Nuclear Engineering and Design 42 (1977) 265-275 265 © North-Holland Publishing Company FLOW OF INDIVIDUAL PEBBLES IN CYLINDRICAL VESSELS t F.C. GATT * Research performed at AAEC Research Establishment, Lucas Heights, Australia Received 3 January 1977 The movement of individual pebbles in a simulated recirculating pebble bed nuclear reactor has been investigated. Ex- perimental and statistical results are presented concerning the transit number spectra of groups of pebbles and the transit of individual pebbles in recirculated random packings of identical pebbles. A cylindrical vessel with a variable base angle and a single axial outlet contained the pebbles which varied in diameter, shape, and specific gravity. The pebbles flowed downward under the influence of gravity and through a rotating extractor in the base. Transit number spectra were found by seeding many coloured pebbles at a pdrticular radius and noting the amount of recircuiation required before they emerged. While the packing descended, a radioactively tagged pebble inserted at the top of the bed was tracked as it moved through the vessel. Tracks and velocities of pebbles for various combinations of seeding radius, bed and pebble parameters were determined. Using these tracks, patterns and effects of flow zones were deduced. 1. Introduction 1.1. Concept of experimental study In a pebble bed nuclear reactor, fuelled pebbles enter at the top of the reactor vessel and undergo a nuclear reaction producing heat. They pass through the bed and out through the base of the vessel via an extractor. Important parameters are the pebble path and relative velocity through the bed, since excessive time spent in parts of the bed could result in severe irradiation and thermal damage to the pebble with possible fission product escape. In this experiment, radioactively tagged pebbles were seeded at various radii and tracked in three di- mensions during their passage through a simulated pebble bed nuclear reactor. Also, coloured pebbles were seeded in circles in the bed in order to deter- mine transit number spectra of pebbles seeded at vari- ous radii. The pebble transit number Twas defined as the number of pebbles recirculated between the t This study is reported in detail in the following series issued by the Australian Atomic Energy Commission. * Present address: Biophysics, P.O. Box 257, Bondi Junction, NSW 2022, Australia. seeding of the pebble in the pebble bed and its exit from the bed, expressed as a fraction of the total num- ber of pebbles in the bed. The levels of the pebble and bed parameters were selected to ensure that data ob- tained would be applicable to a pebble bed nuclear re- actor model. Tingate [1] outlined several of the methods em- ployed in the investigation of flow patterns of peb- bles in a container. The methods included the use of two-dimensional models, flow visualization techniques (glass marbles immersed in a fluid of equal refractive index), contrasting coloured and colourless marbles, computer models, and pills equipped with radio trans- mitters. However, as far as could be ascertained from the literature, individual elements in a recirculating pebble bed have not been tracked. 1.2. Objectives The objectives of the work were: (1) to determine the track, transit number spectra, and velocity of individual pebbles seeded in the bed for various combinations of bed and pebble parameters; and (2) to find the effects on the T spectral properties and flow zone shapes of changes in vessel and pebble parameters.
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`266 F.C. Gatt /Flow of individual pebbles in cylindrical vessels 2. Equipment 2.1. Vessel The vessel (figs. 1,2, and 3, Szomanski [2]) was an upright aluminium cylinder with diameter 30 in. and height 60 in. A conical base (concave as viewed from above) formed the lower end of the vessel. The base angle measured 15 °, 25 °, 35 °, or 45 ° from the horizon- tal (fig. 4). In the centre of the base was located a peb- ble extractor. 2.2. Pebbles Six types of pebbles were pressed from plastic (poly- vinyl alcohol) bonded zirconite sand, cured to the de- sired hardness and plastic coated to provide wear re- sistance. The finished pebbles had the properties as shown in table 1. Aspherical pebbles were used to simulate worn spherical fuel elements. In effect, two sizes of aspheri- cal pebble were produced by removing from each lu Tagged pe~b [e ~) ManualLy formed insertion tube | top cone of ; / ( I1..~ Oo o ,.~. )) /a~gte of .;, Cotoured seeded pebbles u Vesset E ¢J J Fig. 1. Pebble bed. Crane III ~ Tagged pebble ~ =~t==iH-r~ p~bbt~ N I IIIII] tr,ckiog vo,,o, II II lie d ..... cOPnersaot['eng LJ . ill~.~ 'f !. ~ ..~.,,£= , I . ......... -. ~-... .... ...[~...~'. ,. 0"0% o Fig. 2. Experimental equipment. spherical pebble a slab of thickness 0.1 D centred on the pebble equator and then joining the identical halves. Throughout the individual tracking trials a tagged (cobalt-60) pebble of the same sphericity, diameter, specific gravity, and surface finish as those constituting the pebble bed was used. The 6°Co source emits gam- ma rays enabling the position of the tagged pebble in the bed to be determined by monitoring. Source activ- ity was varied to allow for shielding effect at different radii. bble inLet PebbLe tracker etect ors "~" Vessel Fig. 3. Pebble tracking device.
