D
EVELOPMENT
OF
C
OMPUTER
S
IMULATION
S
OFTWARE
FOR
S
INGLE
G
RAIN
K
ERNEL
D
RYING,
T
EMPERING,
AND
S
TRESS
A
NALYSIS
C.–C. Jia, W. Yang, T. J. Siebenmorgen, A. G. Cnossen
ABSTRACT. The quality traits of a single grain kernel can produce an index of the overall quality of the bulk grain, as individual
kernels comprise a grain bulk. Therefore, single–kernel drying behavior is important in understanding the overall quality of grain. A Matlab based software package with C++ compiler was developed in this study for describing single–kernel drying, tempering, and internal stress analysis. Non–linear and transient partial differential heat and mass transfer equations describing the single kernel drying and tempering processes were solved using the finite element method. Temperature– and moisture–dependent viscoelastic properties were applied to the stress analysis of a single rice kernel. A graphical user interface and 2D/3D graphics for temperature, moisture content, and stress changes were developed. This software package is a useful tool for engineers, operators, and educators to predict temperature, moisture content, and internal stress distributions inside a single kernel.
Keywords. Computer simulation, Drying, Thin–layer drying, Tempering, Stress, Grain, Single kernel, Finite element method, Software development.
ice is usually dried in multiple passes to retain its head yield. In the U.S., the common practice is to dry the rice from 18%–20% wet basis (w.b.) harvest moisture content (HMC) to 12%–13% w.b. in three to four passes, depending on the HMC, with each pass lasting 20 to 40 min, at a temperature ranging from 49³C to 65³C (120³F to 150³F). After one drying pass, rice is held in a storage bin until the next drying pass. During the holding, tempering of rice takes place, in which the moisture inside rice kernels becomes equilibrated.
Although grain is usually dried in bulk, individual kernels interact with the drying medium. The drying behavior, as described by moisture, temperature, and stress distributions inside a kernel during drying and the quality traits of individual grain kernels, affects the overall quality of the grain dried in a dryer (Brooker et al., 1992; Kunze, 1979; Yang et al., 2000a; Yang et al., 2002). Therefore, it is important to examine the internal behavior of a single grain kernel in order to improve the drying process and product quality. Because grain kernels are small, internal changes of temperature and moisture conditions are not easily measured. Computer simulation has emerged as a powerful tool for achieving this goal. The development of professional software has had a great impact on the design of dryers and
Article was submitted for review in August 2001; approved for publication by the Food & Process Engineering of ASAE in April 2002.
The authors are Canchun Jia, ASAE Member Engineer, Research Associate, Wade Yang, ASAE Member Engineer, Research Assistant Professor, Terry J. Siebenmorgen, ASAE Member Engineer, Professor, and Auke G. Cnossen, Research Specialist, Department of Food Science, University of Arkansas, Fayetteville, Arkansas. Corresponding author: Dr. Wade Yang, Dept. of Food Science, University of Arkansas, 2650 N. Young Ave., Fayetteville, AR 72704; phone: 479–575–4678; fax: 479–575–6936; e–mail: [email protected].
the quality evaluation of grains, and has made the tedious and time–consuming heat and mass transfer calculation, opti-mization, and quality assessment process much easier. Much work has been done to simulate the temperature, moisture content, and stress distributions inside single grain kernels (Haghighi and Segerlind, 1988; Lague and Jenkins, 1991; Irudayaraj and Haghighi, 1993; Sarker et al., 1996; Lan et al., 1999; Jia et al., 2000a, 2000b). However, little scientific literature is available discussing the development of user– friendly simulation software for the drying, tempering, and stress analysis of single grain kernels (Jia et al., 1997).
In the University of Arkansas Rice Processing Program, emphasis has been placed on single–kernel drying behavior, which has helped formulate the glass transition hypothesis (Cnossen and Siebenmorgen, 2000; Perdon et al., 2000; Yang et al., 2000a, 2000b), and a heat/mass transfer study (Yang et al., 2002) for individual rice kernels. Based on recent research findings, a computer simulation package for simulating internal temperature, moisture content, and stress distributions for a single rice kernel has been developed. The features of this software included 2D/3D graphics for temperature, moisture content, and stress changes; interac-tive data inputs and fault–tolerance treatments; and multiple outputs of calculation results. The purpose of this article is to synopsize the development process, describe the main features of the software, and provide some application examples.
