b. prakash, t. j. siebenmorgen - university of arkansas

Transactions of the ASABE

Vol. 61(5): 1757-1765 © 2018 American Society of Agricultural and Biological Engineers ISSN 2151-0032 https://doi.org/10.13031/trans.12927 1757

MATHEMATICAL MODELING OF A CROSS-FLOW RICE DRYER WITH GRAIN INVERTERS

B. Prakash, T. J. Siebenmorgen

ABSTRACT. Industrial-scale cross-flow dryers are commonly equipped with grain inverters to improve the uniformity of drying across the column thickness. While a few mathematical models have been reported that include the operation of grain inverters, such models were rarely validated with experiments comprising grain inversions. In this study, a mathe-matical model was developed to evaluate the impact of grain inverters on the uniformity of grain moisture content (MC) across the column in cross-flow dryers. To improve the accuracy of model predictions, the impact of using two thin-layer drying equations, the Newton and modified Page equations, in the model was also investigated. An experimental setup was fabricated to simulate grain inversion, and drying experiments were performed to measure rice MC and air temperature across the column thickness, which were then compared with model-predicted values. When the modified Page equation was used in the model, the model predictions matched the experimental observations more closely than when using the Newton equation. The model successfully predicted grain and air properties when 0, 1, and 2 grain inversions were used; the root mean square error between predicted and measured values of rice MC and air temperature were within 0.1 to 0.2 percentage points and 1°C to 4°C, respectively. Grain inversions were shown to improve the uniformity of drying in rice kernels; in the tested drying conditions, a single grain inversion produced more uniform drying than two or more grain inversions in the column. The presented results demonstrate the usefulness of the developed model in investigating the role of grain inversion in cross-flow drying of rice. As such, the model could be readily used to improve dryer design, particularly the number and arrangement of grain inverters, and optimize rice drying operations.

Keywords. Deep-bed drying, Grain inverters, Mathematical modeling, Reversed airflow, Thin-layer drying.

rying is an important post-harvest operation that affects the shelf-life, milling yield, and overall quality of rice. Dryers of various configurations are used in the rice-producing regions of the

world. In the U.S., cross-flow column dryers are the most popular type of rice dryer used at the industrial scale (Rum-sey and Rovedo, 2001; Schluterman and Siebenmorgen, 2004). In such dryers, grain flows vertically downward be-tween perforated metallic screens, forming grain columns (fig. 1a). Heated air flows through the grain columns in a direction perpendicular (or “cross”) to that of the grain movement; therefore, such dryers are called cross-flow dry-ers. In this article, “rice” refers to rough rice (paddy), the unhulled form of the crop, unless specified otherwise.

In cross-flow dryers, depending on the location across the column thickness, rice kernels dry at different rates due to drastically different drying air conditions across the column. Rice kernels closer to the heated-air plenum interact with hotter air and dry faster than kernels positioned away from the plenum, which interact with cooler, more humid air. Due

to these differences in drying rates, the difference in mois-ture content (MC) across a drying column can be significant, observed to be as high as 9.1 percentage points (w.b.) for maize (Bakker-Arkema and Liu, 1997) and 3.6 percentage points (w.b.) for rice (Prakash et al., 2017). Such non-uni-formity within cross-flow dryers presents two challenges: underdrying or overdrying of kernels and generation of fis-sures, which is of paramount importance in the case of rice kernels. To improve the uniformity of drying, industrial-scale cross-flow dryers are often equipped with grain invert-ers (also called turnflows or grain exchangers) that reverse the position of kernels in the column with respect to the dry-ing airflow (fig. 1b). Alternatively, the dryer column can be divided into several sections, and the direction of airflow can be reversed in each section, producing a similar effect as grain inverters on the uniformity of drying (fig. 1c).

Mathematical modeling is an important research tool to study grain drying. Models can be used to facilitate optimi-zation of drying operation parameters, as well as to evaluate improvements in dryer design, such as the inclusion of grain inverters. While several models have been reported for cross-flow grain dryers (Thompson et al., 1968; Otten et al., 1980; Brooker et al., 1992; Bakker-Arkema and Liu, 1997; Rumsey and Rovedo, 2001), only a few studies have in-cluded the operation of grain inverters or airflow reversals in their models (Paulsen and Thompson, 1973; Khatchatourian et al., 2013; Nguyen et al., 2016). Furthermore, reported models have been rarely validated by performing experi-ments comprising grain inversion or reversed airflow.

