Mathematical Problems in Engineering

Volume 2015, Article ID 539846, 13 pages

http://dx.doi.org/10.1155/2015/539846

## Numerical Simulation and Experimental Study of Deep Bed Corn Drying Based on Water Potential

^{1}College of Biological & Agricultural Engineering, Jilin University, Changchun 130022, China^{2}Academy of State Administration of Grain, Baiwanzhuang Street 11, Xicheng District, Beijing 100037, China

Received 11 March 2015; Revised 8 June 2015; Accepted 10 June 2015

Academic Editor: Valentin Lychagin

Copyright © 2015 Zhe Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The concept and the model of water potential, which were widely used in agricultural field, have been proved to be beneficial in the application of vacuum drying model and have provided a new way to explore the grain drying model since being introduced to grain drying and storage fields. Aiming to overcome the shortcomings of traditional deep bed drying model, for instance, the application range of this method is narrow and such method does not apply to systems of which pressure would be an influential factor such as vacuum drying system in a way combining with water potential drying model. This study established a numerical simulation system of deep bed corn drying process which has been proved to be effective according to the results of numerical simulation and corresponding experimental investigation and has revealed that desorption and adsorption coexist in deep bed drying.

#### 1. Introduction

Drying is one of the important parts in agricultural production [1]. It is an important research topic for how to effectively predict and control the drying process to ensure food quality after drying. However, drying is a complicated process involving simultaneous heat and mass transfer phenomena, and the essence is the moisture migration process. It is not only affected by material properties and medium parameters, but also has an important relationship with climate conditions and drying process. Therefore, the research on simulation of drying process has attracted many domestic and foreign scholars’ attention in the frontier field of agricultural engineering science. The most common type of cereal dryers is the deep bed dryer, also known as fixed bed dryers [2, 3]. Deep bed models for grain drying simulation can be classified as logarithmic, heat and mass balance, and partial differential equation [4]. The partial differential equation (PDE) model is more detailed, accurate, and valid for deep bed models for cereal drying simulation [5]. Since 1967, Bakker-Arkema et al. proposed a set of partial differential equations to describe grain drying process according to the basic theory of heat and mass transfer [6, 7]. In 1969, Spencer [8] derived a nonequilibrium model according to Bakker-Arkema but employed a different drying rate equation. The model was solved by a centered finite difference method. In order to test the model predictions, comparisons were made with the experimental work of Woodforde and Lawton [9] and Clark and Lamond [10, 11]. Reasonable agreement has been obtained with the average moisture content, but the comparison of exit air dry bulb temperature was unsatisfactory. In 1982, Sharp [12] neglected accumulation terms from energy and mass balance equation in his model. He justified this simplification by reference to earlier work of Bakker-Arkema et al. and Spencer. In 1995, Sun et al. [13] developed a static bed drying model including rewetting and condensation effects. In this model, the energy accumulation terms from air energy balance equation were conserved. Comparisons between the predictions and measured results have shown that their model predictions correspond to the measured values within experimental errors. In 2002, Srivastava and John [14] developed a grain drying model and they proposed a solution by an implicit numerical scheme and Runge-Kutta method to predict air humidity and temperature as well as grain temperature evolution with variation of bed height during drying. In this model, the accumulation terms from mass and energy balance were kept but their results were not compared with experimental data. In above models, the impact of pressure in the drying process was not considered; that is, above models were only suitable for the analysis of the drying process under atmospheric pressure but were not suitable for vacuum drying system which included the influence of pressure factor.

Water potential is one of the important applications of the concept of chemical potential in agriculture and biology. The concept of water potential was proposed by our country scholars Tang and Wang on the basis of the chemical potential in 1941 [15] and thus was widely used in foreign countries since the 1950s and in China after the 70s. In 2003, water potential theory was applied to the moisture migration model in the corn drying process by Wu for the first time [16]. In 2006, water potential theory was applied to analyze heat and mass transfer in corn grains internal in vacuum drying process, and the model was established in corn low temperature vacuum drying process based on water potential by Yin et al. [17–19]. Xu et al. established the rate model of moisture migration in paddy rice vacuum drying process based on analysis of the water potential theory [20]. In 2002, water potential model analytical solution was solved by Laplasse by Yang and its application was more convenient [21].

In this paper, water potential drying model and the traditional deep bed drying model were integrated. An effective new simulation method of deep bed drying process was found and thus could overcome the shortcoming that the application range of the traditional model is narrow and thus is not suitable for vacuum drying system which included the influence of pressure factor. And this model can be used generally. A numerical simulation system of deep bed drying grain was developed by the combination of MATLAB and LabVIEW, and the results of numerical simulation and the tests were contrasted.