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`F.C. Gatt/ Flow of individual pebbles in cylindrical vessels 267 Rotating extractor ~ e= i Extractor tube ~ 'm ~ Pebbles enclrcle Low position extractor extractor and drop through hole into extractor tube ~ , I k'-S.Sdla.-~ I I"-- B d ta.-'l Fig. 4. Extractor and base. Throughout the T spectra trials coloured pebbles of the same sphericity, diameter, specific gravity, and surface finish as those constituting the pebble bed were used. 2.3. Vessel loading procedure and packing The vessel was filled by loading the pebbles into a cylindrical hopper fitted with a trapdoor in its base. The hopper was loaded into the vessel and the trapdoor was released allowing the pebbles to form a random and relatively loose packing as the hopper was slowly raised. The packing of identical pebbles was made up as follows (fig.l): (1) the base section, extending from the vertex of the vessel base to the top or widest part of the conical base of the vessel; (2) the cylindrical section, extending from the top of the vessel base to the top of the cylindrical section Table 1. Surface finish (projections) Sphericity Nominal pebble diameter D and tolerance Specific gravity -+ 0.001 in. -+ 2% 1.00 ± 0.02 in. or 0.75 ± 0.02 in. 3.00 ± 0.07 or3.40 ± 0.07 of the bed - the length of this cylindrical section at the start of the recirculation was the pebble bed height H; and (3) a naturally or manually formed top conical section of pebbles extending from the top of the cylindri- cal section to the apex of the cone. 2.4. Pebble circulation Pebbles left the bed at controlled rates through the vessel extractor (fig. 4) located in one of two positions in an 8 in. diameter outlet tube positioned in the centre of the vessel base. The extractor rotated while the peb- bles were held almost stationary by the weight of the pebble packing above. As pebbles were extracted one by one, the bed flowed under its own weight down the vessel into the extractor. Pebbles leaving the extractor were counted photoelectrically. Coloured pebbles used in the experiment were picked out manually and the number registering on the counter was noted. The ra- pebble Collimator and counter following pebble movement Via computer Voltage proportional to collimator(or pebble) position Temporal and )osrtronaL data punched paper tape Tempo ra ry "~mag ne t ic tape Jdata storage Amplifier Temporal and L positiona I data t a pe olt ag es proportional to pebble pos;tion ~ versi~ ~11 program converts --'-- l tr,cker J.~" coord~nat e Graphical output mputer f ~J Sem;-permanent pr;nter [ ) magnetic tape \,~._,,,~ res u t t s storage Fig. 5. Tagged pebble experimental data flow.
