: . LOFT ORNL P 1798 . 4 : : . 1 in: . . 3 IH " 1.1 12.0 11:25 1.1.4 1.6 MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS - 1963 vino . ORNLP - 1998 Cont-660302-1 MIT itthon DEC 21 RELKASID FOR AWOLXCAMINT II NUCLEAR SCIENCE ABSTRACTS CFSTI PXICES NG $3.00; AN. 65 VELOCITY MEASUREMENTS FOR BEDS OF LARGE, UNIFORM-DIAMETER SPHERES PACKED IN A FULL-SCALE MODEL OF A PEBBLE-BED NUCLEAR REACTOR R. D. Eudy and H. W. Hoffman Res.ctor Division TOTTEET vironme for Submitted for resentation at the Third Southeastern Conference on Theoretical and Applied Mechanics to be held at the University of South Carolina, Columbia, South Carolina, on March 31. - April 1, 1966. LEGAL NOTICE This report Wan prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with rospect to the accu- racy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosad in this report may not Infringe privately owned rights; or B. Assumes any llablütles with respect to the use of, or for damages resultag from the use of any information, apparatus, metbud, or process disclosed in the roport. As used in the above, "person acting on behalf on the Commission" includes any em- actor of the Commission, or omployee of such contractor, to the extent that such employee or contractor of the Commission, or employee of such contractor proparos, disseminates, or provides access to any information pursuant to his employment or contract with the Commission, or his employment with such contractor. Oak Ridge National laboratory Operated by Union Carbide Corporation for the U. S. Atomic Energy Commission VELOCITY MEASUREMENTS FOR BEDS OF LARGE, UNIFORM-DIAMETER SPHERES PACKED IN A FULL-SCALE MODEL OF A PEBBLE-BED NUCLEAR REACTOR R. D. Bundys and H. W. Hoffmanes Reactor Division ABSTRACT Velocity profiles were determined for shallow beds of randomly packed spheres to provide information needed in the thermal analysis of pebble-bed nuclear reactors, such as the PBRE being developed at one time by the Oak Ridge National laboratory. Concurrent measurements of the void fraction and superficial angie of repose for these beds supplied data useful in the interpretation of the velocity profiles. The beds examined were formed of 1 1/2-in.-diam graphite spheres packed by various techniques in a full-size, Plexiglas, PBRE core model having approximately a conical bottom and a cylindrical body. An upward air flow simulated the helium reactor coolant. Point velocities were ob- tained above the exit face of the bed with a hot-wire anemometer. Bed weli configurations included complete beds capped by fill cones and flat- topped arrangements of several depths. Void fractions measured for full beds ranged from 0.393 to 0.401; superficial angles of repose varied between 16 and 29 deg with consider- able circumferential fluctuation (2 to 12 deg) from the mean. For beds Research sponsored by the U. S. Atomic Energy Commission under con- tract with the Union Carbide Corporation. SMember, Heat Transfer-Fluid Mechanics Section, Engineering Science Department, Reactor Division. lef, Heat Transfer-Fluid Mechanics Section, Engineering Science Department, Reactor Division with lill coles, the radial velocity profiles displayed a peak normalized velocity of 1.8 near the vessel wall and a minimum of less than half the mean superficial velocity near the core longitudinal axis. For beds with level tops, the profil.es were considerably flattened, allowing maximum velocities about 1.3 times the mean end minimum velocities about three fourths of the mean. The velocity profile at a given bed height was virtually fixed by the packing arrangement in a thin region of the bed immediately below that height. Wave-like fluctuations in the mean radial velocity profiles in the central region of the beds were attributed to variations in the packing density. Significant variations in the local velocities with circumferential position at a given radial location were observed. These variations were greater with fill-cone capped beds than with flat-topped beds and, for the beds with the pill cones, were greater in the central region than near the wall. The most common separation be- tween local maxima or local minima in the velocity data – a measure of the distribution of loosely and densely packed clusters - was three sphere diameters. INTRODUCTION Nucl.ear reactors using spherical, rardomly packed fuel elements cooled by a gas flow have received consideration during the past few years; the designation "pebble bed" has most often been attached to this concept. Knowledge of the flow distribution within the core region of such pebble-bed reactors is important in two aspects. First, the average radial velocity distribution will establish the average bed radial temper- ature profile and, hence, the maximum power output of the core. Second, local deficiencies in the velocity may cause local overheating ar?, hence, fuel-element damage including fission-gas release. Vessels packed with a variety of solid shapes have been used for many yeare in the chemical processing industry, and radial velocity pro- Piles for fluids flowing through packed beds have been reported in the literature frequent).y.1-12 Because of the random structure of these beds, velocity-profile measurements within the beds are difficult; and most in- vestigators have chosen to measure the velocity outside of the bed near the exit face. These studies have also generally considered cylindrical beds with relatively large bed height-to-diameter ratios and flat inlet and exit faces. In contrast, the bed for a nuclear reactor may be quite shallow – perhaps with a bed depth less than the diameter, may have a hemispherical or conical bottom with protrusions for control-rod or sphere- discharge mechanisms, and may be topped by one or more fill cones result- ing from recycling of the fuel. These geometrical differences provided one motivation for this study. A second stimulus derived from the conflicts in the published data. Thus, Schwartz and Smithe state that their measured velocity profiles were independent of bed depth; while Morales, Spinn, and Smith? Pound that the Facked-bed velocity profile approached that of an empty tube as the