Submitted for review in May 2018 as manuscript number PRS 12927;

approved for publication by the Processing Systems Community of ASABE in July 2018.

The authors are Bhagwati Prakash, Research Associate, and Terry J. Siebenmorgen, Distinguished Professor, Department of Food Science,University of Arkansas, Fayetteville, Arkansas. Corresponding author:Terry J. Siebenmorgen, 2650 N. Young Ave., Fayetteville, AR 72704;phone: 479-575-2841; e-mail: [email protected].

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1758 TRANSACTIONS OF THE ASABE

Recently, Prakash et al. (2017) reported a cross-flow dryer model that was validated by comparing profiles of grain and air properties across the column thickness in an experimental dryer column. The current study extends this model to include the role of grain inversion in the drying col-umn; an experimental setup was also fabricated to simulate grain inversion in the dryer and was used to validate the de-veloped model.

The lack of accurate thin-layer drying equations has been identified as the key factor that affects the accuracy of deep-bed drying models (Morey and Li, 1984; Brooker et al., 1992). The two-parameter Page and four-parameter Midilli equations are commonly reported to be successful in describ-ing thin-layer drying of rice (Cnossen et al., 2002; Haciha-fizoglu et al., 2008; Ondier et al., 2010; ASABE, 2014). However, the presence of two or more interdependent pa-rameters in these equations makes it difficult to quantify the impact of air temperature and RH on these equation param-eters (Jayas et al., 1991; Cnossen et al., 2002). Prakash and Siebenmorgen (2018) addressed this problem by developing accurate single-parameter drying equations for contempo-rary long-grain rice cultivars; the use of such equations is hypothesized to improve predictions of cross-flow dryer models.

The goal of this study was to develop a mathematical model that accurately describes the role of grain inverters in cross-flow drying of rice. First, the impact of using an im-proved thin-layer drying equation in the dryer model was in-vestigated. Secondly, the model reported by Prakash et al. (2017) was enhanced to describe the rice flow patterns inside cross-flow dryers that certain grain inverters produce. Ex-periments were then performed to simulate grain inversion in a lab-scale dryer; the measured grain and air properties were used for validation of the model. Finally, the role of

grain inverters in affecting the uniformity of MC across the column thickness was measured and evaluated.

MATERIALS AND METHODS MODEL DEVELOPMENT

The model developed in this study is very similar to the model presented by Prakash et al. (2017); therefore, only a brief outline and the modifications from the previously re-ported model are described here. The entire grain column is conceptualized to comprise voxels (or volume elements) that are rectilinearly arranged and are fixed relative to the dryer. The grain and air travel through these voxels during the dry-ing process. A series of moisture and heat transport equa-tions are solved in each voxel to determine the properties of the grain and air leaving the voxel. To solve these equations, knowledge of the inlet conditions of the grain and air enter-ing each voxel is required. Therefore, a specific sequence of voxel computations is employed in this model, which en-sures that the inlet properties are known for every voxel in subsequent steps (fig. 2). It should be noted that the sequence shown in figure 2 is different from the sequence reported by Prakash et al. (2017); this variation was necessary to account for the grain flow patterns produced by grain inverters.

When rice kernels encounter the grain inverter in the col-umn, the position of the rice kernels is assumed to instantly switch in the thickness direction, i.e., in the x-direction in fig-ure 2a. For example, rice kernels entering the column in voxel 1 travel through the voxels 6, 11, and 16 and then encounter the grain inverter, which switches the grain position so that these kernels enter voxel 25. Similarly, the grain inverter forces kernels leaving voxel 17 to enter voxel 24, kernels leav-ing 18 enter 23, kernels leaving 19 enter 22, and kernels leav-ing 20 enter 21. Two representative voxels are shown in figure

Figure 1. Schematic of (a) cross-flow dryer and (b) grain inverter in a grain column and (c) illustration of airflow reversal in a grain column.

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2b to demonstrate the flow patterns and resulting input grain and air conditions before and after the grain inverter.

