to Nr2, where N represents the number of electrodes. For a 12-electrode system, the six principal measurements may be exemplified by the capacitance values associated with electrode combination 1–2, 1–3, . . . ,1–7. Thus, the subject of analysis is the set of six capacitances C1J for given ´ and the set of six capacitance changes DC1J due to a change in ´ . These values should obey the following conditions: Ø DC1J should be relatively large, to provide good measurement resolution, but maximum value of C1J should not exceed ca. 2 pF to avoid the electronic system saturation w12x; Ø DC1J values should be relatively uniform, i.e., the ratio of minimum to maximum values should not be too small; Ø There should be a functional dependence of ´ Ž C1J ., i.e., each value of capacitance should correspond with one unique dielectric constant value; Ø The above dependence should be close to linear and also should be stable, i.e., small changes in DC1J should yield small changes of ´ . Since only two parameters can be adjusted, it is difficult to fulfil these four conditions exactly. However, for the gas–solid flows considered here, the variation in dielectric constant between phases does not exceed a factor of two or three. For such moderate values, the deflection of the electrostatic field due to the presence of the wall Žanalogous to the so-called ‘soft field’ problem. is small. Thus, in gas–solid systems, contrary to gas–liquid systems, the two last conditions are fulfilled almost automatically. Since the use of driven Žnot grounded. guard electrodes is used, the electrostatic field existing in the sensing area filled with homogeneous medium is close to the 2-dimensional field. To simulate it, the procedure presented by Ostrowski et al. w13x has been applied. This method, based on the conjugate harmonics application, solves the Laplace equation in two domains: the sensing region consisting of the wall of the pipe having the dielectric constant equal to ´ PL , and the pipe interior having arbitrary, but constant
3
dielectric constant, ´ . Dirichlet boundary conditions were imposed on the electrodes and gap surfaces and conditions of the second kind w13x were imposed on the inner wall interface. The known distribution of stream Žcurrent. function over the electrode contour returns the straightforward method of the electrode capacitance calculation being linearly related to the stream Žcurrent. increment D c J between its two-edge points: C1J s
´ O ´ PL L V
D cJ ,
Ž 1.
where V is the voltage difference between the source and the detecting electrodes. Since the solution may be easily normalised, an algorithm can be deduced, which calculates the values of C1J and DC1J for a given set of initial parameters: D 1rD 2 , N, ´ MIN r´ MAX , ´ PLr´ MAX and ´ PL for a unit axial length of the sensing electrode. This procedure was adopted to assess the required sensor geometry for the conveying application as discussed below. In the present experiment, the ECT sensor was placed on the horizontal pipe for which D 1 s 52 mm and D 2 s 60 mm Žsee Section 3 for details.. The pipe liner permittivity was equal to ca. 2.5. The values of ´ MIN and ´ MAX correspond with 1 Žair. and about 2.4 Ždielectric constant of solid packed bed.. Experimental evaluation of several differing sensor configurations eventually led to the axial length of sensing electrode, L, and the gap width being selected as 100 and 2 mm, respectively. Generally, the capacitance increment is directly proportional to L Ž2-dimensional approach., while the influence of the electrode gap size is more significant for measurements between adjacent electrodes. Since the value of ´ MA X is, by necessity, a mean nominal value, calculations have been performed for three values of ´ MA X Ž2.2, 2.4 and 2.6. to check the stability of the results obtained. Table 1a, b, c presents the calculated values of C1J and DC1J for selected ´ MIN and ´ MAX . It should be pointed out that these data provide only a partial measurement of capacitance resulting from the ‘inner’ electrostatic field interaction. The total capacitance is larger because of additional effects such as the capacitance of the connection leads. Since these effects, however, may be assumed to be constant Ži.e., independent of the dielectric constant of the sensed medium. the DC1J values return the trial estimation of the range of expected capacitance increments. The results in Table 1 indicate satisfactory stability within this range of ´ MA X . The maximum change of DC1J is close to 20 fF Žpair 1–2. and maximum relative change Žpair 1–7. is no greater then 40%. It was therefore concluded that the proposed sensor dimensions were appropriate for the intended powder conveying application. To make the sensor movable along and around the pipe, the radial guard electrodes were not inserted into a pipe wall but their edges were placed on its outer surface. Sensing and driven electrodes were made from 50-mmthick copper foil, cut to a length of 100 and 40 mm,
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Table 1 Theoretical predictions of calibration data of the ECT sensor designed for present measurements; ´ PL s 2.5, ´ MIN s1.0 and ´ MAX Žsolid bulk permitivitty. s 2.2 Ža., 2.4 Žb. and 2.6 Žc.