bed became shallover. Further, there la dispute among various investigators as to the shape of the radial velocity profile. The data of several researchers (normalized 80 as to be independent of the flow rate) are compared in Fig. 1; there 18 disagreement on both the location of the velocity maximum near the wall and on the radial distribution of the nor- malized. velocity. For example, maximum velocities vary from 178 down to 113% of the mean velocity; and minimum velocities, from 87 to 47% of the mean. Finally, while most published data on radial velocity profiles derive from circumferentially a eraged measurements, limited results of Morales et al? and of Jenkins, Morgan, and Stoverd2 suggest that large variations in velocity with angular position do exist at any given radial distance. As noted above, this factor is of significant importance in pebble-bed reactor design. This combination of disagreements, uncertainties, and hinted trends in the open literature led to the decision to pursue experimentally the determination of the velocity distribution for a specific reactor config- uration - Pebble-Bed Reactor Experiment (PBRE) – then being seriously studied at the Oak Ridge National Laboratory. Further, since these experi- ments were to be made on a full-scale system – in contrast to previous studies in which small-scale models were universally used – some insight into the scaling laws for packed beds was anticipated. URNL-DWG 65-BRZ REFERENCE Dlin.) Delin.) , Zlin.) 4 0.25 16 > 20 4 0.188 21.3 - 3 0.156 19.2 23 2 0.125 16 > 24 INVESTIGATORS FLUID DORWEILER AND FAHIEN AIR --- COLLINS AIR .. SCHWARTZ AND SMITH AIR CAIRNS AND PRAUSNITZ WATER - - 12 1.8 mo Walit. 0 : 0.2 0.4 0.6 0.8 4.0.. ... . Fig. 1. Comparison of Normalized Velocity Profiles Measured by Different Investigators. O APPARATUS The experimental facility constructed for this study* (shown sche- matically in Fig. 2) consisted of (1) a core model containing the packed bed, (2) an alr-Bupply system, (3) a sphere-handling system, and (4) a system for measuring the velocities above the bed. Each of these items is considered separately in the paragraphs which follox. Core Model. The core model was constructed from two flanged Plexi- glas sections. The upper portion was a cylinder of 30-in. inside diameter and 48-in. height. Located beneath this was the inlet section shown in the photograph of Fig. 3. The base of this section was an expanding cone with an included solid angle of 120 deg which merged at ühe top, on a 5 1/4-in. radius, with the cylindrical section. The sphere-discharge dome, located on the axis at the bottom of this inlet section was a 2-in.-ligh, ROT right-circular cylinder capped by a 120-deg cone with a rounded apex. Air was admitted to the bed through three sets of gas-inlet slots in the boitom face of the inlet section: (1) primary radial slots (3/8-in. wide ] ex- tended from a radius of 6 1/2 in. to within 3/8 in. Oll the wall, (2) sec- ondary slots, 3/8-in. wide also, were located between the primary slots in tise outer region within 5 in. of the wall, and (3) circumferential, 3/8- in.-wide slots were milled into the conical dome (not shown in Fig. 3). No air entered the bed in the region between a radius of 4.75 in. and a radius of 6 1/2 in. The spheres were machined of graphite and had a mean diameter of 1.501 in. with a standard deviation of 0.006 in. based on a sample of 45 spheres. When filled, the core model held about 12,000 spheres. "A more detailed accounting of this research can be found in Ref. 13 submitted to the University of Tennessee in partial fulfillment of the requirements for the Master of Science Degree in the Chemical Engineering Department. ORHL-LA-DWG 7907ORAR ELECTRIC EYE COUNTER SPHERE STORAGE VESSEL ZZZZZZZZZZZZZ ELECTRIC EYE COUNTER SPHERE RETURN LINE TRAVERSING MECHANISM- . PACKED BED- - SPHERE RETURN LINE (VACUUM) SPHERE DISCHARGE DOME UPSTREAM SECTION -- 30-in.-diam FLOW-DISTRIBUTION · CHAMBER SUPPORT STANDS – ROTATING FUEL-SPHERE DISCHARGE LINE DALL TUBE OR ORIFICE 10-in. - diam PIPE DISCHARGE-DOME DRIVE MOTOR --: - 30-in.-diam FLOW-OSCILLATION- DAMPING SECTION ... - EXHAUST MUFFLER WIIIIIIIIIIZZEZZ BLOWER FLOW CONTROL VALVES- 1.3. 1.14.2 CONCRETE PAD ken - .--. --... . .. .-........ ... ......... .. ...-.poco.. .-.-.- .- .- Fig. 2. Schematic Diagram of the Experimental Facility. Hr-mi. . ............. ... ..... ........... .. - . . ... Phiv. 38593AR . INCHES ויויויוייוייי! יוי!י!ידיניוניזיגידידך Hoteller Nu . OUAL SLOTS ANNEN . :: . SINGLE SLOTS . mi on. ! gugreedyebab... SPHERE-DISCHARGER DOME V NO-FLOW REGION " ! . 2 - .. . .. ' ! many as soon a 1 . 1 .. i i. 1 .. USD iii! ? ; wanneer heel in , iar .: .:.: '.:. . 71:.; * is dwe isi asus . M . . . * *...-: ;. : . . . 2. . . Han erabilera alumnados con what SL Fig. 3. Bottom Geometry of Pebble-Bed Reactor Experimental Core Model. -- -- -- -- - - - ..... ..- . . ............. -- . . . . . . . . . . . . . . .... - - ... ---- . Air Supply. Up to 6000 scfm of low-pressure air was supplied to the .- -- bed from a blower located outside of the building. The air flowed from the blower to a 9-ft-long section of 30-in. pipe which served to reduce flow fluctuations to an acceptable level. A 6-in.-long section of 3/8- in.-wide honeycomb material, located just downstream of this damping cham- ter in the 10-in.-diam supply line, assisted in straightening the flow. The flow was metered by a 6-in.-diam (B = 0.6), square-edged orifice posi- tioned in the supply line 177 in. downstream of the damping chamber. The air emerging from the supply line passed into a 30-in.-diam pipe within which the jet of air was broken up by a two-plate, sieve-type mixer and was directed upward by a 30-in.-diam elbow. The air velocity in this -. Wo - large diameter elbow was sufficiently low as to have negligible effect on the velocity profile in the bed; the velocity head in the elbow was ~0.5% of the pressure drop across the complete bed and 3% of the AP across four layers of spheres. Positioned above this elbow and immediately upstream of the core model was a pipe section designed to assure a uniform inlet flow to the core; this region is 111ustrated in Fig. 4. The air emerging from the elbow was was directed to the core through 272 (3/4-in. ID 18 1/4-in. long) tubes arranged in a triangular pattern on 1 1/2-in. centers. The resistance to air flow in the discharge dome was matched to that in the rest of the en- trance section; this was accomplished by causing the air to flow first through a set of 1/2- or 3/4-in.