Pressure drop in packed beds with horizontally or vertically stratified structure

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Original Article

Pressure drop in packed beds with horizontally or vertically strati

ﬁed

structure

Liangxing Li

*

, Wei Xie, Zhengzheng Zhang, Shuanglei Zhang

State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, China

a r t i c l e i n f o

Article history:

Received 26 November 2019 Received in revised form 27 March 2020 Accepted 4 May 2020 Available online 6 May 2020 Keywords: Pressure drop Packed bed Stratiﬁcation Single/two-phaseﬂow

a b s t r a c t

The paper concentrates on an experimental study of the pressure drop in double-layered packed beds formed by glass spheres, having the configuration of horizontal and vertical stratification. Both single-phase and two-single-phaseflow tests are performed. The pressure drop during the test is recorded and the measured data are compared with those of homogeneous beds consisting of mono-size particles. The results show that for the horizontally stratified bed with fine particles atop coarse particles, the pressure drop in top layer is found higher than those of homogenous bed consisting of the same smaller size particles, while the measured pressure drop of bottom part is similar with those of similar homogenous bed. But for the homologous bed with upside-down structure, the stratification has little or no effect on the pressure drop of the horizontally stratified bed, and the pressure drop of each layer is almost same as that of homogeneous bed packed with corresponding spheres. Additionally, in vertically stratified bed, the pressure drops on the left and right side is almost equal and between those in homogeneous beds. It is speculated that vertically stratified structure may lead to lateral flow which redistributes the flow rate in different parts of packed bed.

1. Introduction

Packed bed is commonly used in many engineering applications, ranging from agricultural, biotechnology, chemical technology, nuclear engineering, petrochemical industry to food industry [1e6]. Basic transport phenomena in a packed bed are described by the relationship between the pressure drop and thefluid velocity. Therefore, it is of great importance to better understand thefluid flow characteristics in a packed bed [7,8].

Particularly, in theﬁeld of nuclear engineering, a porous debris bed may be formed through fuel coolant interactions (FCI), which occur in various stages of a postulated severe accident [9,10]. Therefore, theﬂow characteristic and heat transfer in debris bed should be deeply concerned.

Many experiments have been conducted to investigate the characteristics of single-/two-phaseﬂow and heat transfer in par-ticulate beds [11e21]. While the review work [21,22] show that most of the previous experimental studies are conducted based on the homogeneous packed beds. Only a few experiments [21e23] are

performed with the heterogeneous packed beds (e.g. stratified bed). However, packed beds with stratified structure are commonly founded in various scientific fields like petroleum reservoirs [24], porous materials [25] and so on [26e28]. Especially, in the severe accident of nuclear reactor, the scoping studies on debris bed for-mation and configuration from FCI experiments [29,30] indicate that the stratification of debris bed would be most expected. Nield & Kuznetsov [31] consider that the throughflow in combination of heterogeneity tends to heighten the possibility of local thermal non-equilibrium. Some researchers regard the mixing offluid as one significant part of the effective thermal conductivity in packed bed [32,33].

Inspired by the interaction between bed structure and fluid flow, this paper presents an investigation of the flow characteristics in particulate layered packed beds, trying to answer the question how the particle-bed configuration (such as the stratified structure and the arrangement of layers) affect its pressure drop and other flow characteristics.

2. Modeling of single-/two-phaseﬂow through packed bed Based on the experimental studies, a great number of analytical models and empirical correlations have been developed to predict

* Corresponding author. Xian-ning West Road 28#, Xi'an city, 710049, China. E-mail address:[email protected](L. Li).

Contents lists available atScienceDirect

Nuclear Engineering and Technology

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / n e t

https://doi.org/10.1016/j.net.2020.05.001

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the pressure drop in packed beds. The models are related to the theoretical knowledge and treatment of single-/two-phase flow and heat transfer in porous media. Specific to single-phase flow through a porous media packed with mono-size spheres, plenty of previous works [34,35] indicate that the simple semi-empirical model like Ergun equation [36] is able to predict the pressure drop in beds composed of spherical particles and the mean devi-ation is within 10%.

