Hysteresis and moisture buffering of wood

Transcription

1 Hysteresis n moisture buffering of woo Jn Crmeliet, Prof. Deprtment of Civil Engineering, Lbortory of Builing Physics, Ktholieke Universiteit Leuven, Ksteelprk Arenberg 5, 3 Leuven, Belgium jn.crmeliet@bwk.kuleuven.c.b, Mrtin H.D. e Wit, Prof. Fculty of Builing n Architecture, Builing Physics Group, T.U.Einhoven, P.O. box 53, 56 MB Einhoven, The Netherlns m.h..wit@bwk.tue.nl Hns Jnssen, PhD., Deprtment of Civil Engineering, Lbortory of Builing Physics, Ktholieke Universiteit Leuven, Ksteelprk Arenberg 5, 3 Leuven,Belgium; hns.jnssen@bwk.kuleuven.c.b, KEYWORDS: hysteresis, sorption isotherm, woo, hygroscopic buffering. SUMMARY: Hysteresis of ok is nlyse using the empiricl moel of Peersen (99) n new hysteresis moel bse on the moel of Mulem (974). Peersen s moel necessittes the experimentl etermintion of the min sorption n esorption curves s well s the primry sorption n esorption loops. The fitte prmeters seem to lck physicl bckgroun n the cpcity follows highly vrying tenency. The new moel is bse on the well-known ink-bottle theory n hs the potentil to preict scnning curves only bse on the knowlege of the min sorption n esorption curve. In n nlysis of the moisture blnce of room, hysteresis ws shown to ply minor role, while the vpour permebility is of high importnce... Introuction Wter vpour trnsport in porous mterils is escribe combining Fick s lw n the conservtion of mss eqution. For one-imensionl isotherml cses, the eqution res w pv ρ l = δ () t x x with w the moisture content, p v the wter vpour pressure n δ the wter vpour trnsport coefficient, epening on the vpour pressure. Rewriting eqution () gives w ρ l = ρ lξ = pvstδ ( ) () t t x x with ρ l the ensity of liqui wter, the reltive humiity, p vst the sturte wter vpour pressure n ξ the moisture cpcity. The moisture cpcity cn be experimentlly etermine mesuring sorption isotherms. For lot of mterils like woo, sorption shows hysteresis between sorption n esorption. The bounry conition for vpour trnsport is given by q = β p vi p ) (3) ( vs with β the wter vpour surfce coefficient, p vi the wter vpour pressure of the insie environment, p vs the wter vpour pressure t the surfce of the mteril. Purpose of this pper is twofol:

2 How to etermine n moel hysteresis? Is hysteresis importnt when nlysing the moisture buffering cpcity of woo? First we present the mesurements. Then, the empiricl moel s propose by Peersen is use to escribe hysteresis. A new hysteresis moel is presente bse on the moel of Mulem (974). The behviour of the two hysteresis moels is compre. Finlly the influence of hysteresis on the moisture blnce for room is nlyse.. Mesurements The mteril stuie is ok. The sorption isotherms re etermine grvimetriclly on cylinricl specimen fter ttining equilibrium in n exsicctor, where the reltive humiity is controlle by sturte slt solution. The min sorption isotherm ws etermine conitioning three ry specimen t ifferent reltive humiity, or using the Enerby s nottion w ( ) = ( ). The min esorption isotherm is.97 etermine on specimen primrily conitione t 97%, or w ( ) = ( ). The symbol will be use to enote the inepenent vrible or n intermeite vlue of the reltive humiity, while enotes certin en vlue of the reltive humiity. The primry sorption curve is etermine by sorption from specimen, which where first conitione.97 on the min esorption curve, or w ( ) = ( ). The mximl reltive humiity ws chosen 97 %. The primry esorption curve is etermine by esorption of specimen, which where first conitione on the w ( ) =. min sorption curve t reltive humiity, or ( ) The min sorption n esorption curve re escribe by / n ln w ( ) = wmx A, / n ln w ( ) = wmx A (4) with A, n, w mx prmeters to be etermine. w mx is chosen s the moisture content t reltive humiity of %. FIG. shows the mesurement results n fitte curves for the min sorption n esorption isotherms. The prmeters re given in tble. The mximl moisture content is equl to.5 kg/kg reltive humiity (-) FiG. : min sorption n esorption curve: mesurements n fitte curve 3. Hysteresis moelling 3. Empiricl pproch Hysteresis is commonly escribe by n empiricl pproch (Peersen, 99, 99b, Roe n Clorius 4) using the weighte vlues of the cpcity or slope of the sorption n esorption curve

