Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 8
Issue 4
Agricultural Engineering
Available Online: http://www.ejpau.media.pl/volume8/issue4/art-67.html


Marek Molenda1, Józef Łukaszuk2, Józef Horabik2
1 Department of Physical and Technological Properties of Agricultural Materials, Institute of Agrophysics, Polish Academy of Science, Lublin, Poland
2 Institute of Agrophysics, Polish Academy of Sciences, Lublin, Poland



Airflow resistance of grains and oilseeds has been extensively studied. Traditionally the data has been presented assuming that airflow resistance is independent of grain depth. Grain undergoes compaction during storage that changes the porosity and airflow resistance. A study was conducted to estimate the degree of influence of filling method and grain moisture content on the airflow resistance of wheat column 0.95 m high and 0.196 m in diameter. Both the fill method and grain moisture content were found to influence the airflow resistance. Gravitational axial filling of the grain column resulted in an uneven distribution of airflow resistance along the height of the column.

Ergun’s equation was used to model experimental relationships between airflow resistance and air velocity. Results suggested that the equation with appropriate coefficients is capable to model the process adequately, and could be utilized for the design and analysis of grain aeration systems.

Key words: grain, airflow resistance, porosity, density, moisture content.


Commonly used methods of design of grain drying and aeration systems do not consider variability of airflow resistance in various regions of stored grain. In reality local changes of airflow resistance in various regions of bedding may cause variations in efficiency of technological operations comprising flow of gases such as: drying, aeration, cooling or fumigation. The main task of design of drying or aeration system is to define the operating airflow that in match with pressure-drop-air-velocity relationship will assure the desired course of designed process. Apart from air velocity, other factors were found to influence the resistance of the bedding to airflow and, consequently pressure drop.

Theoretical modeling of static-bed-drying of grain employs four variables [1]: mass flow rate of air, the air humidity ratio, the air temperature and the kernel temperature. In developing the mathematical model several simplifying assumptions have to be introduced one of those being that airflow through the grain is uniform and one dimensional, with no transfer in transverse direction. However, moisture and temperature distribution in a bin is generally non-uniform in practical storage conditions. Thus for aeration control location of humidity and temperature probe is recommended in the area with the least airflow, typically in the center of the bin about 30 cm under the grain surface [1]. The goal is to assure safe storage environment everywhere in the bin rather than just on average conditions for the bin as a whole. According to the authors of “The mechanics and physics of modern grain aeration management” [9] the airflow resistance calculated from recommended equations or read from figures are for loose-filled, clean, dry grain with airflow in vertical direction and in general give a conservative estimate. The authors recommend that magnitudes of increase or decrease in such obtained airflow resistance must be determined experimentally. They also point out that the performance efficiency of an aeration system depends primarily on the uniformity of the airflow distribution in different regions of grain bed.

In experimental investigations first density (interrelated with porosity) was recognized as a factor determining resistance to airflow through the layer of grain. Then the influence of the content of fine material was examined because it decreased amount void space among grains increasing airflow resistance. Stephens and Foster [10] in their experiments with corn in commercial bin found the increased resistance to airflow of up to 300% when using grain spreaders as compared to that when no spreader was used. These same authors [11] conducted similar test program with wheat and grain sorghum. Filling the bin with the grain spreader produced airflow resistances 110% greater in sorghum and 101% greater in wheat than those produced by filling from the central spout. The authors suggested that possible reason for observed increase in bulk density and resistance to airflow could be in part compaction due to an action of spreader, while in grains with higher amounts of fine material, part of the increase arose from fine material occupying spaces between whole kernels.

Direction of airflow also appeared to influence resistance of the bedding to airflow. Kumar and Muir [6] found that at an air velocity of 0.077 m/s resistances to vertical airflow compared with horizontal airflow were up to 60% higher for wheat and 115% for barley. Based on air velocity of 0.077 m/s airflow resistances for layer filling were higher than for end filling by 25 to 35% for vertical airflow and 50 to 75% for horizontal airflow. Hood and Thorpe [4] found that for the velocity range up to 0.2 m/s and for ten grains the resistance to airflow in the vertical direction was about double that in the horizontal. These authors indicated that conventional engineering analyses that consider resistance to be isotropic overestimate the pressure drop across aerated grain bulks.

