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Research ArticleSome Movement Mechanisms and Characteristics inPebble Bed Reactor

Xingtuan Yang,1 Yu Li,1 Nan Gui,1 Xinlong Jia,1 Jiyuan Tu,1,2 and Shengyao Jiang1

1 Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineeringand Safety, Ministry of Education, Beijing 100084, China

2 School of Aerospace, Mechanical & Manufacturing Engineering, RMIT University, Melbourne, VIC 3083, Australia

Correspondence should be addressed to Shengyao Jiang; [email protected]

Received 16 November 2013; Accepted 4 May 2014; Published 1 June 2014

Academic Editor: Yanping Huang

Copyright © 2014 Xingtuan Yang et al.This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The pebblebed-type high temperature gas-cooled reactor is considered to be one of the promising solutions for generation IVadvanced reactors, and the two-region arranged reactor core can enhance its advantages by flattening neutron flux. However,this application is held back by the existence of mixing zone between central and peripheral regions, which results from pebbles’dispersion motions. In this study, experiments have been carried out to study the dispersion phenomenon, and the variation ofdispersion region and radial distribution of pebbles in the specifically shaped flow field are shown. Most importantly, the standarddeviation of pebbles’ radial positions in dispersion region, as a quantitative index to describe the size of dispersion region, is gottenthrough statistical analysis. Besides, discrete element method has been utilized to analyze the parameter influence on dispersionregion, and this practice offers some strategies to eliminate or reduce mixing zone in practical reactors.

1. Introduction

The high-temperature gas-cooled reactor (HTGR) [1] isgenerally recognized as a probable solution for the generationIV advanced reactors [2, 3] for its advantages of security,environmental applicability, high efficiency, and industrial-process heat applied in producing hydrogen. A pebble bed-type reactor core is one of the mainstream types for HTGRs,which has been adopted in many tests or demonstrationreactors such asHTR-10 [4–6] inChina, PBMR [7, 8] in SouthAfrica, and their prototype reactor known asAVR [9–11] earlyin Germany. Compared with conventional reactors, a pebble-bed reactor is formed with spherical coated fuel pebblesand graphite pebbles instead of fixed fuel assembles. Pebblesdescend along the core under gravity, whose movementsare determined by pebble flow. Pebble-bed HTGR runs ina recirculating way, in which fuel pebbles are drained outfrom discharge hole at the bottom of the core and loaded intothe core from the top. When pebble bed reaches equilibriumstate, the number of pebbles in the core approximatelyremains constant.

The two-region arranged reactor core is expected as apromising technique for pebble bed HTGRs [12]. In thisconcept, the reactor core is divided into two distinct regions,a central column region consisting of graphite pebbles (calledgraphite region) and an outer annular region consisting offuel pebbles (called fuel region). In running circumstances,at the top of the core, graphite pebbles are inserted into thecore from a single central spot and fuel pebbles are loadedfrom several positions in the annular periphery of the core.All the pebbles are discharged from the base hole. The two-region arrangement brings numerous advantages. It flattensthe neutron flux and consequently allows a significantlyhigher power output without reducing safety margin. Thedecay heat also transfers a shorter distance from the core tooutside during accidents [13].

It was found that a stable two-region arrangement couldbe formed under experimental conditions [14, 15]. There isstill a crucial issue remained to be verified. As the two-regionarrangement formed, a mixing interface appeared betweenthe fuel-pebble region and the graphite-pebble region as aresult of the pebble dispersion. Figure 1 depicts the sketch

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014, Article ID 820481, 10 pageshttp://dx.doi.org/10.1155/2014/820481

2 Science and Technology of Nuclear Installations

Loading and transport unit

Singularizing device

Conveying and separating device

Graphite regionMixing interface

Fuel region

Reactor core

Experimental vessel

Discharging transport unit

Conveying and separating device

Discharge hole

Figure 1: Experimental installation at INET of Tsinghua Universityand sketch of the two-region arranged reactor core.

map of the two-region arranged reactor core. The mixinginterface is limitedwithin several diameters of pebbles, whichapproximately has no impact on the stability of two-regionarrangement. However, neutron moderation in the mixinginterface is enhanced, which leads tomore intensive reactionsas well as more heat. Obviously, the temperature in mixinginterface is higher and the fuel pebbles are easier to bedamaged. In other words, in order to meet the requirementsof reactor security, the mixing interface should be smallenough. To some extent, the feasibility of two-region dependson the size of mixing interface which is directly related to thedispersion of pebble flow.

