GRAIN PRESSURE IN A MODEL SILO AS AFFECTED BY MOISTURE CONTENT INCREASE. J. Horabik, M. Molenda

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1 Int. Agrphysics, 2000, 14, GRAIN PRESSURE IN A MODEL SILO AS AFFECTED BY MOISTURE CONTENT INCREASE J. Hrabik, M. Mlenda Institute f Agrphysics, Plish Academy f Sciences, Dœwiadczalna 4, P.O. Bx 201, Lublin 27, Pland Accepted January 5, 2000 A b s t r a c t.swelling pressure f wetted grain was measured in a mdel sil. Experimental set was designed t simulate the cnditins under which grain is subjected t wetting by ambient air f the humidity higher than the equilibrium relative humidity crrespnding t the existing misture cntent f grain. The mdel invlves superpsitin f tw basic kernel reactins t water supply: (i) swelling f kernels, (ii) decrease in kernels elasticity with an increase in the misture cntent. The mdel prperly describes the relatin between swelling pressure and the increase in the misture cntent in a range f the misture cntent increase up t Swelling pressure f the wetted grain is strngly influenced by the initial bulk density which depends n the precmpressin histry. The experiments perfrmed indicate that distributin and value f the swelling pressure in the mdel sil is nt unifrm and depends n the path f wet air mvement. Keywrds:grain, sil, pressure, swelling INTRODUCTION Grain stred in sils may becme subject t wetting by rainwater ingress r by ambient air f humidity higher than the equilibrium relative humidity crrespnding t the existing misture cntent f the grain. During the near-ambient drying prcess, ambient air is blwn thrugh the bedding t cl the grain and lwer the grain misture. When the air with a specific temperature and relative humidity is passed thrugh a bed f grain, the grain will either lse r absrb misture, depending n its equilibrium relative humidity crrespnding t the existing misture cntent that can be abve r belw the relative humidity f the drying air [8]. When the grain absrbs misture, kernels swell, and the grain bulk tends t expand. This expansin is restricted by the sil wall, and cnsequently the swelling grain impses additinal pressure n the sil wall [1-3,6,8,13]. Changes in the misture cntent affect bth the prperties f an individual kernel and bulk prperties f grain, thus affecting bin lads. There is a big differentiatin in the values f swelling pressure reprted by varius authrs. Dale and Rbinsn [3] investigated the effects f misture cntent changes n the pressure f grain in bins. Their test results indicated that when the misture cntent f grain was increased by 4 % w.b., the lateral wall pressure increased as much as six times and the vertical flr pressure increased fur times. Blight [1] bserved that the swelling pressure f wetted grain under cnstant vertical stress with zer lateral strain may duble in value. Kebeli [7] nticed that an increase in the misture cntent f 11% d.b. resulted in the five fld increase in the lateral pressure and tw fld increase in the vertical pressure. Brittn et al. [2] mnitred vertical frces n the wall f a mdel bin during the wetting prcess. After 15 h f wetting the gravitatinal frce due t the grain mass was cmpletely balanced by the upward frce f grain swelling. Hrabik and Mlenda [6] fund that the swelling pressure f wetted grain is strngly influenced by the initial bulk density, i.e., it depends n precmpressin histry. The

