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d < 3)
Accepted Manuscript Experimental characterization of pressure drop in slender packed bed (1 < D/d < 3) Zehua Guo, Zhongning Sun, Nan Zhang, Ming Ding, Jiming Wen PII: DOI: Reference:
S0009-2509(17)30533-X http://dx.doi.org/10.1016/j.ces.2017.08.022 CES 13765
To appear in:
Chemical Engineering Science
Received Date: Revised Date: Accepted Date:
23 April 2017 26 July 2017 22 August 2017
Please cite this article as: Z. Guo, Z. Sun, N. Zhang, M. Ding, J. Wen, Experimental characterization of pressure drop in slender packed bed (1 < D/d < 3), Chemical Engineering Science (2017), doi: http://dx.doi.org/10.1016/ j.ces.2017.08.022
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Experimental characterization of pressure drop in slender packed bed (1 < D/d < 3) Zehua Guoa, b, Zhongning Suna, b, Nan Zhanga, b *, Ming Dinga, b, Jiming Wena, b a
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Heilongjiang 150001, PR China;
b
College of Nuclear Science and Technology, Harbin Engineering University, Heilongjiang 150001, PR China. * Corresponding author. Tel. /fax: +86 451 82569655.
E-mail addresses: [email protected] (N. Zhang), [email protected] (Z. Guo). Tel. /fax: +86 451 82569655. Abstract Experiments on single-phase flow through packed beds at 1.025 < D/d < 2.88 are conducted using water, where the packed beds have advantages such as high radial mixing intensity, intensified heat and mass transfer, safety and uniformity of temperature. The structure of slender packed beds has remarkable influence on the pressure drop characteristics. For packed beds at 1.03 < D/d < 1.98, the coefficients of the Ergun equation show strong dependence on the aspect ratios. With the aspect ratios increasing to D/d > 2, more than one stable configuration can be found at the same aspect ratio. Hence, the influence of assembly method and its corresponding structure on the pressure drop are investigated. It is found that a minor change on the local structure could lead to notable pressure drop difference with very same porosity value in packed beds. And the pressure drop increase is observed as well with increasing mean porosity in the experiment. Therefore, the empirical correlations in literature fail to satisfy the experimental results. Furthermore, with proper assembly method, a highly order structure of packed bed can be achieved, which shows good performance on the pressure drop reduction. These experimental 1
results would be useful for the optimum design in industrial applications as well as understanding the transport phenomena in packed beds.
Keywords: slender packed bed; pressure drop; channeling effect; structure characteristic; pressure drop reduction.
1.
Introduction Packed beds have wide applications in the chemical, agricultural and metallurgical industries
as reactors, dryers, filters, heat exchangers, and adsorbers. The popularity of packed beds originates largely from the convenience in construction and operation as well as their low cost. It has driven an almost incredible number of studies investigating the mechanisms of heat and mass transfer, and the flow and pressure drop of the fluid through the bed of solid for the high economic value represented by packed beds, and continue to do so (Calis et al., 2001).
Packed bed reactors with large aspect ratios (D/d) suffer from high flow resistance and low heat transport in radial direction. If the process is exothermic, the low heat transport can lead to hot spots in the reactor bed. Therefore, in order to create a highly efficient reactor, slender packed beds are used as reactor tubes, which have advantages on pressure drop reduction and uniformity of temperature (Langsch et al., 2014). It is a promising approach towards the enhancement of packed bed reactors. For industrialization, further investigations and optimizations with regard to an acceptable pressure drop, rapid heat removal and higher reaction rates are necessary.
2
Understanding the associated pressure drop characterization in porous media is critical as it directly influences convection heat transfer, chemical reaction rates and filtration effectiveness, as well as the required pumping power in applications (Dukhan et al., 2014). Fluid flow in packed beds is complex mainly due to the structure of the media in the path of the fluid. The structure drastically changes the flow field: it destroys boundary layers and compels the fluid travel only through winding and tortuous open flow passages. These effects cause vigorous mixing and occurrence of an added mechanism called dispersion (Bağcı et al., 2014). Therefore, the fluid mechanisms are sensitive to the structure properties in the packed beds.
The superficial axial velocity variations along radial direction are consistent with the radial porosity variations of packed beds, and as expected at places of low porosity, high velocities are observed (Das et al., 2017; Eppinger et al., 2011). Since the geometry of the packing is interrupted by confining wall, the porosity approaches unity in the vicinity of the wall in packed beds. As a result, the velocity profile inside a packed bed can be severely distorted near the wall where the fluid velocity reaches the maximum. This phenomenon is known as flow channeling effect (White and Tien, 1987). Clearly, the annular zone near the wall comprises an increasing fraction of the cross-sectional area in a cylinder column as the aspect ratios decrease. Therefore, the influence of the wall upon the flow distribution becomes more significant with the D/d progressively decreasing and it could lead to non-uniform head loss in packed beds.
The most widely used correlation for pressure drop is the Ergun equation (Eq. (1)) (Ergun, 1952) in packed bed with large aspect ratios. Ergun also defined the modified friction factor fk as 3
Eq. (2-3) with the coefficient a = 150 and b = 1.75.
P (1 ) 2 u (1 ) u 2 (1) 150 1.75 L 3 d2 3 d
a 1 u 2 P b (3) fk 3 (2) , f k Rem L d
It expresses the pressure drop as the sum of the viscous and inertial energy losses.
When the aspect ratios decease to a certain extent, the Ergun equation is not applicable due to the wall effect. It is thought the wall has twofold influences on pressure drop in packed bed. In the creeping flow regime, the pressure drop may be increased due to the additional wall friction. On the other hand, in turbulent flows, the pressure drop might be reduced by the channeling effect in the near-wall region. Therefore, the flow parameters in Ergun equation become functional dependent upon D/d ratios: the contribution of the confining walls to the hydraulic radius is accounted for analytically by the coefficient a and the channeling effect at high Reynolds numbers is empirically described by the coefficient b (Cheng, 2011; Eisfeld and Schnitzlein, 2001).
The radial porosity distribution for mono-sized spheres in cylindrical containers has been investigated extensively using experimental and numerical methods for decades (Antwerpen et al., 2010; Mueller, 2010). Extensive studies in literature conclude that the radial porosity profile follows an oscillatory fashion with the amplitude decreasing as increase distance from the wall (Klerk, 2004; Mueller, 1992; Suzuki et al., 2008). However, when the aspect ratio decreasing to D/d < 3, radial porosity profiles of slender packed beds are radically different from the profiles in packed beds with relative large aspect ratios. In D/d < 2, the particles in packed bed tend to be arranged in a highly ordered way, being always in contact with the confining wall (Govindarao et 4
al., 1992; Mueller, 1992). As the aspect ratio increases to 2 < D/d < 3, a porosity peak at the center of packed beds is found by experiments and numerical method (Benenati and Brosilow, 1962; Guo et al., 2017; Mueller, 1992; Theuerkauf et al., 2006). This indicates that a free channel can exist along the centerline with quite low porosity in packed bed at 2 < D/d < 3.
Consequently, the fluid mechanism in the packed bed is affected by the structure variations. Ren et al. (2005) studied the visualization of flow in packed beds by Nuclear Magnetic Resonance (NMR) method. For packed bed with large aspect ratios, the velocity maximum was found near the wall. However, a more pronounced velocity peak was observed in the center of the packed bed at D/d = 2.7. Yang et al. (2015) used the electrochemical technique to test flow transitions in random packed beds. For the packed bed at D/d = 2.6, a much higher Reynolds number (Re = 500) was obtained for the end of laminar flow regime than the others at D/d > 5.3 (Re = 110).
With the different packed bed structure and abnormal hydraulic phenomena in packed bed, the pressure drop characteristics of the slender packed beds are expected different from the packed beds with small aspect ratios. Fand et al. (Fand et al., 1993; Fand and Thinakaran, 1990) studied the pressure drop in packed beds at 1.08 < D/d < 40. They found that, with the wall effect, the flow parameters became functional dependent upon the aspect ratios at D/d < 40. But the variations of the parameters were different below D/d < 1.40 (where they were monotonically decreasing with aspect ratios) from what was above D/d > 1.40 (where they were monotonically increasing). Bai et al. (2009) studied the pressure drops in packed beds at D/d < 4 by numerical and experimental method. They found that the modified friction factors fk varied dramatically, 5
which confirmed the inconsistency and unreliability of the empirical correlations for the packed beds in this range of aspect ratios. Montillet et al. (2007) studied the pressure drop characteristics of packed beds at 3 < D/d < 14.5. The experimental result of D/d < 3.5 failed to follow the tendency of the others in the analysis. Therefore, they suggested that the pressure drop of packed bed should be investigated separately in this range of aspect ratios.
These studies above demonstrate that not only the local behavior but also the macroscopic characteristics of fluid flow in slender packed bed (D/d < 3) are affected by the geometric features. However, there is scarce experimental work devoted to the pressure drop in slender packed beds in literature. Especially for the pressure drop characteristics in high superficial velocity regime, it is of interest for practical applications of the slender packed bed as reactor tubes for applications such steam reforming or nuclear reactors, which typically operate at high Reynolds numbers (up 4
to 10 ) (Dixon et al., 2012; Hassan et al., 2012).
Additionally, for validation of Computational Fluid Dynamics (CFD) simulations in packed beds, most studies have computed pressure drop, which was then compared to literature correlations. There is a wide range of pressure drop correlations for fixed beds, especially if wall effects are to be taken into account, different ones have been used in the various studies, with varying agreement (Dixon et al., 2012). Meanwhile, the CFD simulation by Dorai et al. (2015) showed that slender packed bed had a tendency to be subject to high variability on pressure drop. Even pressure drop increase was observed with the increase of mean porosity in packed bed at D/d = 3 (Freund et al., 2003). However, the simulations of packed beds at D/d < 3 can hardly been 6
examined with the scarce experimental data.
