Document e12mOVYX32a1o38rkomEdRQYE

Contains confidential information Responsibility of recipient. When no longer needed/ destroy by burning or shredding. CDP-ES-79-24 Issued 1/2/80 Copy No . 13 Distribution on last page. EXPERIMENTAL STATION RESEARCH AND DEVELOPMENT DIVISION TECHNICAL REPORT CHEMICALS, DYES AND PIGMENTS DEPARTMENT E. I. DU PONT DE NEMOURS & COMPANY COANDA-FLOW CLASSIFICATION OF TKU Work Done By: Approved By: Patent Situation Approved By; Previous Related Reports: Project Code; Type Technical Work: Period Covered: Notebook Nos.: Personnel: L. S. Wilkens K. K. Bhatia J. W. Heberling Date: PTD-SA-78-2B 7053-182088 IEB Sept., 1978 to Oct., 1979 E16067, E19622 G, A. Schurr(Engg.), C. A. Perry, J.Thompson, E. Danisavich (Engg.) 11/8/79 ABSTRACT Coanda-flow classification has been shown to effectively handle Ti02. Present applications include removal of Ti02 scrub solids grit and fine-cut (1--3 ym) separations. Potential energy benefits (primarily micronizer steam savings) from such classifi cations are now being studied. Removal of 7-8 wt. % + 325 mesh grit has already been shown to significantly reduce grinding energy requirements. Fine-cut separations are still being evaluated. In conjunction with the experimental program, a mathematical model of the Coanda-flow separation technique was formulated. The resulting cut-size predictions were in good agreement with the experimental results. This mathematical model was further used to analyze larger slot dimensions, etc. which would be more amenable to plant-scale N40793 - 2 CDP-ES-79-24 COANDA-FLOW CLASSIFICATION OF TiCU INTRODUCTION Size classification of Ti02 is being investigated as a means of reducing energy consumption in the micronizer. The micronizer is the primary energy consumer in the plant, using "1/3 of the total energy, and the particle size distribution of its feed is thought to affect its grinding efficiency. In particular, the presence of 5 to 10 wt. % scrub solids grit (+325 mesh) has been shown to significantly increase the micronizer steam consumption. In the present program Coanda-flow classification has been studied and shown to be effective in removing such grit. This same Coanda-flow technique is also being used to make fine-cut classi fications . If the micronizer feed can be separated into two frac tions , one of which is very fine, these two fractions could be micronized separately and thus avoid any overgrinding of the fines. Since TiOg is particularly sticky and hard to handle, past classi fication techniques have had difficulty with Ti02, and none have been able to make a fine enough cut-size to accomplish the above goal. The present technique shows the greatest promise for success. It has been shown to handle Ti02 well and to make a cut as low as 2-3 urn. OBJECTIVES Assess the feasibility of classifying Ti02 in a Coanda-flow classifier. Determine the micronizer energy usage and pigment quality result ing from such size classification. PATENT SITUATION Patent Protection : None Filing Action: None contemplated. PROGRAM A laboratory model based on Coanda-Flow principle is being constructed at the Engg. Test Center. Experimentation is planned for this Boundary-Layer classifier to determine what if any flowbalance problems may occur with the exit streams and to determine potential energy savings. DUP050059301 3 CDP-ES-79-24 * PUBLICATION STATES No plans for paper(s) at this time. SPECIAL SAFETY PRECAUTIONS Ear protection necessary. ENVIRONMENTAL CONSIDERATIONS None. ACKNOWLEDGEMENTS George Schurr had the original idea of using the Coanda-flow principle for scrub solids classification and has actively partici pated in the experimental programs discussed in this report. Phil Muhlmichl is responsible for the design of the laboratory apparatus. Professor Loffler and K. Mali (University of Karlsruhe, West Germany) are responsible for running our Ti02 samples on their Uternal Jet classifier. $ DUP050059302 4 - CDP-BS-79-24 TABLE OF CONTENTS Introduction .............................................. .......... 2 Objectives ................................................................................................. 2 Patent Situation ....................................................................................... 2 Program Publication Status .................................................................................. 2 3 Special Safety Precautions ..................... .................................... 3 Environmental Considerations .......................... ...... 3 Acknowledgements .................. Table of Contents ..................... ............ 3 4 Summary & Conclusions ............... Discussion ...................................................................................................... 5 6 I. Description of Coanda-flow Separation . Principle 6 II. Classifier Design ........... 6 A. TiOj Scrub Solids Classification B. Classification of Micronizer Feed III. Theoretical Analysis .......... 7 Experimentation .................. 10 Scale-up Considerations .............. 11 I, Scrub Solids Classification ...... 12 II. Classification of Micronizer Feed . . . 15 Other Applications . . . . . 16 References.................................... . 16 Indexing Terms ...... ..................... ........ 16 Figures 1 thru 20 ................. 17-36 Appendix: Computer Program ....... ..................... 