Il II I wII' ‘I I I II I I I III I I l I I I I II II I AIRFLOW-PRESSURE DROP CHARACTERISTICS OF PACKED BEDS OF BIOLOGICAL PARTICLES Thesis for the Degree of M .. S. MICHIGAN STATE UNIVERSITY RICHARD J. PATTERSON 1969 I! III III" II II I II III III III I « '[fiEbIS ABSTRACT AIRFLOW-PRESSURE DROP CHARACTERISTICS OF PACKED BEDS OF BIOLOGICAL PARTICLES by Richard J. Patterson The resistance to airflow of randomly packed beds of plastic spheres, cherry pits, shelled corn and navy beans was determined in the airflow range of 10 to 120 cfm per square foot. The effect of bed porosity, product moisture content and air temperature on the pressure drOp was evaluated for shelled corn and navy beans. Three semdtheoretical relationships, the Leva, Matthias and Ergun equations, each describing the pressure draps through randomly packed beds, are tested and their value in predicting pres- sure drOps through grain beds evaluated. A new equation, the modi- fied Ergun equation, is preposed for predicting the airflow resist- ance in beds of biological products: 0) 2 2 .1413 3 RE [ 150 3—2.1“: n---“ + 1.75 --—1' L: J 63 dag ea 00 where kE is the modified Ergun product constant. The values of RE were determined for beds of cherry pits, shelled corn and navy beans. The results for beds containing no fines are: Richard J. Patterson RE for cherry pits - 1.1 to 1.2 RE for shelled corn - 3.7 to 4.5 RE for navy beans - 1.8 to 2.0 Adding fines to a bed of biological particles increases the RE value according to the percentage of fines in the bed. Approved [a W%a Major Professor 8, /. 69 Approved W4 /' x‘ . 0 1m “Ca; Department Che n f- f. 69 c7 AIRFLOW-PRESSURE DROP CHARACTERISTICS OF PACKED BEDS OF BIOLOGICAL PARTICLES By Richard J. Patterson A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1969 ACKNOWLEDGEMENTS The author wishes to express his deep appreciation and many thanks to Dr. Fred W. Bakker-Arkema for his advice, encour- agement, and friendship during the past four years. Thanks and appreciation are extended to Dr. William G. Bickert for his assistance and council. The author also wishes to express his appreciation to Dr. Steven T. Dexter for serving on the author's committee. A very sincere thank you is extended to all those who con- tributed in many ways towards the compilation of this research and thesis. A special thanks to "Jut", "Jumpy" and "Tyke". ii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS . . . . . . . . . . . i1 LIST OF TABLES . . . . . . . . . . . V LIST OF FIGURES . . . . . . . . . . . V1 LIST OF SYMBOLS . . . . . . . . . . . V111 Chapter I. INTRODUCTION . . . . . . . . . . 1 II. LITERATURE REVIEW . . . . . . . . . 3 2.1 General . . . . . . . . . 3 2.2 Ergun Equation . . . . . . . 7 2.3 Leva Equation . . . . . . . 8 2.4 Matthias Equation . . . . . . 8 2.5 Bed depth and wall effect . . . . 9 III. EXPERIMENTAL . . . . . . . . . . 11 3.1 Bed materials . . . . . . . 11 3.2 Porosity determination . . . . . 13 3.3 Apparatus ‘ . . . . . . . . 16 3.4 Procedure . . . . . . . . 13 IV. RESULTS AND DISCUSSION . . . . . . . 21 4.1 Spheres . . . . . . . . . 21 4.2 Biological products . . . . . . 24 4.3 Leva Equation . . . . . . . 38 4.4 Matthies Equation . . . . . . 39 4.5 Ergun and Modified Ergun Equation . . 40 4.6 kE VALUES . . . . . . . . 43 4.7 kEI Values . . . . . . . . 45 Chapter Page v. SUMMARY AND CONCLUSIONS . . . . . . . 50 Suggestions for Further Study . . . . . 51 REFERENCES . . . . . . . . . . . . 52 APPENDIX . . . . . . . . . . . . 56 iv Table LIST OF TABLES Page Empirical pressure drop-airflow data on biological products available in the literature . . . . 4 Equivalent particle diameter of cherry pits, navy beans and corn at various temperatures and moisture contents . . .' . . . . . . . . 13 Values of n and EL, as functions of the Reynolds number and AP/h, for the pressure drOp through a bed of cherry pits (porosity a 0.42) as given by the Leva equation. . . . . . . . . 38 Values of EM, as a function of Reynolds number, and (AP/h) for the pressure drop through a bed of cherry pits (porosity - 0.42) as given by the Matthies equation. . . . . . . . . . . 40 Values of (AP/h), at various air velocities, for the pressure drOp through a bed of cherry pits (porosity = 0.42) as given by the Ergun equation . 43 kE and kEI values for corn and navy beans at different product moisture contents, bed porosities, air temperatures and percentages of fines . . . 44 Porosity and bulk density values of beds of corn and navy beans at 50°F at different moisture contents . . . . . . . ‘ . . . . 47 10. 11. 12. 13. LIST OF FIGURES Resistance of grains and seeds to airflow Porosity determination instrumentation . . . Pressure drOp determination instrumentation . . . Static pressure drop through beds of smooth spheres of two diameters . . . . . . Matthies plot of the pressure drOp through spheres of two diameters . . . . . . Resistance to airflow through a bed of smooth spheres as given by the Leva, Matthies, and Ergun equations . Resistance to airflow through a bed of cherry pits at two porosities . . . . . . . . . The effect of porosity on the pressure drOp through corn . . . . . . . . . . . The effect Of porosity on the pressure drOp through navy beans . . . . . . . . . . . The effect of moisture content on the pressure drOp through corn . . . . . . . . The effect of moisture content on the pressure drOp through navy beans , The effect of air temperature on the porosity and the pressure drOp through corn . . . . . . . The effect of air temperature on the porosity and the pressure drOp through navy beans vi Page 15 15 22 23 25 26 27 28 30 31 33 34 Figure Page 14. Resistance to airflow of cherry pits at two different bed porosities . . . . . . . 35 15. Resistance to airflow through beds of corn con- taining various percentages of fines . . . . 37 16. The laminar and turbulent airflow contribution to total bed resistance' . . . . . . . . 42 17. Resistance to airflow of corn and navy beans as given by the modified Ergun equation . . . . 