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`268 F.C. Gatt /Flow of individual pebbles in cylindrical vessels dioactively tagged pebbles were automatically separated from the main stream and reinserted into the vessel when and where required. The uncoloured and untagged pebbles were elevated to the top of the bed by a bucket conveyor. The re-entry of pebbles into the bed was de- signed to ensure an even distribution over the bed. The pebble flow rate throughout the experiment had a variation of +- 125 pebbles/rain (228-478 pebbles/min). These variations had very little effect on T. The flow rate was repeatedly checked throughout each experi- ment using a 5-rain impulse counter connected to the photoelectric cell pebble counter. 2.5. Pebble tracker similar pebbles were seeded (fig. 1) on the horizontal upper surface of this packing at R values of 3, 6, 9, 12, and 14.5 in. using a seeding jig. The number of coloured pebbles seeded at each radius for the packings com- posed of 0.75 in. D pebbles were 25, 49, 75,100, and 118 respectively for the above radii, and 25% less for the 1.00 in. D pebbles, thus completing the full circle of coloured pebbles at the respective radii. The top cone was manually formed over the seeded pebbles and recirculation of the bed was begun. The T of each col- oured pebble was noted at the moment of its extrac- tion and thus five T spectra were formed for each chosen combination of pebble and vessel parameters. Movement of the tagged pebble was followed by a tracking device (fig. 3) using pairs of collimated radi- ation detectors. The central pair (axial detector) was used to establish the vertical position of the tagged peb- ble and then the outer pairs were rotated to fix its hor- izontal position. The equipment was designed to locate the tagged pebble in successive positions automatically at given time intervals, display the results, type them, and record them on punched paper tape for computer processing (fig. 5). 3. Experimental procedure For the determination of individual pebble tracks the vessel was filled with untagged identical pebbles to the required H with the top cone of pebbles being formed manually. The tagged pebble was introduced through an insertion tube to a point just below the level of the top cone surface at the desired R. Recirculation of the bed and location and tracking of the tagged peb- ble was then begun and continued as the tagged pebble descended with the bed. When the tagged pebble emerged, its T was noted. In all tagged pebble trials, the pebble extractor was located in the low position (fig. 4). Analysis of the track utilized the temporal and positional data from the pebble tracker punched onto five-channel paper tape. The records were proces- sed to calculate pebble track and velocity and then re- produced graphically. For determination of T spectra for each group of tagged pebble tracks the vessel was filled with uncol- oured identical pebbles to the required H. Coloured 4. Results and discussion 4.1. Analysed trials A total of 103 separate trials in 15 groups were car- ried out. The 15 group specifications are given in table 2 and the spectral parameters of each group are given in table 3. The trial numbers, and value of R and T for each of groups 3, 4, and 5 (generally representative of all groups) are listed in table 4. The pebble tracks of these groups (figs. 6, 7 and 8) show the projection (onto one vertical plane across a bed radius) of the axial and radial components of the path of the pebble (with the trial number indicated at the top of each track). The bed centre is represented by the vertical axis. The flow of pebbles through the bed was stream- lined. After descending the bed in a vertical direction (relatively low velocity) the pebbles approached the base and began to move uniformly towards the outlet (relatively high velocity). The numeral at each point on the track is indicative of the number of pebble tracker 'fixes' on the pebble as it passed within the boundaries of each numeral or point. Towards the top of each track the pebble velocity was low, shown by the generally larger numeral plotted on the track. With an increase in velocity, the magnitude of the plotted numeral decreased. When the numeral assigned to each point reached 1 (or '.') and the pebble velocity was still increasing, the distance between each point increased. Pebbles followed fairly straight paths down the cylin- drical section of the bed with very little interference or crossing between paths. Some of the pebbles seeded at the wall tended to move inward as soon as recircula- tion had begun.
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`F C. Gatt I Flow of individual pebbles in cylindrical vessels 269 Table 2. Group specifications• Group D Pebble number shape Pebble H Base specific angle gravity (degrees) 1 1.00 sph 3.4 32 15 2 1.00 sph 3.4 29 35 3 0.75 sph 3.4 30 35 4 0.75 sph 3.4 30 15 5 0.75 sph 3.4 30 45 6 1.00 sph 3.0 30 35 7 1.00 sph 3.0 24 35 8 1.00 sph 3.4 24 35 9 1.00 asph 3.4 24 35 10 1.00 asph 3.4 30 35 11 1.00 asph 3.0 24 35 12 1.00 asph 3.0 30 35 13 0.75 asph 3.0 24 35 14 0.75 asph 3.0 30 35 15 0.75 sph 3.4 24 35 sph: spherical. asph: aspherical. 206 202 205 201 20~ 208 211 213 70 203 207 210 212 !!! ¢ o m 40 3O F 20 R : 12 10i 100 90 80 7( 6C F 5( RzlA.5 40 3( 2C 1C "--] ; g 1'o 15 2 T PEBBLE BED RADIUS. in Fig. 6. Individual pebble tracks and spectra for group 3. 2 o w i o to m ta m W 134 130 133 129 125 135 132 12~ 75 131 128 126 122 : 12 ~ ~ 2 -~ // i;? ~' 2 ;2 ; 2;.-. 3 4 i: ; ( rl 2' ~' • : ;/ 2 2" ; •. :~ .-~ (,! ', ' 4 • 'o , S:/i'~ /'~ 2 /" 2 I d / 2 i O 5 I0 15 PEBBLE BED RADIUS. in. 40 F 20 80 70 60 50 F 40 3C 2C lC 07 01~ 09 1.0 13.6 T = .5 I(] 2(3 T Fig. 7. Individual pebble tracks and spectra for group 4.
