ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR SUMMARY REPORT ON THE STUDY OF THE FLOW OF PASTE Seymour Calvert, Robert H. Miller Alberto Molini Nallam S, Chari Project 2396 ATOMIC POWER D.JELOPMENT ASSOCIATES, INC, DETROIT, MICHIGAN November 1956

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The University of Michigan ~ Engineering Research Institute TABLE OF CONTENT'S Page LIST OF FIGUIRES iii ABSTRACT vii OBJECTIVE vii INTR ODUCT I ON 1 OBJECTIVES OF RESEARCH SINCE JANUARY, 1956 4 SUIARY 5 1. LITERATURE SEARCH 5 2. HAIRPIN FLOW 5 3. FLOW THROUGH ORIFICES 4. COEFFICIENT OF FRICTION MEASUREMENTS 6 d. EXPLORATORY DOWNWFARD AND HORIZONTAL FLOW SYSTEMS 6 6 C ONVIPETE RE ACTOR FLOW SYSTEMS 6 RE SELA, n C R RESUL.T.'.S 6 LITERA [TUJRE SEARCH 7 1H1AIRPIN SYSTEMS 7 FLOW OF PASTE THROUGH ORIFICES 15 COEFFICIENT OF FRICTION 23 EXPLORATORY EXPERIMENTS ON DOWNWARD AND HORIZONTAL FLOW SYSTEMS 26 COMPLETE REACTOR FLOW SYSTEMS 27 REFERENCES 30 ii

The University of Michigan ~ Engineering Research Institute LIST OF FIGURES Figure Page 1 Hairpin exits. 8 2 Solids flow rate versus pressure drop for upward flow of glass beads in a 10.3-nmm-ID hairpin with overflow exit. 31 3 Total flow rate versus pressure drop for upward flow of glass beads in a 1053-mm-ID, 2-ft-long hairpin with overflow exit. 32 4 Total flow rate versus pressure gradient for the downward flow of glass beads in a 10,3-mm-ID hairpin with overflow exit. 33 5 Total flow rate versus pressure drop for downward flow of glass beads in a 10.3-mm-ID hairpin with various exit types. 34 6 Pressure drop versus flow rate for downward flow of 82-micron Ottawa sand in a 10.2-mm-ID, 2-ft-long hairpin with overflow exit. 35 7 Pressure drop versus flow rate for downward flow of 82-micron Ottawa sand in a 10.2-nmm-ID, 4-ft-long hairpin with overflow exit. 36 8 Pressure drop versus flow rate for downward flow of 98-micron Ottawa sand in a 10.2-umm-ID, 2-ft-long hairpin with overflow exit. 37 9'Total flow rate versus solid flow rate for upward flow of Ottawa sand in a lO.2-mm-ID hairpin with overflow exit.:38 10 Total flow rate versus solid flow rate for upward flow of copper shot in a 1053-nm-ID hairpin with overflow exit. 39 11 Total flow rate versus solid flow rate for upward flow of 100/120-mesh glass beads in a 10o3-nun-ID tube with various exit types. 40 iii

The University of Michigan ~ Engineering Research Institute LIST OF FIGURES (Conto) Figure Page 12 Paste velocity versus pressure drop for downward flow of Ottawa sand in a 17.8-mm-ID, 4-ft-long hairpin with overflow exit. 41 13 Paste velocity versus pressure drop for upward flow of Ottawa sand in a 17.8-mm-ID, 4-ft-long hairpin with overflow exit. 42 14 Volume fraction solids versus paste flow rate for 100/140mesh Ottawa sand in a 17.8-mm-ID hairpin with plain- and washed-overflow exits. 4 15 Total flow rate versus solids flow rate for upward flow of 100/140-mesh Ottawa sand in a 178-mmm-ID hairpin with washed exit. 44 16 Flow rates versus pressure drop for downward flow of 100/140-mesh Ottawa sand in a 17.8-mm-ID hairpin with washed exit. 45 17 Volume fraction solids versus solids flow rate for upward flow of 100/140-mesh Ottawa sand in 8-mm-ID and 17o8-mm-ID tubes. Porosity determined by electrical conductivity method. 46 18 Total flow rate versus solids flow rate for upward flow of 100/120-mesh glass beads in an 8-mm-ID hairpin with washed exit. 47 19 Predicted free water velocity versus particle diameter with volume fraction solids as parameter for spheres with density of 2.49 gm/cm3 flowing upward at Row = io 48 20 Predicted free water velocity versus particle diameter with volume fraction solids as parameter for spheres and "round sand" with density of 2,65 gm/cm3 flowing upward at Row - 1. 49 21 Predicted free water velocity versus particle diameter with volume fraction solids as parameter for spheres with density of 8,65 flowing upward at Row = 1o 50 22 Predicted free water velocity versus particle density with particle diameter as parameter for upward flow of spheres at Row - 1 and (l-X) = 0o55o 51 iv

The University of Michigan ~ Engineering Research Institute LIST OF FIGURES (Cont,) Figure Page 23 Predicted free water velocity versus particle density with particle diameter as parameter for upward flow of "round sand"' at Row = 1 and (l-X) = 0.955 52 24 Sketch of equipment. 53 25 Pressure drop versus solids flow rate with orifice diameter as parameter for the flow of 80/100-mnesh Ottawa sand paste. 54 26 Pressure drop versus solids flow rate with orifice diameter as parameter for the flow of 140/200-mesh Ottawa sand paste. 55 27 Pressure drop versus solids flow rate with orifice diameter as parameter for the flow of 200/325-mesh Ottawa sand paste. 56 28 Pressure drop versus solids flow rate with orifice diameter as parameter for the flow of 140/200-mesh copper shot. 57 29 Pressure drop versus solids flow rate with orifice diameter as parameter for the flow of 140/200=-mesh lead shot. 58 30 Logarithm of the slope function versus reciprocal of orifice diameter. 59 31 C2 versus particle diameter. 60 32 C1 versus reciprocal of particle density. 61 33 Coefficient of friction between a zinc plate and 150/200.-mesh Ottawa sand paste. 62 34 Coefficient of friction between a glass plate and 150/200-mesh Ottawa sand paste. 63 35 Coefficient of friction between a glass plate and -325-mesh iron-powder paste. 64 36 Viscometer apparatus sketch, 65 37 Viscomneter torque versus fraction solids for 100/140-mesh Ottawa sand. 66 38 Viscometer torque versus fraction solids for l00/14O0mesh copper shot. 67 v

The University of Michigan ~ Engineering Research Institute LIST OF FIGURES (Concl ) Figure Page 39 Viscometer torque versus fraction solids for 100/120-mesh glass beads. 68 -40a Complete reactor configuration. 69 40b Experimental model configurationO 69 41 Reactor top and bottom configurations. 70 vi

The University of Michigan ~ Engineering Research Institute ABSTRACT A thorough survey of the literature yielded little worth-while information. Work on hairpin-type systems has been completed and a correlation.of liquid and solid flow rates and pressure drop is presented~ The special significance of small restrictive force at the tube exit is discussed. Work on nonflow systems intended to determine the frictional properties of pastes is described and the results are shown to agree with flow-experiment results. Data and a tentative correlation for flow through orifices are presented. The correlation includes particle diameter and density, orifice diameter, pressure drop across the orifice, and flow rates. Exploratory work on hori — zontal and multiple-hairpin downward flow is discussed. Design concepts for a complete reactor system and an experimental model are discussed. OBJECTIVE The object of this study is to establish a generalized correlation of the variables involved in the flow of high-density sediments through tubes. This will include experimental and analytical studies of both flow through tubes alone and complete, continuous flow loopso vii

The University of Michigan ~ Engineering Research Institute INTRODUCTION This report covers the work done during the period from January, 1956, to September, 1956, on a study of the flow of pastes. The study which began in June, 1955, had its origin in the desire of the Atomic Power Development Associates to investigate the feasibility of using a paste fuel composed of uranium (or uranium compound) particles in liquid sodium. This application requires that the paste have a high density (solids content) and that it move at extremely low velocityo Because of these requirements we are concerned with a type of flow which has received practically no study in the past. Considerable information is available on the flow of suspensions, but this is not:applicable here because it does not cover systems where force may be transmitted independently through particle-to-particle contact~ As has been learned in this study, this mechanism of force transmission can produce profoundly distinct effects. This brief explanation points out the underlying factors which required that much of the study be exploratoryo The first step in the study was to learn whether the paste would flow at all at the density desired. Next came the determination of what variations of flow parameters were possible and, following that, what the order-of-magnitude force relationships were for the flow. This ground was covered in the work performed prior to the first of this year, although there were still lessons to be learned on the nature of the significant variables. The first three months' work was reported in Summary Report on a Preliminary Study of the Flow of Paste, September, 1955. Its nature is shown in the following excerpts from that report. "Subject -The determination of the pressure-drop —flow-rate relationships for the flow of high-density pastes through tubes is required for the estimation of design requirements of a reactor. The system contemplated would have the following characteristics: 1o Paste is composed of uranium oxide or uranium powder suspended in molten sodium or sodium potassiumo a0 Density should be at least 40-50 volume-percent solids. b. Particle size maybe varied to obtain optimum flow character1