D

p

D

z¼

m

KJþ

r

h

J2¼150ð1 εÞ 2

_m

d2_ε3 Jþ 1:75ð1 εÞ

r

dε3 J2 (1)

where

D

p is the differential pressure,

D

z is the height of the bed. Thefirst term of the right side is the viscous loss and the second term is the inertial loss. J is the_{fluid superficial velocity through} porous media. The parameters K and

h

are permeability and pass-ability. d is the particle diameter, andε is the bed porosity.

The Ergun equation [36] was extended to the case of two-phase ﬂow through packed beds by adding the parameters of relative permeability Kr, relative passability

h

r and interfacial drag Fi.

Inspired by this approach, many models and formulas [37e45] have been raised to predict the pressure drop of two-phase ﬂow in packed bed, but results of calculation from different models are not in accordance with each other [8]. Eq. (2) shows the general expressions. dpl dz ¼

rl

gþ

ml

KK_r;lJlþ

rl

hhr;l

JljJlj F_i 1

a

(2a) dpg dz ¼

rg

gþ

mg

KKr;gJgþ

rg

hhr;g

JgJg þF

_a

i (2b)

where dp/dz means the pressure gradient along the bed height. Parameters of liquid and gas phases are distinguished through the subscripts of l and g. The parameters Krand

h

rare called relative

permeability and relative passability. Fiis interfacial drag,

a

rep-resents void fraction, g is gravitational acceleration.

Numbers of models applying to two-phaseﬂow in packed bed have been summarized in our previous study [9,21]. It is found that

models given by different researchers mainly differ in the expres-sions of some important parameters, such as Kror

h

rin Eq.(2).

Particularly, there is no consensus on how to calculate or simplify the interfacial drag Fiyet. In detail, Lipinski model, Reed model and

Hu& Theofanous model [37e39,43] ignore interfacial drag and relevant term in Eq. (2) is assumed as zero according to those models. On the contrary, other scholars, such as Schmidt [14], Tung & Dhir [22], Tutu et al. [40], Schulenberg & Muller [41] and Taherzadeh& Saidi [44] keep a watchful eye on the interfacial drag. Consequently, varying treatments for key parameters led to different predicting results even for the same conditions, which is definitely illogical. Chikhi et al. [8] also considers it necessary to draw a crucial conclusion in this field. Moreover, most of the models are proposed based on the homogenous bed, could these models be still available for the heterogeneous beds with strati fi-cation configurations?

The present study is a follow-on work with the purpose to better understand the flow characteristics in stratified bed, as well to verify the existing models ground on the experimental data on the stratified beds. The tests are performed on an adiabatic test facility and three types of packed beds packed in the cylindrical test section are employed. Type-1 bed is homogeneous bed packed with mono-size spheres. Type-2 and Type-3 beds are both double layer beds formed by two sizes of glass spheres, with the configuration of horizontal stratification and vertical stratification respectively.

3. Description of experiments

Experiments are performed in the DEBECO-LT facility (Debris Bed Coolability-Low Temperature), which is designed and con-structed to investigate adiabatic single/two-phaseﬂow character-istics in packed bed. Fig. 1 introduces working principle of the facility whileFig. 2is the detailed structure of test section.

3.1. Test facility and its instrumentation

The test facility contains water supply system, air supply system, gas-liquid mixed structure, test section and the data measurement system. The main test section is a Plexiglas pipe, while the inner diameter is 120 mm and the height is 600 mm. During the tests, the workingﬂuids are deionized water and air, and all tests are carried out in atmospheric pressure (around 0.1 MPa) and room temper-ature (around 20C).

Along with the horizontal direction, four differential pressure transmitters (accuracy is less than±0.02%) are employed to mea-sure the presmea-sure drop with different distances, as shown inFig. 2. Flowmeters with different measuring ranges (accuracy is less than ±2%) are also used to record and adjust the flowrates of gas and water. Water/air temperatures are measured by k-type thermo-couples to calculate the viscosity and density of fluid. Prior to experiment, all pressure sensors andflowmeters are calibrated for accuracy. A Data Acquisition System (DAS) based on the National Instruments data input instruments is constructed in LabView environment, collecting data from all those measurement tools. More details can be found in previous articles.