Pressure drop data for airflow through agricultural products are usually presented as curves or equations [1, 9]. One of frequently applied relationships is Ergun‘s equation Based on Reynold’s theory of resistance to fluid flow Ergun [2] hypothetized that the pressure drop was the summation of the viscous and kinetic energy loses. Ergun’s general equation for uniform products can be written as [7]:

deltaP = pressure drop (m),
deltaL = length (m),
V = superficial air velocity (m/s),
a, b = product dependent coefficients,
mu = viscosity of air (N/m×s),
p = volume equivalent particle diameter (m),
epsilon = porosity (dimensionless),
rho = density of air (kg/m3).

Giner and Denisienia [3] measured the pressure drop through wheat as a function of air velocity, moisture content and fines. They found that Ergun’s equation provided a better estimate of the pressure drop data than Shedd’s or Hukill and Ives’ equation. Molenda et al. [8] used Ergun’s equation to predict the pressure drop through column of three types of grain at three moisture content levels. These authors concluded that the data collected indicated that Ergun’s equation could be successfully applied to grain aeration design and analysis. Following approach of Giner and Denisienia [3] for the simplicity of use factors other than velocity in the equation 1 will be lumped in two parameters also in our analysis.

The objective of the research reported in this article was to examine range of variability of airflow resistance of wheat generated by variation in grain moisture content and method of formation of the bedding (filling procedure).


The system used for measuring airflow resistance is shown in figure 1. A cylindrical acrylic plastic pipe with a diameter of 0.196 m and a height of 1.08 m was used to hold the grain during the testing procedures. Air was introduced through a plenum in the bottom of the cylinder. The differential static pressure was measured at a distance of 0.95 m. Four taps evenly distributed along the column circumference were mounted at the both levels and each four connected to average possible pressure fluctuations. In the case of testing longitudinal distribution of airflow resistance three more levels of air taps were used that were evenly distributed between the two (see figure 6). Variable reluctance pressure transducer with accompanying equipment (Validyne DP45, Northridge, CA) with a diaphragm with a maximum pressure rating of 2.25 kPa and an accuracy of ±0.25% full scale was used to measure pressure drop. Leaving the column the air flew through outlet air plenum and through the 0.05 m diameter outlet duct in that air velocity was measured. Commercial hot-wire anemometer (ANT 2000) was used to measure air velocity in a range from 0 to 30 m/s with a resolution of 0.1 m/s. Airflow resistance versus air velocity relationships were determined for apparent velocity in a range from 0.03 to 0.4 m/s. Two replicates of the air-velocity-pressure-drop curve were performed for each variant of experiment (with emptying end refilling the column) and results averaged.

Figure 1. Schematic of apparatus for measuring airflow resistance in seeds

Three methods were used to fill the grain column as shown in figure 2. The loosest filling was termed “A filling method” and was accomplished using a funnel that was kept within 2 cm of the grain surface during filling. In this case the grain during filling formed a conical sloping surface with the vertex directed upward and the grains tending to rest with their long axes along a line of the formed cone. To obtain a higher bulk density the outlet of the conical filling hopper was located at the top of the grain column (method “B”) or at the height twice of that of grain column (method “C”). After filling the column, the grain was weighed using a digital scale and the bulk density was calculated.

Figure 2. Methods used to fill the grain column using a funnel filling method and stream filling methods from two heights

To obtain prescribed higher densities the test column after funnel or hopper filling was placed on vibrating table and shaken with frequency of 15 Hz and amplitude of 10 mm.

Influence of grain moisture content and porosity on airflow resistance was tested with winter wheat of initial moisture content of 10.2% (wet basis) and uncompacted bulk density of 736 kg/m3. Testing of an influence of filling method on airflow resistance was performed with winter wheat of initial moisture content of 11% and uncompacted bulk density of 773 kg/m3.


Moisture content and consolidation by vibration. Figure 3 presents pressure drop for wheat at four levels of moisture content: 10.2, 13.4, 15 and 19% using funnel filling A. No distinct differences in airflow resistance were observed for the grain samples of the 10.2, 13.4 and 15% in moisture content. Porosities of these samples were of 43, 44 and 45%, respectively, not markedly different as well. The sample of grain of 19% moisture content posed distinctly lower airflow resistance than the three drier samples. At air velocity of 0.4 m/s it was of 0.81 kPa/m or 0.58 of the highest value of pressure drop of 1.39 kPa/m found for grain of 10.2% moisture content. The observed ramp down in airflow resistance was a result of an increase in porosity, which for 19% in moisture content grain was found of 47%. The probable reason for the increase in porosity was higher than proportional increase in coefficient of intergranular friction. Horabik and Molenda [5] found in their testing on wheat kernels that the coefficient of friction against glass increased from 0.116 to 0.134 (or of 0.18) with an increase in moisture content of 7% (from 8 to 15%), while further increase in moisture content of 3% (to 18%) resulted in an increase of coefficient of friction to 0.154 (or of 0.2). The authors indicated softening of wheat grain as a main reason for the observed effect.

