Acta Polytechnica Vol. 43 No. 112003 Modified Glaser's Condensation Model T. Ficker, Z. Pode5vovri Glaser's conl,msation scheme with incorporated non-isothermal dffision is presented and its consequences are sturlied. Keywords: non-'isothermn'l dffision, partinl pressure Prortk, condensation in building structures, Glaser's condensation scherte. I Introduction It is well-known that Glaser's model []-[7], a combined graphical and numerical method to assess the condensation of water vapor in building stnrctures t8l-t91, suffers from some drawbacks which make the model rather debatable. For example, the model includes neither hygroscopic nor liquid transports and also omits the transition from the liq- uid into the solid phase. In addition, the numerical part of the model is based on isothermal diffusion. However, real building envelopes, especially in the winter season, are considerably non-isothermal. These inconsistencies raise the question: What will happen with the model if fully non-iso- thermal conditions are incorporated into its scheme. This paper aims to implement non-isothermal diffusion into Glaser's model and discusses some features of the modified scheme. 2 Non-isothermal steady-state diffusion In our previous paper I I 0] we developed two basic models for describing non-isothermal steady-state diffirsion of water vapor through porous building materials, namely the DIAL and DRAL models. The DIAL model (Diffusion through an Immobilized Air I-ayer) led to the following basic relations (ll(4) that hold for a non-isothermal structure (wall) of thickness d, which is embedded into an air environmenr Dry air is supposed to have a constant concentration co on both sides of the wall. The wall shows, however, different temperatures ?,, ?", and concentrations c,*, c2w of water vapour on its two sides (internal and external). The concentration profile y(r) and diffi-rsion flux qi, expressed within the DIAL non-isothermal model, read *r r C,,,( X\I (r) = -:7Y , t(x)= c,(x) + co , (l) cu\x ) + ca [r-"^ I lnl --- tzu t ^* - Ll-lr"J-)ru'-):, 11lJ_-*-------l-l R.ft R.fl fte{I =+ [kg-r .m2.s], ueff ^* 0.l9kb" Tr -79ilen= -p ;l:;---;Z;=t'La ,l -tZ A\ 5629.10-8 7't -7i -. -r -,-'--n-o-------;m INE rrr .s l.il TU,IY TV.l:, st rl -r2 The symbols p and fijn" are the diffusion resistance factor and diffusion resistance of the structure, respectively, while p., stands for the pressure of dry air. More details concerning the derivation of (l)-(a) can be found in [0]. The DRAL model (Diffusion through a 'Rigid'Air Layer) is based [10] on the following relations C1,,, - Co,,, -, _, -t.5,,,=- lt(g.m -.s .1. &n R n =!- [*-r.r], (5) ueff ^ oslftrTt-Ts\ - .) _r-D"$=_-_;-- [m-.s 'J, p(ry-' -ri-') ,,,,, = !Jz- lks . m-3 l, cq,,,- Pz, I ks . ,n-il, RrTt RTTz (6) ft =8.9718.10-10 im2.s-1.K-l'811, where p1r, p2. are the partial pressures ofwater.vapour on the two sides of the structure and rR, = 462 J. kg-' .K-' is the gas constant of water vapour. For more details see [0]. The computational part of Glaser's standnrd model is based on the isothermal approximation [0] no =Pw- Fz,, no =4, 6=1.881.r0-r0s, (7) P.:6 F(*)=fru-Pt,-P2, r. (8) a 3 Glaser's condensation schemes Glaser's graphical method [7] for finding the condensa- tion region inside a building structure enables us to incorpo- rate straightforwardly not only isothemnl dffision (coordinate system (R2,p)), as initially introduced by Glaser (stnndard model), but also non-isothermal dffision within the models of (3) / T T \0.19.l ?0.19 lT 't-'2 ^,1 | ' \' d .) | [r - fz.I r,t re -T2o re ILr--l r' I (2) l cl, c2u )lu =e, J2r= C1, I Co C2u+ ca 34 Acta Polytechnica Vol. 43 No. 112003 x [m] ?tKl Glaser's standard model DIAL model DRAL model Rd.lo-e . -1,LM'S I Yu IP"] /r( satur. )ru tPal 4n'to" ., -l -1. [Kg. m .s I )r'10' ,Gatur.). 193 R.6'l0+ . -tlm 'sl cr.l03 lkg.rn-31 cGatur.).103 ., -3.[Kg'm I 0 293.r5 0 r402 2337 0 9.1 08 15.09 0 10.35 17.25 0.0733 286.82 3.60 I 186 1564 2.255 7.770 10.15 2.568 8.930 11.80 0.1467 280.48 7.20 969.8 1025 4.554 6.405 o.o /+ 5.245 7.452 7.910 0.2200 274.t5 10.81 753.6 oc/ 6.892 5.0 l8 4.288 8.029 5.V15 5.1 87 0.2933 267.8r t4.41 D5 t.