Dispersion of pebble flow is investigated through experi-ments and numerical simulations. Some fundamental mech-anisms underlying pebble flow remain unknown, and theexperimental way is still a principal approach to study it.The phenomenological method [15] is widely accepted tostudy experimental phenomena of pebble flow, which isan approach to study the dense pebble flow by means ofinvestigating the interface features of different areas com-posed of differently colored pebbles. Several representativeexperimental facilities related to their ownHTGRs have beenbuilt, including the installation developed by INET, TsinghuaUniversity, according to the HTR-PM in China. Modeling ofpebble flow which can be called granular flow in a broaderterm began during 1960s. Over the past 50 years, a number oftheoretical approaches have been proposed for granular flow.Models based on continuum assumption are derived fromother science branches, which fail to predict the dispersion ofpebble flow and can only be applied into two extreme forms:quasistatic flow and rapid flow [16]. Some other models,such as the void model [17, 18] and spot model [19], providedifferent ideas for dense pebble flow and achieve certainagreements with the process of pebble motion but lead tosome unexpected problems. Among these models, discreteelementmethod [20, 21] is recognized to bemore appropriate

Table 1: Main parameters of experimental facility.

Experiment vessel(width × height × thickness)

800 × 1000 × 120mm;800 × 2200 × 120mm

(higher vessel)Base cone angle 30∘

Diameter of discharge hole 120mmDiameter of particle 12mm

Number of particle 70,000;150,000 (higher vessel)

and its qualitative accuracy has been verified. The DEMsimulation has been utilized to investigate the influence ofsome key parameters on pebble flow.

2. Experimental Installation

The experimental installation (Figure 1) is designed on thebasis of the two-region pebble bed reactor with the scale of1 : 5. The 2-dimensional experimental vessel is equivalent toan axial central cut piece of the 3-dimensional cylinder withthe same ratio. The geometries of the vessel, including thebase angle and the discharge-hole diameter, are supposedto have great effect on pebble flow. Experimental vesselsfor various combinations of bed and pebble parameters areplanned to be set up to determine the parameter influences onthe characteristics of pebble flow. Experiments discussed inthis paper are for one combination of these parameters. Moredetails can be found in [15]. Table 1 shows the main designparameters.

As a 2-dimensional model, the pebble flow in the experi-mental pebble bed is not fully the same as the one in practicalreactor core. However, important geometries and pebbleparameters are in accord with similarity theory, includingbase angle, discharge-hole diameter, and pebble size. There-fore, the studies still have an important practical meaningof guidance, whose conclusions can also be considered asgeneral rules of the pebble flow in a reactor core.

In addition, the DEM methods used for comparativestudy and its application in pebble flows can be found inrecently published papers of our group.

3. Experimental Results

3.1. Experimental Observation. Experiments were designedto investigate the establishment of the two-region arrange-ment and the mixing interface between the two regions.Experimental vessel was first filled with about 70,000 col-orless pebbles to form the initial state of random pebblepacking. During the recirculating procedure, black pebbleswere loaded from the central inlet tube while colorless peb-bles were loaded from the two-side inlet tubes. Meanwhile,pebbles were discharged from the bottom outlet tube at areasonable rate to keep summation of pebbles constant. Aftera period of time, black pebbles were expected to form thecentral region (representing the graphite region) of the two-region arrangement by replacing initial colorless pebbles.

Science and Technology of Nuclear Installations 3

Central region (graphite region)

Mixing interface

Side region (fuel region)

Scattering pebbles

(a) (b)

Figure 2: Equilibrium state of the two-region arrangement after about 7.5 h (a) and the counterpart obtained by DEM simulation (b).

Likewise, loaded colorless pebbles were expected to form theside regions (representing the fuel region). Different states ofthe development of two-region arrangement were recordedby snapshots at intervals. Figure 2 depicts the equilibriumstate of two-region arrangement.

It is shown that two-region arrangement reached anequilibrium state after a period of running. Obviously, therewas a quite rough boundary between central region and sideregion, which is the mixing interface. The maximum sizeof the mixing interface was about 4 to 5 times of pebblediameter. In addition, the appearance of some scatteringpebbles results from the pebbles which are bounced awaywhen theywere loaded at the top of vessel, which is not causedby dispersion.

