Mathematical modelling and experimental verification of wood drying process

Energy Conversion and Management 45 (2004) 197–207 www.elsevier.com/locate/enconman

Mathematical modelling and experimental verification of wood drying process H.S.F. Awadalla

a,*

, A.F. El-Dib b, M.A. Mohamad a, M. Reuss c, H.M.S. Hussein a

a

b

Department of Solar Energy, National Research Centre, El-Tahrir, Dokki, Giza, Egypt Department of Mechanical Power Engineering, Faculty of Engineering, Cairo University, Giza, Egypt c Institute of Agriculture Engineering, Technical University, Munich, Germany Received 5 January 2003; accepted 2 June 2003

Abstract In this paper, the wood drying process is investigated theoretically under transient conditions. The governing equations of heat and mass transfer in wood are presented. The finite elements method is used to solve the set of governing equations by means of a simulation program. For verification of the present model, the wood model is executed within the TRNSYS program with experimental data of wood drying experiments conducted at Wood Research Institute of Munich, Germany, and with previous theoretical works. For steady state and transient conditions, the computational results show considerable agreement with previous experimental and theoretical works.
2003 Elsevier Ltd. All rights reserved. Keywords: Theoretical analysis; Experimental investigation; Wood drying; Governing equations; TRNSYS program

1. Introduction Wood continues to be a principal raw material for a large number of products as in building construction and in furniture industry, although other competitive materials as metal and plastics are available. To ensure a suitable and usable end product of wood, most of its moisture content must be removed by drying. So, drying is an important step for improving wood quality before it can be manufactured into stable finished end products. The required energy for drying wood in

*

Corresponding author. Fax: +20-233-709-31. E-mail address: [email protected] (H.S.F. Awadalla).

0196-8904/$ - see front matter
2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0196-8904(03)00146-8

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Nomenclature A cp D EMC h hD k Le m_ p Pr Q_ r R Re t T v V X y q

area, m2 specific heat, kJ/kg K diffusion coefficient, m2 /s equilibrium moisture content, kgwa /kgw;dr convection heat transfer coefficient, kW/m2 K mass transfer coefficient, m/s thermal conductivity, kW/m K Lewis number, dimensionless mass flow rate per unit surface area, kg/m2 s atmospheric pressure/partial pressure, kPa Prandtl number, dimensionless heat flow rate, kW latent heat of vaporization of water, kJ/kg gas constant, kJ/kg K Reynolds number, dimensionless time, s temperature, K air velocity, m/s volume, m3 moisture content of wood, kgwa /kgw;dr humidity ratio of air, kgwv /kga;dr density, kg/m3

Subscripts a drying air conv convection cond conduction cs cross-sectional dr dry evap evaporation ex exit in initial m mean value mt moisture or wet s surface of wood board Si wood segment i St wood stack w wood wa water wv water vapor

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conventional dryers ranges from 600 to 1000 kW h/m3 , depending on wood types and thickness [1]. Helmer et al. [2] developed that a computer simulation model for a solar timber dryer and a solar dehumidification dryer. Experimental data were taken on the two dryers and compared well with the computer predication. They concluded that the computer simulation model predicts the performance of their dryers. The test results indicate that the solar dehumidification dryer can reduce energy consumption by about 50% while achieving about equal drying times and yet with improved wood quality. Taylor [3] used numerical simulation and experimental measurements to examine the performance of a glasshouse type solar wood dryer. A fairly simple model, two differential equations, gives a reasonable fit to the drying curves. The solar kiln dries about 5 cubic meters of mahogany from green to equilibrium states in about three weeks. Steinmann [4] constructed a simulation system to overcome the problem of non-repeatability of weather conditions to determine the optimization of solar dryer performance. Duffie and Close [5] optimized a solar timber dryer equipped with an absorbent energy store. Their work aimed to develop a fast simulation program that can determine the minimum cost. They concluded that an optimized solar kiln plus heating system is cheaper than a conventionally heated drying system when the energy used is electricity. Nadler et al. [6] constructed a mathematical model for the diffusion of water in wood during drying. Their model is based on capillary action above the fiber saturation point and diffusion below fiber saturation. The results of these studies show the possibility of producing a high quality product at low cost in a solar powered dryer, or optimizing drying schedules to reduce drying time and increase product quality. The TRaNsient SYstem Simulation program TRNSYS [7] is a widely used scientific simulation tool in solar energy, which is also experimentally validated. It is a transient simulation program with a modular structure, which gives the program a tremendous flexibility and facilitates the addition of any mathematical model not included in the standard TRNSYS library. The present work aims at developing the TRNSYS simulation tool to enable optimization methods of solar timber drying. So, a computer subprogram for wood drying will be constructed based on a transient theoretical analysis and will be added to the TRNSYS deck. Also, the present work aims to verify the present model with previous experimental work and compare it with previous theoretical works.

