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An experimental determination of the critical diffusion coefficient and critical relative humidity (RH) of drying air when optimizing the drying of three hardwood species (birch, aspen, and black alder)

Hannes Tamme
Hannes Tamme
, 
Regino Kask
Regino Kask
, 
Peeter Muiste
Peeter Muiste
 and 
Valdek Tamme
Valdek Tamme
   | Apr 13, 2024
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Article Category: Research paper
Published Online: Apr 13, 2024
Page range: 3 - 20
DOI: https://doi.org/10.2478/fsmu-2023-0009
Keywords
© 2023 Hannes Tamme et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

(a) interior view of the climate chamber, and (b) sensor placement schematic.
(a) interior view of the climate chamber, and (b) sensor placement schematic.

Figure 2.

A comparison of the average moisture content levels, and the moisture content levels which were obtained using the slicing method at a depth of 12 mm on the example of alder wood.
A comparison of the average moisture content levels, and the moisture content levels which were obtained using the slicing method at a depth of 12 mm on the example of alder wood.

Figure 3.

Alder wood drying experiment. Identification of the critical RH of the drying air according to the separating line of the first and second drying phase (Tamme et al., 2021a). Drying curves for the layers of alder wood at different depths, and the RH graph for the drying air on an axis with a different scale, while the time axis is unchanged.
Alder wood drying experiment. Identification of the critical RH of the drying air according to the separating line of the first and second drying phase (Tamme et al., 2021a). Drying curves for the layers of alder wood at different depths, and the RH graph for the drying air on an axis with a different scale, while the time axis is unchanged.

Figure 4.

Alder wood drying experiment. Thermocouple data, with the temperature input based on the drying plan (see Table 1), and displacement sensor data depending on the drying time.
Alder wood drying experiment. Thermocouple data, with the temperature input based on the drying plan (see Table 1), and displacement sensor data depending on the drying time.

Figure 5.

Aspen wood drying experiment. Identification of the critical RH of the drying air according to the separating line of the first and second drying phase. Drying curves for layers of aspen wood at different depths, and the RH graph for the drying air on an axis with a different scale, while the time axis is unchanged.
Aspen wood drying experiment. Identification of the critical RH of the drying air according to the separating line of the first and second drying phase. Drying curves for layers of aspen wood at different depths, and the RH graph for the drying air on an axis with a different scale, while the time axis is unchanged.

Figure 6.

Aspen wood drying experiment. Thermocouple data, with temperature input based on the drying plan (see Table 1), and displacement sensor data depending on the drying time.
Aspen wood drying experiment. Thermocouple data, with temperature input based on the drying plan (see Table 1), and displacement sensor data depending on the drying time.

Figure 7.

Birch wood drying experiment. Identification of the critical RH of the drying air according to the separating line of the first and second drying phase. Drying curves for layers of birch wood at different depths, and the RH graph for the drying air on an axis with a different scale, while the time axis is unchanged.
Birch wood drying experiment. Identification of the critical RH of the drying air according to the separating line of the first and second drying phase. Drying curves for layers of birch wood at different depths, and the RH graph for the drying air on an axis with a different scale, while the time axis is unchanged.

Figure 8.

Birch wood drying experiment. Thermocouple data, with temperature input based on the drying plan (see Table 1), and displacement sensor data depending on the drying time.
Birch wood drying experiment. Thermocouple data, with temperature input based on the drying plan (see Table 1), and displacement sensor data depending on the drying time.

Figure 9.

A comparison of drying curves in different hardwood species under the same drying plan (see Table 1).
A comparison of drying curves in different hardwood species under the same drying plan (see Table 1).

Figure 10.

Moisture profiles for different tree species at different times of drying: (a) alder; (b) aspen; (c) birch; and (d) pine, with moisture profiles-based data which is used in the article (Tamme et al., 2021a).
Moisture profiles for different tree species at different times of drying: (a) alder; (b) aspen; (c) birch; and (d) pine, with moisture profiles-based data which is used in the article (Tamme et al., 2021a).

Figure 11.

A comparison of differences in surrounding air temperature and wood surface temperature for different tree species: (a) alder; (b) aspen; (c) birch; and (d) pine (according to the paper by Tamme et al. (2021a)).
A comparison of differences in surrounding air temperature and wood surface temperature for different tree species: (a) alder; (b) aspen; (c) birch; and (d) pine (according to the paper by Tamme et al. (2021a)).

Figure 12.

A comparison of the behaviour of the surface layer displacement sensor as a function of time, for different tree species.
A comparison of the behaviour of the surface layer displacement sensor as a function of time, for different tree species.