-diam holes and then through 3/8-in.-wide circumferential slots. Sphere Handling. Spheres were removed singly from the bottom of the bed through a 1 5/8-in.-diam hole in the side of the discharge dome as this revolved and vacuum lifted to a storage vessel located above the core. ONNL-DWO 66-1937 - 20 DIAM - - 15 DIAM +14% DIAM —35816 DIAM – if 10% DIAM 942 DIAM (MIN) - - NOTE: ALL DIMENSIONS ARE IN INCHES HOLE CENTERS ARE SPACED ON 12 TRIANGULAR PITCH WELD, BOLTS, etc. ARE NOT SHOWN - ORILE -------- TINTIIN -- 25% ---- KEY - - - 7/8 OD * 3/4 10 * 1814 ALUMINUM TUBE (TYPICAL) VID STEEL ESTA OAK WOOD - - - 30 in SCH 10 PIPE- - SZZSZIVATTIIIIIIIIIIIIIIIIIIIIIIIIIIIIIITT! - - - - - - - - - - - - - - -- - -- - IIIIIIIIIIIIIIIIIIIIII - - - - - - - - - AS COUNTERSORE N 14 DEEP (TYPICAL) - - : - - - 5116 - - - - - - - le..3/4 (TYPICAL) ------..............3538 DIAM -- SECTION A-A Fig. 4. Upstream Region. - . - Spheres were added singly to the bed by free fall from this storage chamber at a rate of one per second through a supply line that terminated on the longitudinal axis of the core at a position 6 1/2 in. above the model. Photoelectric cells mounted on the sphere-transport piping counted the spheres taken from or added to the bed. Velocity Measurement. A constant-resistance-ratio, Flow Corporation 55B1, hot-wire anemometer was used to measure point velocities in the air stream emerging from the bed. This probe was mounted above the bed on a traversing mechanism that could both position the instrument and indicate the location with an accuracy of 0.1-in. radially, 0.1-in. vertically, and l-deg angularly relative to an arbitrarily defined coordinate system. A 4000-microfarad capacitor was placed across the anemometer output to reduce fluctuations caused by turbulence. The anemometer was calibrated against a known air flow in a 4-in., schedule 40 pipe; the air flow was metered by an 0.875-in. orifice (B. = 0.22) which was preceded by 72 diameters of straight pipe. The large number of velocity measurements necessary to establish the -- distribution across the exit face of the several beds (over 13,000 data points) required atutomatic data recording and processing. This data handling system as designed around a Giannini K-101 encoder. The output from the anemometer was transmitted along two parallel channels. The .:- :.:.-M first part of the signal was put on a Brown recorder as a back up to the NES autoznatic system. The second part of the signal was amplified by a Kay Lab 111c amplifier and sent to the encoder, which converted the analog signal to an octal value and punched the data on paper tape. This infor- mation was then transferred to magnetic tape and processed automatically. A known, variable voltage was used to calibrate periodically the automatic e n.... ies --:.:.:: data-recording system. Lori 12 EXPERIMENTAL PROCEDURE Detailed studies of velocity distributions were made above five beds (designated 5, 8, 13, 14, and 15). These beds were packed by slightly different techniques so that the effect of minor variations in the bed loading on the velocity profile could be observed. The void fraction and the angle of repose of spheres along the slope of the fill cone were also measured for each bed as an aid in interpreting the results of the velocity measurements. Bed Loading. The nature of the sphere-handling system fixed some of the physical characteristics of the bed. Thus, spheres were always added singly and from the same position; and spheres were removed singly from the same radial position at the bottom of the bed. Differences in the bed- loading conditions are summarized in Table 1. Bed 5 was formed by withdrawing spheres in groups of about 55 spheres from the previous bed and adding these spheres to the top of the bed be- fore a second batch was removed. This transfer process was continue u until the entire bed had been cycled. There was no upward flow of air os during the formation of this bed. Bed 8 was formed by adding spheres to the empty core model against an upward superficial air velocity of 7.3 ft/sec. Bed 13 was located in a manner similar to that used for Bed 5 with the exceptions that the batch size was increased to 250 spheres and an upward air flow of 8.7 1t/sec existed. Three other modifications of this bed were also studied: (1) the fill cone was removed to form Bed 13-FT by withdrawing spheres without disturbing the underlying levels; (2) Bed 13-I was formed by removing all spheres in the top half of the core model; Table 1. Bed-Loading Conditions Sphere Impact Velocity Bed Designation (ft/sec) Gas Flow During Loading (lb/sec.ft2 At Bottom Technique Bed 4 cycled once by batch removal (65 spheres) from the bottom and addition at the top of the core model At Top 10.9 - 12.0 Spheres added to empty core model 17.9 – 18.7 0.51 10.7 – 11.8 10.7 – 11.8 0.61 Bed 12 Cycled once by batch removal (249 spheres) from the bottom and addition at the top of the core model 13-FT Spheres removed from the top of the bed until it had a flat exit face at the desired height (47.4 in.) above bottom of the core model 13-1 Spheres removed from the top of the bed until it had a flat exit face at the desired height (27.1 in.) above the bottom of the core model 13-E Spheres removed from the top of the bed until it had a flat exit face at the desired height (8.5 in. ) above the bottom of the core model Spheres added to empty core model 17.9 – 18.7 10.7 – 11.8 10.7 – 11.8 10.7 – 11.8 0.61 0.60 Bed 14 cycled once by batch removal (255 spheres) from the bottom and addition at the top of the core model 15-FT Spheres removed from the top of the bed until it had a flat exit face at the desired height (48.8 in.) above the bottom of the core model and finally (3) Bed 13-E was crex ted by removing all spheres in the cylindrical portion of