Evaluation of changes in thermodiffusion properties of mineral wool resulting from treatment with water and re-drying

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1 Evaluaton of changes n thermodffuson propertes of mneral wool resultng from treatment wth water and re-dryng Zbgnew Perkowsk,*, Macej Grygorowcz, and Kaml Jeż Opole Unversty of Technology, Faculty of Cvl Engneerng and Archtecture, Opole, Katowcka 48, Poland Abstract. The work presents the formulaton of nverse problem that allows to estmate the basc parameters descrbng coupled thermodffuson of mosture n porous fbrous materal and constructon of the measurng stand n order to obtan the necessary data to carry out calculatons for ths purpose. Ths approach was used to evaluate the changes n the thermodffuson propertes of stone wool samples for the ndoor applcatons that were treated wth water and re-dred. In the mathematcal model, one ntroduced a smplfcaton that couplng n the thermodffuson process s unlateral and ncludes only the nfluence of heat transport on mosture transport. 1 Introducton Mneral wool s one of the basc materals for thermal nsulaton n cvl engneerng, but t s also used as a materal for nsulaton of ppes, acoustc barrers, fre protecton, artfcal sol for plant breedng and core of sandwch panels. If the wool s properly protected aganst mosture, n the case of ts usng as thermal nsulaton n buldngs envelops, t combnes very advantageous features: t s a very good thermal nsulator, does not resst sgnfcantly mosture transport and hardly absorbs most. Its propertes are addtonally mproved from the applcatve pont of vew by strvng to produce a materal wth optmal entanglement and fbre orentaton, the use of specal ant-mold, ant-dustng, hydrophobc or hydrophlc admxtures. Partcular attenton should be pad to the hydrophobzaton or hydrophlzaton process from the pont of vew of controllng the thermodffuson propertes. For example, t leads to sgnfcant dfferences n the mosture accumulaton capacty under the hygroscopc condtons shown n Fg. 1 n the lght of varablty n the sorpton sotherms of mneral stone wool. It can be seen that the type of admxture used can be easly dentfed as a result of such testng. It can be also deduced that the use of hydrophobzaton reduces the possblty of mosture absorpton n the lower part of hygroscopc range and s a benefcal phenomenon n typcal operatng condtons. However, f there s a relatvely large mosture mass flux and no temperature gradent, t may unexpectedly lead to the precptaton of water drops n the space between the fbres of the wool and to ts sgnfcant dampness. Such a * Correspondng author: z.perkowsk@po.opole.pl The Authors, publshed by EDP Scences. Ths s an open access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense 4.0 (

