Determination of the surface emission factors in wood sorption experiments

Tom Morén, Jarl-Gunnar Salin, Ove Söderström

Determination of the Surface

Emission Factors in Wood

Sorption Experiments

Paper presented at 3rd lUFRO International

Wood Drying Conference, Vienna,

August 18-21,1992

Trätek

IN WOOD SORPTION EXPERIMENTS

Paper presented at 3rd lUFRO International Wood Drying Conference,

Vienna, August 18-21, 1992

Trätek, Rapport I 9302011

ISSN 1102- 1071

ISRN TRÄTEK - R - - 93/011 - - SE

Nyckelord

diffusion

drying

moisture distribution

moisture sorption

Stockholm februari 1993

UNDERSTANDING THE W O O D DRYING PROCESS

69

DETERMINATION OF THE SURFACE EMISSION

FACTORS IN WOOD SORPTION EXPERIMENTS

Tom Morén,

Dept. of Wood Techn., Luleå University, Skena 3,93187 Skellefteå, SWEDEN

Jarl-Gunnar Salin,

CTS-ConsultingLtd,P.O.Box27,SF-00131 Helsinki, FINLAND

Ove Söderström,

Swedish Inst. f. Wood Techn. Research, P.O. Box 5609, S-11486 Stockholm,

SWEDEN

dt dx dx

e x p r e s s e d by t h e r e l a t i v e c o n t e n t change d e f i n e d a s :

F =

The i n t e r a c t i o n between t h e wood s u r f a c e and t h e a m b i e n t a i r i s d e s c r i b e d by t h e e q u a t i o n s f o r s i m u l t a n e o u s h e a t and mass t r a n s f e r . The h e a t f l u x i s t h e p r o d u c t of t h e h e a t t r a n s f e r c o e f f i c i e n t a and t h e t e m p e r a t u r e d i f f e r e n c e between t h e ambient a i r and t h e wood s u r f a c e . The mass f l u x of m o i s t u r e i s c o r r e s p o n d i n g l y t h e p r o d u c t o f t h e mass t r a n s f e r c o e f f i c i e n t B and t h e d i f f e r e n c e i n vapour c o n c e n t r a t i o n between t h e a i r c l o s e t o t h e wood s u r f a c e and t h e ambient a i r . T h i s m o i s t a i r c l o s e t o t h e wood s u r f a c e i s i n e q u i l i b r i u m w i t h t h e wood and t h e r e l a t i o n b e t w e e n t h e v a p o u r c o n c e n t r a t i o n and t h e wood m o i s t u r e c o n t e n t i s g i v e n by t h e s o r p t i o n c u r v e . F o r a t u r b u l e n t f l o w t h e boundary l a y e r t h e o r y g i v e s a r e l a t i o n between a and R. By c o m b i n a t i o n of t h e s e f a c t s , t h e f o l l o w i n g e x p r e s s i o n i s o b t a i n e d (Söderström and S a l i n 1 9 9 2 ) :

S =

av

/ du

i s r e f e r r e d t o a s t h e c l a s s i c a l v a l u e .

s u c h a s k n o t s and c o m p r e s s i o n wood, and had n e v e r been d r i e d below t h e f i b e r s a t u r a t i o n p o i n t b e f o r e . The t h i c k n e s s e s o f t h e l a m e l l a e were 3 mm and t h e y were edge c o a t e d w i t h s i l i c o n e on t h e a x i a l s u r f a c e s . The s p e c i m e n s were exposed t o an a i r s t r e a m w i t h a v e l o c i t y o f about 5 m/s, r a n g e o f t e m p e r a t u r e from 26°C t o 48°C and r e l a t i v e h u m i d i t y from 25% t o 45%. The main p u r p o s e o f t h e e x p e r i m e n t was t o s t u d y t h e m e c h a n o - s o r p t i v e c r e e p d u r i n g d r y i n g , and f u r t h e r d e t a i l s about i t i s found e l s e w h e r e (Morén 1 9 9 0 ) . The m o i s t u r e f l u x was measured c o n t i n u o u s l y and, by u s i n g an i t e r a t i v e p r o c e d u r e t h e s u r f a c e e m i s s i o n f a c t o r f o r s e v e r a l t e m p e r a t u r e s was d e t e r m i n e d a s a f u n c t i o n of t h e mean m o i s t u r e c o n t e n t o f t h e l a m e l l a . T h i s r e s u l t i s shown i n F i g . 1. The measured v a l u e i s i n t h e r a n g e o f 1-5*10"^ m/s. The c l a s s i c a l v a l u e , c a l c u l a t e d w i t h Eg. 4 above, i s i n t h e range o f 50-200*10"^ m/s. The v a r i a t i o n of t h i s l a t t e r v a l u e i s m a i n l y due t o t h e t e m p e r a t u r e dependence of t h e s a t u r a t i o n m o i s t u r e c o n c e n t r a t i o n o f t h e a i r .