Ø slug frequency and distribution, Ø correlation analysis of the above parameters.
Ža. Electrode number
Minimum capacitance wpFx
Maximum capacitance wpFx
Capacitance increment wpFx
1–2 1–3 1–4 1–5 1–6 1–7
1.638 0.088 0.037 0.024 0.019 0.017
1.737 0.172 0.079 0.051 0.041 0.038
0.098 0.084 0.042 0.027 0.022 0.020
1.638 0.088 0.037 0.024 0.019 0.017
1.747 0.184 0.085 0.056 0.044 0.041
0.109 0.096 0.048 0.032 0.026 0.024
1.638 0.088 0.037 0.024 0.019 0.017
1.756 0.196 0.092 0.060 0.048 0.044
0.118 0.108 0.055 0.036 0.029 0.027
Žb. 1–2 1–3 1–4 1–5 1–6 1–7 Žc. 1–2 1–3 1–4 1–5 1–6 1–7
respectively. The cylindrical outer screen, of 76-mm diameter was fabricated from 0.5-mm-thick copper sheet. 2.3. Visualisation and analysis of tomograms The captured images were reconstructed as described earlier. Image files were then transferred to a workstation for rendering in the form of a three-dimensional animation movie. For this purpose, the AVS software visualisation package was adopted as a standard. Hence, bursts of individual tomographic images could be stacked together to form a three-dimensional image against time. The information can be stored in this form and subsequently viewed in any orientation, e.g., useful two-dimensional isocontour slices can be taken in radial or axial directions. Movies viewed from inside or outside the pipe can be generated. Reconstructed images can be time-gated to enable quantitative analysis. In the context of this paper, individual images were used to deduce: Ø the average volume occupied by solids, Ø the height of the solidrgas interface Žif present., and sequences of images were used to extract Žin combination with calibration measurements using a video, see Section 3.2.: Ø slug length and distribution of slug lengths, Ø slug velocity and velocity distribution,
3. Conveying plant 3.1. General description The experimental vacuum conveying system is shown in Fig. 3. The system was designed to enable different types of powder flows to be generated in a controlled and repeatable manner. It is a closed loop system for solids and an open system for air. Solids sucked from solid tank are transferred through an standpipe 11 m in length and stored in the vacuum conveyor. Induced air is pushed through a filter and removed by the vacuum pump to atmosphere. Vacuum is achieved by using a multistage injector ŽPIAB, MLL 800 model w14x., driven by air supplied from compressor. For an air pressure in the pump inlet section equal to ca. 0.5 MPa, the possible pressure vacuum and maximum induced air flow rate are 80 kPa and 0.1 N m3 sy1 , respectively. These parameters are sufficient to generate a wide range of flow patterns, from dense slug flow up to dilute, fast flow with low solids concentration. In order to facilitate visual observations of the flow regime, a 3-m-long horizontal test section was made from transparent pipe ŽExcelon R-4000, 60 mm OD and 52 mm ID.. The rest of the pipeline was made from transparent or opaque PVC, except for two stainless steel bends used to minimise pipe wall attrition. The height difference between the bottom and upper horizontal sections of the standpipe is approximately 2.7 m. The experimental system is controlled using eleven valves, allowing adjustment of the flow parameters which correspond to particular flow regimes. The valves numbered from V1 to V6 ŽFig. 3. are Georg-Fisher w15x electrically actuated units, thus may be operated automatically. The functions of particular valves are listed briefly below, since an understanding of their operation shows how the manipulation of combinations of these valves can be used to produce differing flow regimes. Ø V1—main air inlet valve, may be actuated with different frequencies to obtain various slug patterns; Ø V2—butterfly valve dividing the vacuum conveyor and solid tank; when all the solids are transferred through the standpipe, this valve is opened to discharge vacuum conveyor, otherwise, it remains closed during the plant operation; Ø V3, V4—auxiliary valves to cut off the system from vacuum pump and equalise the pressures in vacuum conveyor and solids tank; Ø V5–injection valve to remove a solid plug from vertical part of pipeline Žsuitable for solids of low fluidity., to feed the system with solids and to generate additional pressure pulses if necessary;
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Fig. 3. Schematic diagram of an experimental vacuum conveying system and data acquisition equipment.