The University of Michigan * Engineering Research Institute isticso A size range around 50-micron diameter is envisioned. 2. Tube diameter will be in the range of 1/4 to 1 in. Tube material will be stainless steel, probably 304. 3o Flow rate is anticipated to be in the range of 1/3 to 10 ft per day. 4. The orientation of the tube may range from horizontal to vertical. "Objecte-The object of this preliminary study is to obtain orderof-magnitude data on the pressure drop required to produce the desired flow rate and some insight into the mechanism of flow. "For highly concentrated suspensions such as those of present interest, there are four general possibilities for the type of flow. If there is no appreciable attraction between the particles there are two possibilities: the suspension will flow as a viscous fluid whose viscosity depends only on solids concentration and particle-size distribution, or the suspension may be so concentrated that it must increase in volume when sheared (i.e., it is dilatant). If there is attraction between particles, then the third possibility will occur and the behavior will be non-Newtonian and will exhibit a yield stress. "The fourth possibility, which is dependent on the methods of feeding and withdrawal, is that the liquid could flow at a different linear velocity than the solido "Because of the range of possible modes of flow and the lack of generalized information which would-enable the prediction of flow characteristics, it will be necessary to conduct an experimental study. "The variables to be investigated as time permits are: 1o Flow rate 2, Paste density 5, Particle-size and size distribution 4, Tube material and wall finish 5. Tube geometry- turns and fittings 6. Vibration of the tube and/or pulsation of the pressure. "In view of the exploratory nature of this work, its course was discussed frequently in meetings with A.P.D.A. personnel, Dr. McDaniel, Mr. Ro | Thomas, and Mr, L. Kintner. These discussions made it possible to direct our efforts to the most significant points in the overall problem of determining the feasibility of the proposed system as the picture gradually took shape in the light of each new finding. 2__

The University of Michigan ~ Engineering Research Institute SUMMARY "The key fact disclosed by this study is that the mechanism of flow corresponds to the fourth possibility suggested above. The solids settle to a bed of about 61 to 62 volume-percent solids which will move under the influence of fluid passing through it. If, on the other hand, the motive force bears directly upon the solid particles, as when a piston is used for pushing, the bed cannot be moved if its length is more than about 2-1/2 tube diameters Measurements of shear stress versus rate of shear with a concentric-cylinder viscometer are not directly applicable to flowing systems since the shear stress (or friction) depends on the bearing force exerted by the weight of the solids on the rotating cylinder. In facts the rotating cylinder can be stopped by pressing with a finger on top of the sand surrounding the cylinder. "Once it was demonstrated that force was transmitted through the continuous sediment of particles as well as through the fluid, it became apparent that our previous knowledge of the flow of suspensions was not applicable.o Our attention was then directed to the study of the flow of fluids through moving porous bedso Most of this work was done with water and silica flowing through glass tubeso Exploratory experiments with glass beads and copper metal powder indicated the same type of behavior as is exhibited by the silica. Flow through horizontal runs generally exhibits stratification with most of the water flowing in the upper 1/4 of the tub:e Consequently, attention was centered on vertical upward and downward flow." The work for the next four months had. substantially the same objective and was reported in Summary Report on Continuation of the Study of the Flow of Paste, January, 1956. The summary of that work was presented in the report as follows: SUMMARY "The work performed during this four-month period was in five areas. 1. Construction of apparatus and obtaining data on paste flow in vertical hairpins up to 8 ft in length (16 ft of tube length). All the data, except one run on copper powder, are for rounded or angular silica particles. There are not yet sufficient data to pe-rmit any quantitative generalizationso 2. Construction of apparatus and obtaining data on the pressure drop re quired for fixed-bed expansiono The data show the inapplicability of the point of first expansion as a criterion of frictional effects. The points of 5 _

The University of Michigan ~ Engineering Research Institute maximum and equilibrium pressure drop seem promising as criteria. 3. Investigation of the applicability of electrical-conductivity measurement as a means of determining bed porosity. The method appears to be sat isfactory and will be used in future work. 4. A literature search. No applicable information was found in the areas and time period covered~ 5. Design conception and exploratory experimentation on continuous-flow loop systems. A system incorporating downward flow of dense paste inside a tube and low-density left for solids recycle was operated satisfactorily on sand and water. Examples of various conceivable system types are discussed." OBJECTIVES OF RESEARCH SINCE JANUARY, 1956 The work reported here began in January, 1956, and its scope was set forth in a proposal for a continuation of the study as follows: "Object: The object of this study is to establish a generalized correlation of the variables involved in the flow of high-density sediments through tubes This will include experimental and analytical studies of both flow through tubes alone and complete, continuous flow loops. The variables to be investigated are: Scope: 1o Flow parameters a. Paste rate 0 to 30 ft/day. b o Liquid rate -as required to give desired paste flow rate. o co Paste density. 2.o Particle parameters a. Size and size distribution - concentrate on size distribution like that of actual fuel particles. Mixtures will run from 44 to 200 microns with a 100 micron median size. bo Density- cover as wide a range as possibleo co Shape - Rounded and angular parameters. 35 Tube a. Cross-section - Round and rectangular. b. Diameter - 1/4" to 1"0 c. Length - up to 20 ft total. d. Geometry - Straight downward sections~ single hairpins, and multiple hairpins e. Material and surface finish. 4,

The University of Michigan * Engineering Research Institute 4. Effect of geometries such as manifolds, contractions, and turns. 5. Effect of all components and controls required for continuous flow loop operation. Method: The method of approach to the problem will be as follows: 1o Complete the literature search. 2. Conduct experiments on flow systems. 35 Conduct such experiments on non-flow systems as will yield information on the characteristics of the paste which may be correlated with behavior in flow systems. 4. Analyze and correlate the data. 5. Apply the correlations to a representative design or designs for a paste flow reactor system." SU MARY The results of the work performed during this period are summarized as follows. 1. LITERATURE SEARCH The literature search has been completed and the result confirms our preliminary finding that no significant information is available. 2. HAIRPIN FLOW Following a period of considerable difficulty in obtaining data on hairpins with 180~ exit bends and overflow-type exits, it was discovered that washing the particles away from an overflow exit results in flow at a constant pressure drop in the upward leg. When the exit is washed or submerged, the pressure drop in the upward leg is always equivalent to the buoyant weight of the solids. Data on 180~ exit bends and uniwashed overflow exits are now recognized as relating to special, incompletely defined cases in which some unknown force is applied to the particles at the exit. A mathematical analysis substantiates the validity of the conclusion from experimental data. 3o FLOW TEHROUGH ORIFICES Work, which is still in progress, on the flow of paste through 5

The University of Michigan * Engineering Research Institute orifices yielded data showing a clear relationship between flow rates and pressure difference across the orifice, orifice diameter, and particle diameter The data are not yet sufficient to permit a correlation of all variables a 40 COEFFICIENT OF FRICTION MEASUREEMENTS The coefficient of friction as a function-of bed density was determined by means of a loaded sled apparatus and is shown to decrease at a critical density~ Friction between a rotating cylinder and beds of particles with water flowing upward through the bed has been measured. In this case there is also a change in friction at about the same bed density as for the sled measurements. 5. EXPLORATORY DOWNWARD AND HORIZONTAL FLOW SYSTEMS It was discovered that downward and horizontal flow without stratification may be obtained if the tube exit is restricted. The ratio of solids flow rate to liquid flow rate required to make the tube run full of solids is maintained because of the exit-orifice characteristics. 6. COMPLETE REACTOR FLOW SYSTEMS Consideration of the requirements of the complete reactor system has resulted in the formation of several concepts of top and bottom paste distribution and collection schemes. An experimental model based on one such concept was built and preliminary experiments with it were inconclusive. RESEARCH RESULTS The nature and results of the research carried out during this period will be presented below. The major topic divisions are: 1. Literature searcho 2. Hairpin systems. 3. Flow through orifices. ~4. Coefficient-of-friction measurements 5. Downward and horizontal flow systems. 6. Complete reactor flow systems. L _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ 6

The University of Michigan ~ Engineering Research Institute LITFRAATTTRE SEARCH A literature search covering the references in Chemical Abstracts back to 1927 disclosed no significant aamount of background information. A large number of patents dealing with the flow of particulate material have been examined, but no worth-while data were found. There are four references which deal with special cases of the paste-flow problem. These are as follows: 1i "Flow of Granular Material Through a Circular Orifice," F. C. Frarnklin and Lo N.. Johansen,. Chem. Eng Science, 4, 119 (1955). 2. "Forces Acting in Flowing Beds of Solids," Jo W. iDelaplaine, AIChE,,1237 (1956). 5. "Flow of Solid Particles Through Orifice," Go Kwai, Chem. Eng. (Japan), 18, 453 (1953). 4. "Discharge Bate of Solid Particles From a Nozzle Steeped in Liquid," Y. Qyama and Ko Nagano, Repts. Scio Research Insto (Japan), 29, 349 (1953). The firstthree references deal with the flow of dry particles and the last with the flow of particles and water with a constant head of water above the orifice, A comparison of these data with the experimental results of this program is presented in a later section of this report. HAIRPIN SYSTEMS The previously initiated study of flow through vertical hairpin tubes was extended to cover a wider range of variableso It was intended that continuous-flow, automatically controlled systems be used for this work, but it was not possible to find liquid controls suitable for such low flow rates. Consequently, the apparatus was the same as that used previously, that is, it involved a batch-loaded solids reservoir and water rate was adjusted manually. After a period of considerable difficulty in obtaining reproducible data and steady-state conditions within a working day, the exit configuration was changed. Since it was suspected that the 180~ bend was exerting force on the particles, an overflow-type exit was introduced. The configuration of this exit is shown in FigO 1. With the overflow exit the data were still erratic and did not check the data obtained with the 180~-bend exit. Finally it was discovered that the small mound of particles which builet up on the tube exit had a profoeund effect on the pressure drop. A small 7