In addition to the Newton equation used by Prakash et al. (2017), a modified form of the Page equation was also used in the current model version. The Newton-type equation is given by:

( )MR expe

i e

M Mkt

M M

−= = −

− (1)

( )5 68 088 10 5 050 10k . . T− −= − × + × (2)

where M is the instantaneous MC of the grain (dec. d.b.), Me is the equilibrium MC of rice (dec. d.b.), Mi is the initial MC of the rice (dec. d.b.), MR is the dimensionless moisture ratio (dec.), t is the drying duration (min), and k is an experimen-tally determined drying constant that depends on the temper-ature of the drying air (T, °C). The equilibrium MC of the grain corresponding to given temperature T and relative hu-midity (RH, %) air conditions was determined using the Chung-Pfost equation (ASABE, 2012) with parameters ob-tained by Ondier et al. (2011):

( ) ( )0 01 511 7649

ln0 2316 22 1226 ln 0 01 RHe

. .M

. T . .

−= × + × × (3)

The modified Page equation for long-grain rice was given by (Prakash and Siebenmorgen, 2018):

( )0 52MR exp .e

i e

M Mkt

M M

−= = −

− (4)

( )( ) ( )( ) ( )( )

3 4

3 5 2

5 2 5

9 93 10 5 07 10

1 17 10 RH 2 04 10

1 23 10 RH 1 00 10 RH

k . . T

. . T

. . T

− −

− −

− −

= − × + ×

+ × + ×

− × − × ×

(5)

The mathematical model was developed and solved in the MATLAB computation environment (ver. R2015b, The MathWorks, Inc., Natick, Mass.). For all model simulations, the voxel thickness (Δx) was selected to be 12.7 mm and the grain duration in a voxel (Δt) was 60 s. Because the grain column was assumed to be 381 mm thick, the number of voxels along the column thickness was 30 in all simulations. The number of voxels along the column height depended on the drying duration; for example, a simulation with a 90 min drying duration had 90 voxels along the column height, while a simulation with a 15 min drying duration had 15 voxels along the column height. Decreasing Δx or Δt did not produce any significantly different model predictions; therefore, the selected values were deemed appropriate for the simulation runs. The computation time was typically less than 5 s on a desktop computer (Dell, Intel i7-4790 CPU, 3.60 GHz, 16 GB memory).

LABORATORY DRYER Prakash et al. (2017) illustrated the conceptual equiva-

lence between a continuous-flow, cross-flow dryer and sta-tionary-bed dryer and simulated cross-flow drying using a laboratory-scale, stationary-bed dryer; a similar dryer setup was used in this study to validate the model. Drying air of the desired temperature and RH was produced by a 0.91 m3 controlled-environment chamber (Espec North America, Inc., Hudsonville, Mich.) using in-built electrical heating, re-frigeration, and control components (fig. 3). A 0.56 kW cen-trifugal fan (Dayton Electric Manufacturer Co., Chicago, Ill.) was mounted outside the chamber to avoid high-temper-ature exposure. The fan suctioned air from the chamber and forced it through the grain in the drying bed via insulated air ducts.

The dryer assembly inside the controlled-environment chamber comprised a wooden box and a cylindrical acrylic-glass sample holder that served as the drying column. The wooden box served as a plenum, and the air properties therein were measured to represent the inlet air conditions to the rice column. The sample holder was comprised of three detachable components: a main component that held the grain, a perforated metallic disc, and a top component that resembled the lower part of the main component (fig. 3c). During a drying experiment, rice was first placed in the main component of the sample holder, and the perforated metallic disc placed over the rice. The top component was then placed on the main component and secured using the screw knobs. An O-ring ensured an airtight fit between the sample holder and the wooden box flange. The design of the sample holder allowed it to be detached and flipped such that the grain column could be reversed with respect to the airflow, allowing experimental simulation of grain inversion in the lab dryer.

Six fiber-mesh woven pouches were used to hold rice ker-nels, approximately 40 g in each pouch; this rice was taken from the same lot as that used to fill the sample holder. These pouches were placed at six equidistant locations (0, 76, 152, 229, 305, and 381 mm from the plenum) within the grain column during filling of the sample holder. The use of these pouches facilitated collection of rice samples from specific

Figure 2. (a) Sequence of voxel computations, as indicated by voxelnumbering, in a cross-flow dryer model containing a grain inverter,and (b) two representative voxels, one above and one below the graininverter, showing inlet grain and air conditions for the computations.


locations within the column after the completion of a drying run; these rice samples were used for measurement of rice MC.

