Pressure Drop Through Wheat as Affected by Air Velocity, Moisture Content and Fines

J. agric. Engng Res. (1996) 63, 73 – 86

Pressure Drop Through Wheat as Affected by Air Velocity, Moisture Content and Fines S.A. Giner;*†‡ E. Denisienia* * Centro de Investigacio´ n y Desarrollo en Criotecnologı´a de Alimentos (CIDCA). Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Calle 47 y 116 (1900)-La Plata, Provincia de Buenos Aires, Argentina † Facultad de Ingenierı´a, Universidad Nacional de La Plata ‡ Researcher of the Comisio´ n de Investigaciones Cientı´ficas de la Provincia de Buenos Aires, Argentina (Receiy ed 9 January 1995; accepted in rey ised form 2 September 1995)

Pressure drops were measured in clean wheat beds for superficial air velocities up to 0?42 m / s at grain moisture contents in the range of 12?8 – 22?3% w.b. At 12?8% moisture content, pressure drops were determined in wheat for fines contents up to 10?60% (w / w). It was found that pressure drops decreased by up to 30% with moisture content and increased with fines by up to 75%. The selection of a model was made using the results of clean grain. A Shedd-type equation (model 1), the Hukill & Ives’ equation (model 2), and an Ergun-type equation (model 3), all of two parameters, were examined. Model 3 behaved better than model 2 and both gave lower errors than model 1. Model 3 was simplified by considering the parameter of the quadratic term as a multiplier of that of the linear term. The resultant expression (model 4) behaved better than model 2 and was called the approximate, Ergun-type equation. With this model, the non-linear influence of grain moisture content was better predicted than with a linear model proposed previously. With regard to the effect of fines, the use of model 4 permitted a linear relationship between pressure drop ratio and fines content that was independent of air velocity, a feature that was substantially adequate to describe the experimental results. Model 4 is suggested for further work on the resistance to airflow of grain beds. ÷ 1996 Silsoe Research Institute

sufficiently low temperature to avoid microbial and insect growth.1 In near ambient dryers,2 forced air is necessary to remove the moisture from the grain whereas in hot-air drying,3 the airflow is used both to provide the heat of vaporisation of moisture and to take the humidity thus produced out of the grain bed. The basis of the design of aeration systems lies in the knowledge of the pressure-drop – air-velocity curves of bed and ducts to establish relationships that can be matched with those of fans,4 so as to define the operating airflow. Apart from air velocity, other variables affect the pressure drop5 such as grain moisture, fines content, bulk density and direction of airflow. The effect of moisture on pressure drop needs to be considered because of the increasing use of aeration of high moisture grain6 and of the need to calculate non-linear air streamlines in beds with grain moisture gradients, as shown by Mao and Nellist.7 On the other hand, fines contents can lead to pressure drops twice as much as those of clean beds8 or even higher, so its influence must be assessed. Previous studies carried out to evaluate the effect of fines and moisture content were made for grains such as maize.8,9 In these studies, authors generally found that increased fines content led to higher pressure drops but they have different opinions on whether the effect of fines changes with velocity or not. With regard to the effect of moisture, most authors found a decrease in pressure drop with increasing moisture content, though such results are in conflict with those obtained by Patterson et al .10 for maize, who observed that pressure differences increased with increasing moisture content. For wheat, Shedd11 reported pressure drops at different airflows for clean, dry grain with a loose fill and also made a limited study of the effect of moisture

1. Introduction Design of aeration systems for wheat storage and drying is an important stage in the construction of such equipment. In storage bins, aeration is necessary to maintain the previously dried grain at uniform and 0021-8634 / 96 / 010073 1 13 $12.00 / 0

73

÷ 1996 Silsoe Research Institute

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S. A. GINER ; E. DENISIENIA

content. Kumar and Muir12 studied the airflow resistance as affected by the airflow direction, filling method and small proportions of waste materials, but not moisture. On the other hand, Haque et al .13 measured pressure drops in beds of wheat, maize and grain sorghum at several moisture contents and found a decrease of pressure drop with increasing moisture content. They represented the results by a two-term Ergun-type equation to which a third term was added to include a linear influence of moisture content. The literature offers limited coverage on the pressure drop of wheat at several grain moisture contents and on how pressure drop through wheat beds is affected by fines contents. Recent work by Li and Sokhansanj14 on wheat and other seeds showed perhaps a move towards the use of equations with a better physical basis in pressure drop studies and these may result in a better understanding of the many and interactive factors affecting pressure drop. They used the full form of the Ergun15 equation to evaluate the influence of moisture content, and fines. However, such work showed that there was a need to improve the calculation of grain density and particle diameter, especially in beds of grains mixed with fines, before a generalized equation can be used for design purposes at low airflows. Therefore, besides the need for more experimental evidence on how moisture content and fines affect pressure drops in wheat beds, intermediate approaches with simplified, yet physically well founded models are also needed. The object of this work was (1) to determine pressure drops of wheat at several moisture contents and, for dry grain, at several fines contents; (2) to select a simple model, preferably based on the Ergun equation, to quantify the effect of air velocity, moisture content and fines.