2. Theoretical analysis For simplicity, the mathematical model of wood drying is based on the following assumptions: 1. The wood stack inside the drying chamber is divided into (m) columns in the air flow direction. 2. For each column, each wood board is divided into (n) segments from its surface to its center, while the drying air volume between wood boards in each column is divided into two segments. 3. The changes of temperature and moisture content of wood segments in each column are assumed one dimensional because the thickness of the wood segments is small compared to its width. 4. The change of the drying air temperature between wood boards in the wood stack is assumed one dimensional in the flow direction, while it is constant in each column.

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5. Because of the heterogeneous structure of wood, average values of the physical properties of wood, such as sorption isotherms and diffusion coefficient, can be assumed independent of the position in the structure [8,9]. 6. The specific binding energy of water in wood can be neglected [8]. 7. The drying air flow rate is uniformly distributed between wood boards (i.e. the volume flow rate of drying air between wood boards is equal). 8. The density of the drying air in each column is constant. 9. The outlet temperature of the drying air from each column is assumed equal to the temperature of the drying air in this column at the previous time step. 10. The initial temperature of the wood segments are constant at ambient temperature at the start of simulation. 11. As the thickness of wood segments is small compared to their width, the heat and mass transfer between drying air and the sides of wood segments can be neglected. The energy rate balance (kW) of a drying air segment adjacent to the wood segment (0) throughout the wood board shown in Fig. 1 can be represented as follows: 1 dTa 1 Va qa;mt cpa;mt ¼ vAcs qa;mt cpa;mt ðTa;in
Ta;ex Þ þ Q_ evap
Q_ conv 2 2 dt

Fig. 1. Energy rate balance on drying air segment and wood segments.

ð1Þ

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where Q_ evap and Q_ conv (kW) are the evaporation and convection heat transfer rates between the drying air and wood segment 0, which can be calculated as follows [8]: Q_ evap ¼ rm_ wv;s AS

ð2Þ

Q_ conv ¼ hAðTa
TS0 Þ

ð3Þ

The specific water vapor mass flow rate (m_ wv;s ) (kg/m2 s) from segment (0) to the drying air segment can be calculated as follows [8]: m_ wv;s ¼

hD ðPwv;s
Pwv;a Þ Rwv TS0

ð4Þ

The vapor pressure on the wood surface can be determined from the sorption isotherms of wood [10]. The mass transfer coefficient (hD ) (m/s) can be calculated from the convection heat transfer coefficient (h) (kW/m2 K) as follows [8]:   1 pwv;m hD ¼ h 1
ð5Þ qa;mt cpa;mt Le0:58 p The energy rate balance (kW) of a wood segment (0) throughout the wood board shown in Fig. 1 can be represented as follows: qw;mt VS0 cpw;mt

dTS0 S0 S1 ¼ Q_ conv þ m_ wa jS1 As cpwa ðTS1
TS0 Þ
Q_ evap
Q_ cond jS0 dt

ð6Þ

The specific water mass flow rate (m_ wa ) (kgwa /s) from segments (1) to (0) can be represented as follows [10]: m_ wa ¼ Dqw;dr jrX j

ð7Þ

The conduction heat transfer (Q_ cond ) (kW) between segments (0) and (1) can be represented as follows [10]: Q_ cond ¼ kAs jrT j