M
ATERIALS ANDM
ETHODS SOFTWARE DEVELOPMENT FLOWCHARTFigure 1 shows the detailed processes involved in the development of the software package. In brief, the flowchart contains the components related to grain type selection, data input, drying–air conditions, grain initial conditions and
drying durations, finite element segmentation, numerical computation, and data output (moisture content, tempera-ture, and stress distributions). During the software develop-ment, the following main expressions were considered: S Grain Kernel Expression: Grain type selection, kernel
geometric definition (i.e., length, width, and thickness), and finite element segmentation.
S Drying Computation Expression: Drying condition input, governing and boundary equations, and numerical solution by the finite element method (FEM).
S Property Expression: Input of physical and thermal properties of the selected grain.
S Output Expression (Moisture and Temperature): Output of drying and tempering results in terms of internal temperature and moisture content distributions at selected nodes and the average values of the entire kernel. The output also included the maximum moisture content gradient (MMCG), especially for rice kernels, as this is an important parameter related to the head rice yield during
the drying process, as reported by Yang et al. (2000a, 2002).
S Output Expression (Internal Stresses): Stress analysis output for the drying and/or tempering processes. PROGRAMMING LANGUAGES
The software is referred to as “KernelSimu” in this work, and the following programming environment was used in the development of the software:
S Microsoft Windows 95/98 platform.
S Professional MATLAB 6.0, including the Partial Differential Equation (PDE) toolbox, C++ compiler, Graphical Library, and Math Library.
MATLAB 6.0 was used to perform the finite–element computation to solve the governing equations. The PDE toolbox was used to generate the optimized finite–element meshes and to produce node and element information. The Graphical Library was used to generate 2D/3D, fully colored graphical outputs to enhance the data presentation and the
visual effects to the end–users. The Math Library provided a useful tool to conduct regular numerical computations and to aid the conversion from MATLAB codes to C++ codes (combined with C++ complier). C++ compiler converted the MATLAB codes into C++ codes and generated stand–alone executable programs.
THEORETICAL CONSIDERATIONSFOR DRYING, TEMPERING, AND STRESS ANALYSIS
The following is a synopsis of the mathematical models and numerical techniques used in the software development, which have been reported in detail by Yang et al. (2000a, 2002) and Chen et al. (1999).
Drying Models
The governing heat and mass transfer equations used in this study are shown below in a cylindrical coordinate system (Yang et al., 2002; Jia et al., 2000b):
∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ 2 2 1 2 2 z M D r M r D r M D t M (1) M t M fg Q g z T k r T r k r T k t T g c g +ρ ∂∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ ρ 1 1 2 2 1 2 2 (2) The corresponding boundary and initial conditions for equations 1 and 2 during drying are:
) (M Me m h n M D = − ∂ ∂ − (3) ( ) [ ] M A V t M T a T v c fg Q g a T T t h n T k + ∂ ∂ − + ρ + − = ∂ ∂ − 1 1 ) ) ( (4) 0 , 0 , 0 M M T T t= = = (5) Tempering Models
Theoretically, tempering is a process following drying in which grain is kept in an airtight and well–insulated environment for moisture inside the grain kernels to equili-brate. No moisture escapes from and no heat is conducted out of the grain during tempering. Under these conditions, there is no change in the average temperature and moisture content of the grain due to tempering. The only change during tempering is in the moisture distribution in the kernels (Jia et al., 1996). As mentioned earlier, the tempering process is often seen in rice drying practice when rice is temporarily held between passes in a multi–pass drying system or transferred to a storage bin immediately after drying. The diffusion principle used in drying also fits in the tempering process, with two differences. First, during drying, moisture diffuses from inside the kernel and is constantly removed from the surface of the kernel by drying air, so the diffusivity (D) for the hull, the most external layer of a rough rice kernel, is high. However, during tempering, no moisture goes through the hull layer and is removed from the surface. Instead, moisture is only redistributed inside the kernel, so the D for the hull layer during tempering should be much smaller than that during drying. The second difference is that the tempering boundary conditions differ from those of drying, as shown below:
0 = ∂ ∂ n M (6) 0 = ∂ ∂ n T (7) At the onset of tempering, the moisture profile in the kernel equals the profile at the end of drying, i.e.:
ti T T ti M M t=0, = , = (8) Stress Models
The viscoelastic strains in the kernel as a consequence of heat and mass transfer were proposed by Hammerle (1972) and Christensen (1982), who wrote the constitutive equations between stress and strain in a cylindrical coordinate system as:
{ } {σ = σrr σθθ σzz τrz}T=[ ]{} { }R(ε−ε0) (9) where [R] is the compound viscoelastic modulus of the kernel. { } ( ) ∆ β + ∆ α = ∆ β + ∆ α ∆ β + ∆ α ∆ β + ∆ α = ε 0 1 1 1 0 0 TT MM T M M T (Ti Tj Tm) T= ∆ +∆ +∆ ∆ 3 1 , and (Mi Mj Mm) M= ∆ +∆ +∆ ∆ 3
1 for a triangle element. For axisymmetric strain or stress problems in a cylindrical coordinate system, the following mechanical equilibrium conditions were applied at each point within the grain kernel: {} {ε=εrr εθθ εzz γrz}T=[ ]{ }BU (10)
where [B] is the strain–deformation gradient matrix of the kernel.
