**Research on structural optimization of high-density wood panel equilibration chamber based on computational fluid dynamics**,”

*BioResources*19(3), 6747-6767.

#### Abstract

To guarantee the uniformity of the flow field within an equilibration chamber during the process of hot air baking and to elevate the quality of high-density wood panels, an in-depth analysis was conducted, focusing on the impact of various factors such as the number of side air inlets in the chamber, the spacing between panel gaps, and the configuration of the bottom air inlet spacing. The aim was to optimize the structural parameters to enhance the uniformity of temperature and wind speed. The results indicated that the factors influencing the flow field uniformity within the equilibration chamber were, in descending order of importance, the number of side inlets, the spacing between the bottom inlets, and the distance between the plate gaps. In addition, the optimized hot air increased the average velocity by 0.16 m/s and the average temperature by 6.44K. The percentage of boards passing the inspection of its substandard products was only 9.2%, an improvement of 11.8 percentage points, and the average moisture content was also reduced to 8.76%. The simulation and analysis program effectively improved the uniform distribution of temperature and air velocity in the equilibration chamber and improved the quality of panel production. Therefore, the adoption of this solution helps to achieve efficient drying of wood-based panels and reduce costs.

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#### Full Article

**Research on Structural Optimization of High-Density Wood Panel Equilibration Chamber Based on Computational Fluid Dynamics**

Luxin Zhan,^{a} Fuqiang He,^{a,}* and Fajiang Chen ^{b}

To guarantee the uniformity of the flow field within an equilibration chamber during the process of hot air baking and to elevate the quality of high-density wood panels, an in-depth analysis was conducted, focusing on the impact of various factors such as the number of side air inlets in the chamber, the spacing between panel gaps, and the configuration of the bottom air inlet spacing. The aim was to optimize the structural parameters to enhance the uniformity of temperature and wind speed. The results indicated that the factors influencing the flow field uniformity within the equilibration chamber were, in descending order of importance, the number of side inlets, the spacing between the bottom inlets, and the distance between the plate gaps. In addition, the optimized hot air increased the average velocity by 0.16 m/s and the average temperature by 6.44K. The percentage of boards passing the inspection of its substandard products was only 9.2%, an improvement of 11.8 percentage points, and the average moisture content was also reduced to 8.76%. The simulation and analysis program effectively improved the uniform distribution of temperature and air velocity in the equilibration chamber and improved the quality of panel production. Therefore, the adoption of this solution helps to achieve efficient drying of wood-based panels and reduce costs.

*DOI: 10.15376/biores.19.3.6747-6767*

*Keywords: High-density wood panels; Drying kilns; Balance chambers; Structural optimization*

*Contact information: a: Guizhou University, Guiyang 550025, China; b: Guizhou Jingmu Building Materials Co., Ltd, Guiyang 550025 China; * Corresponding author: fqhe@gzu.edu.cn*