the bed. In this latter bed, the mean height of the exit face above the bottom of the vessel was 8.5 in. Bed 14 was formed by again allowing the spheres to fall into the empty core model against an upward gas flow; in this instance the air velocity was 8.7 ft/sec. Bed 15 was constructed as a duplicate of Bed 13; the recycle batch size was slightly larger (255 spheres), and the upward air velocity was essentially the same at 8.6 ft/sec. Again, in similar fashion to Bed 13, the fill cone was removed to form Bed 15-FT. Void Fraction. The void fractions of all beds were determined by subtracting the volume occupied by the spheres (average volume per sphere times the number of spheres) from the predetermined core volume below the exit face of the bed. Prior to such measurements, the fill cone was re- moved because the volume occupied by the spheres in this region was diffi- cult to determine precisely. Angle of Repose. The superficial angle of repose was defined as the angle between the horizontal and an imaginary line joining the center of the sphere at the top of the fill cone with the center of a sphere adjacent to the wall at the base of the fill cone. This measurement was made along four arbitrary radii dividing the core into quadrants. Velocity. Initial measurements at a number of heights above the exit face of the first bed led to the selection of 9 in. (6 sphere diameters) above the bed as the optimum height for taking velocity data. For measure- ments above fill cones, the radial traverses were arbitrarily divided into three zones: between 0 and 4.5 in., between 4.5 and 9.0 in., and greater than 9.0 in. The probe was positioned 9 in. above the average bed height 15 in each of these zones. The anemometer was recalibrated against a known flow of air through the bed prior to the initiation of operation each morning, at noon, and at the end of each day of data taking. An additional check between the hot- wire anemometer, the anemometer-output chart, and the data-logger was made by recording on the first traverse after any significant time lapse between traverses the reading displayed on the anemometer scale. Data were taken only after equilibrium was reached following each flow rate change. Velocity traverses began at the center of the bed and ex- tended radially outward along a 0-deg line in 1/2-in or 3/4-in. increments to within 0.3 in. of the wall; the probe was then angularly displaced and the traversing direction reversea. A summary of the angular and radial velocity measurement positions is given for the five beds studied in Table 2. Average superficial velocities at which data were obtained are given in Table 3 for the various bed configurations. RESULTS AND DISCUSSION Void Fraction and Angle of Repose. The results of the void-fraction and the angle-of-repose measurements are summarized in Table 4. Void fractions for complete beds ranged from 0.393 to 0.401. The standard deviation in the void-fraction data attributable to measurement errors - estimated from the standard deviations of the individual measurements made in obtaining the void fraction – was calculated to be 0.002. Denton24 observed that the standard deviation of very accurately measured overall void fractions was 0.001 when spheres were repeatedly repacked in the same container by the same procedure. Thus, within the accuracy of the data and the known variation in the void fractions of identically packed beds, 16 Table 2. Velocity Measurement Locations Bed Bed Distances from Wall (in.) Distance from Wall Angles (deg) 0.3, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5.7.0 7.5' 8.0, 8.5, 9.0, 9.5, 10.0, 10.5, 11.0, 11.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, 15.0 0, -10, 10, 90 80, 100, 180, 170, 190, 270, 260, 280 0, -10, 10, 90, 80, 100, 180, 170, 190, 270, 260, 280 0.3, 0.5, 1.0, 1.5, 2.25, 3.0, 3.75, 4.5, 5.25, 6.0, 6.75, 7.5, 8.25, 9.0, 9.75, 10.5, 11:25, 12.0, 12.75, 13.5, 14.25, 15.6 0.3, 0.5, 1.0, 1.5, 2.25, 3.0, 3.75, 4.5, 5.25, 6.0, 6.75, 7.5, 8.25, 9.6, 9.75, 10.5, 11.25, 12.0, 12.75, 13.5, 14.25, 15.6 13-15 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, -10, 10, 80, 100, 170, 190, 260, 280 Table 3. Flow Conditions for Velocity Measurements Bed Configuration Average Linear Superficial Velocity (Ft/sec) Atsona 5-FC 8-FC 13-FC 13-FT 13-1 9.0, 5.8, 3.8 6.3, 4.3, 2.6 9.1, 6.7, 4.8, 3.0, 1.7 12.4, 10.0, 3.9, 1.9 13.6, 10.0, 5.1, 2.2 12.0, 9.4, 4.8, 2.1 8.8, 4.4 8.8, 4.2 8.7, 4.5 13-E 14-FC 15-FC 15-FT "Key to bed-designation symbols: FC, fill cone in place; FT, fill cone removed to leave a flat-topped bed; I, top half of the bed removed to leave a flat-topped bed; E, all spheres removed from the cylindrical part of the core model to leave a flat-topped bed in the lower part of the core model. Based on hot-wire anemometer data; actual velocities varied slightly from the nominal values listed. Table 4. Void i'ractions and Angles of Repose Bed Designation Angle of Repose (deg) Void Fraction ܟ 18–25 0.398 ܣ 19-21 ܚ 17–29 0.395 0.4012 0.393 0.399 £ 18-26 16-25 ܟ "The void fraction of the lower half of Bed 13 was 0.402; the void fraction of the bed in the lower (entrance ) portion of the core model was 0.366. the effect of the different bed-loading techniques used in this study was quite small. The void fraction of the lower half of Bed 13 did not differ significantly from that for the complete bed. However, the spheres in the bottom region (Bed 13-E) were more densely packed than those in the bed as a whole; void fractions measured for this region differed from the values for complete beds by much more than the estimated standard deviation at- tributable to experimental error (0.005 for this case). In a concurrent study, Thadani and Peebles15 obtained a value of 0.377 $ 0.033 for beds of 3/8-in.