The principle of virtual displacement (Hammerle, 1972)was applied for every control volume in the computa-tional domain. The deformation/displacement of the nodal points can be written in the usual form:
[ ][ ] [ ]K U= F (11)
where
[ ]K =
∫
BTRBdV[ ]F =
∫
BTRε0dV+∫
NTFbdVand[N] = shape function matrix of the kernel.
The physical and thermal properties of each part of the kernel are regarded as a function of temperature and moisture content, given invariable drying conditions, that is, air relative humidity, temperature, and velocity are considered to be invariable during drying. No variable–condition drying cases were involved in this study.
NUMERICAL SOLUTION TECHNIQUES
The main computational method applied with this soft-ware was the finite element technique, which divides an elliptical grain kernel into a large number of small triangular
elements across a section of the kernel and describes the variation of a field within an element by use of interpolating polynomials (Lague and Jenkins, 1991; Irudayaraj and Haghighi, 1993; Sarker et al., 1996; Lan et al., 1999; Jia et al., 2000a, 2000b). In addition, the finite difference method was also used for time domain discretization. The significant advantage of the finite element method is the fact that it can handle irregular geometry and variable spacing of the nodes routinely. Another main advantage of the finite element method is the ease with which non–homogeneous and anisotropic materials may be handled. This is extremely important for heat/mass transfer and stress analysis because thermal, hygroscopic, and material properties are functions of temperature and moisture content, and the temperature and moisture content are functions of spatial coordinates. MODEL VERIFICATION
The mathematical models shown above were presented by Yang et al. (2002) and Jia et al. (2002) and have been verified with thin–layer drying data of rice. These models were used directly in the numerical computation and software develop-ment in this study without repeating the verification process.
R
ESULTSANDD
ISCUSSIONDESCRIPTIONOFTHE SOFTWARE PACKAGE “KERNELSIMU” This software is comprised of three modules:
S Drying process calculation.
S Tempering process calculation following drying. S Stress analysis during the drying process and the
tempering process.
The information flowchart for the development of this software is shown in figure 1. This software was designed for a broad range of users and featured a user–friendly interface for human–machine communication.
Graphical Output
Figure 2 shows the main window of the software. There are five selection buttons (same under “Tasks”): Drying, Tempering, Stress Analysis, Restart, and Close. After clicking on the Drying, Tempering, or Stress Analysis button, an input window will pop up. Using Drying as an example, figure 3 shows the input window. Under “Grain Type,” a list of different grain types is given for selection. It was intended for this simulation software to be developed for all major cereal grains, including rice, corn, wheat, barley, etc., but at the current stage, emphasis was placed on rice drying, tempering, and stress analysis, more specifically, for rough rice, brown rice, or white rice. Under “Kernel Size” are three inputs, i.e., length (mm), thickness (mm), and width (mm). For the rice drying simulation, since the finite element computation was based on a 2D axisymmetrical configura-tion of a rice kernel, a mean was taken of the thickness and width specified here for calculation. The “End Conditions” section is where the total drying duration, average moisture content, and average temperature at the end are specified. Within 2.5 min, the kernel temperature would approach drying air temperature for single–kernel rice drying (Chen et al., 1999; Yang et al., 2002). This means that the temperature would be the same as drying medium temperature after 2.5 min drying. If no temperature input was given, the software will treat it automatically as the drying medium temperature. The “Heated Air” section is where drying air conditions are input, which includes “Drying air relative humidity (%),” “Drying air temperature (³C),” and “Airflow rate (m3/m2 min).” In the “Grain Conditions” section, inputs can be made for the “Initial grain moisture content (%w.b.),” “Initial grain temperature (³C),” and “Calculation time step (sec).” For other modules, such as Tempering and Stress Analysis, the input windows are also quite self–descriptive and easy to follow.