Afterfilling test section with the particles, water is pumped to flow up through the test beds in very low flowrate so that it will infiltrate the packed bed slowly and push all air out from the pores. For excluding gravity differential pressure in pressure drop reading, the impulse lines of the differential pressure transmitters are flooded with single phase fluid by operating the valve manifolds properly.

Nomenclature

d particle diameter (m) Fi interfacial drag (N m3)

g gravitational acceleration(m s2) J superﬁcial velocity (m s1₎

K permeability (m2) Kr relative permeability M mass (kg) p pressure (Pa) V0 volume (m3) z bed height (m)

a

void fraction ε porosity

h

passability (m)

h

r relative passability

m

dynamic viscosity (Pa s)

r

density(kg m3) g gas phase l liquid phase r relative

L. Li et al. / Nuclear Engineering and Technology 52 (2020) 2491e2498 2492

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3.2. Test beds

Nine test beds are employed in the present study, named as Bed-1 to Bed-9 respectively. Detailed information is listed inTable 1.

The test bed porosity is calculated through Equation (3) ac-cording to the material density of glass sphere and the particles mass (without moisture) poured into test section.

ε ¼ 1 M=

r

V0

(3) where M and

r

are the mass and density of the packed particles

respectively, V0is the volume occupied by the packed particles.

Beds 1e4 are packed with mono-size spheres whose diameter are 1.5 mm, 2 mm, 6 mm and 8 mm respectively. Beds 5e9 are all stratified beds consist of two sizes glass spheres, and particles of each size occupy half volume of the test section. Specifically, Bed-5 is a horizontally stratified bed whose bottom half part is packed with 1.5 mm spheres while the other half is filled with 6 mm spheres. Bed-6 is also a horizontally stratified bed consisting of the same spheres as those of Bed-5, while the top part is 1.5 mm spheres and the bottom part is 6 mm spheres. Bed-7 and Bed-8 have the same situation as Bed-5 and Bed-6 except for the parti-cles are 2 mm and 8 mm spheres correspondingly. Bed-9 is a vertically stratified bed where the left half part is packed by 1.5 mm spheres while the right part is with 6 mm spheres.

4. Results and discussions

As a follow-on work, the inspection of test facility has been done in previous work where single-phaseﬂow tests are conducted on the homogenous beds packed with mono-size glass spheres. The measured pressure drop is compared with the calculated results of Ergun equation [36] to qualify the measurement system and its uncertainties. The mean relative errors between the experimental data and results predicted by Ergun equation are within 7% [21], which ensures accuracy and comparability of the experimental data.

4.1. Single phaseﬂow tests on horizontally stratiﬁed bed

After the qualification of test facility, single phase flow tests are performed on the horizontally stratified bed. The schematic of horizontally stratified bed is shown inFig. 3. The pressure drop of each half part and the whole bed are all recorded. It should be noted that for the tests on horizontally stratified bed,

D

p1 is used to measure the pressure drop of top half bed, and

D

p2 means the

Fig. 1. System diagram of DEBECO-LT facility.

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pressure drop of bottom half bed, while

D

p3 records the pressure drop of whole packed bed.

Obviously, Bed-5 and Bed-7 are the horizontally stratified beds where the top part is packed with larger size particles and the bottom part consists of smaller size particles. When waterflow up though Bed-5 and Bed-7, the water enters the smaller particle layerfirstly and then enters the larger particle layer. While Bed-6 and Bed-8 just invert the two size particles of Bed-5 and Bed-7 correspondingly, and water enters the smaller particles layer from larger particles layer.

Fig. 4(a)-(d) shows the measured pressure drop of Beds 5e8 respectively. For comparison, the predictions of Ergun equation with each part are also plotted inFig. 4. As shown inFig. 4(a) and(c)

corresponding to Bed-5 and Bed-7, the measured pressure drop in each part are comparable with the calculated results by Ergun equation. It seems that the stratification has less effect on the flow resistance to each part of the stratified bed.