Thus, the existence of mixing interface is evident, andthe size of mixing interface is finite. According to thephysical calculations for the PBMR reactor, the size of mixinginterface should be less than 5.5 times of pebble diameterto meet security requirements [12]. It seems that the mixinginterface obtained from the experiment agrees with practicalapplication, but the safety margin is not large enough.

Mixing interface depends on the pebble’s dispersion. Inthe recirculating mode of the two-region pebble bed reactor,the motion of individual pebble determines the two-regionarrangement as well as the mixing interface. For the purposeof exploring the characteristics of pebble motion, statisticalinvestigations have been undertaken.

3.2. Study on Pebble Tracks. The pebble motions were re-corded at intervals by tracing the tagged pebbles, when theydescended with the overall downward movement of pebbleflow. At the beginning, the experimental vessel was filledwith colorless pebbles.Then, the pebbles taggedwith differentcolor were distributed uniformly along the radial length andpairwise symmetrized against the central axis of the vessel.When the installation ran, positions of each tagged pebble at

0

0

500

1000

400 800

Hei

ght (

mm

)

Radial position (mm)

Figure 3: Descending tracks of tagged pebbles.

particularmoments were visually detected. In this way, tracksof tagged pebbles were determined and they are found to begenerally like “streamline” form, while these tracks are not assmooth as those of common fluids.

The above experimental procedure was repeated fornumerous times. Each tagged pebble was placed at the samestarting point repeatedly and a bunch of tracks for eachtagged pebble were obtained. The motion characteristics ofindividual pebble are analyzed statistically based on the tracksof tagged pebbles and visual observation. Figure 3 plots alltracks for each tagged pebble.


As seen in Figure 3, the tracks of tagged pebbles locatedat the same initial position are different, but the differencesbetween them are small. It is recognized that pebbles inthe pebble bed move randomly to a small extent, andtracks of pebbles can only be statistically determined. Themovements of pebbles are greatly confined by their neigh-bors, which makes dispersion among pebbles limited and istotally different from general flows.Therefore, the two-regionarrangement is capable to be establishedwithout breaking theconfiguration during running, and consequently the mixinginterface can be constrained to a small size.

Some characteristics of pebble dispersion can be con-cluded preliminarily. Due to randomness of pebble flow, itcan be considered that the descending track of a pebbleis not a single “stream line” but a statistical “stream tube”consisted of a bunch of “stream lines” starting from the samepoint. The diameters of “stream tubes,” which indicate theextent of dispersion, are varied in the vertical and horizontaldirections. Specifically, dispersion of each pebble increases tothe maximum at the midvessel and then decreases accordingto the specific geometry of bottom vessel. The decrease ofdispersion at the bottom of vessel results from the small dis-charging hole which forces pebbles to move more compactly.In addition, pebbles staying away from the central axis have atendency of larger dispersion through the visual stream linesin Figure 3.

After adequate experimental observations and statisticalanalysis, a common view on the behavior of individualpebble has been obtained. Individual pebbles in the sameinitial position at the top of the vessel move downwardwithin a limited region and rarely exceed the slim region.To put it simply, these pebbles flow in the pebble bed likeflowing in a stream tube, which is mentioned above. In otherwords, pebbles’ random movements have been restricted bytheir surrounding pebbles, which lead to a finite dispersionconstrained in a tube-like region. Next, the distribution ofpebbles in the tube-like region is going to be discussed, asthe mixing interface in two-region arrangement is actuallya tube-like region located at a particular radial position.Features of mixing interface, such as size and shape, aredetermined by the behaviors of a series of pebbles flowing ina specific tube-like region.

3.3. Radial Distribution of Pebbles in Dispersion Region.After a period of stable running, attentions are paid to thedistribution of pebbles within a tube-like region which havesame starting-point at a particular height by getting enoughpebble tracks. The tube-like region is a dispersion region of aseries of pebbles. At a particular height, the dispersion regionis divided into several equal intervals, and the number ofpebble tracks within each interval is calculated, as shown inFigure 4 (the upper inset). The tagged pebbles are locatedinside certain intervals according to their initial positions ofmass center. For instance, pebble A belongs to interval 6 andpebble B belongs to interval 10.