49 vii LIST OF SYMBOLS product constant, dimensionless in. H 0 per ft. 2 product constant, in. H20 per ft. product constant, dimensionless in. H 0, min sq per ft3 2 product constant, in H20, min sq per ft3 particle diameter, ft. subscript, equivalent friction factor, f (Re) conversion factor, 1bm ft per 1b sec sq f bed height, ft product constant, dimensionless state-of-flow factor, f(Re) superficial air velocity, ft per sec pressure drOp, lb per sq ft, or in. H20 air viscosity, lb per ft sec porosity, dimensionless decimal particle shape factor, dimensionless air density, lb per cu ft product bulk density, lb per cu ft Reynolds number, dimensionless as subscript, Ergun as subscript, Leva as subscript, Matthies viii I. INTRODUCTION The resistance to airflow through a packed bed of biological particles is a function of the air and bed characteristics. These include air temperature, air relative humidity, bed particle moisture content, bed particle diameter, bed porosity and the percentage of intermixed fine material. .All influence the resistance to airflow and, therefore, should be taken in account when predicting the pressure drOp through a bed of biological particles. A good deal of empirical data has been published on the pres- sure drOp through beds of biological materials. An example of such data is that published in the American Society of Agricultural Engineers Yearbook (1969) entitled Data D 272 (figure 1). Unfortun- ately, such data does not reflect the effects of the above mentioned bed and air characteristics (except as stated in a footnote). This data is, therefore, only reliable for pressure drOp-airflow conditions closely resembling those for which the data was obtained. For researchers, designers and Operators of drying and cooling equipment and processes, data in the form of ASAE D 272 is of limited value. The chemical engineering profession has been the source of rather extensive investigations into the pressure drop-airflow rela- tionships of beds of nonbiological particles and several relationships have evolved which adequately describe the air and bed parameters. The purpose of this investigation is to test three of these semitheoretical relationships, Leva, Matthies and Ergun, on beds composed of biological particles, namely cherry pits, corn and navy beans. .3onuHm cu woman can magnum we mucoumwmom .H ousmwm om: .Erad m e m. m. e. we. mo. 5.80. moo. - _ :: Lo>o_o C\l ox_m_m (I) ‘MOIJ- JIV CD 2.. CD (\I lJ/wJO 8 O _I+ _ mhmo m 10, with a somewhat higher limit for irregular particles (Haughey, et a1., 1969). Since the Dw/Dp ratio in the experiments performed in this study were well above ten, it was not necessary to compensate for the wall effect. 10 III. EXPERIMENTAL 3.1 Bed Materials The semitheoretical expressions were tested on beds composed Of various materials. Beds Of acetate spheres were used to calibrate the experimental set-up and tO verify the results Of investigations made by previous researchers. Two lots Of Spheres, having diameters of 0.250 in. and 0.375 in. with a size tolerance of plus or minus 0.005 in. and a sphericity Of 0.005, were purchased commercially. The cherry pits used in this study were acquired from a Michigan processor of red tart cherries. The pits had an initial moisture content ranging between 45 and 50 percent wet basis and were stored in closed containers at 40 degrees F. until used for testing purposes. The cherry pits were sized and an equivalent diameter deter- mined using a Tyler Rotap sizer. The pits ranged in size from 0.250 in. to 0.371 in. in diameter with an average of 0.031 in.. The corn and navy beans were purchased at a local commercial elevator. The corn was Of the yellow dent type graded as NO. 2. The specific variety was unknown. It was screened using a screen with round Openings Of 0.187 in. in diameter. Material passing through these Openings was considered as "Fines". The navy beans were Of the Michelite variety and were graded as choice hand picked. A screen with slotted Openings of dimensions 0.187 in. by 0.75 in. was used to remove all split beans. A screen with round Openings Of 0.343 in. in diameter was used to remove excessively enlarged or deformed beans. 11 The screened lots Of corn and navy beans were each divided into three additional lots for purposes Of moisture content adjust- ment. In the case Of corn, the three lots were adjusted to moisture contents Of approximately 16, 19 and 24 percent wet basis. Like- wise, the navy beans were adjusted to moisture contents of approxi- mately 15, 18 and 25 percent wet basis. The moisture contents were adjusted by adding predetermined amounts Of water to each lot Of product. Each lot was then agitated in a cement mixer, placed in sealed containers and stored at 40 degrees F. until used in per— forming a test. MOisture content determinations Of the cherry pits, corn and navy beans were made using an air oven. Samples were exposed to temperatures controlled at 210 degrees F. for a period Of twenty- four hours. Samples, approximately seventy-five grams in initial weight, were weighed using a balance reading to 0.01 grams. The equivalent particle diameter, determined by Bakker-Arkema, et a1. (1969)b, Of corn at 16 percent moisture content wet basis and navy beans at 15 percent moisture content wet basis was 0.03222 and 0.02224 feet respectively. For the higher moisture content lots Of corn and navy beans the equivalent particle diameter was adjusted according to the information presented by Pabis, et a1. (1962). The compensation for variation in particle diameter due tO a temperature change was adjusted based on the information given by Ekstrom, et a1. (1966). Table 2 gives the values for equivalent particle diameter at various moisture contents and temperatures for the corn and navy beans used in this study. 12 Table 2. Equivalent particle diameter of cherry pits, navy beans and corn at various temperatures and moisture contents. Mbisture Tem erature Equivalent Product Content, p °F ’ Diameter, Z W.B. Feet Cherry pits 45 76 0.02600 Navy beans 15 85 0.02224 Navy beans 15 120 0.02228 Navy beans 18 85 0.02250 Navy beans 25 85 0.02309 Corn 16 85 0.03222 Corn 16 120 0.03227 Corn 19 85 0.03259 Corn 24 85 0.03321 3.2 Porositquetermination One Of the more important characteristics Of a fixed bed, which influences the pressure drOp-airflow relationship, is the bed porosity. Therefore, in order tO relate bed porosity tO pressure drOp and airflow, a porosity measurement was required Of the same fixed bed for which pressure drop and airflow data were taken. The porosities Of the beds used in the investigation were determined by two different methods. In the first studies, using acetate spheres and cherry pits as bed materials, the porosity was determined using the water displacement method. By slowly submerging the bed of particles into a water-filled container, a volume Of water was displaced equal to the volume Of the submerged bed particles. Porosity is then equal to the difference in volume between the bed particles and the test bed volume. This method was satisfactory in the case Of acetate spheres and cherry pits since 13 the Spheres were impervious to water and the cherry pits were sufficiently high in initial moisture content to prevent further absorption of water. In the studies involving corn and navy beans, use Of the water displacement method Of porosity determination was unsatis- factory. These relatively low moisture content products tended to absorb the water, resulting in inaccurate porosity determinations. Consequently, a device for determining porosity was constructed similar to that described by Day (1964)b. This instrument, termed an air Comparison pycnometer, was constructed to enable the entire bed Of product, as it was used to collect pressure drOp and airflow