To fill this gap, a series of experiments are carried out to investigate the pressure drop characteristics of slender packed beds at high Reynolds numbers. The new set of experimental data is presented. And it is compared with the correlations in literature to discuss and confirm their applicability. Some interesting phenomena are observed in current work. And the data presented might be used for CFD validations and the optimum design in industrial applications.
2.
Description of experiments
2.1. Test facility The experimental apparatus used in this investigation is depicted schematically in Fig. 1. It mainly consists of three parts: water flow loop, test section and measurement equipment. Water is supplied by the centrifugal pump from the reservoir tank to the test tube in most cases. For tests at low flow rate, an elevated tank is used to guarantee a steady and constant water head. The flow rate is adjusted by the inflow valve and the bypass valve. After passing through the test tube, water is collected and back to the reservoir tank. The test section is made of polymethyl methacrylate (PMMA) with the length of 1000 mm. Three pairs of pressure taps are set uniformly to measure the pressure drop at different positions. To avoid the inlet and outlet effects, two pairs of pressure taps are 200 mm away from both ends of the column and another pair of pressure taps in the middle. Pressure taps are drilled on the tubes. Each pair of taps makes a 120 degree angle with radial holes 2 mm in diameter to provide an average pressure reading and prevent blockages. At both the inlet and the outlet of the test section, two pieces of porous plate are placed between the 7
flanges to support the bed and prevent the particles from leaving the bed.
Two Keller differential pressure transmitters with high accuracy are mounted on the test section to measure entire and half pressures drops for high and low range, respectively. The flow rates of water are measured by Endress+Hauser mass flow meter. The temperature is monitored by a thermometer immersed in the reservoir tank. The flow meter and differential pressure transmitters are calibrated prior to experiment. A Data Acquisition System is realized via National Instruments data acquisition products and a computer program written in LabVIEW.
2.2. Test sections All experiments are conducted with glass spheres. The diameters of spheres used as packing material are 40.0 mm, 30.0 mm, 16.2 mm, 15.0 mm and 14.2 mm. The diameters of cylindrical columns are 50.5 mm, 40.9 mm and 28.2 mm. The properties of the packed beds tested in this work are presented in Table 1. The size of the spheres and tubes is measured using a caliper with a precision of 0.05 mm. For determination of the particle diameter, one hundred particles (n = 100) of each size are measured. The average particle diameter (d) and standard deviation (s) are calculated as follows: n
d
s
d i 1
n
i
(4)
1 n 2 di d (5) n 1 i 1
Follow the instruction in the study by Hassan et al. (2012), three independent methods—water displacement, weighting and particle counting—were used to characterize the 8
porosity of each packed bed. The average value of the measurements by different methods for each packed bed, which are within ±1% of the mean value, are used in the data reduction.
For the assembly of packed beds at D/d < 2, several batches of particles are dropped into the column slowly. Then, the packed beds are gently vibrated for minutes by hands in vertical direction. By the transparency of the PMMA, the highly ordered structure can be visualized. This structure is found consistent with the description of Govindarao et al. (Govindarao et al., 1992). And the porosity values make a satisfied agreement with the predictions of Eq. (5-6) (Govindarao et al., 1992) as shown in Fig. 2. 2 d
1 3 D
1
3
1 D 3 (6) , 1 1 d 2 2d 1 D
8 2 2 2D D 2D D D 3 2 d d d d d 2
, 1+
3 D 2 (7) 2 d
For packed beds at D/d > 2, although many empirical correlations are proposed to predict the value of mean porosity for packed beds with varying agreement in literature, more than one stable packing configuration can be found at the same aspect ratio (Klerk, 2004). For example, two extreme configurations are possible for the packed bed at D/d = 2.5, which are illustrated in Fig. 3 by Langsch et al. (2014). In the densest packing four spheres are arranged in each horizontal layer, which is twisted by 45◦ around the tube axis in comparison to the neighboring layers. This packing has the lower mean porosity value of 0.48. In the loosest packing, horizontal layers of three spheres alternate with horizontal layers of only one sphere resulting in a bed porosity of 0.63. Therefore, packed beds of different configurations could be achieved with the aspect ratio at a constant value. 9
In current work, the influence of packing method as well as the corresponding structure on the pressure drop characteristics is investigated. Two regular packing methods are involved, which are always used in literature (Klerk, 2004; Montillet et al., 2007).
The pouring packing method: pouring particles into the column.
The pouring-vibration packing method: alternations of pouring particles into the
column and gentle vibrations in the assembly stage.
For the pouring-vibration packing method, an interesting phenomenon is observed. Some beads, which are located at the central part initially in pouring, rise up at the center of the top end to new positions (Fig. 4 (a), D/d = 2.88) or shift directly to new positions adjacent to the wall (Fig. 4 (b), D/d = 2.73) as vibrations. Hence, a semi-regular pentagonal arrangement is favored and segments of free channels form along the centerline.
The pictures from the top end are shown in Fig. 5 for packed bed at D/d = 2.73 by different packing methods. It is clear that the packed bed by the pouring-vibration packing method is much ordered than the packed bed by pouring, with most particles in contact with the wall. Therefore, the porosity values in Table 1 of packed bed by the pouring method and the pouring-vibration method are denoted as “Random” and “Quasi-structured”, respectively.
3.
Result and discussion
3.1. Packed beds at D/d < 2 10
The experimental results of measured pressure drops at D/d < 2 are presented in Fig. 6. The general trend of the pressure gradient is that it increases with the superficial velocity. Remarkable pressure drop increase is obtained of packed bed at D/d =1.025. Even compared with the packed beds, which have the same mean porosity at large aspect ratios, it is still much higher. For instance, at a velocity of about 0.1 m/s, the pressure gradient in packed bed at D/d = 1.025 is about 100 kPa/m, while at the same velocity the pressure drop of infinite packed bed with equal porosity is only 5.68 kPa/m by Ergun equation. By inspection of the packed bed structure, the column is almost blocked completely by the big spheres. Consequently, the fluid can only go through the very narrow annular path with great resistance.
Beside the fluid flow velocity, the pressure drop also depends on the porosity and nature of the flow channels such as the size of column and particle. Plotting the modified friction factor fk versus the modified particle Reynolds number Rem helps identifying the characteristics of the flow. It could be obtained from Fig. 7 that the curves of modified friction factors vary dramatically for different aspect ratios. Since the Ergun equation is expressed as fk=150/Rem+1.75, it suggests that the modified friction factor fk should lie on the same trend-line regardless of the aspect ratio changes. The variations in Fig. 7 point to one important aspect of the flow parameter for Ergun equation: no single choice for the values of the two coefficients in this equation can give a satisfactory fit to data over the aspect range 1 < D/d < 2.
The relationship between modified friction factor fk and the aspect ratios is shown in Fig. 8 for given modified Reynolds numbers. It is clear that the variations show a non-monotonic 11
function relationship with the aspect ratios. And the packed beds at D/d > 1.74 have a lower modified friction factors than packed bed at D/d < 1.74 with the equivalent mean porosity value. It means that the particle system has not been properly represented just by the mean porosity in data reductions.
Therefore, the aspect ratios are suggested be specified to fix the value of modified friction factor, not only by the modified Reynolds number Rem—this fact underlines the necessity of a pressure drop correlation including a description of the D/d effect. Mathematically, while—for example—the Ergun equations have the form fk=f (Rem), the prediction of the modified friction value at D/d < 2 shows the functional relationship fk=f (Rem, D/d). The subsequent modifications are presented in section 4.
3.2. Packed beds at 2
It can be seen that a semi-regular pentagonal arrangement is favored in the quasi-structured 12
packed bed as shown in Fig. 5. With the free channel along the centerline, a pronounced velocity peak was observed at the center of the packed bed by the NMR method (Ren et al., 2005). It causes significant bypass flow through the packed bed with less resistance, which leads to the distinct decrease on pressure drop than the random packing. And, with the increasing aspect ratio, the size of the free channel will be enlarged. Therefore, although the two quasi-structured packed beds have very same porosity value, the packed bed at D/d = 2.88 has a much lower pressure drop with the enlarged free channel.
The reaction or heat transfer in packed bed is seriously affected by the flow distribution. For the analysis of transport phenomena in packed bed, the researchers only assumes the channel effect at the wall for packed bed with small tube to particle diameter ratios in previous works (Aparicio-Mauricio et al., 2017; Guo et al., 2014). However, when the aspect ratio decreases to a certain extent, the void channel as well as the bypass flow at the center of packed bed has been reported in recent studies (Das et al., 2017; Dorai et al., 2012; Eppinger et al., 2011; Huang et al., 2009). Therefore, the channel effect inside the packed bed should be taken into consideration in the analysis of transport phenomena in slender packed bed.
One of the drawbacks for packed bed is the poor effective heat conduction in radial direction. In order to improve the thermal-hydraulic performance in packed bed, different methods are proposed to restrain the wall effect in packed bed, such as imposing appropriate wall structure (Zobel et al., 2012) or using composite packed bed with small particles at the wall (Yang et al., 2016). These methods try to increase the fluid velocity as well as convection heat transfer inside 13
the packed bed to achieve more homogenous temperature distribution. From this point of view, the geometry of quasi-structured packed beds can satisfy these requirements. With the inner channels, much higher superficial axial velocity could be anticipated at the central region, which will promote heat transfer inside the packed bed. To make good use of the quasi-structured packed beds, it needs further investigations on the interactions between structure and transport phenomena.
3.3. The influence of local structure variations The main advantage of packed bed with small aspect ratio is the pressure drop reduction, which can satisfy the low pressure drop requirements or demands for rapid heat removal in industries. The formation of free channel along the centerline has a significant advantage on the improvement of the pressure drop reduction. And the optimization on the packed bed structure is easy to implement by a simple assembly method (the pouring-vibration packing method).