It can be seen fromFig. 4(b) and(d)that at bottom part of Bed-6 and Bed-8, which consists of relatively larger size particles, the measured pressure drops (

D

p2) are relatively close to the pre-dictions of Ergun equation. While for the top part with smaller size particles, the Ergun equation underestimates the measured data (

D

p1) in both Bed-6 and Bed-8 and the mean relative errors are above 23%. Comparing with the measured pressure drop of Bed-1 with 1.5 mm spheres, the experimental data in top part of Bed-6 is relatively higher too (around 1.2 times). Obviously, the strati ﬁ-cation increases theﬂow resistances in top part, even if the bottom part consists of larger particles with higher permeability and passability (6 mm spheres with the permeability of 3.240 108

and passability of 2.893 104_{in Bed-6 versus the 1.5 mm spheres}

with the permeability of 1.872 109 and passability of 6.759 105_{in Bed-1). Same conclusion can be obtained based on}

the comparison results between Bed-8 and Bed-2. In summary, it is concluded that the stratiﬁcation has little effect on pressure drop of

bottom layer packed with larger size particles, but it increases the pressure drop of the top layer consists of smaller size particles.

In addition, the measured pressure drop of stratiﬁed bed (

D

p3) are between the values measured from the top part (

D

p1) and bottom part (

D

p2). The pressure drop of the whole bed is a little lower than the one with smaller size particles, but higher than that of bed with larger size particles. On the other hand, it can be seen fromFig. 4that all the measured pressure drop from bottom part have good agreement with the calculated results by Ergun equa-tion, no matter it consists of larger size particles or smaller size particles. Therefore it can be concluded that the horizontally stratiﬁcation has less effect on the pressure drop of bottom part.

Overall, for the horizontally stratified bed where the top part is packed with larger size particles and the bottom part consists of smaller size particles, the stratification has less effect on the flow resistances in each part of the stratified bed. While for the hori-zontally stratified bed with fine particles atop coarse particles, it is believed that the stratification has little effect on the bottom part layer, but it will increase the pressure drop of the top part layer. Of all the possible reasons one might think when fluid flows from coarse particles layer at bottom which having higher permeability and passability into the topfine particles layer with relatively lower permeability and passability, theflow channel maybe regarded as a sudden contraction which may lead to an extra force or _flow instability between the coarse particles layer and fine particles layer. More efforts including theoretical analysis and numerical simulation should be conducted to specify the mechanism and expression of such phenomena.

4.2. Single phaseﬂow tests on vertically stratiﬁed bed

Single phaseﬂow tests are also carried out on vertically strati-ﬁed bed of Bed-9, where the left half part is packed with 1.5 mm

Table 1

Information of test beds.

Bed Bed information Sizes (mm) Porosity Permeability Passability

Bed-1 Homogenous bed (Mono-size spheres) 1.5 0.368 1.872 109 _6.759₁₀5

Bed-2 2 0.369 3.365 109 _9.100₁₀5

Bed-3 6 0.375 3.240 108 _2.893₁₀4

Bed-4 8 0.378 5.956 109 _3.970₁₀4

Bed-5 Horizontally stratiﬁed bed (Two size spheres) 6/1.5 0.375/0.368

Bed-6 1.5/6 0.368/0.375

Bed-7 8/2 0.378/0.369

Bed-8 2/8 0.369/0.378

Bed-9 Vertically stratiﬁed bed (Two size spheres) 1.5/6 0.368/0.375

Fig. 3. Schematic diagram of horizontally stratiﬁed bed. L. Li et al. / Nuclear Engineering and Technology 52 (2020) 2491e2498 2494

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sphere and the right half part is 6 mm spheres.Fig. 5shows the measured pressure drop of waterﬂow up through Bed-9, where

D

p_1.5 is measured by differential pressure transmitter in left half part packed with 1.5 mm spheres, and

D

p_6 is provided by mea-surement in right half bed with 6 mm spheres. The pressure drops of homogenous bed of Bed-1 with 1.5 mm spheres and Bed-3 with 6 mm sphere are also plotted inFig. 6for comparisons.