**INTRODUCTION**

The multi-functional wood panel is an innovative type of panel crafted primarily from wood powder. The manufacturing process involves thorough mixing and stirring of the raw material, followed by precise paving, hot pressing, sawing, and sanding to achieve the desired finish. Roasting is a key component in reducing moisture content. The process of reducing moisture content in multifunctional wood panels primarily involves introducing hot air and precisely regulating various factors within an equilibration chamber (which also can be called a kiln or a ‘balance chamber’), including temperature, humidity, and air intake speed. This ensures a consistent and sustained heating and baking environment, optimizing the wood panels’ moisture reduction process. The equilibration chamber considered in this work has a footprint of 30 m^{2}, encompassing a comprehensive setup of 24 air inlets and a solitary air outlet. The air inlets are designed to maintain a temperature of 70 °C and a wind speed of 10 m/s. In terms of production, the sheet-baking process involves accommodating over 400 sheets within this chamber, which are then left to bake for a duration of three consecutive days. The manner and direction of the hot air circulation in the chamber affects the wind speed field and temperature field changes. The uniformity determines the drying quality and efficiency of wood-based panels. A well-conceived equilibration chamber design holds significant value, as it has the potential to substantially curtail the baking cycle for wood-based panels. This expedited process enhances the evaporation of moisture, ultimately leading to improved production efficiency and a successful reduction in moisture content. Therefore, the thorough study of the equilibration chamber’s structural design is of utmost importance. In numerous studies, most of the scholars have employed Computational Fluid Dynamics (CFD) for flow field simulation. Román *et al*. (2012) optimized box dryer air distribution *via* fluid simulation, reducing moisture content variance by over 50% through enlarged inlets and diffusers. Xing *et al.* (2023) designed an adjustable air nozzle for the uneven distribution of flow field of gravure printing drying box and other problems. At the same time, to enhance the drying efficiency of the oven and ensure a more even distribution of hot air, a baffle was added to the midpoint between the oven’s interior and the air inlet. Additionally, a chamfer was installed at the exit of the drying box, effectively optimizing the original oven structure. Guo *et al. *(2014) developed a simulation model that replicated the combustion chamber of a hot convection oven, aiming to analyze the temperature and flow field patterns within the burner. Their findings indicated that the burner equipped with either 19 or 21 combustion nozzles achieved the most optimal performance, optimizing both temperature distribution and airflow efficiency. Delele *et al. *(2014) optimized a dryer design *via* simulations, enlarging the inlet gap and eliminating gaps between ducts. This ensured even airflow, speeding up moisture reduction. Zdanski *et al*. (2015) employed the Ansys simulation software to investigate the width dimension and inlet flow rate of the drying kiln, aiming to achieve optimal flow uniformity throughout the entire stack. Chavan *et al*. (2021) enhanced the performance of a grain dryer through the utilization of computational fluid dynamics (CFD) analysis, optimizing the fan’s size and positioning. Furthermore, they introduced orifices to intensify airflow, ultimately proposing two innovative dryer designs: a finless model and a finned variant. Hao *et al.* (2021) conducted simulations and thorough analyses of two deflector modes – parallel deflection and v-shaped deflection – within the hot air distribution system. Their findings revealed that the v-shaped deflector significantly diminished air velocity disparities, thereby enhancing the uniformity of airflow distribution to a considerable degree. Smolka *et al. *(2010) performed a comprehensive 3D CFD optimization study to examine the effects of structural parameters such as the varied shapes of fan baffles and diverse heater positions in a laboratory drying oven. The test results effectively guided the airflow distribution, significantly enhancing the temperature uniformity of the device, ultimately leading to its successful commercialization. Zhang and Deng (2017) used FLUENT software to study the effect of three structures, without deflector plate, with ordinary deflector plate and with winged deflector plate, on the moisture content of the material in the dryer. The study demonstrated an overall reduction in the water content of the wing deflector plate and an improvement in the homogeneity of the water content of the material. Zafar *et al.* (2019) conducted a numerical and parametric study of the solar oven, discovering that the incorporation of L-shaped absorber panels, in addition to internal reflectors, led to a notable enhancement in thermal performance.

Much of the current research still revolves around adjusting dryer structures or increasing inflow devices, among other methods. However, there remains a significant gap in the research pertaining to the mass production of large-scale structural equilibration chambers capable of efficiently producing large-sized panels. Specifically, there is a lack of studies on achieving homogeneous flow fields within these chambers and optimizing their structural design. This paper addresses the issue of non-uniformity in the wind velocity and temperature fields within the equilibration chamber for wood-based panels. Utilizing CFD technology and Fluent software, the real production environment was simulated by establishing a three-dimensional model of the equilibration chamber. Through the design of orthogonal experiments and the establishment of comprehensive evaluation indices, impact of structural parameters on indoor flow uniformity and comprehensive indices was analyzed.

Based on these analyses, the structural parameters of the equilibration chamber were analyzed with the goal of enhancing the uniformity of the indoor temperature and wind velocity fields. The aim was to improve the performance of the equilibration chamber for wood-based panels, providing valuable references for subsequent design and research. This work also offers theoretical support for the enhancement of production processes in the panel industry.

**EXPERIMENTAL**

**Equilibration Chamber Working Principle and Simulation Method**

*Equilibration chamber working principle*

The panel kiln equilibration chamber primarily consists of a square chamber, a transmission device, and a ventilation control system. The working principle involves fixing the panel onto a bracket, which is then transported into the interior of the square chamber along the conveyor chain. Once inside, the ventilation system is activated, allowing hot air to flow into the panel baking area from the bottom and side inlets, initiating the baking process. Subsequently, the heated air is pumped out through the top air outlet, completing a cycle of heating and reuse. By monitoring the changes in temperature and humidity *via* the controller, adjustments can be made to the process parameters accordingly. Ultimately, this process achieves the desired work requirements of reducing the water content. The specific physical diagram and internal structure are shown in Fig. 1, and the main parameters of the equilibration chamber are shown in Table 1.