The University of Michigan ~ Engineering Research Institute 1800 -RETURN-BEND OVERFLOW EXIT EXIT EXIT Fig. 1. Hairpin exits. nozzle was placed above the tube exit so that the particles leaving the tube could be washed away and not pile up above the tube end. The remaining runs were made with the washed overflow exit. A summary of the valid runs made since January, 1956, is presented in Table Io The data for most of the runs listed in Table I are represented in Figs. 2 through 18o In cases where the data are for upward flow at an overweight ratio (Row) of 1.0, the plots show total flow rate versusesolids flow rate as points and the predicted values (to be discussed later) as lines. No plots are given for runs 8 through 11 since the flush-water rates and thus total flow rates were not known accurately. These were the first runs in whilch the washed exit was used and their value lies in the fact that they show flow at an overweight ratio of 1.0. Some of the runs with the washed exit indicated a decrease in flowing density with flow rate, as shown in Fig. 14. Upon further investigation it was found that the density irn the uIpward lneg rremained constant at- the loosely settled density at all flow rates once a high enough flow rate was attainedo In other words, flow at a density higher than the loosely settled density is an unstable situation which can be eliminated by either "breakingin" the system at a high flow rate or by letting it run for a long periodo 8_[

The University of Michigan * Engineering Research Institute TABLE I SUMMARY OF HAIRPIN RUNS Tube Tube Upward Leg Run Figure Diameter Length Particles Exit Overweight (mrm) (ft) Ratio (approx.) 1 10 2 82 g O.So overflow 1 2 6-9 10 2 98 o 0.S. overflow 1 3 l10 4 82 Bt 0.S. overflow 1 4 f18 4 100/140 0oS. overflow 1.1-2.0 5 12-16 j18 4 140/200 0oSo overflow 1.1-2.0 6 8 4 -200 O.S. overflow 11-2.0 7 18 4 100/140 O.S. washed 1.0 8 8 10 100/120 G.B, overflow 2-3 9 8 10 100/120 G.B. washed 1.0 10 8 10 20/28 G.Bo washed 1.0 11 8 6 140/200 OoSo washed 1.0 12 10 2 100/120 GoB. overflow 2o0-4.0 13 10 2 170/200 GoBo overflow 1.8-4,0 14 2-5 10 2 270/325 GoBo overflow 1o3-8 5 15 0 2 16/20 GBo, overflow 2o0-2.5 16 10 2 32/35 GoB. overflow 2,2-2.8 17 10 2 80/100 G.B. overflow 1.6-2.5 18 1 0 2 140/200 Cu overflow 1.0 10 19 10 2 200/325 Cu overflow 1.0 20 10 2 100/120 G.B notched overflow 1.0 21 10 2 100/120 G.B. washed 1.0 11 22 110 2 100/120 G.Bo 900 bend 1.0 23 10 2 100/120 G.B. 180~ bend 1.0 24 11 18 2 100/120 G.B. washed 1.0 25 15 18 2 100/140 O So washed 1.0 26 11 18 2 100/120 GBo washed 1.0 27 15 18 2 100/140 0,,So washed lo0 28 18 82 100/120 G.Bo washed 1.0 9,,, _

The University of Michigan ~ Engineering Research Institute Figure 17 shows this effect. It is quite clear from the data shown here and from our prior data on 1800 exit-bend systems that the only definable (or reproducible) system is the washed-exit type. In some cases a 180~ exit bend will cause a high pressure drop and in others it gives the same result as a washed exit. Tthe same can be seen for the plain overflow system. The essential difficulty is that thie restraining force at the exit depends on the particular way in which particles pile up at the exit and this has not been consistent for the return bend and plain overflow exits. Correlation of Data —Once the nature of the upward flow system was known it became possible to describe its behavior. That is) we base the description on the following facts: 1. The washed-exit system is the basic upward flow situation with no restraining force on the particles at the exit. 2. Friction between the flowing paste and the tube wall is negligible in upward flow. 3. The paste flows at approximately its loosely settled density in the upward leg and at a higher density, approaching the tightly settled density; in the downward leg of a hairpin with washed exit. We must add a further restriction that this correlation will apply only to systems of the hairpin type where the solids flow rate is not restrictedo Another way of putting this is that this covers the case of minimum ratio of liquid rate to solid rate. This is to differentiate the high-density flow regime from the low-density regime in which for any solid rate there can be a range of liquid rates. With. the above restrictions. the only problem remaining is to find a relationship which will indicate the liquid flow rate required to exert drag on the particles equal to the weight of the particles. We found that the correlation by Leva et al.1 for the laminar flow of fluids through porous medi is satisfactory for this purpose. The method of correlation is as follows: Vs Vw = VT - (1) where Vw = free liquid velocity (cm3/min/cm2) (based on the total crosssectional area of the tube), VT = total flow velocity (cm3/min/cm2), Vs = dry-solids velocity (cm3/min/cm2), and 10

The University of Michigan ~ Engineering Research Institute X = volume fraction voids in flowing paste. Thus Vw is the liquid velocity relative to the moving paste based on the total tube cross section. It is this velocity which is related to the frictional pressure drop. Leva's correlation for the laminar flow of fluids through porous media is Ap 200 G a L x2 (1-_)2 (2) Dpf gc 83 forG Re 3 < 10, where AP = frictional pressure drop over bed (lb/ft2) G = mass flow rate (lb/sec/ft2) (based on total cross-sectional area of tube), t = fluid viscosity (lb/ft/sec), L = bed length (ft), "2 = empirical shape factor which is 1,0 for spheres, 135 for round sand, and 2.25 for sharp sand, a = volume fraction voids, Dpf = particle diameter (ft), p' = fluid density (lb/ft3), g = 322 (ft/sec2), and Re = Reynolds number. This relationship can be evaluated at the point where the pressure drop per unit length is equivalent to the buoyant density of the solid particles in the bed. After doing this and changing some of the variables to more comfortable units, we have C1 (ps-p) DPD X wee C1 = a constant depending on shape, and equal to C94 x 0 >1 Ps = density of dry solid (gm/cm3), 11..

The University of Michigan ~ Engineering Research Institute p = density of liquid (gm/cms3), Dp = particle diameter in microns, and X = 6 = volume fraction -voids. Equation 3 is represented in graphical form in Figso.19 through 230 Ifn each of the first three figures free water rate is plotted against particle diameter with volume fraction solids as the parameter for a particular solid density. In the last two figures (22 and 23), free water rate is plotted against solid density with particle diameter as the parameter and for (l-X) = 0.55 The value of (1-X) = 0.55 for average flowing density seems to be a fairly good approximation for rounded and spherical particles. Spherical particles such as glass beads exhibited flowing and loosely settled densities of about 57% solids while rounded sand ran about 55%. The loosely settled densities were determined in tubes of various diameters from -8 mm to about 50 mm and were not appreciably affected by tube diameter in this range. Since the effect of bed density is slight (see Figs. 19 through 21) in this range, this is not a crucial point. Prediction of Floiw Rates.-The application of the above correlation simply requires the determination of paste and free liquid flow rates for the upward flow of a particular solid and their addition to give total flow rate. Since the flowing density is constant, paste flow rate is a linear function of solid flow rate and is represented by a straight line going through the origin on Cartesian coordinates. Free liquid rate is a constant value if bed density is constant, so the line representing total flow rate lies parallel to the paste flow line and the intercept at Vs = 0 is the free liquid rate. Discussion of Results —The most significant result of this study was the realization of the overwhelming importance of small changes in the restraining force at the tube exit, By way of hindsight, this observation can be verified mathematically as follows. Consider a differential element of paste in a vertical tube of radius r and represent the steady-state condition by a force balance across the element. F + Ff + Fw - Fd (F + dF) = 0 (4) and dF = Ff + Fw - Fd where F = force acting on particles in the downward direction, 12

The University of Michigan ~ Engineering Research Institute Ff = force acting on particles due to wall friction, Fw = force due to the weight of the particles, Fd = force due to fluid drag on the particles, and dF = increase in force across the element. Then, assuming that wall friction is due to a normal component of "pressure" acting on the particles, C 2F (2cr) f - r (2) C2and F(2r) - _ r d} (6) where C2 = a constant relating axial "pressure" to frictional force; AP = frictional pressure drop across element due to fluid flow; in the strict sense this should be -AP, but what is meant here is that a decrease in pressure in the upward direction corresponds to a positive AP, this convention is employed to make the relationship between AP/L and Pb more clear; = buoyant bed density of particles; that is, particle density minus fluid density times volume fraction solids; and L bed lengtho Integration of Equation 6 yields 2In22 p r = r L + C3 (7) 2C ~n -- r - At L = 0, F =Fo force at exit and C3 = r2 [n2C ( —— 4\ TrT (8) r 2C2F 2 C3., 202 r L /lb Combining Equations 7 and 8 yields 2C2- = 2n' r / (9) rj2C2r Fo - Pb rj 15

The University of Michigan ~ Engineering Research Institute We now need to estimate "tC2,"t which is the product of the ratio of normal to axial particle-to-particle pressure times the coefficient of friction. This will be about 0.5 x 0o.6 = 0.3. Equation 9 shows that even for a short tube of length = 20 radii the ratio of the numerator to the denominator on the right side of the equation is about 106, Thus the difference between the two terms in the denominator must be extremely small or an impossibly large force will be exerted upon the solids at the bottom of the upward leg. That is, 2C2Fo (AP p)r2 (10) r L -- - ~r2 If we now assume that Fo is due to a hemisphere of solids of radius r, sitting on top of the exit, F0 3 (3 l) Then, substituting in Equation 10, (.o 6)z1 33r3 Pb = - ) tr2 (12) and AP L Pb: = - 8 pb ~ AP By definition, R = (13) ow Pb R _ 18 pb - 1.8 (14) OW Pb Equation 14 indicates that the effect of a small restraining force at the exit of an upward leg can require an overweight ratio of considerably more than one. The variation in overweight ratio required for upward flow, as shown in Fig. 2, for examples can now be interpreted as being dependent on the ability of particles to remain in a distinct heap. The smaller the particles are, the more restrained they are by the surface tension of water, and the larger the mound at the exit can grow. Flowing Densityo-For the purpose of prediction in cases where there are no data on the actual material the values of 55% for upward flow density and 60% for downward flow density are adequate for rounded particles of fairly uniform diameter~ _14