i

The s p e c i m e n s were sawn o u t from g r e e n S c o t s p i n e ( P i n u s s i l v e s t r i s ) and g r e e n Norway s p r u c e ( P i c e a a b i e s ) . The l a m e l l a e were f r e e from v i s i b l e d e f e c t s .

3.2 E v a p o r a t i o n from wooden s u r f a c e s The e v a p o r a t i o n from wooden s u r f a c e s o f S c o t s p i n e h a s been s t u d i e d w i t h a method d e s c r i b e d i n an e a r l i e r p u b l i c a t i o n ( L a u r i l a 1 9 9 2 ) . The r e s u l t s

f o r 40°C a r e p r e s e n t e d i n F i g . 2, where t h e r a t i o o f measured and c l a s s i c a l mass t r a n s f e r c o e f f i c i e n t s i s g i v e n a s a

f u n c t i o n o f t h e wood m o i s t u r e c o n t e n t i n t h e s u r f a c e l a y e r o f t h e p i e c e f o r f o u r d i f f e r e n t d r y i n g c o n d i t i o n s .

UNDERSTANDING THE W O O D DRYING PROCESS 71 0.00 Temp 40 »c _• • • • « •* • • • • • • • 0.00 0.40 0.80 1.20 MoMura oontant. kg/kg 1.60 2.00 F i g u r e 2: The r a t i o o f m e a s u r e d and c l a s s i c a l mass t r a n s f e r c o e f f i c i e n t s f o r v a r i o u s d r y i n g c o n d i t i o n s a s a f u n c t i o n of t h e m o i s t u r e c o n t e n t i n t h e s u r f a c e l a y e r o f wood. 3.3 I n f r a - r e d thermography The s u r f a c e of a d r y i n g wood p i e c e h a s been s t u d i e d w i t h a c a m e r a e g u i p m e n t s e n s i t i v e t o i n f r a - r e d r a d i a t i o n . The m o i s t u r e f l u x i s assumed t o be p r o p o r t i o n a l t o t h e h e a t f l u x w h i c h , i n i t s t u r n , i s p r o p o r t i o n a l t o t h e t e m p e r a t u r e d i f f e r e n c e between t h e wood s u r f a c e and t h e ambient a i r . T h e r e f o r e , by s t u d y i n g t h e s u r f a c e t e m p e r a t u r e , i t i s p o s s i b l e t o q u a l i t a t i v e l y d e t e r m i n e t h e m o i s t u r e f l u x . An e x a m p l e o f a photo i s s e e n i n F i g . 3. The a i r v e l o c i t y was about 2.8 m/s, t h e w e t - b u l b t e m p e r a t u r e 11.2°C and t h e d r y - b u l b t e m p e r a t u r e 23.5°C. F u r t h e r d e t a i l s a b o u t t h e measurements a r e found e l s e w h e r e (Morén

