Heat-fluid-solid coupling heat transfer analysis and parameter optimization in walnut drying device based on finite element method

Abstract

The moisture content of freshly picked walnuts is very high. In order to facilitate storage and transportation, it needs to be dried to prevent mildew. In this study, the pre-drying simulation and experimental study were carried out on the walnut drying equipment made by the research group to determine the optimal drying parameters. The effects of different inlet temperatures (353K, 373K, 393K), drying wind speeds (1.1 m/s, 1.4 m/s, 1.7 m/s) and drying time (30min, 45min, 60min) on the temperature and velocity fields of fluid and walnuts in the drying device were investigated by using the orthogonal test method of three factors and three levels. FLUENT software was used to simulate the drying process of open walnuts under hot air heating, and the distribution of fluid temperature field and velocity field in the drying device and the temperature change law of walnuts were obtained. The results show that when the inlet temperature is 393K, the inlet velocity is 1.7 m/s, and the drying time is 45min, the temperature field distribution of fluid and walnut in the drying device is the best and the change is the most uniform. In addition, the temperature change of the simulation results is consistent with the test results through experiments, which verifies the reliability of the simulation results. In order to more accurately simulate the change law of temperature and humidity transfer in hot air drying of walnuts, the walnut was modeled as a sphere consisting of three layers: walnut shell, air gap and walnut kernel. The reliability of the parameters was verified by surface response analysis. Taking inlet temperature, velocity and drying time as influencing factors and temperature change rate as evaluation index, the determination coefficient of regression model was R² = 0.9966, and the correction determination coefficient Adj. R² = 0.9922, indicating three influences. This study provides a theoretical basis for determining the optimum operating parameters of open walnut pre-drying, and has application value for walnut food processing.

1. Introduction

The freshly harvested walnuts have a high moisture content and must be dried to reduce the moisture content for storage and transportation purposes [1]. With the growth of China's economy, people have increasingly higher requirements for the nutritional value and taste of food. Because walnuts have high nutritional value, there are more and more walnut-related foods being developed, and the drying quality of walnuts directly affects the nutritional value and taste of walnuts [2], making walnut drying an important part of walnut processing [3].

With the annual increase in walnut production, timely harvesting and proper drying techniques are very important for further walnut processing [4]. During the walnut harvesting season, rainy weather and other factors can cause the moisture content of the walnuts to be high, which can lead to mold growth and affect the quality of the walnuts [5]. According to relevant literature, the moisture content of walnuts needs to be dried to 8 % to prevent mold growth [6]. Currently, most areas in China still use traditional manual processing methods for walnut processing [7], where most steps from peeling to cleaning are manually operated [8], and natural air-drying is used for drying purposes after cleaning [9], which is time-consuming, labor-intensive, requires continuous turning, and is susceptible to weather conditions, as well as contamination [10].

Previous researchers have conducted much research on hot air dryers, but most of them are based on fixed bed or box dryers. Traditional box dryers usually dry walnuts at a hot air temperature of 43 °C [11]. If the drying temperature is too low, the drying time will be too long, resulting in low efficiency and energy waste, which will affect the economic benefits. Walnut drying by hot air is a transient phenomenon that involves heat and moisture transfer. Improper drying conditions can lead to a deterioration in walnut quality. Zhang Zhongxin used a high temperature of 125 °C to dry open walnuts with hot air and found that when the air velocity was 1.75 m/s and the flow-through time was 2 h, the dried walnuts reached the ideal state for roasting nuts [12]. Luo Fan et al. investigated the effects of three drying methods of hot air, infrared radiation and microwave radiation on the physical and chemical quality of walnut kernel and pressed walnut oil, and found that hot air heating at 120 °C for 90min had the least effect on the oil content of walnut, and the acid value and total color difference were the lowest, the acid value was 0.375 mg/g, and the peroxide value was 0.073g/100 g, all within the scope of walnut oil safety standards [13]. Han Yongxiang et al. studied the chemical composition, fatty acids, total flavonoid content (TFC), total polyphenol content (TPC) and minerals of walnuts after freeze-drying (55 °C) and hot drying (60 °C, 105 °C, 140 °C), and on the whole, the quality of walnuts dried at 105 °C was the best, but the study showed that different drying conditions had no significant effect on each fatty acid [14]. Chen et al. dried Chandler walnuts by hot air at a temperature of 73 °C and air velocity of 1.4 m/s and found that it took 6 h to dry walnuts to a moisture content of 6 % [15]. Wang Qinghui et al. conducted experiments on walnuts and determined that a temperature of 45 °C and an air velocity of 1.5 m/s were necessary to reduce the moisture content of walnuts to 12 % in 32 h [16]. Xu Fengqin found that high-temperature hot air drying can accelerate the evaporation of moisture in walnuts and increase the relative content of protein, soluble sugars, polyphenols, carbohydrates, and flavonoids in walnut kernels. However, when the temperature exceeds 140 °C, it can damage the nutritional content of walnuts [17]. However, most scholars have studied the complete drying of walnuts and at low drying temperatures, resulting in long drying times and low efficiency. This study focuses on pre-drying treatment for freshly picked green walnuts to study their drying characteristics. After pre-drying treatment, the moisture content of green walnuts is reduced, and farmers can sell the treated green walnuts to food factories to increase economic benefits, while the food factories can conduct secondary food processing. Studies have shown that segmented processing of green walnuts results in better taste and can maximize the retention of original nutrients. Taking above into consideration, the aim of study was to determine the reliable parameters of walnut pre-drying and drying.