Ø V6, V9—valves controlling auxiliary bypass which enable the supply of compressed air directly to the solids tank Žsuitable for solids of low fluidity.; Ø V7, V8—ball and needle throating valves which control air flow rate; Ø V10—compressed air cut-off or throating valve; Ø V11—outlet valve to drain water from compressed air pipeline. As mentioned, the conveying plant flow parameters are adjusted mainly by valves V1, V7, and V8. If necessary, the auxiliary valves V5 and V10 may be used for this purpose Žthe latter valve to change the vacuum pump characteristics., while valves V2, V3 and V4 control the discharging process after solids transfer is completed. Since the conveying plant has been designed to examine the flow of different types of powders or plastic pellets, the plug valve ŽPV, Fig. 3. has been mounted at the solids inlet to adjust its cross-section.
section through valve V1 while the second is supplied to the top of solid tank and then drawn through the packed bed of solids within the hopper. The ratio of both streams depends on the valve V1 adjustment, on the height of solid bed in the holding tank and also on the type of particulates. The instantaneous value of total volumetric flow rate is obtained by measurements of pressure drop caused by the OPF restriction and absolute pressure to calculate the fluid density in the orifice plate assembly. These values are provided by two strain gauge pressure transducers P1 and P2 having ranges 2 kPa and 0.1 MPa, respectively. In order to cover as wide as possible a range of air flow rates, a set of four orifice plates have been fabricated with diameters of the orifice openings equal to 4, 6.2, 7.1 and 12 mm. These correspond to air flow rates equal to approximately 0.5, 1.2, 2, 5 N m3 sy1 obtained for the maximum pressure drop equal to 2 kPa. Then the air volumetric flow rate could be calculated following the known relationship:
3.2. Measurement procedure
'
QA s g A P 2 D prr , In addition to the data supplied by ECT system, two other parameters, the gas and the solid flow rates, were measured. Atmospheric air enters system through valves V7, V8 and then is drawn through an orifice plate flowmeter ŽOPF.. The air stream leaving the orifice plate flowmeter is subsequently split. One stream is directed to the inlet
Ž 2.
where QA , g , A P , D p and r are the volumetric flow rate Žat conditions in the orifice plate assembly., the discharge coefficient Žbeing a function of Reynolds number and specific geometry., the area of the orifice opening, the
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pressure drop and the air density. Since departures from standard geometry and installation Že.g., British Standard 1042. were unavoidable the empirical discharge coefficients were unknown. Calibration of the system was therefore required for each orifice plate. To obtain appropriate values at any other position in the standpipe or at normal conditions ŽNTP., it is necessary to calculate the actual value of air density. Air pressure reduction along the length of the pipeline, i.e., gradual decompression of the transportation media, will result in a corresponding increase in both gas velocity and volumetric flow rate. This phenomenon greatly affects the slug shapes and velocities along the length of the pipeline. Because of this effect, the slugs which enter the vacuum conveyor and cause changes of the load cell signal are different from those which were observed and monitored in the test section. This effect strongly depends on flow pattern. It has been found that for slow slug flow Žsee Section 4.1 for details. the total pressure drop in the standpipe is equal to 0.03–0.04 MPa. Thus, the outlet volumetric air flow rate is about 1.4–1.7 of its inlet value. The direct influence of this increment on slugs shape and velocity is difficult to estimate because of significant slug dispersion Žparticularly in the vertical part of pipeline. and air filtering through the slugs Žsee Section 4.1.. It has been observed however that the slugs in the upper horizontal section travel at a much higher velocity than those passing through the test section. The mass flow rate of material was estimated by means of the changes of vacuum conveyor mass measurements with time. The vacuum conveyor was suspended elastically with a Kulite strain gauge load cell ŽLC. placed at the top point of its frame, and supported at two other points. Since the vacuum conveyor was attached to the solid tank with flexible rubber bellows, calibration of the load cell and associated signal conditioning circuitry was relatively straightforward. However, minor