2. Materials and methods 2.1. Materials Wheat cv. ‘‘Prointa, Isla verde’’ grown during the 1993 / 94 season at Pergamino, Argentina was used. Grains were harvested after natural field drying and received in four 50 kg bags as ‘‘seed free from broken grains and foreign material’’ according to a national classification.16 Mean moisture content at reception was 12?9% w.b. (hereafter, moisture content will be expressed on a wet basis). Immediately after reception, the content of each bag was transferred to corresponding sealed polyethylene bags and placed in a cold store at 08C.

For the study of the effect of fines on pressure drop, ‘‘wheat reject’’ was also provided as a source of fines. The ‘‘reject’’ is defined as the material separated from clean whole grains larger than a minimum size. From this material, we prepared ‘‘fines’’, defined as the material that will pass through a 9?5 mm 3 1?6 mm rectangular hole sieve, according to a standardized procedure.17

2.2. Determination of moisture content Grain moisture contents were determined by the ASAE method18 (whole grains heated at 1308C for 19 h in an air oven). Triplicate determinations were made in all cases.

2.3 . Grain conditioning For the study of the effect of moisture content on pressure drop of clean wheat, source samples of 50 kg were used for each moisture level. Bag 1 was left at its original moisture content of 12?8% Bags 2, 3 and 4 were moistened to 16?2%, 19?4% and 22?3%, respectively by adding tap water to grains and thoroughly mixed in a rotating drum. The material was then transferred again to sealed polyethylene bags and placed in the cold store at 08C for a minimum of 48 h before use, so as to ensure adequate moisture distribution. For proper water absorption, moistening of bag 3 was made in two stages, with a 3 h intermediate tempering period. Likewise, grains from bag 4 were moistened in three stages. Samples thus prepared were used for duplicate determinations of the pressure drop versus air velocity curves (and bulk density ‘‘in situ ’’), for determinations of kernel density and volume, and for measuring kernel dimensions. The procedure ensured that all experiments were carried out at the same moisture levels.

2.4. Determination of kernel density and y olume , and bulk density For kernel density and volume, hand-counted samples of 500 grains were poured in a 250 ml picnometer, and Xylene (Mallinckrodt AR) was used as picnometric liquid. Grains were weighed in an analytical balance and the picnometer in a precision

PRESSURE DROP THROUGH WHEAT AS AFFECTED BY AIR VELOCITY

digital balance. Triplicate determinations were made in all cases. Bulk densities were determined by weighing the amount of grain needed to fill the pressure drop column (see Section 2.7.) in a digital balance. For comparison purposes, some determinations were also made in a 500 ml matrass.

2.6. Preparation of bulks of grain mixed with fines For the study of pressure drop as a function of fines, we prepared four samples by mixing clean grain of bag 1 (12?8% moisture) with increasing amounts of fines (14?4% moisture) in a rotating drum. The proportion of fines in the samples expressed as kg fines per 100 kg mixture (hereafter ‘‘% fines’’) were : 2?86 (12?81); 5?65 (12?85); 8?42 (12?90) and 10?60 (12?92), the moisture content of the mixtures being indicated in parenthesis.

2.5. Measurement of kernel dimensions The three major axes of the grain were measured with a caliper. To minimize measuring errors, wheat kernels were stuck on to white adhesive paper to observe their lengths and widths in plan view. A 100% amplified photocopy of such a view was obtained and lengths and widths measured on the copy, thus reducing measuring errors. The thicknesses of the same kernels were previously measured directly, since this dimension was not suitable for the technique described. Duplicate determinations (50 grains at each moisture level) were made.