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`270 F.C. Gatt / Flow of individual pebbles in cylindrical vessels Table 3. Group spectral parameters T mean (upper), T standard devi- ation (lower). Group R (in.) number 3 6 9 12 14.5 1 0.47 0.51 0.60 0.89 3.00 0.015 0.013 0.027 0.173 1.318 2 0.70 0.72 0.77 0.87 1.03 0.011 0.010 0.030 0.032 0.055 3 0.75 0.77 0.84 0.95 1.25 0.013 0.013 0.022 0.025 0.194 4 0.35 0.37 0.47 0.71 3.46 0.003 0.010 0.018 0.074 2.403 5 0.79 0.80 0.84 0.93 1.12 0.009 0.011 0.014 0.020 0.072 6 0.73 0.77 0.83 0.96 1.18 0.012 0.016 0.015 0.024 0.053 7 0.61 0.64 0.75 0.95 1.41 0.015 0.014 0.019 0.051 0.116 8 0.68 0.72 0.81 0.97 1.26 0.017 0.019 0.017 0.037 0.076 9 0.68 0.73 0.82 1.00 1.30 0.011 0.012 0.017 0.046 0.063 10 0.72 0.73 0.79 0.92 1.26 0.009 0.009 0.018 0.032 0.108 11 0.51 0.57 0.71 0.98 1.50 0.010 0.015 0.029 0.069 0.111 12 0.71 0.77 0.87 1.03 1.37 0.020 0.018 0.016 0.036 0.094 13 0.57 0.62 0.80 1.09 1.65 0.007 0.018 0.070 0.060 0.126 14 0.74 0.78 0.86 0.99 1.27 0.005 0.009 0.015 0.028 0.083 15 0.65 0.71 0.82 1.00 1.32 0.015 0.016 0.025 0.040 0.113 4.2. Flow zones Deutsch and Clyde [3] have devided the flow pat- terns occurring during discharge into four zones: pipe, pipe feed, dead, and plug flow zones (fig. 9). The peb- bles within the dead zone moved extremely slowly or not at all. The plug flow zone was above the influence of the base and except for a boundary layer effect the velocity profile within this zone was uniform. Peb- bles entering the pipe feed zone gained a radial veloci- ty component. All pebbles left the vessel via the pipe zone, a region in which the velocity was relatively high and vertical. The flow zones formed using each of the four bases Table 4. Trial transit numbers. Group Trial R T number number 3 69 14.5 1.30 70 0.0 0.71 201 0.0 0.67 202 1.0 0.69 203 2.0 0.73 204 3.0 0.75 205 4.0 0.74 206 5.0 0.73 207 6.0 0.79 208 7.0 0.82 210 9.0 0.83 211 10.0 0.90 212 11.0 0.92 213 12.0 0.97 4 75 0.0 0.41 122 13.0 1.11 124 11.0 0.56 125 i0.0 0.56 126 9.0 0.43 128 7.0 0.37 129 6.0 0.34 130 5.0 0.32 131 4.0 0.32 132 3.0 0.32 133 2.0 0.32 134 1.0 0.31 135 0.0 0.30 5 102 0.0 0.70 103 1.0 0.73 104 2.0 0.75 105 3.0 0.75 107 14.5 1.10 108 14.0 1.06 109 13.0 0.98 110 12.0 0.95 112 5.0 0.79 113 6.0 0.81 114 7.0 0.81 were deduced from the pebble tracks (fig. 10). The diagrams generally show that the smaller the base angle then the larger was the dead zone. The extent of the dead zone for the various bases is given in table 5. Even though the base angle increased to 45 ° , the dead zone did not entirely disappear. Furthermore, the inclination of the dead zone increased as the base angle increased. In three separate experiments, a vessel with a 15 ° base was filled to 30 in. with 0.75 in. D spherical peb-
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`F. C Gatt / Flow of individual pebbles in cylindrical vessels 271 .E m m w o_ 103 105 113 102 104 112 11/, 3C • 2 2. 2 232 .' ~g J ; ~ ~/-~ ~L2"i'-' 11 0 I08 109 107 2 ! ? 3' 40 30 F 20 - R : 12 10 - 40 3O / 1_ 2' / ~ 0 / / ~ r._ 2 / F 20 ,0 • , o-- 0 5 10 15 1 T PEBBLE BED RADIUS, in Fig. 8. Individual pebble tracks and spectra for group 5. bles after a tagged pebble was placed: (i) adjacent to the junction of the base and cylinder; (ii) two pebble diameters in and two pebble diameters up from the junction; and (iii) three pebble diameters in and three P OSf O 15 ¸ = io o w 5 li1 m m 0 -5. 5 ::= 0 Lu :c o w-5 Do uJ ~0 O0 O- L -5- 5 10 15 Pipe feed piPe~ 0 -5 -10' Ptu 9 flow 5 10 15 S 10 lS Pipe~ i 5 10 15 PEBBLE BED RADIUS, in. PEBBLE BED RADIUS,in. Fig. 10. Actual flow zones for varying base angle. II IPlug flow zone iPipe feed zone ~Dead zone ~Pipe zone Fig. 9. Flow zones. Arrows indicate approximate relative velocities up from the junction. In cases (i) and (ii), after the re- circulation of 250 000 pebbles, tracking showed that the tagged pebble had not moved from its original position. In case (iii), the tagged pebble began to move slowly and intermittently after a recirculation of 200 000 pebbles and finally emerged after a recircula- tion of 508 000 pebbles. If a pebble becomes lodged in the dead zone it could stay there indefinitely since very little or ho motion occurs at the vessel boundary of the dead zone. The tracks of several trials moved through or grazed the edge of the dead zone. These trials were all seeded at or close to the wall and had a velocity of 0-2 in./min in the region of the dead zone, compared with a maxi- mum velocity of 38 in./min for pebbles in other parts