correction of this was necessary because of an additional suction force resulting from the resistance to air flow through the solids tank. This suction force was monitored by a second pressure transducer ŽP2. and correction was achieved by multiplying the signal from this transducer by the solid tank cross-section and then subtracting the result from the total force registered by the load cell. All three analogue signals were sampled and digitised in the 12-bit analogue–digital converter and fed into a personal computer for further data processing. The sampling frequency was selected as 500 Hz. This value greatly exceeds the typical slug frequency being 0–10 sy1 and consequently the Nyquist frequency based on the slug movement observations. The reason for such a high value, however, was the registration of rapid changes of pressure drop during the slug generation process. In the present experiment, Maranyl nylon plastic pellets were used as solid phase having the following properties as specified by the manufacturer: Ø bulk densitys 750 kg my3 ,
Ø solid densitys 1120 kg my3 , Ø lengths 2–3 mm, Ø aspect ratio s 1–2. For this medium, the maximum mass transferred during a rig single run, before the charge in the solid tank ŽFigs. 2 and 3. was exhausted, was approximately 25 kg. The time needed for complete discharge strongly depended on the flow regime and varied from about 30 s for dilute flow conditions up to 100 s for the dense, slug flow pattern. A significant transient of several seconds was observed, when running the conveying system from an empty pipeline situation, before quasi-periodic Žfor slug flow. or steadystate Žfor dilute flow. conditions were achieved for all observed flow regimes. After this period the data capture system was initiated, providing the time series of data for a duration of 15–20 s. Thus the lengths of the collected digital signals varied from 7500 up to 10 000 data points, although where necessary this raw data was truncated for signal processing purposes. A video camera positioned both upstream and downstream of the tomographic sensor was used to verify the tomographic images and the analogue signals which were fed into the PC. In this way, the video camera film enabled the transfer of time coordinate into the equivalent spatial domain. The camera provided 125 frames sy1 , since the initial moments for all records have been synchronised, so it was possible to compare all recorded data with the corresponding slugs position in the test section. In particular, the slug length and velocity could be estimated, providing data verification of the ECT measurements. The experimental data obtained from the experimental conveying plant consist of three main types: Ø the set of images captured by ECT system with a capture rate of approximately 100 frames sy1 ; Ø the three analogue signals, to calculate the phase flow rates, with sampling frequency of 500 Hz; Ø the video film to estimate slug length, shape and velocity. 3.3. Data acquisition and control system The pneumatic conveyor was controlled by a PC running Windows software based on Labview. This is a program development application based on a graphical programming language Ž‘G’.. It is commonly used in data acquisition and control for creating a virtual instrument, which operates like any other instrument with numeric and graphical controls and indicators, except they are virtual in the host computer. The software regulates a data acquisition and control board ŽLABPCq .. The control PC is capable in total of outputting 24 bits of digital information or receiving 24 bits of digital information Ž0–5V., but not simultaneously in time. It is also capable of accepting four analogue input signals and outputting one analogue signal. The board was configured so that the Labview software interfaced with 12
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bits of digital output to the interfacing electronics, 12 lines of digital input from the interfacing electronics, four wires carrying analogue input and one line carrying analogue output Žnot used. at present. 