data, tO be placed in it while porosity determinations were made. The air comparison pycnometer used in this study is shown in Figure 2. Basically, the pycnometer consisted Of two containers, a mano- meter and connecting tubing with valves. The container designed to hold the test bed was constructed Of 8 in. diameter steel pipe cut to a length Of 24 in. (1 in Fig. 2). A steel plate was welded to one end to form the bottom. A machined ring was welded to the inside tOp edge Of the steel pipe, forming an Opening into the container Of 7 in. diameter. A circular steel plate served as the container lid. Slots were filed to a depth Of 0.25 in. in the inside edge of the container Opening 180 degrees apart. The edge Of the container lid was also filed to a depth of 0.25 in., perpendicular to its radius, at points 180 degrees apart. A rubber gasket was shaped to fit the lid edge to provide a good sealing surface. Under test conditions the container lid was slipped into the container, rotated 90 degrees 14 Figure 2. Porosity determination instrumentation. Figure 3. Pressure drOp determination instrumentation. and then the container was pressurized. The pressure inside the container forced the lid outward against the retainer ring, forming an airtight seal. The second container, a pressurized gas storage tank, served as a reference volume into which the pressurized air of the first container was allowed to expand (2 in Fig. 2). The manner in which the porosity Of a bed was determined is the same as that used by Day. The manometer used to indicate the pressures within the pycnometer had a range of 35 in. of mercury reading to 0.05 in.. 3.3 Apparatus (Figgre 3) The test bed, in which the various materials were placed to determine their pressure drOp-airflow characteristics, was con- structed from a plexiglas cylinder with dimensions Of 15.50 in. in height and 5.56 in. in inside diameter (1 in Fig. 3). The total test bed volume was 376.67 cubic in.. The floor Of the test bed was constructed of sheet metal having round perforations 0.14 in. in diameter, totaling 33 percent Of the entire floor area. Pressure taps were attached to the test bed wall at six inch intervals beginning approximately 1.5 in. above the bed floor. The pressure taps were attached by first drilling a hole 0.25 in. in diameter to a depth Of approximately 0.1875 in. at the desired point on the test bed wall. The tap was then inserted into the opening and secured by applying a plexiglas solvent. When the solvent had dried sufficiently, a 0.125 in. diameter hole was drilled through the tap extending into the interior of the test bed. The interior bed wall was sanded lightly tO remove any burrs that may have resulted 16 from the drilling. This method of pressure tap attachment insured a smooth intersection between the pressure tap Opening and the interior test bed wall. The pressure drOp through the test bed was measured with an inclined manometer reading tO 0.01 in. of water (2 in Fig. 3). During the performance Of a pressure drop-airflow test, the test bed was supported on a base constructed Of plexiglas materials (4 in Fig. 3). It provided an airtight seal between the test bed and the incoming supply of air. Provision was made for the attach- ment Of temperature and humidity sensing devices which were posi- tioned directly beneath the test bed and in the incoming airstream. Thermocouples were used to sense air temperature and were connected to a continuous recording potentiometer (6 in Fig. 3). Relative humidity was measured with an electric hygrometer (3 in Fig. 3). Measurements Of airflow to the test bed were made using a laminar flow element and a micromanometer (9 and 5 in Fig. 3). The pressure differential, created by the measuring section Of the laminar flow element was related to the total airflow through the element. One in. Of water pressure differential across the measuring section correSponded to approximately 5 cfm air. The micromanometer, indicating the pressure differential, had a range Of 0 to 10 in. of water, reading to 0.001 in.. The laminar flow element was attached directly to the inlet Of the base supporting the test bed. Flexible tubing provided the connection between the laminar flow element and the fan circulating the air to the test bed. 17 Conditioned air was supplied by a conditioning unit capable of controlling temperature and humidity (8 in Fig. 3). The air was circulated by a fan equipped with a variable speed motor. An auto- transformer (7 in Fig. 3) was used to regulate the speed Of the series wound motor driving the fan. A computer program was written to accept the collected data and provide values for airflow, air velocity and bed porosity. Most important, however, it was written to compute values for bed pressure drOp, as predicted by the semitheoretical relationships, to compare these values to the experimentally Obtained data and to plot the results if desired. The program is given in the appendix Of this paper. 3.4 Procedure A test schedule was developed to provide for maximum use Of bed materials and to allow for a minimum of adjustment of the test apparatus. A set Of standard test conditions was set up to provide a basis Of comparison for establishing the effect Of the variables to be investigated. Prior to each set of tests the air conditioning unit was started to allow the desired air conditions to stabilize. A check was periodically made on all Of the measuring instrumentation to be sure it was prOperly adjusted. The bed material selected for a given test was placed into the test bed by one Of two methods. Very porous beds were created by placing a section of metal tubing, approximately 4 in. in inside diameter, into the test bed and allowing it to rest on the test bed 18 floor. The bed material was then poured into the metal tubing. By slowly raising the metal tubing the bed material was allowed to flow out, thus filling the test bed in a very porous manner. Test beds of greater density were created through a process Of repeated filling and packing. After each fill of approximately five in. the bed was vibrated to bring about settling of the bed material. Through the use of an established method of filling test beds Of nearly the same porosity could be attained. Once the test bed was prepared in the desired manner and placed on its base, actual pressure drOp-airflow testing could begin (late in the study the test bed was weighed before beginning an airflow-pressure drOp test). At this time the variable speed fan was adjusted to Obtain the desired airflow and readings Of bed pressure drop, air relative humidity, air temperature and airflow were recorded. The fan speed was then readjusted, at approximately 2.5 cfm intervals, and the data recording process repeated. The testing proceded in this manner until the pressure drOp through the test bed was approximately 4 in. of water column. When the pressure drOp-airflow