Application of Penetration Method to Evaluation of Non-uniformity of Particle Bed Structure

Based on the fluid penetration, an evaluation method of the non-uniformity of a particle bed structure was developed. The newly developed apparatus has a cubic sample box that can be set at any direction. Pressure drops through the packed bed in the same direction as the packing direction and the cross direction of that were measured in the apparatus. It was found that the fluid penetration resistance in gravitational direction (=packing direction) was higher than that in cross direction to gravity. The differences between them depend on the particle size and shape. In order to represent the differences as the apparent alignment of packed bed structure, the experiments using the model packed bed constructed by uniform circular bars having a diameter of 4mm were conducted. Through the experiments, correlation between aligned angle and the ratio of specific surface area of the cross direction to that in the gravitational direction was obtained. By means of the correlation, the non-uniformity of the packed bed structure can be evaluated as the apparent


Introduction
Packed particle beds are used in many processes, for combustion control or as catalyst beds or as particle bed filters.In combustion control applications in particular, they have been used for fixed bed combustion in refuse incinerators, coal power generator boilers and blast furnaces.Incidentally, because of growing needs for higher combustion efficiency and cleaner combustion processes to satisfy environmental and energy-related requirements, a highly sophisticated control for fixed bed combustion must be realized.In diverse research conducted to date, a packed particle bed is assumed to be a homogeneous porous body 1) .However, it is clear from much research on heat transmission 2) that the size and shape of particles in a packed particle bed considerably affect the behaviors in terms of the transfer of heat and/or mass.Therefore, for effective research into combustion on packed beds with relatively large particles, such as those of RDF (Refuse Derived Fuel) and coal, it is important to evaluate a packed particle bed, with the fuel particle size and particle shape taken into consideration.
When the propagation velocity of combustion plane is measured in a packed particle bed combustion process of counter flow operation, a powder material of a smalle size， either spherical particles or crushed particles (non-sphere particles), features a greater propagation velocity if the superficial air velocity remains unchanged; and crushed particles rather than spherical particles shows a greater propagation velocity for a given size 3) .The effect of the fuel particle shape and air velocity on the combustion plane propagation velocity can be evaluated, based on an effective mass transfer coefficient calculated by using an equivalent sphere size determined by the air-permeability method as a representative size. 4)his seems to be because the equivalent sphere size determined by the air-permeability method is a value that reflects contact efficiency; this assumption in turn means that the equivalent sphere size and spe-cific surface area determined by this method reflect, as has been claimed to date, the data for the passage the fluid passes in an actual particle bed.Thus, the air-permeability method appears to be useful, not only in measuring the fluid drag with a packed powder material (which is also possible with a conventional method) but equally in evaluating an air flow passage through a packed bed.Therefore, presuming the air-permeability method to be useful for an air flow passage in a packed particle bed, the authors have attempted to express an air flow passage structure for a millimeter-order-thick packed particle bed, based on the anisotropic pattern in fluid drag; more specifically, we attempted to define nonuniformity in a packed particle structure.For example, let us consider a particle bed, such as that shown in Fig. 1 (not fully packed).When viewed from the top, the pattern with the particles in this structure is relatively random; while viewed from the side, the pattern is significantly non-uniform.In other words, there are tightly or Loosely packed regions in this structure.The pressure drop on the air flow in the cross direction through this type of packed particle bed relative to the gravity ΔPc appears to be smaller compared with the pressure drop ΔPp on the air flow parallel with the gravity through the same particle bed.Therefore, the authors considered that we were able to evaluate the three-dimensional non-uniformity of a packed particle bed structure by measuring pressure drops in two orthogonal directions on a packed particle bed and comparing the values thus obtained.For this purpose, the authors fabricated a prototype fluid permeability experimental apparatus capable of measuring bidirectional fluid drags on a packed particle bed by varying the insertion direction of a packing cell, wherein the packing cell is a cubic body filled with a particle material.To be able to define an apparent orientation direction, as an index for evaluating non-uniformity in the packed particle bed, based on the obtained fluid drags in two directions, the authors performed a series of experiments with models, thereby studying the interrelation between the orientation direction of the packed particles and the fluid drag.