-diam spheres packed in a 1/4-scale model of the PBRE core. However, these investigators loaded their bed in an inverted position and in a man- ner different from that employed in this study. The measured superficial angle of repose ranged between 16 and 29 deg and usually varied considerably (by 2 to 12 deg) from the mean at dif- ferent angular positions around the same bed. No relationship between either the average angle of repose or the angular variation in the angle of repose and the bed-loading condition was apparent. Mean Radial Velocity Profiles. Mean radial velocity profiles were derived by averaging the velocity data – after correction in accordance with instrument calibrations - obtained at a given radial location over all angular positions. Thus, the twenty* local values, u, obtained at each radial location were arithmetically averaged to give the mean velocity, V, at the radius. Numerical integration of the mean radial velocity pro- file gave the mean superficial velocity, Vmi and finally, the data were normalized by dividing V at each radius by V. Mean radial velocity profiles measured above the same bed at different flows were similar but not identical. The data for Bed 13 with the fill Local velocities were measured at only twelve angular positions above Beds 5 and 8. 20 cone in place are shown in Fig. 5; these results are typical of those obtained. A detailed analysis of the data revealed no consistent trend in the normalized velocities with flow rate. This result is consistent with most theoretical models 8,18-23 for turbulent flow through packed beds which do not predict a flow-rate dependence. Further, Schartz and Smith, Dorweiler and Fahien, 10 and Collins11 also concluded from their experimental studies that the velocity profiles were independent of the total flow rate. Therefore, the normalized velocities based on measure- ments at different flows were averaged to give an overall mean radial velocity, v/m; and the differences between these normalized velocities were treated as random errors. Overall mean radial profiles above beds capped by fill cones are - compared in Fig. 6; the solid lines in this figure delineate the maximum and minimum bounds on the data obtained for the five beds. There was no - - - discernable effect on the velocity profile of the average angle of repose, B, of the bed-loading conditions, or of the void fraction, e. Each data set is characterized by (1) a maximum normalized velocity of about 1.8 near the wall, (2) a rapid decrease in the velocity to about 0.7 times the mean velocity at 0.4 of the distance from the wall to the center of the vessel, and (3) a minimum velocity, which was less than half of the mean superficial velocity, near the center of the vessel. The velocity peaking near the wall results for two reasons. First, in any bed, spheres cannot pack as densely against the wall as they can in the bed interior. Hence, the void fraction is greater, 14,24,25 and the resistance to flow is less, near the wall. Frictional drag at the wall causes the velocity to decrease in the immediate vicinity of the wall. Second, for these beds with fill cones, the additional flow resistance 27 ORNL-CWG 65-3603 31.07 OVERALL MEAN RADIAL VELOCITY PROFILE V/V.M - - -- 0 0 0 OO Vm (ft/sec) o 9.1 • 1.7 4 3.0 A 4.8 06.7 O O - 0.2 0.4 ... 0.6 0.6 0.8 10 YR 1 Fig. 5. Mean Velocity Profiles Measured Above Bed 13 with the Fill Cone in Place. ORNL-DWG 65-3612R Leo To II "A/A 0.4 BED NO. B (deg) 5 24 8 20 0 13 15 0.2 L 0.2 cu o 0000D O 0.398 0.395 0.401 0.393 0.399 24 45 24. 0 0.2 0.4 0.6 0.8 1.0 . YIR ; Fig. 6. Overall Mean Velocity Profiles Measured Above Full Cones. ...................... 23 afforded by the increase in bed height with distance from the wall forces still more of the flow toward the wall. Radial velocity profiles measured above Beds 13 and 15 after the fill cones had been removed to give flat exit faces are compared in Fig. 7 with - - profiles obtained by previous investigators. 8,10,11,13 The results for Beds 13 and 15 are seen to be quite similar, with maximum velocities of about 1.3 times the mean near the wall and the same general variations through the central part of the bed despite the absolute difference in the radial positions at which these variations occur. The present data UN show a velocity maximum which is of greater magnitude and nearer the wall than observed by other experimenters8,10,12 with the exception of Dorweiler and Fahien. The distance the wall effect persists into the bed is par- tially dependent on the particle Reynolds modulus. Since the particle Reynolds moduli in this experiment were 5 to 30 times greater than those of other studies and since the bed diameter was more than seven times as great, the relative extension of the wall effect into the bed was less than that in the other investigations. The velocity data in the published literature 8-10,12 also do not exhibit the wave-like variations observed in the profiles for Beds 13 and 15 with flat exit faces. This result is not unexpected, since the profiles reported by other investigators were based on only 3 to 6 velocity measure- ments along the vessel radius and, hence, would miss variations occurring over small distances. The source of these small oscillations in the mean velocity profile can be attributed to the nature of a packed bed, which is conceived of as a random arrangement of regions of different packing density. The size, location, and packing density of these regions will vary about certain mean values that are the characteristic void fraction and flow ORNL-OWG 65-3613R % 20 4.5 20 INVESTIGATORS REFERENCE O(in.) Deling) O BED NO. 13 30 A BED NO. 15 30 1.5 --- DORWEILER AND FAHIEN 9 4 0.25 COLLINS 104 0.188 - SCHWARTZ AND SMITH 8 0.156 - CAIRNS AND PRAUSNITZ 12 2 0.125 2.0 Žlin.) . 49 47 >20 - 23 > 24 16 21.3 19.2 16 NA 1.6 ūIT 0 0.2 0.4 0.6 0.8 1.0 Y/RW Fig. 7. Overall Mean Velocity Profiles Measured Above Flat- Topped Beds. - --- i ...