data had been collected, the bed of material was measured for porosity. This entailed removal Of the test bed from its base support and placing it into the air comparison pycnometer. The pycnometer chamber containing the test bed was then pressurized to approximately 30 in. mercury. Two minutes were allowed, after pressurization was completed, for the system to come to equilibrium. The mercury level, on the manometer indicating the pycnometer pressure, was then recorded. The valve 19 connecting the two pycnometer chambers was then Opened permitting the pressure within to equalize. Again two minutes were allowed for equilibrium to be reached before the mercury level was noted and recorded. The procedure of pressurizing and expanding the air within the pycnometer was repeated three times for each bed Of test material. An average of the three pressure readings was calculated and read into the computer for purposes Of porosity determination. Adjustment Of the air conditioning unit, filling Of the test bed, recording Of pressure drOp-airflow data and porosity measurement Of the test bed material constituted the data collection procedure. This information was then punched on computer cards in a form compatible with the program given in the appendix of this paper. 20 IV. RESULTS AND DISCUSSION 4.1 Spheres Figure 4 shows the effect of particle diameter on the pressure drop through two fixed beds of uniformly dimensioned smooth acetate spheres Of different diameter. As expected, the smaller particles (d = 0.0280 ft.) Offer more resistance to a given airflow than do the larger bed particles (d = 0.0312 ft.). In order to check the accuracy of the experimental measuring devices, the data of Figure 4 was plotted on a Matthies plot (section 4.4) as shown in Figure 5. It can be seen that the experimentally Obtained data points given by two curves in Figure 4 are represented well by one curve in Figure 5, the Matthies curve. Since the Matthies curve was checked by a number of investigators (Burke, et a1. 1928; Fehling, 1939; and Kling, 1940) using beds composed Of uniformly dimen- sioned spheres, it can be accepted as an accurate representation Of pressure drOps through beds Of spheres. The fact that the pressure drOp data Obtained in this study, on beds composed Of uniform acetate spheres, agreed with the accepted data from the literature, verifies the accuracy Of the experimental set-up. Pressure drOp data Obtained using beds composed of biological products unfortunately, do not fall on the Matthies curve due to their nonspherical character. Beds Of irregularly shaped particles as com- pared to smooth Spheres will have a different distribution of points Of contact, a different voidage distribution and a resulting increase in resistance to airflow at the rough particle edges. Therefore, the pres- sure drop data Of beds composed Of biological products (all irregular in shape) can be expected to fall above the Matthies curve for spheres given in Figure 5. 21 .muouoamaw oau mo mononam Suoosm mo moon nwsounu none unannouo ufiuaum .O shaman om: .c_..a.m o.m m.e o.F mes a a u d .s_n=omm. j .s_n.msm.. O (\I om éii/wio‘MOIiayv 00.. 22 .muouoEmdu 25 mo mouosom smacks”. noun 9.3393 23 mo uoHa mownuumz .m whom; om BE E IeI 4. >1 23 The Leva and Ergun equations agree reasonably well with the Matthies equation in predicting the pressure drOp through beds of uniformly sized spheres (Figure 6). 4.2 Biological products The experimental results Of tests performed to determine the resistance to airflow through randomly packed beds Of cherry pits, corn and navy beans are given in Figures 7 through 11. The effect Of bed porosity and bed particle moisture content is illustrated. Porosity more than any other bed parameter, affects the amount Of power required to circulate air through a bed of particles, (see Figures 7, 8 and 9). As illustrated by Figure 7, a decrease in bed voidage from 0.42 to 0.33 increased the required static pressure, at an airflow Of 100 cfm per square foot, from 0.9 to 2.3 in. water column. This amounts to an increase Of over 100 percent. Similar Observations can be made regarding the effect Of bed porosity on pressure drOps through beds Of corn and navy beans. The porosity Of a bed Of biological particles is related to the method of loading. A grain bin loaded by a method of mechanical elevation and free fall will result in a bed Of a different voidage than one loaded by a pneumatic method. Matthies (1956) compared these two modes of filling a commercial sized grain bin with shelled corn and measured a range Of porosities from 0.44 (mechanical loaded) tO 0.34 (pneumatically loaded). Figure 8 reflects the variation in resistance to airflow through two beds of corn with different porosities. The range Of porosities for beds Of biological products, mea- sured by Matthies (1956), was found to be between 0.32 and 0.50. Thompson, et a1. (1967) measured values for grain voidage between 0.39 and 0.64 percent. 24 .maofiumsoo aswum pom .mownuumz .m>mu way an cm>Hw mm mononam suooam we own m :wOOMSu Segundo ou mucounwmom om: .c_..m.m 0.? mh.o m.o mm.o J q 1 L camcm «>04 mo_cyym2 _wucoe_couxo 004 o shaman W ,. J om n... O M O |+. m 8 1. 5+ .8 8e 25 .mowufimouoa can um mafia kuuoao «0 won m swsouau Seamuam cu oucmumamom om: .53...” .v m m - d ‘ xtmocoa mmmél. a xw_mocoa um¢.0|lo e .n shaman A/WJO‘M°|}4!V 02 um 26 .cuoo awsousu mono unannoua 0:» co muwmouoa mo uoowmo on& .m shaman om: .c_..a.w m w r 3.0m mowmn.a50h 4 mm ‘ c J nvmw m.¢u x mm.uw - \‘ éii/wio ‘MOIiayv ‘\ LIJ m.¢u e . m¢.uw l 00—. 27 .mcmon m>mc awoouau mono ouswmoun ecu co auamouoo wo uommmo use .m ouswam om: .c_..a.m a. m m m LON RONm" 0 Q9305- .\ c «0...... . 0 .2 ‘1 \s 0 CO éTI/WIO ‘MOIiayv .. . 0.Numx .00.. m ‘r. . II (A) 28 The porosity ranges studied in this thesis for cherry pits, corn and navy beans can be expected to be representative Of situa- tions encountered in actual conditioning Operations. The porosity range for cherry pits was between 0.33 and 0.42, between 0.33 and 0.43 for corn and between 0.35 and 0.43 for navy beans. Thus a much narrower overall range of bed porosities is Observed with randomly packed beds of irregularly shaped biological products than with beds of uniformly dimensioned spheres where voidage values between 0.26 and 0.47 were measured (Haughey, et a1., 1969). .The effect of moisture content Of the bed particles on the resistance tO airflow through a bed is minor compared with the porosity effect. In addition, it is not certain what effect a change in moisture content will have. For corn, as shown in Figure 10, the pressure drOp decreases with a decrease in moisture content while Figure 11 shows the Opposite trend for navy beans. The result for corn does not agree with the findings of Shedd (1953) who made the general statement that "the resistance pressure for a given rate of airflow is lees for a lot of grain at 20 percent or higher mois- ture than for the same lot Of grain and the same method of filling after drying to a lower moisture content". Pressure drop data on corn at different moisture contents published by Matthies (1956), howv ever, agree with the findings Of this study. Aas, et a1. (1960) also found that the trend of the moisture content effect on the pressure drOp is dependent on the grain and the moisture content range being tested. 