In Figure 3, it is easy to find that most tracks lie near thecenter of the dispersing region, and track numbers near theborder of dispersion region aremuch less. Figure 4 (the lower

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1817

A

B

(a) The way to determine pebbles’ radial intervals

Hei

ght (

mm

)


210

208

206

204

202

200

198

196

0 10 20 30 40 50−50 −40 −30 −20 −10

(b) Distribution of tagged pebbles at the height of 204mm

Figure 4: The method to illustrate radial distribution of pebbles.

inset) also demonstrates the phenomenon that most taggedpebbles are concentrated in the central intervals. All thetagged pebbles start from the radial position of 0, and theirradial positions are recorded at the height of 204mm to formthe radial distribution.

In order to study the distribution at a particular heightstatistically, the probability density of radial distributionis defined as quantity fraction of pebbles in each intervaldivided by the length of interval (5mm). In thisway, the curveof probability density of radial distribution at the height of204mm (Figure 4) is gotten and shown in Figure 5. Severalfeatures of the curve should be noticed.The curve has a decentsymmetry whose shape is high in the middle and low in bothsides, which looks quite similar to the Gaussian distribution.

The relevance of the probability density curve toGaussiandistribution has been investigated through curve fitting basedon the experimental data. The obtained fitting curve agreeswith those data points on probability density to a large extent,as is shown in Figure 5. The radial position of symmetryaxis of the Gaussian fitting curve, 0.4mm, is close to themean value of radial positions of these data points, −0.2mm.Therefore, at least the radial distribution at the height of204mm of such pebbles which start from the specific radialposition, 0mm, accords with Gaussian distribution.

According to the uniform characters of pebble flow inexperiments, it is supposed that the radial distributionslocated at different heights of pebbles starting from differentradial positions accord with Gaussian distribution, whichhas been justified by the coincidences between experimental


Probability density pointFitting curve

Starting point: 0mmHeight: 204mm

0.000

0.015

0.030

0.045


Prob

abili

ty d

ensit

y (m

m−1)

0 10 20 30−30 −20 −10

Figure 5: Gaussian fitting curve on probability density of radialdistribution.

data and fitting curves (Figure 6). Therefore, in the entirepebble flow field, it can be generally recognized that radialdistribution of pebbles which have the same starting pointagrees with Gaussian distribution at a particular height indispersion region.

If a random variable 𝑥 obeys the Gaussian distributionwhose expectation and deviation are 𝜇 and 𝜎, the probabilitydensity of 𝑥 accords with the following formula:

𝑓 (𝑥; 𝜇, 𝜎) =

1

𝜎√2𝜋

exp(−(𝑥 − 𝜇)

2

2𝜎2

) , (1)

where 𝜇 determines the location of Gaussian curve and 𝜎determines the range of distribution. The characteristics ofGaussian distribution define that the area surrounded by thecurve and horizontal axis is 1. When the selected regionranges from −2𝜎 to 2𝜎 by the sides of mean value (𝜇), thesurrounded area is 0.9545.

When the law of Gaussian distribution is applied to thedispersion region, a statistical conclusion can be obtained. Itis not difficult to find agreements between Figures 3 and 6.The slim part of dispersion region in Figure 3 correspondswith the “tall” and “thin” distribution in Figure 6, andsimilarly the bulky part of dispersion region relates to the“dumpy” distribution. A small standard deviation means aconcentrative distribution, which represents a small disper-sion region. Therefore, one of the parameters in Gaussiandistribution, namely, the standard deviation 𝜎, indicates thesize of dispersion region.

We investigate standard deviations of radial positions atdifferent heights and radial positions, in order to find the vari-ation trend of standard deviations along the descending path.Figure 7 shows tracks starting from different radial positions.The tracks and variation trends of standard deviations are gotthrough calculating the mean value of radial coordinates atdifferent heights. Actually, there are essential resemblancesbetween Figures 3 and 7, and identical conclusions can also be

drawn from Figure 7. Four curves in Figure 7 reveal that thestandard deviations increase to the maximum at the heightof about 300mm and then begin to decrease, which is likethe variation trend of sizes of dispersion regions. Besides, thecurve of id3 has relatively large values, for pebbles representedby id3 stay far away from the central axis, which can also beobserved in Figure 3 that pebbles in side region have largerdispersion.

