# Effects of the Broken Kernel on Heat and Moisture Transfer in Fixed-Bed Corn Drying Using Particle-Resolved CFD Model

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Experimental Apparatus

#### 2.3. Experimental Procedure

_{p}= 100 mm. The corn, along with the combined mass of the drying chamber and the air distributor, was weighed to determine the mass of the grain sample. To ensure the comparability of results, samples with different levels of broken kernel content were adjusted to have the same total mass. The corn samples were filled into the drying chamber using free-fall and adjusted the frequency converter to achieve 16 different inlet air velocities (ranging from 0.05 m/s to 0.8 m/s). A digital micromanometer was used to measure the pressure variations through the corn pile at different velocities. In order to ensure uniform corn temperature, the corn was left at ambient temperature for 24 h, the room temperature was 298.15 K. The temperature control panel of the hot air blower was adjusted, setting the inlet air temperature to 323.15 K. T-type thermocouples were placed at 25 mm intervals on the surface of the corn pile to measure the temperature changes within the bed. To determine the moisture content changes during grain drying, the drying chamber, along with the air distributor, was moved to a digital balance every 60 min from the start of the experiment. After the mass was recorded, the apparatus was quickly moved to the drying platform to minimize disturbance to the corn pile, allowing the calculation of the instantaneous moisture content through continuous weighing. Once a drying cycle was completed under a specific operating condition, the heat and moisture transfer measurements were performed for samples with different levels of broken kernel content following the same procedure. To ensure the precision of the experimental results, three replicates were conducted for each condition.

## 3. Numerical Simulation Models and Methods

#### 3.1. Rigid Body Dynamics Modeling

_{w}) and half kernels (N

_{b}) varied as follows for different packing models: N

_{w}= 1448 N

_{b}= 0 (0%); N

_{w}= 1300 N

_{b}= 296 (10%); N

_{w}= 1156 N

_{b}= 584 (20%); N

_{w}= 1012 N

_{b}= 872 (30%). Figure 3 illustrates the fixed-bed packing structure with various broken kernel content.

#### 3.2. Computational Domain and Mesh Generation

_{p}) of the fixed-bed packing region were determined to be 100 mm, 98.2 mm, 97.1 mm, and 96.4 mm for the broken kernel contents of 0%, 10%, 20%, and 30%, respectively. The inlet region has a length of H

_{i}= 25 mm, and the outlet region has a length of H

_{o}= 25 mm. Figure 4 provides a schematic of the geometric model for the corn packing structure.

_{p}had a minimal impact on the pressure drop and the flow behavior. Similarly, Bai et al. [36] applied the gap method with a 0.5% d

_{p}reduction in particle diameter and experimentally and numerically studied fluid flow between spherical and cylindrical particles, achieving good agreement between the simulated and experimental pressure drop in the bed. We have previously published relevant work exploring meshing techniques for both spherical and non-spherical grains [37]. In this study, the gap method is used to handle the contact between corn particles and the contact between the particles and the wall. The diameter of all corn particles is reduced by 0.5% d

_{p}, allowing for a more accurate depiction of the flow and temperature distribution. Given the complexity of particle shapes and bed structures, the ANSYS Fluent meshing is employed to generate hexahedral grids for both the air and particle regions. The grid size is 1/20 d

_{p}, and the number of boundary layers of the particles and the outer surface of the fixed bed is six, with a growth factor of 0.42 in the normal direction for each layer. Figure 5 illustrates the contact processing and mesh generation.

#### 3.3. Governing Equations

_{f}, k

_{f}, c

_{f}, are the density, thermal conductivity, and specific heat of the fluid, kg/m

^{3}, W/(m∙K), J/(kg∙K); µ

_{f}is the dynamic viscosity of the fluid, kg/(m∙s); T

_{f}is the temperature of the fluid, K; Y

_{f,db}is the moisture content of the fluid, % (d.b.); D

_{f}is the moisture diffusion coefficient of the fluid, kg/(m∙s).

_{s}, k

_{s}, and c

_{s}, are the density, thermal conductivity, and specific heat of the particle, kg/m

^{3}, W/(m∙K), J/(kg∙K); T

_{s}is the temperature of the particle, K; Y

_{s,db}is the moisture content of particle, % (d.b.); D

_{s}is the moisture diffusion coefficient of the particle, kg/(m∙s).

_{s}is the heat transfer coefficient, W/(m

^{2}∙K); h

_{m}is the mass transfer coefficient, m/s; T

_{0}and Y

_{s0}are the initial temperatures and moisture of corn, respectively, K, %(d.b.); Me is the initial moisture of the air, %(d.b.).

#### 3.4. Data Processing Methods

_{w}and B

_{w}are the dimensionless coefficients.

_{p}is the volume of the particles, mm

^{3}; A

_{p}is the area of the particles, mm

^{2}.

^{3}; T

_{in}and T

_{out}is the temperature of the inlet and outlet, K; $\overline{T}$ is the average temperature of heat exchange fluid, K. A

_{s}is the total heat transfer surfaces of particles, mm

^{2}.

#### 3.5. Boundary Conditions and Related Parameters

^{−6}.

## 4. Results and Discussion

#### 4.1. Radial Porosity Distribution

_{p}is the non-dimension distance; r is the distance between the measurement point and the central axis of the fixed bed; R is the radius of the fixed bed.

#### 4.2. Pressure Drop

#### 4.2.1. Experimental Pressure Drop

#### 4.2.2. Numerical Simulation of Pressure Drop

_{0}= 0.5 m/s was chosen for the study. Figure 8 shows the streamlines and pressure drop at the Y = X plane in fixed beds of corn with varying levels of broken kernel content. It can be observed that the airflow paths within the fixed beds are quite complex, and as the broken kernel content increases, the curvature of the airflow paths also increases. The flow reversal at the top becomes more pronounced, providing a visual representation of the increased resistance in the fixed bed [43]. Pressures in the inlet and outlet sections remain almost unchanged, indicating unobstructed fluid flow in these regions. The pressure gradually decreases along the axial direction within the packed bed, exhibiting a stratification phenomenon. In the fixed bed with 30% broken kernel content, the pressure stratification and fluctuation phenomena become more pronounced. The axial pressure distribution at the Y = X plane of fixed beds with different broken kernel contents is illustrated in Figure 9. Each point on the graph corresponds to a specific pressure drop value at a spatial location on the Y = X plane. The pressure drop increases in the inlet section with broken kernel content, while the pressure drop approaches 0 Pa in the outlet section. The fluctuating points on the graph represent local variations in pressure at the cross-section. Maximum fluctuations occur in 30% broken kernel content, consistent with the axial pressure drop contour plot. The pressure drop at the center cross-section of the fixed bed exhibits a linear decrease with increasing height. The slope of the curve increases with higher broken kernel content, indicating an accelerated rate of pressure drop reduction with increasing broken kernel content.

#### 4.3. Velocity Distribution

_{0}= 0.5 m/s was selected to investigate velocity fields in different fixed beds. Figure 11 illustrates velocity distribution at plane z = 20 mm, 50 mm, and 80 mm for corn fixed beds with varying levels of broken kernel content. The intricate shape of corn grains contributes to increased randomness in their arrangement, and the presence of irregularly arranged grains with angular orientations or sharp edges leads to more tortuous airflow paths, resulting in an uneven distribution of velocities along the axial direction of the fixed bed. This non-uniformity diminishes as the proportion of broken kernels increases. This can be attributed to the fact that some broken particles fill the gaps between whole grains, making the pore structure of the fixed bed more uniform and reducing the interconnected pathways for airflow, thus improving the uniformity of the velocity distribution within the fixed bed. Simultaneously, the fluid is forced to pass through numerous small pores and channels within the fixed bed, leading to a decrease in overall fluid velocity [45].

_{0}) for different fixed bed configurations is illustrated in Figure 13. The horizontal axis represents the radial dimensionless distance from the wall, facilitating comparison with the porosity distribution, while the vertical axis represents the dimensionless ratio of the radial sectional average velocity to the inlet velocity. The radial dimensionless velocity exhibits similar periodic oscillations as the porosity distribution. The velocity is notably higher near the fixed bed wall, and as the proportion of broken kernels increases, the local maximum velocity gradually decreases to 1.98, 1.93, 1.88, and 1.82 times higher than the inlet velocity. Fluctuations become smoother with increasing broken kernel content. The average velocity decreases with increasing broken kernel content. Under conditions of 0%, 10%, 20%, and 30% broken kernel content, the average flow velocities are 0.85 m/s, 0.83 m/s, 0.79 m/s, and 0.75 m/s, respectively. Figure 14 presents the axial distribution of dimensionless average velocity (V(z)/V

_{0}) and porosity for different fixed bed configurations. The horizontal axis represents the dimensionless axial distance from the wall. It can be observed that the axial dimensionless velocity follows a pattern similar to the radial dimensionless velocity distribution, with the only difference being the opposing trends in velocity magnitude at the two sides. This distinction arises because the contact area between the particles at the bottom in the fixed bed and the Z = 0 plane is relatively large. Specifically, the particle area extracted from the horizontal cross-section exceeds that of the cylindrical radial section. Consequently, the axial average velocity is lower at the inlet and outlet sections. In the vertical direction of the fixed bed, the axial dimensionless velocity also decreases with increasing broken kernel content and exhibits smoother fluctuations, similar to the axial porosity distribution.

#### 4.4. Temperature Distribution

_{0}= 0.5 m/s and a drying temperature of T

_{i}= 328.15 K, we investigated the distribution pattern of temperature fields in fixed beds. The initial temperature of the corn pile was set at 298.15 K. Figure 15 shows the temperature contour at the plane of Z = 20 mm, 50 mm, and 80 mm in fixed beds after 7 min of drying. There is a noticeable stratification of the temperature along the axial direction of the fixed bed, with the bottom of the bed exhibiting higher temperatures compared to the top. The hot air, upon entering the fixed bed, interacts with the particles at the bottom, causing its temperature to increase rapidly. However, in the upper regions of the fixed bed, hot air undergoes heat transfer to the low-temperature particles in addition to complex pore paths, resulting in a slower temperature increase. This leads to a distinct temperature stratification within the bed, characterized by axial temperature gradients. Figure 16 presents the temperature distribution contour map at the Y = X plane after 7 min of drying, considering different levels of broken kernel contents. Along the radial direction within the various fixed bed configurations, there is an uneven distribution of temperature between the fluid and solid particles. This uneven distribution arises from the non-uniform packing structure and fluid velocity distribution, causing the temperature at the wall surface to be higher than in the central region. This corresponds to the position at the higher value of the velocity field.

^{2}∙K), 52.71 W/(m

^{2}∙K), 54.50 W/(m

^{2}∙K), and 59.72 W/(m

^{2}∙K), respectively. The corresponding peak Nu values are 14.52, 15.28, 15.56, and 17.31, while the peak heating transfer powers are 18.52 W, 21.75 W, 23.93 W, and 25.86 W. The transient heat transfer characteristic parameters of the fixed bed during drying increase with an increase in broken kernel content.

#### 4.5. Moisture Distribution

_{0}= 0.5 m/s and a ventilation temperature of T

_{i}= 328.15 K. Figure 20 illustrates the moisture distribution at different times at the Y = X plane. During the drying process, in contrast to the heat transfer process, moisture is transferred from the interior to the surface of the corn grains. Convection mass transfer near the surface of the grains is evident, while moisture migration and diffusion become relatively slower towards the central region. As a result, a moisture gradient forms within the grains, and even after 2 h of drying, the corn in the fixed bed remains in a high-moisture state. After 6 h of drying, it is noticeable that the moisture in the fixed bed with 30% broken kernels is significantly lower than in the bed without broken kernels (0%), indicating that the moisture transfer rate in the fixed bed increases with the broken kernel content. This can be attributed to the increased mass transfer surface area due to the addition of broken kernels, providing more interfaces for mass transfer and facilitating the interaction between the mass transfer medium and the particles. Furthermore, small intergranular pores offer more pathways for mass transfer, allowing the mass transfer medium to penetrate and diffuse into the particle interiors more easily, thereby further enhancing the mass transfer rate [46]. Figure 21 illustrates the moisture distribution at different heights, Z = 20 mm, and 80 mm, inside the fixed bed after 6 h of drying. The uniformity of axial drying within the fixed bed is quite good, with a reduction in moisture gradients within the corn particles as the drying time increases. Similarly to temperature gradients, the moisture gradient is greater in the radial direction than in the axial direction.

## 5. Conclusions

- (1)
- The RBD method can effectively capture the oscillation phenomenon of radial porosity in a fixed bed. Compared to whole grains, a higher content of broken kernels tends to fill the larger pores, resulting in a decrease in local porosity as the broken kernel content increases.
- (2)
- The increase in the broken kernel content leads to higher curvature in the air-flow paths within the fixed bed, increasing the pressure drop. The PRCFD model takes into account the influence of particle characteristics, providing direct estimates of pressure drop in realistic bed configurations. It agrees well with the experimental results in different bed configurations, with an average error of less than 15%. With an increase in broken kernel content, the velocity within the fixed bed gradually decreases, resulting in smoother fluctuations.
- (3)
- The increase in broken kernel content amplifies the contact area between the particles and the heat transfer medium, thereby enhancing the heat transfer process. The PRCFD model integrates both convective heat transfer in the fluid phase and thermal diffusion in the solid phase, without simplifying any specific models or heat transfer mechanisms, yielding calculation results that align well with experimental data. The characteristic parameters of the transient heat transfer exhibit an increasing trend with increasing broken kernel content.
- (4)
- The addition of broken kernels increases the surface area for mass transfer, thereby enhancing the rate of moisture transfer in the fixed bed. Compared to the fixed bed without broken kernels (0%), which requires 560 min to dry the corn pile to a safe moisture level of 14% (d.b.), the drying time is reduced by 60 min, 100 min, and 130 min for the respective broken kernel contents of 10%, 20%, and 30%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A_{p} | the area of the particle |

A_{s} | total heat transfer surfaces of particles |

A_{w}, B_{w} | the dimensionless coefficient |

c_{f} | the specific heat of the fluid |

c_{s} | the specific heat of the particle |

D | the diameter of the packing structure |

d_{p} | the equivalent diameter of the particle |

D_{f} | the moisture diffusion coefficient of the fluid |

D_{s} | the moisture diffusion coefficient of the particle |

E_{st} | the total energy |

H_{i} | the length of the inlet region |

H_{p} | the length of the packing region |

H_{o} | the length of the outlet region |

h_{m} | the mass transfer coefficient |

h_{s} | the heat transfer coefficient |

k_{f} | the thermal conductivity of the fluid |

k_{s} | the thermal conductivity of the particle |

L | the height of the packing structure |

M_{e} | the initial moisture of the air |

N_{b} | the number of half kernel |

N_{w} | the number of the whole kernel |

n | the non-dimension distance |

P_{st} | the heat transfer power |

R | the radius of the fixed bed |

r | the distance to the central axis of the fixed bed |

T_{f} | the temperature of the fluid |

T_{s} | the temperature of the particle |

T_{0} | the initial temperatures of corn |

T_{in} | the temperature of the inlet |

T_{out} | the temperature of the outlet |

$\overline{T}$ | the average temperature of the fluid |

µ_{f} | the dynamic viscosity of the fluid |

V_{p} | the volume of the particle |

Y_{f,db} | the moisture content of the fluid |

Y_{s,db} | the moisture content of the particle |

Y_{s0} | the initial moisture of corn |

ρ_{f} | the density of the fluid |

ρ_{s} | the density of the particle |

ε | the non-constrained porosity |

∆p | the pressure drop |

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**Figure 8.**Streamlines and pressure drop at the Y = X plane in fixed beds: (

**a**) 0%; (

**b**)10%; (

**c**) 20%; (

**d**) 30%.

**Figure 10.**Comparison of experimental and simulated pressure drop in fixed beds: (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; (

**d**) 30%.

**Figure 11.**Velocity distribution on Z = 20 mm, 50 mm, and 80 mm plane in fixed beds: (

**a**) 0%; (

**b**)10%; (

**c**) 20%; (

**d**) 30%.

**Figure 12.**Velocity distribution at the Y = X plane in fixed beds: (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; (

**d**) 30%.

**Figure 14.**The axial distribution of dimensionless average velocity and porosity in fixed beds: (

**a**) axial dimensionless velocity; (

**b**) axial porosity.

**Figure 15.**The temperature distribution contour at the Z = 20 mm, 50 mm, and 80 mm plane after 7 min of drying: (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; (

**d**) 30%.

**Figure 16.**The temperature distribution contour at the Y = X plane after 7 min of drying: (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; (

**d**) 30%.

**Figure 17.**The axial and radial average temperature distribution curve: (

**a**) axial temperature; (

**b**) radial temperature.

**Figure 19.**Parameters of the characteristic transient heat transfer for different drying stages in fixed beds: (

**a**) heat transfer coefficient; (

**b**) Nusser number; (

**c**) heat transfer power; (

**d**) total energy.

**Figure 20.**The moisture distribution at different times at the Y = X plane: (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; (

**d**) 30%.

**Figure 21.**The moisture distribution at the Z = 20 mm and 80 mm plane after 6 h of drying: (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; (

**d**) 30%.

Parameters | Value | Symbol |
---|---|---|

Geometry size | 100 × 100 | D × L, mm |

Particle density | 1058.7 | ρ_{s}, kg/m^{3} |

Gravity acceleration | 9.81 | m/s^{2} |

Integration time step | 0.1 | s |

Surface friction coefficient of particles | 0.4 | - |

Surface bounciness of particles | 7.6 × 10^{8} | - |

Surface friction coefficient of walls | 0.2 | - |

Surface bounciness of walls | 0.02 | - |

Material | Parameters | Symbol | Value |
---|---|---|---|

Corn | Density | ρ_{s}, kg/m^{3} | $\text{}{\rho}_{\mathrm{s}}=1000+14.556{Y}_{\mathrm{s},\mathrm{db}}+217\mathrm{exp}\left(-{Y}_{\mathrm{s},\mathrm{db}}\right)$ |

Specific heat capacity | c_{s}, J/(kg∙K) | ${c}_{\mathrm{s}}=2000+35.5\left({Y}_{\mathrm{s},\mathrm{db}}/1+{Y}_{\mathrm{s},\mathrm{db}}\right)$ | |

Thermal conductivity | k_{s}, W/(m∙K) | ${k}_{\mathrm{s}}=\mathrm{exp}\left(\begin{array}{l}-1.74-3.7{Y}_{\mathrm{s},\mathrm{db}}+4.72{\mathrm{e}}^{-3}{T}_{\mathrm{s}}\\ +6.48{Y}_{\mathrm{s},\mathrm{db}}^{2}-1.5{\mathrm{e}}^{-4}{T}_{\mathrm{s}}^{2}+6.27{\mathrm{e}}^{-2}{Y}_{\mathrm{s},\mathrm{db}}{T}_{\mathrm{s}}\end{array}\right)$ | |

Mass diffusivity | D_{s}, m^{2}/s | ${D}_{\mathrm{s}}=4.203{\mathrm{e}}^{-8}\mathrm{exp}\left(-\frac{2513}{{T}_{\mathrm{s}}}+\left(0.045{T}_{\mathrm{s}}-5.5\right){Y}_{\mathrm{s},\mathrm{db}}\right)$ | |

Air | Density | ρ_{f}, kg/m^{3} | ${\rho}_{\mathrm{f}}=8.666\times {10}^{-6}{T}_{\mathrm{f}}^{2}-4.318\times {10}^{-3}{T}_{\mathrm{f}}+1.288$ |

dynamic viscosity | μ_{f}, kg/(m∙s) | ${\mu}_{\mathrm{f}}=1.691\times {10}^{-5}+4.984\times {10}^{-8}{T}_{\mathrm{f}}$ | |

Specific heat | c_{f}, J/(kg∙K) | ${c}_{\mathrm{f}}=1002.9+0.0054{T}_{\mathrm{f}}$ | |

Thermal conductivity | k_{f}, W/(m∙K) | ${k}_{\mathrm{f}}=-2.401\times {10}^{-8}{T}_{\mathrm{f}}^{2}+7.554\times {10}^{-5}{T}_{\mathrm{f}}+2.364\times {10}^{-2}$ | |

Mass diffusivity | D_{f}, m^{2}/s | ${D}_{\mathrm{f}}=2.89{\mathrm{e}}^{-5}{\left(\frac{{T}_{\mathrm{f}}}{40+273.15}\right)}^{1.81}$ |

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## Share and Cite

**MDPI and ACS Style**

Liu, W.; Chen, G.; Zheng, D.; Ge, M.; Liu, C.
Effects of the Broken Kernel on Heat and Moisture Transfer in Fixed-Bed Corn Drying Using Particle-Resolved CFD Model. *Agriculture* **2023**, *13*, 1470.
https://doi.org/10.3390/agriculture13081470

**AMA Style**

Liu W, Chen G, Zheng D, Ge M, Liu C.
Effects of the Broken Kernel on Heat and Moisture Transfer in Fixed-Bed Corn Drying Using Particle-Resolved CFD Model. *Agriculture*. 2023; 13(8):1470.
https://doi.org/10.3390/agriculture13081470

**Chicago/Turabian Style**

Liu, Wenlei, Guixiang Chen, Deqian Zheng, Mengmeng Ge, and Chaosai Liu.
2023. "Effects of the Broken Kernel on Heat and Moisture Transfer in Fixed-Bed Corn Drying Using Particle-Resolved CFD Model" *Agriculture* 13, no. 8: 1470.
https://doi.org/10.3390/agriculture13081470