37-45 DUP050059303 -5- CDP-ES-79-24 SUMMARY AND CONCLUSIONS The initial stage of this study included the design/ con struction/ and testing of a laboratory Coanda-flow classifier for separating out TiC>2 scrub solids grit. (In the plant TiOj scrub solids, when used, constitute 4 to 8 wt. % of the TiC>2) This technique was shown to be an effective way to make such a separa tion and the resulting decrease in grinding energy usage was signif icant. in conjunction with the laboratory experiments, this classi fication technique was analyzed theoretically. Particle trajec tories were mathematically modeled. By comparing the trajectories for different-sized particles, it was possible to predict the separ ation for different classifier conditions. The results were in good agreement with the experimental results, indicating that the model could be used to predict cut sizes under scaled-up conditions. In the second part of this study fine-cut classifications were made on micronizer feed. A German Uternal Jet classifier (also based on the Coanda-flow principle) was used for these tests. The results were particularly good. The classifier effectively separated the TiC>2 and produced a very fine cut size (2-3 ym diameter top size). This is in agreement with the theoretical predictions. The investigation of energy usage and pigment quality is not completed yet, but some of the unmicronized fine fractions behaved very closely to standard grade pigments. Plant-scale implementation has also been considered. Poten tial problem areas were identified and some of them were considered in detail. In particular, dimension changes Were evaluated theor etically to determine whether the desired separations could still be made. The results suggest that such plant-scale separations are possible. DUP050059304 6 CDP-ES-79-24 DISCUSSION I. Description of Coanda-flow Separation Principle Coanda flow occurs when a high velocity stream attaches itself to a solid and flows along the surface. In such case, the surface may be curved, irregular, etc., and the stream will deflect and follow the surface curvature rather than continue in a straight pathway. This principle can easily be adapted to produce a particlesize separation by using a convexly-curved surface, the resulting centrifugal force throwing the larger particles away from the surface while the fine particles are carried with the gas stream (Figure LSW-1) II. Classifier Design A. Ti02 Scrub Solids Classification To separate out TiOj scrub solids grit, a laboratory classi fier based on the Coanda flow principle was designed and constructed (Figure LSW-2). To aid in the design, a theoretical analysis was made of the behavior of various size particles subjected to differ ent gas velocities and radii of curvature. (This will be discussed in a later section.) The results of this analysis were used in selecting the dimensions for the laboratory model * They include: slot = 1/8" x 4"; radius of curvature - 4"; wedge + 3" from surface and displaced 60 from start of curvature. The fine fraction was collected by means of a bag filter while the coarse fraction was either collected by cyclone or allowed to fall by gravitation into a cotton bag. Both of these methods were satisfactory. The ideal location for such a classifier in the plant would be at the end of the flue legs (i.e, after the pigment has been formed and cooled, and after the scrub solids have served their pur pose of keeping the pipe walls clean and free of sticky pigment)* At this point the pigment is dispersed in chlorine gas and is traveling at a velocity of -100 ft/sec. The gas (air) used in the laboratory experiments differs only slightly in physical properties from the higher temperature (-150C) chlorine in the flues. Also the air velocity used in the experiments (at the slot exit) was -100 ft/sec to match that in the flues. B. Glassification of Micronizer Feed To make a fine cut on micronizer feed, a German-made Uternal-Jet classifier was used. This required shipping the pigment samples to the University of Karlsruhe for the tests. George Schurr (ESD) observed some of these tests, and returned with a diagram of the classifier (Figure LSW-3), This classifier is also based on the Coanda-flow principle but has some slight differences (as compared to the scrub solids classifier) which give more control over the boundary layer flow of the gas. Thus it can produce a DUP050059305 - 7 CDP-ES-79-24 finer separation. The velocity was 100 m/sec and the radius of curvature was 3/4"i Also, a secondary gas stream flows at the same velocity as the pigment/gas mixture, and a curved section confines this stream as it flows ~30 to 40 around the Coanda surface. Thus a high velocity is maintained (i.e., the gas stream is not allowed to expand) while much of the pigment separation is occurring. Some expansion of the gas occurs as it proceeds farther around the Coanda surface, but surface suction is used to help keep the stream attached. III. Theoretical Analysis To predict cut size for a Coanda-flow classifier, a mathe matical model was developed to compute particle trajectories for different-sized particles. For each individual particle a force balance was made. Since the particle is generally traveling in a direction different from the surrounding gas stream, the particle velocity was broken down into components - one in the direction of the gas flow; the other perpendicular to it. The gas velocity in this perpendicular direction was assumed to be zero. Force Balances: In the direction of gas flow: drag force = acceleration 1/2 Ppirr2 (vg - vpg)2CD = + (4/3) irr3pp In perpendicular direction: drag force - deceleration 1/2 ppirr2 (vpp)2CD = - (4/3) irr3pp ^ where r = particle radius (cm) pp = particle density (gm/cm3) Vpg = particle velocity in direction of gas flow (cm/sec) Pg == gas density (gm/cm3) vpp ~ particle velocity in direction perpendicular to gas flow (cm/sec) CD - drag coefficient Vg = gas velocity (cm/sec) (Note: All particles are assumed spherical and gravity has been neglected.) DUP050059306 -8- CDP-ES-79-24 If the particle is large and manages to escape the flowing gas stream, the force balance reduces to a single expression for the direction of particle travel. Drag Force " deceleration 1/2 ppirr2 (Vp) 2C.D = - (4/3) irr3pp ^ Where Vp = particle velocity (cm/sec) The drag coefficient, and more importantly its functionality, vary with Reynolds number (Re = 2pgvr/pg and v - particle velocity, Pg = gas viscosity). However, the Reynolds number can be broken down into several ranges for which the resulting functionalities are all fairly simple (the commonly known relation for stokes drag is CD = 24/Re). However, solution of these two force balances is complicated by the constantly changing direction of movement (and consequently the direction of the forces). Solution must therefore he done in small incremental time steps. At each time step, the