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`272 F.C Gatt / Flow of individual pebbles in cylindrical vessels Table 5. F10w zone geometry. Base Dead * angle zone extent (degrees) (in.) 2s 1 ----. Dead ** Plug *** zone inclina- flow zone :l-" 2 tion (degrees) extent (in.) 20 - 45 12 ": • - ]-- 50 10 2 55 6 c~ I 62 6 ~ is._ [" 3= 2 fD m tzJ Q_ (-9 laA "l- X 15 6.5 25 6.5 35 4.5 45 4.5 * Dead zone extent is the distance that the dead zone rises up the cylindrical section of the bed. ** Dead zone inclination is an average inclination of the dead zone surface to the horizontal. *** Plug flow zone extent is the distance from the base of the cylindrical section to the lower end of the plug flow zone. of the bed. Pebbles passing through the bed close to the dead zone all exhibited low resultant velocities. The extent of the plug flow zone was measured from fig. 10 (see table 5). With an increase in base angle the size of both the plug flow zone and pipe zone increased mainly at the expense of the pipe feed zone, thereby increasing T for pebbles seeded in the centre of the bed and decreasing T for pebbles seeded at or near the vessel wall. 4.3. Pebble velocity At a constant recirculation rate in a fixed geometry bed the downward velocity of the pebble varied with its axial and radial position. An examination of the radial, angular, and circumferential velocities indicated intermittent movement throughout the whole of the transit. Resultant velocities were small at the top cone and cylindrical section and increased sharply towards the base section. A typical plot of the resultant pebble velocity versus the axial height of the pebble in the bed is given in fig. 11. The resultant pebble velocity versus the radial position of the pebble in the bed is shown in fig. 12. As the pebble neared the centre of the peb- ble bed its resultant velocity increased indicating the higher velocity regions of the pipe feed and pipe zones. No sign of an increase in the circumferential velocity was noted as the pebble neared the extractor. A problem encountered during recirculation of fuel elements was crystallization or an ageing effect which 10 -5 Tr;at 363 Group 15 R = 6 i = 1 2 3 4 RESULTANT PEBBLE VELOCITY, in. per rnin. Fig. 11. Resultant pebble velocity versus pebble axial position. was the formation of regular packings in layers near the wall. This increased the time taken for pebbles near the wall tO transit the bed and could have been a contribut- ing factor to the excessive time spent by the tagged pebble traversing the bed in several trials. For a detailed outline of the mechanisms of individual pebble flow in- cluding the above effect, see Tingate [1 ]. 4.4. Pebble transit numbers 3]ae T spectra may differ in many ways. In practice the salient features of each may be represented by a small number of statistics - a measure of position (mean), a measure of extendedness (unbiased standard