**(a) (b)**

**Fig. 1.** (a) Equilibration chamber, and (b) internal structure of the equilibration chamber

**Table 1.** Structural Parameters of the Equilibration Chamber

**Model Building**

*Physical modeling*

Due to the excessively large physical size of the research object in three-dimensional modeling, the computational requirements for the established model were excessively high. Furthermore, considering the negligible impact of the internal flow field parts, a simplified modeling approach was employed. This involves deleting parts that are not involved in the flow field analysis. The specific simplification steps are outlined below. Based on the existing three-dimensional model of the equilibration chamber, it was decided to delete the internal transmission device, brackets, and other components. The original model in the overall design was a symmetrical structure, and therefore, in order to reduce the amount of calculations, the length of the model was first cut in half. After halving the structure from 5000 mm x 6000 mm x 3000 mm, the size of the bottom air inlet remained unchanged, with a total of 12 units. The top air outlet remained at 1, and in the absence of a subsequent design program, the side air inlet was excluded from the final design. A total of 100 panel models were drawn inside the equilibration chamber, with fixed positions to ensure the size remained unchanged. Finally, the entire model was set with a symmetry plane for simulation and analysis. The simplified model is shown in Fig. 2.

**Fig. 2.** Equilibration chamber model drawing

**Parameterization of Control Equations and Boundary Conditions**

*Governing equation*

During the baking of the panels, the ventilation system provides hot air at high speeds from a constant fan power source. For the purpose of simulation, the following refined assumptions were formulated: Considering the panel as an isotropic continuous medium material, the airflow within the pores of the panel passes uniformly. The fluid medium in question is hot air, which is treated as an incompressible ideal gas, while the gravitational influence of the gas is disregarded. It is assumed that the hot air does not exchange heat transfer and components with the panel. Heat exchange between the equilibration chamber and the external environment is neglected (An *et al*. 2021; Bai *et al*. 2017; Chang *et al*. 2018). The following governing equations depend on the assumptions mentioned above.

The continuity equation, which can be also called the mass conservation equation for the fluid, is as follows,

where *ρ* is the density of hot air (kg·m^{-3}); *u*, *v*, *w* are the velocity components in x, y, z directions (m·s^{-1}); *t* is the flow time of hot air (s); and S_{M} (kg·m^{-3}·s^{-1}) is the water vapor mass source.

The conservation of momentum equation can be expressed as follows,

where *p* is the pressure (Pa); *μ* is the dynamic viscosity of hot air fluid (kg·m^{-1}·s^{-1}); and *S*_{u}, *S*_{v}, and *S*_{w} are the momentum source components (N·m^{-3}).

The k^{–}εmodel is widely used in fluid dynamics simulations. This is because such models are easy to code and can be utilized directly, and the computation time is short. In this paper, the following model was used for analysis,

*Boundary condition parameterization*

The walls of the equilibration chamber were set to be adiabatic and all non-slip wall surfaces at room temperature (25 °C). The velocity inlet boundary condition was set to a hot air wind speed of 10 m/s and a temperature of 343 K. There was only one outlet in the equilibration chamber, so the outlet boundary condition was set to a pressure outlet and the value of the pressure was standard atmospheric pressure. Finally the simulation was carried out using SIMPLE algorithm based on pressure and velocity coupling with the following mathematical equation,

**Table 2.** Material Parameters

**Irrelevance and Reliability Verification**

In numerical simulation calculations of a physical model using Fluent software, a model with too few meshes or a large mesh size will result in poor mesh quality. Low mesh quality can lead to inaccurate model calculations or incorrect convergence. However, the large number and density of the meshes, coupled with the stringent hardware requirements of the computer, often results in significantly extended convergence time and heightened convergence challenges. An optimal number of meshes and the appropriate size of the results not only can favor the accuracy of the outcomes but also it can enhance the overall efficiency of the process. It is imperative to verify grid independence. Consequently, the physical model of the equilibration chamber was segmented into six distinct grid groups, comprising 800,000, 1,530,000, 2,510,000, 3,270,000, 3,520,000, and 3,840,000 grids respectively. Test calculations were conducted under identical boundary conditions, utilizing the mean temperature and average wind speed as benchmarks for validating grid independence. As can be seen from Figs. 2 to 3, with the increase in the number of grids, the temperature and wind speed were gradually decreasing and leveling off. In this work, 3.27 million grids are used for the calculations, taking into account factors such as time and computational cost.