Figure 3. Data input window for single–kernel rice drying process simulation.
b c a
Figure 4. An output window for rice drying process simulation (a = outer bran on short axis; b = kernel center, and c = outer bran on long axis). Figure 4 shows an output window for drying process
simulation. In the lower right corner, users can make several output selections, such as the finite element (triangular) grid, mean temperature of the kernel, mean moisture content of the kernel, temperatures at specified nodes, moisture contents at specified nodes, etc. When a selection is made, the graph will change to comply with the selection. For example, in figure 4, “Node moisture content” is selected, and the three nodes (i.e., the junction of outer bran layer with short axis, kernel center, and the junction of outer bran layer with long axis) were specified. The graphical output on the top shows
the relationships of the moisture contents at these three nodes vs. drying duration. In addition, a summary of the “Drying Results” is listed below the graph. The results in figure 4, showing that node a dried faster than node c, are supported by Sarker et al. (1996). Both Sarker et al. (1996) and Yang et al. (2002) found that among nodes a (outer bran on short axis), b (kernel center), and c (outer bran on long axis), the drying at node b was the slowest and the drying at node a was the fastest. The drying rate at node c is between that of nodes b and a. This is because the moisture content gradients were found to be much higher along the short axis than the long
Figure 5. An output window for single–kernel stress simulation during drying. axis by both Sarker et al. (1996) and Yang et al. (2002). This
means that node a would lose more moisture during drying than node c, given the same drying duration.
Figure 5 shows an output window of 3D axial stress distribution on the longitudinal cross–section (i.e., cut along the long axis) of a 1/4 kernel of rough rice after 30 min of drying. The graphical output on the top corresponds to the selection at the lower left, and a summary of the conditions on which the stress calculation was based is given at the lower right.
Data Output
The graphical output features of the software have been described above. This software is also capable of providing the drying, tempering, and stress analysis results in text format, which is stored in a *.dat file and can be retrieved and plotted in a spreadsheet program.
APPLICATION EXAMPLES Drying Curves
Drying curves (i.e., the relation of average kernel moisture content vs. drying duration at given drying conditions) can be easily generated from this software. Figure 6 shows the drying curves for three different drying conditions.
10 12 14 16 18 20 22 0 10 20 30 40 50 60 Ta 40 Deg. C, RH42% (A) Ta 50 Deg. C, RH25% (B) Ta 60 Deg. C, RH17% (C)
Drying duration (min)
A vearge moisture content (%w .b.) A B C
Figure 6. Predicted effect of drying temperature (Ta) and air relative hu-midity (RH) on the drying rate of rough rice kernels. The initial kernel moisture content was 21.1% (w.b.), and the initial kernel temperature was 29.2³C.
Internal Stress Distribution
This software can predict the distribution of axial, radial, shear, and tangential stresses inside a grain kernel. For example, the predicted maximum axial tensile stress within the kernel, which is regarded as a main source of rice breakage (Kunze and Choudhury, 1972), is shown in figure 7. As can be seen in figure 7, increase in drying air temperature caused an increase in the peak magnitude for the
0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 Ta 40 Deg. C, RH42% (A) Ta 50 Deg. C, RH25% (B) Ta 60 Deg. C, RH17% (C)
Drying duration (min)
Maximum axial stress (MPa)
C B A
Figure 7. Predicted effect of drying temperature (Ta) and air relative hu-midity (RH) on maximum tensile axial stress within a rough rice kernel. The initial kernel moisture content was 21.1% (w.b.), and the initial kernel temperature was 29.2³C.
maximum axial stress, but the peak stress occurred only in the first few minutes of drying. After that, the maximum stress declined gradually.
Calculation of Maximum Moisture Content Gradient (MMCG)
Sarker et al. (1996), Chen et al. (1999), and Yang et al. (2000a) found that moisture content gradients (MCGs) inside the rice kernel greatly affected rice milling quality. The highest gradient was along the short axis in the kernel cross–section. Here, MCG was defined as dM/dy, where dM is the moisture content difference between the outer bran (node a) and center point (node b), and dy is their coordinate difference (fig. 8). By means of the software, MCG can be calculated. Figure 8 shows that a steep increase in MCG appeared in the early drying stage and was followed by a slow decline after passing the MMCG. The drying duration around which the MMCG was reached depended on the drying conditions. For example, a higher drying air temperature could cause a greater magnitude of MCG.