2.7 . Pressure drop experiments 2.7 .1 . Apparatus Fig. 1 shows a diagram of the equipment. The 1?5 kW, 2800 rev / min centrifugal fan (A) is preceded by a manual diaphragm valve (B). To avoid unstable airflows through the fan when low airflows were required in the grain bed, a manual bleed butterfly valve (C) was installed. To avoid propagating vibra-

G1

H Outlet air

G

0·194m

J1

1·00 m

L F Grains

J2

K

E

M

I

B

Inlet air D

A N

75

C

Fig. 1 . Apparatus for pressure drop experiments

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S. A. GINER ; E. DENISIENIA

tions, a flexible rubber tube was used to connect the fan to the test column. The flow was conducted to the inlet air plenum (D) to create a uniform velocity profile. To assist this effect, the air was passed through a perforated metal sheet with 1?5 mm diameter holes and 23% open area before entering a gradual contraction (E) before the test column (F), the supporting base of which was a perforated metal sheet similar to that already described. The test column (F) consisted of a transparent acrylic cylinder 1?20 m long and 0?194 m internal diameter. Pressure taps, made as suggested in Perry,19 were located immediately below the column base and, above it, at 1 m. At both levels, two opposite pressure taps were connected to obtain average values. The column diameter exceeded the minimum of 20 particle diameters20 required for scaling up results. The bed depth (1 m) was sufficiently deep to give large pressure drops which are necessary for accurate determinations at low airflows. After the column, the air flowed towards an outlet air plenum (G) before entering the 0?05 m diameter outlet air tube (H). This tube allowed for measurement of much larger air velocities than those of the column, reducing the measurement errors of the digital hot-wire anemometer (I). Low (0 – 10 mm H2O) and medium (10 – 25 mm H2O) pressure drops were measured with analogue pneumo-magnetic micromanometers (J1 and J2, respectively). Once pressure drops exceeded their corresponding maximum measuring capacity, they were protected by closing spherical valves located beside them. Larger pressure drops were determined by a U tube (K) filled with distilled water and inclined at the desired angle. Instruments were mounted on a panel (L), and the whole apparatus on a framework (M), its base being adjustable (N) to ensure that the main axis of the column was vertical. 2.7.2. Experimental procedure In all experiments, grain was removed from the cold store and left at room temperature for 24 h before pressure drop determinations. Grains were loaded into the column using a pneumatic conveying system powered with an industrial vacuum cleaner (not shown in Fig. 1 for clarity). Grains entered the tube (H) and fell into the column from distances varying from 1?50 m (empty column) to 0?5 m (full column). On loading grain, the conveying airflow escaped through the point G1. Bulk density and porosity values shown later in this work (see Section 3.1) suggested a dense packing, a fact that can be attributed to the method of filling21 because the grains had a definite initial velocity at the

point of entry and were not totally dispersed in the fall. In this regard, results obtained should be safer for design, since pressure drops are higher in dense packed beds. The same filling procedure was used in all experiments. Once the column was filled, and the lid (G1) sealed, the fan was switched on, the diaphragm valve (B) partially opened and air temperature was allowed to stabilize with the bleed butterfly valve (C) fully open , i.e. no flow through the column. After this, pressure drop determinations were performed at increasing velocities, their values being the same in all experiments to make data processing and subsequent comparisons easier. An increase of air velocity, at low values, was achieved by closing gradually the bleed butterfly valve (C). Once it was totally closed, greater values were obtained by enlarging the aperture of the diaphragm valve (B). By using this procedure, a reasonably large velocity range was attained without unstable fan operation and noticeable air heating. Two replicates of the air-velocity – pressure-drop curve were performed at each moisture content level (with intermediate column emptying and refilling) and the results averaged. Air temperature determined during the eight duplicate runs was 22?78C Ú 1?68C and the average relative humidity, as determined with an electric hygrometer, was 57?2 Ú 3?8%.

3. Results and discussion

3.1 . Characterization of grains

Table 1 shows kernel dimensions, volume and density (r k), bulk density (r b) in the pressure drop column and bed void fraction (» ) at the same moisture contents (M ) as those of the pressure drop experiments. The bed void fraction was calculated as

» 512

rb rk

(1)

Values at M 5 0 were obtained on samples dehydrated in two stages, first at 408C for 24 h and then at 1308C for 19 h, to avoid excessive shrinkage. Unlike the other samples, the bulk density of the M 5 0 sample was determined in a 500 ml matrass, so we checked whether or not values thus measured were comparable with those of the pressure drop column. Grains at 12?8% moisture were used for this comparison and determinations were made with and

77

PRESSURE DROP THROUGH WHEAT AS AFFECTED BY AIR VELOCITY

Table 1 Results from determinations performed to characterize the wheat used in this study Moisture content , M , % w.b. 0 12?8 16?2 19?4 22?3