For the experimental results of quasi-structured packing presented in Fig. 9, a certain number of particles (2 for D/d = 2.88; 12 for D/d = 2.73) are still located at the centerline. Inspired by the improvement on the pressure drop reduction of the free channel, packed beds are fabricated on purpose without any spheres along the centerline. The mean porosity values of the hollow packed beds are 0.476 and 0.492 for D/d = 2.73, 2.88 respectively.
The comparison between the quasi-structured packing and hollow structure on the pressure gradients is presented in Fig. 10. It can be seen that the changes on local structure have a strong 14
influence on the global pressure drop characteristics. Although only a small portion of the free channel in length is occupied by the particles (5% for D/d = 2.88 and 30% for D/d = 2.73) in packed beds with quasi-structured packing, the performance on the pressure drop reduction is significantly improved after the blockage removal. For packed beds at D/d = 2.88, the pressure gradient of hollow structure reduces about 30% over the quasi-structured packing with the very same mean porosity; for packed beds at D/d = 2.73, a more notable decrease (50% of the quasi-structured packing) is obtained with even 2% reduction on the mean porosity value.
Erdim et al. (2015) reviewed 38 correlations in literature for pressure drop estimation in packed bed. Then, they modified the coefficients of Carman correlations (Carman, 1937) by fitting a large number of experimental data that involved the packed bed at D/d = 4 with fair well accuracy: fk
160 2.81 (8) Rem Rem0.096
Hassan et al. (2012) studied the pressure drops in packed beds with small tube to particle diameter ratios by experiment. After compared 18 pressure drop correlations with experimental result, they expressed the coefficient of the inertial term in empirical correlation as a function of aspect ratios, which was recommended for 20000 < Rem < 29936 and D/d < 5: fk
160 1 (9) Rem 0.2 3.6 D d
The correlations proposed by Erdim et al. (2015) and Hassan et al. (2012) serve as reference approaches for comparison with the experiment result at 2 < D/d < 3.
Fig. 11 shows a comparison of the experimental results with the predictions of Eq. (8) and (9) 15
at D/d = 2.73, 2.88. The experimental result varies in a wild range at a given modified Reynolds number for the packed beds with the same aspect ratio. Even the downward trends of the curves are inconsistent with each other at very high modified Reynolds numbers. Although the empirical correlation could satisfy the experimental result at a specific case, the deviations are significantly beyond the acceptable error limit for others. It indicates that the empirical correlations in literature are hardly applicable in predicting pressure drop in packed beds at 2 < D/d < 3.
Fig. 12 displays the local structure variations in quasi-structured packed bed at D/d = 2.73. It can be seen that multiple forms of local structure exist in the packed bed, such as hollow structure, completely blockage with a particle just at the center, and the deformed pentagonal arrangement of the layer. The packed bed consists of these local structures, and the proportions of each form depend with some level of uncertainty. Since minor changes on local structure can result in notable pressure drop difference with the same mean porosity, varying curves of modified friction factors can be obtained in quasi-structured packed beds with not completely the same on local structures. Moreover, with different packing method, the local structure variations in packed bed will be more complicate. Therefore, bands of modified friction values could exist for the packed bed at the constant aspect ratio.
The mean porosity can give an approximate of the geometry in packed beds at large aspect ratios. But for the packed beds at 2 < D/d < 3, the diversity of local structure could occur at any place without notable mean porosity variations. Since it could cause inconsistent influence on the pressure drop behavior, empirical pressure-drop correlations, using only the mean porosity as 16
system describing parameter, can hardly reflect the remarkable influence of the local structure on the global pressure drop. Therefore, it is unlikely to develop a correlation that could correct for those variations by making further modifications on coefficients of the Ergun or Carman equations.
4.
Modifications to empirical correlation Although the in-homogeneneities are not well represented by the mean porosity, packed beds
at 1 < D/d < 2 have relative ordered structure. The analysis in section 3.1 provides an indication of the possible functional relationship between the aspect ratios and the flow parameters. Therefore, it seems possible for predicting the pressure drop of packed beds in this range by empirically expressing the coefficient term as functions of aspect ratios.
Fand et al. (Fand et al., 1993; Fand and Thinakaran, 1990) expressed the modified friction factors as Eq. (10) and (11) using the equivalent diameter defined by Metha and Hawley (Mehta and Hawley, 1969), which took the extra wetted surface of the wall into consideration based the concept of hydraulic radius. fk
a 2d M 2 bM (10), M 1 (11) Rem 3D 1
In order to fit the non-monotonic variation and sharp increase of the flow parameters at very low aspect ratios (1.08 < D/d < 1.17), the piecewise regression analysis on the modified friction factor variations were performed in ranges of aspect ratios: 1.08 < D/d < 1.17, 1.17 < D/d < 1.40 and D/d > 2 (Fand et al., 1993; Fand and Thinakaran, 1990).
17
It is worth notice that the variations of the modified friction factor should be a horizon line at high Reynolds numbers according to the Eq. (10). However, in Fig. 7, this simplication cannot satisfy the experimental result. The curves of the modified friction factors could continue to go downwards even at very high modified Reynolds numbers. Clearly, the correlation by Fand et al. (Fand et al., 1993; Fand and Thinakaran, 1990) are hardly applicable for the prediction. This inapplicability is expected because their experimental work are mainly performed at Rem < 1000. The pressure drop characteristic in high velocity regimes was not totally exhibited.
Therefore, a new modified empirical correlation (Eq. (12)) is presented for pressure drop calculation in packed bed at 1 < D/d < 2 where the packing has relative ordered structure. D 1004 d fk
9.69
1
D D D 57.6 1964 502.7 1984 d d d (12) 1 D D 3.183 1.785 5.241 d d
Rem
Rem
For Eq. (12), in order to rationally present the pressure drop characteristics, different data are used for the determination of the coefficients in viscous term and inertial term. The experimental data in current work can well characterize the pressure drop in high velocity regime where turbulent effect is dominate. Therefore, they are used for the fitting of coefficients in inertial term. On the other hand, the coefficient a presented in Table 2, which are obtained in Rem < 1000 by Fand et al. (1993) are used for the fitting of the coefficient function in viscous term.
The comparison between the experimental data and the predictions is plotted in Fig. 13. Eq. (12) can well represent the variations of experimental results. The mean deviation between the calculations and experimental result is 15%. 18
5.
Conclusions Experiments on single-phase flow through packed beds have been carried out using water at
1.025 < D/d < 2.88. Considering the existence of various stable packing configurations at D/d > 2, the assembly method and its corresponding structure are investigated of the influences on the pressure drop characteristic. Then experimental results are compared with the predictions of empirical correlations in literature. And the major findings are as follows:
1)
The mean porosity is hardly to represent the geometrical influence on pressure drop in slender packed bed. For packed bed at D/d < 2, the modified friction factors for packed bed at D/d > 1.74 are lower than them at D/d < 1.74 for the same porosity range 0.567 <
ε < 0.682. And for packed bed at 2.73 < D/d < 2.88, since minor changes on the structure can lead to notable pressure drop difference, varying modified friction factors are obtained for packed bed with different structures at a constant aspect ratio. Moreover, the pressure drop increase is observed with increasing mean porosity, which is contradictory to the general idea.
2)
Different assembly method results in varying geometrical configurations. This has significant influence on the pressure drop performances in packed bed. The pouring-vibration packing method is more likely to form a highly ordered structure with a free channel along the centerline in packed beds at 2 < D/d < 3. As a result, the channeling effect inner the packed beds could cause significant bypass flow with less 19
resistance. It has notable advantage on the improvement of the pressure drop reduction, which can satisfy the low pressure drop requirements or demands for rapid heat removal applications. And the assembly method is easy to implement in industry.
3)
The experimental results of packed beds at 1 < D/d < 2 provide an indication of the functional relationship between the aspect ratios and the flow parameters. Therefore, a new modified empirical correlation for packed beds at 1 < D/d < 2 is developed by fitting the experimental results in current work (for high superficial velocity regime) and literature (for low superficial velocity regime). It is a competent correlation to satisfy the variations of the pressure drop characteristics in this range.
The single-phase flow performance in slender packed beds constitutes the basis for studying multiphase flow through packed beds, which is of particular interest to trickle bed reactors. Therefore, novel transport phenomena are expected in the multiphase studies. More work should therefore be carried out to develop more fundamental and comprehensive investigations on the transport phenomena in slender packed beds. This requires the use of experimental method and computational fluid dynamic for modeling the flow field and structural properties for transport in packed beds.