Currently, walnut dryers are roughly divided into fixed bed, tray, drum, and belt dryers, with fixed bed and tray dryers being the most commonly used on the market. In practical work, tray-type and fixed bed dryers cannot be operated continuously and can only start the next round of drying after drying all the walnuts in the dryer. However, due to the different drying medium flow rates and temperature distribution at different locations in the drying device, the walnuts in different locations are exposed to different heating conditions. In particular, the walnuts located near the edge of the drying device experience slower drying medium flow rates and lower temperatures than those in the center position [18]. There are differences in temperature distribution on the windward and leeward surfaces of individual walnuts, too. If the drying time is insufficient, the drying effect of walnuts will be affected, and the final drying quality may be difficult to guarantee.

Although the drum-type drying device can process continuously and overcome uneven heating problems, the constant rotation of the drum causes the walnuts to collide violently and easily cause damage during the drying process [19]. Compared with the previous drying methods, the belt-type drying device has significant advantages: it can operate continuously, run smoothly, and not cause damage to the walnuts. By combining the hot air drying principle with the belt-type drying device and improving the uneven drying temperature and low drying efficiency of walnuts, a multi-layer conveyor belt is installed inside the designed drying device [20]. The inlet can continuously transport walnuts to the drying chamber through the conveyor belt, and the walnuts continuously follow the conveyor belt to move. When the drying is finished, the walnuts are transported to the outlet by the conveyor belt, completing the drying process. However, during the drying process, external factors and walnut drying parameters can affect the quality of the drying. Considering the above situation, the purpose of the study is to determine the relevant parameters affecting the pre-drying of walnuts. It is known that the parameters mainly affecting the drying of walnuts are the inlet temperature, inlet air velocity, and drying time. By using the orthogonal test method of three factors and three levels to design an orthogonal experiment, the influence of the inlet temperature, inlet air velocity, and drying time on the temperature and flow fields of the walnut drying device and walnuts are simulated using FLUENT software. The temperature change curve of the fluid inside the drying device and the walnuts is obtained by comparing the data under different parameters to obtain the optimal drying process parameters. The study of walnut pre-drying parameters lays the theoretical foundation for subsequent walnut drying and provides practical reference significance for future walnut food processing.

2. Numerical method

In this chapter, the heat-fluid-solid coupling model in the drying device was established, the CFD-FLUENT software was used for two-dimensional simulation, the coupling algorithm is used to decompose the space region into a set composed of discrete control bodies through grid division. The algebraic equations of discrete variables are constructed on the control bodies in integral form, and the discrete equations are linearized. Then, the iterative solutions of variables are obtained by solving the linearized equations [21], and the conservation equations in the gas-solid heat transfer process in the walnut drying process are solved.

2.1. Overall structure design of drying device

The walnut drying device model uses the drying equipment designed by the research group. There are seven layers of conveyor belts in the equipment. Walnuts enter the first layer from the feeding throat and are transported to the second layer by the conveyor belt. During the transmission process, the windward side of the walnuts changes, the drying position is also changed. Walnuts are dried in this way, so that they are heated evenly. The drying device is driven by the motor through the gear drive shaft with a diameter of 50 mm to drive the conveyor belt to move, thus achieving the purpose of conveying walnuts. The gear transmission ratio is 1:1, and the transmission speed of each layer is the same. Most of the gears are distributed on one side of the motor, and two big gears are distributed on the other side. one hand, this design is mainly due to the large distance between the air inlet layers and the increased diameter of the gears. which interferes with the next-stage transmission shaft and affect the movement transmission. On the other hand, is necessary to ensure the same moving speed of the conveyor belt. Based on the above two reasons, the two-layer transmission gears with the largest layer spacing are arranged on the other side of the motor. The external structure of the dryer is shown in Fig. 1-a, and the internal structure is shown in Fig. 1-b [22].

Fig. 1.

Internal and external structure diagram of drying device (a) external structure diagram of drying device; (b)internal structure of drying device.

The main parameters are shown in Table 1.

Table 1.