Figure 3. Airflow resistance of wheat bedding formed using funnel filling (method A) at four levels of moisture content

Figure 4. Airflow resistance of wheat at four levels of moisture content compacted by vibration to common porosity of 43%

The samples of grain filled with method A (except the driest one) after testing for airflow resistance were compacted by vibration up to common porosity of 43% and tested again. The pressure drop versus air velocity relationships of compacted samples are shown in figure 4. Common level of porosity of all samples would suggest equal level of airflow resistance. However tendency was observed that wetter the sample higher the increase in pressure drop. At 0.4 m/s pressure drop in 19% m.c. sample was found equal to 1.78 kPa/m in a factor of 2.2 as compared to uncompacted sample (see figure 3). The effect of difference in airflow resistance at the same level of global porosity of tested samples may be attributed to uneven porosity within grain column. Wetter grain was more susceptible for deformation and when vibrated might form very dense packing in certain area of the column that increased airflow resistance of the whole column. The effect requires further testing. Values of density and porosity of tested samples are shown in table 1.

Table 1. Moisture content (wet basis), bulk density and porosity of wheat used for testing. Estimated parameters a and b of equation (1) and coefficients of determination (R2)

Moisture content

(kg× m-3)















































11 A






11 B






11 C






Figure 5. Airflow resistance of 11% of moisture content wheat sample formed using three filling methods

Height of axial filling. Influence of filling method on airflow resistance is presented in figure 5. Filling methods A, B and C produced samples of densities: 773, 790 and 810 kg/m3, respectively. Higher kinetic energy of grain falling from higher height produced grain bedding of higher bulk density. Increase in sample density resulted in an increase in airflow resistance, at air velocity of 0.4 m/s pressure drop for the least dense sample was found of 1.5 kPa/m while for the densest sample it was equal to 2.15 kPa/m. Thus the 1.047 increase in sample density resulted in 1.43 times increase of pressure drop.

Estimation of Ergun’s coefficients. Table 1 lists the values of a and b in equation 1 that were determined using regression procedure performed with the data in figures 3, 4 and 5. Uncompacted samples resulted in a range of values for a from 1200 to 630, and for b from 6420 to 3680. Giner and Denisenia [3] reported for wheat at moisture contents from 12.8 to 19.4% a decreasing from 3220 to 2640, ad b decreasing from 8470 to 7700. Considering that these authors were using wheat of markedly higher bulk density than this study (of 859 kg/m3 at moisture content of 12.8%) results may be treated as similar. Compaction of the bedding resulted in distinct increase in b, particularly high, from 3680 to 9230, in the wettest sample. Parameter a increased much less, in order of 300 compared to initial value of approximately 1000. Testing on 11% in m.c. wheat with three filling methods have shown that both a and b increased with an increase in bedding density, but approximately twofold increase in a was particularly high. Observed change in values of the parameters was comparable to that generated by changes in moisture content in samples formed using one filling method.

Longitudinal distribution of airflow resistance. Values of pressure drop calculated for laboratory experiments are related to the length of grain column and do not bring information about distribution of pressure drop along the column. Figure 6 shows pressure drop at air velocity of 0.3 m/s measured in four sections of grain column in the case of grain bedding formed by three filling methods. The earlier observed tendency that higher density and higher pressure drop was found for higher height of grain fall was confirmed in these tests. In the case of methods B and C higher pressure drop was found for sections of grain column situated lower. This effect is a result of higher kinetic energy of grains reaching free surface of grain column and, possibly pressure of layers of higher layers of grain. In the case of method C the highest pressure drop observed in the lowest section of the column was approximately 1.18 higher than the lowest found in the highest section. In the case of filling method A no clear differences in pressure drop were observed in different sections of grain column. Method A was quasi – static filling through the funnel moving slowly up, thus grains had very low kinetic energy that did not change during filling the column. The ratio of the highest to the lowest pressure drop for tests results in figure 6 was found of 1.65.