Nomenclature a
coefficient of viscous loss term
b
coefficient of inertial loss term 20
d
particle diameter [mm]
di
diameter of the i-th sphere [mm]
fk
modified friction factor
n
number of particles
r
radial position [mm]
s
standard deviation
u
fluid superficial velocity [m/s]
D
column diameter [mm]
L
height of the test section [m]
M
wall correction factor
Re
particle Reynolds number [ρud/μ]
Rem
modified Reynolds number [ρud/μ/(1-ε)]
Greek letter
△P
pressure drop of packed bed [Pa]
△PExp
experimental results of pressure drop [Pa]
△PCal
predictions of pressure drop [Pa]
ε
porosity
εb
porosity of infinite packed bed
ε(r)
radial porosity
kinematic viscosity coefficient [Pa·s]
density [kg/m3] 21
Acknowledgments This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References Antwerpen, W.V., Toit, C.G.D., Rousseau, P.G., 2010. A review of correlations to model the packing structure and effective thermal conductivity in packed beds of mono-sized spherical particles. Nuclear Engineering & Design 240,(7), 1803–1818. Aparicio-Mauricio, G., Ruiz, R.S., López-Isunza, F., Castillo-Araiza, C.O., 2017. A simple approach to describe hydrodynamics and its effect on heat and mass transport in an industrial wall-cooled fixed bed catalytic reactor: ODH of ethane on a MoVNbTeO formulation. Chemical Engineering Journal 321, 584-599. Bağcı, Ö., Dukhan, N., Özdemir, M., 2014. Flow Regimes in Packed Beds of Spheres from Pre-Darcy to Turbulent. Transport in Porous Media 104,(3), 501-520. Bai, H., Theuerkauf, J., Gillis, P.A., Witt, P.M., 2009. A Coupled DEM and CFD Simulation of Flow Field and Pressure Drop in Fixed Bed Reactor with Randomly Packed Catalyst Particles. Industrial & Engineering Chemistry Research 48,(8), 4060-4074. Benenati, R.F., Brosilow, C.B., 1962. Void fraction distribution in beds of spheres. Aiche Journal 8,(3), 359-361. Calis, H.P.A., Nijenhuis, J., Paikert, B.C., Dautzenberg, F.M., Bleek, C.M.V.D., 2001. CFD modelling and experimental validation of pressure drop and flow profile in a novel structured catalytic reactor packing. Chemical Engineering Science 56,(4), 1713-1720. Carman, P.C., 1937. Fluid flow through granular beds *. Chemical Engineering Research & Design 75,(1), S32–S48. Cheng, N., 2011. Wall effect on pressure drop in packed beds. Powder Technology 210,(3), 261-266. Das, S., Deen, N.G., Kuipers, J.A.M., 2017. A DNS study of flow and heat transfer through slender fixed-bed reactors randomly packed with spherical particles. Chemical Engineering Science 160, 1-19. Dixon, A.G., Walls, G., Stanness, H., Nijemeisland, M., Stitt, E.H., 2012. Experimental validation of high Reynolds number CFD simulations of heat transfer in a pilot-scale fixed bed tube. Chemical Engineering Journal s 200–202,(16), 344-356. Dorai, F. et al., 2015. Fully resolved simulations of the flow through a packed bed of cylinders: Effect of size distribution. Chemical Engineering Science 129, 180-192. Dorai, F., Rolland, M., Wachs, A., Marcoux, M., Climent, E., 2012. Packing fixed bed reactors with cylinders: Influence of particle length distribution, 20th International Congress of Chemical and Process Engineering20th International Congress of Chemical and Process Engineering - CHISA 2012, Prague, Czech Republic. Dukhan, N., Bağcı, Ö., Özdemir, M., 2014. Experimental flow in various porous media and reconciliation of Forchheimer and Ergun relations. Experimental Thermal & Fluid Science 57,(9), 425-433. Eisfeld, B., Schnitzlein, K., 2001. The influence of confining walls on the pressure drop in packed beds. Chemical Engineering Science 56,(57), 4321-4329. 22
Eppinger, T., Seidler, K., Kraume, M., 2011. DEM-CFD simulations of fixed bed reactors with small tube to particle diameter ratios. Chemical Engineering Journal 166,(1), 324-331. Erdim, E., Akgiray, Ö., Demir, 0., 2015. A revisit of pressure drop-flow rate correlations for packed beds of spheres. Powder Technology 283, 488-504. Ergun, S., 1952. Fluid flow through packed columns. Journal of Materials Science & Chemical Engineering 48,(2), 89-94. Fand, R.M., Sundaram, M., Varahasamy, M., 1993. Incompressible fluid flow through pipes packed with spheres at low dimension ratios. Journal of Fluids Engineering 115,(1), 169-172. Fand, R.M., Thinakaran, R., 1990. The influence of the wall on flow through pipes packed with spheres. Journal of Fluids Engineering 112:1,(1), 84-88. Freund, H. et al., 2003. Numerical simulations of single phase reacting flows in randomly packed fixed-bed reactors and experimental validation. Chemical Engineering Science 58,(3–6), 903-910. Govindarao, V.M.H., Ramrao, K.V.S., Rao, A.V.S., 1992. Structural characteristics of packed beds of low aspect ratio. Chemical Engineering Science 47,(8), 2105-2109. Guo, X., Sun, Y., Li, R., Yang, F., 2014. Experimental investigations on temperature variation and inhomogeneity in a packed bed CLC reactor of large particles and low aspect ratio. Chemical Engineering Science 107,(107), 266-276. Guo, Z., Sun, Z., Zhang, N., Ding, M., Cao, X., 2017. Radial porosity peak at the centerline of packed beds with small tube to particle diameter ratios. Powder Technology 319C, 445-451. Hassan, Y.A., Kang, C., Dominguez-Ontiveros, E.E., 2012. Pressure drop in packed bed reactor under high Reynolds number. Nuclear Engineering & Design. Huang, A.Y.L., Huang, M.Y.F., Chen, R.H., Capart, H., 2009. Influence of Aspect Ratio on the Distribution of Porosity and Velocity in Columns of Spheres. Journal of the Chinese Institute of Engineers 32,(3), 421-426. Klerk, A.D., 2004. Voidage variation in packed beds at small column to particle diameter ratio. Aiche Journal 49,(8), 2022-2029. Langsch, R., Zalucky, J., Haase, S., Lange, R., 2014. Investigation of a packed bed in a mini channel with a low channel-to-particle diameter ratio: Flow regimes and mass transfer in gas –liquid operation. Chemical Engineering & Processing Process Intensification 75,(6), 8-18. Mehta, D., Hawley, M.C., 1969. Wall Effect in Packed Columns. Ind.eng.chem.process Des.dev 8,(2), 280-282. Montillet, A., Akkari, E., Comiti, J., 2007. About a correlating equation for predicting pressure drops through packed beds of spheres in a large range of Reynolds numbers. Chemical Engineering & Processing Process Intensification 46,(4), 329-333. Mueller, G.E., 1992. Radial void fraction distributions in randomly packed fixed beds of uniformly sized spheres in cylindrical containers. Powder Technology 72,(3), 269-275. Mueller, G.E., 2010. Radial porosity in packed beds of spheres. Powder Technology 203,(3), 626-633. Ren, X.H., Stapf, S., Blümich, B., 2005. Magnetic Resonance Visualisation of Flow and Pore Structure in Packed Beds with Low Aspect Ratio. Chemical Engineering & Technology 28,(2), 219-225. Suzuki, M. et al., 2008. Study of the Wall Effect on Particle Packing Structure Using X-ray Micro Computed Tomography. Advanced Powder Technology 19,(2), 183-195. 23
Theuerkauf, J., Witt, P., Schwesig, D., 2006. Analysis of particle porosity distribution in fixed beds using the discrete element method. Powder Technology 165,(2), 92-99. White, S.M., Tien, C.L., 1987. Analysis of flow channeling near the wall in packed beds. Heat & Mass Transfer 21,(5), 291-296. Yang, J., Bu, S., Dong, Q., Wu, J., Wang, Q., 2015. Experimental study of flow transitions in random packed beds with low tube to particle diameter ratios. Experimental Thermal & Fluid Science 66, 117-126. Yang, J., Wu, J., Zhou, L., Wang, Q., 2016. Computational study of fluid flow and heat transfer in composite packed beds of spheres with low tube to particle diameter ratio. Nuclear Engineering & Design 300, 85-96. Zobel, N., Eppinger, T., Behrendt, F., Kraume, M., 2012. Influence of the wall structure on the void fraction distribution in packed beds. International Journal of Chemical Reactor Engineering 71,(3), 212-219.
24
Figure & Table captions: Table 1: The properties of the packed bed tested in current work. Table 2: Experimentally determined values of flow parameters by Fand et al (1993).
Fig. 1. Schematic of experimental system. Fig. 2. Mean porosity variations of packed bed at D/d < 2 tested in present work. Fig. 3. Cases of packing structure for D/d = 2.5 drawn by Langsch et al. (2014). Fig. 4. Schematic of the pouring-vibration packing method and the formation of structured configuration: (a) D/d = 2.88, (b) D/d = 2.73. Fig. 5. Pictures from the top end for packed bed at D/d = 2.73 by different packing methods: (a) pouring packing method; (b) pouring-vibration packing method. Fig. 6. The pressure gradient vs. superficial velocity for packed beds at 1 < D/d < 2. Fig. 7. The modified friction factor fk vs. the modified Reynolds numbers for packed beds at 1 < D/d < 2. Fig. 8. The relationship between modified friction factor and aspect ratios at constant modified Reynolds numbers. Fig. 9. The pressure gradient vs. the superficial velocity for packed beds of random and quasi-structured packings at 2 < D/d < 3. Fig. 10. The pressure gradient vs. the superficial velocity for packed beds with quasi-structured packing and hollow structure. Fig. 11. The comparison of the experiment results with the predictions of Eq. (8) and (9): (a) D/d = 2.73; (b) D/d = 2.88. Fig. 12. The local structure variations at D/d = 2.73 in the quasi-structured packed bed: (a) Hollow structure (b) Blockage (c) Layer deformation. Fig. 13. Comparison of the experimental data and the values calculated by Eq. (12).
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Tables Table 1 The properties of the packed bed tested in current work. D
d (mean±one standard deviation)
D/d
ε
40.9
40.00±0.39
1.023
0.365
50.5
40.00±0.39
1.263
0.567
40.9
30.00±0.48
1.363
0.616
28.2
16.20±0.12
1.741
0.682
28.2 28.2
15.00±0.13 14.20±0.16
1.88 1.986
40.9
15.00±0.13
2.727
40.9
14.20±0.16
2.88
0.637 0.558 0.487(Quasi-structured), 0.505(Random) 0.493(Quasi-structured), 0.461(Random)
Table 2 Experimentally determined values of flow parameters by Fand et al (1993). D/d
a
b
1.08
542.05
2.17
1.17
270.85
1.07
1.29
185.47
0.808
1.40
108
0.567
1.838
107
0.746
41
Highlights Pressure drop in slender packed bed is investigated by experiment in Rem > 5000. A minor change on structure could lead to notable pressure drop difference. The structuration of slender packed bed is benefit for pressure drop reduction. A new modified empirical correlation for packed beds at 1 < D/d < 2 is developed.