2 stuaton may occur partcularly n nsulatons nsde buldngs n the lower parts of nsulaton boards [1]. In ths case, the use of hydrophlc addtves wll mprove the transport of mosture and may avod the descrbed stuaton. Fg. 1. A pctoral comparson of mneral stone wool sorpton sotherms n the case of usng hydrophobc and hydrophlc admxtures and wthout any admxtures (based on [1] for the wools wth bulk densty of kg/m 3 at temperature 3 o C). On the other hand, n the lterature, one can fnd the frst of all works orented on the study of thermal conductvty of mneral wool, ncludng ts varablty under the nfluence of temperature change [], dampness [3, 4] and takng nto account the nfluence of radaton [5, 6] or ar convecton [7]. Less often one can fnd works devoted also to detaled nvestgatons of hygrc features (sorpton sotherms, parameters determnng mosture dffusvty and lqud water transport) [1, 4]. There are bascally no works devoted to drect determnaton of coeffcents descrbng coupled thermodffuson mosture transport n mneral wool wth hydrophobc or hydrophlc propertes and formulatons of effectve nverse problems for ths purpose, despte the fact that the subject matter of coupled heat and mosture transport n porous materals s generally well descrbed from theoretcal pont of vew (e.g. [8-1]), as well as from the sde of numercal modellng and expermental measurements both n homogeneous and complex (layered) systems (e.g. n [13-17] n the feld of cvl engneerng problems). It s worth to note that n the case of expermental research, the mult-pont measurement of temperature, relatve ar humdty n materal pores and lqud water concentratons n buldng envelopes has become a standard. In the lght of the observatons quoted, ths work s devoted to the presentaton of an effectve and relatvely quck way to evaluate the basc parameters descrbng the basc coupled thermodffuson characterstcs of mneral wool n the hygroscopc range. In the example of expermental research, samples of stone wool avalable n trade and dedcated for the nternal applcatons were used. In the mathematcal model of the process, a unlateral couplng the nfluence of heat transport on mosture transport was only ncluded n order to smplfy the consderatons. In addton, due to the practcal aspect of the problem, the effect of water saturaton and re-dryng on changes n the thermodffuson wool parameters was examned because, n many stuatons as a result of mproper storage at constructon stes and nattenton of contractors, the product s exposed for drect ran before or durng nsertng nto buldng envelopes. In partcular, for the wool mpregnated wth hydrophlc agents, t should be expected that ths process wll change the orgnal favourable thermodffuson characterstcs, even though the wool has dred up agan. Materals and measurng stand 6 samples of mneral stone wool wth densty of ~50 kg/m 3 avalable n commercal were tested. The samples had dmensons of ~100 x 100 x 75 mm. Accordng to the manufacturer, the wool wth a declared thermal conductvty of W/(m K) was dedcated to nsulatons

3 of nternal parttons. 3 samples (marked as D1, D, D3) were dred to constant weght at changng gradually temperature startng from 60 o C and endng at 105 o C wthn weeks. The remanng 3 samples (marked as M1, M, M3) were mmersed n water for 4 hours n the temperature o C. After ths tme, they were removed from the water and left for one week n room condtons to allow the lqud water to dran freely from ther pores. Then they were subjected to the same dryng process as the frst 3 ones. After ths prelmnary preparaton of the samples, all of them were kept freely n a closed room (durng a heatng season) n whch a measurng stand was stuated, untl ther masses were stablzed. The stand made as part of the work [18] was used for the measurements, the scheme of whch s shown n Fg.. After the mass stablzaton, the samples of mneral wool together wth a plate of acrylc glass wth a thckness of ~ 1 mm and known thermal conductvty and dffusvty were placed ndvdually n a sealed chamber wth the same dmensons as the sample-plate system. The chamber was located n the mddle between two 300 x 300 x 300 mm glass contaners wth water. The contaners and chamber were thermally nsulated usng extruded polystyrene, and the chamber was protected by the exchange of mosture wth the surroundng. The system ncludes combned sensors of temperature (thermocouple) and relatve humdty (RH) of ar on both sdes of the sample and on the outsde of the acrylc glass plate. The rght measurement started when the ndcatons of sensors were stablzed. Due to the method of preparaton of samples, ther ntal temperature and relatve humdty of the ar n ther pores corresponded to the ambent condtons prevalng n the room n whch they were stored before nserton nto the measurement system (respectvely from 1 o C to 6 o C and from 34% to 45% dependng on the sample). After nsertng a sample nto the test chamber, the water n the contaner from the sde of the acrylc glass plate was heated wth the electrc heater wthn 3 h to a temperature of approxmately 35 o C. The temperature was kept constant due to the use of a thermostat for about the next 10 hours. The temperature and RH ndcatons were archved every 10 s. Fg.. A scheme of the measurng stand for the assessment of thermodffuson propertes of mneral wool [17]. Wthn a range of supplementary study, selected ponts of sorpton sotherms were determned for the tested mneral wool at o C correspondng to RH of the ar n the surroundng equal to 30, 40, 50, 70, 80% (by placng samples n the clmatc chamber) and 98% (by placng samples n the desccator above the water surface). In the case of sorpton sotherms, the samples used for ths purpose were also dfferentated due to the methods of ther preparaton analogous to those for samples D1-D3 and M1-M3. The expermental 3