Six holes of 3.2 mm diameter were drilled in the sample holder through which K-type thermocouples (Omega Engi-neering, Inc., Stamford, Conn.) were inserted to measure the air temperature at these locations within the grain column; these locations corresponded to the locations of the woven pouches. A seventh thermocouple was inserted into the wooden box to measure the plenum air temperature. All seven thermocouples were connected to an external datalog-ger (CR300, Campbell Scientific, Inc., Logan, Utah). A min-iature, standalone temperature and humidity datalogger (Mi-croRHTemp, MadgeTech, Inc., Warner, N.H.) was also placed midway inside the grain column (fig. 3a). Another datalogger (HOBO UX100-011, Onset Computer Corp., Bourne, Mass.) was placed at the top of the grain column to measure exhaust air conditions.

RICE SAMPLES Rice of long-grain cultivar Roy J was used for all drying

experiments. The rice was harvested at the University of Ar-kansas Rice Research and Extension Center near Stuttgart, Arkansas, at approximately 18% MC (w.b.) in 2017. The rice was cleaned using a dockage tester (XT4, Carter-Day, Minneapolis, Minn.) to remove foreign material and unfilled kernels and then stored at approximately 4°C in plastic con-tainers prior to the drying experiments. While all rice used in this study was from the same lot, the rice MC changed slightly during storage, producing different initial MCs dur-ing the drying experiments.

DRYING EXPERIMENTS Three experiments were performed in the lab dryer to val-

idate the model; each experiment consisted of several drying runs with various drying conditions (table 1). Experiment 1 was conducted to compare the performance of the model us-ing the Newton-type and the modified Page-type thin-layer drying equations. Rice was dried for five durations while not performing any grain inversion. This comparison was then

used to select the better thin-layer drying equation, which would be used in the model for all further analyses in this study.

The second and third experiments were both performed to validate simulation of grain inversions in the model. Two different plenum air conditions, 60°C - 10% RH and 45°C - 20% RH, were used in the second and third experiments, respectively. Both selected plenum air conditions had the same humidity ratio of 0.012 kg of water per kg of dry air; this humidity ratio is common for ambient air during the rice drying season in the mid-south U.S. The data from the sec-ond and third experiments were also used to evaluate the im-pact of grain inversions on the uniformity of grain MC across the column thickness.

For all drying runs involving grain inversion, the total drying duration was 60 min. For no grain inversion, the rice was dried continuously for 60 min. For a single grain inver-sion, the grain column orientation was reversed after 30 min into the drying runs. For two inversions, the orientation of the column was reversed once at 20 min and again at 40 min to model two grain inverters in a column. The order of drying runs in each experiment was randomized. All corresponding measurements of grain and air properties obtained from the duplicate drying runs performed at given drying conditions were averaged for subsequent analyses.

Prior to any drying run, rice was taken from the refriger-ated storage and equilibrated to room temperature in closed

Figure 3. (a) Schematic of the laboratory-scale, stationary-bed grain dryer, (b) key dimensions of the sample holder, and (c) exploded view showingthe assembly of various components of the sample holder.

Table 1. Initial grain and plenum air conditions for drying experiments.

Condition Experiment[a]

1 2 3 Initial rice MC (% w.b.) 17.6 (0.1) 17.2 (0.1) 16.8 (0.1)

Initial rice temperature (°C) 26 (1) 25 (2) 22 (1) Plenum air temperature (°C) 60 60 45

Plenum air RH (%) 10 10 20 Drying duration (min) 15, 30, 45,

60, 90 60 60

No. of grain inversions 0 0, 1, 2 0, 1, 2 No. of replicate drying runs 2 2 2 Total number of drying runs 5 × 2 = 10 3 × 2 = 6 3 × 2 = 6

[a] Numbers in parentheses are standard deviations of measured values for the various drying runs in an experiment.

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plastic bags; 2910 g of rice was used in each drying run. Ap-proximately 40 g of rice was placed in each of the six woven pouches. The miniature datalogger, pouches, and remaining rice were carefully placed in the sample holder so that the datalogger was located at mid-height, i.e., 190 mm from the air plenum. The drying column thus formed in the sample holder was of cylindrical shape with a diameter of 127 mm and height of 381 mm. To perform grain inversion, the sam-ple holder was raised from the wooden box, flipped verti-cally, and then refitted to the wooden box; the time required to perform a grain inversion was approximately 10 s. After completion of the drying runs, the rice in the sample pouches was stored in sealed plastic bags at ambient conditions (22°C to 26°C) before subsequent measurement of MC using an oven method.