Figure 6. Airflow resistance at air velocity of 0.3 m·s-1 for wheat bedding, formed by the three filling methods, measured in four fragments of the column

Figure 7. Airflow resistance at air velocity of 0.3 m·s-1 for wheat bedding formed by filling methods A and C and vibrated, measured in four fragments of the column

Compaction of the bedding by vibration resulted in an increase of airflow resistance as shown in figure 7 for filling methods A and C and for air velocity of 0.3 m/s. Pressure drops after vibration for the bedding in particular sections of the column were found approximately equal, thus the highest increase in pressure drop occurred in the highest quarter of the column. The ratio of pressure drop after and before vibration was found 1.34 and 1.29 for C and A filling methods, respectively. Vibration, as applied in reported project resulted in an increase of airflow resistance in an order of 30% but did not eliminate the influence of filling method. Originally denser sample gained after vibration more airflow resistance than originally looser sample.


Airflow resistance in the bulk of cereal or pulse crops is an important factor in a modern conservation and quality control technology. Air distribution in an ensiled crop controls efficiency of drying, aeration, chilling by refrigerated air and fumigation. In general air distribution within ventilated bed of seeds is not homogenous and depends on amount and geometry of free air space. The reported project examined the effects of a method of formation of a bedding on its resistance to the airflow through the bedding of wheat.

Different filling methods of test column produced packing structures of various density ranging and porosity that resulted in considerable variability of airflow resistance. Axial gravitational filling methods with dry grain falling from the height from 0 to 2H above the column floor produced beddings of density from 773 to 829.9 kg/m3 and maximum pressure drop at v = 0.4 m/s ranging from 1.5 to 2.15 kPa/m i.e. of a factor of 1.43. Observed increase in airflow resistance was a result of increase in bedding density as a consequence of higher kinetic energy of grains falling from higher height.

An increase in moisture content of grain resulted in an increase in porosity and decrease in airflow resistance of the samples. For samples of moisture contents of 10.2, 13.4, 15 and 19% decrease in airflow resistance between levels of 15 and 19% was particularly high, found from 0.81 to 1.39 kPa/m at v = 0.4 m/s. Consolidation of axially filled samples by vibration to common porosity of 43% resulted in strong increase in airflow resistance that was particularly distinct in the case of 19% in m.c. sample when increase from 0.81 to 1.78 kPa/m or of a factor of 2.2 was found. Despite of equal global porosity of grain samples of different moisture contents airflow resistance was found varying from 1.38 to 1.78 kPa/m (v = 0.4 m/s). The probable reason of this effect was higher compressibility and friction of wet grain that resulted in stronger compaction in lower region of the column.

In the tests with axial gravitational filling with dry grain airflow resistance increased from 0.24 kPa/m to 0.4 (or at a factor of 1.7) with an increase in the height of fall of grains. Airflow resistance varied also along the height of the grain column where, in the case of the highest location of outlet of filling container it was found increasing from 0.34 to 0.4 kPa/m. Consolidation of the bedding through vibration brought about equalization and increase of airflow resistance up to 0.45 kPa/m, i.e. in a factor of 1.3 as compared to the lowest value of 0.34 kPa/m.

Two parameters Ergun’s equations well fitted the experimental results in a relatively large air velocity range. The parameter of the quadratic term a was about five times higher than b that of the linear term. Relatively high ratios of the maximum to the minimum values of parameters found 3.3 and 2.3 for a and b, respectively points out to possibility of efficient use of the equation in design of drying and aeration systems.


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  8. Molenda M., Montross M.D., McNeill S.G., Horabik J., 2005. Airflow resistance of seeds at different bulk densities using Ergun’s equation. Trans. ASAE 48(3), 1137-1145.

  9. Navarro S., Noyes R., 2002. The mechanics and physics of modern grain aeration management. CRC Press.

  10. Stephens L.E., Foster G.H., 1976. Grain bulk properties as affected by mechanical grain spreaders. Trans. ASAE 19(2), 354-358.

  11. Stephens L.E., Foster G.H., 1978. Bulk properties of wheat and grain sorghum as affected by a mechanical grain spreaders. Trans. ASAE 21(2), 1217-1221.

Marek Molenda
Department of Physical and Technological Properties
of Agricultural Materials, Institute of Agrophysics,
Polish Academy of Science, Lublin, Poland
Do¶wiadczalna 4,
P.O. Box 201, 20-290 Lublin 27, Poland

Józef Łukaszuk
Institute of Agrophysics,
Polish Academy of Sciences, Lublin, Poland
Do¶wiadczalna 4, 20-290 Lubln 27, Poland
phone: (+48 81) 744 50 61
fax (+48 81) 744 50 67

Józef Horabik
Institute of Agrophysics,
Polish Academy of Sciences, Lublin, Poland
Do¶wiadczalna 4, 20-290 Lubln 27, Poland
phone: (+48 81) 744 50 61
fax (+48 81) 744 50 67

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