1 9 9 2 ) . The heartwood i s e x p o s e d t o t h e s u r f a c e o f t h e f l a t s a w n p i e c e . The d i f f u s i o n c o e f f i c i e n t f o r h e a r t w o o d i s l o w e r t h a n f o r sapwood. T h i s i s s e e n i n F i g . 3 a s t h e r e g i o n w i t h a h i g h e r t e m p e r a t u r e , i . e . a l o w e r m o i s t u r e e v a p o r a t i o n from t h e h e a r t w o o d . The growth r i n g s a r e a l s o s e e n i n t h e heartwood i n t h e b e g i n n i n g o f t h e d r y i n g p r o c e s s . F i g u r e 3; Thermography o f wooden s u r f a c e s . Dark a r e a s mean a l o w e r t e m p e r a t u r e t h a n l i g h t a r e a s . Top: 7 m i n u t e s a f t e r s t a r t . I n t h e h e a r t w o o d t h e e a r l y w o o d t e m p e r a t u r e i s a b o u t 2°C l o w e r t h a n t h e t e m p e r a t u r e i n t h e l a t e w o o d . Bottom: 62 m i n u t e s a f t e r s t a r t . The t e m p e r a t u r e o f t h e sapwood i s a b o u t 5°C l o w e r t h a n t h e heartwood t e m p e r a t u r e . 4 DISCUSSION

The r e l a t i v e change o f t h e mean m o i s t u r e c o n t e n t F from Eg. 4 i s s e e n i n F i g . 4. With t h e a s s u m p t i o n o f c o n s t a n t d i f f u s i o n c o e f f i c i e n t and s u r f a c e e m i s s i o n f a c t o r a m a t h e m a t i c a l a n a l y s i s shows t h a t no i n f o r m a t i o n c o n c e r n i n g t h e s e p a r a t i o n o f t h e i n t e r n a l and e x t e r n a l c o n d u c t a n c e s c a n be o b t a i n e d from t h e l i n e a r p a r t o f t h i s c u r v e . However, t h e h a l f - d r y i n g t i m e method, s u g g e s t e d e a r l i e r , i s a u s e f u l method f o r t h i s