* 390 9.278 3.600 2.524 I0.937 4.310 3.150 0.3667 261.48 18.01 32r.2 oqA 1 1.706 2.156 1.466 13.967 2.637 1.850 0.4400 255.15 21.61 105 t25 t4.183 0.688 0.8 187 17.133 0.895 1.060 Lq,qa =421' lo-8 1kg'm-2's-ri (from Ftg. l) Lqen = 4.4 'rc-s ftg'm-2's-rl (flom Fig. 2) LQm =35' tg-a 11g'tn-2't-r1 (from Fig. 3) Table l: Condensation region according to Glaser's method LQan = 4,q - 8n ' DIAL (coordinate system (RJri,fr)) and DRAL (coordinate system (R"ff,co,)). Let us have, for example, a building envelope realized by a plain brick wall (without plaster, g = 9) of thickness d--44 cm. -fhe wall seParates a heated room of a usual environment (surface temperature and relative humidity: Tr=293.15 K, 9F60Vo RH) from an outdoor space (Tr=293.15 K,qr=60 7o RH). Table I and Frgs' l, 2, 3 show the results of Glaser's schemes based on isothermal and non-isothermal diffusions and applied to the structure given above. Since the structure is only 'weakly' non-isothermal (7,-Tr< 40K), Iarge differences in results cannot be ex- pected (see the discussion in [10]). P*/Pa o osx'lo- lulu arl | 40 K) the difference may be signifi- cantly larger [10], and in such cases the DIAL model will yield a more realistic prognosis as compared with the standard model. which overestimates the amount of condensate occur- ring in building stmctures. However, thanks to the ability to overestimate the condensate, Glaser's standard model yields prognoses that are on the 'safe side', though not always on the 'economical side'. 4 Conclusion It has been illustrated that Glaser's standard condensat- ion model can be modified to include fully non-isothermal calculations ofwater condensate appearing in building struc- tures. Such calculations do not lead to very diflerent results in normal Central European climatic regions (AT < 40 K). Howeve! in extreme climatic regions (LT > 40 K) essential differences can be expected and in such events the DIAL model offers a good tool for a more realistic assessment of condensation problems. In conclusion, it should be stressed that Glaser's standard condensation scheme provides an as- sessment that is on the safe side, but especially in extreme non-isothermal cases it will not lead to an economicallv opti- mal design of building stmctures. References tll Glaser, H.: Einfluss der Temperatur auf dm Dampfdurch- gang durch trockme Isolicntrinfu. Kiiltetechnik, Vol. 9, 1957, No.6, p. 158-159. 121 Glaser, H.: Wtirmekitung unl" Feuchtigheitsdurchgong durch Klhlraumisolierungen. Kiltetechnik, Vol. 10, 1958, No. 3, p. 86-91. t3l Glaser, H.: Temperatur- und Dam.pfdru,ckuerlnuf in einer homogenen Wand bei Feuchtigheitsausscheid,ung. K:iltetech- nik, Vol. 10, 1958, No.6, p. 174. i4l Glaser, H: Vereinfachte Berechnung der Dampfdtfusion durch geschi.chtete Wcinde bei Ausscheid,ung am Wasser md Eis (I). Kahetechnik, Vol. 10, 1958, No. I l, p. 358-364. t5l Glaser, H.: Vereinfachte Berechnung der DampJilifirion funch geschichtete Wcind,e bei Ausscheidung aon Wasser und. Eis (II). Kiiltetechnik, Vol. 10, I958, No. 12, p. 386-390. t6l Glaser, H: Zur Wahl dzr Difiuionsuiderstandsfaktorm uon mehrschir.htigm Kiihlraumw(mfun. Kaltetechnik, Vol. I l, 1959, No.7,p.214-222. t7l Glaser, H: Graphisches Vetfahren zur Untersuchung aon Difusionsuorgtingen. K:iltetechnik, Vol. I l, 1959, No. 10, p.345-349. t8l Germnn Therm"ol Standnrd: DIN 4108. Deutsches Institut fiir Normung, Berlin, 1999. tgl CzechThermal Standnrd: CSN ZS 0540.Cs. normalizainf institut, Praha, 1994. [0] Ficker, T., Podeivovi, Z.:, Modtls for Non-isotlwnnal Steadt-State Difusion in Porous Buil.d,ing Materiak. Acta Polytechnica (accepted for publication). Assoc. Prof. RNDr. Tom:i5 Ficker, DrSc. phone: + 420 541 147 661 e-mail : fyfrc@fce.vutbr. cz Department of Physics Ing. Zdenka Pode5vovd Department of Building Structures University of Technology Faculty of Civil Engineering Zrikova 17 662 37 Brno, Czech Republic 36 Scan 34 Scan 35 Scan 36