2 386 J. HORABIK, M. MOLENDA maximum value f the swelling pressure f wheat grain measured in an edmeter after precmpressin t 0.5 MPa resulting in the initial bulk density f 835 kg m -3 was fund t be apprximately 0.17 MPa, and ccurred at the misture cntent increase f 0.2. The bjective f this study was t explre the swelling pressure f the wetted grain cntained in a mdel sil. Experiments were perfrmed simulating the behaviur f the grain when subjected t wetting by the ambient air f higher humidity than the equilibrium relative humidity crrespnding t the existing misture cntent f the grain. decrease with misture cntent increase (MPa), K - effective elastic mdulus f grain in bulk (MPa), K - packing parameter [11], p - cnfining pressure (MPa). The ttal vlumetric strain f grain in bulk, v, is the sum f tw independent cmpnents: the vlumetric strain resulting frm cnfining pressure, c, and the vlumetric expansin resulting frm swelling f wetted grain, u, (Fig. 1): p ku v. K p, u (4) 1 u w THEORETICAL APPROACH Zhang and Brittn [13] prpsed a theretical mdel predicting hygrscpic lads in grain strage bins. A vlume increase f the wetted grain kernel was assumed t be equal t the vlume f water absrbed by the kernel [9]. The vlumetric strain f the grain bulk u, caused by the misture cntent increase was calculated frm the swelling f individual grain kernels: V ku u (1) V 1 u where: - initial misture cntent (d.b), u - misture cntent increase (d.b.), k - density f kernel (kg m -3 ), w - density f water (kg m -3 ). Cnsidering the Hertzian type f interactins between individual kernels [10,11], the fllwing relatinship between an effective elastic mdulus f grain in bulk, K, the cnfining pressure, p, and the misture cntent, u, was pstulated by Hrabik and Mlenda [5]: 2 1 Kp, u K E u 3 p 3 (2) where the mdulus f elasticity f kernels, E(u), decreases linearly with an increase in the misture cntent [4,12]: Eu Eu de u du (3) where: E - mdulus f elasticity f kernels (MPa), de/du - rate f mdulus f elasticity w v The fllwing relatinship between the cnfining pressure, p, and the misture cntent increase, u, can be fund frm the Eq. (4) in the case f swelling in a rigid cntainer ( v =0): K pu 1 u k u 2 Eu c <0 u >0 vlumetric strain = cmpactin + swelling Fig. 1. Illustratin f vlumetric strain resulting frm cmpactin by cnfining pressure and kernel swelling. w 3 de u. du (5) This functin has the maximum fr u 3Eu / 5dE / du. When kernels swell, the cntact frces increase. At the same time the mdulus f elasticity decreases. As a cnsequence, the pressure reaches its maximum value and then decreases. Apprximatin f an initial part f the swelling prcess f wheat, p(u), clsed in a rigid edmeter btained by Hrabik and Mlenda [6] is shwn in Fig. 2. The mdel prperly predicts the swelling pressure in the range f the misture cntent increase f up t The maximum f the swelling pressure ccurred at the misture cntent increase f 0.2.

3 GRAIN PRESSURE IN A MODEL SILO 387 Swelling pressure p (MPa) p = u u R = = Misture cntent increase, u Fig. 2. Apprximatin f the initial part f the swelling pressure - misture cntent increase relatin [6]. EQUIPMENT AND PROCEDURE The mdel sil was 0.61 m in diameter and 0.75 m in high (Fig. 3). The flat bttm and tp cver f the sil cnsisting f five cncentric rings with an equal surface area were used t measure radial distributin f the vertical pressure v. Each ring, and the sil wall, was supprted independently n the three lad cells separated by an angular distance f 120.T measure the mean lateral pressure, n, a galvanised steel cylinder 3 mm thick was cnstructed in tw semicircular halves cut alng the axis. The tw semicircular halves were cnnected with fur lad cells installed in pairs n tw cnnectin lines, which restred the cylindrical shape f the wall. This cnfiguratin allwed fr the determinatin f vertical pressure distributin n the sil flr and tp cver and mean lateral and tangent pressure n the sil wall [6]. Air utlet Sil wall Air plenum Sil bttm Humidifying chamber Fan Air cnditiner Fig. 3. Mdel sil with wetting equipment.

4 388 J. HORABIK, M. MOLENDA The air humidifying system cnsisted f an air cnditiner, a centrifugal fan, a humidifying chamber, and an air plenum that was used t increase misture cntent f the grain in the sil. A perfrated cylindrical air plenum lcated centrally in the sil supplied grain with wet air and a perfrated circumferential chamber lcated at upper part f the sil wall was used as the air utlet. Air with relative humidity f up t 95% and the temperature f 36 C was blwn thrugh the mdel sil filled with wheat grain. Temperature and relative humidity f the air in the sil inlet and utlet, change in grain misture cntent and swelling pressure exerted n the sil cnstructin were measured during the experiment. The sil was centrally filled frm the filling device lcated 1.2 m abve the sil. The device had a shape f a cne with its vertex directed dwnward and aligned with the center axis f the sil. Grain was depsited n the pile thrugh an rifice at the vertex f the cne. As a result, the grain frmed a cnical slping surface with the vertex directed upwards and the kernels tended t rest with their lng axis alng the generatrix f the frmed cne. After filling, the grain was cmpacted under the pressure f 10 kpa fr 24 h t eliminate cntributin f irreversible displacement f grain int the vlumetric strain. Bulk density after the precmpressin was 780 kg m -3. Next the vertical pressure was decreased t the value f 3 kpa created by the weight f the tp cver f the sil and the height f the bed f grain was fixed. In the last step f the experiment, wet air was blwn thrugh the bulk f grain and the swelling pressure was measured. The initial misture cntent f the grain was set t abut 0.07 t increase the rate f misture absrptin frm the ambient air. RESULTS Radial distributin f the vertical pressure v n the sil bttm fr several values f the misture cntent increase is presented in Fig. 4. The vertical pressure increase was the highest near the sil centre and decreased twards the sil wall. This is the result f a decreasing rate f water absrptin alng the path f air mvement. The mean lateral pressure n n the sil wall as influenced by the misture cntent increase fr tw values f the initial misture cntent was presented in Fig. 5. The swelling pressure increased linearly with the misture cntent increase with the rate f 125 kpa kg kg -1. Cmparisn f the tw experimental relatins fr very clse values f the initial misture cntent presented in Fig. 5, indicates that the swelling pressure is strngly influenced by the initial misture cntent f grain. Anther factr influencing the value f the swelling pressure 10 Vertical pressure, kpa v u = 0, 0.23, 0.5, 0.71, 0.81, 1.07, 1.24, 1.37, 1.6 * 10-2 = Radius, m Fig. 4. Radial distributin f vertical pressure v n the sil bttm as influenced by the misture cntent increase.