As shown inFig. 5(b), the pressure drop of left part are the same as those of right part in Bed-9. Comparing with the experimental data of Bed-1 and Bed-3, the pressure drops of vertically stratified bed (Bed-9) are much lower than those of Bed-1 with 1.5 mm spheres but a little higher than that of Bed-3 with 6 mm spheres under the sameflow conditions. It can be speculated that when water_{flows through the left part with smaller size particles, some of} themflow up through the bed while the others may flow laterally into the right part with larger size particles, due to the relatively higher porosity in the bed of larger size particles. In other words, the reducedflow (moves to the layer with larger size particles) in the small particle layer leads to pressure drop reducing. While for the part with larger size particles, the lateralflow increases the flowrate in the layer and consequently improve the pressure drop in this part. It is believed that multi-dimensionflow should be exist in the vertically stratified bed, and the vertical stratification configuration

produces a signi_{ficant effect on the flow resistance. However,} considering the difficulty in measurement of pressure and mass flow in each part of vertically stratified beds, numerical simulation method is a reliable way to get more information about the multi-dimensionflow. Based on our preliminary calculated results with FLUNET software [46], it is found that part of thefluid in smaller size particles layer willflow laterally into the part of larger size particles due to the relatively higher permeability and passability in larger size particle layer. The lateralflow leads to pressure drop reducing in smaller particle layer while rising in larger particle layer. More efforts should be made in both experiment and simu-lation regarding on the lateralflow existing in the vertically strat-ified bed.

4.3. Two phaseﬂow tests on vertically stratiﬁed bed

Besides the single flow tests, air-water co-current two-phase flow tests are carried out to investigate, the pressure drop of two-phaseflow through the vertically stratified bed. During the tests, waterflowrate is adjusted to a preset value and stayed unchanged, while airflowrate is increased gradually. After that, the water flow is changed and the same procedure is repeated. Based on the measured pressure drop at the gas velocity of 0.3 m/s, Fig. 6 Fig. 4. Pressure drop of waterflow through horizontally stratified beds.

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illustrates the measured pressure drop of two-phaseﬂow through Bed-9, together with the experimental data of Bed-1 with 1.5 mm spheres and Bed-3 of 6 mm spheres under the two-phaseﬂow test conditions.

Obviously, different variation trends of the measured pressure drop can be found inFig. 6. For homogenous bed of Bed-1 packed with 1.5 mm spheres, the measured pressure drops of two-phase flow increase with the flowrate gradually. While for Bed-3 con-sists of larger size particles with 6 mm spheres, the pressure drop appear decreasing tendency in the present working conditions. Generally, when two phaseflow up through the homogenous bed, the homogenous bed with smaller particles produces higher pressure drop, similar with those of the single-phase_{flow through} the homogenous beds of spherical particles. While for the vertically stratified bed of Bed-9 under two phase flow conditions, the measured pressure drop shows different variation tendency. The pressure drop appear decreasing tendencyfirstly under the lower flowrate, and then increasing along with the flowrate. In general, the measured pressure drops are lower than those of Bed-1 but

higher than those of Bed-3. Also, the measured data from left part and right part of Bed-9 have the same value. Similar with analysis results from single phaseflow tests, it is believed that the lateral flow exists in the vertically stratified bed, and the vertical stratifi-cation in a particulate bed will produce a significant effect on the flow resistances which should be studied furtherly.

To verify the capabilities of analytical models for the pressure drop of two phase_{flow through packed beds with} homogeneous-ness and stratification configurations, both of the experimental data and the calculated results using various models are showed in

Figs. 7e8, corresponding to the tests on Bed-1, Bed-3 and Bed-9. The calculated results are expressed with different types of lines, and the experimental data are illustrated as circular and triangle symbols. It should be pointed out that the models employed in

Figs. 7e8 are common recommended in the debris coolability analysis codes like DEBRIS or MEWA code, excepted for the latest model of Li et al. [21]. A signiﬁcant difference among these models

Fig. 5. Pressure drop of waterﬂow through vertically stratiﬁed bed (Bed-9).