4. On-line measurement results 4.1. Flow characterisation The vacuum experimental system described in Section 3.1 may operate in two general modes: one under control in which the powder slugs are generated automatically, and the other in which additional pressure pulses may be supplied to the system Že.g., by closing and opening some valves periodically.. In this case, it is possible to adjust some of the slug characteristics by manual or sequenced perturbations. Results from operating under automatic slug generation will form the basis of discussion within this paper, for which the following factors are important: Ø the characteristics of pneumatic source driving the conveyor, Ø the geometry of the system, Ø the adjustment of the set of operating valves, Ø the solid phase properties. If the solid phase is coarse enough Ži.e., the air gaps between the pellets are not very small., it is possible to obtain significant air flow through the packed bed and also through the slugs. In this case, the air averaged velocity is larger than that of solids. Thus, behaviour may be subdivided into two different types, defined as follows: Ža. Air is supplied together with solids through the common inlet from solid tank, thus valve V1 ŽFig. 3. is closed. Žb. Valve V1 is opened, thus the bulk of air is supplied through the separate inlet. Both methods enable the observation of dense, slug flow regimes having apparently similar flow parameters. Table 2 presents the set of phases flow rates and their superficial velocities. It is evident that the differences between type Ža. Žlabelled record number 1 in the table. and Žb. Žrecord numbers 2–7. are not significant as far as these basic flow parameters are concerned. However, a
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number of very different flow features are evident between the two types of behaviour. Fig. 4 shows examples of averaged values of the normalised dielectric constant in the sensing region registered by the ECT system. Fig. 5 indicates the air flow rate profiles Ž Q . against time for the corresponding data sets. System adjustment allowing operation in Ža. provides a flow pattern which may be considered as slow, slug flow ŽFigs. 4a and 5a.. It is characterised by long and slow slugs generated with relatively regular frequency. Since the low velocities of solids are compensated by higher averaged volume fraction Žsimulated by the mean value of ² ´ N : in Table 3., the solid mass flow rate, as well as solid superficial velocity may be approximately the same as for Žb. ŽFigs. 4b–d and 5b–d.. The latter generates a fast slug flow regime. It is evident that perturbations are shorter and more irregular. Moreover, the minimum solid level is also a random parameter and may vary widely during the time of data capture. Because of this effect, the definition of the ‘slug’ is of necessity arbitrary. Generally, the fast slug flow represents more disordered structure than the slow slug flow. In order to show the differences between both slug flow patterns more clearly, it is useful to calculate and plot some basic stochastic estimators. Fig. 6 shows examples of autocorrelation functions calculated for both types of flow, from which it is apparent that flow phenomena occur at different length scales being larger for slow slug flow by about one order of magnitude. Thus, calculation of autocorrelation is a simple, effective and robust tool to distinguish between particular dense flow patterns. If the slug frequencies are to be considered, it is more suitable to calculate power spectral density of the signal. Since spectral leakage is generally present, it is common practice to taper the original signal Ž² ´ N : in Fig. 4. before transformation, reducing any discontinuities at its edges. Many different windows have been recommended for this purpose. Window selection depends on the nature of the signal and on the type of information to be extracted from its spectrum. In the present analysis, it was essential to select one type of window for all signals assuming that the type of flow pattern is unknown a priori, so this information should result from previously completed calculations. The Parzen, Hanning, Hamming and Welch
Table 2 Flow parameters for seven different modes Žrecords. of operation of a pilot-plant for dense phase pneumatic conveying considered in present analysis No. of record
Air flow rate a wm3 sy1 x = 10 3
Air superficial velocity a wm sy1 x
Solid flow rate wkg hy1 x
Solid superficial velocity wm sy1 x
1 2 3 4 5 6 7
0.89 0.48 0.70 0.79 0.87 0.89 0.93
0.42 0.23 0.33 0.37 0.41 0.42 0.44
1370 1210 1320 1370 1410 1440 1480
0.16 0.14 0.15 0.16 0.16 0.17 0.17
a
The given values refer to normal conditions ŽNTP..
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Fig. 4. Registered averaged in ECT sensor volume value of normalised constant ² ´ N : as powder slugs pass through the sensor vs. time wsx, for flow conditions corresponding with Table 2 ŽŽa. No. 1, Žb. No. 2, Žc. No. 5 and Žd. No. 7.. Tomographic visualizations of the powder slugs are shown beneath each graph for the time increment indicated by the arrow.