Main parameters of drying device.

serial number	project	index
1	Transport layers	7
2	Transport method	Roller
3	Total transmission length (mm)	11,900
4	Type of drive	Electric drive
5	Width of conveyor belt (mm)	1050
6	Speed (m/s)	adjustable

2.2. 2D modeling of walnuts

Chen et al. respectively measured the effective moisture diffusivities in walnut by distinguishing walnut shell and kernel model. The simulation results show that the stability of the model distinguishing walnut shell and walnut kernel is better than that of the “lumped” model [23]. Combined with the above, In this study, walnut is modeled as a sphere with walnut shell, walnut gap and walnut kernel, and the diameter of walnut is 32 mm, the walnut model is shown in Fig. 2.

Fig. 2.

2D model of the walnut.

2.3. Basic governing equations of heat-fluid-solid coupling

The fluid medium of walnut drying is air, which involves the heat exchange between fluid and solid in the drying process. During the coupling process, the movement of drying medium follows the law of conservation of mass, momentum and energy.

2.3.1. Mass conservation equation

The mass conservation equation is also called the continuity equation. The change in the mass of the fluid inside the object per unit time is equal to the difference between the inflow and the outflow. The differential form of the continuity equation is shown in Equation (1).

$$\frac{\partial \left(\rho u_x\right)}{\partial x}+\frac{\partial \left(\rho u_y\right)}{\partial y}+\frac{\partial \left(\rho u_z\right)}{\partial z}=0$$ (1)

$u_x、u_y、u_z$ components of velocity in three directions (m/s).

2.3.2. Momentum conservation equation

The fluid in the drying device satisfies the conservation of momentum, and the momentum equation for unit object: $\nabla p=Ft$.The equation for the momentum of a three-dimensional object is shown in Eqs. (2), (3), (4)).

$$\frac{\partial \left(\rho u_x\right)}{{\partial }_t}+\mathit{div}\left(\rho u_x\mathrm{u}\right)=-\frac{\partial p}{{\partial }_x}+\frac{\partial {\tau }_{yx}}{{\partial }_x}+\frac{\partial {\tau }_{yx}}{{\partial }_y}+\frac{\partial {\tau }_{yx}}{{\partial }_z}+F_x$$ (2)

$$\frac{\partial \left(\rho u_y\right)}{{\partial }_t}+\mathit{div}\left(\rho u_y\mathrm{u}\right)=-\frac{\partial p}{{\partial }_y}+\frac{\partial {\tau }_{xy}}{{\partial }_x}+\frac{\partial {\tau }_{yy}}{{\partial }_y}+\frac{\partial {\tau }_{zy}}{{\partial }_z}+F_y$$ (3)

$$\frac{\partial \left(\rho u_z\right)}{{\partial }_t}+\mathit{div}\left(\rho u_z\mathrm{u}\right)=-\frac{\partial p}{{\partial }_z}+\frac{\partial {\tau }_{xz}}{{\partial }_x}+\frac{\partial {\tau }_{yz}}{{\partial }_y}+\frac{\partial {\tau }_{zz}}{{\partial }_z}+F_z$$ (4)

• $\rho$—unit fluid pressure (Pa);

• ${\tau }_{xx}、{\tau }_{xy}、{\tau }_{xz}$—the component of viscous stress caused by molecular viscosity (Pa);

• $F_{\mathrm{x}}、F_{\mathrm{y}}、F_{\mathrm{z}}$—unit mass force in three directions (m/s²);

• $p$—the pressure on the infinitesimal body,N.

If the direction is vertical and downward under the action of gravity, then $f_x=f_y=0,f_z=-g$.

The generalized law of internal friction is shown in Eqs. (5), (6), (7)).

$${\tau }_{xx}={\tau }_{yx}=\mu \left(\frac{\partial u_x}{\partial y}+\frac{\partial u_y}{\partial x}\right)$$ (5)

$${\tau }_{xz}={\tau }_{zx}=\mu \left(\frac{\partial u_x}{\partial z}+\frac{\partial u_z}{\partial x}\right)$$ (6)

$${\tau }_{yz}={\tau }_{zy}=\mu \left(\frac{\partial u_y}{\partial z}+\frac{\partial u_z}{\partial y}\right)$$ (7)

Where $\mu$ is the dynamic viscosity (Pa·s); $\lambda$ is the Second viscosity (Pa·s), usually take −2/3.