The value of standard deviation is in proportion to thesize of dispersion region. Virtually, the concept of dispersionregion is also statistical, since it is only realistic for the regionto comprise a majority of pebbles instead of all of them. Forinstance, the dispersion region can comprise 95.45% pebblesif radiuses of this region are set to be 2 times of standarddeviations at different heights. To some extent, it is acceptableto regard 2 or 3 times of standard deviation as radius ofdispersion region in engineering. In conclusion, quantity andvariation trend of standard deviation display the features ofdispersion region well, and it is applicable to treat standarddeviation as a quantitative index of dispersion region.

3.4. Experiment in Heightened Vessel. Inherent safety ofHTGR in china is insured by its fuel characteristics andpassive safety system, which is attributed to the specificdesign of small radius of reactor core to some extent. Smallradius allows the decay heat to transfer from the inner coreto the outside more easily because of a shorter distance,so that passive approaches like radiation heat transfer andheat convection can meet the requirements of heat-transfercapacity during accidents. On the other hand, in terms of thetotal power, such design restricts the output due to the size ofthe core.Thus, enlarging the height of the core is the adoptiveway, which can drive up the total power and maintain thepassive safety capacity at the same time.

As mentioned in the section of experimental installation,the height of the experimental vessel can be heightened to aheight of 2.2m. Similar experiments have been conducted inthe heightened vessel so as to study whether there would bedifferences or not.

Figure 8 shows the tracks in the heightened vessel. Thetracks in the heightened vessel are also smoothly varied andsymmetric which is similar to those in 1m vessel. As a resultof the cone-shaped bottom and the small discharging hole,tracks bend towards the axis and flowmore compactly.Thereis a region in the upper vessel where the tracks are uniformlystraight, and these tracks do not bend until they reach thebottom vessel. In terms of tracks, there is not an essential linkbetween the upper and bottom regions. The flow field below1m in heightened vessel shares many features with that instandard vessel.

The standard deviation in heightened vessel depictedin Figure 8 reveals more characteristics. The curve of id4is based on relatively limited data, and it perhaps cannotrepresent the physical law well. Compared with the resultsin the last section shown in Figure 7, several differencesare concluded. In general, pebble flow in heightened vesselhas larger dispersion regions, because standard deviationsin Figure 8 reach maximums above 20mm, whereas they


Prob

abili

ty d

ensit

y (m

m−1)

0 10 20−20 −10

0.02

0.04

0.06id0Height: 760mm


(a)

0 10 20−20 −10

0.02

0.01

0.04

0.05

0.03

id0Height: 369mm

Prob

abili

ty d

ensit

y (m

m−1)


(b)

0 10 155−15 −5−10

0.02

0.04

0.06 id0Height: 0mm

Prob

abili

ty d

ensit

y (m

m−1)


(c)

Prob

abili

ty d

ensit

y (m

m−1)

80 90 100 110 120

0.02

0.01

0.04

0.05

0.03

id1

Height: 716mm


(d)

0.01

0.00

0.03

0.02

20 40 60 80

id1

Height: 204mm

Prob

abili

ty d

ensit

y (m

m−1)


(e)

0.02

0.04

0.06

10 20 30

id1Height: 51mm

Prob

abili

ty d

ensit

y (m

m−1)


(f)

Prob

abili

ty d

ensit

y (m

m−1)

175 180 185 190 195 200 205

0.02

0.00

0.06

0.04

id2 Height: 760mm


(g)

70 80 90 100 110

0.02

0.01

0.04

0.03

id2Height: 592mm

Prob

abili

ty d

ensit

y (m

m−1)


(h)

0.00

0.01

0.02

0.03

80 90 100 110 120

id2Height: 204mm

Prob

abili

ty d

ensit

y (m

m−1)


(i)

Prob

abili

ty d

ensit

y (m

m−1)


id3

270 275 280 285 290 295 300

0.04

0.02

0.08

0.06

Height: 760mm

(j)


190 200 210 220 230 240 250

30

35

0

5

10

15

20

25

id3Height: 423mm

×10−3

Prob

abili

ty d

ensit

y (m

m−1)

(k)


160 170 180 190 200 210

30

5

10

15

20

25

id3Height: 314mm

×10−3

Prob

abili

ty d

ensit

y (m

m−1)

(l)

Figure 6: Coincidences between probability density points and fitting curve at different heights and radial positions.

are about 12mm in Figure 7. What is more, apart from id4,curves do not split until they reach the depth of 1000mm,which refers to the uniform flow region in upper vessel.Of course, several laws are justified again. The standard

deviations increase to maximums at the middle vessel andthen decrease. Pebbles staying far from axis have largerdispersion, which can be illustrated by the curve of id3. Atlast, from the perspective of engineering, the most important


0

18

16

14

12

10

8

6

4

2

800 600 400 200 0

Stan

dard

dev

iatio

n (m

m)

Height (mm)

id0id1

id2id3

Figure 7: The variation trend of standard deviations of tracks.