#### 2. Mathematical Modelling

##### 2.1. The Relationship between Changes of Water Potential and Drying Rate in Drying Process

Water potential is widely used in agriculture and biology; it can fully reflect the moisture migration process. The expression of water potential is as follows [17]:

In the formula, the first is referred to as the osmotic potential, the second as pressure potential, and third as gravitational potential [17].

During the drying process, the exchange between grains and the surrounding air water is carried out by particles in the epidermis. The skin of particles which has internal porous structure has a certain thickness and pore [16].

Ignoring the effect of pressure and gravity, the water potential of inner cereal grains is expressed aswhere is water activity coefficient of grain internal, and the calculation formula of is shown as follows:

Similarly, outside of the cereal grains, air water potential is defined aswhere is moisture migration potential.

For , internal moisture is migrated outside. This is the analytical process of granular material.

For , internal moisture and external moisture are balanced. Granular material internal moisture is equilibrium moisture. In this case, grain is under equilibrium.

For , external moisture is migrated inward. This is the moisture absorption process of granular material.

Therefore, we can think that granular material moisture migration rate () depends on the moisture migration potential:

According to corn drying characteristic curve [22], there appears to be a linear relationship between the average humidity of corn and drying time in most of the area. For convenient calculation, we assumed that there is a linear correlation between and , and differential equation of can be derived as follows:where is the equilibrium moisture content of corn under atmospheric pressure. Henderson equation is adopted as equilibrium moisture equation [23]. That is,where the coefficients , , , and are given by the expressions: , , , and

Therefore, (6) becomes

Applying the Taylor series expansion, we can obtain formula (13) from (11):

Applying the Runge-Kutta method of order 4 to solve formula (13), we can obtain formulas (14)~(18). Therefore, formulas (14)~(18) are the analytical solution of corn drying model based on water potential:where the model coefficient is related to temperature and vacuum degree. In this paper simulation and experiment were studied under atmospheric pressure, so the influence of the pressure gradient is ignored. That is, the value is only related to temperature. The 100 g and uniform size corn samples were selected which initial moisture content was 20%. The corn sample was put into the sieve bowl and the weight was recorded. The temperature was set up under the condition of normal atmospheric pressure, and thus the temperature drying was selected at 40°C, 45°C, 50°C, 55°C, 60°C, and 65°C, respectively. The corn samples were placed in the drying oven when the temperature reached equilibrium. The weigh was recorded per 1 hour, which was converted into the wet basis moisture content of corn. The test was not stopped until the corn quality reached the equilibrium state. The equilibrium state can be considered as no more than 0.2 g mass difference between the former and latter half-hour weigh and thus can be considered to reach equilibrium moisture content of corn. The model parameters of (12)~(17) were substituted by test datum, and then the value of can be solved. The value of and the temperature were regression analyzed, and then the model of about hot air temperature was obtained:

##### 2.2. Partial Differential Drying Model during Drying Process

Brooker et al. proposed a theoretical model which is based on heat and mass transfer theory for the drying process. That model describes the grain drying process with a series of partial differential equations, including changes of grain temperature , medium temperature , and humidity of the air [24]. The corn drying model based on the heat and mass transfer is very complex, and, in order to simplify the drying model and reduce the complexity and computational time, the proposed fixed bed drying model is based on the following assumptions [24, 25]:(1)The volume shrinkage is negligible during the drying process.(2)The temperature gradients within individual particles are negligible.(3)The bin walls are adiabatic with negligible heat capacity.(4)The particle-to-particle heat conduction is negligible.(5)The air flow and grain flow are plug flow.(6)An accurate thin layer equation is known.

###### 2.2.1. Mass Balance Equation

The amount of grain moisture evaporation is equal to wet air moisture obtainment. Mass balance equation is established to solve humidity of the hot air at the outlet.

###### 2.2.2. Balance on the Enthalpy of Grain

The heat enthalpy transmitted from air to the grain by means of convective heat exchange is equal to the enthalpy required for water evaporation in the grain kernels over the control volume and for heating the water vapor extracted from the kernels and heating the kernels. Heat balance equation for obtaining the temperature of the thin layer kernels is shown as follows:where the volumetric heat transfer coefficient () for corn in a bed was calculated using Barker’s equation [26]:where and are constants ( and ), is the equivalent particle radius equal to 0.008 m for corn, and is the specific surface area of corm equal to 784 m^{2}/m^{3}. is air viscosity:

###### 2.2.3. Balance on the Enthalpy of Air

Convection heat of transfer process is equal to the difference of enthalpy before and after air entering the thin layer of grain, plus the enthalpy change of the air between kernels in time step. In order to figure out hot air temperature at a thin layer outlet, heat transfer balance can be established as follows:

Initial and boundary conditions for (12), (13), and (15) are , , , and .

##### 2.3. Required Equations

###### 2.3.1. Properties of Corn

Corn with different varieties and moisture content has different characteristics during the drying process. Equations are listed in Table 1 to get properties of corn [23, 27].