s e p a r a t i o n (Choong and S k a a r 1969, 1972). T h i s method h a s t h e d i s a d v a n t a g e of t h e e x p e r i m e n t s h a v i n g t o be performed w i t h s e v e r a l wood p i e c e s o f d i f f e r e n t t h i c k n e s s e s . A n o t h e r method, where o n l y one t h i c k n e s s i s needed, h a s a l s o been p u b l i s h e d ( L i u 1 9 8 9 ) . However, both t h e s e methods a r e o n l y e m p i r i c a l a p p r o x i m a t i o n s . A r i g o r o u s a n a l y s i s shows t h a t t h e h a l f - d r y i n g t i m e f u n c t i o n can be d e v e l o p e d i n t o a s e r i e s i n t h e i n v e r s e o f Sa/D (Söderström and S a l i n 1 9 9 2 ) . A t h i r d a l t e r n a t i v e i s t o u s e n u m e r i c a l methods ( D r o i n e t a l 1988; D r o i n - J o s s e r a n d e t a l 1988, 1 9 8 9 ) . v € ( V s ) F i g u r e 4; F v s . T h e d o t s a r e " e x p e r i m e n t a l p o i n t s " and t h e f u l l l i n e t h e i r r e g e s s i o n l i n e . T h e d o t t e d c u r v e i s a c a l c u l a t e d c u r v e w i t h a s u r f a c e e m i s s i o n f a c t o r i n c l u d e d . T h e d a s h e d c u r v e i s c a l c u l a t e d w i t h a n e f f e c t i v e d i f f u s i o n c o e f f i c i e n t a n d no e x p l i c i t s u r f a c e e m i s s i o n f a c t o r . The c l a s s i c a l a p p r o a c h o f t h e mass t r a n s f e r c o e f f i c i e n t h a s r e c e n t l y been q u e s t i o n e d . P r o b a b l y t h e f i r s t q u a n t i t i v e r e s u l t s f o r wood were p r e s e n t e d some y e a r s ago a n d showed t h a t t h e p r e s e n t e d v a l u e s w e r e o n e o r d e r o f magnitude lower t h a n t h e o n e s o b t a i n e d from c l a s s i c a l t h e o r y (Plumb e t a l 1985) . T h i s o b s e r v a t i o n i s c o n f i r m e d by t h e two f i r s t e x p e r i m e n t s p r e s e n t e d above. Both t h e s e l a t t e r e x p e r i m e n t s show a t e n d e n c y o f i n c r e a s i n g s u r f a c e e m i s s i o n f a c t o r w i t h i n c r e a s i n g wood m o i s t u r e c o n t e n t . The r e a s o n f o r d e v i a t i o n from c l a s s i c a l t h e o r y i s n o t f u l l y u n d e r s t o o d . B a s e d on, f o r i n s t a n c e , r e s u l t s o b t a i n e d f o r b e d s o f g l a s s beads, i t c a n be c o n c l u d e d t h a t t h i s phenomenon i s n o t u n i q u e f o r a h y g r o s c o p i c m a t e r i a l and a l s o t h a t t h e d i f f e r e n c e c a l c u l a t e d and t h i s d e p e n d e n t form o f t h e r e l a t i o n s h i p between c o r r e c t i o n f a c t o r and m o i s t u r e c o n t e n t i s d i f f e r e n t f o r d i f f e r e n t m a t e r i a l s ( K a v i a n y and M i t t a l 1 9 8 7 ) . On t h e o t h e r hand t h e thermography s t u d y showed t h a t a wood s u r f a c e d r i e s i n a n o t h e r way t h a n a bed o f g l a s s beads. The o b s e r v a t i o n made e a r l i e r , t h a t t h e b e d o f g l a s s b e a d s d r i e s n o n u n i f o r m l y i s n o t s e e n f o r wood (Maneval e t a l 1990) . 5 CONCLUSIONS The s u r f a c e e m i s s i o n f a c t o r i s a v e r y i m p o r t a n t p a r a m e t e r i n wood d r y i n g as i t i n f l u e n c e s t h e d e v e l o p m e n t o f t h e s u r f a c e m o i s t u r e c o n t e n t . When t h a t q u a n t i t y goes below t h e f i b e r s a t u r a t i o n p o i n t , t h e m a t e r i a l s t a r t s t o s h r i n k and s o s e v e r e t e n s i o n s c a n o c c u r t h a t a s u r f a c e check a p p e a r s . T h e r e f o r e , i t i s i m p o r t a n t t o f i n d a method t h a t c o r r e c t l y s e p a r a t e s t h e i n t e r n a l and e x t e r n a l c o n d u c t a n c e s f o r t h e m o i s t u r e t r a n s p o r t . T h e r e i s a c o n s i d e r a b l e between t h e m e a s u r e d and mass t r a n s f e r c o e f f i c i e n t s d i f f e r e n c e i s s t r o n g l y on t h e m a t e r i a l and t h e s u r f a c e c h a r a c t e r i s t i c s . Wood a l s o seems t o d r y i n a c o m p l e t e o t h e r way t h a n a n o n h y g r o s c o p i c p o r o u s m a t e r i a l . A l l t h e s e f a c t s and o b s e r v a t i o n s i m p l y t h a t i t i s n e c e s s a r y t o p e r f o r m more e x t e n s i v e t h e o r e t i c a l and e x p e r i m e n t a l i n v e s t i g a t i o n s o f t h e i n t e r a c t i o n between a wood s u r f a c e and a n a m b i e n t a i r . Such s t u d i e s a r e underway. REFERENCES A v r a m i d i s , S t . and J . F . S i a u : An i n v e s t i g a t i o n o f t h e e x t e r n a l a n d i n t e r n a l r e s i s t a n c e t o m o i s t u r e d i f f u s i o n i n wood. Wood S c i . T e c h n o l . 21:249-256 (1987) . Choong, E . T . and C. S k a a r : S e p a r a t i n g i n t e r n a l and e x t e r n a l r e s i s t a n c e t o m o i s t u r e r e m o v a l i n wood d r y i n g . Wood S c i e n c e 1:200-202 ( 1 9 6 9 ) . Choong, E . T . and C. S k a a r : D i f f u s i v i t y and s u r f a c e e m i s s i v i t y i n wood d r y i n g . Wood and F i b e r 4:80-86 ( 1 9 7 2 ) . D r o i n , A., J . L . T a v e r d e t and J.M. V e r g n a u d : M o d e l l i n g t h e k i n e t i c s o f m o i s t u r e a d s o r p t i o n by wood. Wood S c i . T e c h n o l . 22:11-2 0 (1988) . D r o i n - J o s s e r a n d , A., J . L . T a v e r d e t and J.M. Vergnaud: M o d e l l i n g t h e a d s o r p t i o n and d e s o r p t i o n o f m o i s t u r e by wood i n an a t h m o s p h e r e o f c o n s t a n t and programmed r e l a t i v e h u m i d i t y . Wood S c i . T e c h n o l . 22:299-310 (1988) .