For all drying runs, the airflow rate through the rice was 0.53 m3 s-1 m-2, which was measured with a vane-type ane-mometer (HHF141, Omega Engineering, Inc., Stamford, Conn.). The experimental setup allowed continuous meas-urement of air temperature at six locations in the grain col-umn. However, the grain MC at these six locations, i.e., in each of the six pouches, could be measured only once, at the end of a drying run. The MC of the rice was determined by drying a 15 g sample for 24 h in a convection oven, which was operated at 130°C (Jindal and Siebenmorgen, 1987).

Model simulations were run for every drying condition of the three experiments, and the root mean square error (RMSE) was determined to quantify the accuracy to which the model predicted the experimental data:

( )2

1RMSE

Nm en

X X

N=

−=

(6)

where X is the grain or air property being compared, and N is the number of compared data points measured across the grain column. The subscripts m and e indicate whether the property was determined from the model or experiments. It should be noted that each Xe is an average of two measure-

ments obtained from the duplicate drying runs performed in identical drying conditions; using the average value reduces experimental errors, and thus provides a better estimate of the true grain or air property for comparison with the model-predicted value during RMSE calculation. Because the ex-perimentally determined values of rice MC and air tempera-ture were measured at six locations in the rice column, the value of N was 6 for all reported RMSEs, except for air tem-peratures in experiment 1. For experiment 1, the air temper-ature was not measured at the 0 mm location from the ple-num; therefore, N was 5 while calculating the corresponding RMSEs.

RESULTS AND DISCUSSION COMPARISON OF THIN-LAYER DRYING EQUATIONS

For each drying condition of experiment 1 (table 1), two sets of model simulations were run. The simulation sets dif-fered in the selection of the thin-layer drying equation used in the model. One set used the Newton equation (eqs. 1 and 2), while the other set used the modified Page equation (eqs. 4 and 5). The rice MC and air temperature profiles predicted from these simulations were compared with experimental measurements to evaluate the model performance using each thin-layer drying equation (figs. 4 and 5). It should be noted that rice at the end of a drying run in the lab dryer was equiv-alent to rice exiting a cross-flow dryer column in the model.

Figures 4 and 5 clearly show that the model predictions match the experimental measurements more closely when the modified Page equation was used in the model. While Noomhorm and Verma (1986) and Nguyen et al. (2016) evaluated the role of thin-layer drying equations in deep-bed rice dryers, the equations they evaluated were different from those used in the current study; therefore, the presented re-sults could not be corroborated with their work. To quantify and compare the accuracy of model predictions of grain and air properties, the RMSEs were determined when using each thin-layer drying equation in the model (table 2).

(a) (b)

Figure 4. Comparison of rice moisture content profiles within a grain column, as predicted by a mathematical model and measured experimentally, after drying for the three indicated drying durations. Each experimental data point is the average of two drying run replications. Model simulations were run using two thin-layer drying equations: (a) the Newton equation (eqs. 1 and 2) and (b) the modified Page equation (eqs. 4 and 5). For thesedrying runs, the plenum air conditions were 60°C and 10% RH, and the initial MC of rice was 17.6% (w.b.).

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The magnitudes of the RMSEs obtained in this study, es-pecially when the Newton equation was used in the model, are similar to those of Prakash et al. (2017), who obtained RMSEs of rice MC and air temperature of 0.6 to 0.9 percent-age points and 3°C to 5°C, respectively. When the modified Page equation was used in the dryer model, lesser RMSEs were obtained for both MC and air temperature predictions, demonstrating that using an improved thin-layer drying equation accrues benefits that contribute to the overall accu-racy of the dryer model. The presented results reconfirm the need to develop accurate thin-layer drying equations for each grain being modeled.

SIMULATION OF GRAIN INVERTERS IN DRYER MODEL For each drying condition in experiments 2 and 3

(table 1), model simulations were run using the modified Page equation in the model. To validate the model when sim-ulating the use of grain inverters in the drying column, a comparison of model-predicted and experimentally meas-ured rice MC and air temperature profiles is presented in fig-ures 6 and 7, respectively. For the air temperature profiles in figures 7a and 7b, drying durations of 35 and 45 min were selected, respectively; the selected durations demonstrate the air profiles 5 min after performing grain inversions in each drying run.