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`F.C. Gatt / Flow of individual pebbles in cylindrical vessels 27 3 c 3 c~ Lid flD Z CQ ,.n 2 b- 0 Z 0 0 ~L ¢v Triat 363 Group 15 __, R - 6 °Bo 3 • ~.:.-2 -6-. i 6 i i i 3 /- S RESULTANT PEBBLE VELOCITY. in. per rain. Fig. 12. Resultant pebble velocity versus pebble radial position. deviation), a measure of symmetry and a measure of peakedness (spectral shape, the degree to which the observations from a sharp mode as opposed to a fiat one). The range of T spectral means and standard devia- tions are given in figs. 13 and 14 and include the re- sults of other similar experiments. The T spectra at the 12 and 14.5 in. R are plotted in figs. 6-8 and show the frequency of seeded pebbles emerging from the vessel. For example, at the 14.5 in. R the spectrum of group 4 (fig. 7) would indicate that the frequency of seeded pebbles emerging from the vessel would be high at the start and then decrease rapidly. The T spectrum of the 14.5 in. R of group 3 (fig. 6) could indicate two main streams of pebble flow. The majori- I Fig. 13. Range of transit number spectral means for varying base angle and seeding radius. ty of the seeded pebbles would emerge relatively quick- ly perhaps moving through the pipe feed zone to the pipe zone, while another portion would take a longer route perhaps by grazing the dead zone. A measure- m ~ 0.25 -o t ; ~ ,, ~ o.2 ¢ ', ~ , f', "' ""', OAS ".. i ' "', x~ -, 0.05 Fig. 14. Range of transit number spectral standard deviations for varying base angle and seeding radius.
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`274 F. C Gatt / Flow of &dividual pebbles in cylindrical vessels 1.5 o I. z ~ ~, in. 14,S 1.3 o 12 : 1.0 E 0.9 6 0.8 ~ 0.7 22 24 2'6 28 30 3'2 0.2 value '"= 0.15 z/14.5 ~ .05 ~o jo 12 O o /9 ' o ~ -- ~ ~3 z2 2~ 26 28 3; ;2 p__ H, in Fig. 15. Average of mean and standard deviation of transit numbers versus pebble bed height. ment of the spectral shape would impart some know- ledge of the spread of pebbles which emerged from the bed and would give an indication of the proportion of pebbles which followed the various available paths through the bed. 4. 5. Effect of seeding radius and base angle The spectral parameters (table 3, and figs. 13 and 14) showed that the effect on T of increasing R was to increase both the mean and the standard deviation of the T spectrum. When R was greater than 12 in. both mean T and the spread of the T spectrum gener- ally increased sharply implying a greater probability of error in predicting T values in this region. It was evident from fig. 13 that the larger the base angle then the smaller was the spread of the means. The 45 ° base had the least change in mean Tacross the vessel radius, and by extrapolation a constant T (unity) across the vessel radius could result using a 60 ° base angle. The radius at which unity T occurs was approxi- mately 12 in. for the 15 ° base angle, and decreased as the base angle increased. As the base angle increased, mean T to the right of the unity T point decreased and mean Tto the left of the point increased as base angle increased, since the integrated T was constant. 4. 6. Effect of pebble bed height on transit number The averages of each of the T means and T standard deviations at each radius (together with the results of other similar groups) were plotted against H for 35 ° base angle trials (fig. 15). For pebbles seeded near the wall, a minimum mean and standard deviation was evident at an H of 27.5 in. The mean T curves were fitted with a quadratic dependant on H together with an exponential dependant on R as shown in table 6. Table 6. Transit number expression. Form Coefficients Constraints T = a 1 + a2H + a3 H2 + a 4 exp(asR) a 1 =' +8.6555 a 2 = -0.59783 24 -< H < 30 a 3 = +0.011083 a 4 = +0.010874 3 < R < 14.5 a s = +0.2728
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`F.C. Gatt / Flow of individual pebbles in cylindrical vessels 275 The maximum percentage error and maximum absolute error between actual T and calculated T was 16% and 0.17, respectively. 