windows were taken into account Žsee, e.g., Ref. w16x for details.. From these, the Hanning window was chosen as the best in this sense that returns a narrow main spectral lobe to prevent ‘local’ spreading of the spectrum, and also low side-lobe levels to reduce ‘distant’ spectral leakage Žit should be pointed out that usually these two requirements are in conflict.. The examples of power spectrum densities calculated using above data tapering and then Fast Fourier Transform are shown in Fig. 7. Slow slug flow is characterised by small power spread with distinctive strong peak at about 0.3 Hz. Frequency components above 1 Hz may be neglected. Fast slug flow represents the wider spread, up to 3 Hz, with a few maximas. All power spectral densities calculated for this flow regime Žnot shown in the paper. are similar to each other and there is no clear dependence
of their shape on the phase flow rates within the test ranges utilised during present experimentation. Generally, it should be pointed out that the fast and slow notation of flow regimes are rather qualitative and used to distinguish between two types of phenomena, presently under consideration, which are however fundamentally slow. In fact, the rate of frame capture provided by ECT system Žsee Section 2.1. of about 100 sy1 exceeds many times the Nyquist frequency that is required for the accurate observation of ² ´ N :Ž t . signals. On the other hand, a total data capture time of 18 s Ž1800 data points in discrete series., enables the capture of images corresponding to 5–10 slugs passing through the sensor. Since the signals shown in Fig. 4 suggest the ² ´ N : distributions are close to bimodal Ži.e., representing the minimum and maximum solid levels., the histogram esti-
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mators were calculated as an initial statistical test. The associated bar-graphs are shown in Fig. 8. The range of ² ´ N :, which lies within the range ²0, 1:, was subdivided into one hundred quantisation levels. It is seen that slow flow represents more symmetrical distribution than the fast flow. For the former, the maximum probability occurs from relatively high values of ² ´ N :, while from the latter, low solid levels are more probable. In Table 3, the mean value, standard deviation and median for all, seven recorded ² ´ N :Ž t . signals are presented. It is clear from this data, that standard deviation it is not a robust tool for distinguishing between the two types of slug flows Žall values are close to each other.. More promising indicators are the mean value and, particularly, the median. It is possible to extend the number of estimators and include, e.g., higher order moments: skewness and kurtosis as the additional tests. It has been found, however, that neither provide a clearer method of flow pattern recogni-
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Table 3 The basic statistical estimators of averaged dielectric constant signals ² ´ N :Žt. for seven records having flow parameters presented in Table 2 No. of record
Mean value of ² ´ N :
Standard deviation of ² ´ N :
Median of ² ´ N :
1 2 3 4 5 6 7
0.51 0.17 0.17 0.20 0.18 0.17 0.24
0.26 0.24 0.23 0.23 0.24 0.23 0.24
0.53 0.06 0.08 0.13 0.12 0.06 0.10
tion and, because of that, they have not been deployed in this analysis. 4.2. Slug size and shape The design of pneumatic conveying systems is notoriously difficult. The fragility of an apparently viable design
Fig. 5. Registered air flow rates Q wlrsx Žunder NTP conditions. plotted vs. time wsx. Flow parameters correspond with the numbers in Table 2: Ža. No. 1, Žb. No. 2, Žc. No. 5 and Žd. No. 7.
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Fig. 6. Comparison of autocorrelation functions of ² ´ N :Ž t . signals for slow slug flow ŽNo. 1., left, with fast slug flow ŽNo. 5., right.
has often been shown by relatively minor rerouting of the pipeline, a change in material to be transported, or natural variations in environmental conditions Žparticularly humidity.. In virtually all industrial situations, plugging of the conveying pipeline must be avoided. The conveying properties of some particulate materials are predictable and repeatable, in which case, provided the pipeline diameter, the air volume and the conveying capacity have been correctly selected, pneumatic conveying can be performed in a stable range without a tendency to plug. Other materials, particularly those which have been ground to very fine powders, or are brittle or ‘sticky’ by nature, tend to plug very easily. A well-established technique for dealing with these materials is to use a secondary air valve, which is opened intermittently, in order to artificially produce discrete moving slugs of a manageable length. Clearly, under these circumstances, the ability to visualise on-line, the size and shape of individual slugs would form an invaluable tool in terms of: Ø determination of the conveying properties of sample materials, through standard test sections;
Ø the commissioning of industrial systems designed by standard empirical methods; Ø the adaptive control of the secondary air valve. On-line visualisation of powder flow is now possible for different flow conditions, by means of time-stacking ECT cross-sectional images. Fig. 9 shows such a pseudo three-dimensional image obtained from the experimental rig described in Section 3. This serves to demonstrate how ECT can be used to visualise the size and shape of plugs, which is a valuable tool for process diagnosis and in the validation and development of fundamental slug-flow models. 4.3. Implication for on-line process control It has already been illustrated how the ECT data together with additional standard measurements provides the possibility of flow regime identification by analysing a number of statistical estimators. So far, this analysis has been performed off-line and could be easily enhanced by
Fig. 7. Comparison of power spectral densities of ² ´ N :Ž t . signals forslow slug flow ŽNo. 1., left, with fast slug flow ŽNo. 5., right.