42
S0009-2509(17)30533-X http://dx.doi.org/10.1016/j.ces.2017.08.022 CES 13765
To appear in:
Chemical Engineering Science
Received Date: Revised Date: Accepted Date:
23 April 2017 26 July 2017 22 August 2017
Please cite this article as: Z. Guo, Z. Sun, N. Zhang, M. Ding, J. Wen, Experimental characterization of pressure drop in slender packed bed (1 < D/d < 3), Chemical Engineering Science (2017), doi: http://dx.doi.org/10.1016/ j.ces.2017.08.022
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Experimental characterization of pressure drop in slender packed bed (1 < D/d < 3) Zehua Guoa, b, Zhongning Suna, b, Nan Zhanga, b *, Ming Dinga, b, Jiming Wena, b a
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Heilongjiang 150001, PR China;
b
College of Nuclear Science and Technology, Harbin Engineering University, Heilongjiang 150001, PR China. * Corresponding author. Tel. /fax: +86 451 82569655.
E-mail addresses: [email protected] (N. Zhang), [email protected] (Z. Guo). Tel. /fax: +86 451 82569655. Abstract Experiments on single-phase flow through packed beds at 1.025 < D/d < 2.88 are conducted using water, where the packed beds have advantages such as high radial mixing intensity, intensified heat and mass transfer, safety and uniformity of temperature. The structure of slender packed beds has remarkable influence on the pressure drop characteristics. For packed beds at 1.03 < D/d < 1.98, the coefficients of the Ergun equation show strong dependence on the aspect ratios. With the aspect ratios increasing to D/d > 2, more than one stable configuration can be found at the same aspect ratio. Hence, the influence of assembly method and its corresponding structure on the pressure drop are investigated. It is found that a minor change on the local structure could lead to notable pressure drop difference with very same porosity value in packed beds. And the pressure drop increase is observed as well with increasing mean porosity in the experiment. Therefore, the empirical correlations in literature fail to satisfy the experimental results. Furthermore, with proper assembly method, a highly order structure of packed bed can be achieved, which shows good performance on the pressure drop reduction. These experimental 1
results would be useful for the optimum design in industrial applications as well as understanding the transport phenomena in packed beds.
Keywords: slender packed bed; pressure drop; channeling effect; structure characteristic; pressure drop reduction.
1.
Introduction Packed beds have wide applications in the chemical, agricultural and metallurgical industries
as reactors, dryers, filters, heat exchangers, and adsorbers. The popularity of packed beds originates largely from the convenience in construction and operation as well as their low cost. It has driven an almost incredible number of studies investigating the mechanisms of heat and mass transfer, and the flow and pressure drop of the fluid through the bed of solid for the high economic value represented by packed beds, and continue to do so (Calis et al., 2001).
Packed bed reactors with large aspect ratios (D/d) suffer from high flow resistance and low heat transport in radial direction. If the process is exothermic, the low heat transport can lead to hot spots in the reactor bed. Therefore, in order to create a highly efficient reactor, slender packed beds are used as reactor tubes, which have advantages on pressure drop reduction and uniformity of temperature (Langsch et al., 2014). It is a promising approach towards the enhancement of packed bed reactors. For industrialization, further investigations and optimizations with regard to an acceptable pressure drop, rapid heat removal and higher reaction rates are necessary.
2
Understanding the associated pressure drop characterization in porous media is critical as it directly influences convection heat transfer, chemical reaction rates and filtration effectiveness, as well as the required pumping power in applications (Dukhan et al., 2014). Fluid flow in packed beds is complex mainly due to the structure of the media in the path of the fluid. The structure drastically changes the flow field: it destroys boundary layers and compels the fluid travel only through winding and tortuous open flow passages. These effects cause vigorous mixing and occurrence of an added mechanism called dispersion (Bağcı et al., 2014). Therefore, the fluid mechanisms are sensitive to the structure properties in the packed beds.
The superficial axial velocity variations along radial direction are consistent with the radial porosity variations of packed beds, and as expected at places of low porosity, high velocities are observed (Das et al., 2017; Eppinger et al., 2011). Since the geometry of the packing is interrupted by confining wall, the porosity approaches unity in the vicinity of the wall in packed beds. As a result, the velocity profile inside a packed bed can be severely distorted near the wall where the fluid velocity reaches the maximum. This phenomenon is known as flow channeling effect (White and Tien, 1987). Clearly, the annular zone near the wall comprises an increasing fraction of the cross-sectional area in a cylinder column as the aspect ratios decrease. Therefore, the influence of the wall upon the flow distribution becomes more significant with the D/d progressively decreasing and it could lead to non-uniform head loss in packed beds.
The most widely used correlation for pressure drop is the Ergun equation (Eq. (1)) (Ergun, 1952) in packed bed with large aspect ratios. Ergun also defined the modified friction factor fk as 3
Eq. (2-3) with the coefficient a = 150 and b = 1.75.
P (1 ) 2 u (1 ) u 2 (1) 150 1.75 L 3 d2 3 d
a 1 u 2 P b (3) fk 3 (2) , f k Rem L d
It expresses the pressure drop as the sum of the viscous and inertial energy losses.
When the aspect ratios decease to a certain extent, the Ergun equation is not applicable due to the wall effect. It is thought the wall has twofold influences on pressure drop in packed bed. In the creeping flow regime, the pressure drop may be increased due to the additional wall friction. On the other hand, in turbulent flows, the pressure drop might be reduced by the channeling effect in the near-wall region. Therefore, the flow parameters in Ergun equation become functional dependent upon D/d ratios: the contribution of the confining walls to the hydraulic radius is accounted for analytically by the coefficient a and the channeling effect at high Reynolds numbers is empirically described by the coefficient b (Cheng, 2011; Eisfeld and Schnitzlein, 2001).
The radial porosity distribution for mono-sized spheres in cylindrical containers has been investigated extensively using experimental and numerical methods for decades (Antwerpen et al., 2010; Mueller, 2010). Extensive studies in literature conclude that the radial porosity profile follows an oscillatory fashion with the amplitude decreasing as increase distance from the wall (Klerk, 2004; Mueller, 1992; Suzuki et al., 2008). However, when the aspect ratio decreasing to D/d < 3, radial porosity profiles of slender packed beds are radically different from the profiles in packed beds with relative large aspect ratios. In D/d < 2, the particles in packed bed tend to be arranged in a highly ordered way, being always in contact with the confining wall (Govindarao et 4
al., 1992; Mueller, 1992). As the aspect ratio increases to 2 < D/d < 3, a porosity peak at the center of packed beds is found by experiments and numerical method (Benenati and Brosilow, 1962; Guo et al., 2017; Mueller, 1992; Theuerkauf et al., 2006). This indicates that a free channel can exist along the centerline with quite low porosity in packed bed at 2 < D/d < 3.
Consequently, the fluid mechanism in the packed bed is affected by the structure variations. Ren et al. (2005) studied the visualization of flow in packed beds by Nuclear Magnetic Resonance (NMR) method. For packed bed with large aspect ratios, the velocity maximum was found near the wall. However, a more pronounced velocity peak was observed in the center of the packed bed at D/d = 2.7. Yang et al. (2015) used the electrochemical technique to test flow transitions in random packed beds. For the packed bed at D/d = 2.6, a much higher Reynolds number (Re = 500) was obtained for the end of laminar flow regime than the others at D/d > 5.3 (Re = 110).
With the different packed bed structure and abnormal hydraulic phenomena in packed bed, the pressure drop characteristics of the slender packed beds are expected different from the packed beds with small aspect ratios. Fand et al. (Fand et al., 1993; Fand and Thinakaran, 1990) studied the pressure drop in packed beds at 1.08 < D/d < 40. They found that, with the wall effect, the flow parameters became functional dependent upon the aspect ratios at D/d < 40. But the variations of the parameters were different below D/d < 1.40 (where they were monotonically decreasing with aspect ratios) from what was above D/d > 1.40 (where they were monotonically increasing). Bai et al. (2009) studied the pressure drops in packed beds at D/d < 4 by numerical and experimental method. They found that the modified friction factors fk varied dramatically, 5
which confirmed the inconsistency and unreliability of the empirical correlations for the packed beds in this range of aspect ratios. Montillet et al. (2007) studied the pressure drop characteristics of packed beds at 3 < D/d < 14.5. The experimental result of D/d < 3.5 failed to follow the tendency of the others in the analysis. Therefore, they suggested that the pressure drop of packed bed should be investigated separately in this range of aspect ratios.
These studies above demonstrate that not only the local behavior but also the macroscopic characteristics of fluid flow in slender packed bed (D/d < 3) are affected by the geometric features. However, there is scarce experimental work devoted to the pressure drop in slender packed beds in literature. Especially for the pressure drop characteristics in high superficial velocity regime, it is of interest for practical applications of the slender packed bed as reactor tubes for applications such steam reforming or nuclear reactors, which typically operate at high Reynolds numbers (up 4
to 10 ) (Dixon et al., 2012; Hassan et al., 2012).
Additionally, for validation of Computational Fluid Dynamics (CFD) simulations in packed beds, most studies have computed pressure drop, which was then compared to literature correlations. There is a wide range of pressure drop correlations for fixed beds, especially if wall effects are to be taken into account, different ones have been used in the various studies, with varying agreement (Dixon et al., 2012). Meanwhile, the CFD simulation by Dorai et al. (2015) showed that slender packed bed had a tendency to be subject to high variability on pressure drop. Even pressure drop increase was observed with the increase of mean porosity in packed bed at D/d = 3 (Freund et al., 2003). However, the simulations of packed beds at D/d < 3 can hardly been 6
examined with the scarce experimental data.
