Measurement and calculation of moisture content distribution during drying

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Anders Samuelsson, Jesper Arfvidsson

Measurement and Calculation

of Moisture Content

Distribution during Drying

Paper presented at 4th lUFRO International

Wood Drying Conference ^Improving Wood

Drying Technology ^\ Rotorua, New Zealand,

August 9-13,1994

LUND INSTITUTE O F T E C H N O L O G Y Division of Building Physics

Trätek

Anders Samuelsson, Jesper Arfvidsson M E A S U R E M E N T A N D C A L C U L A T I O N OF MOISTURE CONTENT DISTRIBUTION D U R I N G D R Y I N G Trätek, Rapport I 9409047 ISSN 1 1 0 2 - 1 0 7 1 ISRN T R Ä T E K - R - - 94/047 - - SE Nyckelord drying moisture content moisture gradient moisture measurement Stockholm september 1994

Rapporter från Trätek — Institutet för träteknisk forskning — är kompletta sammanställningar av forskningsresultat eller översikter, utvecklingar och studier. Publicerade rapporter betecknas med I eller P och numreras tillsammans med alla ut-gåvor från Trätek i löpande följd.

Citat tillätes om källan anges.

Reports issued by the Swedish Institute for Wood Technology Research comprise complete accounts for research results, or summaries, surveys and

studies. Published reports bear the designation I or P and are numbered in consecutive order together with all the other publications from the Institute. Extracts from the text may be reproduced provided the source is acknowledged.

Trätek — Institutet för träteknisk forskning — be-tjänar de fem industrigrenarna sågverk, trämanu-faktur (snickeri-, trähus-, möbel- och övrig träför-ädlande industri), träfiberskivor, spånskivor och ply-wood. Ett avtal om forskning och utveckling mellan industrin och Nutek utgör grunden för verksamheten som utförs med egna, samverkande och externa re-surser. Trätek har forskningsenheter i Stockholm, Jönköping och Skellefteå.

The Swedish Institute for Wood Technology Re-search serves the five branches of the industry: sawmills, manufacturing (joinery, wooden hous-es, furniture and other woodworking plants), fibre board, particle board and plywood. A research and development agreement between the industry and the Swedish National Board for Industrial and Technical Development forms the basis for the Institute's activities. The Institute utilises its own resources as well as those of its collaborators and other outside bodies. Our research units are located in Stockholm, Jönköping and Skellefteå.

S A M M A N F A T T N I N G

Vid trätorkning är utvecklingen av fuktkvotsgradienten i trämaterialet av stor vikt för kvali-teten efter torkning. En stor skillnad i fuktkvot mellan det inre och ytan av en träbit kan lätt orsaka sprickbildning och deformationer. Därför har en metod för beräkning av fuktkvots-fördelningen i trä under torkning utvecklats och även publicerats tidigare. Dessa beräkningar är här jämförda med praktiska mätningar av fuktkvotsfördelningen under torkning.

Mätningarna har utförts på furu {Pinus silvestris) från mellersta och norra Dalarna. Prover har tagits ur en planka vid olika tidpunkter under pågående torkning. Dessa prover har hackats upp i 65 stycken små rektangulära träbitar. Fuktkvoten i dessa träbitar mättes med hjälp av torrviktsmetoden. Den således uppmätta fuktkvotsfördelningen har därefter jämförts med beräknade värden för motsvarande tvärsnitt uppdelat i 65 beräkningsceller. Jämförelsen mellan beräknade och uppmätta värden visade på en mestadels god överensstämmelse. V i d beräkningarna användes olika fuktflödeskoefficienter i tangentiell och radiell riktning för både kärn- och splintved. Dessa koefficienter har med vissa svårigheter tagits ur litteraturen. Jämförelsen visar att nya fuktflödeskoefficienter behöver tas fram för radiell, tangentiell och longitudinell riktning till årsringarna.

Några resultat från en ny serie mätningar redovisas. Dessa mätningar är utförda på små provbitar av antingen furusplint eller furukärna. Fuktkvotsfördelningen i dessa har mätts under uttorkning i radiell och tangentiell riktning separat. Dessa mätningar har utförts för att möjliggöra en utvärdering av nya fuktflödeskoefficienter till beräkningsmodellen för

M E A S U R E M E N T AND C A L C U L A T I O N O F MOISTURE CONTENT DISTRIBUTION DURING DRYING

A. SAMUELSSON' and J. ARFVIDSSON'

'Trätek, Swedish Institute for Wood Technology Research, Box 5609, S-114 86 Stockholm, Sweden

^Lund Institute o f Technology, Dept. o f Building Physics, Box 118, S-221 00 Lund, Sweden

ABSTRACT

The moisture distribution in wood during drying is important for the timber quality after drying. A great difference in moisture content between the centre and the surface o f a board could easily cause checks and deformation. A method to calculate moisture content distribution during drying has been developed and published earlier. The calculations are compared with a set o f measurements o f moisture content distribution during drying. The measurements have been performed on Scots pine {Pimis silvestris). Samples have been taken from a board at different times during drying. These samples have then been cut into small rectangular pieces for which the moisture content has been measured with the help o f the dry weight method. The measured moisture content distribution has then been compared with calculations. The comparison between calculations and measurements showed mostly a good agreement. Different flow coefficients were used in the tangential and radial directions, both for sapwood and heartwood.