Figure 13.

A comparison of the total deformation in the surface layer depending on the drying time, for different tree species.
A comparison of the total deformation in the surface layer depending on the drying time, for different tree species.

Hypothesis testing results for hardwood species. Independent x-value is moisture content (MC) in the depth level of 1 mm from the surface. Dependent y-value is the MC in the depth level of 12 mm from the surface.

Type of wood Equation: 12mmMC (y) ~ 1mmMC (x) R R2 p-value
Black alder y = 0.951x + 17.303 0.989 0.977 < 0.001
Aspen y =1.275x + 11.8 0.979 0.958 < 0.001
Birch y =1.302x + 12.028 0.965 0.931 < 0.001
*Pine sapwood y =0.9377x + 57.898 0.992 0.984 < 0.001

The same drying schedule for drying all hardwoods.

Time (h) Surrounding air temp. (°C) Wet bulb temp. (°C) Surrounding air RH (%)
0 20 19.44 60
1 47 46.11 95
12 48 47.10 95
36 50 48.13 90
60 52 48.02 80
84 52 45.54 69
108 52 43.05 59
132 52 40.27 49

A comparison of the effective diffusion coefficient (EDC) (Deff) for different tree species under quasi-stationary drying conditions.

Type of wood Deff (*10−4 mm2/s)
Black alder 11.92
Aspen 11.44
Birch 4.18
*Pine sapwood 9.58

Equations of experimentally determined parabolic moisture profiles for different tree species, and an R-squared approximation. Independent x-value is the depth level (mm) from the board surface. Dependent y-value is the moisture content (MC%) at the depth level.

Type of wood Time (h) Equation of parabolic MC profile R2
Black alder (Figure 10a) 0 --------- ------
61 y = − 0.0976x2 +3.0933x +30.2 0.9512
96 y = − 0.0655x2 +2.0568x+ 12.884 0.9964
119 y = − 0.047x2 +1.5694x + 6.4665 0.9974
Aspen (Figure 10b) 0 ----------- --------
50 y = − 0.1197x2 +3.4894x+32.592 0.8463
99.5 y = − 0.0597x2 +1.9168x + 11.8 0.9916
125 y = − 0.0315x2 +1.18x +9.1838 0.993
Birch (Figure 10c) 0 ----------- --------
46 y = − 0.1154x2 +3.9316x +23.5 0.9698
94 y = − 0.0599x2 +2.0472x +13.274 0.9981
122 y = − 0.0547x2 +1.9479x +10.274 0.9984
*Pine sapwood (Figure 10d) 22 y = − 0.054x2 +1.5471x +91.484 0.87
92 y = − 0.0781x2 +2.3962x +24.791 0.8978
116 y = − 0.0867x2 +2.2641x +18.533 0.8615
140 y = − 0.0625x2 + 1.8709x +11.191 0.9769

The experimentally determined moment of time, for the separating line (SL) and the corresponding average moisture content in the wood at the point at which the wood's surface layer transitions from the first drying phase into the second drying phase, and figures related to that transition.

Type of wood Separating line (SL) (h) of drying phases Avg MC (%) Related figures
Black alder 61 55 Figure. 9, line 1; Figure. 11a
Aspen 50 62 Figure. 9, line 2; Figure. 11b
Birch 46 64 Figure. 9, line 3; Figure. 11c
*Pine sapwood 94 60 Figure. 11d

Section-linear calibration functions determined on the basis of Formula (7) at depths of 1 mm and 4 mm from the surface, using the example of alder wood. Independent x-value is electrical resistance of wood (unit 10LogR). Dependent y-value is the moisture content (MC) of wood.

Depth (mm) AB BC CD
1 mm y = −8.0269x+475.3 y = −0.676x+61.97 y = −0.41x+43.335
4 mm y = −12.813x+714.47 y = −1.474x+119.696 y = −0.721x+69.18

The critical diffusion coefficient (Dcr) for the surface layer of three hardwood species and pine sapwood, along with the corresponding critical air humidity (RHcr) and the ratio of the diffusion coefficients for the first drying phase and the second drying phase in the surface layer (Dcr/D2ph), for different tree species.

Type of wood Dcr (*10−4 mm2/s) RHcr (%) D2ph (*10−4 mm2/s Dcr/D2ph
Black alder 36.57 75.6 13.87 2.64
Aspen 30.71 85.4 11.72 2.62
Birch 16.35 85.4 6.92 2.36
*Pine sapwood 27 81 18 1.5
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