Convert equations (5), (6), (7) to Eqs. (8), (9), (10).

$$\frac{\partial \left(\rho u_x\right)}{{\partial }_t}+\mathit{div}\left(\rho u_x\mathrm{U}\right)=-\frac{\partial p}{{\partial }_x}+\frac{\partial }{{\partial }_x}\left(\mu \frac{\partial u_x}{{\partial }_x}\right)+\frac{\partial }{{\partial }_y}\left(\mu \frac{\partial u_x}{{\partial }_y}\right)+\frac{\partial }{{\partial }_z}\left(\mu \frac{\partial u_x}{{\partial }_z}\right)+S_u$$ (8)

$$\frac{\partial \left(\rho u_y\right)}{{\partial }_t}+\mathit{div}\left(\rho u_y\mathrm{U}\right)=-\frac{\partial p}{{\partial }_y}+\frac{\partial }{{\partial }_x}\left(\mu \frac{\partial u_y}{{\partial }_x}\right)+\frac{\partial }{{\partial }_y}\left(\mu \frac{\partial u_y}{{\partial }_y}\right)+\frac{\partial }{{\partial }_z}\left(\mu \frac{\partial u_y}{{\partial }_z}\right)+S_v$$ (9)

$$\frac{\partial \left(\rho u_z\right)}{{\partial }_t}+\mathit{div}\left(\rho u_z\mathrm{U}\right)=-\frac{\partial p}{{\partial }_z}+\frac{\partial }{{\partial }_x}\left(\mu \frac{\partial u_z}{{\partial }_x}\right)+\frac{\partial }{{\partial }_y}\left(\mu \frac{\partial u_z}{{\partial }_y}\right)+\frac{\partial }{{\partial }_z}\left(\mu \frac{\partial u_z}{{\partial }_z}\right)+S_w$$ (10)

Here $S_u、S_v、S_w$ are generalized source terms respectively.

2.3.3. Energy conservation equation

Heat exchange takes place between the walnuts and the drying medium, and the fluid system containing the heat exchange satisfies the law of conservation of energy, as shown in Equation (11).

$$\frac{\partial \left(\rho T\right)}{{\partial }_t}+\mathit{div}\left(\rho uT\right)=\mathit{div}\left[\frac{h}{c_p}•gradT\right]+S_T$$ (11)

• $\mathit{h}$—heat transfer coefficient [W/(m². K)];

• $\mathit{T}$—temperature, °C;

• $c_p$—Specific heat capacity, (J/kg.°C);

• $S_T$—heat source within the fluid and heat energy due to the viscous action of the fluid, J.

2.4. Turbulence model

In FLUENT, there are some turbulence models such as the spalart-allmaras model and the standard k-ε model. In this paper, the standard k-ε model is used for simulation analysis. simulation analysis. The governing equations for the turbulent energy k and turbulent dissipation rate ε of the standard K-ε model are shown in Equations (12), (13)).

$$\frac{\partial \left(\rho k\right)}{\partial t}+\frac{\partial \left(\rho k{u}_i\right)}{\partial x_i}=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{u_t}{{\sigma }_k}\right)\frac{\partial k}{\partial x_j}\right]+G_k-\rho \epsilon$$ (12)

• ${\sigma }_{\mathrm{k}}$—the

$$\frac{\partial \left(\rho \epsilon \right)}{\partial t}+\frac{\partial \left(\rho \epsilon u_i\right)}{\partial x_i}=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{u_t}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial x_j}\right]+C_{1\epsilon }\frac{\epsilon }{k}\left(G_k+C_{3\epsilon }{G}_b\right)-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}+S_{\epsilon }$$ (13)

• $G_{\mathrm{k}}$—additional term of turbulent kinetic energy;

• ${\sigma }_{\mathrm{k}}$ is the Plante number corresponding to the turbulent flow energy, ${\sigma }_{\mathrm{k}}=1.0$.

• ${\mathrm{\sigma }}_{\mathrm{\epsilon }}$—Prandtl number corresponding to dissipation rate, ${\mathrm{\sigma }}_{\mathrm{\epsilon }}=1.3$;

• $C_{1\mathrm{\epsilon }}、C_{2\mathrm{\epsilon }}$—empirical constant, the values are 1.44 and 1.92 respectively.

3. Materials and methods

3.1. 2D meshing of walnut drying units

The two-dimensional space model is directly established in the fluent-geometry module of ansys19.2 software. In order to save calculation time, the simulation model and the actual model of the comparative test group are set at a ratio of 1:3. The key points (left, center, and right) of each layer of the dryer (named line1-line7 from top to bottom) were arranged with walnuts, and the two-dimensional model is shown in Fig. 3. The model after the walnut placement was meshed and simulated by fluent-meshing, of which a total of 8585 nodes were divided, the number of grids was 14,022, the average mesh quality was 0.917, the mesh quality was better, and the mesh division of the key points of the drying device where the walnuts were placed was shown in Fig. 4.

Fig. 3.

A 2D model of the drying unit.

Fig. 4.

Key points placed in the model meshing of walnuts.