To fill this gap, a series of experiments are carried out to investigate the pressure drop characteristics of slender packed beds at high Reynolds numbers. The new set of experimental data is presented. And it is compared with the correlations in literature to discuss and confirm their applicability. Some interesting phenomena are observed in current work. And the data presented might be used for CFD validations and the optimum design in industrial applications.
2.
Description of experiments
2.1. Test facility The experimental apparatus used in this investigation is depicted schematically in Fig. 1. It mainly consists of three parts: water flow loop, test section and measurement equipment. Water is supplied by the centrifugal pump from the reservoir tank to the test tube in most cases. For tests at low flow rate, an elevated tank is used to guarantee a steady and constant water head. The flow rate is adjusted by the inflow valve and the bypass valve. After passing through the test tube, water is collected and back to the reservoir tank. The test section is made of polymethyl methacrylate (PMMA) with the length of 1000 mm. Three pairs of pressure taps are set uniformly to measure the pressure drop at different positions. To avoid the inlet and outlet effects, two pairs of pressure taps are 200 mm away from both ends of the column and another pair of pressure taps in the middle. Pressure taps are drilled on the tubes. Each pair of taps makes a 120 degree angle with radial holes 2 mm in diameter to provide an average pressure reading and prevent blockages. At both the inlet and the outlet of the test section, two pieces of porous plate are placed between the 7
flanges to support the bed and prevent the particles from leaving the bed.
Two Keller differential pressure transmitters with high accuracy are mounted on the test section to measure entire and half pressures drops for high and low range, respectively. The flow rates of water are measured by Endress+Hauser mass flow meter. The temperature is monitored by a thermometer immersed in the reservoir tank. The flow meter and differential pressure transmitters are calibrated prior to experiment. A Data Acquisition System is realized via National Instruments data acquisition products and a computer program written in LabVIEW.
2.2. Test sections All experiments are conducted with glass spheres. The diameters of spheres used as packing material are 40.0 mm, 30.0 mm, 16.2 mm, 15.0 mm and 14.2 mm. The diameters of cylindrical columns are 50.5 mm, 40.9 mm and 28.2 mm. The properties of the packed beds tested in this work are presented in Table 1. The size of the spheres and tubes is measured using a caliper with a precision of 0.05 mm. For determination of the particle diameter, one hundred particles (n = 100) of each size are measured. The average particle diameter (d) and standard deviation (s) are calculated as follows: n
d
s
d i 1
n
i
(4)
1 n 2 di d (5) n 1 i 1
Follow the instruction in the study by Hassan et al. (2012), three independent methods—water displacement, weighting and particle counting—were used to characterize the 8
porosity of each packed bed. The average value of the measurements by different methods for each packed bed, which are within ±1% of the mean value, are used in the data reduction.
For the assembly of packed beds at D/d < 2, several batches of particles are dropped into the column slowly. Then, the packed beds are gently vibrated for minutes by hands in vertical direction. By the transparency of the PMMA, the highly ordered structure can be visualized. This structure is found consistent with the description of Govindarao et al. (Govindarao et al., 1992). And the porosity values make a satisfied agreement with the predictions of Eq. (5-6) (Govindarao et al., 1992) as shown in Fig. 2. 2 d
1 3 D
1
3
1 D 3 (6) , 1 1 d 2 2d 1 D
8 2 2 2D D 2D D D 3 2 d d d d d 2
, 1+
3 D 2 (7) 2 d
For packed beds at D/d > 2, although many empirical correlations are proposed to predict the value of mean porosity for packed beds with varying agreement in literature, more than one stable packing configuration can be found at the same aspect ratio (Klerk, 2004). For example, two extreme configurations are possible for the packed bed at D/d = 2.5, which are illustrated in Fig. 3 by Langsch et al. (2014). In the densest packing four spheres are arranged in each horizontal layer, which is twisted by 45◦ around the tube axis in comparison to the neighboring layers. This packing has the lower mean porosity value of 0.48. In the loosest packing, horizontal layers of three spheres alternate with horizontal layers of only one sphere resulting in a bed porosity of 0.63. Therefore, packed beds of different configurations could be achieved with the aspect ratio at a constant value. 9
In current work, the influence of packing method as well as the corresponding structure on the pressure drop characteristics is investigated. Two regular packing methods are involved, which are always used in literature (Klerk, 2004; Montillet et al., 2007).
The pouring packing method: pouring particles into the column.
The pouring-vibration packing method: alternations of pouring particles into the
column and gentle vibrations in the assembly stage.
For the pouring-vibration packing method, an interesting phenomenon is observed. Some beads, which are located at the central part initially in pouring, rise up at the center of the top end to new positions (Fig. 4 (a), D/d = 2.88) or shift directly to new positions adjacent to the wall (Fig. 4 (b), D/d = 2.73) as vibrations. Hence, a semi-regular pentagonal arrangement is favored and segments of free channels form along the centerline.
The pictures from the top end are shown in Fig. 5 for packed bed at D/d = 2.73 by different packing methods. It is clear that the packed bed by the pouring-vibration packing method is much ordered than the packed bed by pouring, with most particles in contact with the wall. Therefore, the porosity values in Table 1 of packed bed by the pouring method and the pouring-vibration method are denoted as “Random” and “Quasi-structured”, respectively.
3.
Result and discussion
3.1. Packed beds at D/d < 2 10
The experimental results of measured pressure drops at D/d < 2 are presented in Fig. 6. The general trend of the pressure gradient is that it increases with the superficial velocity. Remarkable pressure drop increase is obtained of packed bed at D/d =1.025. Even compared with the packed beds, which have the same mean porosity at large aspect ratios, it is still much higher. For instance, at a velocity of about 0.1 m/s, the pressure gradient in packed bed at D/d = 1.025 is about 100 kPa/m, while at the same velocity the pressure drop of infinite packed bed with equal porosity is only 5.68 kPa/m by Ergun equation. By inspection of the packed bed structure, the column is almost blocked completely by the big spheres. Consequently, the fluid can only go through the very narrow annular path with great resistance.
Beside the fluid flow velocity, the pressure drop also depends on the porosity and nature of the flow channels such as the size of column and particle. Plotting the modified friction factor fk versus the modified particle Reynolds number Rem helps identifying the characteristics of the flow. It could be obtained from Fig. 7 that the curves of modified friction factors vary dramatically for different aspect ratios. Since the Ergun equation is expressed as fk=150/Rem+1.75, it suggests that the modified friction factor fk should lie on the same trend-line regardless of the aspect ratio changes. The variations in Fig. 7 point to one important aspect of the flow parameter for Ergun equation: no single choice for the values of the two coefficients in this equation can give a satisfactory fit to data over the aspect range 1 < D/d < 2.
The relationship between modified friction factor fk and the aspect ratios is shown in Fig. 8 for given modified Reynolds numbers. It is clear that the variations show a non-monotonic 11
function relationship with the aspect ratios. And the packed beds at D/d > 1.74 have a lower modified friction factors than packed bed at D/d < 1.74 with the equivalent mean porosity value. It means that the particle system has not been properly represented just by the mean porosity in data reductions.
Therefore, the aspect ratios are suggested be specified to fix the value of modified friction factor, not only by the modified Reynolds number Rem—this fact underlines the necessity of a pressure drop correlation including a description of the D/d effect. Mathematically, while—for example—the Ergun equations have the form fk=f (Rem), the prediction of the modified friction value at D/d < 2 shows the functional relationship fk=f (Rem, D/d). The subsequent modifications are presented in section 4.
3.2. Packed beds at 2
It can be seen that a semi-regular pentagonal arrangement is favored in the quasi-structured 12
packed bed as shown in Fig. 5. With the free channel along the centerline, a pronounced velocity peak was observed at the center of the packed bed by the NMR method (Ren et al., 2005). It causes significant bypass flow through the packed bed with less resistance, which leads to the distinct decrease on pressure drop than the random packing. And, with the increasing aspect ratio, the size of the free channel will be enlarged. Therefore, although the two quasi-structured packed beds have very same porosity value, the packed bed at D/d = 2.88 has a much lower pressure drop with the enlarged free channel.
The reaction or heat transfer in packed bed is seriously affected by the flow distribution. For the analysis of transport phenomena in packed bed, the researchers only assumes the channel effect at the wall for packed bed with small tube to particle diameter ratios in previous works (Aparicio-Mauricio et al., 2017; Guo et al., 2014). However, when the aspect ratio decreases to a certain extent, the void channel as well as the bypass flow at the center of packed bed has been reported in recent studies (Das et al., 2017; Dorai et al., 2012; Eppinger et al., 2011; Huang et al., 2009). Therefore, the channel effect inside the packed bed should be taken into consideration in the analysis of transport phenomena in slender packed bed.
One of the drawbacks for packed bed is the poor effective heat conduction in radial direction. In order to improve the thermal-hydraulic performance in packed bed, different methods are proposed to restrain the wall effect in packed bed, such as imposing appropriate wall structure (Zobel et al., 2012) or using composite packed bed with small particles at the wall (Yang et al., 2016). These methods try to increase the fluid velocity as well as convection heat transfer inside 13
the packed bed to achieve more homogenous temperature distribution. From this point of view, the geometry of quasi-structured packed beds can satisfy these requirements. With the inner channels, much higher superficial axial velocity could be anticipated at the central region, which will promote heat transfer inside the packed bed. To make good use of the quasi-structured packed beds, it needs further investigations on the interactions between structure and transport phenomena.
3.3. The influence of local structure variations The main advantage of packed bed with small aspect ratio is the pressure drop reduction, which can satisfy the low pressure drop requirements or demands for rapid heat removal in industries. The formation of free channel along the centerline has a significant advantage on the improvement of the pressure drop reduction. And the optimization on the packed bed structure is easy to implement by a simple assembly method (the pouring-vibration packing method).