Internal Moisture Distribution During Tempering
Figure 9 illustrates the intra–kernel moisture content responses during a high–temperature (60³C) tempering
0 2 4 6 8 10 12 0 10 20 30 40 50 60 Ta 60 Deg. C, RH17% (A) Ta 50 Deg. C, RH25% (B) Ta 40 Deg. C, RH42% (C)
Moisture content gradients
between a and b (%d.b./mm)
Drying duration (min)
a b
A B C
Figure 8. Predicted moisture content gradients between node a (outer bran on short axis) and node b (kernel center point) at three drying condi-tions. Ta is drying air temperature, and RH is air relative humidity. The initial kernel moisture content was 21.1% (w.b.), and the initial kernel temperature was 29.2³C. 6 8 10 12 14 16 18 20 22 0 10 20 30 40 50 60
Tempering duration (min)
a b c Node a Node b Node c
Node moisture content (%w
.b.)
Figure 9. Predicted moisture contents of a rough rice kernel at nodes a, b, and c during 60³C tempering after 60 min drying at 60³C and 17% air relative humidity. The initial kernel moisture content was 21.1% (w.b.), the initial kernel temperature was 29.2³C, and the average moisture con-tent of rice kernels at the beginning of tempering was 14.5% (w.b.). process, immediately following a drying process at the same temperature, at nodes a (outer bran on the short axis), b (kernel center), and c (outer bran on the long axis). As soon as tempering began, the moisture content difference between nodes a and b decreased gradually, as the moisture content at node a increased and that at node b decreased. Moisture content at node c change little during tempering in this case. With tempering, moisture contents at these locations would eventually approach the same magnitude, around 16% w.b., given sufficient time (Steffe and Singh, 1980; Gustafson et al., 1983; Cnossen and Siebenmorgen, 2000; Yang et al., 2002). The internal moisture distribution analysis of rice kernels will help determine the most suitable tempering duration for a drying system.
C
ONCLUSIONSA Matlab based software package with C++ compiler has been developed to enable users to obtain the information on temperature, moisture, and stress distributions inside a single grain kernel during the drying and tempering process. The software is a useful tool for engineers or operators to develop optimum drying and tempering conditions to improve grain quality or for university educators to demonstrate grain drying to students from a single–kernel perspective. ACKNOWLEDGEMENTS
The authors would like to thank the Arkansas Rice Research and Promotion Board and the corporate sponsors of the University of Arkansas’ Rice Processing Program for their financial support of this research, and the Rice Research and Extension Center in Stuttgart, Arkansas, for supplying rice for this research. Special thanks should go to Billy Davidson and Zhihui Liu for their experimental assistance.
R
EFERENCESBrooker, D. B., F. W. Bakker–Arkema, and C. W. Hall. 1992.
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N
OTATIONSA = surface area of the kernel (m2)
B = strain–deformation gradient matrix of the kernel (1/m)
c = specific heat (J/kg ³C) D = diffusion coefficient (m2/s) Fb = body force (N)
hm = convective mass transfer coefficient (m/s)
ht = convective heat transfer coefficient (W/m2³C)
k = thermal conductivity of the kernel (W/m ³C) M = moisture content of the kernel (d.b.)
M = average moisture content of the kernel (d.b.) N = shape function matrix of the kernel
n = flux in a normal direction Qfg= latent heat of vaporization (J/kg)
r, z= r and z axes in a cylindrical coordinate system R = synthetical viscoelastic modulus of the kernel t = drying time (s)
T = temperature of the kernel (³C)
T = average temperature of the kernel (³C) U = virtual displacement, m)
u = air velocity (m/s)
V = volume of the kernel (m3)
e = normal strain (m/m)
s = normal stress (Pa)
g = shear strain (m/m)
t = shear stress (Pa)
a = thermal expansion coefficient (_1C) ρ = density (kg/m3)
b = hydro expansion coefficient (d.b.1 ) SUBSCRIPTS
qq, zz, rr, rz= tangential, axial, radial, and shear
0 = initial
a = drying air
e = equilibrium
g = grain
ti = at the end of drying