ð8Þ

The energy rate balance (kW) of wood segments (i) from i ¼ 1 to n
2 throughout the wood board shown in Fig. 1 can be represented as follows: qw;mt VSi cpw;mt

dTSi Siþ1 _ þ m_ wa jSi ¼ Q_ cond jSi Si
1
Qcond jSi Siþ1 As cpwa ðTSiþ1
TSi Þ dt Si
1
m_ wa jSi As cpwa ðTSi
TSi
1 Þ

ð9Þ

The energy rate balance (kW) on wood segment (n
1) at the core of the wood board as shown in Fig. 1 can be represented as follows: dTSn
1 _ wa jSn
2 ð10Þ ¼ Q_ cond jSn
1 Sn
2
m Sn
1 As cpwa ðTSn
1
TSn
2 Þ dt The mass rate balance (kgwv /s) of the drying air adjacent to wood segment (0) throughout the wood board shown in Fig. 2 can be represented as follows: qw;mt VSn
1 cpw;mt

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1

Fig. 2. Mass rate balance on drying air segment and wood segments.

1 1 ð11Þ Va q dya ¼ vAcs qa;dr ðya;in
ya;ex Þ þ m_ wv;s As 2 a;dr dt 2 The mass rate balance (kgwv /s) of wood segment (0) throughout the wood board shown in Fig. 2 can be represented as follows: qw;dr VS0

dXS0 _ wv;s As ¼ m_ wa jS0 S1 As
m dt

ð12Þ

The mass rate balance (kgwa /s) on wood segment (i) from i ¼ 1 to n
2 throughout the wood board shown in Fig. 2 can be represented as follows: dXSi _ wa jSi
1 ð13Þ ¼ m_ wa jSi Siþ1 As
m Si As dt The mass rate balance (kgwa /s) on wood segment (n
1) at the core of the wood board shown in Fig. 2 can be represented as follows: qw;dr VSi

qw;dr VSn
1

dXSn
1 Sn
2 ¼
m_ wa jSn
1 As dt

ð14Þ

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Solutions of the governing equations of the drying air and wood segments are obtained using the finite elements method by means of a simulation subprogram. This subprogram will be connected with the TRNSYS program. The temperature and humidity ratio of the air segments adjacent to wood segments are discretized into 10 nodes. The temperature and moisture content of the wood segments are discretized into 10 · 6 nodes. A time step of 15 s is used in the computation of the model.

3. Experimental verification of present model To verify the present model experimentally, the present model was executed within the TRNSYS program with experimental data of wood drying experiments conducted at Wood Research Institute of Munich [11]. These experiments comprise two groups of experiments and were conducted on spruce wood. The first group of experiments has been conducted for drying spruce using the typical tunnel industrial dryer with drying air velocity ranging from 2.5 to 3 m/s. Spruce boards having dimensions of 0.5 m · 0.18 m · 0.09 m and initial moisture content of 0.8 and 0.4 kgwa /kgw;dr have been dried at constant drying temperatures of 60 and 75 C, respectively. The second group of experiments has been conducted using the solar tunnel dryer for drying spruce at transient conditions. The meteorological conditions, such as temperature, relative humidity, intensity of solar radiation and wind speed have been measured and recorded during the drying process. Spruce boards having dimensions of 0.5 m · 0.1 m · 0.025 m and initial moisture content of 0.35 kgwa /kgw;dr have been dried at transient condition. The drying air velocity was kept constant at 3 m/s during the drying process. Figs. 3 and 4 illustrate the comparison between the previous experimental results and their corresponding theoretical results of wood average moisture content and the deviation of the

Fig. 3. Comparison between previous experimental results and theoretical results and deviation between them for wood drying process at constant temperature of 60 C.

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Fig. 4. Comparison between previous experimental results and theoretical results and deviation between them for wood drying process at constant temperature of 75 C.

