Simulation of moisture transfer during wood vacuum drying

Results in Physics 12 (2019) 1299–1303

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Simulation of moisture transfer during wood vacuum drying Zhengbin He , Jing Qian, Lijie Qu, Zhenyu Wang, Songlin Yi ⁎

⁎

T

Beijing Key Laboratory of Wood Science and Engineering, College of Material Science and Technology, Beijing Forestry University, No. 35, Qinghua East Road, Haidian District, Beijing 100083, PR China

ARTICLE INFO

ABSTRACT

Keywords: Wood Vacuum drying Heat and mass transfer Diffusion coefficient Drying rate

Vacuum techniques are commonly used in material drying applications as they provide good quality at fast rates. In this study, wood samples were dried under absolute pressure of 0.02 MPa at 80 °C to assess the drying characteristics. A heat and mass coupling transfer model was established and verified to determine the wood temperature and interior moisture content at various time points during the drying process. Results indicated that the average drying rates for wood with moisture content above fiber saturation point (FSP) is about 2.91 times than that below the FSP. Wood temperature increases over time and nears the ambient temperature at about 60 min. The diffusion coefficient decreases as wood moisture content decreases; it varies from 1.32 × 10−7 to 2.65 × 10−7 m2/s when wood moisture content is above FSP and from 0.46 × 10−7 to 1.32 × 10−7 when wood moisture content is below FSP. The pressure gradient and water volume fraction gradient can be considered wood vacuum drying forces, and the moisture content from the heat and mass coupling transfer model is similar to the actual measured value. The proposed model effectively predicts wood moisture content during wood vacuum drying.

Introduction Wood drying is one of the most important applications in the wood processing industry. It consumes about 40–70% of the total energy, and a great deal of the labor and time, in the entire wood product fabrication process [1]. Defects such as deformation and cracking emerge in wood products in the usage stage if the wood has not been dried appropriately, which is significantly detrimental the product’s value [2]. Air drying [3], steam treatment and drying [4], microwave drying [5], ambient pressure drying [6], vacuum drying [7], and solar drying [8] has all been historically utilized to obtain high-quality wood product. Among the available methods, vacuum drying is an interesting alternative which yields dry wood rapidly under low temperature and pressure conditions [9–11]. The pressure gradient and volume fraction gradient are the primary components of the drying force, and the drying force for wood vacuum drying are larger than those for ambient pressure drying, thus, commercial vacuum drying operations have achieved drying rates 3–17 times faster than ambient pressure drying [12,13]. Vacuum drying has been widely applied in food, wood, and other material drying industries [14–17]. The extant research on its efficacy centers on drying characteristics, drying schedules, and drying quality, while few researches have explored heat and mass transfer models for relevant temperature and moisture content variations, though such

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variations affect wood quality and drying cost significantly. In the present study, wood was dried at 80 °C and 0.02 MPa absolute pressure to establish a heat and mass transfer model which reflects the water migration process. This model might provide useful theoretical guidance for future vacuum drying applications. Material and method Material Chinese walnut wood (Juglans regia) provided by Huaguoshan Wood Product Ltd. (Guangdong Province, China) was taken to form specimens. Samples without dead knots, collapses, or cracks were randomly selected from the board and cut into the dimensions of 200 mm length by 100 mm width by 20 mm thickness. Its initial moisture ranges from 50 to 53%. To simulate the actual production process, the wood end cross section was covered with adhesive to prevent water transfer along the longitudinal direction. Wood vacuum drying Wood samples were dried at absolute pressure of 0.02 MPa at 80 °C in a vacuum drying chamber (Shanghai Laboratory Instrument Works

Corresponding authors. E-mail addresses: [email protected] (Z. He), [email protected] (S. Yi).

https://doi.org/10.1016/j.rinp.2019.01.017 Received 28 November 2018; Received in revised form 29 December 2018; Accepted 6 January 2019 Available online 09 January 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

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Co. Ltd., Shanghai, China). Wood weight was collected at an interval of 30 min. The wood was dried at 103 ± 2 °C to absolute dry in an oven after vacuum drying. Moisture content was calculated as follows:

MC =

m

md

thus,

Rw = k v Rw = 0

(1)

md

Ps =

where MC is moisture content; m is the sample’s weight during the vacuum drying process, g; and md is the absolute dry of the sample, g.