5. Summary and conclusions Paths of pebbles through the bed were streamlined. The motion of individual pebbles was intermittent and there was very little interference or crossing between pebble paths. Resultant pebble velocities were small near the top cone but increased sharply towards the base section and towards the centre of the bed. There was no notice- able rotational component of the resultant pebble ve- locity in the base section, indicating very little effect of the extractor on pebble motion. All four pebble zones existed for all base angles tested. Pebbles seeded near the wall tended to move toward the centre of the bed thus avoiding the very slow-moving dead zone. This inward movement ap- peared to begin anywhere throughout the height of the cylindrical section. The time spent by a pebble in the bed was increased by grazing the dead zone. Parts of the dead zone formed by a 15 ° base appeared to be permanently fixed, not moving at all ag recirculation progressed. As the base angle was increased to 45 ° the dead zone still existed and affected pebble flow. Again when the base angle was increased, the pipe feed zone size generally decreased, and the pipe zone and plug flow zone sizes increased, resulting in an increase in the transit number of pebbles seeded near the vessel centre and a decrease in the transit number of peb- bles seeded near the vessel wall. The transit numbers of the individual trials were in agreement with statistics of previous work. When the seeding radius was located near the vessel wall both the mean and standard deviation of the transit number spectrum increased sharply, this increase being more pronounced as the base angle decreased. The larger the base angle then the more horizontal was the veloci- ty profile and the more predictable the transit number. For a 35 ° base angle with seeding near the vessel wall, transit number spectra appeared to have a minimum mean and standard deviation at approximately 27.5 in. pebble bed height. Pebble diameter and pebble specific gravity had no noticeable effect on the transit number spectra; how- ever, the range of variation of these parameters was small. In relation to nuclear reactor design there would be a need for a steep cone at the vessel base if flat transit number spectra are to be achieved. The results could be applied directly to the design of a very small reactor core, but care needs to be taken in extrapolating the results to large core sizes. The following parameters should create optimum flow conditions in a pebble bed nuclear reactor vessel. For equality of transit number across the bed and for least spread of transit number spectrum the optimum base angle would be 45 ° or greater. Within the limits investigated, the pebble diam- eter and specific gravity should have no effect. Opti- mum pebble shape would be spherical. With a 35 ° base angle the optimum pebble bed height would be approx- imately 27.5 in. It may be preferable to use the low extractor position because of heat and nuclear radia- tion effects. Nomenclature al a2 a3 a4 a5 D F H T = coefficients for transit number expression = nominal pebble diameter (in.) = frequency of seeded pebbles emerging from the vessel = pebble bed height, the height of the cylindrical sec- tion of the pebble bed at the start of recirculation (in.) = distance from the pebble bed centreline, of a pebble when initially seeded (in.) = pebble transit number, defined as the number of peb- bles recirculated between the seeding of the pebble in the pebble bed and its exit from the bed, expressed as a fraction of the total number of pebbles in the bed. References [1] G.A. Tingate, Nucl. Eng. Des. 30 (1) (1974) 36. [2] E. Szomanski, Mech. Chem. Eng. Trans. MC3 (1) (1967) 40. [3] G.P. Deutsch and D.H. Clyde, Amer. Soc. Civ. Eng., J. Eng. Mech. Div. 93 (EM6) (1967) 103, paper 5660. [4] F.C. Gatt, Flow of spheres and near spheres in cylindri- cal vessels, Part II - Pebble transit in recirculated random packings,-AAEC/E207 (1970). [5] F.C. Gatt, Flow of spheres and near spheres in cylindrical vessels, Part III - Transit spectra for recirculated random packings, AAEC/E225 (1972). [6] F.C. Gatt, Flow of spheres and near spheres in cylindrical vessels, Part IV - Individual flow paths in recirculated random packings, AAEC/E273 (1973).
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