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Fig. 8. Comparison of ² ´ N :Ž t . signals histograms for slow slug flow ŽNo. 1., left, with fast slug flow ŽNo. 5., right.
increasing the number of statistical tests applied to the data set. However, the constraints imposed by the need to progress to on-line analysis are somewhat more rigorous, since it is necessary to carefully select the estimators to be used to fulfil two basic requirements: Ø These estimators should be robust, i.e., should provide enough information to the control system to make up decision by a simple set of logical operations. Ø The number of estimators as well as time needed to complete their calculations have to be limited since the answer of the control system should be fast. It is difficult to precisely quantify the above constraints, since these are not only dependent on the action of a particular control system, but also on the parameters of the pneumatic conveying system itself. With respect to dense phase conveying, a typical control system should realise following main functions: Ø The phase velocities should be kept low to avoid significant attrition, but
Ø These velocities should not be too low to avoid choking of the standpipe, also Ø The supplied mechanical energy per unit mass of transferred solid should be minimised. The comprehensive analysis of such control systems and a general set of data used within them, is beyond the scope of this paper. However, we will suggest two simple estimators which can be used if control is based on the data obtained from ECT system only. Adjustment of the individual phase velocities is in effect equivalent to an adjustment of the flow regime. The boundaries between particular regimes are of necessity arbitrary. According to results presented in Section 4.1, however, it is possible to direct the simple system towards two main aims: Ø to distinguish between slug Ždense. flow and other flow patterns which are expected to occur Ždilute flow, stratified flow, dune flow.; and Ø to distinguish between slow Žvery dense. slug flow and fast Žless dense. slug flow.
Fig. 9. Three-dimensional visualisation of slug traveling at approximately 0.25 m sy1 .
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Assuming that the time required to complete these flow recognition is too short to calculate and analyse autocorrelations, power spectra or histograms the selection of estimators should be based on only a few values obtained. The data presented in Table 3 suggest one of several possible solutions, viz.: Condition A: Calculate the standard deviation of the ² ´ N :Ž t . signal Žits length depends on particular requirements. and follow the instruction: If standard deviation) critical value A, then slug flow occurs, otherwise there is another Ždilute flow, stratified flow, dune flow. flow pattern in the standpipe. Condition B: Calculate the median of the ² ´ N :Ž t . signal and follow the instruction: If median) critical value B, then slow slug flow occurs, Žotherwise fast slug flow.. The nature of selected signals resulting from the final response depends on the pneumatic system parameters and its equipment. Also, the values of critical values A and B above strongly depend on the geometry of the system and type of the transferred solids thus should be selected in each, individual case.
Voltage Time
Greek
aG g D ´ ´0 ´ MA X ´ MIN ´N ²´ N : ´ PL r C
Gap angle ŽFig. 2. Discharge coefficient ŽEq. Ž2.. Increment or difference Dielectric constant Permittivity of free space, 8.85 = 10y1 2 F my1 Maximum dielectric constant Minimum dielectric constant Normalised dielectric constant Normalised dielectric constant averaged spatially in the sensing region Pipe liner dielectric constant Air density Stream Žcurrent. function
Subscripts I J
Source electrode Detecting electrode
Acknowledgements
5. Conclusions The visualisation capability of ECT systems shows great potential for both increasing our understanding the flow dynamics of particulate, and in the further development of empirical design methodologies for the conveying systems themselves. In addition, the use of statistical analysis of the pixel values within ECT images would appear to be a reliable method for the identification of both slow and fast slug flow regimes within dense phase conveying. This strategy can be incorporated as part of a control scheme for industrial conveyors to enable their efficient operation for various feedstocks, under conditions where attrition or power consumption can be minimised.
6. Nomenclature A AP C D D1 D2 D3 fS L N p Re Q
V t
Area of cross-section Area of the orifice opening ŽEq. Ž2.. Capacitance Diameter Pipe ID Pipe OD Diameter of outer shield ŽFig. 2. Frequency of capacitance measurements Length of sensing electrode Number of electrodes Pressure Reynolds number Air flow rate
The authors acknowledge financial support from the CSM Trust and the Engineering and Physical Science Research Council.
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w12x M. Byars, Process Tomography, Cheshire, personal communication, 1996. w13x K.L. Ostrowski, S.P. Luke, R.A. Williams, Application of conjugate harmonics to electrical process tomography, Meas. Sci. Technol. 7 Ž1996. 316–324. w14x Vacuum Conveying—PIAB Catalogue No. 2, 1994. w15x Instruction Manual, Georg-Fischer Rohrleitungssysteme, 1994. w16x W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Verrerling, Numerical Recipes—The Art of Scientific Computing, Cambridge Univ. Press, Cambridge, 1986.