4 results obtaned n the way descrbed above were used to assess the thermodffuson propertes of the tested wool ncluded n the appled mathematcal model of the problem. They were presented and compared wth the results of model calculatons n paragraph 4. 3 Mathematcal model In order to descrbe theoretcally the thermodffuson process n the samples, ts smplfed model was used n whch t was assumed that: no separate vapor and surface mosture transport s dstngushed (whch mples omsson of local sources of mass and heat), couplng of the dffuson and thermal process may be consdered approxmately as unlateral (the heat flux affects the mass flux, and the mpact of the mass flux on the heat flux s neglgble), the sorpton/desorpton sotherm s approxmated by a lnear functon, and materal parameters are effectvely treated as constant n the studed ranges of temperature and humdty, the materal s sotropc, the heat and mosture transport s one-dmensonal n the samples. Then, the equatons descrbng the coupled heat and mosture transport and the ntal-boundary condtons, correspondng to the condtons prevalng n the measurement system (.e. n the sample and acrylc glass plate as shown n Fg. ), can be generally expressed as: T C w j, j w Dw C wdtw T for I t x l, l II (1) T w c w q, q w T for I t x l, l II () T ac c ac q, q ac T for II t x l, l III (3) 0 T T x li,t T, T x liii,t TIII, q x lii,t qx lii,t (4) C t 0,x C, jx li, t 0, jx lii, t 0 (5) x,t 0, I 0 where: T temperature [K], T 0 ntal temperature [K], T I and T III temperatures [K] measured by sensors I and III, respectvely; C mosture mass concentraton [kg/kg], C 0 ntal mosture mass concentraton [kg/kg], densty of dry materal [kg/m 3 ], c specfc heat capacty [J/(kg K)], thermal conductvty [W/(m K)], D mosture dffusvty [m /s], D T thermodffuson coeffcent [m /(s K)] expressng nfluence of the heat transport on the mosture transport, q heat flux densty vector [W/m ], j mass flux densty vector [kg/(m s)], 0 zero vector, x space varable [m], t tme varable [s], nabla operator [1/m], w subscrpt denotng the parameters for mneral wool, ac subscrpt denotng the parameters for acrylc glass. The space coordnates of sensors I, II and III (marked n Fg. ) are equal to l I, l II and l III, respectvely. The heat and mass flux densty vectors for the formulated problem are of components: q x,t,0,0, x,t q x j,0,0 (6) Accordng to the smplfyng assumptons, the followng relatonshp was assumed n the above system of equatons between the mosture mass concentraton C n the wool samples and the measured RH of the ar n ther pores: j x m w C (7) 4

5 where: relatve humdty of pore ar [-], m w proportonalty coeffcent [-] between and C correspondng to the analysed varablty of humdty. In the analysed measurement system after swtchng on heatng n contaner 1 (as denoted n Fg. ) and re-stablzaton of temperature ndcatons n the sensors, t could be assumed that the heat transfer process s quas-statonary. Thus, after about 13 hours from the start of measurements, the thermal conductvty w of the sample was estmated n a smple way from equalty occurrng between the heat fluxes n the mneral wool sample and plate of acrylc glass wth the known coeffcent ac assumng lnear temperature dstrbutons n ndvdual layers of the system, whch dstrbutons were determned on the bass of ndcatons of sensors I, II and III. Subsequently, knowng the thermal dffusvty of acrylc glass a w= w/( wc w), the thermal dffusvty of the sample a w= w/( wc w) was estmated by mnmzng the functon of the sum of square errors between the temperatures measured by sensor II and calculated accordng to the model at the pont correspondng to the poston of ths sensor,.e.: arg mn TII t t T x lii, t t, y aw where: t -th measurement moment, y varable correspondng to the a w parameter n the ntal-boundary problem defned by equatons ()-(4). After ths step, D w, D Tw and m w parameters were estmated by mnmzng the functon of the sum of square errors between the relatve ar humdty n the sample pores measured by sensors I and II, and calculated accordng to the model at the ponts correspondng to the postons of these sensors,.e.: argmn t t x l, t t, y, y, y t t x l, t t, y, y, y I I 1 w 3 D, D Tw, m w II II 1 3 where: I and II relatve humdty [-] of the pore ar measured by sensors I and II, respectvely; y 1, y and y 3 varables correspondng to the D w, D Tw and m w parameters, respectvely, n the ntal-boundary problem defned by equatons (1)-(6). After obtanng the values of materal parameters, the consstency of the measurement data and the model was each tme evaluated by calculatng the global relatve errors of fttng the expermental and theoretcal curves of temperature and relatve humdty of ar accordng to the followng relatons: e D e T T II t T l, t T II t It l I, t IIt l II, t I t IIt II (8) (9) for the estmated a w (10) for the estmated D w, D Tw and m w (11) The soluton of the presented ntal-boundary problem was obtaned usng the Fnte Dfference Method, and the fndng of the mnmum error functon usng the Levenberg- 5