The University of Michigan ~ Engineering Research Institute For cases in which there is a wide range of particle size or where the particles are angular, it would be best to determine the freely settled density experimentally-. It is not possible to characterize flowing density as a function of flow rate alone, as is seen from the difference in upward and downward leg densities, The density is affected by force exerted on the particles at the tube exit, but we are unable to define this relationship from the data we have, Prediction of Flow Rates, —As can be seen in Figs. 9, 10, 11, 15, 17, and 18, the predicted relationship is generally quite good for glass beads and copper shot, while it is less accurate for the Ottawa sand, The deviation between experimental data and prediction for the glass beads in the 8 —mm tube (Fig. 18) is not understood and seems quite strange in view of the agreement obtained for the same beads in a 10.5-mm tube (Figo 11). From the standpoint of the objectives of this program it is not worthwhile to pursue the subject of hairpin flow any further at this timne. The correlation based on Levats equation is sufficiently accurate for the purpose of engineering design and will make possible a fairly accurate estimate of energy requirements, etca for a hairpin reactor system. Sufficient work has been done by previous investigators to indicate that the prospect of obtaining an extremely accurate general correlation for flow through porous media is quite dismal. If a hairpin system should appear advantageous at some future time (although it does not now), the next step would be to work with the actual solid particles in order to obtain more precise results. FLOW OF PASTE THROUGH ORIFICES In practically any paste-flow reactor system one can envision the use of an orifice at some point as necessary. Either the orifice will be used to restrain solids flow in the paste channel or it will be used to control the flow of solids into the low-density lift system. Since the prior knowledge of the flow of paste through orifices was very spotty and inadequate, it was necessary to perform an experimental studyo The method and results of this study are presented below, following a discussion of the literature, A tentative correlation of the data has been made, and while it is sufficiently accurate for engineering design estimates we are not satisfied with it and will modify it in the future as more data become available. It should also be emphasized that the system studied did not encompass a very wide range of geometric variations, so these results should be thought of as pertanining to a special case until we learn more about it. Review of Literature. —A number of investigators have studied the mechanism of flow of solid particles being discharged through orifices. The 15

The University of Michigan ~ Engineering Research Institute first to perform a thorough investigation of the factors influencing the flow of solid particles through orifices were Bingham and Wikoff.2 They were trying to characterize some of the inherent proper-ties of powders by means of simple free-flow gravity tests Their work was of such a fundamental nature that a discussion of their results is very much indicated. While for real liquids the effect of temperature upon the flow rates lis of great iinmportance, for solid particles it was found to be quite negligible "for real liquids the head above the orifice would control the rate of discharge; however, with solid particles it was found that doubling the head did not increase the flow rates, On the contrary, higher heads caused lower discharges, supposedly due to denser packing near the orifices. The length of the capillaries was found to have a very important effect on the discharge rates, -Larger flows were obtained with longer capillaries, especially when working with the finer particles, This was explained by the air-suction effect produced by the free fall of the particles. Bingham and Wikoff2 arrived at an empirical formula which expressed the discharge rates proportional to Do265, where Do was the diameter of the capllary. Wieghardt3 studied the discharge of sand from cylindrical vessels having a small hole at the bottom. Provided that the diameter and the height of the vessel were both sufficiently larger than the diameter of the hole, he found that the discharge rates were proportional to Dob25, where Do was the diameter of the orifice' This value for the exponent applies for orifices, not for capillaries~ Brown ard Hawksley4 studied the flow patterns of a bed of particles bei ng discharged through an orifice. The flow was characterized by definite regi.ons withiin the bed w-vhere the particles had different velocities., This flow pattern has been used as a second explanation for the higher flow rates obtained. with longer capillaries by Bingham and Wikoff.o The contention is that longer tubes favor the development of plug flow instead. of turbulent flow. The plug flow will give higher efflux rates,, Brown5 has shown that a true plug flow, in which all particles of the moving bed have similar velocities, may be induced by merely fixing a few widely spaced horizontal rods at strategic points inside the vessel. Oyama and Nagano6 studied the discharge rate of solid particles from an orifice steeped in water. Their results indicate also that the discharge rate is proportional to Do2,5 for sand, diatomaceous earth, and marble. They found a direct proportionality between discharge rate and particle diameter as longas the o/Dp was larger than 7. At values lower than 7, the particles would bridge the orifice and completely stop the flow. However, they found that the discharge rate was approximately proportional to Dp~ 5.........__ 6... _. _' _- _. _. _ SC6

The University of Michigan * Engineering Research Institute Mehring7 has reported that the discharge rate of the particles in an air atmosphere is inversely proportional to particle size. In this case the main factor which affects the discharge rate is simply the friction between the particles and between the particles and the wall. In Oyama and Nagano' s experiments, the liquid is completely enclosed Ghus the same volume of water has to flow up the orifice as the volume of particles flowing down. Kuwai studied the discharge of solid particles under low air pressures His results indicate a direct proportionality between the particle flow rate and the driving force or air pressure, The particle flow rate was found to be inversely proportional to the particle diameter at a constant pressure for any one of the orifices tested. Also, the flow rate was affected by the orifice diameter, vessel diameter, and the bed height. Higher bed heights gave lower particle flow rates, The flow rates increased with increasing orifice diameters and also with increasing vessel diameter for any constant orifice size, However, the increase with vessel diameter gradually approached a constant valueo Experimental Work,-All of the experimental flow-rate data were takenr using solid particles made of the following three dlfferent materials, io Silicon dioxide: The silicon dioxide particles were obtained from the Ottawa Silica Sand Company of Ottawa, Illinois. The sand was not of an even particle size, and it had to be classified into "cuts" of different sizes by screening0 Flow-rate data were obtained using "cuts" of 80/100 mesh, 140/200 mesh, and 200/325 meshl 2. Copper.: The copper shot was obtained from the Metals Disintegrating Company, Elizabeth, New Jersey~ It also was not of a regular size and had to be classified, The flow-rate data were obtained, using the "cut" of 140/200 mesh.o 3. Lead: The lead shot was also obtained from the Metals Disintegrating Company, Since it also was not of a regular size, it had to be classified by screening into "cuts" of different mesh sizes. The flow-rate data were obtained, using the "cut" of 140/200 mesh. The orifice plates were made of brass, and they were 0.40 inch thick. The orifices were 010, 0.15, and 0.20 inch in diameter and 0.30 inch long, The greatest portion of the flow-rate data was taken, using the above orifices. However, a slight amount of work was done with sharp-edge orifices, having the same diameters as the straight ones. All of the experimental flow-rate data of particles flowing downward through orifices were taken, using the continuous flow unit shown schematically in Fig0 24~ Preliminary experiments in a batch system indicated the need for a -7

The University of Michigan ~ Engineering Research Institute continuous system if reproducible data were to result. The unit consists of the following parts: Part No. Name Particle reservoir? Orifice plate 3 Particle-receiving reservoir 4 Particle-water ejector 5 Water-recirculating pump 6 Pressure-control valve 7 Siphon.-level control 8 Orifice-pressure tap 9 Water manometer to measure orifice pressure drop 10 Mercury manometer to measure over-all bed-pressure drop 11 Particle-dispersing baffle 12 Particle-water low.density line 13 Water-:overflow line 14 Bucket 15 Ejector-water-control valve 16 Pump-recycle valve The very first thing done in getting the unit ready for operation was to fill the bucket (14) with clear water. The ejector-water-control valve (15) was closed, and the pump-recycle valve (16) was opened all the way. The particle-receiving reservoir (3) was filled with clear water to the overflow level (13)o The water-recirculating pump (5) was started, and the ejectorwater-control valve (15) was opened all. the way. The solid particles to be worked with were poured into the particle-receiving reservoir (3), and the pumlp recycle valve (16) was closed slowly. As soon as the water started operating the ejector (4),9 the particles were conveyed to the particle reservoir (1) as a low-denlsity slurryO The pressure-con.trol val.ve (6) was opened all the way, and a finger was held against the orifice (2) until. all of the particles had been carried to the particle reservoir (1)o The particle-receiving reservoir (3) was kept full of water at all times during the loading operation. The flow rate of the paste through the orifice was controlled by means of the pressure-control valve (6). Closing this valve increases the pressure inside the particle reservoir (t), thus increasing the flow rate of the particle paste through the orifice. A very fine control of the pressure was obtained by means'of the siphon.-l evel control (7) which is movable up or down. The particl.e paste and the overflow water from the particle reservoir (1) are both received by the particle-receiving reservoir (3). The particles settle to the bottom, where they are picked up by the particle-water ejector (4) and are returned to the particle reservoir (1)o The overflow of the particle-receiving reservoir (3) is returned (13) to the bucket (14), where it 18....