Kernel dimensions , mm ————————————————— Length Width Thickness n.d. 6?08 6?41 6?46 6?52

n.d. 3?00 3?07 3?27 3?40

Kernel

y olume , mm 3 22?5 24?8 26?3 28?2 30?9

n.d. 2?82 2?86 2?91 3?02

without vibration. We found that the vibrated i.e. densely packed 12?8% moisture sample gave a bulk density almost equal to that of the pressure drop column, so vibration was used for the M 5 0 sample and the result is included in Table 1. The difference between bulk densities with and without vibration was about 8%. Table 1 also shows that, as expected, grain dimen-

Kernel Bulk density , density , r k , rb , Bed y oid fraction , » kg / m 3 kg / m 3 1310 1330 1300 1280 1280

806 859 811 786 776

0?383 0?356 0?374 0?387 0?393

sions and hence kernel volume increase with moisture content. On the other hand, kernel density increases in the low moisture zone and then decreases for higher moistures, showing a complex behaviour also observed by Nelson22 in another wheat variety. The results for r k could also explain the behaviour of the bulk density (r b) and » in Table 1, since they are related as shown by Eqn.(1).

3000 300

3500

200

100

Pressure drop, Pa/m

2000

0 0·00

0·02

0·04

0·06

0·08

1500

1000

500

0 0·00

0·10

0·20

0·30

Air velocity, m/s

0·40

0·50

Fig. 2. Main graph. Experimental pressure drop per unit of bed height as a function of air y elocity for the following moisture contents (% , w.b.): ( s) 12?8% , ( x) 16?2% , ( =)19?4% , ( .) 22?3%. Inset graph . Values at low airflows and low pressure drops in magnified scale

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However, r b and therefore » , are also affected by the degree of packing of the bed, which is in turn influenced by the method of fill, as seen in the previous section. In this regard, bulk densities were higher, and hence void fractions lower, than those of Haque et al .13, and Li and Sokhansanj,14 but the differences were of the same order as those encountered here between dense and loose packed samples. 3.2. Pressure drop through clean wheat y ersus air

y elocity at different moisture contents

3.2.1. Experimental data Fig. 2 shows the pressure drop as a function of the superficial air velocity (hereafter air velocity) for the four levels of moisture content analysed in clean grain. At each moisture level, it can be seen that pressure drop increased with air velocity and that, at each velocity, the pressure drop decreased for increasing moisture content. Results of 12?8% moisture grain are comparable, but somewhat higher, than those of Shedd,11 possibly because of our dense packing and of differences in grain variety. The overall trend is similar to that obtained previously by Haque et al .13 for another wheat variety, although data of the present paper was measured in wider velocity and moisture content ranges. Comparison between pressure drops obtained here at the highest and lowest moisture contents showed, at 0?21 m / s air velocity, a reduction of 30% in pressure drop. A similar comparison using results of Haque et al .13 but at 0?15 m / s resulted in a decrease of almost 40% in a slightly narrower moisture range. These trends held for other velocities, so the previous authors found a stronger influence of moisture content. They assumed that pressure drop decreased linearly when plotted against moisture content but their experimental results13 suggest that a non-linear dependence, stronger at higher moisture contents, could also have been proposed. Their model will be discussed at the end of the next section. 3.2.2. Selection of a model In order to interpret the results of Fig. 2 , three models, each containing two parameters were proposed. Model 1 is that of Shedd,11 who fitted data for several grains by considering the airflow to be a function of the pressure drop. Pressure drop (DP ) per unit of bed depth (L) is expressed as a function of air velocity (V ) as follows DP 5 A1 V B1 L

(2)

where A1 and B1, are constants (the nomenclature ‘‘model number’’ is used instead of the more precise ‘‘equation number’’ to avoid confusion with numbered equations). Model 2 is that of Hukill and Ives23 who proposed an empirical equation to improve predictions of model 1, given by DP A2 V 2 5 L Ln (1 1 B 2 V )

(3)

where A2 and B2, are constants. Model 3 is that of Ergun,15 who made a thorough study of the pressure drop versus air velocity relationship for particulate materials. He used particle sizes smaller than agricultural grains and developed an equation based on fluid-dynamic principles. Ergun’s model has two-terms, the first term being a linear function of air velocity and the second a function of V 2. Ergun’s model include the influence of the bed void fraction, particle diameter and of air density and viscosity. For simplicity of use, factors other than velocity can be lumped in two parameters for each agricultural grain, so model 3 becomes an Ergun-type equation24 of the form DP 5 A3 V 1 B 3 V 2 L

(4)

where A3 and B3, are constants. The three models were fitted to experimental values at each moisture level by using non-linear leastsquares regression solved by a quasi-Newton numerical method.25 Fitted parameters, their standard deviations [s (A1) , s (B 1) , etc.], correlation coefficients (r2) and standard deviation of the estimate (sy) are given in Table 2. sy expresses the average deviation between experimental and predicted values, and is defined as follows