Examples from a new series of measurements are presented. There are four flow coefficients (sapwood and heartwood with the two directions tangential and radial). The moisture content distributions at different times are measured separately in the four cases.

INTRODUCTION

A major problem in timber drying is the development o f moisture content distribution. The moisture distribution causes quality loss, such as checks, case hardening and deformations. Therefore, it is important to be able to predict the moisture distribution for specific timber species with defined dimensions and drying schedule.

Theoretical work on moisture transport in wood during drying has been done by Claesson and Arfvidsson (1992) among others. In that paper the concept using Kirchoff potentials was described. This concept covers the whole process, from evaluation o f measurements to numerical calculation o f moisture content distribution. A short recapitulation will be made in the present paper.

The aim of this work is to compare their calculation method for moisture distribution during drying with measurements on ordinary sawn timber. This work is part o f a research program on moisture distribution, tensions and deformations that occur during drying. The aim o f the research program is to create a method to calculate drying schedules for industrial kilns that reduce quality loss.

T H E O R Y

The model used in this study is still under development. It is based on the theory o f moisture transport using Kirchhoff potential (Arfvidsson and Claesson 1989) extended to the anisotropic case (Claesson and Arfvidsson 1992). This potential, which is a true flow potential, is defined as:

Here ^ denotes any moisture state variable. The moisture balance equation, using Kirchhoff potentials, is for the anisotropic case in two dimensions:

^ ± [cos ^ ( 6 ) ^ . sm\Q)^ . sin(e)cos(e)-^(i|r, - + , ) ] * (2)

dt dx dx dx dy

. — [ c o s ' ( 6 ) ^ . s i n ' ( 6 ) ^ . sin(e)cos(e)—(i|f^-i|r, )]

dy dy dy dx

cos ^(6) = sin'(6) = sin(0)cos(e) = — x ^ ^ . v ^ x'^y' x' * y'

Index r denotes radial direction and / tangential direction. The equation is solved numerically by an explicit difference method. In this method the piece o f wood is divided into a rectangular mesh, in the same way as the measurements are performed. The moisture content by volume is known at time t This moisture content is then converted into Kirchhoff potentials ij;, fi-om relations based on measurements. From this ij;-distribution the moisture flow between each cell in the mesh can be calculated in both the x and y direction. The flow equations are in the two directions:

-g^ = c o s \ d ) ^ * s i n 2 ( 6 ) ^ * sin(e)cos(e)—(i|r^-i|r^ ) (3) dx dx dy

-g = c o s \ e ) ^ • sin ^ ( 6 ) ^ • sin(e)cos(e)—(i|r^-i|r^ )

dy dy dx

The new moisture content at time t + A t is calculated from the net inflow to each cell. This procedure is repeated step by step until the end o f the simulation time is reached. In this way the moisture content distribution can be calculated at different times during the drying process.

MEASUREMENT Test material

The material used in the measurements was three specimens o f Scots pine (Pinus silvestris) which were numbered from 1 to 3. These specimens had at start the following dimensions: length 1200 mm, width 144 mm and thickness 50 mm. The average density was 417 kg/m^, where the density was defined as dry weight over dry volume. All specimens contained both sapwood and heartwood. The heartwood percentage was for piece No. 1: 76%, No. 2: 63% and No. 3: 76%. The material from which the specimens were cut, was taken from a sawmill in green condition.

Method

The specimens were dried in a small experimental kiln in two different constant climates. The used climates were as follows, from drying time 0 - 7 2 hours, 52.0°C dry-bulb temperature and relative humidity 67%, and from 72 - 143 hours, 53.3oC dry-bulb temperature and relative humidity 52%. These climates were kept with an accuracy o f ± 0.2 °C. From the three specimens samples were taken at five different times after start o f drying, 0, 23, 46, 71 and 143 hours. The samples had a length o f 31 mm. Figure 1 shows where the samples were taken in the specimens. The distance between the samples in the specimens was 130 mm. After each cut the new crosscuts o f the specimens were insulated with silicone. This was done to prevent moisture transport along the fibre direction.

' / / / / / .

specimen

71

Figure 1. Sites where samples were taken in the specimens.