Experimental Apparatus and Method
The present experimental apparatus of fluid permeability is schematically illustrated in Fig. 2. The packed particle cell (test cell) was a cubic body, the side length being 100 mm in the clear.The frame of the test cell consisted of aluminum angle pieces, and two opposing faces made of acrylic panels to ensure the mechanical strength of the apparatus while the remaining four faces were made of metal mesh, with an opening size approximately 0.5 mm.One mesh face could be opened and closed to allow the particles to be loaded into the apparatus.As shown in the diagram, the cell was situated in the apparatus such that its mesh face capable of opening/closing was at the top and its acrylic panels were located toward the flow passage walls.It was possible in this setup to measure the fluid drag-induced pressure drop Δ Pc in the cross direction relative to the packing direction of the particles.In contrast, the cell was turned by 90 degrees and situated in the apparatus such that the mesh face capable of opening/closing was situated toward the air inlet and the acrylic panels were located toward the flow passage walls; in this setup it was possible to measure the fluid drag-induced pressure drop ΔPp in the parallel direction relative to the direction of packing the particles.
In each of the upstream and downstream sides of the cell, a layer packed with spherical glass beads was inserted to regulate the air flow.The pressure drop on the test cell was measured with a manometer connecting to the pressure taps placed between the packed glass beads layers and the test cell.The compressed air was supplied by a compressor, and desiccated by a dryer, its flow rate was adjusted with a pressure control valve and a mass flow controller, and then it was introduced into the test section.The powder specimen used was a granulated spherical particle product of millimeter-order (GAC from Hokutan Sangyo) derived from the same primary particle material (active carbon particles, Feret diameter; 1-30μm).The spherical particles were classified with a sieve into three spherical particle groups (S, M, and L), each group having a unique particle size range.Additionally, the granulated spherical par ticles were fur ther crushed and the resultant product was classified with a sieve into three nonspherical crushed particle groups (NS, NM, and NL).Also, two additional powder specimens were used, each having a more non-isotropic shape compared with crushed particles and consisting of a material almost equivalent to that of the granulated spherical particle product.These specimens were the PAC, which is a particle product with particles having been formed into columns through a granulation product and the YAC, whose particles are flake-shaped.The individual columns in the PAC each measured approximately 4 mm in diameter and 6-8 mm in Length; while the individual flakes in the YAC measured 1.5-2 mm in thickness, and the flat surtace in each flake measured approximately 6×8 mm 2 .Typical shapes of these particle groups are shown in Fig. 3, and the particle size ranges of the spherical particle and nonspherical crushed particle groups are summarized in Table 1.The experimental conditions are summarized in Table 2.In filling particles into the test cell, an amount of powder was taken from the container with a shovel, allowed to drop into the test cell via grav-ity, and the powder in the test cell was not tapped.Consequently, the packing fraction with the packed particles fell within the range 0.5 to 0.6.Incidentally, even when the test cell with packed particles was turned through 90 degrees for the pressure drop   measurement, no reorientation of the particles was observed.Furthermore, since the powder specimen used in the experiment was a granulated product, its void fraction measured with the adsorption method (BET) stood at 0.2; which suggests that the specimen was a porous material.However, because this void fraction is low compared with that of the particle bed (1φ ), it appears that no air penetrated the interior of the individual particles in the specimen.
The pressure drop ΔP was measured for the superficial air velocity within the range of u=0.012 to 0.165 m/s.This superficial air velocity range corresponds to the particle Reynolds number being in the range 3 to 50 in the case of spherical particles M (Dp=(4.0+5.6)/2=4.8mm) , for example.The particle Reynolds number is defined by