29 .cuoo smacks“. mono 35393 0:» co ucouoou muss—ado... mo uuomwo BE. .2 whom; om: .c m 4 mommn.aEOh m.mume m¢.uw aemu.o.2 ¢.mume m¢.uw meu.0.2 \\ n 4 0 \\ k‘ l‘ L‘ \\ \\ m.eumx m¢.uw ameu.o.2 0m 0 CO éii/wlo ‘MOIialv 009 30 314/1040 ‘Mouaw 31 The effect Of moisture content on the pressure drOp through navy beans. Figure 11. Figures 12 and 13 illustrate the effect of air temperature on the resistance to airflow through beds of corn and navy beans. In both cases increased air temperatures resulted in increased static pressure at the same airflow. At the same time the beds Of corn and navy beans became less porous at the higher temperature. This decrease in porosity, resulting in greater resistance to airflow, may be explained by an increase in bed particle diameter due to expansion with increased temperature. The effect Of bed porosity, air temperature and particle moisture content on the pressure drOp through beds Of grain has been illustrated above. These facts, however, are not sufficiently accounted for by the airflow-pressure drOp data (ASAE D 272) recognized and published by the American Society Of Agricultural Engineers. Figure l is representative Of ASAE D 272. While this data is accurate as presented, it will unfortunately, hold only for beds of products similar to those used to Obtain this data. Although it is indicated in a footnote to this graph, that a curve gives reliable data for only loosely filled beds of relatively dry (and clean) grain, no specific mention is made as to how these curves should be corrected in case these standard conditions are not prevailing. As an example, notice in Figure 14 the difference illustrated by a log-log plot Of the pressure drop requirements Of two beds Of cherry pits. The two beds differ only in porosity. If it were desired to add information per- taining to the pressure drOp through cherry pits to ASAE D 272, the question might well be asked which line Of Figure 14 should this be. 32 .cuoo swsounu oouo musmmoua may one muamouoa wsu co ousumuooEOu ago 00 avenue Oak .NH mpswwm om: .E..n_.m a m w e . V $7.30.: M... .ONI. m.mu m: .. J m a one? a .o 0.00 um .. i. . . e m n... - CIT? . .3 .. 50“ h 0 . a: .8. 33 .mcmmn m>mc swoouau mono ousmmoua Ono pom huamouoa on» so ououmuoafiou ago we uoommo may om: .c_..a.m e m N F .MH ouswfim q d d umwu.0.§ .. \ m..umx . “mnvnumw—.nuh. AV - mm.uw - . d . F.mmz mommnh \\ 00.nw ‘\ 40m é. (I) éii/WIO‘MOIIJIV L 09. '36 .mmwuamouoa own ucouommao ska um mafia huuoso mo sofimuwm cu oucmunwmom .¢H ouswwm om: .E..n_.m m m _. .v N _. #0. m0. a q a 1 m _ a H L .2. W J Ir .8 m. M O .3. w... 330.com umm...n_ L H xtmocoa 3.3.6 n+ .8? a 35 It is Obvious that the ASAE D 272, in its present form, does not adequately represent the probable range Of pressure drOp-airflow characteristics of a bed Of a given biological material. The lines on Figures 1 and 14 are not completely straight. This means that the Ramain equation does not exactly describe the data points in these figures. In addition, the product constants, a and b, would vary not only from product to product, but also from porosity to porosity (Figure 14) and from moisture content to mois- ture content. It has long been recognized that the presence of foreign material (fines) intermixed with grain tends, in general, tO increase the resistance to airflow if the foreign material is Of a smaller equivalent diameter than that of the grain. Figure 15 illustrates this for beds Of 16 percent moisture corn intermixed with various percentages of fines. (Fines were considered as material passing through a 0.1875 in. diameter round-hole dockage sieve.) It has been previously illustrated with corn that with an increase in bed porosity, a decrease in pressure drOp would result. This is not the case when the increase in voidage is a result Of the addition Of fines as illustrated in Figure 15. In this case, a bed containing 10 percent fines and having a porosity Of 0.43 requires a lower static pressure than a bed with 40 percent fines and a voidage Of 0.49. The importance Of keeping the percentage of fines tO a mini- mum is illustrated well in Figure 15. Here it is indicated that a bed with 20 percent fines will require a static pressure, at 60 cfm per square foot airflow, Of 3 in. water column per foot Of depth which is three times as high as a bed Of corn containing no fines. 36 mommucoouoo msowum> maaaqmucou cuoo mo moon awaousu Seamuwm ou moamumanom .— .— __ .. woe: .moafiw mo om: .Ettm m m P “mm uom no— mm 0: d 4 1 1 me. 2V. .3. me. me. oe. me. 5.59.8 ciao l CU.£2 (J'IS d)'+- €31 .mH ouswam cm W 4 _Ir m M 8 o I... w / .l—a a+. ../u ooa 37 4.3 Leva Equation TO calculate the resistance to airflow through a bed Of particles using the Leva equation the terms f the Leva friction L’ factor, and n, the state-Of-flow factor, both functions Of the Reynolds number, were found. Table 3 shows the values of fL and n as they were Obtained for a test using cherry pits as bed material. The table also shows the calculated and experimental values for pressure drOp (AP/h). It is evident that the theoretical and experi- mental data do not agree. For this reason the ratio between the experimental and the theoretical values was calculated (last column in Table 3) and the average determined. This average was called kL, the Leva product constant for cherry pits. The average kL for this test was 1.2. The pressure drOp data calculated using the Leva equation was Obtained using the following relationship: 2 1-8 a-“ 29:] AP h = kL E fL 3-n 3 dg (7) e where 9, the particle shape factor for cherry pits was taken to be 1.1. Table 3. Values Of n and f , as functions of the Reynolds number, and AP/h for the pressure drOp through a bed of cherry pits (porosity = 0.42) as given by the Leva Equation. (AP/h)ex ‘52 n .fL (AP/h)L (AP/h)exp. 7357ggz—2 63.4 1.58 1.69 0.06 0.08 1.41 84.5 1.68 1.48 0.10 0.12 1.28 105.6 1.72 1.38 0.14 0.18 1.30 126.7 1.75 1.30 0.19 0.24 1.25 147.9 1.80 1.25 0.26 0.32 1.24 169.0 1.82 1.19 0.32 0.40 1.23 190.1 1.84 1.16 0.40 0.50 1.23 211.2 1.85 1.13 0.48 0.60 1.23 232.4 1.86 1.10 0.56 0.70 1.21 253.5 1.86 1.08 0.66 0.82 1.20 274.6 1.87 1.06 0.75 0.94 1.20 295.7 1.88 1.04 0.88 1.10 1.21 316.9 1.89 1.03 0.99 1.24 1.21 38 Although the modified version Of the Leva equation predicted the pressure drOp through beds of cherry pits satisfactorily, testing the equation on beds Of additional kinds of biological pro- ducts was not conducted because Of the relative complexity involved in finding