0

5

10

15

20

25

30

35

Stan

dard

dev

iatio

n (m

m)

2000 1600 1200 800 400 0

Height (mm)

id0id1id2

id3id4

Figure 8:The standard deviations of tracks in the heightened vessel.

issue that we should be concerned about is that heighteningreactor core will bring larger dispersion region, which is notexpected.

4. Discussions

The main factors that determine the phenomenon of dis-persion still remain unknown. It is generally accepted thatthe qualitative accuracy of DEM has been verified. DEMsimulation has been adopted to discuss principal parameters’influence on dispersion. The standard deviation at a partic-ular height, as a quantitative index to show the size of thedispersion region, will be investigated with the change ofother parameters.

4.1. Radial Velocity. It is natural to associate dispersion withradial velocity which can be detected in DEM simulation.Figure 9 illustrates variation trend of standard deviation aswell as radial velocity both in 1m vessel and heightenedvessel. The unit of radial velocity (d/s) means diameter persecond and the data were drown from those pebbles startingat half-radius position. In Figure 9, the size of dispersionregion does not correlate well with radial velocity, since thestandard deviation has a sharp increase whereas the radialvelocity remains stable at a low level in the upper vessel. Theoverall correlations have been proved weak, with the Pearsoncorrelation coefficients of 0.0823 and 0.19725, respectively.

In Figure 10, which set radial velocity as abscissa axis,correlation between these two parameters is illustrated moreobviously. When radial velocity is less than 0.005 (d/s), stan-dard deviation has a wide range and is not affected by radialvelocity. Due to the majority of spots standing at low velocity,the overall correlation is not apparent. However, when radialvelocity is larger than 0.005 (d/s), a much more significantcorrelation appears, with Pearson correlation coefficients of−0.9618 in 1m vessel and −0.9648 in heightened vessel,respectively. It means that there is a critical value of radialvelocity, above which the size of dispersion region drops withthe rise of radial velocity.

Enlarging radial velocity seems to help in dispersion con-trol as shown in the above figures, if this rule can be appliedin practice. Nevertheless, the pebble flow in experimentalvessel as well as in practical reactor belongs to quasistaticflow, so velocity of most pebbles is under the critical value(appropriate 0.005 d/s). Only in bottom vessel larger radialvelocity can be realized, and the size of dispersion regiondeclines to some extent. Additionally, we cannot focus on thegrowth of radial velocity to announce that it directly leadsto the decrease of dispersion region, because radial velocityrises at the result of specific bottom geometry whichmay alsoexerts impact on dispersion.

4.2. Base Cone Angle and Friction Coefficient. The vesselgeometry impacts the overall pebble flow dramatically. Tosay specifically, the base cone angle in bottom vessel playsan important role in developing the main features of pebbleflow, including the dispersion region. The base cone angle ofexperimental vessel can be adjusted from 30 to 60 degrees,and corresponding DEM simulations are carried out as well.

As shown in Figure 11, dispersion regions in vessels whosecone angles are 30 and 45 degrees are nearly matched,which means that this change has little impact on the sizeof dispersion region. However, with angle changing from45 to 60 degrees, the maximum size of dispersion regionhas a significant drop. Therefore, geometry influences thephenomenon in a nonlinear way. Perhaps there is also aparticular angle or a specific geometry that can minimize thedispersion. Moreover, the standard deviation does not showdifferences until they reach the middle vessel, which meansthe bottom geometry fails to influence flow pattern in theupper vessel.This enables simplified researches of heightenedvessel, and we can concentrate on the bottom flow field onsome occasions.