6 Marquardt algorthm. All the calculatons have been carred out by the authors n the Matlab envronment usng own procedures wrtten n the form of so-called m-fles. 4 Results and dscusson The measured bulk denstes and estmated materal parameters usng the calculaton procedures descrbed n the prevous paragraph are summarzed n Tables 1 and for each of 6 samples D1-D3 and M1-M3. The average values of these quanttes are also gven. In turn, the measured ponts on the sorpton sotherms of wool untreated by water and freely saturated by water durng mmerson and re-dred are shown n Fg. 3. Comparng them to the characterstc runs of sorpton sotherms n the case of mneral wool treated by hydrophlc agents or not (Fg. 1), t can be concluded that the samples tested had hydrophlc propertes, and after beng saturated wth water and re-dred, these propertes were reduced because of possble partal leachng the agent, and/or ts structural changes, and/or ts chemcal changes. Table 1. Bulk densty and estmated thermc parameters of stone wool samples wth global errors of temperature curve fttng. Type of sample curng Sample Densty w [kg/m -3 ] Coeffcent of thermal conductvty w [W/(m K)] Thermal dffusvty aw [m /s] x 10-7 Global error of temperature curve fttng accordng to formula (10) [-] D not mmersed D D Mean value h water M mmerson M and re-dryng M Mean value Type of sample curng not mmersed Table. Estmated hygrc parameters wth global errors of RH curve fttng. Sample Coeffcent of mosture dffuson Dw [m /s] x 10-6 Thermodffuson coeffcent DTw [m /(s K)] x Coeffcent n formula (7) adopted for the sorpton sotherm mw [-] et Global error of RH curve fttng accordng to formula (11) ed [-] x 10-3 D D D Mean value M M M Mean value h water mmerson and re-dryng For the purpose of a qualtatve comparson, these curves are presented together wth the estmated dependences whch consttute ther lnear approxmaton found n the nverse 6

7 problem, whch also may confrm ths observaton. In addton, the outputs shown n Tables 1- allow to deduce that the appled water mmerson for ths type of mneral wool after dryng does not result n a change of ts densty, as well as n sgnfcant changes n ts conductvty and thermal dffusvty. On the other hand, ths process sgnfcantly ncreases the dffuson transport of mosture (ncreasng the value of D w and D Tw coeffcents by an order of magntude!). Whle the value of the dffuson coeffcent D w of the tested wool before the water mmerson was lower than the typcal values due to the admxtures used n ts producton, after ths treatment and re-dryng, the mosture dffusvty ncreased to the level commonly found n the lterature. The followng explanaton of ths fact can be proposed: n the frst case, slower surface dffuson may be a domnant mechansm of mosture transport as a result of adsorpton of water vapour on the wool fbres forced by the hydrophlc agent, and n the second due to the decrease n ths effect, water vapour dffuson may be a domnant one as faster n ths stuaton because of the relatvely hgh porosty of wool. Ths hypothess needs further studes takng nto account possble changes of fbrous structure of the wool and from the pont of vew of the theory of thermodffuson. Fg. 3. Sorpton sotherms of the stone wool not mmersed and mmersed n water and re-dred compared wth ther lnear approxmatons found n the nverse problem. Fg. 4. Measured temperature tme-courses by sensors I, II and III n sample D1. The temperature at sensor II s compared wth the outcome of the adopted mathematcal model for the estmated thermc parameters from Table 1. 7