the prOper values of fL, n and 9. .544 Matthies Equation TO calculate the pressure drop through a bed Of particles at a certain airflow using the Matthies equation, one has to know the values for kM and in. The friction factor fM, like fL, is a func- tion Of the Reynolds number. The various values Obtained for fM for a particular test on cherry pits are given in Table 4 along with values for km. The Matthies product constant, kM, would not be expected to vary a great deal if the‘Matthies equation prOperly describes the pressure drOp through a cherry pit bed. As expected, the values for kM in Table 3 are approximately the same for the various Reynolds number values. The average kM for this particular test was 1.09. Matthies (1956) Obtained RM values for a number of agricultural products. They varied from 1.05 for peas, to 2.70 for barley to 3.80 for oats. For spheres kM is equal to one and since cherry pits are nearly spherical, a kM for cherry pits Of approximately one would be expected. As indicated in the previous paragraph, this is the case. 39 Table 4. Values of fin, as a function of Reynolds number, and (AP/h) for the pressure drOp through a bed of cherry pits (Porosity = 0.42) as given by the Matthies Equation. AP/h ex O (AP/h)M (1113711)M Re :11 (Al’lh) ea. 63.4 1.69 0.08 0.08 1.09 84.5 1.48 0.12 0.12 1.05 105.6 1.38 0.18 0.16 1.08 126.7 1.30 0.24 0.22 1.06 147.9 1.25 0.32 0.30 1.08 169.0 1.19 0.40 0.36 1.09 190.1 1.16 0.50 0.46 1.10 211.2 1.13 0.60 0.56 1.10 232.4 1.10 0.70 0.64 1.09 253.5 1.08 0.82 0.74 1.09 274.6 1.06 0.94 0.86 1.09 295.7 1.04 1.10 0.98 1.12 316.9 1.03 1.24 1.12 1.11 In comparing the Leva and Matthies equations it can be said that both predict pressure drOps through beds of cherry pits ade- quately, but the Matthies equation is easier tO use. 4.5 Ergun and MOdified Eggun Eqpation Table 5 contains the calculated pressure drOp data, as given by the Ergun equation, and the experimental pressure drOp data for a bed composed Of cherry pits at various airflow rates. Along with this data the ratio of these last two values is given. It was found that the Ergun equation always predicts a value for the pressure drOp through cherry pits which is low by 15 to 20 percent. For this reason the Ergun equation was modified to: - 3 _ 2 A}: ... k [150 S_?_1 e u —“ + 1.75 —1 e ——p“ 1 (8) where kE is the Ergun product constant. For the bed of cherry pits analyzed in Table 5 the average value of RE was 1.17. The Ergun equation is the combination Of an equation for laminar flow and an equation for turbulent flow (Section 2.2). The data of a typical pressure drop-airflow test as given by the Ergun equation is plotted in Figure 16. The prOportion of the total pressure drOp contributed by the laminar and the turbulent portion Of the Ergun equation is illustrated. At the low end Of the airflow range, 0.29 feet per second, the laminar portion Of the total pres- sure drOp through the bed is approximately 55 percent. As airflow increases to 2.65 feet per second the laminar contribution to total bed resistance has decreased to approximately 13 percent. The fact that the Ergun equation contains terms for both laminar and turbulent airflow emphasizes its suitability in describing the air circulation requirements Of most drying and cooling Operations. Comparing the results Of the Leva, Matthies and Ergun equa- tions (Tables 3, 4 and 5) illustrates that any one of these relation- ships is able to describe and, therefore, predict with comparable accuracy, the resistance to airflow of packed beds of cherry pits. However, they do differ with respect to ease Of use. Leva's equation is the most difficult to use (9, fL and n values have to be found first) followed by the Matthies equation (EM has to be determined as a function Of the Reynolds number). Comparatively, the modified Ergun equation has no special terms requiring additional calculations. Thus, on the basis Of its simplicity plus its satisfactory prediction characteristics, it was decided to use the modified Ergun equation for the remainder Of the pressure drOp tests. 41 .wocmumamou own Houou ou coausnuuucoo Seamuam ammusnuau one umcaEmH use .oom\.u+.>u_oo_o> c_< N F cmc_am_ flxnxxnxa:.:fi.z. .////.//.// // // / yco_3nc1u A .0fi ouswwm 42 Table 5. Values Of (AP/h), at various air velocities for the pressure drOp through a bed of cherry pits (porosity = 0.42) as given by the Ergun Equation. (AP/h) Exp. u, ft.[min. (AP/h)E (AP/h) Exp. (AP/h)E 24.3 0.06 0.08 1.21 32.4 0.10 0.12 1.15 40.5 0.14 0.18 1.19 48.6 0.20 0.24 1.16 56.7 0.26 0.32 1.19 64.8 0.34 0.40 1.17 72.9 0.42 0.50 1.19 81.1 0.50 0.60 1.18 89.2 0.60 0.70 1.16 97.3 0.70 0.82 1.16 105.4 0.82 0.94 1.14 113.5 0.94 1.10 1.17 121.6 1.08 1.24 1.16 4,6 kE Values The Ergun product constants, kE for corn and navy beans are given in Table 6. The data is for three moisture contents, three porosity ranges and two air temperatures. Each kE value is based on three tests. The data shows, in the case of navy beans, that the kE values are consistent for beds containing no fines. This means that the modified Ergun equation, with a kE value between 1.8 and 2.0, will predict correctly the effect Of moisture content, bed porosity and air temperature on the pressure drOp through beds Of navy beans. For beds of corn the results are not as consistent. Although the modified Ergun equation does predict rather accurately the effect of porosity and air temperature (with a kE between 3.7 and 4.5), a change in bed particle moisture content from 16 to the 19 tO 24 per- cent moisture content range increased the kE value from about 4.0 to 43 .ucoouoo on no hueoqaas o>wumaou was was mooofi no ousumuanou Ham .00.0 n o ..uw «0.0 n woo no woman one .03 How mosHm> may "meoz muHHom xoa o.m n.~ ~0.o no «No. 00.0H momma macaw N00 «.0 ~.N0 00.0 no «no.0 ~0.0H : macaw eon m.m 0.0m a0.o Am «mo.o Ho.0H : macaw xou m.0 0.5H 00.o so «mo.o Ho.0H : macaw Nos m.0 0.0a m0.o so «no.0 Ho.0H : 00:00 Nm 0.~ 0.0 m0.o no «no.0 Ho.0H : macaw Nu 0.m 5.0 00.0 50 «no.0 H0.0H cuou gaaw Hmahoa 0.H o.~ H0.o no mmo. Ho.mN : Haam “mayo: 0.H o.N 00.0 no mmo. 0m.wH : UKQU 000 m.N ®.H mm.o MHH NNO. w®.¢H : “~00 assoc: ~.N m.H om.o no «No. 00.0H : Hfiam Hmauoc m.~ o.N 00.0 no «No. 00.0H mason aaam flushes 0.~ 0.0 m0.o no mmo. ~A.m~ : Haum Haauoc 0.~ 0.0 m0.o >0 mmo. no.0H : easy use m.m n.m mm.o o- «no. ~o.0H : Hahn cacao 0.N 0.0 0m.o no «no. Ho.0a : Hfiam Hashes ¢.~ 0.0 m0.o so «no. Ho.0H cuoo 3558 -mlx m.— u a. .mfiu . m0 0.. oz 00:06.5 . .um .0 .aocau mo mowsuoouuoa was nouauouoaaou was .uouuanouoa 000 .mucOucou onsuuaoa nosooua ucououmao um mason >>mo one case How mo=~m> .03 one ma .0 agony 44 6.5. It is not well understood why one value for kE in the modified equation predicts accurately the pressure drOp through navy beans while different values have to be used for corn tO accomplish the same thing. Increasing the percentage Of fines in a bed results in larger kE values due to the larger pressure drop in the beds. For corn the value Of kE increased from 5.7 at 2 percent fines to 9.2 at 40 percent fines. 