Experimental Results and Discussion
As examples of the results, the pressure drop measurements for the crushed particle products NS, NM and NL are shown in Fig. 4. The plotted pressure drop values ΔP were obtained by deducting the pressure drop value unique to the experimental apparatus (pressure drop through the test cell, which was not yet filled with a particle product) from the total pressure drop measurements.
The pressure drop ΔP of each particle type was nearly proportional to the superficial air velocity u.
With the same particle type, the pressure drops in the direction parallel to gravity (p) are apparently greater than those in the cross direction (c) relative to the gravity.Based on these pressure drop values, we calculated the equivalent sphere diameters Dpe by using the Ergun Equation 5) .
Also, the authors calculated the specific surface area Sv, determined from the interrelation between the calculated equivalent diameter Dpe and specific surface area (Sv=6/Dpe).As is clear in Eq. ( 2), the equivalent diameter Dpe is smaller as the pressure drop increases.Incidentally, as the reciprocal of the equivalent diameter Dpe, the specific surface area Sv is greater with a greater pressure drop.Now, we attempt to engage in discussion using the specific surface area Sv, whose magnitude corresponds to that of the pressure drop.
The calculated specific surface areas Sv relative to the superficial air velocities u are illustrated in Fig. 5.It is found that except for the results for NL at lower air velocities, where the measured pressure drop is low, the specific surface area Sv remains almost constant, regardless of the superficial air velocity, meaning that the results in Fig. 5 can be expressed with the Ergun Equation.Based on this finding, the present experimental apparatus can be considered a sound design, which is capable of measuring the pressure drop with a packed particle bed (the objective of the Ergun Equation is to determine such a pressure drop).
The specific sur face area values Sv, which remained constant regardless of the super ficial air  3.For reference, Table 3 also lists the equivalent diameters Dpe.When considering the difference between the data for the parallel direction (p) and that for the cross direction (c) of a given particle group in this table, the specific surface area in the parallel direction Svp is almest the same as the specific surface area in the cross direction Svc with a spherical particle of any particle size and it is thus apparent that there is virtually no difference in pressure drop due to the difference in air penetration direction.In contrast with any non-spherical crushed particle product, the specific surface area in the cross direction Svc is smaller than that in the parallel direction Svp.
Here, we determined the specific sur face area ratios Svc/Svp as representative values standing for the difference in specific surface area between the parallel and cross directions.Following evaluation in terms of the specific surface area ratio, the specific surface area in the cross direction with a non-spherical crushed particle product is apparently 13% to 15% smaller.Among non-spherical particle products, the PAC particle product (like a spherical particle product), which comprises column-formed particles with relatively uniform shapes, features a specific surface area ratio of approximately 1; while the YAC, which comprises flake-type particles, is characterized by a specific surface area ratio in the cross direction that is almost 30% smaller compared with a similar ratio in the direction parallel with gravity.
In the present experiment, measuring operations  were performed on each of the packed particle beds with varied air penetration directions.Therefore, the variation in the specific surface area for a given packed particle bed between the air penetration directions appears attributable to the variation in void structure on the packed particle bed.More specifically, the void structure on a packed bed comprising spherical particles is the same, regardless of the air penetration direction through the packed particle bed (almost random in any direction).In contrast, with the void structure on a packed bed comprising nonspherical particles, the air passages formed through the voids between particles viewed in the parallel direction are relatively small.While the packed bed is viewed in the cross direction, there are regions with more tightly packed particles and regions with more loosely packed particles, thereby the air typically flows through more loosely packed regions where the air drag is low.Such difference between the parallel and cross directions seems attributable to the fact that since powder was uniformly packed in each layer, the particles are arranged at random when the packed particle bed is viewed in a parallel direction relative to gravity; and that because no compacting efforts, including tapping, were attempted after filling with powder and since reorientation seldom occurs with non-spherical par ticles being allowed to fall under gravity, tightly or Loosely packed regions are present on the resultant packed particle bed when viewed in the cross direction.
To sum up, the authors believe that by using the two-directional air-permeability method, the threedimensional non-uniformity of the void structure of a packed particle bed can be numerically evaluated.For this purpose, the authors attempted to evaluate this non-uniformity in terms of the apparent packing structure.Let us consider a packed bed, whose particles are oriented in a particular direction, wherein like with the previously mentioned particle bed, consisting of non-spherical particles, the packed particle bed provides hard-to-penetrate air passages when viewed in the parallel direction and a void structure that allows easy penetration by air when viewed in the cross direction.Therefore, we performed a series of experiments, using a model packed bed consisting of rods, in an attempt to evaluate the three-dimensional non-uniformity of the packed particle bed as represented by a specific surface area ration Svc/Svp as an equivalent apparent aligned angle.
For the model cell packed with rods, pieces of dia. 4 mm drinking straws, each filled with putty, which had been 100 mm (a length that coincides with the inside measurement of one side with the test cell), these were filled into the test cell such that almost all were oriented in a particular direction as shown in Fig. 6.The resultant aligned angleθwas determined by taking photos of the straw pieces, measuring the angles of the same, and then obtaining the average for these angles.With the group of rods in Fig. 6, aligned angles of θ =9.7 degrees when the air was blown from above; and θ=80.3 degrees when the air was blown from the left were revealed.Incidentally, portions with an aligned angle of 0 degrees (parallel with the air penetration) and those with an aligned angle of 90 degrees (cross to the air penetration) were regularly arranged in a staggered pattern.
Pressure drop measurements were obtained with varied penetration air velocity, and substituted in the Ergun Equation (Eq.( 2)) to determine specific surface areas, with the latter plotted in  degrees), the specific area once decreases and then increases as the flow velocity increases: namely there is no clear-cut correlation between the variation in specific surface area and the increase in flow velocity at a given aligned angle.This may be because the interaction between the wakes generated by the rods varies depending on the flow velocity.However, because the flows in the groups of rods are very complicated 6), the true reason for such variation remains unclear.
Since the authors believe that for cases where the Ergun Equation applies, the specific surface area Sv should remain constant regardless of air flow velocity, we believe the use of the Ergun Equation for low air flow velocity will be problematic.Incidentally, at a higher air flow velocity range, the specific surface area calculated by this equation tends to gradually approach a specific value, the authors considered this equation to be useful for a higher air flow velocity range, and adopted the resultant asymptotic values as representative specific surface area values Sv for various aligned angles.
Taking the specific sur face area at a standard aligned angle θ as the Svp and that in the cross angle (90-θ) as the Svc, the specific surface area ratios Svc/Svp were determined and plotted relative to the aligned angle θ, and the result of plotting is shown in Fig. 8. Since in this plotting, the effect of the apparent aligned angle of 45 degrees is the same for both the packing (parallel) direction and cross direction, this aligned angle represents a random packing mode, wherein the corresponding specific surface area ratio Svc/Svp is 1.
As can be understood from Fig. 8, the specific surface area ratio Svc/Svp of the model packed particle bed simply decreases as the aligned angle increases and is plotted as a near-straight line on a semilogarithmic graph.Based on this data, the authors attempted to develop an experimental formula, thereby the equation below was obtained with a correlation function of R 2 =0.999: The specimen NL, for example, which is a nonspherical crushed particle, has a specific surface area ratio Svc/Svp of 0.848.Based on the results of experiments on this model paeked bea, this packed particle bed has an air flow passage structure that is equivalent to a group of rods apparently oriented by 51 degrees to the horizontal direction relative to the packing direction (vertical direction) or a group of rods shifted by 6 degrees to the horizontal direction, relative to the random packing direction (=45 degrees).Thus, by determining the ratio of the specific surface area in the packing direction (parallel direction) to that in the cross direction through experiments on a model packed bed, it is possible to evaluate the three-dimensional non-uniformity of a packed particle structure as the equivalent apparent aligned