5 GRAIN PRESSURE IN A MODEL SILO 389 Mean lateral pressure, kpa n = = Misture cntent increase, u Fig. 5. Mean lateral pressure n n the sil wall as influenced by the misture cntent increase. was bedding structure f the grain created during the filling prcedure. The bedding structure influences the pre structure and distributin and, ultimately, permeability f the grain layer. Althugh the filling prcedure was exactly the same in each replicatin f the experiment, the bedding structure may have differed cnsiderably amng replicatins. This is the mst prbable reasn fr a relatively large variatin f the swelling pressure values amng replicatins f the test. The initial bulk density was the majr factr influencing swelling pressure. The results f the tests perfrmed n the mdel sil (small precmpressin - v = 10 kpa, =780 kg m -3 ) as cmpared t the results f the edmetric test (strng precmpressin - p=0.5 MPa, =835 kg m -3 [6]) indicate that the swelling pressure is strngly influenced by the initial cmpactin f the grain. The rate f swelling pressure increase btained in the edmetric test was abut 30 times higher than the rate f pressure increase btained in the mdel sil test fr the same range f misture cntent increase. The swelling pressure f wetted grain btained in this study shuld be treated as a lwer limit f a pssible swelling pressure increase. Tangent pressure t n the sil wall decreased linearly with the misture cntent increase (Fig. 6). Cndensatin f water n the sil wall during blwing wet air thrugh the grain decreases the wall frictin cefficient. Sftening f the kernel seedcat with an increase in the misture cntent is als an imprtant factr leading t a decrease in the tangent pressure. Sftening f the seedcat decreases bulk shear mdulus and, cnsequently, decreases tangent frces at cntact pints between kernels. Lateral t vertical pressure rati as influenced by the misture cntent increase was presented in Fig. 7. Initial value f the pressure rati after filling the mdel sil was 0.4 and slightly increased during precmpressin. Unlading f the grain after precmpressin resulted in an increase in the pressure rati t abut Increase in the value f the pressure rati was the result f the vertical pressure relaxatin and nt the relaxatin f the lateral the pressure due t the rigid sil wall. This value f pressure rati can be reduced t its initial value during next cycle f lading. Swelling f grain clsed in a cnstant vlume can be treated as the next cycle f external lading. Accrding t the Eq. (4), cmpactin due t external lading and swelling f grain due t water absrptin are the tw independent cmpnents f vlumetric strain prducing the same effects. Therefre, swelling f grain influences the pressure rati in a similar

6 t 390 J. HORABIK, M. MOLENDA Tangent stress, kpa = = Misture cntent increase, u Fig. 6. Tangent pressure t n the sil wall as influenced by the misture cntent increase. 0.8 Lateral t vertical pressure rati = = Misture cntent increase, u Fig. 7. Lateral t vertical pressure rati as influenced by the misture cntent increase. way as the next cycle f external lading. The lateral t vertical pressure rati decreased with the misture cntent increase r swelling f grain resulted in faster increase in the vertical rather than the lateral pressure. The analytical mdel prpsed in this paper is based n tw elementary reactins f kernels t water additin: swelling f kernels and decrease in their elasticity with the misture cntent increase prperly predicts the swelling pressure in the range f the misture cntent increase f up t This range f the misture cntent increase may ccur during accidental wetting by ambient air. The mdel can be used t predict hygrscpic lads in grain strage sils if it is equipped with apprpriate experimental values f the effective elastic mdulus and shear mdulus. Effective elastic mdulus f grain in bulk expressed as the pwer functin f cnfining pressure and decreasing with the misture cntent increase reflects real cnditins f cmpressin between kernels in cntact. Frm the basic assumptins n the frce between spheres in cntact accrding t the Hertz s thery, it can be cncluded that the effective shear mdulus f grain in bulk