**Fig. 3.** Physical model meshing

After successfully conducting the grid-independence verification, to validate the credibility of the CFD flow field model and the simulation outcomes of the equilibration chamber, anemometers and temperature sensors were deployed within the chamber to conduct empirical measurements of both wind speed and temperature within its confines. By gathering the actual data from the 20 monitoring points and subsequently comparing it with the simulation data, the outcomes are presented in Figs. 5 and 6. The actual values and the measured values at each point of the data differed, with an error range of approximately 5% to 9%. However, the overall trend of change remained consistent, indicating that the CFD model simulation possesses a certain degree of reliability and can be utilized for subsequent optimization program analysis.

**Fig. 4.** Grid-independent verification

**Fig. 5.** Comparison of measured and simulated wind speeds at monitoring points

**Fig. 6.** Comparison of measured and simulated temperature values at monitoring points

**Evaluation Indicators**

The position of the air inlet and the variation in the stacking configuration of the plates will cause air flow in the equilibration chamber, thereby resulting in different velocity and temperature distributions within the chamber. Therefore, in order to analyze the flow field homogeneity inside the equilibration chamber, it is necessary to introduce corresponding evaluation indices to judge the simulation results. In Fluent software, the distribution cloud obtained by simulating the actual conditions provides the most intuitive and clearest representation of the simulation results. Due to the research needs, this paper is mainly represented by the temperature and velocity cloud maps. To quantitatively analyze the simulation data, based on the chamber’s structure, a cross-section at *Y*=1500 mm (half-height) along the X-Z plane was selected, featuring 20 equivalent monitoring points for analysis. Introduction of the inhomogeneity coefficient in the data analysis serves as an indicator of the fluid motion’s uniformity. A higher coefficient signifies greater inhomogeneity in the simulation results, whereas a lower coefficient reflects a high degree of homogeneity in the flow field. The inhomogeneity coefficient is given as,

where *C*_{v} is the velocity inhomogeneity coefficient, *S*_{v} is the standard deviation of wind speed at monitoring points (m/s), is the mean value of wind speed at monitoring points (m/s), *V _{i}* is the wind speed at each monitoring point (m/s),

*µ*

_{T}is the temperature inhomogeneity coefficient,

*M*

_{T}is the standard deviation of temperature at monitoring points (K), is the mean value of temperature at monitoring points (K),

*T*

_{i}is the temperature at each monitoring point (K), and

*n*is the number of monitoring points.

When analyzing the flow field inside the equilibration chamber, it is necessary to consider both wind speed and temperature; hence, a combined weighted scoring method was utilized. The principle employed is to transform the temperature and wind speed indicators into comprehensive indices of the test results for optimization analysis. According to the importance of the uniformity of the flow field distribution and its impact on the baking of the panel, the weights of temperature and wind speed were assigned 0.6 and 0.4 respectively, and the order of magnitude and scale of the indices was unified. The formula was as follows (Wang *et al*. 2023),

where is the positive specification value of the simulation test value of the I^{th} indicator *J*, *Y*_{I,J} is the simulation test indicator value of the I^{th} indicator *J*, *Y*_{I,max} is the maximum value of the I^{th} indicator, and *Y*_{I,min} is the minimum value of the I^{th} indicator.

The weighted scores for each indicator are added together to give a composite weighted score value, calculated as follows,

where is the composite weighted score value of simulation test No. J, and *W*_{I} is the weight of the I^{th} indicator.