3 ξ w =, ξ w = (5) The sorption fter series of lternting processes of sorption n esorption is escribe by γ ( w w ) ξ + ( w w ) ξ ξ hys, = (6) ( w w ) The esorption fter series of lternting processes of sorption n esorption is escribe by ( w w ) ξ + γ ( w w ) ξ ξ hys, = (7) ( w w ) with γ, γ prmeters to be etermine. The prmeters γ, γ cn be fitte bse on the mesure primry sorption n esorption curve. FIG. gives the fitte primry sorption n esorption curve. In FIG. 3 the mesure cpcities re compre to the fitte cpcities. The prmeters γ, γ re given in tble. We observe goo greement between mesurement n fitting for primry esorption. For primry sorption the greement is less showing some lck of flexibility of the hysteresis moel. The hysteresis moel further lcks physicl bckgroun n nees the knowlege of primry sorption n esorption curves for etermining the prmeters γ, γ. We note tht the prmeters γ, γ o iffer lot (.9 n.9). Primry esorption Primry sorption reltive humiity (-) reltive humiity (-) FIG. (left) Comprison of mesure (she line n bullets) n fitte primry esorption curves (soli line). (right) Comprison of mesure n fitte primry sorption curves cpcity (-) cpcity (-) reltive humiity (-) reltive humiity (-) FIG 3. (left) Comprison of mesure n fitte cpcities for the primry esorption curves. (right) Comprison of mesure n fitte cpcities for the primry sorption curves.

4 Tble A /n γ Asorption Desorption New hysteresis moel A phenomenologicl hysteresis moel, which is bse on the Mulem moel (974) using the ink bottle concept, is presente in this section. The possible sorption sites re istribute ccoring to function f(). A sorption site cn be fille or unfille. The ccessibility to the sorption sites is escribe by normlise ccessibility function (). Sorption processes cn be schemticlly represente in f- spce, lso clle Mulem spce (FIG.4). The bcis gives the possible sorption sites, while the orinte represents the ccessibility function. Integrtion in the f- spce mkes it possible to clculte the moisture content by multiplying the fille sorption sites with their ccessibility. The min sorption curve is given by (FIG. 4): w( ) = w ( ) = f ( ) ( ) = F( ) A() = F( ) (8) The integrl over the rnge from to of the ccessibility function inictes tht ll pores re ccessible uring sorption. Since () is normlise, A()=. During esorption to reltive humiity, the pores ccessible between mx n esorb. Accoring to FIG. 4b the moisture content uring min esorption is given by w mx ( ) = w ( ) = w ( wmx w ( )) mx ( ) (9) or w mx ( ) = w ( ) = w ( ) + ( w w ( ))( A( )) = w ( ) + ( w mx mx w ( )) A( ) () The eqution shows tht the ccessibility function A() cn be etermine from the min sorption n min esorption curve, or w ( ) w ( ) A( ) = () wmx w ( ) The process of primry esorption (esorption from the min sorption curve) is given in FIG. 4c. Integrtion in the f- spce gives w ( ) w ) + ( w ( ) w ( )) A( ) = () ( The process of primry sorption (sorption from the min esorption curve) is given in FIG.4. Integrtion in the f- spce gives w mx ( ) w ) + ( w w ( )) A( ) = (3) ( mx Formuls for sorption or esorption fter series of lternting processes of sorption or esorption cn be foun in Mulem (974). FIG. 5 compres the mesure n clculte primry sorption n esorption curve. FIG. 6 compres the mesure n clculte primry sorption n esorption curve. We observe tht compre with the

5 Peersen hysteresis moel, the propose hysteresis moel shows less greement, but follows the generl tren of the mesurements. min sorption min esorption primry esorption primry sorption f f f f FIG. 4: Min sorption, min esorption, primry esorption, primry sorption processes represente in the f- spce, where f represents the sorption sites n the ccessibility function. Primry esorption Primry sorption reltive humiity (-) reltive humiity (-) FIG. 5: (left) Comprison of mesure n fitte primry esorption curves. (right) Comprison of mesure n fitte primry sorption curves cpcity (-) cpcity(-) reltive humiity (-) reltive humiity (-) FIG. 6: (left) Comprison of mesure n fitte cpcities for the primry esorption curves. (right) Comprison of mesure n fitte cpcities for the primry sorption curves. 3.3 Comprison of hysteresis moels FIG. 8 gives the mteril response for the two hysteresis moels uring loing protocol s given in FIG. 7. FIG. 9 gives the moisture cpcity for min sorption, min esorption n uring the loing protocol. The Peersen hysteresis moel follows fter cycling the min sorption curves, while the new moel follows intermeite curves between the two min sorption curves. The esorption curves in the Peersen moel re concve n convex, while the sorption curves sty convex. The cpcity shows highly vrying