>0 or

w

(3)

Ps < Pa

(4)

if

w

if

w

<

e

(5)

e

(6) (7)

w w/ s s 3

where ρw is water density, (kg/m ); kv is water evaporation rate, 1/s; B is constant for different conditions; Ps is the water saturation pressure at temperature t, kPa; Pa is the pressure in vacuum drying chamber kPa; t is temperature, °C; θw is the water volume fraction; θe is the water volume fraction when wood moisture content is equal to the equilibrium moisture content; A and α are constants. Wood is a porous material. Under the assumption that wood volume does not change during the drying process, the interior of the wood is replaced by gas when water is dried from the material. Therefore,

(1) The samples are symmetrical in length, width, and thickness. (2) Moisture percentage continuously decreases during the drying process. (3) No shrinkage or degradation of the solid wood occurs. Geometry of the samples

a

The geometry of the wood is presented in Fig. 1. Mass transfer in the longitudinal direction was not considered because the end cross section was covered and the length is much longer than the width or thickness. Thus, the mass transfer for samples was simplified as a 2D model of its cross-section (ABCO). Boundary AO and boundary OC are symmetrical boundaries, and no mass transfer occurs on symmetrical boundaries and convective heat and mass transfer occur on the boundaries AB and BC.

=1

(

s

+

(8)

w)

where θa is the gas volume fraction in wood; θs is the wood solid volume fraction in wood; θw is the water volume fraction in wood. (2) Heat transfer The energy mainly used to improve wood and water temperature is heat which drives the evaporation of water during the vacuum drying process. The heat transfer process can be expressed as follows [18]:

Heat and mass transfer model

e ce

Wood vacuum drying is a heat and mass coupling transfer process. The pressure gradient and volume fraction gradient are the primary components of the drying force and operate under the aforementioned assumptions. The general heat and mass transfer equations as well as the initial conditions for the cross-section (ABCO) are as follows [18,19].

t

+

·(

e

t)

Rw = h (ta

t)

(9)

3

where ρw is wood density (kg/m ), ce is specific heat, J/(kg·K); λe is wood thermal conductivity, W/(m·K); γ is the latent heat of water vaporization, kJ/kg; h is heat transfer coefficient, W/(m2·K); ta is the treating medium temperature, oC; t is wood temperature, oC; e

(1) Mass transfer

=

w w

+

s s

+

(10)

a a 3

where ρe is wood density with a certain moisture content (kg/m ); ρw is water density (kg/m3); ρa is gas density (kg/m3).

Water transfer occurs in two different processes during vacuum drying: a portion of the water is diffused by capillary tension as capillary flows through wood vessels, and the remaining water evaporates in wood gaps and diffuses through wood pits. The mass transfer equation can be written as follows [18]: w)

e)

w

<0

0.00867t2 + 0.000159t3

0.59 + 0.2846t

M=

The following assumptions were imposed for the heat and mass transfer model during wood vacuum drying:

·(Dw

if w

k v = Ae BMC

Assumptions

=

Pa) / Pa if

Dw = ( Dw = 0

Moisture and heat transfer in wood samples during vacuum drying process

w

w (Ps

ce = (

+

s s cs

+

(11)

a a ca)/ e

where ce is wood specific heat, J/(kg·K); cw is water specific heat, J/ (kg·K); cs is wood specific heat, J/(kg·K); ca is gas specific heat, J/(kg·K).

Rw

e

(2)

w

w w cw

=

dry

+

w ( wet

dry )/(1

(12)

s)

where λe is wood thermal conductivity, W/(m·K); λdry is wood thermal conductivity at absolute dry, W/(m·K); λwet is the thermal conductivity of fully saturated wood, W/(m·K).

where θw is the water volume fraction in the wood; τ is time, s; Dw is the water apparent diffusion coefficient (m2/s); Rw is the water evaporation rate in wood vessels (kg/m3/s); and ρw is water density, (kg/m3). The pressure gradient and volume fraction gradient in the inner wood and at the wood surface are considered the drying force [18,19],

(3) Initial conditions

t (x , y )| = 0 = t 0

MC (x , y )| = 0 = MC0

(13)

where t0 is the initial temperature, °C; M0 is the initial water volume fraction in the wood. (4) Heat and mass transfer simulation The heat and mass transfer coupling model was solved using COMSOL Multiphysics software (Comsol Inc., USA). The parameters were calculated based on wood, water, and vapor characteristics [19,20]. The parameter values are listed in Table 1.

Fig. 1. Wood geometry.

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Results and discussion

Table 1 Parameters. t0 ta Mc0 Pa ρa ρw ρs ca cw cs A

20 °C 80 °C 0.51 0.02 MPa 0.13 (kg/m3) 983.16 (kg/m3) 610 (kg/m3) 7.908 (kJ/(kg·K)) 0.8312 (kJ/(kg·K)) 1.112 (kJ/(kg·K)) 9.847e−8

γ α A λwet λdry θe θs h B γ α

There are two kinds of water in the wood inner: free water in the cell cavities, and bound water in the cell walls [21]. The free water is mainly diffused by capillary tension with a high drying rate, while the bound water is mainly diffused as gas with a low drying rate. The drying properties of free water and bound water markedly differ. The critical point between free water and bound water is the fiber saturation point (FSP), which decreases linearly as temperature increases. FSP is reduced 0.1% when the temperature increases by 1 °C, and FSP is 30% when the temperature is 20 °C [11]. FSP can be expressed as follows:

2357.6 [kJ/kg] 1.847e−6 [m2/s] 9.847e−8 0.385 [W/(m·K)] 0.137 [W/(m·K)] 0.01 0.48 5 [W/(m2·K)] 10–14 2357.6 [kJ/kg] 1.847e−6 [m2/s]

MFSP = 0.3

0.001(t

20)

(12)

where MFSP is the fiber saturation point; t is temperature, °C. Wood FSP is 0.24 when the drying temperature is 80 °C Wood vacuum drying characteristics The wood drying characteristics were showed in Fig. 2. It shows that wood moisture content and drying rate decreases as time progresses. It took about 768 min for wood drying from 0.51 to 0.12 during the whole drying process, and about 335 min for wood drying from 0.51 to 0.24. The average drying rate was 8.06 × 10−4/min. It took about 433 min for wood drying from 0.24 to 0.12, and the average drying rate was 2.77 × 10−4/min. The drying rate above FSP was about 2.91 times than that below FSP. Temperature variations inner wood Wood temperature directly impacts wood mass transfer. The wood temperature distribution reflective of the heat transfer process is shown in Fig. 3. Wood temperature increases with time; the highest temperatures were 58 °C, 69 °C, 75 °C, 78.2 °C, 79.5 °C, and 80 °C, and the lowest temperatures were 46 °C, 62 °C, 71.5 °C, 76.6 °C, 79.1 °C, and 79.9 °C, respectively, at 10 min, 20 min, 30 min, 40 min, 50 min, and 60 min. The rate of increase in temperature slowed over time as the

Fig. 2. Wood drying characteristics.

Fig. 3. Temperature distribution with time. 1301

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Z. He et al.

Fig. 4. Diffusion coefficient of interior wood with time.

Fig. 5. Actual and theoretical moisture content of wood above and below FSP.

temperature difference between wood and the environment decreased with time; and the temperature rising rate increased as this disparity intensified [22]. The highest temperature was identified at the cross section of the surface boundary, and the lowest at the symmetrical boundary. That is for the reason that the conventional heat transfer was faster than heat conducting in the wood inner.

content during vacuum drying under the conditions we assessed (See Fig. 5). Conclusions A heat and mass coupling transfer model was established in this study with pressure gradient and water volume fraction gradient as the vacuum drying force for wood samples. The model was tested against experimental results. Our conclusions can be summarized as follows.

Moisture transfer from wood Moisture transfer characteristics The wood drying process has two stages: 1) moisture transfer from the inner wood via capillary flow and diffusion to the surface and 2) water evaporation from the wood surface to the environmental drying medium. Moisture at the wood surface evaporates into the drying medium in a short time during vacuum drying, so the moisture migration rates in the wood control the overall drying speed. The total diffusion coefficient is the most important parameter in water transfer at the wood interior during vacuum drying. Fig. 3 shows that the total diffusion coefficient of wood decreases over time. The total diffusion coefficient at moisture contents above FSP is higher than that at moisture content lower than FSP. The diffusion coefficient varies from 1.32 × 10−7 to 2.65 × 10−7 m2/s above and from 0.46 × 10−7 to 1.32 × 10−7 below FSP as-reflective of changes in moisture content over time.

(1) Wood moisture content and drying rate decrease as dying time increases. It took about 768 min to dry wood from moisture of 0.51–0.12. The average drying rates for wood with moisture content above FSP is about 2.91 times that below FSP. (2) Wood temperature increases along with the drying time and becomes constant at about 60 min. Temperature increase rates at the wood surface are much higher than those in the wood interior. (3) The total diffusion coefficient decreases with drying time. The diffusion coefficient at moisture contents above FSP is higher than that below FSP. The diffusion coefficient varies from 1.32 × 10−7 to 2.65 × 10−7 m2/s above and that varies from 0.46 × 10−7 to 1.32 × 10−7 when wood moisture content below FSP. (4) The theoretical and measures wood moisture contents are closely matched, which suggests that the proposed model effectively predicts wood moisture content during vacuum drying under our test conditions.

Actual versus theoretical moisture content values As shown in Fig. 4, we compared the actual (measured) and theoretical (calculated) moisture content of wood samples above and below FSP to validate the proposed model. The values are closely matched, which suggests that our model accurately predicts wood moisture

Acknowledgements This work was supported by the National Key R&D Program of 1302

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China [2018YFD0600305]; the Fundamental Research Funds for the Central Universities of China [2015ZCQ-CL-01]; the Hot Tracking Project in Beijing Forestry University, China [2017BLRD04); and the China Scholarship Council (CSC), China Scholarship.

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