- 1 25 resistance of a random packing as obtained by averaging the local vari- ations over a sufficiently large volume. On the other hand, the velocity profile above a packed bed is affected most strongly by the packing pres- ent at the exit face of the bed. The circumferential-average velocity is affected only by that region of the exit face that is approximately under a circle at the radius of measurement. As the center of the bed is ap- proached, the circumference of this circle decreases; and it becomes in- creasingly improbable that the area of the bed affecting the circumferential- local variations in packing density and resistance to flow. Thus, the velocity profile will show random oscillations near the bed center. Overall mean radial velocity profiles for the several configurations of Bed 13 examined are shown in Fig. 8. The velocity profile above the bed in which only the entrance section was filled with spheres is partic- ularly significant. Although the depth of this bed was only six sphere diameters at the maximum and decreased to two sphere diameters at the wall and three sphere diameters above the discharge dome, the velocity profile is no discernable effect on the profile of either the variation in bed depth or the geometry of air inlet slots. This result further verifies that the velocity distribution at any level in a packed bed is essentially controlled by the packing in the very shallow region immediately upstream. Angular Variations in the Velocity. Since local velocities were ob- tained in this study, a detailed evaluation of the flow was possible. * W "A complete tabulation of the velocity data - as local normalized velocities - is available on microfiche from Laboratory National Laboratory, P. O. Box X, Oak Ridge, Tennessee; this data listing constitutes an unpublished appendix to Ref. 13. . 26 ORML-OWO 66-3614R • THE FILL CONE IN PLACE O THE FILL GONE REMOVED HALF OF THE BED REMOVED I ONLY THE ENTRANCE REGION FILLED WITH SPHERES 0 0.2 0.4 0.6 0.8 1.0 ... ...... . ............ - Fig. 8. Overall Mean Velocity Profiles Measured Above Bed 13. ... ... ... .... .. . The velocity assigned to each point in the measurement gria* was obtained by averaging the Iccal normalized values, u/vme over the several flow rates. If the resultant quantity (ūlīn) 18 divided by ilin (see previous section), there obtains ū/– the ratio of the flow-rate averaged point velocities to the mean circumferential velocity at a given radius averaged over all flow rates – which provides a normalized measure for the angular variation in the local velocity. The angular variation in the local velocity (ūſū) above the various configurations of Bed 13 is given in Figs. 9 through 12 in terms of the percentage of mean local velocities less than a given fraction of the circumferential-average velocity. The data are considered in these fig- ures both as a complete set (solid circles and line labeled "smoothed grouped data") and as individual groups differentiated according to dis- tance from the vessel wall. The absolute magnitude of the angular velocity variations was greatest near the wall since the velocity was greatest in that region; however, the ratio of the angular variation to the mean velocity at the same radius was a much weaker function of the radial posi- tion. Thus, Figs. 10 through 12 for the flat-topped configurations of Bed 13 show that the velocities measured at a given radius varied some - times by more and sometimes less than did the data taken as a single set. Note that in this probability plot a horizontal line at ü/ũ = 1 corres- ponds to complete correlation or no variation in the data, while a verti- cal line shows zero correlation or infinite scatter in the data. With this in mind and considering by way of example only the measurements in "For Beds 13 through 15, this grid comprised 440 points (22 radial locations at 20 angular positions); for Bed 8, there were only 264 points in the array (22 radial locations at 12 angular positions). Bed 5 was not examined in that the 31 radial locations (giving a grid of 392 points) was incompatible with the computer program as written. · ORNL-DWG 65-3920 - 100% Y/R -SMOOTHED . . 0 -100% 0 0.02 Lo 0.033 o 0.067 -0 0.100 • 0.450 ^ 0.20-0.45 0.50 -4.00 ALL RADII .NO 28 0.01 0.1 5 10 20 40 60 80 90 98 99.9 99.99 PERCENT OF THE MEASURED VELOCITIES THAT WERE LESS THAN THE INDICATED AMOUNT -- - -- - - - - -- ...-.. -.-.-.-..- . . . - - -- -- --. in - ...-------- ---- : Fig. 9. Angular Variation of Velocities Measured Above Bed 13 with the Fill Cone in place. .... ...... mu ORNL-DWG 65-3924 mozog 100% SMOOTHEDI GROUPED DATA to to 100% ty/R! 0 0.02 A 0.033 o 0.067 0 0.10 ~ 0.15 * 0.20-0.45 0.5-1.0 • ALL RADII . 0.4 .. 0.2 -0.01 99.99 0.1 1 5 10 20 40 60 80 90 98 99.9 PERCENT OF THE MEASURED VELOCITIES THAT WERE LESS THAN THE INDICATED AMOUNT -....--.-- . ..... - . - :--. .. --... -- -- -- Fig. 10. Angular Variation o ? Velocities Measured Above Bed 13 with the Fill Cone Removed. - --- ORNL-DWG 65-3922 - 100% -E/R SMOOTHED GROUPED DATA . Vzo 100% . o 0.02 s 0.033 0 0.067 0 0.10 * 0.15 A 0.20-0.45 • 0.5-4.0 • ALL RADII ülü . 0.04 0.1 1 5 10 20 40 60 80 90 98 99.9 99.99 PERCENT OF THE MEASURED VELOCITIES THAT WERE LESS THAN THE INDICATED AMOUNT Fig. 11. Angular Variation of Velocities Measured Above the Lower Hall of Bed 13. ------ -- .. , --- .. . . www.e ---- : . . . .. .,;. .- - .. . - . - . . . - - --- - - -- - ORNL-DWG 65-3923 - - ...- ---- - . - - - --- - - ORNL-DWG 65-3923 nap 100 % 1.8 SMOOTHED GROUPED DATA → 1.6 .: 100 % Y/R 0 0.02 A 0.033 + 0.067 -o 0.10 » 0.15 * 0.20-0.45 • 0.5-4.0 • ALL RADII ū v en 40 - 0.6 : 0% 0.4 99.99 0.01 0.1 1 5 10 20 40 60 80 90 · 98 99.9 PERCENT OF THE MEASURED VELOCITIES THAT WERE LESS THAN THE INDICATED AMOUNT. ... Fig. 12. Angular Variation of Velocities Measured Above Spheres that were Packed in the Entrance Region of Bed 13. -.-.:' -ena...-..:.icio.--. - - - - - .