**RESULTS AND DISCUSSION**

**Flow Field Analysis**

*Analysis of initial conditions*

Initially, without side air inlets, a 300 mm bottom air inlet spacing, and a 80 mm panel gap, the wood-based panels suffered from cracking, warping, deformation, and other defects. Furthermore, the boards’ average water content stood at 14%, leading to a staggering 20% defective product percentage, significantly impeding production efficiency and driving up costs. Finally, the initial conditions of the equilibration chamber were modeled and simulated, with the velocity and temperature contours in the X-Z plane captured to observe the distribution of hot air and its variations upon entering the chamber, as depicted in Fig. 7.

As hot air enters the equilibration chamber through the bottom inlet, it spreads from the center to the sides, forming a large vortex between plate rows. This reflux vortex arises due to the chamber’s vast size and limited bottom airflow. Horizontal barriers prevent even dispersion, while vertical gaps allow air to concentrate at the ends. Consequently, the bottom and middle regions exhibit higher wind speeds and temperatures, while the edges and upper ends remain cooler.

In addition to this, the simulation data were derived to calculate the indicators according to the evaluation scheme described above. As shown in Table 3, the inhomogeneity coefficient under the initial conditions was high, indicating a mediocre comprehensive index score and poor overall homogeneity of the flow field. It is necessary to take measures to optimize and improve the equilibration chamber of the initial conditions in order to improve the homogeneity of the flow field, to reduce the substandard production rate, and to improve the quality of the product.

**Table 3.** Initial Conditions Monitoring Point Data

**Fig. 7****.** Initial program wind speed and temperature cloud

**Effect of Different Factors on the Flow Field**

*Panel gap distance*

Because the panels are baked in large quantities in the equilibration chamber, the distance between the panels is one of the important factors affecting the uniformity of the whole internal flow field. Under the condition that the spacing of the bottom air inlet was 300 mm and the number of side air inlets was 0, the panel gap distances were set to 65, 70, 75, 80, and 85 mm for a one-factor sensitivity test, and the X-Z surface was selected for analysis. Figure 8 shows the effects of different panel void distances on the velocity and temperature inhomogeneity coefficients and the average velocity and temperature of the flow field inside the equilibration chamber. It can be analyzed that as the panel gap distance increases, the volume of the space between the panels through which the hot air passes also increases, although this does not have much effect on the average velocity. However, the relative ventilation velocity between the panels decreases, reducing the difference with the low-wind velocity region at the edge of the chamber, resulting in a smaller velocity inhomogeneity coefficient and a more balanced wind velocity.

**Fig. 8.** (a) Effect of panel void distance on temperature inhomogeneity coefficient and mean temperature; (b) effect of panel gap distance on velocity inhomogeneity coefficient and mean velocity

In the temperature analysis, as the gap between the panels widens, the volume of hot air flowing through them increases, subjecting the panels to continuous high-intensity heat baking. This, in turn, elevates the average temperature within the chamber, while the temperature unevenness coefficient undergoes a reduction, indicating a more homogeneous thermal distribution. However, with the continuous increase of the distance of the panel gap, the wider the distribution of the panel arrangement, the edge of the low wind speed area range extends to the pile between the material, so the average temperature and wind speed exhibits a slight decline in the trend. Due to the size of the equilibration chamber, it is not possible to increase the distance between the panels without limitation, in order to be able to bake as many panels as possible at the same time in a single session. Therefore, it is determined that the range of the distance between the panels is 70 to 80 mm.

**Fig. 9.** (a) Effect of the number of side air inlets on the average temperature and temperature inhomogeneity coefficient; (b) effect of the number of side air inlets on the mean air velocity and velocity inhomogeneity coefficient

*Number of side air inlets*

When hot air is solely provided through the bottom air inlet, it travels upward along the bottom and then transfers to both sides. As it does so, the temperature and wind speed gradually decrease. This results in the edges of the panels in the chamber experiencing low-temperature and low-speed areas, while the main baking area in the middle remains significantly warmer, with faster speeds. The large difference between these areas negatively impacts the overall flow field uniformity within the chamber. Therefore, considering this factor, the number of air inlets on the side of the equilibration chamber was set as 0, 2, 4, 6 and 8 respectively, and placed symmetrically, taking the distance of the panel gap as 80 mm, and the spacing of the air inlets at the bottom as 300 mm for the one-factor simulation calculation.