differential equations can be solved analytically. The particle is then assumed to travel vAt in the appropriate direction and the procedure is repeated. A computer program was written to perform these calcula tions and to plot the resulting particle trajectories (Appendix). Knowledge of the gas velocity profile is also necessary for this analysis. For the initial calculations (for the scrub solids classifier) a gradually expanding box-like profile was assumed (Figure LSW-4). No boundary layer (i.e., velocity dropping to zero) at the Coanda surface was included, as it was assumed to be so small that it would not play a role in the separation. Estimation of the boundary layer thickness based on boundary layer theory (Schlichting, 1968, p.26) confirms this. The calculated value at 1 cm from the slot exit is s10~5 cm, i.e., less than the diameter of a particle. Actual velocity profiles were measured using a pitot tube and are shown in Figure LSW-5. The minimum distance from the surface at which a measurement could be made was 1/16". The surface boundary layer thickness was always less than 1/16", and therefore was never actually measured. Thus, the boundary layer as shown is not intended to be accurate in its indicated thickness, but rather to emphasize that such a boundary layer does exist. These measured profiles are similar to those reported in the literature, but such profiles were not used in the theoretical calculations because they were too complex, and no correlation based on the slot exit velocity was available. More important, however, was the fact that the measured expansion rate of the gas stream was in fair agreement with the assumed rate, as this rate may affect the sharpness of the cut as well as the cut size. DUP050059307 - 9 CDP-ES-79-24 The results of this mathematical analysis for a set of conditions similar to those in the flues (i.e., chlorine gas @ 150 C with a gas exit velocity of 100 ft/sec) and a Coanda surface radius of curvature of 10 cm with a 1/8" slot width are shown in Figure LSW-6. These calculated trajectories indicate that the small par ticles (ClOym diameter) follow the gas stream around the Coanda surface. Slightly larger particles (10 to 50 urn) have sufficient inertia to escape the flowing gas stream, but are then decelerated by the surrounding quiescent gas. The trajectory end points shown do indeed represent stopping points, but once the particle slows down (or stops), gravity will soon take over, causing it to fall back into the gas stream, and likely continue to move with the edge of this stream. The larger particles (> 50 urn) escape the gas stream immediately and continue for long distances (>10") before gravity has any effect. The easiest way to separate the grit will therefore be to place the separating wedge so that all of the gas flows along with the fine fraction. The expected cut size will then be -50 yin. Based on this information the laboratory scrub solids classifier was set up with the wedge about 3" from the surface at -60 around. A typical experimental run gave the following results Wet screen analysis of feed +80 mesh -80 +325 mesh 6.53 wt.% 1.32 wt.% Classified - Fine fraction +80 mesh 0.30 wt.% -80 +325 mesh 0.42 wt.% This indicates that the cut was near 325 mesh as predicted. (Although it appears that only -2/3 of the 80 to 325 mesh was classified out, the actual value is probably higher (possibly as high as 80%) . This is due to a small loss of fines when running small samples in the , present system. The accuracy of the mathematical model was further demon strated when it was used to predict the cut size for the Uternal Jet classifier. (A non-expanding gas profile was assumed for these cal culations/) In this case the separating wedge actually splits the gas flow, and the sharpness of the cut will depend more strongly on the height of the slot. For instance, if a sharp cut between 2 and 3 ym is desired, a 3 ym particle exiting next to the surface (Fig. LSW-7) must be separable from a 2 ym particle exiting from the top of the DUP050059308 10 CDP-ES-79-24 slot (Pig. LSW-8). Based on the particle trajectories a reasonable separation can be made as low as 1 to 2 ym, but a really sharp separ ation is probably possible only at "5 ym. For the present loca tion of the separator (1/4" from the surface and ~120 around)/ the predicted cut is between 1 and 2 ym with top size of ~1.5 ym, and indeed the resulting fine fraction had a top size of 2 to 3 ym. The coarse fraction, as expected, did contain some of the fine particles, but only a small percentage of the original sample. EXPERIMENTATION Samples of R900 and R960 dryer discharge (micronizer feed) were classified in the Coanda-flow scrub solids classifier. The "as is" R900 DD contained ~8 wt.% +325 mesh grit. Almost all of this grit was in the size range 20 to 40 mesh. The R960 DD, on the other hand, contained <1 wt.% grit (apparently it had been produced using salt scrubs). For testing purposes ~7 wt.% grit (20 to 40 mesh) was added to it. The Coanda classifier effectively separated out the grit in both of these samples. However, pigment stickiness arid ease of deagglomeration are important. A sample of R101 containing 6 wt.% grit could not be classified well because much of the fine pigment remained agglomerated in the injector and thus behaved like grit during classification (i.e., much of the fine pigment was collected in the coarse fraction), To determine grinding energy requirements, samples were classified and micronized at various steam/pigment levels in the Edge Moor 8" micronizer. They were then compared to unclassified samples similarly micronized. Since gloss is the property most strongly affected by the grinding energy level, all samples were analyzed for gloss in both alkyd and aqueous formulations. The results (Figs. LSW-9 and 10) show reduced grinding energy require ments for grit-free samples. The actual energy requirements of the large plant micronizers may, however, differ somewhat from those of the 8" experimental micronizer, but the present results do suggest that significant grinding energy reductions may be possible. The purpose of