- - - -- - - - - - - - - - - • • • the outer radial region of the core (open symbols), the data in Fig. 10 show more variation (steeper slope), in Fig. 11 less variation, and in Fig. 12 about equal variation with that displayed by the grouped values. A comparison of the grouped data for the four configurations of Bed 13 studied is given in Fig. 13. For the three flat-topped arrangements, the results are similar; the differences in the curves probably only measure scatter in the experimental data. The fill cone does, however, modify the distribution significantly with the increased angular variation pos- sibly deriving from the strong radial flow that exists in the fill cone. For beds with fill cones, a trend in the relative magnitude of the angular variations with radius was more evident. Velocities measured near the wall in these beds showed consistently a smaller circumferential vari- ation from the mean velocity at the same radius than did the velocities near the center of the bed; the results given in Fig. 9 are typical of the data obtained with this bed configuration. A summary comparison of the grouped data for four beds with fill cones is presented in Fig. 14. Again, the differences seen are felt to be not significant relative to the accuracy of the data. The effect of the mode of bed formation appears to be slight. This is illustrated not only by the data of Fig. 14 for beds with fill cones but also by the comparison of Fig. 15 for Beds 13 and 15 after removal of the fill cone. Radial Separation in Local Velocity Extrema. Since local variations in the velocity above packed beds are presumed to arise from short-range differences in the packing arrangement near the bed exit face, the dis- tances between adjacent maxima and adjacent minima along each radial velocity traverse were determined as a measure of the dimensions of more ORNL-DWG 65-3929 BED CONFIGURATION FILL CONE IN PLACE -- FILL CONE REMOVED -.- TOP HALF OF BED REMOVED .-.-- ONLY ENTRANCE REGION FILLED WITH SPHERES ülv. 33 0.04 0.1 1 5 10 20 40 60 80 90 98 99.9 99.99 PERCENT OF THE MEASURED VELOCITIES THAT WERE LESS THAN THE INDICATED AMOUNT Fig. 13. Angular Variation of Velocities Mac Fig. 13. Angular Variation of Velocities Measured Above Different ORNL-DWG 65-3927 BED NO. --- 13 --- 14 --- 15 0.24 0.01 0.1 1 5 10 20 40 60 80 90 98 99.9 99.99 - PERCENT OF THE MEASURED VELOCITIES THAT WERE LESS THAN THE INDICATED AMOUNT - - - - - - :- - -- -.-. -.-- -- - - ... on Fig. 14. Angular Variation of Velocities Measured Above Beds with the Fill Cone in Place. : ------- Seri - - -- -- .. -------...--..-. .. . - .. . . . - - - - . - - - - -- - - - ***-- - - --- - -- - - - - - . - - - - ORNL-DWG 65-3928 BED NO. - 13 - 15 . : 0.6 . : 0.4 0.2 . .. 0.01 0.1 5 10 20 40 60 80 90 98 99.9 99.99 PERCENT OF THE MEASURED VELOCITIES THAT WERE LESS THAN THE INDICATED AMOUNT - - - - --- Fig. 15. Angular Variation of Velocities Measured Above Beds with the Fill Come Removed. 37 ; ORNL-DWG 65-393 MAXIMA ---- MINIMA . -. - - -- - - PERCENT OF LOCAL MAXIMA OR LOCAL MINIMA THAT WERE SEPERATED BY THE INDICATED AMOUNT resi 0 2 4 6 8 10 12 14 DISTANCE BETWEEN MAXIMA OR DISTANCE BETWEEN MINIMA (in.)" Fig. 16. Distribution of All the Radial Distances Between Local Maxima or Between Local Minima in Velocities Measured Above. All Beds When Consiảered. as a Single Set. ............. . .. ... . . ................... ......................... densely or more loosely packed sphere clusters. For each bed configura- tion, the data from all radial traverses were grouped to form a single set and presented in the form of a histogram showing the percentage of the maxima or minima at a given separation. These histograms were not identical for the various bed configuration and, further, differed for the maxima and minima data. However, these differences were random and unrelated to the bed geometry or the loading technique. Accordingly, the data for all configurations were combined to give the histogram shown in - . -. -- - -- - - Fig. 16. For the lumped results of Fig. 16, the distribution in the separation between maxima and between minima appears to be essentially identical. The wakes from individual spheres do not appear to have affected the velocity data appreciably, since (1) only about 6% of the velocity maxima or minima were separated by a single sphere diameter and (2) less than 10% of the extrema at a one-sphere-diameter separation differed from the surrounding velocities by 20%. The most common distance between extrema was three WS sphere diameters, thus indicating - since local minima could be expected to occur above the center of densely packed clusters and maxima above the center of loosely packed clusters - a most prevalent lateral separation in . . . both tightly and loosely packed regions of three sphere diameters. Velocity Data Validity. The accuracy of the velocity data was analyzed by conventional techniques. 13 The standard deviation in the mean velocity at a given radius, V, attributable to experimental error was estimated to be ~2% of the mean velocity at that radius; the corresponding standard deviation arising from measurement errors in the mean local velocity, ü, was about twice as high. 38 As indicated throughout this paper, the measured velocities depend strongly on the physical arrangement of the spheres on the bed exit face. However, the close similarity in the mean radial velocity profiles shown in Figs. 7 and 8 for flat-topped beds of various depths suggests that the radial velocity profile throughout most of the axial extent of the bed 18 innsed measured by these data obtained outside the bed structure. The differences between these profiles in the central three-fourths of the bed further suggest random lateral velocities within the bed, arising partially perhaps from flow redistribution around local densely packed regions. Similarly, the steeper velocity profiles for the beds with fill cones leads to the supposition of significant outward radial flow both within the fill cone and within the body of the bed immediately below the fill cone. These radial flows are extremely difficult to measure and were not obtained in this study. To this extent, the velocity data described do not represent the flow structure in the bed. SUMMARY OF RESULTS Void fractions for complete beds of 1 1/2-in.