59-7—1511 ' Values The modified Ergun equation is simple to use once the different parameters in the equation are known. Unfortunately the value Of e, the porosity, Of a bed of grain is difficult to determine. Since it is possible that there exists some linear or non-linear relationship between the porosity Of a grain bed and its bulk density, it might be advisable to replace the e by some value e which is a function of the bulk density of the bed. A further simplification in the use Of equation (8) could be made by writing it in the following form: LP - ’ 2 h - kE (M u +~N u ) (9) a where M = 150 1’9 p, —l— as dag N =- 1.75 -'3- es It is suggested that the values Of M and N be calculated at arbitrarily defined standard conditions. For instance, the standard conditions could be chosen as: an equivalent diameter of 0.02 ft., a 45 porosity of 0.40 and drying air conditions Of 100°F and 50 percent relative humidity. Under these circumstances the values of M and N would be 0.1604 and 0.3356 reapectively. Equation (9) would then be: D‘ID 'd = kE' (0.1604 u + 0.3356 02) (10) In calculating the k ' values at other porosities or bulk E densities, moisture contents and air temperatures, the values for M and N would be kept constant. The result is that the kE’ values will reflect the bulk density, the moisture content and the air pro- perty effects. For each crOp a range Of values for kEI will thus be Obtained. I E values, the kE data. It is clear that unlike the kE values, kE’ will be affected especially Table 6 contains in addition to the k by the bed voidage (or bulk density). Although equation (10) is easier to use than the modified Ergun equation, it is purely empirical in nature. For this reason the use of the modified Ergun equation, using kE rather than k ’ and replacing E the porosity value with the proper bulk density term, is prefered. Bed porosity, a difficult parameter to measure, is not as well understood as the term bulk density. For this reason a number of porosity and bulk density readings were made on beds Of corn and navy beans in order to see if there exists a consistent relationship between porosity and bulk density. If such a relationship can be found, the porosity term in the modified Ergun equation could be replaced by a bulk density term. Table 7 shows the results. The data indicates that for navy beans the product Of the porosity and the bulk density is fairly constant within the 14.88 to 25.01 moisture 46 Table 7. Porosity and bulk density values Of beds Of corn and navy beans at 50°F at different moisture contents. Corn Bulk Bulk Mc,% wb 6 Densityqlb/ft3 Porosity x Density 16.01 .4704 46.42 21.80 16.01 .4439 48.42 21.50 16.01 .4269 49.74 21.30 19.07 .5366 42.62 22.80 19.07 .5062 44.77 22.60 19.07 .4881 46.11 22.50 23.71 .5585 40.93 22.80 23.71 .5304 43.03 22.80 23.71 .5140 44.31 22.80 Beans 14.88 .4805 50.14 24.10 14.88 .4576 51.97 23.70 14.88 .4313 54.18 23.20 18.30 .4898 49.56 24.20 18.30 .4685 51.26 24.00 18.30 .4479 52.65 23.60 25.01 .4953 47.74 23.80 25.01 .4809 49.41 23.70 25.01 .4568 51.12 23.40 moisture content range. For corn this product is constant between 19.07 and 23.7 percent moisture but increases slightly between 16.01 and 19.07 percent moisture content. If the product of the porosity and the bulk density Of a bed is assumed to be constant for a particular product and is called y, the term 6 in the Ergun equation (Equation 8) can be replaced by y/bulk density. For navy beans the value Of y would be 23.70. For corn y would have the value Of 21.50 in the low moisture content range and Of 22.70 above 19.07 percent moisture content. The value of 21.50 (resulting in a lower calculated 6) should be chosen if one value Of y is to be used for the full moisture content range. 47 Finally, the modified Ergun equations for corn and navy beans would take the form: for corn: - 22.0 <1- —--22'°)2 ‘1' T) p p 2 _'_.3 2 3 8 ( ) d g 22.0 p. (T) p for beans: 9 24 0 (1- 24.0) (1_ _) 2 %13= kE[150—L— n-“-+1.75——-L 33—](13) 24.0 3 893 24.0 a 3 (p ) (p ) p p p where p is the bulk density Of the bed product expressed in pounds per cubic foot. The results of applying Equations 12 and 13 to pre- dict the pressure drop through beds Of corn and navy beans are shown in Figure 17. 48 .cOaumsoo comma 00000008 Ono >0 co>ww no mason h>mc one once we Segundo Ou woamumamom .BH ouowam om: .52....0. 0 m m P V .v ll. .om 0 3030.805 ccoo a \ 1. .mo_yocoo:u meson O . . m 30:05.8.“on .. . M . . i. a \ om w / . I... I \ A Q+ .3 a D .02. I O 49 V. SUMMARY AND CONCLUSIONS Three semitheoretical relationships were tested for their ability to accurately predict the pressure drop through fixed beds composed of biological particles at various airflow rates. Bed particles consisted of cherry pits, corn and navy beans. The cherry pits were tested at one air temperature and one moisture content. The corn and navy beans were tested at two air temperatures, three moisture contents and‘with various percentages Of intermixed fines. The experimental set up was verified by comparing experimentally Obtained data, on resistance to airflow through beds Of uniformly dimensioned acetate spheres, with data of previous investigators. The three relationships predicted the resistance to airflow through beds Of cherry pits with equal accuracy. The Ergun equation proved to be the least difficult to work with because Of the required use Of independently calculated terms in the Leva and Matthies equation. Consequently the Leva and Matthies relationships were not tested on beds Of corn and navy beans. The Ergun equation was modified to include a product constant to compensate for the nonSpherical nature Of the bed particles. The results are given which indicate the ability of the modified Ergun equation to predict the resistance tO airflow through beds of corn and navy beans. The effect Of particle moisture content, bed poro- sity and air temperature are discussed. 50 Suggestions for Further Study Find kE values for other grains. Further investigate the effect Of grain moisture content on the kE values. Determine experimentally the pressure drOps at bed depths over 10 feet. Expand the range Of airflow rates beyond the 10 to 130 cfm/ ft.a range. Determine the effect Of moisture content and product tempera- ture on the equivalent diameter of grains. 