Sy 5

—1

N

o (predictedi 2 experimentali)2

i 51

(N 2 2)

2

(5)

where N is the number of data points and (N 2 2) a the number of degrees of freedom. For this relatively large velocity range (lowest velocity in the column was 0?006 m / s), model 1 [Eqn. (2)] predicted with an average sy of 23?8 Pa / m (mean of values at the four moisture levels). Model 2 [Eqn. (3)] showed a better behaviour, with an average sy of 10?7 Pa / m, while model 3 [Eqn. (4)] was the best on average, with a mean sy of 8?1 Pa / m (i.e. less than 1 mm H2O / m). These results were also consistent with preliminary results for 12?2% moisture content wheat

PRESSURE DROP THROUGH WHEAT AS AFFECTED BY AIR VELOCITY

79

Table 2 Results of fitting equations to experimental pressure drop vs air velocity curves of clean wheat at several moisture contents Model 1 (Shedd 11) [Eqn.(2)] Moisture , % (w.b.)

A1

B1

s (A1)

s (B 1)

r2

s y, Pa / m

12?8 16?2 19?4 22?3

9100 8990 7680 6260

1?36 1?38 1?35 1?35

184 233 240 163

0?017 0?020 0?024 0?020

0?999 0?999 0?998 0?999

27?6 24?3 25?5 17?6

Model 2 (Hukill and Iy es 23) [Eqn .(3)] Moisture , % (w.b.)

A2

B2

s (A2)

s (B 2)

r2

s y, Pa / m

12?8 16?3 19?4 22?3

24000 26400 21200 19900

8?20 10?3 8?65 10?9

525 769 650 900

0?32 0?54 0?46 0?92

1 1 1 1

10?3 11?2 9?8 11?5

Model 3 (Ergun 24) [Eqn .(4)] Moisture , % (w.b.)

A3

B3

s (A3)

s (B 3)

r2

s y, Pa / m

12?8 16?2 19?4 22?3

3220 2820 2640 2210

8470 9270 7700 6220

43?1 53?3 30?0 21?6

127 186 104 74

1 1 1 1

10?3 11?5 6?2 4?5

of the same variety but grown in the 1991 / 1992 season (data not shown). As the first objective of this section was to observe how models adapt to the whole velocity range, we calculated percentage errors of pressure drop predictions as a function of air velocity. The error, at each air velocity, was defined by Relative Error 5 100

(predictedi 2 experimentali) experimentali

(6)

Graphs such as those shown in Fig. 3 are more adequate to observe the behaviour of models than those in which predicted and observed pressure drops are plotted against velocity since the latter graphs tend to mask large percentage errors at low pressure drops when the range of pressure drop plotted is wide. Fig. 3 [(A) and (B)] shows that model 2 [Eqn. (3)] and model 3 [Eqn. (4)] adapt better to the whole velocity range than model 1 [Eqn. (2)] because the first two give lower errors at low airflows. By similar arguments, comparison of model 2 and model 3 show that the latter adapts better than the former. The flexibility of the Ergun-type equation [model 3, Eqn. (4)] can be

ascribed to its two-term nature, which reflects the transition from laminar flow (linear term) to fully turbulent flow21 (quadratic term). In this regard, the inset graph of Fig. 2 , for results at low airflows, shows that the functionality is mostly linear, where the first term of model 3 [Eqn. (4)] is dominant. However, in order to select a suitable model to interpret the effect of moisture content on pressure drop, a more detailed comparison of the equations was made. In this instance, only models 2 and 3 were considered because of their better predictions with respect to model 1. For model 2 [Eqn. (3)], Table 2 shows that the parameter A2 first increases with moisture content and then decreases, while B2 shows irregularity. In model 3 [Eqn. (4)], the parameter A3 decreases steadily with increase of moisture content thus showing a consistent behaviour but the parameter B3 shows a maximum. Therefore, model 3 is also better to attempt a further modelling of the influence of moisture content on pressure drop, though it is still not ideal. Nonetheless, if Table 2 is inspected again for model 3, it can be observed that B3 is approximately three times A3, so this model could be rewritten as an