As the number of air inlets increases, so does the ventilation rate, leading to a consistent upward trend in wind speed and temperature. When the hot air from the bottom reaches and comes into contact with the hot air entering through the side inlets, the temperature and wind speed of the hot air from the side inlets are higher than that from the bottom, thus accelerating the flow dynamics inside the equilibration chamber and causing an increase in the coefficient of unevenness. In addition, the increase in the number of side air inlets also facilitates the better distribution of hot air to the upper half of the boards and the low-temperature, low-speed areas at the top of the equilibration chamber. This improvement significantly raises the overall average baking temperature, enabling the boards to reduce their moisture content more quickly and evenly, thus minimizing the likelihood of cracking in certain areas and excessive moisture content in others. The hot air stays in the chamber for too short a period of time, such that it cannot achieve the purpose of the baking to reduce the moisture content. Therefore, the combination of the above analyses determined that the number of side air inlets ranges from 0 to 4.

*Bottom air inlet spacing*

After analyzing the panel position and the number of side air inlets, the spacing of the bottom air inlet determines the entry position and, subsequently, the flow direction of the hot air at the bottom. It is also an important factor affecting the uniformity of the flow field in the equilibration chamber. Therefore, under the condition of a panel gap of 80 mm and zero side air inlets, the spacing of the bottom air inlet was set to 150, 200, 250, 300, and 350 mm, respectively, for the one-factor simulation calculation. As shown in Fig. 10, the change curves of the influence of different bottom inlet spacing on the average temperature, temperature inhomogeneity coefficient, average velocity and velocity inhomogeneity coefficient of the indoor flow field were simulated. It can be observed that the average air velocity and velocity inhomogeneity coefficient were gradually decreasing. This can be attributed to the fact that, as the spacing of the bottom air inlet increases, the distribution of airflow through the bottom inlet becomes wider. This wider distribution enhances the wind speed at the indoor edges of the region, while reducing the velocity in the middle region. Both of these effects tend to equalize the flow, resulting in a more stable and uniform velocity field in the equilibration chamber, with reduced differences overall. In terms of temperature, since the bottom air inlet is located closer to the edge area, it is capable of supplying more hot air to the edges. Additionally, the panels located on the outside are exposed to a more direct high-temperature airflow, thus contributing to an increase in the average temperature. However, with the further expansion of the spacing, the temperature distribution becomes more dispersed, the high temperature region shrinks, and the areas of the middle and low temperature regions increase. So the average temperature increases first and then decreases, while the temperature inhomogeneity coefficient decreases first and then increases, but the overall trend for the temperature inhomogeneity coefficient is toward a smaller value. Through the calculation and comprehensive consideration of the uniformity of the flow field inside the equilibration chamber, the preliminary determination of the bottom air inlet spacing range of 200 to 300 mm.

**Fig. 10.** (a) Effect of different bottom air inlet spacing on average temperature and temperature inhomogeneity coefficient; (b) effect of different bottom air inlet spacing on the velocity inhomogeneity coefficient of the mean anemometer

**Structure and Parameter Optimization Orthogonal Experimental Design**

*Orthogonal test program design*

The main factors affecting the uniformity of temperature and wind speed inside the equilibration chamber are the distance between the panels, the number of side air inlets and the spacing of the bottom air inlets. To obtain a better combination of structural parameters to improve the baking efficiency and flow field uniformity, orthogonal tests should be introduced to analyze the effects of different combinations of the above three variables on the flow field of the equilibration chamber. According to the analysis of the impact of different factors in the previous section to determine the range of values for the distance between the panels 70 to 80 mm, the number of side air inlets 0 to 4, the bottom air inlet spacing of 200 to 300 mm. Thus, an orthogonal test design for 3 factors with 3 levels each was created, as shown in Table 4.

The L9 (3^{4}) orthogonal test table was chosen to perform the simulation calculations, where L stands for the orthogonal table, 9 for the number of tests, 4 for the number of factors, and 3 for the number of levels. The results of these simulations are presented in Tables 5 to 7. In the tables, A represents the number of side air inlets, B is the spacing of the bottom air inlet, and C is the distance between the panels.

**Table 4.** Orthogonal Test Factor Level Table

**Table 5.** Orthogonal Test Simulation Results

**Table 6.** Visual Analysis of Velocity Inhomogeneity Coefficients