-diam spheres packed in a full-scale reactor core model ranged from 0.393 to 0.401. There was no --- - - - - - - -- detectable effect of bed-loading methods on these measured void fractions. Superficial angles of repose were between 16 and 29 deg and displayed considerable circumferential variation (2 to 12 deg). No relationship be- tween either the average angle of repose or the angular variation in the angle of repose with bed-loading conditions was apparent. Overall mean radial velocity profiles for beds capped with fill cones showed (1) maximum normalized velocities near the wall of 1.8, (2) a rapid decrease to a velocity of 2.7 at a dimensionless distance of 0.4 (measured from the wall), and (3) a minimum velocity near the vessel center of less than half of the mean superficial velocity. Variations in the angle of respose, bed-loading conditions, and the void fraction had no discernible effect on the velocity profile. For all beds with flat tops, the profiles were flattened in respect to those measured for beds with fill cones, being 1.3 times the mean velocity near the model wall and 0.7 times the mean near the center. The overall mean-radial velocity profiles about the central region of the beds exhibited random, wave-like fluctuations which could be attributed to random variations in the packing density. The velocity distribution at a given height in the beds was virtually controlled by the packing arrange- ment in a very small bed depth immediately below that height. Significant angular variations existed in the local superficial velocities both above and within the beds. The se variations in the velocity with circumferential position were greater above beds with fill cones than above those with level exit faces. A dependence of the magnitude of these variations on the radial position, noted for beds with fill cones, was not observed with flat-topped beds. The velocity profile characteristic for beds with fill cones reflected - - - - . the distortion of the flat exit face profiles by radial flow in the fill cone and upper region of the body of the bed. The most common separation of the centers of densely and loosely packed regions on t'e exit face of the bed was three sphere diameters. Radial lateral velocities effecting flow redistribution around local dense regions within the bed were inferred. H0 LIST OF SYMBOLS vessel diameter sphere (particle) diameter vessel radius local, point, or measured axial velocity average value of u for all flow rates mean (circumferential averaged) superficial velocity at a given radius average value of v for all flow rates mean superficial velocity V flow-rate-averaged mean superficial velocity distance from wall Ź average bed height . . .- - . Greek - . B superficial angle of repose B average superficial angle of repose void fraction REFERENCES 1. J. R. Arthur et al, "The Flow of an Air Stream through a Layer of Granules," Trans. Faraday Soc., Vol. 46, 1950, p. 270. 2. 1. Akehata and K. Sato, "Flow Distribution in Packed Beds," Chem. Eng. (Japan), Vol. 22, 1958, p. 430. 3. E. Hirai, "Flow Distribution of Fluid in Packed Beds," Chem. Eng. (Japan), Vol. 18, 1954, p. 528. . 0. A. Saunders and H. Ford, "Heat Transfer in the Flow of Gas through a Bed of Solid Particles," J. Iron and Steel Institute, Vol. 141, 1940, p. 291. 5. S. P. Kinney, U. S. Bureril of Mines Technical Paper 442, 1929; cited by M. More.ies, C. W. Spinn, and J. M. Smith, "Velocities and Effec- tive Thermal Conductivities in Packed Beds," Ind. Eng. Chem., Vol. 43, 1951, p. 225. HI 6. C. A. Coberley and W. R. Marshall, Jr., "Temperature Gradients in Gas Streams Flowing through Fixed Granular Beds," Chem. Eng. Prog., Vol. 47, 1951, p. 141. M. Morales, C. W. Spinn, and J. M. Smith, "Velocities and Effective Thermal Conductivities in Packed Beds," Ind. Eng. Chem., Vol. 43, 1951, p. 225. 8. C. E. Schwartz and J. M. Smith, "Flow Distribution in Packed Beds," Ind. Eng. Chem., Vol. 45, 1953, p. 1209. 9. V. P. Dorweiler and R. W. Fahien, 'Mass Transfer at Low Flow Rates in a Packed Column," A.I.Ch.E. J., Vol. 5, 1959, p. 139. 10. M. Collins, "velocity Distributions in Packed Beds," unpublished bachelor thesis, University of Delaware, 1958. - - --- - - - - 11. D. M. Jenkins, A. C. Morgan, and R. L. Stover, "Flow and Void Frac- tion Distribution in a Floating Packing Bed," unpublished Memorandum EPS-X-464, KT-547, to C. G. Larson, Massachusetts Institute of Tech- nology Engineering Practice School, Union Carbide Nuclear Company, November 8, 1960. 12. E. J. Cairns and J. M. Prausnitz, "Velocity Profiles in Packed and Fluidized Beds," Ind. Eng. Chem., Vol. 51, 1959, p. 1441. 13. R. D. Bundy, "Velocity and Mass-Diffusion Measurements for Beds of Large, Uniform-Diameter Spheres Randomly Packed in a Pebble-Bed Nuclear Reactor Core," Master's Thesis, University of Tennessee, August 1965; also published as USAEC Report ORNL-TM-1075, Oak Ridge National Laboratory, 1965. 14. W. H. Denton, "The Heat Transfer and Flow Resistance for Fluid Flow Randomly Packed Spheres," p. 370 in "General Discussion on Heat Transfer," Lonżon, Institute of Mechanical Engineers, 1951; also see W. H. Denton, C. H. Robinson, and R. S. Tibbs, "The Heat Transfer and Fluid Flow through Randomly Packed Spheres," Report HPC-35, Atomic Energy Research Establishment (England), 1949. 15. M. C. Thadani and F. N. Peebles, "Variation of Local Void Fraction in a Randomly packed Bed of Equal Spheres, by the Techniques of Radiography and Microphotometry," Report EM 64-8-1, University of Tennessee, 1964. 16. W. E. Ranz, "Friction and Transfer Coefficients for Single Particles and Packed Beds," Chem. Eng. Prog., Vol. 48, 1952, p. 247. 17. T. Baron, "Generalized Graphical Method for the Design of Fixed Bed Calatytic Reactors," Chem. Eng. Prog., Vol. 48, 1952, p. 118. 18. G. de Josselin de Jong, Longitudinal and Transve Granular Deposits," Trans. Am. Geophysical Union, Vol. 39, 1958, p. 67. 42 19. P. G. Saffman, "A Theory of Dispersion in a Porous Medium," J. Fluid Mech., Vol. 6, 1959, p. 321. 20. K. W. McHenry and R. H. Wilhelm, "Axial Mixing of Binary Gas Mixtures Flowing in a Random Bed of Spheres," A.I.Ch.E. J., Vol. 3, 1957, p. 83. J. J. Carberry and R. H. Bretton, "Axial Dispersion of Mass in Flow through Fixed Beds," A.I.Ch.E. J., Vol. 4, 1958, p. 367. 22. J. J. Carberry, "Axial Dispersion and Void-Cell Mixing Efficiency in Fluid Flow in Fixed Beds," A.I.Ch.E. J., Vol. 4, 1958, p. 13M. H. Kramers and G. Alberda, "Frequency Response Analysis of Continuous Flow Systems," Chem. Eng. Sci., Vol. 2, 1953, p. 173. 24. L. H. S. Roblee, R. M. Baird, and J. W. Tierney, "Radial Porosity Variations in Packed Beds," A.I.Ch.E. J., Vol. 4, 1958, p. 460, 25. R. F. Benenati and C. B. Brosilow, "Void Fraction Distribution in Beds of Spheres," A.I.Ch.E. J., Vol. 8, 1962, p. 359. ' : : END .." Y st W DATE FILMED 3/16/67 . . . . I'. . SINI! . MOT