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S. A. GINER ; E. DENISIENIA

20

approximate Ergun-type equation (model 4) of the form DP (7) 5 AV (1 1 3V ) L

0

The above relation has been fitted again to the pressure drop curves of Fig. 2 , and the results are indicated in Table 3, which reveals a continuous decrease of the parameter A with increase of moisture content. Fig. 3 shows that its adaptability to the curve is still good, though sy values (Table 3) are somewhat higher than those of model 3 [Eqn.(4)], particularly at the first two moisture levels. However, the mean sy value is 9?8 Pa / m, still lower than that of model 2 [Eqn. (3)]. Fig. 3 (A) shows that model 4 [Eqn. (7)] still adapts better than model 2 for low air velocities and shows an equivalent good behaviour at higher velocities. This trend is clearer in Fig. 3 (B). In order to interpret the variation of the parameter A of model 4 [Eqn. (7)], their values were plotted against moisture content in Fig. 4 , where a non-linear behaviour can be observed. We tested several fits for this, and the best found was as follows

–20

–40

Percentage error, %

–60

(A) –80

A 5 C 0 2 C 1 exp (C 2 M C3) 20

(8)

Eqn (8) has three fitted coefficients: C 0 , C 2 and C 3. The coefficient C1 is included only to give the units of A to the term including the exponential function and C1 was assumed to be unity. To improve reliability of C0 , C 2 and C 3, the fit was made in two stages. In the first, we fitted Eqn. (8) to the results of Fig. 4 and obtained C0 5 3150 and also obtained preliminary values of C2 and C 3. In the second stage, all the data of pressure drop-velocity and moisture contents were pooled in one file and the combined model formed by Eqn. (7) and (8) was fitted to them. The preliminary values of C2 and C 3 of the first stage were used as initial ones for the second stage (the fitting procedure is iterative). The final results obtained were C2 5 0?774 (0?044) and C3 5 0?705 (0?019), the standard deviation

0

–20

–40

Table 3 Results from exploratory fittings of the approximate, Erguntype equation (Eqn. (7)) to the experimental pressure drop versus air velocity curves of clean grains at several moisture contents

–60

(B) –80 0·0

Moisture 0·1

0·2

0·3

0·4

0·5 content , M , %

Air velocity, m/s

Fig. 3. Percentage error in the prediction of pressure drop as a function of air y elocity: ( d) Shedd-type model (model 1) , ( =) Hukill and Iy es’ model (model 2) , ( .) Ergun-type model (model 3) , ( h) approximate , Ergun-type model (model 4) . (A) data at 12?8% w.b. (B) data at 22?3% w.b.

w.b.

A

s (A)

r2

s y, Pa / m

12?8 16?2 19?4 22?3

3020 2940 2610 2140

10 12 6 5

1 1 1 1

14?7 12?8 6?2 5?3

PRESSURE DROP THROUGH WHEAT AS AFFECTED BY AIR VELOCITY

81

linear dependence proposed in this work makes rather better predictions. Moreover, if Eqn. (10) is inspected again, it can be seen that the third term can be grouped with the first one because both are linear functions of velocity. Therefore, Eqn. (10) can be rewritten as

3000

DP 5 (a 2 g M )V 1 b V 2 L

Parameter A

3500

(11)

which shows that Eqn. (10) assumes that only the linear term of the Ergun-type equation is a function of moisture content, and not the second. This restricts its adaptability to changes in moisture content, a limitation that it is not shown by Eqn. (9) where the moisture dependence affects both terms.

2500

3.3 . Pressure drop y ersus air y elocity at different fines content

2000 10

15

20

25

Moisture content, % w.b.

Fig. 4. Parameter A of the approximate , Ergun-type equation [model 4 , Eqn. (7)] at different moisture contents. In this model , the y ariation of A reflects approximately the change of pressure drop with moisture content

of the parameters being indicated in parenthesis. The value of r 2 was 1, and sy 5 12?8 Pa / m, which is a low value, equivalent to 1?3 mm H2O / m. Consequently, the following equation is proposed to relate pressure drop, air velocity and grain moisture content of clean wheat beds DP 5 [3150 2 exp (0?774 M 0?705)]V (1 1 3V ) L

Material different from whole seeds of a minimum size is always present in the wheat coming from harvest. In many instances, grains may not be properly cleaned before drying or aeration so that important amounts of broken, abnormally small grains and foreign materials can be found in elevators. Previous authors8,9 working with other grains reported that fines considerably increased pressure drop. A photograph of clean whole grains and fines is shown in Fig. 5 . In Argentina, wheat of grade 1 tolerates up to 1?5% fines, grade 2 wheat up to 3% while wheat of grade 3 can have up to 5% fines.17 In order to study the effect

(9)

This model indicates that pressure drop decreases more rapidly as moisture content increases. As seen in Fig. 3 , Eqn. (9) is best applied for velocities greater than 0?02 m / s. In order to compare the behaviour of Eqn.(9) with that of Haque et al .13 their model was also fitted to the pool of data. The expression is DP 5 a V 1 b V 2 2 g MV L