Fig. 6. Pressure gradients of two phaseﬂow through vertically stratiﬁed bed (Bed-9).

Fig. 7. Comparisons of calculated results by models with experimental data in packed beds of homogenous bed (Bed-1) and vertically stratiﬁed bed (Bed-9).

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is whether the interfacial drag is considered or not in the models. Generally, Lipinski model [38], Reed model [39] and Hu& Theo-fanous model [43] are ignore the effect of interfacial drag, while Schulenberg & Muller model [41] and Tung & Dhir model [42] account the interfacial drag in their models particularly. More detail discussion on the interfacial drag can be referenced in our previous study of Li et al. [21].

As shown inFig. 7, the measured pressure drop of homogenous bed packed with 1.5 mm spheres increases with the flow rate gradually. The calculations from all analysis models show the same rising trends with the experimental data, regardless of the inter-facial drag is considered or not in the models. Specifically, Hu & Theofanous model [43] and Schulenberg & Muller model [41] models overestimates the experimental values, while Lipinski model (1984) underestimates the measured pressure drop. Generally, the calculations of Reed model (1982) predicts well the experimental data especially at higher flowrates. However, as shown inFig. 7, all the predictions from above models are obviously overestimate the pressure drop of two-phase_{flow through Bed-9.} There is a clear need to propose more accurate model for the pressure drop of two-phaseflow through the vertically stratified bed.

While for the bed packed with larger size particles (6 mm), the predicted results by different models show different variation trends, as shown inFig. 8. Different with the gradually downtrend of experimental data from Bed-3, the measured pressure drop of Bed-9 decreasesfirst and then increases with the superficial ve-locity. While for the calculated results from the models, it can be seen fromFig. 8that only the predictions of Schulenberg& Muller model [41] show similar tendency, and the calculations from other models just show a gradual rising trend with thefluid velocities. It should be pointed out that such kinds of models did not include the interfacial drags and neglect the contribution of interfacial drag to the pressure drop, which leads to the main difference between the two kinds of models. Even so, the calculated values of these models still have significant deviations from the experimental data. On the whole, the calculating results by Li et al. model [9] have better agreement with the experimental data than other models for the homogenous bed packed with coarse particles. Yet unfortunately, the measured pressure drops of two-phase flow through Bed-9 with vertical stratification configuration could hardly be

predicted well by all the models mentioned above. In particular, under the condition of higher airflowrate, the measured pressure drop of stratified bed are not only much higher than those of ho-mogenous bed packed with same coarse particles, but also higher than the calculation value from all above models. Therefore, there is a clear and strong demand to develop a new model to precisely predict the pressure drop of two-phaseflow through stratified bed. 5. Conclusions

In order to better understand the flow characteristics of par-ticulate stratified beds, the flow resistances of homogeneous beds and stratified beds are investigated in the present study. Totally nine test beds are employed, including the homogenous bed packed with mono-size spheres, the horizontally stratified bed and vertically stratified bed packed with two size spheres. Both single-and two-phaseflow tests are carried out, the pressure drop are measured and recorded during the tests. The results show that for horizontally stratified bed where the top part is packed with larger size particles and the bottom part consists of smaller size particles, the stratification has less effect on the flow resistances in each part of the stratified bed. While for the horizontally stratified bed with fine particles atop coarse particles, it is believed that the stratifi-cation has little effect on the bottom part layer, but it will increase the pressure drop of the top part layer. For a vertically stratified bed packed with different size particles, it is believed that multi-dimensionflow exists in the vertically stratified bed, and the ver-tical stratification will produce a significant effect on the flow re-sistances andflow redistribution. More efforts should be put on this topic in both experimental investigation and predictive analysis models.

Declaration of competing interest

The authors declare that they have no known competing ﬁnancial interests or personal relationships that could have appeared to inﬂuence the work reported in this paper.

Acknowledgments

This work is supported by National Natural Science Foundation of China (grant no. 51406143). The authors thank all the staffs at the Division of Two Phase Flow and Heat Transfer in High Pressure and High Temperature for their constructive discussions and suggestions.

Appendix A. Supplementary data

Supplementary data to this article can be found online at

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