3.2. Selection of drying parameters

3.2.1. Orthogonal experimental design

For walnut drying and heating, there are three main factors that affect walnut drying: inlet temperature, inlet velocity and drying time (when the overall temperature of the fluid is consistent with the inlet temperature, the time for walnuts to enter the drying box for drying). Therefore, this paper takes the above three indexes as the three factors of single factor orthogonal test, and uses orthogonal table L₉ (3⁴) for orthogonal test analysis. There are 9 groups of data. According to the related parameters of walnut discussed above, the inlet temperature determined in this experiment is 353K, 373K and 393K, so as to avoid the influence of low temperature on drying efficiency and high temperature on walnut quality. The inlet velocity should be 1.1 m/s, 1.4 m/s and 1.7 m/s. Too high a velocity will cause energy waste, while too low a velocity will affect the drying rate of walnuts. Drying time The drying time of walnut is 30min, 45min, 60min. Too long drying time will affect the quality of walnut, while too low drying time will cause walnut mildew. The final simulation test factor level table is shown in Table 2.

Table 2.

Orthogonal design table.

Test number	Factors
	Inlet temperature A(K)	Inlet velocity B (m/s)	drying time C (min)
1	353	1.1	30
2	353	1.4	45
3	353	1.7	60
4	373	1.1	45
5	373	1.4	60
6	373	1.7	30
7	393	1.1	60
8	393	1.4	30
9	393	1.7	45

Each group of data was input into Fluent software, and the drying box was made of thermal insulation material, with heat conductivity is 0.032 W/(m·k), heat conductivity of walnut shell is 0.159 W/(m·k), heat conductivity of kernel is 0.147 W/(m·k), outlet temperature is 290 k and outlet pressure is 101.325 kPa. The model was imported into Fluent. The relative convergence of the algorithm was set to 10⁻⁶, the operation time frequency is 0.01s, and the time step is 2000 steps. After the temperature reaches stable, the time step was set again at 1s frequency according to the drying time of each group in the orthogonal test table, Select 0–60s (time interval is 3s, 20 datas in total) datas of temperature change of walnut in the fourth layer of each group, and the temperature change of each group is shown in Fig. 5.

Fig. 5.

Comparison of temperature of walnut in the fourth layer of each group.

Comparing the temperature change data of the nine groups of walnuts above, it was found that the sixth and ninth groups reached stability earlier than the other groups, and the temperature fluctuation was smaller after reaching stability. The temperature data of the right side of each layer of walnuts in the sixth as shown in Fig. 6--a, and ninth groups from 0 to 60s were selected as shown in Fig. 6--b, and the comparison graph is shown in Fig. 6.

Fig. 6.

0–60s temperature change for the right-side walnuts of the sixth and ninth groups.(a) The temperature change curve of walnuts at the right position of the sixth group; (b) The temperature change curve of walnuts at the right position of the ninth group.

Select the temperature data of each layer of fluid and walnuts in the drying device after the sixth and ninth groups are stable again (0–2000s). Select a set of data every 90s, totaling 20 sets of data, and the temperature after stabilization are shown in Fig. 7, the temperature change of each layer of the sixth group is shown in Fig. 7-a, the temperature change of each layer of the ninth group is shown in Fig. 7-b, the temperature change of the rightmost layer of walnuts in the sixth group is shown in Fig. 7-c, the temperature change of the rightmost layer of walnuts in the ninth group is shown in Fig. 7-d, the temperature change of each layer of walnuts in the middle of the sixth group is shown in Fig. 7-e, the temperature change of each layer of walnuts in the middle position of the ninth group is shown in Fig. 7-f, and the temperature change of the leftmost layers of walnuts in the sixth group is shown in Fig. 7-g. The temperature variation of the leftmost layers of walnuts in the ninth group is shown in Fig. 7-h.

Fig. 7.

Temperature change of fluids and walnuts in group 6 and group 9 between 0 and 2000s. (a) The temperature change of each layer of fluid in the sixth group between 0 and 2000s; (b) The temperature change of each layer of fluid in the ninth group between 0 and 2000s; (c) The temperature change of the sixth group of right walnuts between 0 and 2000s; (d) The temperature change of the ninth group of right walnuts between 0 and 2000s; (e) The temperature change of the sixth group of middle walnuts between 0 and 2000s; (f) The temperature change of the ninth group of middle walnuts between 0 and 2000s; (g) The temperature change of the sixth group of left walnuts between 0 and 2000s; (h) The temperature change of the ninth group of left walnuts between 0 and 2000s.

3.3. Experimental preparation

3.3.1. Materials

Freshly picked green walnuts from Jining, Shandong, with a size ranging from 28 to 32 mm, drying equipment independently developed by the laboratory, thermocouple (Chint screw thermocouple, model: WRET-02, specification:2000 mm, with Yao Yi XMTF-608 temperature controller, temperature measuring accuracy: 0.1 °C, using range: 0–600 °C), digital thermometer (WTS digital thermometer, Meister industrial measurement and control instrument, model: WRET-491, using range: 50 + 200 °C).