UNDERSTANDING THE W O O D DRYING PROCESS 73 D r o i n - J o s s e r a n d , A., J . L . T a v e r d e t a n d J.M. Vergnaud: M o d e l l i n g t h e p r o c e s s o f m o i s t u r e a d s o r p t i o n i n t h r e e d i m e n s i o n s by wood s a m p l e s o f v a r i o u s s h a p e s : c u b i c , p a r a l l e l e p i p e d i c . Wood S c i . T e c h n o l . 23:259-271 (1989) . K a v i a n y , M. and M. M i t t a l : F u n i c u l a r s t a t e i n d r y i n g o f a p o r o u s s l a b . I n t . J . Heat Mass T r a n s f e r 3 0 : 7 : 1407-1418 (1987) L a u r i l a , A.-M.: E v a p o r a t i o n from wooden s u r f a c e s ( I n F i n n i s h ) . M. S c . T h e s i s , L a p p e e n r a n t a U n i v e r s i t y o f T e c h n o l o g y , F i n l a n d ( 1 9 9 2 ) .

Maneval, J . E . , M.J. McCarthy and S. W h i t a k e r : Use o f NMR t o d e t e r m i n e m o i s t u r e d i s t r i b u t i o n d u r i n g d r y i n g . 10th I n t . C o n g r e s s o f Chem. Eng., Chem. E q u i p . D e s i g n and A u t o m a t i o n , P r a h a , C z e c h o s l o v a k i a , A u g u s t 26-31 (1990) . Morén, T.: M e c h a n o - s o r p t i v e c r e e p d u r i n g d r y i n g . I n t . Symp. a t M i t i s h c h i , R u s s i a ( 1 9 9 0 ) . Morén, T.: I n r a - r e d t h e n n o g r a p h y i n t h e a n a l y s i s o f m o i s t u r e f l u x from d r y i n g wooden s u r f a c e s . A c c e p t e d f o r p u b l i c a t i o n i n D r y i n g T e c h n o l o g y J o u r n a l ( 1 9 9 2 ) .

Plumb, O.A., G.A. S p o l e k and B.A.

O l m s t e a d : Heat and mass t r a n s f e r i n wood d u r i n g d r y i n g .

I n t . J . Heat Mass T r a n s f e r 2 8 : 9 : 1669-1678 ( 1 9 8 5 ) .

L i u , J.Y.: A new method f o r s e p a r a t i n g d i f f u s i o n c o e f f i c i e n t and s u r f a c e e m i s s i o n c o e f f i c i e n t . Wood and F i b e r S c i e n c e 21:2:133-141 ( 1 9 8 9 ) . Rosen, H.N.: The i n f l u e n c e o f e x t e r n a l r e s i s t a n c e on m o i s t u r e a d s o r p t i o n r a t e s i n wood. Wood and F i b e r 10:218-228 ( 1 9 7 8 ) . Söderström, O. and J.-G. S a l i n : P u b l i c a t i o n i n p r e p a r a t i o n ( 1 9 9 2 ) .

åtminstone när temperaturen är under vattnets kokpunkt. Ytemissionsfaktorn anger hur

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viktig att ta med i analysen av sorptionsförsök. I denna artikel diskuteras tidigare utförda

mätningar och analyser av ytemissionsfaktorn och jämförs med de värden som fås från

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