Fig. 5. Comparison between transient previous experimental and theoretical results of wood temperatures and inlet air temperature.

theoretical results from the experimental ones at constant drying air temperatures of 60 and 75 C, respectively. Fig. 5 illustrates the comparison between the transient previous experimental results and present theoretical results of wood temperature and experimental drying air temperature at the entrance of the solar tunnel dryer and the deviation between them at variable drying temperature. On the other hand, the comparison between the previous experimental results and present theoretical results of the average moisture content of spruce and the deviation between them are shown in Fig. 6. Figs. 3–6 indicate that:

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Fig. 6. Comparison between transient previous experimental and present theoretical results of wood average moisture content.

1. At steady state and transient conditions, the previous experimental results and their corresponding computational ones from the present model have the same trend. 2. The deviation of the present theoretical results of wood average moisture content from the previous experimental ones ranges from )12% to +14% as shown in Figs. 3 and 4. 3. The deviation of the theoretical results of wood average temperature from previous experimental ones ranges from )0.5% to +3% as shown in Fig. 5. 4. The temperature difference between the drying air and wood is large before solar noon and decreases after solar noon because the wood works as storage material as shown in Fig. 5. 5. The transient experimental and theoretical results of wood average moisture content have similar trends for drying features, where the curves exhibit hard drying at the day, followed by humidification of wood at night, when the EMC of wood is greater than the moisture content of wood (i.e. the vapor partial pressure of the air is greater than the vapor partial pressure of the wood surface at night) as shown in Fig. 6. 6. The deviation of the present theoretical results of wood average moisture content from the previous experimental ones ranges from )7% to +13%. This deviation may be attributed to the condensation of moisture at the wood surface at night as shown in Fig. 6.

4. Comparison of present model and previous theoretical works For two different operating conditions, the present model is compared with the theoretical model constructed by Ferguson [12] and the theoretical and experimental works performed by Cronin et al. [13]. The comparison between the previously published results [12,13] and the corresponding theoretical ones from the present model are represented graphical in Figs. 7 and 8. From Figs. 7 and 8, it is concluded that:

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Fig. 7. Comparison between theoretical results of present and Ferguson models.

Fig. 8. Comparison between present theoretical results and CroninÕs theoretical and experimental results.

1. For two different initial moisture content and operating conditions, the results from the present model show considerable agreement with the theoretical and experimental results of Ferguson [12] and Cronin et al. [13]. 2. The difference of results may be due to the physical properties of wood that were used in the different models. 3. The present wood model proved to be an effective tool for the prediction of the drying process of wood.

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5. Conclusions From the theoretical and experimental investigation of the wood drying process and its comparison with previous experimental and theoretical works, it is concluded that: 1. Computational results from the present analysis show considerable agreement with the previous experimental and theoretical results at steady state and transient condition; 2. The present simulation model proved to be an effective tool for the design of a solar timber dryer and the prediction of its moisture content behavior.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

Tsoumis G. Science and technology of wood. Reinhold, USA: Van Nostrand; 1993. Helmer WA, Chen PYS, Vaidya MB. Solar Energy 1982;104:182–6. Taylor KJ. Solar Energy 1985;34(3):249–55. Steinmann D. Solar Energy 1995;54(5):308–15. Duffie NA, Close DJ. Solar Energy 1978;20:405–11. Nadler K, Choong E, Wetzel D. Wood Fiber Sci 1985;17(3):404–23. TRNSYS. University of Wisconsin-Madison, Solar Energy Laboratory, USA, 1994. Krischer O, Kr€ oll AJ. Trocknungstechnik. Berlin, Germany: Springer-Verlag; 1992. Koponen H. Drying 87. Berlin, Germany: Springer-Verlag; 1987. Kollmann F. Principles of wood science and technology. Berlin, Germany: Springer-Verlag; 1968. € berpr€ Benkert S. Modellierung und Experimentielle U ufung einer Pilotanlage zur Solaren Holztrocknung, Master Thesis, Landtechnik Institute, Technische Universit€ at M€ unchen, 1995. [12] Ferguson WJ. In: Turner I, Mujumdar A, editors. Mathematical modelling and numerical techniques in drying technology. New York: Marcel Dekker Inc.; 1996. p. 259–308. [13] Cronin K, Norton B, Taylor J. Appl Energy J 1996;53(4):325–40.