6 behviour. The new moel shows lwys concve curves n the cpcity oes not vry lot. The higly vrying cpcity of the Peersen moel from physicl point of view is less logicvl. The number of mesurement t is too smll to evlute the correctness of both hysteresis moels. reltive humiity (-) loing protocol FIG. 7: reltive humiity loing protocol cpcity (-) reltive humiity (-) reltive humiity (-) FIG. 8: (left) Hygroscopic behviour for the Peersen hysteresis moel uring the loing protocol of FIG. 7 (right) Cpcity for the Peersen hysteresis moel uring the loing protocol of FIG cpcity (-) reltive humiity (-) reltive humiity (-) FIG. 9: (left) Hygroscopic behviour for the new hysteresis moel uring the loing protocol of FIG. 7 (right) Cpcity for the new hysteresis moel uring the loing protocol of FIG Hysteresis n moisture buffering The moisture buffering cpcity of woo is nlyse consiering the moisture blnce for room. The blnce is given by ρ vi V t = G ( ρ ρ ) + G ve vi p Aq sorb (4)

7 with V the volume of the room, ρ ve the wter vpor concentrtion outsie, ρ vi the wter vpor concentrtion insie, G the ir flow rte, G p the moisture prouction, A the surfce covere with woo n q sorb the wter vpour flux ue to sorption into the woo. The wter vpour permebility is given by δ ( ) = + bexp( c. ) (5) The wter vpour flux q sorb is clculte solving eqution (). The woo hs thickness of. m. Stnr vlues re: β = /s, n = /h, V = m 3, A = 7 m, =. -, b =. -4, c = The outsie wter vpour concentrtion is tken from the climte file for Essen. The wter vpour prouction hs the following time sequence:.5 kg/h uring the hours 8, 9,, 3,4, 8 n 9. The clcultions re crrie out for two-yer perios. The new hysteresis moel is use in the simultion. FIG. shows the limite influence of hysteresis on the reltive humiity insie. Asorption give somewht higher vlues but the ifferences re of minor importnce. The ifferences in surfce moisture content re higher (FIG. ), but this is consequence of the ifferences in sorption isotherms. Reson for the limite influence of hysteresis is cuse by the minor ifferences in moisture cpcity between the min sorption, esorption or hysteretic scnning curves. RHi (-) hysteresis sorption esorption moisture content t surfce (kg/m 3 ) hysteresis sorption esorption time (ys) time (ys) FIG. : (left) Reltive humiity insie for five consecutive ys (right) Moisture content t the surfce of woo for five consecutive ys verge 4%, mplituo 5% esorption sorption hysteresis RH (-) x-xis (m) FIG. : Reltive humiity profile in woo expose to 4-hour-perioic sinusoil chnge in reltive humiity insie, with n verge of 4 % n n mplitue of 5%. The penetrtion epth is clculte for perioic sinusoil chnge in reltive humiity insie, with n verge of 4 % reltive humiity n n mplitue of 5% n perio of 4 hours. FIG. gives the mximl profile. We observe tht the penetrtion epths (istnce where the mplitue ecrese to /e of the mximl vlue) re limite with vlues less thn mm for 4-hour-perio signl.

8 5. Conclusions. A new hysteresis moel, bse on the work of Mulem (974), hs been evelope n vlite for woo. Although less greement hs been observe for the new moel compre to the empiricl moe of Peersen, the preictive power n its physicl bckgroun fvour the use of the present hysteresis moel.. Hysteresis hs been foun to hve limite influence on the moisture buffering cpcity of woo when plce in room s hygroscopiclly ctive mteril. 3. The penetrtion epth in woo hs been foun to be limite. Moreover finishing tretments cn reuces strongly the ccessibility to the mteril n thus the moisture buffering cpcity of woo. 6. References Mulem Y (974). A conceptul moel of hystersis, Wter Resources reserch, vol. no. 3. Roe C n Clorius C.O. 4. Moelling of Moisture Trnsport in Woo with Hysteresis n Temperture Depenence Sorption Chrcteristics, Proceeings of the Conference Performnce of Exterior Envelopes of Whole Builings IX, Sherton Sn Key Resort, Clerwter Bech, Flori, December 5-, 4 Peersen, C.R: 99. Combine het n moisture trnsfer in builing constructions. PhD Thesis, Technicl University of Denmrk, Denmrk. Peersen, C. Roe. 99b. Trnsient Clcultions of Moisture Migrtion Using Simplifie Description of Hysteresis in the Sorption Isotherm. Proceeings of the n symposion on Builing Physics in the Noric Countries. Technicl University of Norwy, Tronheim, Norwy.