Conclusion
The fluid-permeability method, in which a fluid is allowed to pass through a packed particle bed to determine the specific surface area from the measured pressure drop, is characterized by its ability to reflect the voids between particles that provide passages for the fluid.By measuring the bidirectional pressure drop of the penetrating fluid utilizing this feature, the authors attempted to evaluate non-uniformity in the packed particles.The authors performed a series of experiments with a packed bed that comprised millimeter-order particles, thereby learning that by allowing air to flow through the same packed particle bed while mutually crossing two directions and measuring the pressure drop in each direction, the non-uniformity of the packed particle structure could be numerically evaluated.It seems possible to express the non-uniformity of the packed particle structure as the equivalent apparent aligned angle by comparing the experimental results obtained from model particle bed.for its support in their present research.

Fig. 4
Fig. 4 Results of pressure drop measurements.

Fig. 5
Fig. 5 Calculated results of specific surface area.

Fig. 7 .
The Ergun Equation is intended for spheres, and may not be fully suitable for rod-shaped objects as used in the present experiment.Based on Fig.7, in the low flow velocity range of u<0.1 m/s in particular, it is apparent that at specific angles (θ=0 to 25.0 degrees, and 80.3 degrees and 90 degrees), the specific surface area Sv decreases as the flow velocity increases; while at other angles (θ =65.0 degrees and 69.2

Fig. 6
Fig. 6 Model packed bed made by uniform rods.

Fig. 7
Fig. 7 Equivalent diameter of model bed calculated by Ergun equation.

Fig. 8
Fig. 8 Relation between aligned angle and specific surface area ratio.

Table 1 Size
range of spherical and non-spherical tested particles(mm)

Table 3
Equivalent diameter and specific surface area