classifying the micronizer feed (dryer discharge) with the Uternal Jet was to split it into two fractions which when micronized separately would require less grinding energy. This would occur if the present process overgrinds the fines or if a narrower particle size distribution is more efficiently ground. Samples of R900 and R931 DD were sent to Germany for classifica tion in the Uternal Jet. Upon return, both coarse and fine frac tions were micronized at various S/P levels and compared to unclas sified samples similarly micronized. Analyses of the samples included particle size distribution for the original R900 DD and R931 DD and the classified samples. (Figures LSW 11 and 12) Accoridng to the sedigraph results the mass does not balance. At the present time We do not know why, but further study is planned once the Engineering Department completes their own boundary layer classifier. Paint formulations were used to determine gloss DUP050059309 11 CDP-ES-79-24 for the R900 samples and hiding power for the R931 samples. The results are plotted in Pig. LSW-13. The most significant result was the high hiding power for the unmicronized R931 fine fraction this sample was just below standard pigment quality in its behavior. Attempts to determine the grinding energy requirement for this fine fraction, however, have been inconclusive. The 8" micronizer could not be run at a S/P ratio low enough to distinguish between the classified and the unclassified (i.e., both samples had good hiding power at this lowest S/P). A low energy hammermill was subsequently tried, but its grinding energy level may have been too low as there was no improvement in the R931 fine fraction. Problems were also encountered with the R900 samples. One of the R900 fine fractions had an impressively high gloss value, but was irreproducible - the initial measurement gave 77 and several repetitions gave 42. The micronization tests were again inconclu sive. This particular sample of R900 micronizer feed was so good that even at the lowest S/P (on the 8" micronizer) a very high gloss pigment resulted. Thus differences in energy requirements between classified and unclassified pigment could not be determined. A further test was made using sandmilling, a lower energy type of grinding. The resulting slurries, however, produced very poor gritty paint films. (It is not certain whether the slurry prepar ation technique*had any effect on this or whether it was solely due to poor pigment quality.) To resolve the question of energy usage, a poorer (more normal) quality R900 micronizer feed will be used in future tests. To determine overall energy requirements, the coarse frac tions must also be evaluated. Some micronization tests have already been done on the R900 coarse fraction. The results suggest that more grinding energy is required (as compared to an unclassified sample), but the observed gloss differences were within the accuracy limits of the measurement and thus inconclusive. The R931 coarse fraction has not been evaluated, as the original sample pelletized in transit to Germany. These pellets were removed before classi fication so it is uncertain whether the resulting coarse fraction (and possibly even the fine fraction) are representative of fresh plant samples. Further experimental work with fresh pigment is planned. SCALE-UP CONSIDERATIONS For scrub solids grit classification either the laboratory model or the Uternal Jet design could be used. However, the laboratory Coanda model would likely use the least amount of extra gas. If such a classifier is to be used at the end of the flues, the pigment would be in a chlorine atmosphere and additional gas would have to be chlorine as well. Thus large quantities may be undesirable. On the other hand, the controlled boundary layer flow of the Uternal Jet would undoubtedly insure a sharper cut at 325 DUP050059310 - 12 - CDF-ES-79-24 mesh. The Uternal Jet could also be used to make a dual separation (grit elimination plus fine-cut classification) after the pigment has been collected in the cyclone. This would require an air stream to disperse the pigment,whereas for classification in the flues we would assume that the pigment is already dispersed (i.e., deagglomerated). However, logistically it may be difficult for the plant to handle two separate streams (the fine and coarse fractions) through the remainder of the process, i.e. wet treatment, filtra tion, drying, and micronization. ft I. Scrub Solids Classification For the present analysis we will first consider the labora tory Coanda design. For scrub solids classification at the end of the flues, the slot height must be large enough to avoid pluggage. Also the JV plant cannot tolerate an in-line pressure drop; i.e. orifice flow must be avoided or additional blowers will be necessary to inject the pigment. Orifice flow can be avoided by maintaining the same cross-sectional area going from the flues into the slot. For example, the flues end with a 12" diameter pipe, thus having a cross-sectional area of 112 in2. To maintain this area, a slot of height 1" would have to be 112" long. A more reasonable size would be either 2" x 56" or 3" x 37". Thus the major scale-up considera tions (assuming gas velocity and pigment concentrations are kept the same) will be: 1) how large (height) a slot can be used without sacrifi cing cut sharpness. 2) how long will the stream stay attached to the Coanda surface if a large slot is used. 3) how much additional gas is needed for mixing as the boundary layer expands. A correlation for detachment angle was given in the literature (B. G. Newman, 1961) . 