Abstract

Materials

Poplar (Populus tomentosa) sapwood specimens were provided by Landbond Furniture Co. Ltd., Shandong, China. The dimensions of the test specimens were 150 mm in length (longitudinal direction) by 100 mm in width (radial direction) by 60 mm in thickness (tangential direction), with initial moisture content of 100 ± 5 percent (according to GB/T 1931‐2009; Zhao et al. 2009). To simulate a real-world production process, all the end cross sections of specimens were blocked by covering them with epoxy resin, and the specimens were placed in a customized incubator with internal dimensions of 150 by 100 by 60 mm. The faces of all specimens (except one, with dimensions of 150 by 100 mm) were covered by the internal wall of the incubator.

Equipment

The vacuum drying system included temperature and pressure controls, through which the temperature and the pressure of the drying medium could be controlled automatically with an accuracy of 0.01°C and 0.002 MPa, respectively. The data collection system included temperature sensors (used to calculate accurate inner wood temperatures automatically), a digital inspection instrument, and a computer. Superheated steam was produced by a steam generator.

Experimental methods and procedures

Experiments were carried out at three different temperature levels (35°C, 55°C, and 70°C) and three different absolute pressure levels (0.03, 0.06, and 0.1 MPa). Thermocouple locations are shown in Figure 1; layer 1 marks the outer layer, layer 2 the secondary layer, and layer 3 the central layer. In each experimental unit, superheated steam was injected into the vacuum drier before vacuum drying, and the temperature value acquisition process was complete when temperatures inside the samples became constant.

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Influence of environmental conditions on wood temperatures

Wood temperature variation over time at environmental temperatures of 35°C, 55°C, and 70°C and absolute pressures of 0.03, 0.06, and 0.1 MPa are shown in Figures 2 through 4. Temperatures inside samples increased with time at the beginning and then rising rates decreased gradually until the temperature became constant. The time for temperatures inside the samples to become constant was different under different conditions: the higher the drying temperature applied, the shorter the time until stability was reached. It took 300 min for wood temperatures to become constant when the temperature of the drying medium was 35°C and 200 and 150 min at temperatures of 55°C and 70°C, respectively. This phenomenon may have been caused by the temperature differences between dying medium and poplar samples, which was larger when the temperature of the dying medium was high and smaller when the temperature of drying medium was low.

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In addition, the ultimate temperatures of inner wood increased as absolute pressure increased at certain temperatures. Specifically, these temperatures were 29.1°C, 32.6°C, and 36.8°C at absolute pressures of 0.03, 0.06, and 0.1 MPa, respectively, at a drying medium temperature of 35°C. They were 49.3°C, 51.4°C, and 53.2°C at absolute pressures of 0.03, 0.06, and 0.1 MPa, respectively, at a drying medium temperature of 55°C, and they were 61.7°C, 64.7°C, and 69.1°C at absolute pressures of 0.03, 0.06, and 0.1 MPa, respectively, when the drying medium temperature was 70°C. Heat transfer capacity decreases as absolute pressure decreases, where air density is low and heat is less readily transferred to the wood; as a result, the wood sample temperature was low under low absolute pressure conditions. Further, ultimate temperatures inside the wood could not reach those of the drying medium at lower absolute pressure conditions.

Wood drying rates increase as absolute pressure decreases during vacuum drying (Mottonen 2006, Chen and Lamb 2007, Hermawan et al. 2013), so to secure the appropriate drying rates at a certain temperature, reasonable pressure must be applied. Compared with conventional wood drying, drying rates can be improved using vacuum conditions by controlling decreases in temperature caused by low pressure. Appropriate drying schedules can be defined by the lowest possible temperature and absolute pressure conditions that still provide desired results, which could save energy and truncate the drying cycle.

Convective heat transfer coefficients under different drying conditions

To obtain the convective heat transfer coefficients under different drying conditions, temperatures at specific locations inside the wood samples were measured and results are shown in Figure 5. Temperature differences among different places in one wood sample were slight (P > 0.05), suggesting that the heat transfer rates in the inner wood were very fast and that the wood could be considered an integrated whole; thus, its biot number (Bi) is less than 0.1 (Zhang and Nie 2000).

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According to Newton's cooling formula:

where q is power (W), h is convective heat transfer coefficient (W/[m²·K]), A is area (m²), T is the wood sample temperature (°C), and T_∞ is the drying medium temperature (°C).

By combining Equation 1 and the mass conservation law, when Bi is less than 0.1, we can draw Equation 2 (Zhang and Nie 2000):

where T is wood sample temperature (°C), ρ is wood sample density (kg/m³), c_p is wood sample specific heat (J/[kg·K]), V is wood sample volume (m³), and τ is time (s).

To solve Equation 2, excess temperature (θ = T − T_∞) is involved, so Equation 2 should be rewritten as follows:

We integrated both sides of Equation 3 and combined it with the known conditions under which T equals T₀ (the initial temperature of the wood sample) at the initial time. Equation 3 was then converted to Equation 4:

Therefore,

The convective heat transfer coefficients under different drying conditions were obtained by comparing experimental data and the calculation results of Equation 5 as shown in Table 1. We found that convective heat transfer coefficient increases as absolute pressure increases at certain temperatures, by 3.33 W/m²·K at 35°C, 2.52 W/m²·K at 55°C, and 7.95 W/m²·K at 70°C when absolute pressure increases from 0.03 to 0.1 MPa. Table 1 also shows where the convective heat transfer coefficient similarly increases alongside temperature at a certain absolute pressure, by 6.24 W/m²·K at 0.03 MPa, 6.68 W/m²·K at 0.06 MPa, and 10.86 W/m²·K at 0.1 MPa as temperature increased from 35°C to 70°C.

Table 1 Convective heat transfer coefficients under different conditions.

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To predict the convective heat transfer coefficient under various drying conditions, the relationship among convective heat transfer coefficient, temperature, and absolute pressure can be established based on experimental results as follows:

where h is the convective heat transfer coefficient (W/[m²·K]), t is the temperature in the vacuum drier (°C), and P is the absolute pressure (MPa). Via Equation 6, we found that the correlation coefficient (R²) was 0.97. This indicates that the equation simulated the experimental results very well and can feasibly be used to predict the convective heat transfer coefficient under different vacuum drying conditions.

Temperatures inside wood samples at different times and under different conditions can be determined by Equations 4 and 6, allowing appropriate temperature and absolute pressure to be optimized according to the wood temperature needed during the poplar drying process in practice. Appropriate drying schedule facilitates both energy and time efficiency during the poplar drying process.