The University of Michigan ~ Engineering Research Institute is used'by the pump (5) to operate the particle-water ejector (4). The pressure drop across the orifice (2) is read from the water manometer (9), which is connected to the orifice-pressure tap (8)o The overall bed-pressure drop is read from the mercury manoameter (10), which is connected to the orifice-pressure tap (8) and the tap of the particle reservoir (Z)ol The continuous flow unit proved to be very satisfactory for taking the flow-rate data of a paste of particles flowing downward through an orifice. The following procedure was used while taking the flow-rate data of the particle paste through the orifice. The pressure-control valve (6) was set at a point, and the operator waited a sufficient length of time in order to obtain a steady state which was indicated by the constancy of the reading in the water manometer (9) U iUsually it would take from fifteen to thirty minutes to reach a steady state. The longer times were required whenworkilzkgwith the smaller particles. This was due mainly to the plugging of the pressure tap with particles and the resulting slow response of the manometer. The paste of particles was collected for a certain length of time in a tared calibrated glass cylinder. The collection time was recorded by a stop watch. Each run consisted of recording the following data. Reading of the water manometer (9), reading of the mercury manometer (10), collecting time as indicated by stop watch, total volume of paste (particles plus water) collected~ and the gross weight of the calibrated glass cylinder. The reading of the settled volume of sand in each run could not be used as a basis to determine the actual volume of sand, dry basis, flowing thhrough the orifice. There was always the possibility that the sand would pack at different porosities when it settled in the calibrated cylinder. Thus, the actual volume of dry sand collected in each run was calculated in the following manner. The total volume of the paste collected in each run has to be equal to the dry particle volume plus the volume of the water, thus VT = VS + Vw (1) Vw = VT = Vs (2) Also, the total weight of the paste collected in each run has to be equal to thet weight of the dry sand collected plus the weight of the water, kthus wT = WWw (5) 19

The University of Michigan ~ Engineering Research Institute or WT = Vsp5 +Vwpw e (4) Substituting Equation 2, WT = Vsps + (VT -Vs)Pw (5) WT = Vs(Ps Pw).+ VTPw (6) WT VTPw Vs= _ - ) (7) The volume of solid particles, as obtained by using Equation 7, is the actual dry volume of the solid-particle material flowing through the orifice during any one of the runs. The volume fraction of water collected in each run was calculated by a material balance, using Equation 20 All of the paste-flow-rate data through orifices, reported herein, are expressed in terms of cubic centimeters of the dry solid-particle material per minute. Results and Correlation. —The experimentally determined data are shown in Figs. 25 through 29,.which are plots of pressure drop across the orifice versus solids flow rate with orifice diameter as the parameter. Each figure is for a constant particle diameter and particle material (constant specific gravity)~ Each one of the figures indicates a straight-line relationship between the flow rate and the pressure drop across the orifice. Thus, it seems possible to express the flow rate in terms of the pressure drop across the orifice as follows: AP = jW + C 9 (8) where ~ = slope of the straight line relating flow rate and pressure, drops for specific particles and orifice diameters and C1 = the intercept on the AP axis at zero flow rates~ Thus, W= - a, (9) The data also indicate that r is dependent only on the orifice diamnetert at any constant particle size, Therefore, it indicates that j can be expressed as: = f1(Do) (10) 20

The University of Michigan ~ Engineering Research Institute or l = f2 (Do/Dp) ()l) Both functions 10 and 11 were treated by means of graphical procedures, Equation 10 yielded a straight-line relationship when the logarithm of n was plotted versus the reciprocal of the orifice diameter. The particle diameter was used as the parameter, as shown in Fig. 30. Thus, the graph yields the following relationship between rl and Do~ log nl = a(l/Do) + C2, (12) where a = slope of the straight lines relating log ql versus (1/Do) and C2 = the intercept of the lines on the (I/Do) axis when rj = 1.0o The intercept value, C2, is different for each particle size studied, as of now. All of the experimental flow-rate data indicate that C2 = f3(Dp). (13) Attempts to obtain a straight-line elationship from Equation 13 were not very fruitful. However, Fig. 31lshows the relationship between C2 and the particle diameter, DBo, This figure brings'up the fact that it is necessary to obtain more data, especially in the particle size range of 100/150 mesh, These screen-mesh numbers represent an average particle diameter of approximately 0.0049 inch, These data would definitely show whether there is a break in the 02 versus Dp correlation at particle diameters of approximately 0.003 inch. Using the data available at the present time one can assume that two straight -line functions represent the relationship between 02 and the particle diameter. One of the functions represents the data including particle diameters from 140/200 to 200/325 mesh, and the other represents the data including particle diameters from 80/100 to 140/200 mesh. Thus, we obtain the following relationships: for particle diameters from 140/200 to 200/325 mesht C2 = mp + C4 (14) and for particle diameters from 80/100 to 140/200 mesh, C2 = bDp + C3 (15) where m and b = slopes of the C2 versus DB plot and * _.21 _ _ __.

The University of Michigan * Engineering Research Institute C4 and C3 = corresponding intercepts when C2 = 0. The constant C1 of Equation 8 originates from the original plot of flow rates versus pressure drop across the orifice. It can be seen that the value of C1 obtained with the flow data of S102 remains constant for any particle or orifice diameter tested. This fact indicates the possibility of.correlating C1 by Eqiuation 15g C1 = f(pp) o (16) Further analysis of the intercept, C 1, obtained with copper and lead, yielded Fig. 32. The point representing CaCO3 was obtained from the data published by KuwaJ,8 He used air instead of water as the driving medium, which makes the correlation more surprising since it would be expected that buoyancy would pla an important part. No explanation can be given, at the present time, for this. Writing the equation for Fig 32, we obtain: C = Q(l/p) + C5, (17) where Q = slope of the C versus 1/p plot and C = intercept when Cl = 0. It is expected that the final relationship of the intercept C and the specific gravity of the particle materiala will keep the general shape of Equation 17. However, the intercept, C5, might vary due to orifice-entranee effects, and the location of the orifice-pressure tap. These facts indicate the desirability of studying the orifice-entrance effects. The final tentative correlation for the flow rate of a paste of particles flowing downward through an orsifice is obtain.ed as follows: Substitute Equation 12 into Equation 9 AP C W a (18).2.305 e Substitute now Equation 17 into Equation 18 AP Q/pp - C5 W 2 a/D0 =+ C2 (19) 20303 ea/D + C Since the C2 values were expressed with two relationships, each one for a specific range of particle sizes, substituting Equations!4 and 15 into Equation 19, we obtain the final general correlation. 22

The University of Michigan ~ Engineering Research Institute For particle diameter ranging from 140/200 to 200/235 mesh: 2.303 ea (20) For particle diameters ranging from 80/100 to 140/200 mesh: 2o303 ea/Do + bDp + C3 The values of the constants Q, -a, b, m, C3, C4, and C5 are given in Table ITo TABLE II VALUE OF CONSTANTS FOR THE FITNAL GENERAL CORRELATION Q = 5.555 a = Oo01621 b = 0,09525 m = 1o3 C3 = )!o002215 C4 =!o00581 C5 = 0.59 COEFFICIENT OF FRICTION Until recently the data on paste flow, even for upward flow, showed, what appeared to be a substantial frictional effect due, apparently, to the behavior of the moving mass of particles. In the light of these apparent facts it was important to attempt to relate the frictional properties of the paste in nonflow systems with that in flow systems. The hope was that from measuremxents of "viscosity" or a coefficient of friction, taken with, perhaps, a concentric cylinder viscometer, one could predict the pressure-drop —flow-rate relationship for the same paste flowing in a tube. Two techniques were investigated The first consisted of simxply pulling a loaded flat-plane sled across a layer of paste and finding the relationship between frictional and normal forces. This still left the problem of evaluating the normal forces in an actual paste.flow system. The second technique took in more of the complete stress system, and it involved the 25

The University of Michigan * Engineering Research Institute measremernt of the torque required to rotate a cylinder in a bed of the paste. The final form of the viscometer apparatus provided for the upward flow of water through the paste bed so that the condition in an upward flow tube could be simulated, For several reasons, which will be brought up later, neither of these techniques has yielded results which are quantitatively reliable, but they are iLmportant' in showing the high dependence of friction on bed density. Especiall |n the light of our present insight into paste flow, the frictional properties of the particle mass appear to be a passive reflection of the demands imposed by the conduit exit. Sled Experiments - The coefficients of friction between a glass plate and 150/200'mesh Ottawa sand paste, a zinc plate and 150/200-mesh Ottawa sand paste, and a zinc plate and -325-mesh iron-powder paste were determined with the sled apparatus. This apparatus consisted of a tank 30" long, 5"' wide, and 3" high for holding the paste, a sled which could be loaded with weights, and an arrangement for pulling the sled by means of a wire, which passed over a pulley and was attached to a weight pan. With this apparatus one could measure normal force, the force required to start motion of the sled, and the force required to sustain motion. The paste layer wAs prepared by spreading the mixture of solid particles and water over the tank bottom, tapping the tank for various lengths of time to increase bed density and finally by scraping the surface level. The bed density was determined from samples of the paste taken after each rui. The data are summarized in Figs. 33, 34, and 35, which are plots of coefficient of friction and volume-fraction solids in the paste. It can be seen that for the sand paste the coefficient drops abruptly as the bed density decreases below about 58% solidso Viscometer Experiments.-Our early attempts to measure the "viscosit' of sedimented pastes by means of a "'Brookfield" viscometer have been described in axn earlier report. It turned out to be impossible to get any meaningful results by running the rSotating cylinder in a beaker of paste due to thle random variation of normal force on the cylinder. The use of this instrument was taken up again in conjunction with an arrangement for forcing water up through the paste bed. As the water rate is increased, the point may be reached where the frictional pressure drop is equal to the head due to the buoyant weight of the solids. At this point the solid particles are, on the average, "weightless "t and there should be no variation in normal force acting along the length of the cylinder. Further increase in water rate will result in an expansion of the bed and wil:l still provide the characteristic of weightless partclles. It might be ~entioned that this is the only way we can see, in which this instrument can b-e applied to dense paste systems with clear-.cut sinficance. 24_