0 = ,45 - 391 <*>/*> sep 1 + (9/8)(b/a) (See Figure LSW-14 for Newman's Coanda configuration) where 0sep = detachment angle (degrees); the angle refers to the angular displacement around the Coanda surface b = slot height a = radius of curvature DUP050059311 - 13 - CDP-ES-79-24 This expression, however, is only valid for ___ numbers (where Re is defined as [ (P - P,) ba/pv2]3*) greater than some limiting value. Newman's experimental results gave a limi value of Re % 4 x 104, but the b/a values which he studied were quite low (0.0067 to 0.04) . He further states, that the Re value should deviate less than 5% for b/a up to 1 and that the value (4 x 104) is not known to that accuracy. (His data suggest an accuracy of -10%.) The following three cases (for the original Coanda-flow design) were selected to represent the range of practical plant-scale conditions: 1) 6 in. radius of curvature; 2" x 56" slot 2) 8 in. radius of curvature; 2" x 56" slot 3) 8 in, radius of curvature; 3" x 37" slot To determine whether these conditions would still give the desired separation, the above correlation was used along with a computer analysis of the particle trajectories. The accuracy of Newman's correlation is not known for the desired range of b/a >0.25 but Newman expects it to be reasonably accurate for b/a <1.0, The expres sion was, therefore, used only to obtain an estimate7 If the original scrub solids classifier design were used, we would need the gas stream to remain attached at least 90. However, to obtain an esti mate a value of 150 was used to include a margin of safety* This resulted in a b/a value of %l/3. As a check on the usefulness of the Newman expression the slot Reynolds number was calculated for the following conditions: ab = 12 (2x6) in2 where p -- 0.004 (CI2 @ 150C) (P-p)oo - H pv2 v = 3000 cm/sec v = y/p y = 0.0002 poise (CI2 @ 150C) The resulting value was 1.5x10^ which is above the desired minimum. Another consideration is the slot aspect ratio (length/ height). In the literature, one study (McGlaughlin and Greber, 1967) was reported in which aspect ratios of 0.8 to 2.4 were used, and the gas streams detached much earlier than predicted by the above expression. Newman's experiments, on the other hand, were in the range of 200 to 1200. It is not known how large the aspect ratio must be to avoid problems, but probably 10 to 20 would be a good guess. In the laboratory scrub solids classifier, a value of *30 was used. In the Uternal Jet the ratio was 11. In the three selected cases, the aspect ratio is >12. DUP050059312 14 - CDP-ES-79-24 The computer results for the three cases are shown in Figs. LSW-i.5 16 and 17. In general, the use of such large slot widths causes a considerable sacrifice in the sharpness of the cut, and the exact location of the separating wedge will be much more critical than it was in the laboratory model. This effect is shown guite clearly in Fig. LSW-18, which gives particle trajectories for particles exiting from different locations in the slot. If the separator is carefully placed, a separation at ~40ym could be made. The cut would not be as sharp as in the lab model, but probably sharp enough. However, this requires the separator to be in the middle of the gas stream and would require gas flow balance and control on the exiting streams. If on the other hand, the separator is placed outside of the gas flow, all of the gas will be associated with the fine fraction and gas handling would be much easier. However, the cut size will be considerably greater, ranging from 70 to 150 ym. Of the three cases, the 2" slot with the 6" radius of curvature gives the finest cut. The case of the 8" radius of curvature with the 2" slot is similar to the previous case, but the gas flow is more expanded. This will cause an even greater.loss in the cut sharpness and possibly some increase in cut size. The third case is the worst and would certainly not be recommended. In fact, in general, the smaller the slot height, the better will be the cut sharpness. Also, a smaller radius of curvature will be possible, which in turn will decrease the cut size. Based on this information, the first case (2" x 56" slot height, with 6" radius of curvature) would be recommended. An even smaller slot height, such as 1% (length = 75") or 1-3/4" (length = 65") would be better, if the slot length does not pose a problem in design and construction. Another consideration for plant-scale feasibility is the amount of surrounding gas which becomes entrained in the pigment/gas jet as it flows around the Coanda surface. No exact correlation was available for the present configuration. However, Giles et al (1965) reported an approximate formula for a logarithmic spiral surface. VE * V2 D `V2''s) where V_i .= entrainment velocity _______ (vol entrained)___________________ ___ or (dist. traveled around surface)(slot length) (time) U = maximum velocity for any given distance around surface Ym/2 = half jet thickness (see Fig. LSW-8) s = distance around surface (i.e., travel distance from slot exit) DUP050059313 - 15 CDP-ES-79-24 This formula was used to obtain an order-of-magnitude estimate for the laboratory Coanda-flow classifier design. For a circular Coanda surface, Ym/2/s is not constant along the surface. Therefore, an average value was used, and based on the experimentally determined velocities, a value of 0.2 Was selected. U also varies as the stream progresses. Again, an average value was used - in this case, one-half of the exit velocity. The resulting value of Vg was 150 cm/sec. For the previously-mentioned case of a 2" x 56" slot with a 6" radius of curvature, the gas flow rate through the slot would be 78 ft3/sec, while the total entrainment would be %18 ft3/sec or 1/5 of the jet flow rate. To avoid undue turbulence in the plant classifier, it may, therefore, be necessary to have a bleed stream of this magnitude situated above the slot. If the Uternal Jet design were used for scrub solids class ification at the end of the flues we would still want a large slot for the pigment feed. Thus we would probably want to change some of the other dimensions such as the radius of curvature. For instance, the radius of curvature could be 4", the pigment slot 1 1/2" and the additional gas slot 2 1/2". 