The samples were chopped up with a knife in 65 small rectangular pieces as shown in Figure 2. The pieces had the dimension 3 1 x 1 0 x 1 0 mm. In these small pieces the moisture content was immediately measured with the help o f the dry weight method.

boundary between sapwood and heartwood

CALCULATIONS

A preliminary version o f the PC-program JAM-W has been used to simulate the drying o f three different wood specimens. Figure 1. Input to the model was boundary conditions and initial conditions, which were the same as in measurements, and material data. The model requires material data for both sapwood and heartwood in both the tangential and radial direction. The data should cover the moisture state both under and above fibre saturation point. We were not able to find any complete set o f material data that could meet these requirements. Instead material data were taken from different measurements at 20°C, recalculated to 50 °C and put together. The shape of the relation between moisture transport variation and moisture content was kept, in the four different cases, in the radial and tangential direction for sapwood and heartwood. Finally the level had to be adjusted to get results that corresponded to the measurements.

RESULTS AND DISCUSSION

The measured and calculated result for specimen No. 2 are given in this section. The measured values are the ones within brackets. The result is given in moisture content mass by mass (kg/kg) at five different times during the drying process. Each measured value should be considered as a mean value for the measured piece and each calculated value should be considered as a mean value in the calculation cell.

T A B L E 1. Measured and calculated moisture content for specimen No. 2 and each chopped piece with corresponding calculation cell. The measured values are those within brackets.

Green state, 0 hours

161 (161) 147 (147) 104 (104) 40 (40) 31 (31) 33 (33) 34 (34) 42 (42) 102 (102) 144 (144) 143 (143) 167 (167) 181 (181) 145 (145) 106 (106) 38 (38) 31 (31) 31 (31) 32 (32) 33 (33) 31 (31) 32 (32) 88 (88) 143 (143) 146 (146) 178 (178) 141 (141) 58 (58) 32 (32) 33 (33) 32 (32) 33 (33) 34 (34) 35 (35) 33 (33) 35 (35) 105 (105) 140 (140) 159 (159) 122 (122) 34 (34) 32 (32) 32 (32) 32 (32) 35 (35) 33 (33) 34 (34) 33 (33) 34 (34) 57 (57) 140 (140) 151 (151) 83 (83) 36 (36) 36 (36) 35 (35) 37 (37) 38 (38) 40 (40) 38 (38) 38 (38) 37 (37) 37 (37) 133 (133) 152 (152)

T A B L E 1 Proceeding 23 hours 13 (24) 38 (25) 27 (26) 19 (24) 19 (24) 19 (29) 20 (43) 30 (70) 45 (78) 52 (94) 50 (93) 24 (72) 48 (26) 77 (29) 55 (28) 28 (29) 28 (31) 28 (31) 28 (31) 30 (37) 94 (72) 112 (86) 114 (103) 55 (79) 48 (28) 66 (29) 30 (30) 31 (30) 31 (32) 31 (32) 31 (32) 31 (32) 31 (33) 107 (78) 119 (94) 61 (82) 33 (26) 49 (30) 27 (29) 27 (30) 28 (31) 28 (32) 28 (31) 27 (30) 27 (31) 82 (45) 103 (94) 51 (79) 18 (21) 19 (23) 19 (22) 19 (22) 19 (23) 19 (25) 19 (25) 19 (25) 19 (24) 19 (26) 43 (73) 23 (54) 46 hours 15 (17) 20 (19) 19 (18) 18 (18) 18 (18) 18 (19) 18 (21) 18 (22) 18 (23) 24 (23) 26 (25) 24 (22) 17 (21) 20 (21) 38 (25) 38 (24) 24 (27) 23 (25) 23 (27) 23 (29) 24 (31) 26 (31) 72 (30) 82 (33) 70 (31) 24 (27) 21 (23) 46 (24) 27 (28) 28 (30) 27 (28) 27 (30) 28 (31) 28 (32) 28 (32) 28 (30) 97 (30) 86 (29) 27 (25) 19 (19) 35 (22) 23 (26) 23 (24) 23 (25) 23 (26) 23 (26) 23 (27) 23 (27) 23 (28) 81 (29) 64 (28) 23 (23) 14 (17) 17 (17) 17 (19) 17 (17) 17 (16) 17 (18) 17 (19) 17 (20) 17 (21) 17 (19) 17 (19) 23 (22) 15 (19 71 hours 13 (13) 16 (16) 16 (15) 15 (15) 16 (16) 17 (17) 17 (15) 17 (16) 17 (16) 20 (17) 22 (16) 20 (16) 15 (13) 16 (16) 21 (18) 21 (20) 21 (21) 21 (20) 21 (22) 21 (21) 21 (21) 23 (20) 46 (21) 53 (23) 38 (20) 19 (16) 17 (17) 23 (21) 23 (22) 23 (21) 22 (22) 22 (24) 23 (24) 23 (25) 24 (24) 26 (25) 76 (25) 52 (23) 21 (17) 16 (17) 22 (19) 21 (21) 21 (20) 21 (20) 21 (21) 21 (24) 21 (22) 21 (22) 22 (23) 66 (21) 38 (22) 19 (15) 13 (12) 16 (15) 16 (16) 16 (14) 16 (14, 17 (15) 16 (17) 16 (16) 16 (16) 17 (16) 18 (17) 20 (16) 15 (14)