3.3.2. Methods

After the green walnut was peeled, it was naturally ventilated for 2 days. Then, they were placed in the left, middle and right positions of each layer of the drying device. Heat the drying device to 390K with imported hot air, preheat it for 10 min, and then add walnuts after ensuring the uniform internal temperature. Temperature sensors were placed at the center and entrance of the first floor (the sixth floor), and thermocouples were inserted into the green walnuts to monitor the temperature change data with time. The interior of the drying device is insulated with heat insulation materials to prevent heat loss to the greatest extent. The physical diagram of the drying device is shown in Fig. 8, the inside of the drying equipment is shown in Fig. 8-a, and the external structure is shown in 8-b.

Fig. 8.

Physical diagram of drying device (a)Externalstructure of drying box (b) Internal structure of drying box.

4. Results and discussion

By comparing the temperature data of 0–60s walnuts, it can be seen that the overall trend of walnuts temperature change in the ninth group reached a stable state earlier than the sixth group, and the temperature difference was small and the temperature distribution was uniform. Comparing the temperature data changes of the fluid in the drying device with walnut after stabilization, it is found that the temperature of the fluid in the ninth group has a relatively uniform change trend, and the temperature of the fluid flowing through the same layer changes little. The temperature difference between each layer is roughly 0.6–0.8 °C, while that of the sixth group is about 0.9–2.1 °C. As for the walnut temperature, due to a single walnut is placed in a special position, there is vortex phenomenon, which will affect the individual walnut temperature. The temperature of walnuts in the middle and right of the 6th group is higher than that at the inlet, while the temperature of walnuts in the middle of the 1st, 4th and 5th floors is slightly lower than that at the inlet. However, the overall temperature change trend of walnuts is better than that of the 6th group, and the temperature difference of walnuts is smaller than that of the 6th group.

It can be seen from the above comparison that the ninth group is better than the sixth group. In the actual drying process, the temperature is an important factor affecting the drying efficiency and drying quality of walnuts. Selecting appropriate drying parameters can improve drying efficiency and ensure drying quality.

4.1. Simulation analysis and verification of drying room covered with walnuts

Each floor of the drying device is covered with walnuts. This time, the grid model is simulated according to 1:1, and the determined parameters are verified by analyzing the temperature and velocity nephogram and the temperature change in the fluid. Input the determined parameters, namely, inlet temperature of 393 k, inlet wind speed of 1.7 m/s and drying time of 45min, into fluent software. Other setting parameters are consistent with the above, but this time, considering the influence of walnut humidity on the overall drying temperature, the grid is simulated in a static state, and the grid division of the two-dimensional model covered with walnuts is shown in Fig. 9-a, a partial enlarged view is shown in Fig. 9-b.

Fig. 9.

2D mesh division of walnut covered drying device. (a) 2D meshing covered with walnuts; (b) Partial enlargement of walnut covered with two-dimensional grid division.

Start running FLUENT software, the humidity of walnuts is initialized with UDF, and walnuts in special positions were selected for monitoring. The selected picture of monitoring walnut is shown in Fig. 10, and the datas change curve and nephogram of temperature and humidity of walnuts in special position during heating are shown in Fig. 11, the humidity change of walnut is shown in Fig. 11-a, and the temperature change of walnut is shown in Fig. 11-b. The variation curves of walnut humidity at each position are shown in Fig. 11-c. The temperature curves of walnut at each position are shown in Fig. 11-d.

Fig. 10.

Walnut monitoring point.

Fig. 11.

Variation diagram of walnut humidity and temperature at monitoring position. (a) nephogram of walnut humidity change; (b) nephogram of walnut temperature change; (c) diagram of walnut humidity change; (d) diagram of walnut temperature change.

4.2. Contour analysis and comparison

The cloud pictures of walnut drying for 45min and walnut-covered drying for 45min are selected in individual locations, as shown in Fig. 12, the temperature nephogram of the middle position of walnut placement is shown in Fig. 12-a, the temperature nephogram of walnut spreading drying room is shown in Fig. 12-b, the velocity nephogram of walnut spreading middle position is shown in Fig. 12-c, and the velocity nephogram of walnut spreading drying room is shown in Fig. 12-d.

Fig. 12.

The temperature contour and velocity contour of walnuts placed and covered with walnuts in individual positions. (a) Temperature contour of walnuts placed in special positions; (b) Temperature contour covered with walnuts; (c) Velocity contour of placed walnuts in special positions; (d) Velocity contour covered with walnuts.

4.3. Simulation analysis results

Through fluent simulation, the cloud chart of humidity distribution in the drying room and the average temperature of walnuts due to humidity data are obtained, and the results are shown in Fig. 13; Among them, the internal temperature of the drying chamber is shown in Fig. 13-a, the average humidity change curve of walnuts is shown in Fig. 13-b, and the average temperature change curve of walnuts is shown in Fig. 13-c.

Fig. 13.