For the experimental results of quasi-structured packing presented in Fig. 9, a certain number of particles (2 for D/d = 2.88; 12 for D/d = 2.73) are still located at the centerline. Inspired by the improvement on the pressure drop reduction of the free channel, packed beds are fabricated on purpose without any spheres along the centerline. The mean porosity values of the hollow packed beds are 0.476 and 0.492 for D/d = 2.73, 2.88 respectively.
The comparison between the quasi-structured packing and hollow structure on the pressure gradients is presented in Fig. 10. It can be seen that the changes on local structure have a strong 14
influence on the global pressure drop characteristics. Although only a small portion of the free channel in length is occupied by the particles (5% for D/d = 2.88 and 30% for D/d = 2.73) in packed beds with quasi-structured packing, the performance on the pressure drop reduction is significantly improved after the blockage removal. For packed beds at D/d = 2.88, the pressure gradient of hollow structure reduces about 30% over the quasi-structured packing with the very same mean porosity; for packed beds at D/d = 2.73, a more notable decrease (50% of the quasi-structured packing) is obtained with even 2% reduction on the mean porosity value.
Erdim et al. (2015) reviewed 38 correlations in literature for pressure drop estimation in packed bed. Then, they modified the coefficients of Carman correlations (Carman, 1937) by fitting a large number of experimental data that involved the packed bed at D/d = 4 with fair well accuracy: fk
160 2.81 (8) Rem Rem0.096
Hassan et al. (2012) studied the pressure drops in packed beds with small tube to particle diameter ratios by experiment. After compared 18 pressure drop correlations with experimental result, they expressed the coefficient of the inertial term in empirical correlation as a function of aspect ratios, which was recommended for 20000 < Rem < 29936 and D/d < 5: fk
160 1 (9) Rem 0.2 3.6 D d
The correlations proposed by Erdim et al. (2015) and Hassan et al. (2012) serve as reference approaches for comparison with the experiment result at 2 < D/d < 3.
Fig. 11 shows a comparison of the experimental results with the predictions of Eq. (8) and (9) 15
at D/d = 2.73, 2.88. The experimental result varies in a wild range at a given modified Reynolds number for the packed beds with the same aspect ratio. Even the downward trends of the curves are inconsistent with each other at very high modified Reynolds numbers. Although the empirical correlation could satisfy the experimental result at a specific case, the deviations are significantly beyond the acceptable error limit for others. It indicates that the empirical correlations in literature are hardly applicable in predicting pressure drop in packed beds at 2 < D/d < 3.
Fig. 12 displays the local structure variations in quasi-structured packed bed at D/d = 2.73. It can be seen that multiple forms of local structure exist in the packed bed, such as hollow structure, completely blockage with a particle just at the center, and the deformed pentagonal arrangement of the layer. The packed bed consists of these local structures, and the proportions of each form depend with some level of uncertainty. Since minor changes on local structure can result in notable pressure drop difference with the same mean porosity, varying curves of modified friction factors can be obtained in quasi-structured packed beds with not completely the same on local structures. Moreover, with different packing method, the local structure variations in packed bed will be more complicate. Therefore, bands of modified friction values could exist for the packed bed at the constant aspect ratio.
The mean porosity can give an approximate of the geometry in packed beds at large aspect ratios. But for the packed beds at 2 < D/d < 3, the diversity of local structure could occur at any place without notable mean porosity variations. Since it could cause inconsistent influence on the pressure drop behavior, empirical pressure-drop correlations, using only the mean porosity as 16
system describing parameter, can hardly reflect the remarkable influence of the local structure on the global pressure drop. Therefore, it is unlikely to develop a correlation that could correct for those variations by making further modifications on coefficients of the Ergun or Carman equations.
4.
Modifications to empirical correlation Although the in-homogeneneities are not well represented by the mean porosity, packed beds
at 1 < D/d < 2 have relative ordered structure. The analysis in section 3.1 provides an indication of the possible functional relationship between the aspect ratios and the flow parameters. Therefore, it seems possible for predicting the pressure drop of packed beds in this range by empirically expressing the coefficient term as functions of aspect ratios.
Fand et al. (Fand et al., 1993; Fand and Thinakaran, 1990) expressed the modified friction factors as Eq. (10) and (11) using the equivalent diameter defined by Metha and Hawley (Mehta and Hawley, 1969), which took the extra wetted surface of the wall into consideration based the concept of hydraulic radius. fk
a 2d M 2 bM (10), M 1 (11) Rem 3D 1
In order to fit the non-monotonic variation and sharp increase of the flow parameters at very low aspect ratios (1.08 < D/d < 1.17), the piecewise regression analysis on the modified friction factor variations were performed in ranges of aspect ratios: 1.08 < D/d < 1.17, 1.17 < D/d < 1.40 and D/d > 2 (Fand et al., 1993; Fand and Thinakaran, 1990).
17
It is worth notice that the variations of the modified friction factor should be a horizon line at high Reynolds numbers according to the Eq. (10). However, in Fig. 7, this simplication cannot satisfy the experimental result. The curves of the modified friction factors could continue to go downwards even at very high modified Reynolds numbers. Clearly, the correlation by Fand et al. (Fand et al., 1993; Fand and Thinakaran, 1990) are hardly applicable for the prediction. This inapplicability is expected because their experimental work are mainly performed at Rem < 1000. The pressure drop characteristic in high velocity regimes was not totally exhibited.
Therefore, a new modified empirical correlation (Eq. (12)) is presented for pressure drop calculation in packed bed at 1 < D/d < 2 where the packing has relative ordered structure. D 1004 d fk
9.69
1
D D D 57.6 1964 502.7 1984 d d d (12) 1 D D 3.183 1.785 5.241 d d
Rem
Rem
For Eq. (12), in order to rationally present the pressure drop characteristics, different data are used for the determination of the coefficients in viscous term and inertial term. The experimental data in current work can well characterize the pressure drop in high velocity regime where turbulent effect is dominate. Therefore, they are used for the fitting of coefficients in inertial term. On the other hand, the coefficient a presented in Table 2, which are obtained in Rem < 1000 by Fand et al. (1993) are used for the fitting of the coefficient function in viscous term.
The comparison between the experimental data and the predictions is plotted in Fig. 13. Eq. (12) can well represent the variations of experimental results. The mean deviation between the calculations and experimental result is 15%. 18
5.
Conclusions Experiments on single-phase flow through packed beds have been carried out using water at
1.025 < D/d < 2.88. Considering the existence of various stable packing configurations at D/d > 2, the assembly method and its corresponding structure are investigated of the influences on the pressure drop characteristic. Then experimental results are compared with the predictions of empirical correlations in literature. And the major findings are as follows:
1)
The mean porosity is hardly to represent the geometrical influence on pressure drop in slender packed bed. For packed bed at D/d < 2, the modified friction factors for packed bed at D/d > 1.74 are lower than them at D/d < 1.74 for the same porosity range 0.567 <
ε < 0.682. And for packed bed at 2.73 < D/d < 2.88, since minor changes on the structure can lead to notable pressure drop difference, varying modified friction factors are obtained for packed bed with different structures at a constant aspect ratio. Moreover, the pressure drop increase is observed with increasing mean porosity, which is contradictory to the general idea.
2)
Different assembly method results in varying geometrical configurations. This has significant influence on the pressure drop performances in packed bed. The pouring-vibration packing method is more likely to form a highly ordered structure with a free channel along the centerline in packed beds at 2 < D/d < 3. As a result, the channeling effect inner the packed beds could cause significant bypass flow with less 19
resistance. It has notable advantage on the improvement of the pressure drop reduction, which can satisfy the low pressure drop requirements or demands for rapid heat removal applications. And the assembly method is easy to implement in industry.
3)
The experimental results of packed beds at 1 < D/d < 2 provide an indication of the functional relationship between the aspect ratios and the flow parameters. Therefore, a new modified empirical correlation for packed beds at 1 < D/d < 2 is developed by fitting the experimental results in current work (for high superficial velocity regime) and literature (for low superficial velocity regime). It is a competent correlation to satisfy the variations of the pressure drop characteristics in this range.
The single-phase flow performance in slender packed beds constitutes the basis for studying multiphase flow through packed beds, which is of particular interest to trickle bed reactors. Therefore, novel transport phenomena are expected in the multiphase studies. More work should therefore be carried out to develop more fundamental and comprehensive investigations on the transport phenomena in slender packed beds. This requires the use of experimental method and computational fluid dynamic for modeling the flow field and structural properties for transport in packed beds.
