Finite Element Simulation of Corn Moisture Adsorption

Thin-layer moisture adsorption tests were conducted by exposing com kernels to different air relative humidities (RH of 75, 80, and 90%) and temperatures (25, 30, 35, and 40°C). A two-dimensional finite element model was developed to simulate moisture diffusion into a com kernel during adsorption. The finite element model satisfactorily predicted experimental moisture ratio of corn samples and performed better than the analytical model in predicting the adsorption behavior of corn kernels. Moisture profiles predicted with the finite element model showed that the moisture gradient between the center and boundary of a corn kernel exposed to air at 25, 30, and 35°C each at 90% RH was about 4% after one hour and reached a maximum of about 9% after 7.5 h and declined during subsequent adsorption. Keywords, Adsorption, Com, Diffusivity, Moisture, Simulation. C orn kernel is hygroscopic which adsorbs or desorbs moisture under changing environmental conditions. Moisture transport within grains during desorption (i.e., drying) has been widely investigated (Irudayaraj et al., 1992; Syarief et al., 1987; Suarez et al., 1981; Steffe and Singh, 1980a, b, c; Misra and Young, 1980). However, moisture transport during adsorption (i.e., wetting) has received only little attention (del Giudice, 1959; Chittenden, 1961; Misra, 1978; Muthukumarappan and Gunasekaran, 1990; Osborn et al., 1991; Lu and Siebenmorgen, 1992). In addition, the pattern of moisture movement inside a corn kernel during adsorption has not been reported. Because of the hysteresis between desorption and adsorption, desorption analyses are not directly applicable to adsorption analyses. Adsorption of com takes place during grain conditioning, storage, deep-bed drying, and aeration processes. For efficient processing operations, quantitative and predictive models relating the physical properties to transient timemoisture profiles that determine product quality are needed. Collecting moisture content data at various locations inside a com kernel as a function of time requires sophisticated sensors and is cumbersome. Mathematical models, based on physical principles, have the potential to accurately predict the moisture distribution inside the kemel during adsorption. The exact solution of the goveming equations might be difficult to obtain. Therefore, approximate solution techniques have to be sought. Development of fissures in com kernels is caused by both external and internal stresses. Fissured or stressArticle was submitted for publication in February 1996; reviewed and approved for publication by the Food and Process Engineering Inst, of ASAE in August 1996. The authors are K. Muthukumarappan, ASAE Member Engineer, Associate Researcher, and Sundaram Gunasekaran, ASAE Member Engineer, Professor, Biological Systems Engineering Department, University of Wisconsin-Madison, Wis. Corresponding author: K. Muthukumarappan, Biological Systems Engineering Dept., University of Wisconsin-Madison, 460 Henry Mall, Madison, WI 53706; telephone: (608) 262-7794, e-mail: . cracked kemels are objectionable because they are quite susceptible to breakage during handling and cause problems in storage, shipping, and processing (Gunasekaran and Paulsen, 1985). Moisture and temperature gradients prevalent within the grain cause undue expansion and contraction in the grain leading to the development of internal stresses (Gunasekaran et al., 1985). In general, moisture gradients have a predominant effect on the expansion and shrinkage of grains while the effect of temperature gradients is negligible (Suresh et al., 1975; Muthukumarappan et al., 1992). If the stresses developed within the kernels can be calculated accurately, better processes can be designed to reduce fissure development. However, such an estimation also requires the knowledge of transient time-moisture profiles and moisture gradients prevalent within a corn kernel during adsorption. Partially coupled heat and mass transfer equations have been solved for an isotropic sphere with constant material properties (Haghighi and Segerlind, 1988) and coupled equations with varying material properties (Haghighi et al., 1990) was used to study the drying of barley, soybean, and com kemels (Irudayaraj et al., 1992). Coupling effects of moisture and temperature, although important for accurately modeling desorption, is not important for adsorption since the adsorption process takes much longer (48 to 50 h) than the desorption process (6 to 10 h). And also when diffusion in a corn kemel