The University of Michigan ~ Engineering Research Institute A sketch of the apparatus is shown in Fig. 56, The volume of the container above the fritted disc was ealibrated as a function of height so that the bed density for a known weight of solids could be determined from a meas ment of the paste bed height. Three spindles were employed; all were 2"' long from the bottom to the gauge mark, and they differed in diameters, which were 1/2"t, 3/4", and 1". The viscometer speeds were 1, 2, 5, and 10 rpm. Each unit on the torque dial is equal to 0.1025 gm cmo The data obtained for 100/140-mesh Ottawa sand are presented in Fig. 37, a plot of torque dial reading versus fraction solids in the bed. Due to the "stick-slip" phenomenon, which is intensified by the torque-spring coupling in the drive shaft, the readings fluctuate widely and are shown as bars rather than points. There was a negligible effect of rotational speed in this and all other data which were taken on this system. The maximum scale reading is 500, and this controlled the highest bed density which could be run in the apparatus. Where data halts at a scale reading below 500, it indicates that any further increase in density (decrease in water rate) would cause the torque gauge to go off scale, Data for 100/140-mesh copper shot and 100/120-mesh glass beads are shown in Figs. 38 and 39. All of these data are subject to uncertainty due both to the stick-slip effect and to the channeling which occurred at high water-flow rates. Discussion of Results -Coefficient of friction data, as determined by the sled. method, would be useful if we had a way of evaluating the normal force acting in a paste-flow system. Since we do not, except for Delaplaine's data, no predictions based on these values are to be made at present. They are of present interest in showing that there is a signifLicant relationship between coefficient of friction and volume-fraction solids. The frictional effect in an upward flow system can be estimated from the viscom.eter data, Although the data are not extensive and reliable enough to support the argument rigorously, we can observe that shear stress (force per unit area of cylinder surface) is approximately constant with the cylinder diameter at the lower bed densities, i.e., torque is proportional to the square of the cylinder diameter, Assuming that this will hold for paste flow through tuabes, we can estimate the frictional force exerted against the tube wallo By extrapolation, we estimate the torque reading for the 1/2" diameter spindle in 100/140-mesh sand at 55% solids to be 1.5. Thus, the torque is 0t,14 gm cm, and the shear stress is 001o16 gm cm, and the shear stress is 00116 gm/cm2. The ratio between frictional force and force due to the buoyant weight of the solids [at (L-X) =.55 for sand] is then computed to be (o05o1/D), where "D" is tube diameter in centimeterso For upward flow in a 1-cm diameter tube this indicates a frlictional forcPe equal to about 5% of the pressure drop at an overweight ratio of 1o.0 In the same manner, we can 25

The University of Michigan ~ Engineering Research Institute estimate that for a reading of 40 for copper shot at 55% solids the ratio of friction to bed-weight "head" would be (O014/D)o What with the uncertainties in the experiumental measuremxent and the necessity for extrapolation to the loossely settled density of 0,55, this is not bad confirmation of the experim.ental observation that frictional effects are negligible for upward flow with a flushed exit. A closer check could be nmade r>y using xmore elaborate techniques and a viscomaeter fitted with a zeroadiSplaceement torque pickup However, this is not warranted as a part of the study of paste flow since this technique is only valid for the upward flow case and direct experimental observation of pressure drop is simpler'to accomplish0 EXPLORATORY EXPERbE S O 1 DOWNWARD ARD 9 HORIZONTAL FLOW SYST9E One of the by-products of the recognition of the effect of the exit on upward flow was the realization that the exit could be equally rimportant for downward and horizontal flowo Our previous experience had been that stratification occurred in these systems. Upon rerunning them, we found that uniformly dense f:low coald be attained in both systems if a restriction were placed at the tube exit. It should be made clear that the downward flow system we refer to here is that case in which a downward leg is added to a hairpin system~ ThusX the paste f lows downward out of the reservoir, then upward, and f inally down.ward againo in this case the ratio of liquid to solid is set by the upward flow leg, and, if the tube exit is unrestricted, this ratio is too high for the tube to run fullo The solids will drop to the tube exit as individual part icles, unless the flow rate is extremely higho By putting a restriction at the tube exit, we in effect, impede thle flow of particles more than the flow of liquid0 The ratio of liquid to solid is set by the oriflice diameter, as we see from the work on flow through orifices. Th us, eventually we should be able to predict the optimum size orifice just to keep the downward flow tube running fullo To do so, we need know the ckharacteristics of both the downward tube and the orif ice0 Horizontal flow is subject to the same general reasoning as givren for downward flow. If we could characterize the behavior of flow in a horizontal. tube as well as in the exit orifice, we could design this type of system. Work along these lines is being planned for the near future. Friction for horW zontal flow will. probably be highk as compared to verti cal flowo We ean estimate the friction as follows~ For a differential cylind rical element of radius r and length dL, with its axis horizontal the force balance is described by:,, 6.....- 6

The University of Michigan ~ Engineering Research Institute 0 = dF+-p r2 dL -C1 Pb cr2 dL - CFdL (15) L r and by rearrangement dF r 2F -, _ C 1p jr2] dL (16) where C1 = coefficient of friction, assume = 0O6 and Other symbols are as described previouslyo By integration of Equation I6 and substitution of numerical values for C, and C2, we get: a~6 ( r 7 r~6 (~) = ~ - o06 Pb) 3r2] By the same reasoning as was applied to Equation 9, we find that o. 6Fo 0.6 pb Or2 e (18) If Fo, the force exerted against the exit orifice, were zero, AL =.6Pb' (196 L This corresponds to an overweight ratido of O6i Since some force will. be exerted against the orifice exit, the actual pressure drop will be higher than thiso Probabldy an overweight ratio of 1.0 would be a fair approxi mation COMPILTE REACTOR FLOW SYSTEMS The ultimate point of interest in this project is the utilization of a paste fuel in a nuclear-reactor system. The general requirements of such a system are as follows. 1o Paste flow passages must be small -enough so that the required rate of heat transfer can be attained with-out necessitating a paste temper-ature approaching the sintering point~ 2o Flow through all of the paste passages should be at a uniform rate and density, 27

The University of Michigan * Engineering Research Institute 5, The system should be "fail safe." There are also the general ideals one would strive to attain, siuch as simnplicity, low pressure drop, and ease of filling and emptying. It is still our belief, as expressed in the previous report, that I the high.density downward flow with low-density lift system offers greater promise than the hairpin type of system. For this reason the design concepts we have envisioned were all based on the low-density lift system. In any case, the major problem remains essentially the same, i.e,, how to distribute the paste to the tops of the individual channels and collect it from the bottoms. After having sketched a number of alternate designs, we found that practically all of our ideas for collection and distribution systems could be represented by two types. One type is illustrated in Fig. 40a and involves picking up the particles in a stream of sweep liquid, lifting the low-density slurry to the top of the reactor by means of an ejector pumpS,.and then distributing the slurry over the tops of the paste channels so that the particles would. settle out. This system would require additional fittings to permit withdrawal of the slurry from the reactor. The other type is shown in Fig. 41, and it involves the introduction of high-density paste from a separator outside the reactor, the mQvement of the paste at high-density from passageoutlet orifices to the ejector, and then low-density lift to the separator. One can make variations on these basic types by providing conical top and bottom geometry to pro.mote the movement of particles by gravity, or It might be desirable to vary the width of the distributtion and collection channels along the radius of the cylinder, in order to attain optimum flow distribution and minimum holdup. Another possibility would be the provision of distribution anld collection passages in the form of a spiral, which might offer less short-circuiting and fewer dead spots. What it all boils down to is that we need to know more about, flow through horizontal and inclined channels. This includes stratified, nonstratified, and low-density flow and there would be particular emphasis on radial flow with multiple insets and outlets. Flow through orifices and the ejector-life system are also significant elements of design information, which are required. The small (8" diameter) model, illustrated in Fig. 40b, was built to represent the flow system shown in Fig. 40ao A few runs were made with this model,'but they were inconclusive, first because the holes in the perforated plate were too large and second because there were too many Interdependent factors, each of which:must be closely designed to match the others. This apparat us does have the ve.ry desirable feature of represerntzng the paste passages by a perforated plate, and this wiSl enabLe the investigation of full-scaLe distrbutitnon and pickup syst-ems with relativtely simple and inexpensive equipme nt. 2_8

The University of Michigan ~ Engineering Research Institute It is planned that the investigation of complete reactor flow systems will form the major part of the program for next year. While the general form of the necessary investigation is shown in the above discussion, there are bound to be special problems appearing as new design concepts come to mind. Work will start on what looks like the most promising schemeothe outside-separator design, shown in Fig. 41. 29

- -- The University of Michigan ~ Engineering Research Institute REFERENCES. -L~eva, M,, et aLo, "Fluid Flow Through Packed and Fluidized Systems, Bullo 504, UoSo Bureau of Mines (1951) 2, Bingham,, Eo Co and Ro WO Wikoff, Jo Rheolo, 2, 395, 414, 416 (1931). 3O Wiegharedt, Ko, Ingenieur -Archivv, 20, 109 (1952) h4_ Brown, Ro L. an.d PO Go W. Hawksley, Fuel, 26, 159 (1947)o 5~ Brown, R, L.,, Flue1, 29j 418 (1950). 6. 0yasma, Y,0 and K. Nagano, Reports. Sci Research Insto (Japan), 29, 349-352 (9.553). 7 NlMehring, Ao I. 0 irndo Eng. Chem., Anal. Ed, 3, 34 (1931)o 8:SKuwai G,j Chemno Engo Japan 17, 4539 (1953)o _.....