0_ for these conditions is -60 (see next section on Uternal Jet fine cut classification for further explanation) . The predicted cut size for this was ~5)jm (Figs. 19 & 20) .. Regardless of the classifier design, the state of pigment agglomeration will be important. If the pigment is not well-dispersed at the end of the flues, a sharp separation cannot be obtained without supplying extra energy to break up the agglomerates. A separate study (W. E. Stevens) is already underway to determine the degree of dispersion at other points along the flues, and we have, requested that he also include a measurement at the end. This information will then be used in our assessment of plant-scale feasibility. II. Classification of Micronizer Feed Scale-up of the Uternal Jet for use as a fine-cut classifier would primarily consist of making the total slot length great enough to handle the pigment rate in the plant. Otherwise, there would be. no change in dimensions. Analysis of the design, however, did clar ify the operation of such a classifier. The slot height (in Newman's expression) is actually the combined heights of the pigment feed slot and the additional air slot totalling -1.25 in. Therefore _ 391(1.25/0.75) sep " 245 ~ 1+' (9/8ra:25/0.T5) = 18,3 (The "Re" was calculated for these conditions and is above the minimum value.) DUP050059314 16 CDP-ES-79-24 This angular distance is quite small, but much of the separation is actually produced within the air slot (i.e., after the pigment exits but within the region of controlled flow). Also the suction on the Coanda surface may be very important in keeping the stream attached. A small pigment feed slot will be important to maintain good cut sharpness, but increasing it from 1/4" to 1/2" may be all right. Some idea of the required length can be determined from the experimental feed rates, if one production line makes 100,000 tons/yr. (10,300 kg/hr.) and the feed rate is twice the experimental (because the slot height has been doubled), - 2x200 = <100 kg/hr., the needed length is (8 cm) " 206 cm* " 82,5 in* This total length could be provided by using several classifiers; for instance 4 classifiers each having ^20" long slot, A possible disadvantage of this unit, however, is the need to balance the flows of exiting gas streams. It is not known how critical this will be, but further studies are planned to determine this. Other Applications The Coanda-flow classification principle can also be used to separate particles of different density. REFERENCES Giles, J. A.; Hayes, A. P., and Sawyer, R. A. "Turbulent Wall Jets on Logarithmic Spiral Surfaces", The Aeronautical Quarterly, 17, p. 201 (1966). ~" McGlaughlinV D. w. and Greber, I., "Experiments on the Separation of a Fluid Jet from a Curved Surface, "ASME - Advances in Fluidics, p, 14, May 9-11 (1967). Newman, B. G., "The Deflexion of Plane Jets by Adjacent Boundaries Coanda Effect", Boundary Layer and Flow Control, edited by G. V. Lachmann, Pergamon Press, Inc., New York, p. 232 (1961). Schlichting, H., Boundary-Layer Theory, McGraw-Hill, Inc., New York (1968). INDEXING TERMS Boundary Layer Classifier Classification Coanda-flow Titanium Dioxide Uternal Jet DUP050059315 - 17 FIGURE LSW-1 COANDA CLASSIFIER CDP-ES-79-24 Slot from which pigment/air mixture exits at high A trajectory of small particle trajectory of large ^ particle Curved Coanda surface Coarse Fraction Separating wedge DUP050059316 - 18 FIGURE LSW-2 t&BORATORY APPARATUS CDP-ES-79-24 DUP050059317 - 19 - CDP-ES-79-24 * Figure LSW-3 Ut ERNAL G t AftSI F.lEft * DUP050059318 - 20 - CDP-ES-79-24 FIGURE LSW-4 ASSUMED GAS VELOCITY PROFILES Note - No initial straight section was assumed, however the actual surface did include one (see Figure LSW-2). This figure is not drawn to scale. \ \ \ \ \ * DUP050059319 21 FIGURE LSW-5 MEASURED VELOCITY PROFILES CDP-ES-79>-24 Exit Velocity 100 ft/sec DUP050059320 P a rtib le T ra je c to rie s in a Coanda C la s s ifie r lO O DUP050059321 - 23 Figure LSW-7 CDP-ES-79-24 "Pa r t ic l e "Tr a j e c t o r ie s CONDITIONS ARj Rm.Temp. y 3000 cM/sec , Ta r t , d e n s A.o <r/c3 DlAMrrens t - I/a w * SL - 51/a w 3 - 3,/Ji.m ^ ^ /tin 5-6 /a w (# ~ 7 yuun 7- 9/*r 8 * I Syu/n 9 ~ I 5^rv DUP050059322 - 24 Figure LSW78 PARTICLE TRAJECTORIES {Same as Figure LSW-7 but Exiting from Top of Slot) CDP~ES-79-24 DUP050059323 EFFECT OF GRIT REMOVAL ON R900 DUP050059324 g r aph ic CONTROLS c o r po r at io n Buffalo. Now York Fwued mU.S.A S8UAXC I I X T T9 TK MALF well AS-M3-9T - 26 CDP-ES-79-24 Figure LSW-10 */ EFFECT OF GRIT REMOVAL ON R960 I I f | m Ml* MCI M-MlJ -IT Sfiifttt I I I I DUP050059325 .cp I Ezi I O H- VI 5 Ui a VI UI u .'Hoc* t ; OJ K .'S DUP050059326 lN3DH3d SSVW 3AllVinWft3 DUP050059327 Figure LSW-13 - 29 - CDP-BS- 79-24 DUP050059328 -* 30 CDP-ES-79-24 FIGURE LSW-il* B. G. NEUMAN'S COANDA-FLOW CONFIGURATION DUP050059329 CWO H & rinH O& 0) 4<3Jd ^ W 5 U CO 0) 8 Is *W O m .0H) m. H O H *0 +> o fa tHj rH CO ft s s* VO eg S*a &8W DUP050059330 F ig u re LSW-16 PARTICLE TRAJECTORIES 8" Radius o f C u rv a tu re , 2" S lo t H e ig h t DUP050059331 DUP050059332 O* H ;t9 K) v9 i. - F ig u re LSW-17 8" Radius o f C urvature 3" S lo t H eight 6" F Ra ig u r d iu s eo fLSCWu-1r v8 a t u r e 2" S lo t H eight %J c< <$ v9 Is* 0" DUP050059333 UTERNAL JET DESIGN R a d iu s o'- C u r v a tu r e DUP050059334 DUP050059335  --------- - -............... -37 a p p c n p ix Co mf ?v t .r 7 -- - -CDP-BS-79-24 00 R 001677 VNER 00 R 0CI617 VRET 00 R 001703 XXX 0000 R 001671 VMET 0000 R 001653 X8 oooo r oooooo y 0000 R 001702 VNU 0000 R 001663 XC oooo r 001720 yy 0000 R 00170C 0000 ft 00164C OOOO R 001704 1# 2* 3* 4* ' '5* 6* 7* 8* 9* 10* 11* 12* 13* _ M* 15* 16* 17* . M* 19* 20* 21* 22* `23* 24* 25* 26* 27* 28* 29* 30* 31* 32* 33* 34* 35* 36* 37* 38* 39* 40* 41* 42* 43* 44* 45* 46* 47* 48* 49* 50* 51* COMMON iNTAT,BT,CT,DTKAYl, KAY2,KAY3,KAY4 DIMENSION Y(3),RRC300),THETA(300),V(300),ITR(9) REAL KAYi,KAY2,KAY3,KAY4 c c c c c D---A--T-A-V--IN-I-T---R--A---n-s--- DM 3 TM vise RHOP 3 3 3 '3','4V'5', '6'.'7', '$','9'/ INITIAL PARTICLE VELOCITY (CM/SEC) PARTICLE DIAMETER (MICRONS) GAS TEMPERATURE (C) GAS VISCOSITY (POISE) OENSITY OP PARTICLE (GM/CM3) c RHOG .3 DENSITY OF GAS (G*/CM3) c PIN S RADIUS OF CURVATURE OF COANDA SURFACE (CM) c VRET 3 TANGENTIAL VELOCITY OF PARTICLE (CM/SEC) c c SLOT TDEL 3 3. PIGMENT FEED SLOT HEIGHT (CM) TIME STEP FOR CALCULATIONS (SEC) . ,c PST 3 STARTING LOCATION OF PARTICLE IN SLOT (0.0 TO l 0 c 0.0 SETS PARTICLE AT SURFACE, 1.0 SETS PARTICLE AT c TOP OF SLOT) NUM * 0 C DRAW COANDA SURFACE CALL PL0TS(0,0,0) _ __ __ __ CALL PLOT(2.0,2.0,3) " CALL ORIGIN (R.0,8.0,-1) " CALL SCALE (0.394,0.394,1) C ADD SPOKES TO INDICATE ANGLES READ (5,100) SLOT, VIN , VISC,TM,RHOG,RIN,TDEL,PST ~ CALL P0L(0. ,0. ,PIN,12,1,0) _____ _____ ____ ______ 100 FORMAT (8F10.0) 102 READ(5,100) DM.PHOP ____ ____ " tr COM) 999,999,150 ......... 