takes place at constant temperature, the moisture diffusion equation alone is sufficient for describing moisture movement. Finite difference and finite element methods (FDM and FEM) have been extensively used to solve problems numerically. Husain et al. (1973) solved simultaneous heat and mass diffusion equations with the aid of altemating direction explicit scheme. They tested the model with rough rice and their prediction agreed well with the experimental data. Fortes et al. (1981) analyzed wheat drying and rewetting by applying a model based on nonequilibrium thermodynamics. Steffe and Singh (1980c) modeled thin-layer drying of rough, brown and white rice using Crank-Nicolson scheme and determined liquid VOL. 39(6) :2217-2222 Transactions of the ASAE © 1996 American Society of Agricultural Engineers 0001-2351 / 96 / 3906-2217 2217 diffusivities of starchy endosperm, bran, and hull of rough rice. The FEM is a powerful numerical technique for solving differential equations. The method assumes that any continuous quantity such as moisture can be approximated by a set of discrete piecewise-continuous functions defined over a finite number of subdomains or elements (Segeriind, 1984; Cook et al., 1989). Zhang et al. (1984) used the FEM to model water diffusion in rice with diffusion coefficient as a function of moisture concentration, and they also were able to account for the increase in the size of rice by swelling during soaking. Chinnan and Bakshi (1984) modeled the moisture transfer in rewetted peas during drying. Their approach was the same as that of Lomauro and Bakshi (1985). Sokhansanj and Gustafson (1980) applied the FEM and solved coupled heat and mass transfer equations for drying cereal grains. Both com and rice kemels were considered. When modeling the rice kemel, they considered endosperm, bran, and hull. But for corn, only the endosperms and germ were considered. The pericarp of the com, which acts as a barrier for moisture diffusion, was neglected. Haghighi et al. (1990) presented the solution of a set of coupled conductive heat and diffusive moisture transfer equations for grain drying simulation of axisymmetric bodies. The model assumed that the moisture diffuses to outer boundaries of the kernel in liquid form and evaporates at the surface of the grain. Lu and Siebenmorgen (1992) simulated the moisture adsorption of long-grain rough rice using the FEM. They determined the diffusivities of the hull, bran, and endosperm by assuming rice kemel as a composite body with the shape of a prolate spheroid. Corn kernel comprises of four major components, namely pericarp, germ, and soft and hard endosperms (Pomeranz, 1987). These components fill the kernel in a complex manner than any other grain which makes the diffusion analysis difficult. The moisture diffusivity of corn germ, pericarp and soft and hard endosperms was reported in Muthukumarappan and Gunasekaran (1994a, b and c). The moisture diffusivity of corn germ, pericarp, soft and hard endosperms was determined using a one-dimensional (1-D) analytical method, a 1-D FDM, and a 2-D FEM, respectively. The main objective of this article was to determine how well we can simulate the moisture diffusion in corn kemels using the diffusivity values reported in Muthukumarappan and Gunasekaran (1994a, b and c). In this study the FEM was used to solve the governing differential equations for the mass transfer during com kernel moisture adsorption. Since the moisture diffusivity of com components was determined using different methods, the moisture diffusion simulated using FEM should be verified against an analytical model. Moreover, the moisture diffusivity of corn germ which was determined using 1-D analytical method was used in the finite element simulation. Therefore it is necessary to compare the moisture diffusion simulated using the FEM with results of the analytical model for com adsorption. The specific objectives of this study were to: (1) develop a finite element model to simulate the moisture adsorption behavior of a whole corn kemel; and (2) verify the model by predicting nodal and average moisture content of the corn and comparing with experimental and analytical results. THEORETICAL CONSIDERATIONS The following theoretical development assumes that diffusivity is the dominant factor in the moisture transport process and, therefore, it is treated as a variable. Cartesian coordinate system was used to represent the corn kernel as a two-dimensional body. The two-dimensional diffusion equation which describes the moisture transport process has the form: