Experimental Study on Variation Characteristics of Pressure Drop and Process Optimization for Corn Kernels During the Hot Air Convective Drying Process

Abstract

To reveal the variation characteristics of the pressure drop during the corn hot air drying process and provide some reference for designing the drying process, a pressure drop model focusing on the dynamic drying process was established based on the response surface methodology and the variation characteristics of the pressure drop has been analyzed in the present work. In detail, a corn convective drying apparatus was established, and a center rotation regression experiment was conducted followed by a Box–Behnken design by considering hot air temperature (T), corn flow velocity (v_c), air velocity (v_a), and thickness of the materials layer (L) as independent variables while and the pressure drop (δP) was considered as the dependent variable. The results show that the v_a has the most significant impact on the δP, followed by L, v_c, and T. The established model δP_RSM shows a better fitting and prediction performance (R² = 0.969, Cook’s distance < 1) than that of commonly used models. In addition, the minimize δP was determined as 368.392 Pa, and the corresponding drying conditions are T of 60 °C, v_c of 0.06 m/s, v_a of 0.2 m/s, and L of 500 mm, and the hot air temperature should be within 72 °C, which can form the basis for designing the corn hot air drying process.

1. Introduction

Corn is the largest grain product in China. In 2022, China’s total grain production was 686.53 million tons, accounting for approximately a quarter of the world’s total grain production. As a principal cereal crop ranking among the three most crucial grain species, corn serves dual roles as both a fundamental dietary ingredient and premium livestock feed, while simultaneously functioning as a critical industrial resource for bioethanol production and starch-derived manufacturing processes [1,2]. Due to the high moisture content of freshly harvested corn, rot, mildew, and other conditions can occur without sufficient drying in time, resulting in huge economic losses [3]. However, during the drying process of corn, the internal pressure drop is affected by the flow rate of corn, the thickness of the drying layer, and the wind speed. Therefore, the variation characteristics of the pressure drop during corn drying were studied to provide a relevant theoretical basis for the design of corn drying equipment.

In recent years, scholars at home and abroad have performed a lot of research on hot air drying technology of corn, such as Zeng Z. [4], Zhang S. [5], da Silva G.M. [6], and Wei S. [7] et al. who studied corn drying mechanical heat exchanger, energy saving and emission reduction technology, hot pipe technology, and convection heat and mass transfer modeling, respectively. Many studies show that energy utilization is the core content of corn concentrated drying technology. Researchers have also performed a lot of work on corn concentrated drying and energy-saving technology from many aspects. The grain layer pressure drop is a key parameter for designing and optimizing the structure of the drying chamber, and it is also an important reference parameter for selecting the fan power [8,9]. In the drying process, due to the porosity of the bed layer and the viscosity of air, there must be a pressure drop in the hot air pressure when the hot air flows through the grain layer. Too high pressure drop may make it difficult for hot air to flow through the grain layer, and further lead to an increase in drying nonuniformity. Too low-pressure drop may lead to a waste of fan power, too short heat transfer time, and a large amount of heat energy carried by the medium is greatly wasted [10,11]. Therefore, it is necessary to seek a reasonable pressure drop under the premise of ensuring the drying quality.

In the past few decades, researchers have used classical pressure drop models (Ergun model, Shedd model) to study the ventilation resistance of grain layer [12,13,14,15]. For example, Gunasekaran S. and Jackson C. [16] used the Ergun model to study the ventilation resistance of sorghum grain layer, and measured the pressure drop of sorghum with moisture content of 16.5%w.b., 18.5%w.b. and 23%w.b. under the air current range of 0.05 m/s to 0.3 m/s. The result shows that the pressure drop increases with the increase in air velocity and grain layer thickness, and increases with the decrease in water content. Li Q. et al. [9] used Shedd model to simulate the ventilation resistance of hot air flowing through the rice bed, and found that the ventilation resistance of hot air increased with the increase in air velocity. Zhang Y. et al. [17] studied the pressure drop of natural air (velocity range 0.1~0.6 m/s) flowing through the grain layer with a depth range of 100~1000 mm, and found that only when the air velocity is lower than 0.2 m/s, the fitting accuracy of the Ergun pressure drop model can be guaranteed. From the above analysis, it can be seen that although scholars at home and abroad have performed a lot of research on the ventilation resistance of agricultural products with different particle, there are few studies on the ventilation resistance of corn grain layer. In addition, although the Ergun pressure drop model is suitable for describing the characteristic of ventilation resistance of particle agricultural products and can investigate the influence of single factor on pressure drop, it cannot analyze the influence of interaction among various factors on pressure drop.

The response surface method (RSM) is widely adopted as an effective modeling method for optimizing the influence of various factors on the target response in multi-variable systems [18,19]. Within the realm of agricultural research, RSM assumes a pivotal role in optimizing process parameters and constructing predictive models. For example, Geng Z. et al. [20] employed RSM to model and optimize key factors such as dry air temperature, speed, and infrared power. Through RSM modeling and optimization of drying parameters, the optimal drying conditions were determined as air temperature 70 °C, speed 1 m/s, and infrared power 0.225 kW. The results show that there is a strong correlation between the experimental values and the predicted values, and the maximum relative error is 3.15%. In order to deal with the optimization of energetic and exergetic parameters of a hybrid solar dryer, Parhizi Z. et al. [21] considered the effects of air temperature and bed thickness, and optimized exergy performance using RSM combined with the center combination design (CCD) and ideal function (DF). The results indicate that the optimal drying conditions are 63.8 °C air temperature and 2 cm bed thickness, where the parameters achieve the maximum utility function value (D = 0.548). In addition, Zeng Z. et al. [22] utilized RSM and Artificial Neural Network (ANN) to optimize the vacuum drying process of konjac, identifying optimal conditions of 60.34 °C, 0.06 MPa vacuum pressure, and 2 mm thickness. The findings demonstrated that the RSM model exhibited superior predictive performance compared to the ANN model. All in all, as the demand for efficient drying processes increases, RSM has gained increasing attention in optimizing drying parameters and enhancing product quality. The response surface methodology (RSM) has been widely applied in multi-objective optimization within the agricultural drying field.

In summary, in order to find a pressure drop model suitable for describing the actual corn drying process, this paper uses the four-element quadratic center rotation combination design method to establish the δP model of corn ventilation pressure drop under different hot air temperature T (60, 70, and 80 °C), different corn flow velocity v_c (0, 0.04, and 0.08 m/s), different hot air velocity v_a (0.1, 0.3, and 0.5 m/s), and different material thickness L (400, 600, and 800 mm), and was compared with the classical Ergun pressure drop model. The effects of the interaction between different factors on δP were investigated in order to obtain the optimal process parameter combination for optimizing practical corn drying operations [23].

2. Materials and Methods

2.1. Materials

The fresh corn sample (Great Wall 799 #) used in this paper was harvested from a local agricultural machinery cooperative in Yongchuan District, Chongqing, China. The initial moisture content averaged 32.2%d.b. through standardized oven drying at 105 °C, in accordance with conventional gravimetric analysis protocols [24]. The uniform and non-destructive samples were selected for the experiment, and the impurity rate of the sample was less than 5%.

2.2. Equipment Apparatus and Instruments

Figure 1 illustrates the schematic diagram of the experimental apparatus. The system comprises a centrifugal fan, a ventilation pipe, a PC, a test pipe (0.3 m in diameter), a paperless recorder, a screen valve, an anemometer, a pressure drop sensor, and a support bracket. Ten pressure measurement ports are uniformly distributed along the axial direction of the test pipe at 0.1 m intervals, each operable via manual control to meet experimental requirements. A stainless steel screen valve is integrated at the base of the test chamber to regulate corn flow rates by adjusting its aperture. To ensure pressure integrity, the corn storage compartment is hermetically sealed with a sealing ring. During preparatory procedures, the screen valve remains closed while corn grains are loaded vertically into the test pipe until the bed attains a predetermined thickness, after which the centrifugal fan is activated. Experimental measurements include inlet air velocity (v_a) via the anemometer, ambient temperature via a calibrated thermometer, and transient pressure drop across the corn bed via the pressure drop sensor, with all data logged by the paperless recorder. Technical specifications of the instrumentation are cataloged in

Table 1. Details of the experimental instruments.

Instruments	Model/Material	Place of Manufacture	Values/Range	Accuracy
Frequency converter	Delta VFD002M43B	Bellme Electrical Technology Co., Ltd., Shenzhen, China	2.2 kW	-
Centrifugal fan	XYFL-170	Jiachangle Electric Appliance Co., Ltd., Guangzhou, China	2.2 kW	-
Screen	Stainless steel	-	2 × 2 mm	-
Digital vernier caliper	MNT-150	Mitutoyo Corporation, Kanagawa, Japan	0–200 mm	0.02 mm
Intelligent air pressure and volume instrument	GZF-S100	Anhui Jixun Automation Instruments Co., Ltd., Anhui, China	0–±5000 Pa	±1 Pa
Thermal resistor	PT100	Lixiang Electronics Co., Ltd., Guangzhou, China	−200–450 °C	±0.1 °C

, while operational parameters of the variable-speed fan are detailed in

Table 2. Parameters related to centrifugal fans.

Parameters	Values
Specification and size	330 × 156 × 220 mm
Maximum air volume	540 m3/h
Noise level	52 dB (A)
Voltage	220 V
Rated power	80 W
Maximum rotational speed	2550 r/min
Pipe diameter	160 mm

.

In order to set the different levels of the corn flow velocity v_c, a valve with six fan-shaped screens was designed and insulted at the bottom of the experimental chamber, as shown in Figure 2. The different v_c are controlled by the valve opening degree l; in detail, the v_c is determined by the mass of corn flowing out of the valve per unit time (v_c = m/ρ_cS). The correlations between the v_c and l are primarily ascertained and tabulated in

Table 3. The correlations between the v_c and l.

Opening Degree l/mm	Corn Velocity vc/m·s−1
15.8	0.02025 ± 0.0001232
17.0	0.02986 ± 0.0000867
18.8	0.04012 ± 0.0002458
20.8	0.05072 ± 0.0000957
22.6	0.06042 ± 0.0003457
24.2	0.06992 ± 0.0000892
26.8	0.08007 ± 0.0001785

. And the approximation of the measured v_c is used for further calculations.

2.3. Experimental Design

In order to achieve the optimum comparability to the actual situation of corn hot air drying, the hot air temperature T, corn flow velocity v_c, air velocity v_a, and thickness of paving materials L were selected as independent variables, and the grain layer pressure drop δP was used as the dependent variable. The central rotation combination experimental design method was used to investigate the effects of various factors and the interaction among factors on the pressure drop. The level of each factor of the independent variable is shown in

Table 4. Experimental design.

Code	Levels
	T/°C	vc/m·s−1	va/m·s−1	L/mm
+r	80	0.08	0.5	800
1	75	0.06	0.4	700
0	70	0.04	0.3	600
−1	65	0.02	0.2	500
−r	60	0	0.1	400

.

2.4. The Fitting Pressure Drop Models

In order to verify the reliability of the pressure drop model (δP_RSM) that was established based on the RSM, the commonly used pressure drop models including Ergun mode, Shedd’s equation, and Hukill equation have been adopted to be the control models in the present work, which are respectively expressed as follows.

2.4.1. Ergun Model

The classic Ergun pressure drop model (δP_Erg) was selected in this paper to fit the experimental data. The Ergun model expression is shown in Formula (1) [25]:

$$-{\displaystyle \frac{\mathrm{\delta }{P}_{Erg}}{L}}={\displaystyle \frac{150\mu {\left(1-\epsilon \right)}^2}{d_c^2{\epsilon }^3}}{v}_a+{\displaystyle \frac{1.75\rho \left(1-\epsilon \right)}{d_c{\epsilon }^3}}{v}_a^2$$

(1)

where δP_Erg is the pressure drop calculated by the Ergun model, Pa; L is the grain layer thickness, m; v_a is the hot air velocity, m/s; ε is the porosity of grain layer, ε = 0.65 [18]; d_c is the equivalent diameter of single corn, m of which d_c can be calculated by the following Equation (2) [26].

$$d_c=3L_0{W}_0{H}_0{\left(L_0{W}_0+L_0{H}_0+W_0{H}_0\right)}^{-1}$$

(2)

where L₀, W₀, and H₀ are the length, width and thickness of a single corn, m, respectively. and the L₀, W₀, and H₀ can be measured, respectively. A total of 50 corn kernels with similar size were randomly selected to be the measured samples, the measured results are depicted in Figure 3, and the average d_c is ascertained to be 7.29 × 10⁻⁴ m.

2.4.2. Shedd’s Equation

The Shedd’s equation is easy to incorporate into mathematical models for predicting the air pressure drop in stored grains [13], which has been widely used for estimating the pressure drops during the grain layer drying processes. The Shedd’s equation is expressed in Equation (3) [27].

$$V_{shedd}=A_1{\left({\displaystyle \frac{\delta P_{shedd}}{L}}\right)}^{B_1}$$

(3)

where δP_Shded is the pressure drop calculated by the Shedd’s equation, Pa; V_Shedd is the inlet air flow rate, m³·s⁻¹·m⁻²; L is the thickness of the grain layer, m; the A₁ and B₁ are the empirical coefficients which can be simulated by the experimental data.

2.4.3. Hukill Equation

The Hukill equation was also adopted to verify the reliability of the pressure drop model as well as investigate the pressure drop during the corn drying process, which is an empirical model proposed by Hukill and Ives in 1955 [28]. The Hukill equation is expressed in Equation (4).

$${\displaystyle \frac{\delta P_{Hukill}}{L}}={\displaystyle \frac{A_2{V}_{Hukill}^2}{\ln \left(1+B_2{V}_{Hukill}\right)}}$$

(4)

where δP_Hukill is the pressure drop calculated by the Hukill equation, Pa; V_Hukill is the inlet air flow rate, m³·s⁻¹·m⁻²; L is the thickness of the grain layer, m; the A₂ and B₂ are the empirical coefficients which can be simulated by the experimental data.

2.5. Statistical Analysis

In the present work, coefficient of determination (R²), mean square error (MSE), mean absolute error (MAE), and root mean square error (RMSE) are used to analyze the experimental results. The R², MSE, MAE, and RMSE can be calculated by the following Equations (5)–(8), respectively [29,30].

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n(Y_{pre,i}-Y_{\exp ,i}{)}^2}{{\sum }_{i=1}^n(Y_{exp,i}-\overline{Y_{pre,i}}{)}^2}}$$

(5)

$$MSE={\displaystyle \frac{{\sum }_{i=1}^n(Ypre,i-Y\exp ,\mathrm{i}{)}^2}{n}}$$

(6)

$$MAE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|Y_{pre,i}-Y_{\exp ,\mathrm{i}}\right|$$

(7)

$$RMSE=\sqrt{MSE}$$

(8)

3. Results and Discussion

3.1. Experimental Results

Hongtu Zhang [31] and colleagues conducted experimental research on the pressure drop characteristics of negative pressure sampling drill rods. By employing dimensional analysis methods with experimental pressure drop data, they established an additional pressure drop coefficient model that can accurately predict the pressure drop in drill rods. According to the experimental design presented in Table 4 above, the paper details the experimental scheme of the four-element quadratic center rotation combination experiment as shown in

Table 5. Experimental design and the results.

Run	Experimental Design				Results
	T/°C	vc/m·s−1	va/m·s−1	L/mm	δP/Pa
1	65(−1)	0.02(−1)	0.2(−1)	500(−1)	474.37
2	75(1)	0.02(−1)	0.2(−1)	500(−1)	534.53
3	65(−1)	0.06(1)	0.2(−1)	500(−1)	324.42
4	75(1)	0.06(1)	0.2(−1)	500(−1)	369.41
5	65(−1)	0.02(−1)	0.4(1)	500(−1)	1244.68
6	75(1)	0.02(−1)	0.4(1)	500(−1)	1367.52
7	65(−1)	0.06(1)	0.4(1)	500(−1)	925.38
8	75(1)	0.06(1)	0.6(1)	500(−1)	998.56
9	65(−1)	0.02(−1)	0.2(−1)	700(1)	1024.68
10	75(1)	0.02(−1)	0.2(−1)	700(1)	1130.33
11	65(−1)	0.06(1)	0.2(−1)	700(1)	749.66
12	75(1)	0.06(1)	0.2(−1)	700(1)	834.05
13	65(−1)	0.02(−1)	0.4(1)	700(1)	2305.92
14	75(1)	0.02(−1)	0.4(1)	700(1)	2592.15
15	65(−1)	0.06(1)	0.4(1)	700(1)	1790.98
16	75(1)	0.06(1)	0.6(1)	700(1)	1951.87
17	60(−r)	0.04(0)	0.3(0)	600(0)	925.38
18	80(r)	0.04(0)	0.3(0)	600(0)	1130.37
19	70(0)	0.00(−r)	0.3(0)	600(0)	1367.52
20	70(0)	0.08(r)	0.3(0)	600(0)	749.66
21	70(0)	0.04(0)	0.1(−r)	600(0)	369.41
22	70(0)	0.04(0)	0.5(r)	600(0)	2305.92
23	70(0)	0.04(0)	0.3(0)	400(−r)	474.37
24	70(0)	0.04(0)	0.3(0)	800(r)	1951.87
25	70(0)	0.04(0)	0.3(0)	600(0)	1335.26
26	70(0)	0.04(0)	0.3(0)	600(0)	1344.99
27	70(0)	0.04(0)	0.3(0)	600(0)	1336.19
28	70(0)	0.04(0)	0.3(0)	600(0)	1368.17
29	70(0)	0.04(0)	0.3(0)	600(0)	1317.38
30	70(0)	0.04(0)	0.3(0)	600(0)	1312.22

below. Experiments were performed sequentially according to the experimental order, each experiment was quickly measured three times and the average value was used for the calculations. The experimental results are tabulated in Table 5.

3.2. Discussion and Analysis

3.2.1. ANOVA Analysis

Substituting the experimental results shown in Table 5 into the Design-Expert 12 software (Produced in the United States Stat-Ease company development), the variance analysis results of the pressure difference δP are obtained, as shown in

Table 6. The results of ANOVA for δP.

Parameter	Deferential Pressure δP/(Pa)
	Degree of Freedom df	Sum of Squares	F-Value	p-Value
Model	14	1.044 × 107	985.56	<0.0001 **
T	1	75,747.49	100.14	<0.0001 **
vc	1	6.552 × 105	866.25	<0.0001 **
va	1	5.615 × 106	7423.23	<0.0001 **
L	1	3.447 × 106	4557.32	<0.0001 **
T·vc	1	2793.92	3.69	0.0738
T·va	1	7566.83	10.00	0.0064 **
T·L	1	7055.58	9.33	0.0080 **
vc·va	1	57,253.72	75.69	<0.0001 **
vc·L	1	32,687.74	43.21	<0.0001 **
va·L	1	2.675 × 105	353.63	<0.0001 **
T2	1	1.594 × 105	210.73	<0.0001 **
vc2	1	1.289 × 105	170.42	<0.0001 **
va2	1	40.48	0.0535	0.8202
L2	1	24,556.46	32.46	<0.0001 **
Residual	15	11,346.17
Lack of fit	10	9318.19	2.30	0.1856 (NS)
Pure error	5	2027.97
Total variation	29	1.045 × 107
Std·Dev	27.50
Mean	1196.91
C.V.%	2.30
R2	0.9989
AdjR2	0.9879
PreR2	0.9746

** is the symbol for extremely significant; NS is a non-significant symbol.

.

According to the variance analysis results shown in Table 6, it can be seen that the p-value of the model is less than 0.0001 while the lack of fit (0.1856) is higher than 0.05, indicating that the model is significant and the lack of fit is not significant. Moreover, it can be seen from Table 6 that the value of the coefficient of variation C.V. is 2.3%, indicating that only 2.3% of the experimental data cannot be explained by the established model. And the values of the AdjR² and PreR² are determined as 0.9879, and 0.9746, respectively, and the AdjR² is in reasonable agreement with the PreR². By comprehensively analyzing the above main results, it can be concluded that the model shows a good fit performance and can be used for further analysis.

On the other hand, it can also be drawn from the p-value test of the ANOVA that the terms of T, v_c, v_a, L, T·v_a, T·L, v_c·v_a, v_c·L, v_a·L, T², v_c², and L² have significant influence (p < 0.0001) on the response δP. For the single factor, the F-value of the terms T, v_c, v_a, and L, respectively, are determined as 985.56, 100.14, 866.25, and 7423.23, indicating that the influence of the single factor on the response in descending order is v_c < v_a < T < L. This means that the material’s thickness has the most significant influence on δP, followed by hot air temperature, hot air velocity, and corn flow velocity. The established δP_RSM model is expressed in Equation (9), and the coefficient of determination R² of the model is 0.9989, which is close to 1 [32], indicating that the established model can be used to predict the δP during the corn convective drying process.

$$\begin{array}{l}\delta P_{RSM}=-15394.016+405.177T+37231.948v_c-\\ 4842.102v_a+1.466L-132.144T\cdot v_c+43.494T\cdot v_a\\ +0.042T\cdot L-29909.688v_c\cdot v_a-22.6v_c\cdot L\\ +12.929v_a\cdot L-3.049T^2-171385v_c^2\\ +121.489v_a^2-0.00299L^2\end{array}$$

(9)

where T is hot air temperature, °C; v_c is corn flow velocity, m/s; v_a is hot air velocity, m/s; L is thickness of corn drying layer, mm; δP_RSM is pressure difference, Pa.

3.2.2. The Influence of Factors on Pressure Difference

Based on the ANOVA analysis above, the influences of the joint actions among the factors on the response δP_RSM, the influence of individual action on the response δP_RSM, and the corresponding statistical analysis have been carried out by Design-expert 12 software, the main results are depicted in Figure 4. Part A shows the joint graphical 3D analysis as a function of each considered variable, Part B shows the influence of each considered variable on the response, and Part C shows the statistical analysis including the Normal plot of residuals, Residuals vs. Run, Box–Cox plot for power transforms, and Cook’s distance.

As can be seen from Part A-1 in Figure 4, the maximum δP occurs in the ranges of 0.45 m/s ≤ v_a ≤ 0.5 m/s and 68 °C ≤ T ≤ 72 °C, while the minimum δP occurs at the point of T = 60 °C and v_a = 0.1 m/s. As for the influences of single factors on the response δP, which obviously can be drawn from the individual action shown in Part B that δP increases with an increase in L and v_a. This may be due to the fact that the length as well as the tortuosity of the air thoroughfare increases with an increase in L, and thus causes an increase in δP. On the other hand, δP decreases with an increase in v_c, which might be due to the fact that the porosity of the corn layer increases with increasing v_c, that is, the higher porosity, the lower ventilation resistance. Similar results have been reported in the paddy grain layer convective drying process by Li T. et al. [11] in 2018. Interestingly, Part B-1 shows that δP increases with an increase in T under 72 °C, which is beyond the 72 °C threshold. By comprehensively considering the drying quality of the product, it can be stated that in order to have a reasonable δP during the corn convective drying process, the hot air temperature should be 72 °C.

The statistical analysis of the established model δP_RSM is presented in part c of Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8. Externally Studentized Residuals are one of the most important indexes used in regression analysis to detect outliers, model hypotheses, and model fitting effects. It can be seen from Part C-1 that from a total of 30 sets of experimental data, the absolute values of Externally Studentized Residuals for the 28 data sets are within the ranges of 2~3 [33], with only two data sets being considered abnormal data and may affect the model fitting performance. However, the reasonable range of the index according to the statistical analysis is determined to be within the range of −3.87982~3.87982, and it can be seen from Figure 5c that there is only one set of data that is considered to be unreasonable. As obviously seen in Figure 5c, the abnormal data set is determined as the 17th data set. Cook’s distance is the key index to evaluate the impact of abnormal data on the model fitting performance [33]. Generally speaking, Cook’s distance of the investigated data set is within the threshold, and the data set is considered to have an acceptable influence on the model fitting performance. It can be seen in Figure 8c that the threshold of the model is ascertained to be 1, and Cook’s distance (0.91) of the 17th data set is within the threshold 1. Accordingly, it can be stated that a total of 30 sets of the experimental data are considered to be reasonable, and the established model δP_RSM shows a good fitting performance.

3.2.3. Model Verification

In order to verify the feasibility of the established regression model δP_RSM shown in the Equation (9), 12 sets of added experiments were conducted, as shown in

Table 7. The verification experimental design.

Experiment Number	T/°C	vc/m·s−1	va/m·s−1	L/mm
1	62	0.05	0.25	550
2	68	0.05	0.25	550
3	74	0.05	0.25	550
4	68	0.03	0.25	550
5	68	0.05	0.25	550
6	68	0.07	0.25	550
7	68	0.05	0.15	550
8	68	0.05	0.25	550
9	68	0.05	0.35	550
10	68	0.05	0.25	450
11	68	0.05	0.25	550
12	68	0.05	0.25	650

. In order to avoid repetition between the experimental design shown in Table 5 and the verification experiments shown in Table 6, different levels of T (62 °C, 68 °C, and 74 °C), v_c (0.03 m·s⁻¹, 0.05 m·s⁻¹, and 0.07 m·s⁻¹), v_a (0.15 m·s⁻¹, 0.25 m·s⁻¹, and 0.35 m·s⁻¹), and L (450 mm, 550 mm, and 650 mm) were selected. And the experimental data were inputted into Equations (1), (3), (4), and (9) for calculating the pressure drop model predicted by the Ergun model (δP_Eur), Shedd’s equation (δP_Shedd), Hukill equation (δP_Hukill), and the established regression model (δP_RSM), respectively. The predicted pressure drops were compared with the experimental values, and the indexes of R², MSE, MAE, and RMSE shown in Equations (5)–(8) were adopted to evaluate the predicting performance of the above models, the results are depicted in Figure 9.