The University of Michigan ~ Engineering Research Institute 20 18 32/35 Mesh 16/20 Mesh 16 - 8cj 1 4 E.N~~~~ / ~100/120 Mesh 80/100 Mesh 0 I LL,)'s$03oetf~s x CI 170/200 Mesh 6 4 0 2 4 6 8 i0 12 14 PRESSURE GRADIENT AP/L IN UPWARD LEG (cm Hg UNDER H20/ft) 3!

The University of Michigan * Engineering Research Institute 40 36 32 32/35 28 E 24 16/20 multiply E I ordinate by 10 80/100 100/120 120 _ _ _ _ _ _ ~~<~~ ~ ~ 20/ 0:.. _J 16.1170/200 A O0 2 4 6 8 10 12 14 PRESSURE GRADIENT IN UPWARD LEG AP (cm Hg UNDER H 0/f t) Fig. 5. Total flow rate versus pressure drop for upward flow of glass beads in a 10o3-5m-iD, 24ft-long hairpin with overfl ow exit~

The University of Michigan ~ Engineering Research Institute 40 0 36 0 32 r 00 C 0 -- ~l) 28 C: 24 E r;24 - E 0 r')~~~~~~~~~~~~~~~~~~~~~~~~" I., 0 o co 00 H~ 20 a: 0 -j ~~~~~o LL U- 1 0 o H~~~~~~~~~ o oo~ 12 0 2 4 6 8 10 12 14 2~~0 2~~~~~~~L Fig. 4. Total f ow rate versus pr~essure gradient for the downwar-d flow of glass beads in a lO.53xmxn-TD hairpin with overflo~w exitt 15

The University of Michigan ~ Engineering Research Institute 20 18 /A 16 14 Notched with flush E E 1800 Bend 900 Bend E 12 E U Fo.Notched Overflow 4 I.0 1 2 3 4 5 6 7 PRESSURE GRADIENT IN DOWNWARD LEG r (cm HgUNDER H /ft) FsgU 59 Total flow rate versus pressure drop for downward flow of glass beads in a 10oS-mm-ID hairpin with various exit types~ 34

U —I a. i C< / 0 W ~ ~ ~ ~ ~ ~ ~ ~ FO RAT —c/in Fig. 0 Pressure drop versus fFree watefor dwwr flow o 2iirnOtw w~sn in aT o ta-lo f nwh -low ex-' na~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~::" w~~~~~~~~~~~~~~~~~~ AA -A —— ~~~~~~~~~~~~~~~~~~~~~~~~: 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ig~A A~ Fressme drpvrulwratefrdwwrd flowof8-irnOtw W~~s n An 0 T~o2-m ~2-t-lnalri wihoeflowext

The University of Michigan ~ Engineering Research Institute I- 5 LL AN a o O o y uJ CL 40n U "' 3 ULd A-Free water flow Er Q I 0-Total flow U-Paste flow at(l-X)=.605 0.5 1.0 1.5 2.0 2.5 FLOW RATE (cc/min) Fig, 7o Pressure drop versus flow rate for downward flow of 82-micron Ottawa sand in a 10o2-mm-ID, 4=ft-iong hairpin with overflow exit~.................36........

5 ~~~~ 0:31 CI~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 4~~~~~~~~~~~~~~~~~~~~~~ UN~~~~~~~~~ >~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 -, m oa:: nW - Free water a. ~~~~~~~~~~~~~~~~~~0 - Total f low U-Pasteflowat(I-X =.605 -~~~ >.5 1.0 1.5 2.0 2.5 3.0 a.~~~~~~~~~~~~~~~~~ FLOW RATE (cc/min) ~~~1 o~~~: w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:3 Fig. 8.?rYessure dr-"op. ver~ sus fl~ow "ate for downward flow o~f" 98-mnicron, Ot-1tawa s andina - Free wath overlow ext a _ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~ 0- Total flow: * ~~~~~~~D - Paste fliow at (I-X a~ -- 60 5:3 e-P.5 I.O 1.5 2.0 2.5 3.O 3.5 4.0 r' FLOW RATE (cc/min) FiEg~ 8o Pressure dr-op versus flow rate f~or do~wrmard flow of 98-micror~, Ottawiua sand Sin a!Oo2- mm~-~S 2~ft-long hairpin: with overflow exit~

The University of Michigan ~ Engineering Research Institute 14 13 13 12 II,o? 10 Ec 2 8 i07 LL 0 82- Micron Ottawa sand flowing at R a 1.01 (-X)..57 (estimated) /op~~ 10 98 - Micron Ottawa sand flowing at Row =1.0 (I-X)=.545 (estimated) 4 2 3 4 5 6 7 DRY-SOLIDS FLOW RATE (cm3/min /cm2) Fig. 9 Total flow rate versus solid flow rate for upward flow of Qttawa sand in a LO.2-x3-ID hairIpin with overflow e xL teo" 3 z /

The University of Michigan ~ Engineering Research Institute 20 0' 0~~0 12 ~ ~ ~ ~ ~~/ Uj~~~~~~~~~~~4 I 0 0~~~~~~~~~~,8~~~~~~~~~~~~~~~~4,6 G/7,. 6V 14-'4 io. E! 2 4 1 0 12 10 _.12 ~/7 /,/,0 ___68 21 D R Y- SO LI DS RATE (cem /m i n/cm2) Ftrig. 10o Total flowF ra-te versuas solid flow rate for urpward flow of copper" shot in a 10o3,-.mmr~-I hairpin with overflow exi~t. 69

The University of Michigan ~ Engineering Research Institute 20.. 18 4)V/ 1 4 Ei.-, / E/ 12/ 1. - l 0 0,0 iNote: L6 ________ 0 - Points represent all of the following exit types: I. Woshed overflow 2. TNotched overflow 3. 90~ bend 4.1800 bend 4 - Poi00/nts for a 17.8-mm tue w ith wshed exit 4 2, 0 I 2 4 6 8 10 12 14 40o..

100,,,,-I f-:3 a>. 901 -r I I r I I r i r <~~~~~~~~~~~~~~~~~~ 700 80 4' H (n ~~mO 40 60 0 I 50 I.4 -,'.6 7 8 9 I. 0 i L4C w0 PRESSURE DROP (psi/ft LENGTH) Fig. 12., Paste velocity versus pressure drop f or downward flow of Ottawa sand'in a 17,,8-mm —D,, 4-ft-Ilong hairpin with overflow exit. 40''L = w 30 = 20 ~p f~ f~ I0 c 8~~~ ".4' 5.6.7 8.9 ~.0 I.I!.2 i.$'".,,., PRESSURE DROP(psi/ft LENGTH) = Fig~ 12o Paste velocity versus p~ressure dr-op for downward flo~w of Ottawia ( sand in a 17o8snmml-~ED, 4ft-long hairpin with overflow exit,

100 > 90 80 60 w 0 00 _J 0 m o 00 240 I30 0 / ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'A 20. 5~ I0~~~~~~~~~~~~~~~~~~~~~~~~~~~.4.5.6.7.8.9 1.0 1.1 1.2 1.3 PRESSURE DROP (psi/ft LENGTH) Fig. 115. Paste velocity versus pressure drop f or upward f low of Ottawa sand in a 17.8 —TD,~ 4-ft-long hairpin with overflow exit.

Downward ".60 0 U) ~ ~ ~ ) 0 Downward ~..58 -0'.57 __ _ o= 0 Lu 54 D 0 _ _ _ _ _ >.53.52... Notes::3 (I-x) determined by conductivity method.5 1 Paste-flow rate calculated at indicated (I-x) Plain overflow exit -.... Washed overflow exit 49 0 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 FLOW RATE OF PASTE (cc/min) Fig. 14. Volume fraction solids versus paste flow rate for lOo/140-mesh Ottawa sand in a l7.8-mm-ID hairpin with plain- and washed-overflow exits.

The University of Michigan ~ Engineering Research Institute 10 0 io 9/ 9 ~/,C"...... ~ lI III E 6 /11' /0 F-. C-) 0,o yFl~~~go~ 5 fO-( -X) constant at /0 0 a0.55 O A-(I-X)varying from 0.538 to 0.588 0 I 2 3 4 5 6 7 DRY-SOLIDS RATE (cm3/min/cm2) Fig~ 15o Total flow rate versus solids flow rate for upward flow of 100/140-mesh Ottawa sand in a 17o8-mm-ID hairpin with washed exit,.... ~~~~~~44

The University of Michigan Engineering Research Institute 20 19. 18 j 17 Note: Paste flow rate calculated from(I-X) 16 in Fig. 14. 15 14 / n- 0 1 93 oj, F0~" 4 5 6 7 8 9 I0 I 12 1:3 14 15 16 17 18 PRESSURE DROP (in. Hg H20 OVER 18" LENGTH) of 5 60/170- 8esh Ottawa sand in a 17. 8-1m-ID hairpin with washed exit~

In 17.8-mm- ID tube: In 8-mm-ID tube 0 - Increasing rate for 17.8 mm tube -.58 -0 - Decreasing rate for 17.8 mm tube I. 0~~~~o - Increasing rate for" 8 mm tube'~ 0 II -Decreasing rate for I 8mm tube.57-, Cn= 0o o.56= U_ 0 0 ~~~~~Im.54' Yb ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 5'530 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 3738 3940 DRY-SOLIDS FLOW RATE (cm/min) Fig. 17o Volume fraction solids versus solids flow rate for upward flow of 100/140mesh Ottawa sand in 8-mm-ID and 17.8-mnm-ID tubes. Porosity determined by electrical conductivity method.