150 WRITE (6,104) SLOT,VIN,DM,VISC.TM 104 FORMAT (1H1///10X,'SLOT s',r8.2*5X,'VIN ',F8.'2,5X,'DM 90~, " 1 F6.2,5X,rVISC =',F7.4,SX,'TM *',F5.0) _ WRITE (6,105) PHOP,RHOG,RIN,TDEL 105 FGPVAT (VX.'PHCP a',F5.1,5X,'PHOC s',F6.3,5X,'RIN *,F6.2,5X, 1 'TDEL *',F8.5) C SET INITIAL P05ITI0" OF PARTICLE RR(1) a PIN PST9SL0T VGAS * VIN TT a 0.0 Y(1) = 0.0 YC2) PR(1) ... y<3) * 0. VC1) = Y(l) THETA(1) = YC3) RAD s DM/2. VREP a 0. VPFT a VIN ~ .................. ` ` ' T) a 0.375*PH0G T2 a PAD*PHDP*1.E-4 RER a PH0G*DM*1.E-4/VISC JaI DUP050059336 i - 38 - CDP-ES-79-24 52* WT s 1 ...................... . - .^ ,. . _________ S3* .54* C DETERMINE GAS VELOCITY AT PRESENT PARTICLE POSITION 200 CALL AGAST (RPC J) ,T HETAC j), VIN, VGAS) ____ ________ ___________ 55* IF (VGAS.LE.1.0) GO TO 500 ,,56* RE * REN*ABS(VRET ^ VGAS) . _____ ______________ ,, 57* J * J * 1 .58* _____ VAN * SORT(VRET*VRET YRER*VRER) .. ... -....... ___ __________ _________ 59* XV = V AN *TDEL 60* . .. TH a ATANCVRER/VRET) ... 61* RHCiJ) a 50RTCXV*XV PR(J-1)*RR(J<-1) - 2.0*XV*RRCJ-l)*COS(1 < 57+TK 62* ......... ... 1 ) . . .......................................... 63* THA a A$IN(XV*SIN(157+TH)/PR(J)) 64* THETA (J) a THA THETACJM) ... ________________ ________ ..._____ 65* C CALCULATE OPAG COEFFICIENT 66* 201 IF (DM.LE.1.3. OR.PE.LF.O. 1) CD: 67* IF (DM.GT.1.3. AND.FE.GT.0 .1) GO 68* IF (DM.GT.1.3) GO TO 202 69* CUNN a 1*0 ( .OOO24TM/0M)4(2.7' .70* CD a CD/CPNM __ __ _ 71* 202 X.B a T1*C0/T2 72* IF (XB*?T.LT*5 0.0) GO TO 203 73* IF <INT.EQ.2) GO TO 302 .74* _ 75* 76* GO TO 301 203 BT a XB CT a VGAS . _____ 77* AT * tVRET - CT)/EXP(-B?*TT} 78* C . EQUATION FORM V*A*EXPC-B*T) * c 79* CO TO 300 * 80* ___ 204 IF CRE.GT.3.0) GO TO 206 81* Cl = 0.0 82* C2 * 24,/PER 83* C3 S 2.4 84* CO TO 208 85* 206 IF CRE.GT.100. ) GO TO 207 86* Cl a -17.5/RER/PER 87* C2 * 34.6/RER 88* C3 0.815 89* CO TO 208 r 90* 207 Cl * 0.0 91* C2 * 7S./RKR 92* C3 * 0.4 93* 208 TNI a (T1*C1 - T1*C7*VGAS, + Tl* 94* TN2 = (Tl*C2 - 2*t1*C3*VGA5)/T2 95* TN3 a (T1*C3)/T7 96* 0 a TN2*TN2 4.*TM*TW1 97* EQUATION FORM V = A/Cl* - B*EXP(-CT)) * 0 94* XC * SOPT(O) 99* IF (XC*7T.CE.50.0) CO TO 345 100* 101* DT a ^(TN2 SQRTCO) )/Tf*3/2.0 AT a SOPT(O)/TN3 102* 103* 104* 105* CT a XC BT a (1.0 - AT/(VRET ~ DT))/EXP(-CT*TT) IF UNT.E0.2) GO TO 210 ATA a AT 106* 107* BTB a RT CTC a CT 109* 104* DTD a DT 341 TW s TT TOEL DUP050059337 i V , no* 111* 112* 113* 114* 115* - 116* 117* 118* 119* 120* 121* 122* 123* 124* 125* ,, 126* 127* ... 129* 129* _130* 131* 132* 133* . 134* 135* 136* 137* 138* 139* 140* 141* 142* 143* 144* '"'145* _ 146* *147* 148* 149* 150* 151* 152* 153* 154* 155* 156* 157* 158* 159* 160* 161* 162* 163* 164* 165* 166* 167* - 39 - CPP-ES-79-24 VNET * ATA/U.O - BTB*EXP(-CTC*TW)) DTD INT a 2 . ____ _ GV * VGAS ___ ___________________ ___________________ _______ VGA5 * 0.0 _ VRET VRER RE a RER*VRER ____ ,,i, ____ ___________________ __ _ GO TO 201 ______ ________ /_.l______________ ____ ______ _ _ 345 IF (2NT.EQ.2) GO TO 343 GO TO 341 ............. ......................... ........... ............................. .. 210 ATT * AT ' BTT a BT .. ..^ _____________ ^ CTT * CT DTT * OT ... _______ _ .. . ......... .. ...... 343 TT * TW VNEP * ATT/Cl.0 - BTT*EXP("CTT*TT)) DTT _ INT a 1 GO TO 350 ______________ _____ _ 300 IF (INT.EQ.2) GO TO 340 ' " * .........~ ATA * At ................. .........................____________ _______________ _______ BTB * BT CTC a CT _____________ ____________________ ______ _ 301 TW a TT + T0E5 VfiET a ATA*EXP(-BTB*TW) t CTC ......... ""INT a 2 . ' GV a VGA5 _ _______ VRET a VRER VGAS a 0.0 RE * RR*VRER _ __ GO TO 201 `"340 ATT a AT ............................. "* BIT BT ____ .. CTT CT " '' 7' 302 TT a TW ___ ____ VNER a ATT*EXPC-BTT*TT) CTT INT a 1 350 VN1 a SORT ( VNET* VNET + VNER*VNER) ' " " * ' - - - TH2 a ATAN(VNER/VNET) VRET a VN1*C0S(TH2 + THA) * " VRER a VN1*SIN(TH2 + THA) __ V(J) a VNI " IF (THF.TA(J).GE.3.0.PF.FR(J).GE.50.0) GO TO 400 IF (tl.EQ.300) GO TO 400 IF (V(J).LE.IO.O) GO TO 400 GO TO 200 C DETERMINE TRAJECTORIES FOR PARTICLES WHICH HAVE ESCAPED HIGH- C VELOCITY GAS STREAM 500 VU a SORT(VRET*VPET + VRER*VRER) XXX = RR(J)*SIN(THETA(J)) YYT * RR(J)*COS(THETMJ)) PHI a ATAN(VRER/VPET) PSI * THETA(J) - PHI 501 RE a REP*VNU C CALCULATE DRAG COEFFICIENT IF (D**LE. 1.3.OR.PE.LE.0.1) CD a 24./REP IF (DM.GT.1.3.AND,RF.GT.0.1) GO TO 504 IF (DM.GT.1.3) GO TO 502 CONN a 1.0 + ( ,O002*TV/DH) * (2.79*0.894*EXP(-2.47E3*DM/T*) ) CO * CD/CUPN DUP050059338 168* 169* 170* 17!* ,172* 173* .174* 175* .176* 177* 178* 179* 180* 181* 182* 183* 184* 185* J86* 187* .188* 189* 190* 191* .192* 193* 194* 195* 196* 197* 198* 199* . 200* 201* 202* ""203* _ 204* 205* 206* 207* 208* 204* 210* 211* 212* 213* 714* 215* 216* 217* 218* 219* 220* 221* 227* 223* 224* 22V* - 40 - CDP-ES-79-24 502 XB = Tl*CO/T2 .........____________________ If CXB*TT.GE500) GO TO 550 BT * XB . ..................... ......................................... CT * 0.0 At * (VNU CT)/EXPC-fT*TT) . _ ______ *___ 550 T * TT Tt # TT + TDEti _________ __________ VNU * AT*EXPC-BT*TT) * CT AA * -AT*CO$CPSI)/BT __ ___________ ________ BB BT CC * CT*CO$CP$I) . .. _ 00 * XXX~AA*EXPC*BB*T) - CC*T XXX * AA*EXP(-BB*TTD * CC*TT * OP _.......... AA * AT*SINCPSI)/8T CC CT*S1M(P5I) DO YYY - AA*EXP(-*B*T) - CC*T YYY * AA*XP(-B6*TT) + CC*TT * DO _ il * .J 1 RR(J) SQRTCXXX*XXY * YYY*YYY) ....____ THETA(J) ATANCXXX/YYY) . IP (TFETACJ).LT.O.0) THETACJ) * THETA(J) * 314 VM) is VNU _ IF (THETA(J)*GE# 3.0,0R . RR(J)GE50.0) GO TO 400 IF ( J.F.0.300) GO tO 400 IF (VfJ).LE.10.0) GO TO 400 GO TO 501 504 IF (RE.GT.3.0) GO TO 506 Cl * 0*0 C2 * 24.0/HER C3 a 2.4 CO TO 508 506 IF CRE.GT.tOO.) GO TO 507 Cl * -17.5/RER/REP C2 * 34.6/RER C3 a 0.815 GO TO 508 ... 