(10)

which is an Ergun-type equation with an added third term including a linear dependence of pressure drop on moisture content. Fitted results were: a 5 5930 (137), b 5 7500 (225) and τ 5 177 (6?6), the standard deviation of parameters being indicated in parenthesis. The correlation coefficient was r 2 5 0?997 and sy 5 32?8 Pa / m, which is almost three times greater than that of Eqn. (9) developed here, so the non-

Fig. 5. Clean wheat grains (left) and fines (right) . The latter passed through a 9?5 mm 3 1?6 mm rectangular hole siey e , and is mainly composed of broken , y ery thin , y ery small grains and wheat straw

82

S. A. GINER ; E. DENISIENIA

3000 500

2500

400

300

200

Pressure drop, Pa/m

2000 100

0 0·00

0·02

0·04

0·06

0·08

1500

1000

500

0 0·00

0·05

0·10

0·15

0·20

0·25

0·30

Air velocity, m/s

Fig. 6. Main graph: experimental pressure drop per unit of bed height as a function of air y elocity for the following fines contents (% , w / w): ( d) 0 (clean grains) , ( =) 2?86 , ( .) 5?65 , ( h) 8?42 , ( j) 10?60. Inset graph: y alues at low airflows and low pressure drops in magnified scale. The moisture content of clean grains was 12?77% w.b.. The mixtures of clean grain and fines had moisture contents of 12?81% , 12?85% , 12?90% and 12?92% w.b. for fines contents of 2?86% , 5?65% , 8?42% and 10?6% w / w , respectiy ely

of fines on pressure drop and to measure it adequately, four bulks of 12?8% moisture content clean wheat with fines proportions (f) of 2?86%, 5?65%, 8?42% and 10?60%, were prepared.

Table 4 Results from exploratory fittings of the approximate Ergun-type equation [Eqn. ( 7)] to experimental pressure drop versus air velocity curves of 12?8% moisture wheat measured at several fines contents Fines content , %

A

s (A)

r2

s y, Pa / m

2?86 5?65 8?42 10?60

3780 4210 4500 5320

26 23 32 28

1 0?999 0?999 0?999

17?9 16?1 21?9 19?1

The experimental data is shown in Fig. 6 , together with the curve for clean (0% fines) wheat (the inset graph shows values at low airflows). It can be seen that pressure drop increased considerably with fines and reached values up to 75% higher than those of clean seeds. This is mainly due to the reduction of the average particle size of the bed, which is caused by the presence of fines.14 In order to quantify the effect of fines, we used the approximate Ergun-type equation (model 4) [Eqn. (7)] developed in the previous section, and fitted it to each curve of Fig. 6 . The preliminary results of the fittings are shown in Table 4. The table shows that, as a general rule, model 4 [Eqn. (7)] behaved well in beds with fines, though not as well as in clean seeds (See Table 3), possibly because of the particle size distribution. The parameter A increased steadily with fines and a linear fit of A versus f gave r 2 5 0?964. But,

PRESSURE DROP THROUGH WHEAT AS AFFECTED BY AIR VELOCITY

to find a consistent expression, it was considered that the intercept of the linear fit should be that of Table 3 for clean (0% fines) wheat at 12?8% moisture. Consequently, we propose A 5 3020 1 Df

(12)

By following the method described in Section 3.2.2., pressure-drop, air velocity and fines contents of Fig. 6 were pooled together in one file and the combined model formed by model 4 [Eqn. (7)] and Eqn. (12) was fitted to them. The only parameter thus fitted in this multiple non-linear regression (D ) was found to be D 5 205 (2?8),where the standard deviation of the parameter is indicated in parenthesis. To indicate the goodness of fit, r 2 was 0?997 and sy was 28?2 Pa / m, equivalent to 2?9 mm H2O / m. Therefore, we propose the following equation to calculate the pressure drop versus air velocity curve of 12?8% moisture wheat for fines contents from 0 to 10?6% DP 5 (3020 1 205f )V (1 1 3V ) L

(13)

On the other hand, previous authors8,9 have studied the effect of fines on pressure drop by fitting the following linear expression to the experimental data:

S D S D

DP L beds with fines 5 1 1 Kf DP L clean beds

(14)

where K is a parameter that could be a function of air velocity. In the present work, it was realized that the same relationship can be found analytically if Eqn. (13) is used both for f . 0 and f 5 0