For the tested drying conditions, the model accurately predicted grain MC (fig. 6). However, the model slightly un-derpredicted the air temperatures (fig. 7); the difference be-tween the model-predicted and experimentally measured air temperature was generally less than 5°C. Such underpredic-tion of air temperature, particularly at locations in the grain column that were distant from the heated-air plenum, was also observed in figure 5b and was probably due to errors associated with the thin-layer drying and moisture isotherm equations in the model. The parameters of both of these equations were determined based on experiments in which the air RH was in the 10% to 72% range; therefore, using these parameters beyond this range could produce errors. It should be noted that air RH in a few locations in the drying column was measured to be as high as 90% during the drying runs performed in this study.

The RMSEs between the predicted and experimental grain MC and air temperatures at different drying durations are listed in table 3. The magnitude of the RMSEs for rice MC and air temperature was 0.1 to 0.2 percentage points and 1°C to 4°C, respectively. The high accuracy of the model predictions could be attributed to the use of an accurate thin-layer drying equation, as well as the design of the sample holder and dryer assembly that allowed well-controlled ex-perimental simulation of grain inversions. The accuracy of the model could be potentially further improved by using moisture isotherm and thin-layer drying equations that are valid for a wider range of air conditions (temperature and RH), as well as for contemporary rice cultivars. Further-more, in commercial cross-flow dryers, harvested rice is typ-ically commingled (mixture of several rice cultivars), ple-num airflow into the rice column is often non-uniform, and grain inverters usually do not produce complete inversion of the rice kernels across the column. These factors might pro-duce additional deviations between model predictions and the actual performance of a dryer; therefore, model valida-tion at commercial-scale dryers is suggested.

(a) (b)

Figure 5. Comparison of air temperature profiles within a grain column, as predicted by a mathematical model and measured experimentally, after drying for the three indicated durations. Each experimental data point is the average of two drying run replications. Model simulations wererun using two thin-layer drying equations: (a) the Newton equation (eqs. 1 and 2) and (b) the modified Page equation (eqs. 4 and 5). For thesedrying runs, the plenum air conditions were 60°C and 10% RH, and the initial MC of rice was 17.6% (w.b.).

Table 2. Root mean square errors (RMSE) between predicted andexperimental grain and air properties after five drying durations inexperiment 1 (table 1) when the Newton and modified Page equationswere used in the dryer model.

Drying Duration

(min)

Rice MC (percentage points, w.b.)

Air Temperature (°C)

Newton Modified

Page Newton Modified

Page 15 0.6 0.3 3.7 2.2 30 0.2 0.3 4.4 2.2 45 0.4 0.2 6.1 2.1 60 0.8 0.1 6.4 1.9 90 1.4 0.1 6.3 2.0

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Table 3. Root mean square errors (RMSE) between predicted andexperimental grain and air properties at specified drying durations forthe conditions listed in experiments 2 and 3 (table 1). GI refers to thenumber of grain inversions performed in the drying runs.

Drying Duration

(min)

Experiment 2

Experiment 3

0 GI 1 GI 2 GI 0 GI 1 GI 2 GI Rice MC (percentage points, w.b.)

60 0.1 0.2 0.2 0.1 0.2 0.1 Air temperature (°C)

15 3.1 1.7 2.5 1.1 1.0 0.6 30 3.2 2.9 4.1 1.7 1.7 1.6 45 2.7 2.2 4.5 1.7 2.0 2.1 60 2.2 2.1 3.1 1.3 1.7 1.2

UNIFORMITY OF DRYING The primary purpose of using grain inverters is to facili-

tate more uniform drying of kernels in the drying column. In this study, such uniformity of drying was quantified by the range of rice MC across the column thickness. Because rice MC was measured from the sample pouches at six locations in the grain column, the range of MC was calculated as the

difference between the maximum and minimum of these six measured MCs and expressed as percentage points on a wet basis.

The range of rice MCs after the drying runs of experi-ments 2 and 3 is shown in figure 8. While a single grain in-version was observed to be beneficial in reducing the range of MCs, performing two grain inversions was counterpro-ductive. Similar observations were reported for commercial rice dryers by Schlutermann and Siebenmorgen (2004); rice MC across the column was less uniform after the second grain inversion than after the first. While simulating airflow reversals in cross-flow drying of soybeans, Khatchatourian et al. (2013) reported a similar phenomenon; switching the airflow direction once resulted in more uniform drying of kernels than switching the airflow direction twice. Such ob-servations could be explained based on differences in the du-ration at which rice kernels dry at the original and inverted locations in the column. When rice kernels spend an equal drying duration in both the original and inverted positions,

(a) (b)

Figure 6. Comparison of rice moisture content profiles within a grain column, as predicted by a mathematical model and measured experimen-tally, after drying for 60 min for the specified number of grain inversions (GI) using two inlet air conditions: (a) 60°C and 10% RH (experiment 2 conditions in table 1) and (b) 45°C and 20% RH (experiment 3 conditions in table 1). Each experimental data point is the average of two dryingrun replications.

