Moisture transport in seasoned wood

Transcription

1 in seasoned wood Coupled diffusion model and model sensitivity Staffan Svensson

2 1976 Syrause Univ. press Wood struture and identifiation H. A.. Core, et al. Wood, a open porous material Softwood has a porosity of % and an open aessible pore system Type size [mm] Pits 5 20 Lumen Rays Resin anal The water moleule is 0.3 nm or mm 2 DTU Civil Engineering, Tehnial University of Denmark

3 Vapor diffusion in woods pore-system Water vapor traverses in the lumens and other open pores of wood. Diffusion moves vapor #. The flow, q v, of vapor; also in the porous system of wood; is desribed by Fik s law of diffusion. q v D v m x where D v is the diffusivity of water vapor in air, m the driving potential and x the spatial oordinate. # onvetion in the porous system is onsidered non-signifiant 3 DTU Civil Engineering, Tehnial University of Denmark

4 Hygrosopi behavior of wood ell wall Every ell wall layer adjaent to lumen, rays, et is the dividing entity (surfae) between the solid wood material and vapor phase. Water and ell wall material interating, with hydrogen bonds. Water sorption is a phase hange involving both heat and mass transfer. Sorption is state dependent Sorption rate RH 20 to 30 % - RH 40 to 50 % - RH 60 to 70 % DTU Civil Engineering, Tehnial University of Denmark normalized Potential 0

5 Sorption Isotherm Equilibrium moisture states The transient proess is only isotherm at equilibrium states. Moisture ontent [kg/kg] normilized Mass Relative humidity [%] DTU Civil Engineering, Tehnial University of Denmark Time [min]

6 Mass balane of moisture transport in wood m t q x m mˆ t q in q out When normalized with the volume: Soure x 0 Dx x Sink t q x ˆ t where onentration, = m/v The soure and the sink are together the mathematial representation of sorption 6 DTU Civil Engineering, Tehnial University of Denmark

7 Vapor transport in wood Is mathematially derived by ombining mass balane with Fik s law: t x D v x ˆ t To aount for the transport in the ell wall, the same reasoning holds. One have to remember, however, that when mass appears in a ell wall it disappears as vapor in a pore. 7 DTU Civil Engineering, Tehnial University of Denmark

8 8 DTU Civil Engineering, Tehnial University of Denmark in wood Is mathematially derived by ombining mass balane with Fik s law twie: t x D x t v v v ˆ t x D x t b b b ˆ Cell wall Cell lumen flow, q v adsorption desorption flow, q b

9 Coupled models Coupled proesses auses experimental diffiulties when determining onstitutive relations. Material parameters are state dependent The state is defined by the proesses Stationary, transient and yli exitation provoke differene in response. Sensitivity analysis of the model is a method that an be used for designing useful experimental researh. 9 DTU Civil Engineering, Tehnial University of Denmark

10 Sensitivity index and studied outome SIf i COV f COV X X ) i ( i The Sensitivity influene shows the influene of an input parameter on the model outome. X represents the material parameters; vapor diffusivity, bound water diffusivity and sorption rate funtion. X i is variations of one material parameter Three model outomes: Total mass hange Conentration of bound water at losed boundary Conentration of bound water at open boundary at two times in the proess have been studied as a result of a uniform step hange of boundary ondition for three different states. 10 DTU Civil Engineering, Tehnial University of Denmark

11 Model sensitivity early in proess SI fi 0.08 (a) mass of water b (x = 0) b (x = w) Center Surfae SI fi DTU Civil Engineering, Tehnial University of Denmark 0.07 (b) High hum. Med. hum. Low hum. SI Dp SI H SI Db

12 Model sensitivity late in proess SI fi (b) High hum. Med. hum. Low hum. SI Dp SI H SI Db mass of water b (x = 0) b (x = w) Center Surfae 12 DTU Civil Engineering, Tehnial University of Denmark

13 Conlusions The simplest model for prediting moisture transport in the open porous material (wood) is a oupled model. In the hygrosopi range three proess; diffusion of vapor in pore system, sorption and diffusion of bound water; onstitute the moisture transport of wood. Model sensitivity may be used to identify what proess and material parameter that have influene on measurements in a test. 13 DTU Civil Engineering, Tehnial University of Denmark