8 Fg. 5. Measured temperature tme-courses by sensors I, II and III n sample M1. The temperature course at sensor II s compared wth the outcome of the adopted mathematcal model for the estmated thermc parameters from Table 1. Fg. 6. Measured RH tme-courses n the pore ar by sensors I and II n sample D1. The relatve humdty at sensors I and II s compared wth the outcomes of the adopted mathematcal model for the estmated thermo-hygrc parameters from Tables 1-. There are also shown for example the temperatures for samples D1 and M1 measured by sensors I, II and III n Fgs. 4 and 5 where, n addton, the temperature from sensor II s compared wth the calculatons based on the ntal-boundary problem defned by equatons ()-(4) usng the materal parameters from Table 1. In ths case, the temperature ndcatons from sensors I and III were used as the boundary condtons of frst-type accordng to relatons (4). Smlarly, the comparson of the relatve humdty of the ar n the pores of samples D1 and M1 measured by sensors I and II wth those calculated n accordance wth the mathematcal model defned by relatons (1)-(7) s shown n Fgs. 6 and 7 for the materal data from Tables 1-. Takng nto account the data from Fgs. 4-5 and global errors n fttng the temperature curves from Table 1, t can be notced that the assumpton of unlateral couplng n the thermodffuson model by consderng only the mpact of heat transport on mass transport s correct from the quanttatve pont of vew n the analysed case. 8

9 Fg. 7. Measured RH tme-courses n the pore ar at sensors I and II n sample M1. The relatve humdty at sensors I and II s compared wth the outcomes of the adopted mathematcal model for the estmated thermo-hygrc parameters from Tables 1-. In turn, the comparson of lnear approxmatons of sorpton sotherms wth the expermental ones (Fg. 3) and the ft of the calculated and measured curves showng tme-changes of relatve humdty of the pore ar n the samples (Fgs. 6 and 7) suggest to use the more advanced descrptons n the dffusve part of the model to ncrease ts accuracy. 5 Conclusons The presented results allow to state that the presented measurement method enables quck determnaton of basc parameters descrbng coupled thermodffuson n samples of fbrous materals. In addton, for the type of wool dedcated for ndoor applcatons and tested wthn a framework of ths work, the obtaned results ndcate that ts exposure to drect atmospherc precptaton at constructon stes can sgnfcantly change ts thermodffuson features orgnally gven to t by manufactures. In ths case, t should be emphaszed that preservaton of these propertes s extremely mportant n operatng condtons of mneral wool boards to avod excessve mosture n them. The authors would lke to thank Prof. Mark Bomberg for valuable encouragement to buld a measurng stand for thermodffuson measurements of ths knd. References 1. M. Jřčková, R. Černý, Effect of hydrophlc admxtures on mosture and heat transport and storage parameters of mneral wool, Constructon and Buldng Materals, 0 (006) A.A. Abdou, I.M. Budaw, Comparson of thermal conductvty measurements of buldng nsulaton materals under varous operatng temperatures, Journal of Buldng Physcs, 9, (005) M.C. Chyu, X. Zeng, L. Ye, Effect of underground water attack on the performance of mneral wool ppe nsulaton, ASHRAE Transactons, 104, (1998) M. Jerman, R. Černý, Effect of mosture content on heat and mosture transport and storage propertes of thermal nsulaton materals, Energy and Buldngs 53 (01)

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