(a) (b)

Figure 7. Comparison of air temperature profiles within a grain column, as predicted by a mathematical model and measured experimentally, at indicated durations in drying runs using (a) one grain inversion and (b) two grain inversions. For these drying runs, plenum air conditions were 60°C and 10% RH (experiment 2 conditions in table 1). Each experimental data point is the average of two drying run replications.

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Model - 45 minExperiment - 45 minPlenum air


as observed in a single grain inversion, more uniform drying is expected. However, when performing two grain inver-sions in the column, rice spends 2/3 of the total drying dura-tion in the original position and only 1/3 in the inverted po-sition.

While limited experimentation was performed to evaluate the effect of the number of grain inversions on the uniformity of drying, the model was used to predict the range of MCs across a grain column that could be expected for greater numbers of grain inversions. Figure 9 shows the model-pre-dicted range of MCs after drying using up to five grain in-versions in the drying conditions listed for experiment 2 in table 1. The model was run using the more accurate, modi-fied-Page thin-layer drying equation.

Similar to the trends observed from the experimental measurements, figure 9 shows that a single grain inversion was more effective in reducing the range of MCs than using two or more grain inversions in the column. Considering the practical significance of these results, more research is needed to ensure that the phenomenon is consistent across the full range of rice and air conditions that may exist in a commercial dryer. Furthermore, the milling quality of rice

needs to be evaluated before making any recommendation to the rice industry.

CONCLUSIONS A mathematical model was developed to predict grain

and air properties throughout the grain column in a cross-flow dryer. Additionally, the model was enhanced to simu-late the operation of such a dryer with grain inverters in-stalled. An apparatus was fabricated that included a reversi-ble sample holder to facilitate simulation of grain inversions in a lab-scale dryer. Drying experiments were performed to validate the mathematical model and to measure the impact of grain inversions on the uniformity of drying across a rice drying column.

Application of two thin-layer drying equations in the model was also investigated. When the modified Page equa-tion was used in the model, the model predictions matched the experimental observations more closely than when using the Newton equation. The RMSEs between the predicted and measured values of rice MC and air temperature were within 0.1 to 0.3 percentage points and 1°C to 2°C, respectively, when using the modified Page equation in the model. Results presented in this study reconfirm the need for using accurate thin-layer drying equations in grain drying models.

The model successfully predicted grain and air properties when grain inversion was used. The RMSEs between pre-dicted and measured values of rice MC and air temperature were within 0.1 to 0.2 percentage points and 1°C to 4°C, re-spectively. As such, it is proposed that the model could be readily used to improve dryer design (particularly the num-ber and arrangement of grain inverters) and optimize grain drying operations when using cross-flow dryers. The use of grain inversion improved the uniformity of rice MCs across the drying column. In the tested drying conditions, a single grain inversion was more successful in improving the uni-formity of MC than two or more grain inversions in the col-umn.

The current study presented two research tools, a mathe-matical model and a lab-scale dryer setup, to evaluate the role of grain inverters in a cross-flow drying operation. With minor modifications, the presented model could also be used to describe flat-bed rice dryer operation using reversed air-flow.

ACKNOWLEDGEMENTS The authors acknowledge the financial support by the

corporate sponsors of the University of Arkansas Rice Pro-cessing Program and the Arkansas Rice Research and Pro-motion Board.

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Figure 8. Effect of the number of grain inversions (GI) on the range ofrice moisture content (MC) across the grain column after drying runsusing two plenum air conditions. Table 1 lists the drying conditions forexperiments 2 and 3. Each experimental data point is the average of two drying run replications.

Figure 9. Effect of the number of grain inversions on the model-pre-dicted range of rice moisture contents (MCs) across the grain columnafter drying for 60 min in 60°C and 10% RH conditions (experiment 2conditions in table 1).

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b. prakash, t. j. siebenmorgen - university of arkansas

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