(a) nephogram of humidity change in drying room; (b)nephogram of average humidity of walnut; (c) nephogram of average temperature of walnut.

4.4. Test verification results

Before the test, the room temperature was 17 °C (290 k), the drying oven was preheated. When the temperature reached 393 k, walnuts were put in. The temperature of walnuts at the entrance P1 and exit P2 was monitored by temperature sensors, and the temperature changes were recorded. The comparison between simulated temperature and actual temperature of walnut at P1 and P2 is shown in Fig. 14.

Fig. 14.

Comparison of temperature between actual test and simulation.

4.5. Surface response analysis

In order to further verify whether the inlet temperature (A), inlet velocity(B) and drying time (C) affect the temperature distribution of walnuts, the Design Expert 10.0.1 software was used to carry out experimental design and verification. Set the three influencing parameters according to the three factor levels of low, medium and high. The coding of factor levels is shown in Table 3.

Table 3.

Orthogonal test results.

test team	inlet temperature A/K	inlet velocity B/(m/s)	Drying time C/min	Temperature change rate/%
1	373	1.4	45	29.73
2	373	.1.7	60	28.79
3	373	1.7	30	30.85
4	353	1.7	45	21.9
5	373	1.4	45	29.73
6	373	1.4	45	29.12
7	393	1.4	30	36.58
8	373	1.1	30	28.8
9	353	1.4	60	22.83
10	393	1.4	60	35.07
11	373	1.1	60	28.75
12	373	1.4	45	29.83
13	393	1.1	45	35.49
14	353	1.1	45	21.59
15	353	1.4	30	22.15
16	373	1.4	45	28.78
17	393	1.1	45	34.9

According to the data results in Table 3, the quadratic multinomial regression equation of walnut temperature change rate and (A) inlet temperature (B) inlet velocity (C) drying time is obtained by using Design–Expert 10.0.1 software:

$$Y_1=29.44+6.7\times A+0.3738\times B-0.3675\times C+0.07\times AB-0.54\times AC-0.5025\times BC-0.5540\times A^2-0.4140\times B^2+0.2735\times C^2$$ (14)

where Y1 is the temperature change rate of walnut,A is the inlet temperature, B is the inlet velocity, and C is the drying time. The results of variance analysis on the datas are shown in Table 4.

Table 4.

Analysis of variances for quadratic polynomial models of the rate of change of the temperature difference in walnuts.

Source of variance	sum of squares	freedom	mean square	F value	P value	significance
model	365.47	9	40.61	228.00	<0.0001	Very significant
A	358.72	1	358.72	2014.13	<0.0001	Very significant
B	1.12	1	1.12	6.27	0.0407	significant
C	1.08	1	1.08	6.07	0.0433	significant
AB	0.0196	1	0.0196	0.1101	0.7498	Not significant
AC	1.20	1	1.20	6.73	0.0357	significant
BC	1.01	1	1.01	5.67	0.0488	significant
A2	1.29	1	1.29	7.26	0.0309	significant
B2	0.7217	1	0.7217	4.05	0.0840	Not significant
C2	0.3150	1	0.3150	1.77	0.2253	Not significant
residual	1.25	7	0.1781	–	–
Misfitting term	0.3884	3	0.1295	0.6034	0.6465	Not significant
Pure error	0.8583	4	0.2146	–	–
sum	366.72	16	一	–	–

CFD-FLUE.

As can be.

The 3D response surface diagram of the interaction effect of each factors are shown in Fig. 15; The response surface of temperature and velocity (A-B) is shown in Fig. 15-a; The response surface of temperature and time (A-C) is shown in Fig. 15-b; The response surface of temperature and time (A-B) is shown in Fig. 15-c.

Fig. 15.

Interaction effect response surface. (a) A-B response surface; (b) A-C response surface; (c) A-B response surface.

4.6. Discussion

As shown in Fig. 11, according to the curve diagram of humidity and temperature, the moisture content of walnuts near the air inlet drops sharply with time. The temperature of walnuts in the middle position rises faster and the moisture content drops faster near the air inlet, while the moisture content of P2 near the air outlet drops first and then rises. This is because the moisture content of P2 decreases with the increase of drying temperature at first, and then the moisture inside walnuts evaporates with the drying of walnuts in the drying device. Gathered near the air outlet, resulting in a large amount of water vapor accumulation, which led to the temperature drop and moisture content increase of walnuts near the air outlet, but with the continuous drying of walnuts, the moisture content will gradually decrease. The position of P4 is the same, but P4 is closer to the vent and the temperature is higher, so the water content decreases more obviously than P2.