The comparison between the experimental and predicted results is depicted in Figure 9a, which shows that the array group representing the RSM prediction values (δP_RSM) are closest to the experimental values, followed by δP_Eur, δP_Shedd, and δP_Hukill. It can be deduced that the established pressure drop model in the present work shows a better prediction performance than the commonly used models. To further confirm the deduction, statistical analysis was conducted, and the results are shown in Figure 9b. It is clear that the R² of δP_RSM is significantly higher than that of δP_Eur, δP_Shedd, and δP_Hukill, and the R² of the δP_RSM, δP_Eur, δP_Shedd, and δP_Hukill, is determined as 0.969, 0.859, 0.680, and 0.581, respectively. The MSE of the δP_RSM, δP_Eur, δP_Shedd, and δP_Hukill is determined as 1911.522, 9222.59, 28,529.49, and 20,098.366, respectively. The MAE of the δP_RSM, δP_Eur, δP_Shedd, and δP_Hukill, is determined as 11.228, 73.486, 136.798, and 129.068, respectively, and the RMSE of the δP_RSM, δP_Eur, δP_Shedd, and δP_Hukill is determined as 43.721, 96.034, 168.907 and 141.769, respectively. Above all, the δP_RSM has the highest R² but the lowest MSE, MAE, and RMSE, concluding that the δP_RSM established in the present work shows a good prediction performance and can be used to predict the pressure drop during the corn hot air convective drying process.

3.2.4. Drying Process Optimization

Based on the above analysis, the optimization function in Design-expert 12 software was used to optimize the corn hot air convective drying process by considering the minimum pressure drop as the goal. The solutions are tabulated in

Table 8. The solution results of the comprehensive optimization.

No.	Drying Condition				Indicator	Desirability
	T/°C	vc/m·s−1	va/m·s−1	L/mm	δPd/Pa
1	65.000	0.060	0.200	500.000	368.392	0.990
2	65.007	0.060	0.201	500.001	370.286	0.989
3	65.018	0.059	0.201	500.001	371.416	0.987
4	65.032	0.060	0.200	502.584	375.625	0.986
5	65.102	0.060	0.200	500.005	372.661	0.984

.

According to the comparison of the pressure drop in Table 8, it can be found that all the results are close to the single objective optimization value, and the desirability for all the solutions is higher than 0.9, indicating that the solutions are reliable. According to the desirability of the evaluations, the first group of schemes is the best, and the result is the comprehensive optimal solution, that is, when the drying temperature is 60 °C, corn flow velocity is 0.06 m/s, hot air velocity is 0.2 m/s, and thickness of layer is 500 mm, the pressure drop has a minimize value of 368.392 Pa, which can provide some reference for the corn practical drying process.

4. Conclusions

In the present work, RSM was adopted to establish the pressure drop model and investigate the influences of the drying conditions on the pressure drop during the corn drying process. The main conclusions depending on the results can be summarized as follows:

(1)

During the corn drying process, the v_a has the most significant impact on the pressure drop, followed by L, v_c, and T. In detail, δP_RSM is positively correlated with factors v_a and L, and negatively correlated with v_c.

(2)

An empirical pressure drop model δP_RSM focusing on the corn hot air convective drying process was established and verified. The determination coefficient R² of the model is determined to be 0.969, and Cook’s distances for the model are within 1, indicating that the model shows a good fitting performance.

(3)

By considering the minimum pressure drop as the goal, the optimal corn hot air drying conditions were determined to be a drying temperature of 60 °C, corn flow velocity of 0.06 m/s, hot air velocity of 0.2 m/s, and layer thickness of 500 mm, and the corresponding minimum pressure drop is 368.392 Pa. This set of parameter values can provide theoretical parameter values for the design of corn drying equipment.

The obtained conclusions can provide some references in the corn hot air drying process. Though the model can be used to provide some reference for designing the corn drying process, further work should be focused on combining the pressure drop and drying behavior of the corn material.