The University of Michigan ~ Engineering Research Institute 40 0 32 - 0 o/ 28 I I 0 E C E w H- 0 20 0 0 Fig 18 Total f rae versus solds flo6 rae o 0 ~ - 0 0 0 0 upward flow of 100/120..nesh glass beads in an 8-rnr-ID hairpin with washed exit ~

The University of Michigan ~ Engineering Researceh Institute MESH SIZE(U.S.STD.) Cx 0 0 0 0 0 0 c -. 0 - 0 0 0 0 0 0 E I0 -J 1.0 -, Ld -u - ~li 10 30 50 70 100 137 200 400 700 1000 PARTICLE DIAMETER (MICRONS) Fig. 19. Predicted free water velocity versus particle diameter with volumne fraction solids as parameter for spheres with density of 2~49 gm/cmn3 flowing upward at Row = lo 48

The University of Michigan ~ Engineering Research Institute 10 E / ARound sand I I I I I / o/ 1, o Ii rC) o / 1 1 vg~X T ) =.5 00 0 30 60 200 400 10 PARTICLE DIAMETER (MICRONS) -49 Fig. 20. Predicted free water velocity versus particle diameter~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,, wIth. vouefrcinsoisa pretefosprsan oud sand wihdniyo 5g/cnflwgupadtRo=,49!,

The University of Michigan ~ Engineering Research Institute 10 E 0 a U0. I Fig~ 21. Predicted free water velocity versus particle diameter with voluume fraction solids as paramreter for spheres with density of 8~65 flowing upward at Row = 1o 50~

The University of Michigan ~ Engineering Research Institute 6 - E o C 0 uiJ 37 LLJ L~~~~~~~~~U.j~~~~~ I 0 I 2 3 4 5 6 7 8 9 I0 15 20 SOLID DENSITY (gin /cm3) Fig~ 22~ Predicted free water velocity versus particle density with particle diameter as parameter for upward flow of spheres at Row = and (N-X) = 0o55o.....51

The University of Michigan ~ Engineering Research Institute 7r/ 3O 1 3 3 4 5 1 1 20? SOLID DENSITY / ) 0 LL 00 SOLID DENSITY (gm/cm3) Fig. 253 Predicted free water velocity versus particle density with particle diameter as parameter for upward flow of "round sand" at Row = 1 and (1-X) = 0o55. 52

The University of Michigan - Engineering Research Institute 7-5/8 4" PRESSURE I/|" TAP 3TAP L -3/16', 3 BOLTS ON 3k2}SUE /16 WCEOUILATERAL PITCH RUBBER GASKET 5/32T I- 1/2u 2-3/8" Fig. 2)-K Sketch of equ:ipn#i!..... 2"e 5 \ I @Sll PUMP Flg o 24, Sketch of equipmento -',,, 3,

The University of Michigan ~ Engineering Research Institute 10 9 - A T 0C.I 0 X a. I E 0 = z 4 i~i 0 -b I I o Do =0.15 A DO =0.10 -2 -4 0 20 40 60 80 100 120 140 160 180 200 Fig~ 25' Pressure drop versus solids flow rate with orifice diameter 54

The University of Michigan * Engineering Research Institute I0 9 6 o z 4 w (D 0 2 0 Orifice diameter - inches X Do =0.20 0 Do = 0.15 A Do= 0.10 _4 0 20 40 60 80 100 120 140 160 180 200 Fig. 26, Pressure drop versus solids flow rate with orifice diameter as paraueter for the flow of l40/00-xesh Ottawa sand paste0 fLW AT f OLDS(m55an

The University of Michigan ~ Engineering Research Institute IC A I1~0 0 o 9.9~~~~~~ 8 7 6 i qu~~0 5 O F__ LC I. Z: 2 04 w o 0 0 Orifice diameter -inches X Do O 0.2 0 Do =0.15 a Do -o.!0 -2 -4_ 0 20 40 60 80 00 120 140 160 180 200 FLOW RATE OF SOLIDS (cm3/min) Fig. 27. Pressure drop versus solids flow rate with orifice diameter as parameter for the flow of 200/525-mes h Ottawa sand paste. i o~~~~~~~~~~5

The University of Michigan ~ Engineering Research Institute 10 9 8 A 7 6 I 03 1/.... o _. _ I / A > l q -t ~~~~~~~~~rifice diameter- inches -_ Do =0 20 12~~~~~~~~~~~~~~~ i Do 0. 10 213 -I FigA 2 Pressurrifie diameter- ice diameter as parameter for the flow of 140/200-mesh copper shot~ 57

The University of Michigan ~ Engineering Research Institute II _.. 6 0 cJ -) 0 |z/. X Do 0.20 A DO =0.10 -3 0 20 40 60 80 100 120 140 160 180 200 FLOW RATE OF SOLIDS (cm3/min) Fig~ 29~ Pressure drop versus solids flow rate with orifice diameter as parameter for the flow of 140/200-mesh lead shot~

The University of Michigan * Engineering Research Institute 1.0 140/200 Lead] 0Mesh 5. /. o Si ~2 80/100 l/0 X siO, 200/325'00eV Cu 140/200 0 000a Pb 140/200.. 5 6 7 8 9 10.01 I/Do Fig~ 300 Logarithm of the slope function versus reciprocal of orifice diameter~ 59

The University of Michigan * Engineering Research Institute PARTICLE DIAMETER-INCHES 0.002 0.003 0.004 0.005 0.006 -1.0014 I -1.0016 -1.0018 Slope b 0.09525 -1.0020 C3= - 1.002215 C2 -1.0022 -1.0024 Slope m 1.3 -1.0026 C4 -1.00581 -1.0028 Fig~ 31o C2 versus particle dianetero 6O

The University of Michigan * Engineering Research Institute 2 RECIPROCAL OF SPECIFIC GRAVITY I/pp 0.1 0.2 0.3 0.4 0.5 CI 0.59 cc/gm ~~~~CoC -2 i Slope=Q-5.555 gin in.H20 ~-3 Pb~ i Cu Pb -4 Fig. 32~ C1 versus reciprocal of particle density. 61

.75.70 -r7~~~~~~~~~~~_ __ _ _.0ILj U0~~~~~~~~~~~~~~~~~~~~~~~~~~~,00~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~u oo H.60 ~L~ S 05 IL IL ~~~~~-;65 ~ ~ ~ ~ ~ ~ ~~~~~~~ 0.60.55 / 0) ~~~~~~50 u,~~~~~~~~~r at n 1020.56.57.58.59.60.61.62.6 3.64.65;7 I-x Fig. 553 Coefficient of friction'between a zinc plate and 150/200mesh Ottawa sand paste.

The University of Michigan ~ Engineering Research Institute.65.60 00y V.55 z.50 L0 I-. 45 LL. U0.35.30,55.56.57.58.59.60.61 I-X Fig. 34~ Coefficient of friction between a glass plate and 150/200.mesh Ottawa sand paste~

.65 0~~~~~~~~~~~~~~~~~~~~~~~~~~~ LL_ Li~ 0 - 3.55.50.40..41.42.43 44.45.46.47 I-x Fig~55 Coefficient of friction betwe-en a glass plate and -3525-mesh

The University of Michigan * Engineering Research Institute CONSTAN T- SPEED VISCOMETER CAN RUN @ 1,2,5, & 10 RPM TORQUE PICKUP RANGE IS OTO 51.25 gm cm 4- cm WATER OVERFLOW <~ PASTE BED E _E*TO MANOMETER FRITTED DISK WATER Fig. 36. Viscometer apparatus sketch~

The University of Michigan ~ Engineering Research Institute 1000 Limit of torque scale 500 100 X. O -1/2 Dia. spindle Iz.0. ca ~ ~ VOUEFATOSrLISI Li, VOLUME FRACTION - OLI- S - X) VOLUME FRACTION SOLIDS (I-X) Figo 37. Visconeter torque versus fraction solids for 100/140.nesh Ottawa sand. 66

The University of Michigan * Engineering Research Institute 1000 Limit of torque scale II 500 - a:... Uj C, 0-3/4" dia. spindle Note'One scale unit =.1025 10 - 5.0.55.56.57.58.59.60.61.62.63.64.65.66.67 VOLUME FRACTION SOLIDS (I-X) 0Fig 38, Viscometer torque versus fracton sol_ ds for lO0/140-~mesh opper shot F- -~i.3. iciee oru essfrcinsld "' ~~o 0010ms cpe ht

The University of Michigan ~ Engineering Research Institute iooo —--— __ Limit of torque scale 500 - x l1 1I z, 50 ~~~...s ~~~~~~~0-. Idia spinle 101 1 I I I B O _s I I I Note: One scale unit.tQ2 5gm cm 10 1.0- -. - ___ - ___ -.55.56.57.58.59.60.61.62.63.64.65.66.67 VOLUME FRACTION SOLIDS (I-X) Figo 39~ Viscorneter torque versus fraction solids for 100l/1l20-mesh glass beads'

The University of Michigan * Engineering Research Institute EJECTOR LIQUID 7JLNLET FROM PUMP -,OUTLET TO PUMP BAFFLE PASTE PASSAGE COOLANT PASSAGE SWEEP LIQUID DOWN COMER LOW - DENSITY LIFT ANNULUS EJECTOR Fig. 40ao Complete reactor configuration., EJECTOR LIQUID TO PUMP BAFFLE __________________~-~~-.~ - _ I PERFORATED //////////-./. r oPLATE.oo o ~ J t ~ ~SWEEP LIQUID I' < td. t DOWNCOMER EJECTOR LIQUID FROM PUMP Flg0 40bo Experimental model configurationo 69

The University of Michigan * Engineering Research Institute TOP EJECTOR AND SWEEP LIQUID K /" ~LOW-DENS ITY SLURRY TO SEPARATOR H IGH - DENSITY PASTE FROM SEPARATOR BOTTOM Fig~ 41o Reactor top and bottom configurationso 70

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