T A B L E 1. Proceeding 143 hours 9 (9) 10 (11) 10 (11) 10 (11) 13 (12) 14 (13) 14 (13) 13 (12) 13 (12) 13 (11) 12 (10) 10 (10) 10 (12) 12 (12) 13 (14) 15 (15) 16 (16) 16 (17) 17 (16) 16 (15) 16 (15) 16 (14) 15 (13) 12 (12) 10 (12) 13 (13) 15 (15) 16 (17) 17 (18) 17 (17) 17 (18) 18 (17) 19 (16) 19 (16) 17 (14) 13 (13) 10 (12) 13 (13) 15 (16) 15 (16) 16 (16) 16 (16) 17 (17) 17 (16) 18 (16) 18 (15) 16 (13) 13 (12) 8 (10) 11 (12) 13 (13) 13 (12) 13 (12) 13 (13) 13 (13) 14 (14) 14 (12) 14 (12) 13 (12) 10 (11)

In table 1 the correspondence between the measured and calculated overall results is quite good. At the boundary between heartwood and sapwood some problems occur especially at the beginning of the simulation. An explanation could be that the boundary is not exactly in the same position in all samples within the specimen. During the first 24 hours the correspondence at the outer boundary is not so good, but later in the process quite good correspondence is achieved. In the beginning of the drying process the moisture flow is very fast. Relevant material's data are in the early phase of the drying process o f great importance for a correct simulation. To get a complete set o f materials data, new measurements have to be carried out. This has just started and some first results are shown below.

Further experiments

New experiments have been started with the aim o f evaluating a complete set o f materials data that is required in the calculations described above. The experiments are performed on small specimens o f Scots pine (Pirns silvestris) with the dimension 30 x 30 x 30 mm. These specimens were made of either sapwood or heartwood. All specimens were insulated on four sides against moisture and heat as shown in Figure 3. In that way the moisture will evaporate f r o m the same areas as those from which the heat is transferred into the wood. The specimens were dried in two different directions, either radial or tangential to grain, for both sapwood and heartwood. This makes four kinds o f specimens.

wood silicone

cellular rubber

Figure 3. The design o f the specimens that have been used for drying o f sapwood and heartwood o f Scots pine separately.

All specimens were dried in a constant climate of 60 °C dry-bulb temperature and 50 °C wet-bulb temperature. During the drying process, measurements were performed at seven different occasions. Each time two samples from each o f the four kinds o f specimens were split with a knife into ten laminae with a thickness o f 3 mm each as shown i Figure 4. The moisture content in those laminae were measured with the help o f the dry weight method. This gives the moisture gradient at seven different times in ten stages from surface to surface in the specimen. In total, 56 specimens were used in the experiment.

' y y y y y y . y y y y ,' ' y y y y y y y y . ^—y—y—

Figure 4. The pattern for splitting the specimen into ten laminae.

In Figure 5 some o f the results from the new measurements are shown. The results shows the moisture gradient in Scots pine at six different times during drying o f sapwood which is dried in the tangential direction to grain. The measurements in Figure 5 does not include the values for the green state (0 hours), where the mean moisture content was 139%. Evaluation o f this kind o f transient measurements requires consideration. Some new evaluation methods are planned to be developed.

40,0 35,0 • • 30.0 • • 25,0 • • U 20,0

6'

Figure 5. The moisture gradient in Scots pine sapwood showed from surface to surface. The gradients are measured at six different times during drying.

CONCLUSION

A first comparison between measured and calculated values showed that the correspondence was general quite good, except some experimental problems that occur in the boundary between sapwood and heartwood. New experiments have to be performed to evaluate a complete set o f new material data for the calculations. New experiments have been performed and more is planned. The method for evolution o f materials data from the experiments has to be further developed. A l l this will lead to an experimental verified calculation method for moisture distribution during drying. These calculations will be used as a part o f a method which calculates drying schedules for industrial kilns.

R E F E R E N C E S

C L A E S S O N , J; ARFVIDSSON, J. 1992: A new method using Kirchhoff potentials to calculate moisture flow in wood. 3rd lUFRO International Wood Drying Conference, Vienna, Austria, August 18 - 21, 1992: 135 - 138.

ARVIDSSON, J; CLAESSON, J. 1989: APC based method to calculate moisture transport. International Symposium, ICHMT, International centre for heat and mass transfer. Dubrovnik, Yugoslavia.

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