Nomenclature a
coefficient of viscous loss term
b
coefficient of inertial loss term 20
d
particle diameter [mm]
di
diameter of the i-th sphere [mm]
fk
modified friction factor
n
number of particles
r
radial position [mm]
s
standard deviation
u
fluid superficial velocity [m/s]
D
column diameter [mm]
L
height of the test section [m]
M
wall correction factor
Re
particle Reynolds number [ρud/μ]
Rem
modified Reynolds number [ρud/μ/(1-ε)]
Greek letter
△P
pressure drop of packed bed [Pa]
△PExp
experimental results of pressure drop [Pa]
△PCal
predictions of pressure drop [Pa]
ε
porosity
εb
porosity of infinite packed bed
ε(r)
radial porosity
kinematic viscosity coefficient [Pa·s]
density [kg/m3] 21
Acknowledgments This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References Antwerpen, W.V., Toit, C.G.D., Rousseau, P.G., 2010. A review of correlations to model the packing structure and effective thermal conductivity in packed beds of mono-sized spherical particles. Nuclear Engineering & Design 240,(7), 1803–1818. Aparicio-Mauricio, G., Ruiz, R.S., López-Isunza, F., Castillo-Araiza, C.O., 2017. A simple approach to describe hydrodynamics and its effect on heat and mass transport in an industrial wall-cooled fixed bed catalytic reactor: ODH of ethane on a MoVNbTeO formulation. Chemical Engineering Journal 321, 584-599. Bağcı, Ö., Dukhan, N., Özdemir, M., 2014. Flow Regimes in Packed Beds of Spheres from Pre-Darcy to Turbulent. Transport in Porous Media 104,(3), 501-520. Bai, H., Theuerkauf, J., Gillis, P.A., Witt, P.M., 2009. A Coupled DEM and CFD Simulation of Flow Field and Pressure Drop in Fixed Bed Reactor with Randomly Packed Catalyst Particles. Industrial & Engineering Chemistry Research 48,(8), 4060-4074. Benenati, R.F., Brosilow, C.B., 1962. Void fraction distribution in beds of spheres. Aiche Journal 8,(3), 359-361. Calis, H.P.A., Nijenhuis, J., Paikert, B.C., Dautzenberg, F.M., Bleek, C.M.V.D., 2001. CFD modelling and experimental validation of pressure drop and flow profile in a novel structured catalytic reactor packing. Chemical Engineering Science 56,(4), 1713-1720. Carman, P.C., 1937. Fluid flow through granular beds *. Chemical Engineering Research & Design 75,(1), S32–S48. Cheng, N., 2011. Wall effect on pressure drop in packed beds. Powder Technology 210,(3), 261-266. Das, S., Deen, N.G., Kuipers, J.A.M., 2017. A DNS study of flow and heat transfer through slender fixed-bed reactors randomly packed with spherical particles. Chemical Engineering Science 160, 1-19. Dixon, A.G., Walls, G., Stanness, H., Nijemeisland, M., Stitt, E.H., 2012. Experimental validation of high Reynolds number CFD simulations of heat transfer in a pilot-scale fixed bed tube. Chemical Engineering Journal s 200–202,(16), 344-356. Dorai, F. et al., 2015. Fully resolved simulations of the flow through a packed bed of cylinders: Effect of size distribution. Chemical Engineering Science 129, 180-192. Dorai, F., Rolland, M., Wachs, A., Marcoux, M., Climent, E., 2012. Packing fixed bed reactors with cylinders: Influence of particle length distribution, 20th International Congress of Chemical and Process Engineering20th International Congress of Chemical and Process Engineering - CHISA 2012, Prague, Czech Republic. Dukhan, N., Bağcı, Ö., Özdemir, M., 2014. Experimental flow in various porous media and reconciliation of Forchheimer and Ergun relations. Experimental Thermal & Fluid Science 57,(9), 425-433. Eisfeld, B., Schnitzlein, K., 2001. The influence of confining walls on the pressure drop in packed beds. Chemical Engineering Science 56,(57), 4321-4329. 22
Eppinger, T., Seidler, K., Kraume, M., 2011. DEM-CFD simulations of fixed bed reactors with small tube to particle diameter ratios. Chemical Engineering Journal 166,(1), 324-331. Erdim, E., Akgiray, Ö., Demir, 0., 2015. A revisit of pressure drop-flow rate correlations for packed beds of spheres. Powder Technology 283, 488-504. Ergun, S., 1952. Fluid flow through packed columns. Journal of Materials Science & Chemical Engineering 48,(2), 89-94. Fand, R.M., Sundaram, M., Varahasamy, M., 1993. Incompressible fluid flow through pipes packed with spheres at low dimension ratios. Journal of Fluids Engineering 115,(1), 169-172. Fand, R.M., Thinakaran, R., 1990. The influence of the wall on flow through pipes packed with spheres. Journal of Fluids Engineering 112:1,(1), 84-88. Freund, H. et al., 2003. Numerical simulations of single phase reacting flows in randomly packed fixed-bed reactors and experimental validation. Chemical Engineering Science 58,(3–6), 903-910. Govindarao, V.M.H., Ramrao, K.V.S., Rao, A.V.S., 1992. Structural characteristics of packed beds of low aspect ratio. Chemical Engineering Science 47,(8), 2105-2109. Guo, X., Sun, Y., Li, R., Yang, F., 2014. Experimental investigations on temperature variation and inhomogeneity in a packed bed CLC reactor of large particles and low aspect ratio. Chemical Engineering Science 107,(107), 266-276. Guo, Z., Sun, Z., Zhang, N., Ding, M., Cao, X., 2017. Radial porosity peak at the centerline of packed beds with small tube to particle diameter ratios. Powder Technology 319C, 445-451. Hassan, Y.A., Kang, C., Dominguez-Ontiveros, E.E., 2012. Pressure drop in packed bed reactor under high Reynolds number. Nuclear Engineering & Design. Huang, A.Y.L., Huang, M.Y.F., Chen, R.H., Capart, H., 2009. Influence of Aspect Ratio on the Distribution of Porosity and Velocity in Columns of Spheres. Journal of the Chinese Institute of Engineers 32,(3), 421-426. Klerk, A.D., 2004. Voidage variation in packed beds at small column to particle diameter ratio. Aiche Journal 49,(8), 2022-2029. Langsch, R., Zalucky, J., Haase, S., Lange, R., 2014. Investigation of a packed bed in a mini channel with a low channel-to-particle diameter ratio: Flow regimes and mass transfer in gas –liquid operation. Chemical Engineering & Processing Process Intensification 75,(6), 8-18. Mehta, D., Hawley, M.C., 1969. Wall Effect in Packed Columns. Ind.eng.chem.process Des.dev 8,(2), 280-282. Montillet, A., Akkari, E., Comiti, J., 2007. About a correlating equation for predicting pressure drops through packed beds of spheres in a large range of Reynolds numbers. Chemical Engineering & Processing Process Intensification 46,(4), 329-333. Mueller, G.E., 1992. Radial void fraction distributions in randomly packed fixed beds of uniformly sized spheres in cylindrical containers. Powder Technology 72,(3), 269-275. Mueller, G.E., 2010. Radial porosity in packed beds of spheres. Powder Technology 203,(3), 626-633. Ren, X.H., Stapf, S., Blümich, B., 2005. Magnetic Resonance Visualisation of Flow and Pore Structure in Packed Beds with Low Aspect Ratio. Chemical Engineering & Technology 28,(2), 219-225. Suzuki, M. et al., 2008. Study of the Wall Effect on Particle Packing Structure Using X-ray Micro Computed Tomography. Advanced Powder Technology 19,(2), 183-195. 23
Theuerkauf, J., Witt, P., Schwesig, D., 2006. Analysis of particle porosity distribution in fixed beds using the discrete element method. Powder Technology 165,(2), 92-99. White, S.M., Tien, C.L., 1987. Analysis of flow channeling near the wall in packed beds. Heat & Mass Transfer 21,(5), 291-296. Yang, J., Bu, S., Dong, Q., Wu, J., Wang, Q., 2015. Experimental study of flow transitions in random packed beds with low tube to particle diameter ratios. Experimental Thermal & Fluid Science 66, 117-126. Yang, J., Wu, J., Zhou, L., Wang, Q., 2016. Computational study of fluid flow and heat transfer in composite packed beds of spheres with low tube to particle diameter ratio. Nuclear Engineering & Design 300, 85-96. Zobel, N., Eppinger, T., Behrendt, F., Kraume, M., 2012. Influence of the wall structure on the void fraction distribution in packed beds. International Journal of Chemical Reactor Engineering 71,(3), 212-219.
24
Figure & Table captions: Table 1: The properties of the packed bed tested in current work. Table 2: Experimentally determined values of flow parameters by Fand et al (1993).
Fig. 1. Schematic of experimental system. Fig. 2. Mean porosity variations of packed bed at D/d < 2 tested in present work. Fig. 3. Cases of packing structure for D/d = 2.5 drawn by Langsch et al. (2014). Fig. 4. Schematic of the pouring-vibration packing method and the formation of structured configuration: (a) D/d = 2.88, (b) D/d = 2.73. Fig. 5. Pictures from the top end for packed bed at D/d = 2.73 by different packing methods: (a) pouring packing method; (b) pouring-vibration packing method. Fig. 6. The pressure gradient vs. superficial velocity for packed beds at 1 < D/d < 2. Fig. 7. The modified friction factor fk vs. the modified Reynolds numbers for packed beds at 1 < D/d < 2. Fig. 8. The relationship between modified friction factor and aspect ratios at constant modified Reynolds numbers. Fig. 9. The pressure gradient vs. the superficial velocity for packed beds of random and quasi-structured packings at 2 < D/d < 3. Fig. 10. The pressure gradient vs. the superficial velocity for packed beds with quasi-structured packing and hollow structure. Fig. 11. The comparison of the experiment results with the predictions of Eq. (8) and (9): (a) D/d = 2.73; (b) D/d = 2.88. Fig. 12. The local structure variations at D/d = 2.73 in the quasi-structured packed bed: (a) Hollow structure (b) Blockage (c) Layer deformation. Fig. 13. Comparison of the experimental data and the values calculated by Eq. (12).
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Tables Table 1 The properties of the packed bed tested in current work. D
d (mean±one standard deviation)
D/d
ε
40.9
40.00±0.39
1.023
0.365
50.5
40.00±0.39
1.263
0.567
40.9
30.00±0.48
1.363
0.616
28.2
16.20±0.12
1.741
0.682
28.2 28.2
15.00±0.13 14.20±0.16
1.88 1.986
40.9
15.00±0.13
2.727
40.9
14.20±0.16
2.88
0.637 0.558 0.487(Quasi-structured), 0.505(Random) 0.493(Quasi-structured), 0.461(Random)
Table 2 Experimentally determined values of flow parameters by Fand et al (1993). D/d
a
b
1.08
542.05
2.17
1.17
270.85
1.07
1.29
185.47
0.808
1.40
108
0.567
1.838
107
0.746
41
Highlights Pressure drop in slender packed bed is investigated by experiment in Rem > 5000. A minor change on structure could lead to notable pressure drop difference. The structuration of slender packed bed is benefit for pressure drop reduction. A new modified empirical correlation for packed beds at 1 < D/d < 2 is developed.
42