507 Cl * 0.0 ________________________ C2 a 75.0/RER C3 a 0.4 ... _____ ___ ,_____ ___________ 508 TNI m TlCl/T2 TN2 * Tl*C2/T2 TN3 = (T1*C3)/T2 0 a TN2*TN2 - 4. *TN1*TN3 XC a SQRTCO) IF (XC*TT.GE.50.0) CO TO 552 DT * -(TN2 + 5ORT(Q))/TN3/2.0 AT a SGRTC0J/TN3 CT = XC BT a (1.0 - AT/CVNO - DT))/EXPC-CT*TT) 552 T a TT TT a TT + TOED VNO = AT/M.O - f>T*FXP(-CT*TT)) DT AA a ATtCOS(PSI) + OT*COS(PSI) BP a AT*COS(PSi)/CT CC a TXX - AA*T - FiR*ALOG( 1.0 - BT*FXC-CT*T)) XXX * AA*TT RR*AUOC(J.O - HT*EXP(-CT*TT)) CC AA a -AT*SIft(PSI) - DT*S1N(PSI) BB a -AT51N(PS1)/CT ... . _. DUP050059339 226* 227* 228* 229* 230* "" 231* 232* 233* 234* 235* 236* 237* 228* 239* 240* 241* 242* 243* 244* 245* 246* 247* 248* * 249* 250* 251* 41 CDP-ES-79-24 CC 8 m - AA*T - B8*LOG(1,0 - BT*EXP(-CT*T)) YYY * AA*TT + 0B*AUO6C1.O - BT*EXP(-CT*TT)) CC J * <3 * 1 RR(J) a SORT(XXX* XXX + YYY*YYY) THETA(J) * TAN(XXX/YYY) " IF (THETAtJ).LT.0.0) THETA(J) THETAtJ) 3.14 ' VCJ) a VKO IF (THETAtJ).GE.3.0.OR.RR(J).GE.50.0) 60 TO 400 IF CJ.EQ.300) GO TO 400 _ IF CV(J).LE.iO.O) 60 TO 400 ' GO TO 501 400 NPT a J _______________ -- -- C PLOT TRAJECTORY CALL POLARtRR,THETA,NPT,1,0,1H*,0.,0.394) HUM 8 NUH 1 LAB a ITRCNUM) TENO * THETAtNPT) 0.05 _ _ _____ XX * RRCNPT)*COS(TEND) ' ~- YY * RR(NPT)*5IN(TFND) _ ___ CALL CHAR(XX,YY,TENO,0.125,LAB,1) WRITE (6,106) (V(I),RR(I),TFETACI),1=1,NPT) 106 FORMAT(1H1,(10X,F.2,5X,F8.2,5X,F8.2 ) ) GO TO 102 __________ ____ "999 CALL PLOTtO.0,0.0,999) STOP ____ END _ _ X END OF COMPILATION: ___ NO .DIAGNOSTICS. A ! 27R3A 35 SL73R1 11/27/79 13:49:52 54C0ANDAC1) ELEMENT TABLE .... _ i. s ___ ;; $ ^VERSION . , B $ s ST ST NOA NDA NO A LOA VAILABLE LOCATION* . TYPE FOR 5YMB FOR SYMB FOR SYMB FOR SY*B FOR SYMB RELOCATABLE RELOCATABLE RELOCATABLE RELOCATABLE r el o c at abl e FOR SY*B r el o c at abl e FOR 5YB RELOCATABLE FOR SYMB RELOCATABLE DATE 30 DEC 77 05 JAN 79 to JAN 79 10 JAN 79 10 JAN 78 11 JAN 78 11 JAN 78 11 JAN 78 11 JAN 78 11 JAN 79 21 NOV 79 21 NOV 79 26 NOV 79 26 NOV 79 27 NOV 79 27 NOV 79 LER PROCEDURE TABLE EMPTY PROCEDURE TABLE EMPTY TIME 11911330 09207:10 11:00257 16203242 16:03:49 09:40:51 09:49:54 09:49:59 09:50:02 09:50:05 11:21:01 lt:2i:p6 13:03:44 13:03:50 13:48:50 13:48:52 SEO 1 2 3 4 5 6 7 8 9 10 it 12 13 -14 15 16 S1ZE-PRE, TEXT 19 7 4 3 3 13 i3 i 23 i4 i 10 2 i2 61 3 79 63 3 76 DUP050059340 I1 Vi CDP-ES-79-24 XOPE*GftAPH.POL,TPFS.PDL ............ 4R1 t -08/23/79-14S24S19 (1,) apMiiie_pp.L ENTRY POINT.000253. RAGE USED: COl)E(l) 0003032 OATA(O) 000065; BLANK C0MMQN(2) 000000 TERRAL REFERENCES ' CBLOCK , NAME)____ *03 PLOT 04 PLfLN 05. NOMPl T 06 EL IPS 07 JJMATHS >10 COSS 4.1_ .S INS___ i_____ _______________ ______ ' )RAGE ASSIGNMENT (BLOCK* TYPE, RELATIVE LOCATION, NAME) )01 000073 123G )00 R 000012 0S )00 ft 000017 0 )00 ft 000006 RX >00 ft 000004 XS 0001 000213 147G 0000 ft 000011 BY 0000 ft 000013 06 _____0000 ft 000007 ftY 0000 ft 000020 XX 0001 000133 2L 0000 ft 000002 C 0000 000023 OYNS 0000 ft 000003 S 0000 ft 000005 YS 0001 00017. 0000 R 00001 0000 I 00001> 0000 R 00.001' 0000 ft 00002 1* 2* 3* 4* 5* 6* _ 7* , 6* 0* 10* 11* 12* 13* 14* 15* 16* 17* 16* 19* 20* 21* `22* ^ 23* 24* 25* 26* SUBROUTINE POL(X ,Y,N,NR,NC ,IOP) T s 360.0/NR RA a .0174533 C CUS(A*T) $ a SIN(RA*T) CALL PLOT (XS,YSr4) XS a 1.0 YS = 1.0 X = n**S HY = K*YS AX 9 RX/NC BY s ftY/NC 6S S .12 OS * ft .06 cc s e SS a S. 00 t I : Ifftft CALL PL >LN(X,Y,X+ftX*CC,YtftY*SS) IP(IOft .Ed. 0) GO TO 3 0 a T*I-9o IF(0-90.0) 2*2*1 1 OS a ft .13 D =0 lao as a -,1ft 2 XX 9 X (Ob *CC d">*SS)*XS YY a V (t)$*SS-BS*CC)*YS DUP050059341 - 43 - CDP-ES-79-24 JT* 28* 29* 30* 31* 32* 33* 3* CALL NUMPLT(XX,rr,RA*0,-.08,T*I,-l) 3C a c 0 1#NC 5 CALL EL IPS CX+AX*I,V,AX*I,dY*I,0.,0.,0.,3) RETURN___________________ _________________________ _ ENO ' END OF COMPILATION: NO DIAGNOSTICS. I.. DUP050059342 U-1 $ A.AGAS.A.A&AS 0T3-01/ll/7&-09:49:59 <2.) 44 - CDP-ES-79-24 8R0UTINE ACAS ENTRY POINT 000050 ORACE USED: CODEC 1) 000062: OATA(O) 00001C; BLANK COMMON!2) QDOjQP ORAGE ASSIGNMENT ((SLOCK. TYPE. RELATIVE LOCATION. NAME) 001 000037 150L 000 R 000001 VH 0001 000044 152L 0001 000045 99?t 9000 R QOQOO 1* SUBROUTINE AGAS(RTH.SLW.RAD.VI.VG) i* If <TH.EQ.0,0) GO TO 999 3 ALEN * 2.0*SLW*TR + SLV 4* IF <R-Ra D.LE.a LE`0 GO TO ISO 5* IF <R-RAD,GE,1,25*ALEN> GO TO 152 6* VH VISLW/ALEN 7* VG * -4,0*VH*(R-RAD-ALENJ/ALEN * VH 8* GO TO 999 9* 150 VG * Vl*SLV/ALEN 10* GO TO 999 11* 132 VC * 0.0 12* 999 RETURN 13* END END OF COMPILATION! NO DIAGNOSTICS, * DUP050059343 IS A.AGAST#.AGAST __ 0T3"O3/2O/79-l4:H :49 (#0) 45 CDP-ES-79-24 SRaUtlNE A6AST ENTRY POINT 00001S ' ........................... ............... 3RAGEUSE0:'CQOE (1) "Vd.6024|HDATA(bT0090d3.}~sCAIK COMMONCZ) 000000 3RAGE, ASSIGNMENT (BLOCK# TYPE* .RELAtlVE LOCATION* NAME) 001 _j >o .q o io ,,150L _ ___0_001 _ 000012 999L 0000 000000 OYNS 1* SUBROUTINE AGAST(R,TH,VI#VG) 2t IF (TH.EQ.O.O) GO TO 999 3* IF (R.LE.5.00) GO TO ISO 4* VG = 0.0 5* GO TO 999 S* ISO VG s VI 7*r 499 RETURN 6* END END 'OF COMPILATION:' NO "oiAGNOSti'CSZ r a. 2 27*3-1 E35 SL73Rf .O3720/79"r4S'lI 5.2 > 4S*C0AN0Ml) ELEMENT TABLE 4E VERSION IB *S AS i'B IS IS 1NOA IftO A VNOA 1NDA 1ST 1ST IVAltAHU LUCA fION* t ype " FOR SYMB FO* 5YM0 FO* SYMB FOR SYMB FOR SYMb RELUCAfArtLc HEl GCAIAbLt .......RELOCATABLE RELOCATABLE .............. KELOCAIAh LE FOR SYMB RELOCATABLE POR SrMB RELOCATABLE FOR SYMB RELOCATABLE ....... DATE 30 d e c 77 05 4 AW 76 10 JAN 76 10 JAN 76 to JAN 70 U J Aim 7 a 11 JAN 76 tr JAN 70 li Ja n 70 it JAN 76 2a JUN 76 26 JUN 7 8 20 M Aw 79 20 MAN 79 20 MAw 79 20 MAN 79 .. t ime - 11:11:30 09:07:10 11:00:57 ' is :03:2' In:03:us 09:49:51 u9:49:54 09349:59 09:so:02 09:SO:05 I4:i7:3s 14:17:54 14:11:47 14:11:49 14:11:5u 14:11:51 SEO M 1 --'2 3 4 5 b 7 8 9 10 11 12 13 1 . .15 lb SIZE-PRE,TEXT t HER PROCEDURE TABLE EMPTY PHOCEOUWE IASEE EMPTY r u p inf m u &uu^ iv v DUP050059344 - 46 DISTRIBUTION CDP-ES-79-24 Copy No. .1. L. S. Wilkens 2. K. K. Bhatia 3. W. J. Marshall, EM 4. H, B. Clark/R. w. Hess 5. R. A. Darby/A. S. Bjornson/ L. T. Frick/J. G, ishikawa 6. E. C. Broge/M. A. Toomey/J. A. Blumberg 7. J. M. Hustler 8. If N. Fisher/G. A. Hapka 9-10. Central Report Index/ ISD, C-3211 11-12, L. A. Wierzbowski, EM 13-17. CD&P Information Center, E336 G. A. Schurr, Engg., Louviers 19. D. P. Fields/P. G. Schmidt 00 DUP050059345