As shown in Fig. 12, from the nephogram of humidity change and the graph of humidity and temperature, we can see that the temperature in the drying room first rises to the inlet temperature, and then as walnuts enter the drying room, the moisture of walnuts evaporates continuously, producing a lot of water vapor, which causes the temperature in the drying room to drop, and the moisture content of walnuts in the upper part of the drying room decreases slowly, but it gradually decreases with the increase of drying time, which is consistent with the actual drying. As shown in Fig. 13, by monitoring the average humidity and temperature of walnuts, it is known that the average moisture content is 14 % after drying for 45 min, at this time, most of the moisture in walnuts can be taken away, which basically meets the requirements of pre-drying treatment. At this time, the average temperature of walnuts is 358K, which is much lower than the inlet temperature. Through the study of walnuts heated by Luo Fan and others at 120 °C for 90min, it is found that the peroxide value of walnut oil under this condition is low, which is within the safe range, and the effect is good [13]. However, the temperature in this study will be lower than 120 °C, and the drying time will be short, and it will not affect walnut oil.

As shown in Fig. 14, it can be seen that the temperature changes at the entrance (P1) and the exit (P2) of walnuts are consistent with the simulated temperature changes, showing an overall upward trend. The actual walnut drying temperature before stabilization is lower than the simulated temperature, because the drying box loses heat at the exit in the actual drying, so the temperature rises slowly, which further proves that the actual walnut drying temperature is low and will not damage the internal oil of walnuts, but the temperature difference after stabilization is not significant, and after drying, the walnut is not damaged.

From Table 4, we can see that the model has p < 0.0001 and the fitting item p > 0.05, which means that the three regression items have significant interaction in the regression model. The determination coefficient R2 of the regression model is 0.9966, which means that the predicted value of the model has a high degree of fitting with the measured value. The correction determination coefficient Adj. R² = 0.9922, which indicates that the predicted value of the model is highly correlated with the measured value. The regression fitting model can be used to predict and analyze the temperature and heat transfer of walnuts. In this regression fitting model, the influence of factor A on the response value is very significant, while B, C, AC, BC and A² are significant, while AB, B² and C² are not significant. Because the temperature of walnut has reached a constant when it rises from the initial temperature to a stable state, the inlet velocity and drying time have little effect on it. From the single factor level analysis, the influence of each factor on the temperature difference change rate of walnut is A (inlet temperature) > B (inlet velocity) > C (drying time).

5. Conclusions

• 1)In this study, a two-dimensional model of a single walnut and a thermal-fluid-solid coupling model inside the drying device were established to more accurately simulate the moisture and heat changes of walnuts during drying. Nine groups of drying influencing parameters were obtained by orthogonal test. By comparing the temperature trend of fluid temperature and walnut temperature, the optimal drying parameters were finally determined as the inlet temperature of 393K, the inlet speed of 1.7 m/s and the drying time of 45min. At this time, the temperature change of walnut was the smallest and the heat flow distribution in the flow field was the most uniform.
• 2)Input the determined optimal parameters into the two-dimensional simulation model covered with walnuts. By comparing the temperature nephogram of covered walnuts with that of walnuts placed in individual positions, it is found that the temperature of the flow field rises first after covered walnuts, but as walnuts are continuously dried, the moisture of walnuts evaporates, which makes the temperature of the upper part of the drying device decrease. However, with the extension of drying time, the moisture content of walnuts tends to decrease. After drying for 45 min, the average temperature of walnuts is 358K, and the average moisture content of walnuts is 14 %. This temperature can take away most of the moisture of walnuts, and with the movement of the conveyor belt in the drying device, the temperature of walnuts shows a dynamic trend, and it will not be dried in one place all the time, resulting in the phenomenon of too high or too low temperature. The temperature difference between the walnut at the entrance and the walnut at the exit is quite different, because the simulation is carried out under the static condition, and the dynamic grid can be considered for further simulation exploration. This paper simulates the pre-drying of walnuts, and verifies the scientificity and realizability of walnuts pre-drying through simulation data, which makes up the blank of open walnuts pre-drying and provides theoretical guidance for actual pre-drying.
• 3)By Box—Behnken design analysis method in the surface response method, the effects of inlet temperature, inlet speed and drying time on walnuts drying were analyzed. The first layer temperature change rate was set as the response value, and its quadratic polynomial mathematical model was established. Combined with finite element technology, the effects of inlet temperature, inlet speed and drying time on the temperature change rate were further analyzed. The results show that inlet temperature > inlet velocity > drying time; The mathematical model can describe the relationship between temperature change rate and inlet temperature, inlet speed and drying time, and verify the reliability of the selected parameters again.

Funding

This research received no external funding.

Ethics declarations

Informed consent is not required for this study as this study is based on a walnut drying study and does not involve ethical issues.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Sanping Li: Methodology, Formal analysis. Jiamei Qi: Writing – original draft, Writing – review & editing, Software. Wu Liguo: Funding acquisition, Formal analysis. Xinlong Wei: Methodology. Longqiang Yuan: Project administration. Haibin Lin: Investigation.

Declaration of competing interest

All authors disclosed no relevant relationships.