51 REFERENCES 52 REFERENCES Aas, Kristian and Kare Time (1960). Resistance to airflow in drying plants for grain. Research Report NO. 5, Norwegian Institute Of Agricultural Engineering, Vollebekk, Norway. American Society Of Agricultural Engineers Yearbook (1969) 16 Edition. Anderson, K. E. B. (1963). Pressure drOp through packed beds. Transactions Royal Institute Technology, Stockholm, NO. 201. Bakker-Arkema, F. W., J. R. Rosenau and W. H. Clifford (1969)b. Measurements of grain surface area and its effect on the heat and mass transfer rates in fixed and moving beds Of biological products. Paper NO. 69-356, presented at the 1969 Annual Meeting of the American Society of Agricultural Engineers, Purdue University. June. Bakker-Arkema, F. W., R. J. Patterson and W. G. Bickert (l969)a. Static pressure-airflow relationships in packed beds Of granular biological materials such as cherry pits. Trans- actions Of the American Society Of Agricultural Engineers, Vol. 12, NO. 1, pp. 134-136 & 140. Barth, W. (1954). Druckverlust beider durchstromung, Fullkorper Saulen, Chem. Eng. Tech., Vol. 23, N0. 12. Borrero, C. (1967). Cooling a stack of fruit: packed bed analysis thesis for degree Of Ph.D., Michigan State University. Bunn, J. M. and W. V. Hukill (1963). Pressure pattern predictions for non-linear airflow through porous media. Transactions Of American Society Of Agricultural Engineers, Vol. 6, No. 1, pp. 32-35 & 36. Burke, 8. P. and W. B. Plummer (1928). Gas flow through packed columns. Industrial Engineering Chemistry, 20 S. 1196/1200. Carman, P. C. (1937). Fluid flow through granular beds. Trans- actions Of Institution of Chemical Engineering (Canadian) 15, 150. Chiam, J. T. (1962). Voidage and fluid distribution in packed beds. Ph.D. Thesis, Manchester College Of Technology. Day, C. L. (1964)b. A device for measuring voids in porous materials. Agricultural Engineering, January. Day, 0. L. (l964)a. Resistance Of hay to airflow. Research Bulletin 864, University Of Missouri, June. 53 Ekstrom, G. A., J. B. Liljedahl and R. M. Peart. Thermal expansion and tensile properties Of corn kernels and their relation- ship tO cracking during drying. Transactions Of the American Society of Agricultural Engineers, 9(4):556-561. Ergun, S. (1952). Fluid flow through packed columns. Chemical' Engineering Progress, Vol. 48, NO. 2, p. 89, February. Fehling, R. (1939). Der Stromungswiderstand Ruhender Schuttungen Feuerungstechn, 27, S. 33/44. Hall, C. W. (1957). Drying of farm crOps. Edwards Brothers, Inc., Ann.Arbor, Michigan. Haughey, D. P. and G. S. Beveridge (1969). Structural properties Of packed beds - a review. The Canadian Journal of Chemical Engineering, Vol. 47, April. Hukill, W. V. and N. C. Ives (1955). Radial airflow resistance Of grain. Agricultural Engineering (VOl. 36, NO. 5, pp. 332- 335) May. Kling, G. (1940). Druckverlust Von Kugel Schuttungen Z-V.C.I. 84, S. 85/86. Lawton, P. J. (1965). Resistance to airflows of some common seeds. Journal of Agricultural Engineering Research, 10, 4. Le Clair, B. P. and A. E. Hamielec (1968). Viscous flow through particle assemblages at intermediate reynolds numbers. Steady- state solutions for flow through assemblages Of spheres. Ind. Eng. Chem. Fundamentals 7, 542-549. Leva, M. (1959). Fluidization. McGraw-Hill, Inc., New York, N. Y. Matthies, H. J. (1956). Der Stromungswiderstand beim Beluften Landwirtschaftlicher Ernteguter. V.D.I. - Forschungsheft 454. Nissing, T. J. (1958). Resistance of seed cottom to airflow. Agri- cultural Engineering, VOl. 39, NO. 3, pp. 160-163 and 165, March. Osborn, L. E. (1961). Resistance to airflow Of grains and other seeds. Journal of Agricultural Engineering Research, Vol. 6, p. 119. Pabis, S. and S. M. Henderson (1962). Grain drying theory 111. The air/grain temperature relationship. Journal Of Agricultural Engineering Research, Vol. 7, NO. 1. Reynolds, 0. (1900). Papers on mechanical and physical subjects. Cambridge University Press, Cambridge, England. 54 Shedd, C. K. (1953). Resistance of grains and seeds to airflow. Agricultural Engineering (Vol. 34, NO. 9, pp. 616-619, Sept.). Sheldon, W. H., C. W. Hall and J. K. Wang (1960). Resistance of shelled corn and wheat to low airflows. Transactions of the American Society Of Agricultural Engineers (Vol. 3, NO. 2, pp. 99, 93 and 94). Stirniman, E. J., G. P. BOdnar and E. N. Bates (1931). Tests on Resistance to the passage Of air through rough rice in a deep bin. Agricultural Engineering 12:145-148. Thompson, R. A. and G. W. Isaacs (1967). Porosity determination Of grains and seeds with an air-comparison pycnometer. Trans- actions Of the American Society Of Agricultural Engineers, Vol. 10, NO. 5, p. 693. Wang, J. K. and S. Win (1968). The effect Of temperature on the resistance of macadamia nuts and coffee beans to airflows. Paper NO. 68-376 presented at the 1968 Annual Meeting Of the American Society Of Agricultural Engineers, Utah State University, Logan, Utah. Yen, I. K. (1967). Predicting packed-bed pressure drOp. Chemical Engineering, March 13. 55 APPENDIX 56 0000000000000 0000 0 000 00000 8 6 001 9 PROGRAM DESPER AFDELTP =PRESSURE DIFFERENTIAL ACROSS. MEASURING SECTION OF LAMINAR FLOW ELEMENT. EXBDELTP=PRESSURE DIFFERENTIAL ACROSS TEST BED. CFM flAIRFLOW CUBIC FEET PER MINUTE PER SQUARE FEET. TEMP HAIR TEMPERATURE AT TEST BED ENTRANCE. TEMPCOR =CORRECTION FACTOR USED IN CALCULATING AIRFLOW. DELTPE =PRESSURE DIFFERENTIAL GIVEN BY ERGUN. DMAIRFLO=DIMENSIONLESS AIRFLOW. RE =REYNOLDS NUMBER DIVIDED BY ONE MINUS EPSILON. U =AIR VELOCITY. AMU 8AIR VISCOSITY. EK =CONSTANT IN MODIFIED ERGUN EQUATION. DELTPKE =PRESSURE DIFFERENTIAL GIVEN BY ERGUN EQUATION CON- TAINING EK. ROONE =AIR SPECIFIC VOLUME. RH =AIR RELATIVE HUMIDITY. PS =SATURATION PRESSURE. EKP IIICONSTANT IN MODIFIED ERGUN EQUATION CONTAINING CON- STANTS M AND N. DELTPMN =PRESSURE DIFFERENTIAL GIVEN BY ERGUN EQUATION CON- TAINING CONSTANTS M AND N. DELTPKEP-PRESSURE DIFFERENTIAL GIVEN BY ERGUN EQUATION CON- TAINING CONSTANTS M,N, AND EKP. TESTNO -TEST NUMBER IA =NUMBER OF DATA POINTS FOR.A GIVEN TEST. H IHEIGHT 0F TEST BED OVER.WHICH PRESSURE DIFFERENTIAL WAS MEASURED. D =EQUIVALENT PARTICLE DIAMETER. PF BFINAL PRESSURE READING IN POROSITY MEASUREMENT. DELTP -DIFFERENCE BETWEEN INITIAL AND FINAL PRESSURE READING IN POROSITY MEASUREMENT. SUMEK -SUM OF EK VALUES FOR A GIVEN TEST. SUMEKP -SUM OF EKP VALUES FOR A GIVEN TEST. EPS =FOROSITY VALUE. EKMEAN =MEAN VALUE OF CONSTANT EK FOR A GIVEN TEST. EKPMEAN =MEAN VALUE OF CONSTANT EKP FOR A GIVEN TEST. DIMENSION AFDELTP(20),EXBDELTP(20),CFM(20),TEMP(20),TEMPCOR(160) DIMENSION DELTPE(20), DMAIRFLO(20). RE(20), 0(20), AMU(170) DIMENSION EK(20), DELTPKE(20), ROONE(20), RH(20), PS(160) DIMENSION EKP(20), DELTPMN(20), DELTPKEP(20) READ(60,8)PS READ(60,8)TEMPCOR FORMAT(10F5,4) READ(60,6)AMU FORMAT(10F5,5) READ(60,9)TESTNO,IA,H,D,PF,DELTP F0RMAT(F3,0,12,F5.0,3F10.0) IF(TESTNO.LE.0) GO To 002 57 READ(60,7) (AFDELTP(I),I=1,IA) READ(60,7) (EREDELTP(J),J=1,IA) READ(60,7) (TEMP(N),N-1,IA) READ(60,7) (RH(M),M=1,IA) 7 FORMAT(15FS.0) K=0 SUMEK=0 SUMEKP=0 IC=O EPS=1-((1144.1639-((893.46*PF)/DELTP))/3/6.67) 20 DO 203 L=1,IA =K+l ~ CFM(K)=((-0.00408754=5.55090626*AFDELTP(K)-0.009/1439*AFDELTP(K)** 13+0.00056478*AFDELTP(K)**4)*TEMPCOR(TEMP(K)))/0.168759 U(K)=CF.(K)/(60) DELTPMN(K)=(H*((.160386662*U(K))+(.33556465*(U(K)**2)))) EKP(K)=(EXBDELTP(K))/(DELTPMN(K)) SUMEKP=SUMERP+ERP