0.0

0.2

0.4

0.6

0.8

Radi

al v

eloc

ity (d

/s)

Stan

dard

dev

iatio

n

Height (cm)80 60 40 20 0

0.000

0.005

0.010

0.015

0.020

0.025

Radial velocity Standard deviation

1m vessel

(a) Simulation in 1-meter vessel

0.0

0.5

1.0

1.5

2.0

Stan

dard

dev

iatio

n

Height (cm)

Heightened vessel

Radi

al v

eloc

ity (d

/s)

0.005

0.000

0.010

0.015

0.020

0.025

0.030

Radial velocity Standard deviation

−20020406080100120140160180

(b) Simulation in heightened vessel

Figure 9: DEM simulations on standard deviation and radial velocity in 1-meter and heightened vessels.

Radial velocity (d/s)

Stan

dard

dev

iatio

n

0.0

0.2

0.4

0.6

0.8

0.0050.000 0.010 0.015 0.020 0.025

Standard deviation

1-meter vessel

(a) Data from 1-meter vessel

Heightened vessel

Radial velocity (d/s)

Standard deviation

Stan

dard

dev

iatio

n

0.0

0.5

1.0

1.5

2.0

0.0050.000 0.010 0.015 0.020 0.025 0.030

(b) Data from heightened vessel

Figure 10: Correlation between standard deviation and radial velocity in 1-meter and heightened vessels.

Friction coefficient is determined by physical propertyof individual pebble. Apart from gravity, the friction is animportant force of driving or resisting. It is natural to supposethat a larger friction restricts the behavior of pebbles. Then,the dispersion would be reduced to some extent. In fact,the friction resulting from surrounding pebbles also actsas driving force which may push pebbles away from itsoriginal path and bring about more obvious dispersion. Asa result, we believe that there is a competitive mechanismbetween driving and resisting effects produced by friction.This hypothesis is demonstrated by Figure 12. It is hardto predict variation trend of dispersion by changing thefriction coefficient, because the relation between them isnot consistent in different friction scopes. Bottom pebblesin the heightened vessel suffer more pressure from above

pebbles and competition between the driving and resistanceforces is more intense. As a consequence, the size of disper-sion approximately remains stable when friction coefficientchanges from 0.2 to 0.4, for resistance force as well as drivingforce increases to some extent.

5. Summary

Through the above analysis, we can summarize the following.In our experiment, the stable two-region arrangement in

pebble bed reactor can be established with a definite andfinite mixing interface. The dispersion happened in mixinginterface results from pebbles’ random motion behavior.Pebbles with the same starting point flow downward in a“tube-like” region and rarely get out statistically. This region


A30A45A60

Starting pointSimulation on different cone angles

Stan

dard

dev

iatio

nHeight (cm)

180 160 140 120 100 80 60 40 20

60

45

30

0 −20

0.0

0.5

1.0

1.5

2.0

Figure 11: Simulation on different base cone angles.

Stan

dard

dev

iatio

n

Height (cm)

0.0

0.2

0.4

0.6

0.8

1.0

80 60 40 20 0

f = 0.1

f = 0.2

f = 0.4

Simulation on different friction coefficients in 1-meter vessel

(a) Simulation in 1-meter vessel

Height (cm)

Simulation on different friction coefficients in heightened vessel

Stan

dard

dev

iatio

n

0.0

0.5

1.0

1.5

2.0

f = 0.1

f = 0.2

f = 0.4

−20020406080100120140160180

(b) Simulation in heightened vessel

Figure 12: Simulations on different friction coefficients in 1-meter and heightened vessels.

is called the dispersion region which directly relates to thesize of mixing interface. The side or peripheral dispersionregions have larger diameters compared with central ones,and, for each region, it usually reaches the maximum sizein the middle of vessel. In dispersion region, the radialdistribution of pebbles at a particular height accords withGaussian distribution and the standard deviation determinesthe size of dispersion as a quantitative index.

In the heightened vessel, apart from the uniform flowfield in the upper vessel, pebble flow has a more obviousdispersion.There is a critical value of radial velocity (approx-imately 0.005 diameter/s) that determines the influence on

dispersion. The rise of radial velocity larger than the criticalvalue can reduce the size of dispersion linearly.

Enlarging base cone angle helps in the control of dis-persion. The impact of friction on dispersion region iscomplicated, because friction is related to driving as well asresistance force of dispersion and the competitivemechanismbetween them remains unknown.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.


Acknowledgments

Theauthors are grateful for the support of this research by theNational Natural Science Foundations of China (Grant nos.11072131 and 51106180) and the research funds of TsinghuaUniversity (no. 2010Z02275).

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