SDLPD SDLPD

beds with fines

5

(3020 1 205f )V (1 1 3V ) 3020V (1 1 3V )

(15)

clean beds

where K 5 205 / 3020 5 0?0678. As the factor including V drops out in this procedure, the model arrived at here assumes that the effect of fines does not change with air velocity. By using Eqn (14), Grama et al .9 found a K value independent of air velocity, so he obtained the same behaviour for maize as we obtained for wheat. However, Haque et al .8 found that K decreased for

83

increasing air velocities, indicating that the effect of fines becomes less pronounced at higher airflows. In order to check if Eqn (15) with constant K obtained here was adequate, the experimental data was rearranged as pressure drop ratios at each fines content and plotted as a function of air velocity in Fig. 7 . The graph shows that the ratios present considerable random variations, with no serious overall change. The most notable variation occured at 8?42% fines, where the ratios decreased by 10% over the whole velocity range. Straight lines fitted to the data of Fig. 7 gave non-significant correlation coefficients (r 2) for three out of the four fines levels, 8?42% being the exception, though with a low value of r 2. The pressure drop ratio probably does diminish with air velocity but the results of Fig. 7 do not allow a definite trend to be established in the form of numerical values. However, to check whether or not the K value analytically calculated for Eqn. (15) was similar to the result of a general regression, the data of Fig. 7 was used to fit a similar expression, which is shown below

SDLPD SDLPD

beds with fines

5 k1 1 k2 f

(16)

clean beds

Fitted results were k1 5 1?000 and k 2 5 0?0664 (r 2 5 0?968), i.e. the parameters are almost equal to those of Eqn. (15) developed from Eqn. (13). Although the expression for pressure drop ratio [Eqn. (14) or Eqn. (15)] is useful, we should point out that Eqn. (13) developed here is more flexible, since a designer can insert air velocities and fines contents at the same time. Besides, as in the study of the effect of moisture content, the function with fines is selfcontained in the original parameter A of model 4 [Eqn. (7)], so it resembles the original form of the approximate, Ergun-type equation developed here. The advantage of model 4 is that the variation of its parameter A with variables other than air velocity reflects directly the variation of the pressure drop with such variables, a feature that cannot be found either in model 2 [Eqn. (3)], or in model 3 [Eqn.(4)]. Therefore, it is considered that the approximate, Ergun-type equation [Model 4, Eqn. (7)] can be a useful expression for pressure drop studies. We believe that the simplification of the Ergun-type equation shown in the present paper could be attempted with other grains. However, the factor relating B3 and A3 in Eqn (4) may vary because, according to the full form of the Ergun15 equation, it mainly depends on

84

S. A. GINER ; E. DENISIENIA

1·9

1·8

Pressure drop ratio, dimensionless

1·7 100

1·6

1·5

1·4

1·3

1·2

1·1 0·00

0·05

0·10

0·15

0·20

0·25

0·30

Air velocity, m/s

Fig. 7. Experimental ratios of pressure drop in beds mixed with fines to those of clean beds , as a function of air y elocity for the following fines contents (% , w / w): ( =) 2?86 , ( .) 5?65 , ( h) 8?42 , ( j) 10?60

particle diameter and bed void fraction. Thus, it is considered that more work is needed to relate the pressure drop with properties of the bed such as bed void fraction and particle diameter, to continue the trend of Ergun15 and Li and Sokhansanj14. 4. Conclusions 1. The pressure drop in beds of clean wheat increased with air velocity and the increase became stronger at higher velocities. The two-parameter, Ergun-type expression fitted the results best in a large velocity range (0?006 – 0?42 m / s). This can be ascribed to its two-term nature, with a linear function of velocity for low (laminar) airflows and a quadratic function for high (turbulent) airflows. 2. The experimental pressure drop of clean wheat decreased by up to 30% with moisture content in the range of 12?8 to 22?3% w.b. The effect of moisture content was more pronounced at higher moistures contents. The parameter of the quadratic term in the Ergun-type equation was about three times that of the

linear term at the four moisture contents tested, a feature which allowed a simplification of the equation to be made. 3. At 12?8% grain moisture content, pressure drop increased with fines content by up to 75%, at 10?6% fines, with respect to clean (0% fines) grain. This is because fines tend to reduce the average particle size of the bed. Acknowledgements Authors thank Dr R.H. Mascheroni, at CIDCA, for general help and advice. The financial support of Consejo Nacional de Investigaciones Cientı´ficas y Te´ cnicas (CONICET), Argentina and of Comisio´ n de Investigaciones Cientı´ficas (CIC), Provincia de Buenos Aires, Argentina is also appreciated.

References 1

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