7 GRAIN PRESSURE IN A MODEL SILO 391 shuld depend n the misture cntent and the cnfining pressure in the same way as the bulk mdulus f grain elasticity. The stress-strain equatins fr a unit element f grain in bulk may be written in terms f the bulk mdulus f elasticity, K, and the effective shear mdulus, G: 2 ij 2Gij K Gv ij 3 (6) where: G - effective shear mdulus f grain in bulk (MPa), ij - Krnecker symbl, ij - strain, ij - stress (MPa), and the Eq. (4) relates the cnfining pressure, p, the misture cntent increase, u, and vlumetric strain, v. The swelling pressure in the grain sil can be calculated by slving stress equilibrium equatins in the lateral and vertical directins. The sil parameters, grain in bulk parameters, swelling mdel parameters (Eq. (4)) and bundary cnditins: wall stiffness (in the lateral directin) and frictin f grain against wall (in the vertical directin) are necessary t predict the swelling pressure in a particular case f a grain sil. SUMMARY A number f factrs, sme f which are prly defined, influence the characteristics f pressure increase during wet air flw thrugh the grain in a sil. This is the reasn fr the incnsistency f experimental findings reprted by varius authrs. Satisfactry replicability f experimental results requires precise replicatin f initial cnditins such as: grain misture cntent, humidity f air passing thrugh the bedding, temperature f passing air and ambient air and spatial structure f bedding. The mdel prpsed in this article allws fr the determinatin f pressure increase in a unifrm bedding and strictly established experimental cnditins. In such a way, an extreme swelling pressure n the sil structure during grain wetting can be determined. A wide range f lad variability, hwever, can be expected in the practical cnditins f a farm sil, where the influencing factrs vary in a wide range f values and cannt be accurately cntrlled. Swelling pressure f wetted grain is strngly influenced by its precmpressin histry. The maximum value f the swelling pressure f wheat grain btained after strng precmpressin ( =835 kg m -3 ) was fund t be apprximately 0.17 MPa and ccurred fr the misture cntent increase f 0.2 [6]. Pressure increase in a range f abut 2 kpa fr the increase in the misture cntent f btained after small precmpressin f grain in the mdel sil ( = 780 kg m -3 ) presents a lwer limit f the swelling pressure. Neither distributin nr value f the swelling pressure is unifrm and they depend n the path f wet air mvement. CONCLUSION Superpsitin f the tw basic reactins f kernels n water absrptin, i.e., swelling f kernels and decrease in their elasticity, allws t predict vlumetric strain f grain in bulk as a functin f cnfining pressure and misture cntent increase. Effective bulk mdulus f grain expressed as a pwer functin f cnfining pressure reflects real cnditins f cmpressin between kernels. The mdel prperly describes the swelling pressure in the range f the misture cntent increase f up t The mdel can be used t predict hygrscpic lads in grain strage sils if they are equipped with apprpriate experimental relatins f the effective elastic mdulus and shear mdulus as the functins f cnfining pressure and misture cntent. REFERENCES 1. Blight G.E.: Swelling pressure f wetted grain. Bulk Slids Handling, 6(6), , Brittn M.G., Zhang Q., McCullagh K.: Misture induced vertical lads in mdel grain bin. ASAE Paper N , St. Jseph, MI, Dale A.C., Rbinsn R.N.: Pressure in deep grain strage structures. Agricultural Eng., 35(8), , Glenn G.M., Yunce F.L., Pitts M.J.: Fundamental physical prperties characterizing the hardness f wheat endsperm. J. Cereal Sci., 13, , Hrabik J., Mlenda M.: Mdelling pressure increase f wetted grain. Prc. 9th. Seminar Prperties f water in fds, Zakpane, 56-61, 1998.

8 392 J. HORABIK, M. MOLENDA 6. Hrabik J., Mlenda M.: Experimental investigatins f pressure increase f wetted grain. Prc. 10th Seminar Prperties f water in fds, Muszyna- Z³ckie, 64-72, Kebeli H.V.: The effects f changes in grain misture cntent n the lads in grain bins. M.Sc. Thesis, University f Flrida, Lewer O.J., Bridges T.C., Bucklin R.A.: On-farm drying and strage systems. ASAE Publicatin N. 9, St. Jseph, MI, Mhsenin N.N.: Physical Prperties f Plant and Animal Materials. 2nd Ed. Grdn and Beach Science Publishers, New Yrk, Timshenk S., Gdier J.N.: Thery f Elasticity. 3rd Ed., New Yrk, Hill, Waltn K.: The effective elastic mduli f a randm packing f spheres. J. Mech. Phys. Slids, (35)2, , WŸniak W.: The effect f misture treatment n mechanical prperties f wheat grain. Prc. 9th Sem. Prperties f water in fds, Zakpane, 62-70, Zhang Q., Brittn M.G.: Predicting hygrscpic lads in grain strage bins. Trans. ASAE, 38(4), , 1995.

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