Accuracy of simplified indoor humidity simulation Olga Koronthalyova, PhD., Institute of Construction and Architecture, SAS, Dubravska c 9, 845 03 Bratislava, Slovakia; usarkoro@savba.sk Peter Mihalka, Ing., Institute of Construction and Architecture, SAS, Dubravska c 9, 845 03 Bratislava, Slovakia; usarmipe@savba.sk KEYWORDS: indoor humidity, simulation,. SUMMARY: Accuracy of simplified indoor humidity simulation, based on concept, was evaluated by a comparison with complex model. The evaluation of the model was done for different moisture production/ventilation regimes, outdoor weather changes and temperature gradients in hygroscopic layer. The analysis was limited to the cases of 1-zone space, constant material properties of hygroscopic layers and negligible vapour transmission through the exterior structures. The accuracy of simplified approach was found satisfactory in cases with limited thickness of hygroscopic layer and on condition that the moisture production and ventilation could be described as regular cyclic process or in cases where the hygroscopic surfaces were mostly placed on inner structures. 1. Introduction Indoor air relative humidity is an important parameter influencing the hygro-thermal performance of building structures and the indoor climate as well. In order to predict the resultant indoor humidity in the zone with the designed inner surfaces and moisture production/ventilation regime and to suggest possible improvements, a sufficiently accurate dynamic model is necessary. The computational codes simulating the interaction between indoor air and interior hygroscopic materials can be divided roughly into two groups: codes using simple lumped models and complex codes using a detailed description of the heat and mass transfer through the building structures. The complex models provide reliable information about resultant indoor humidity as well as the description of the hygro-thermal field in the structures but generally they are relatively time-consuming. Therefore in some cases a simplified approach could be more convenient way of indoor humidity evaluation. The scope of the presented paper was limited to cases when assumption of well-mixed air in interior is acceptable. The analysis was focused on evaluation of accuracy of one of the simplified approaches the approach based on effective moisture penetration depth () concept. Theoretical background of the concept was explained for example in (Cunningham 1992, Cunningham 2003, Rode et al. 2005). A method for determination of in cases when material properties are non-linear was described in (Arfvidsson 1999). Comparison of the simplified and more complex approach to indoor humidity simulation for the case of relatively vapour transmission open exterior walls was presented in (Janssens, De Paepe 2005). In this paper a capability of simplified approach was evaluated for the case when water vapour transmission through the building envelope was negligible in comparison to the convective transfer by ventilation. The analysis was also limited to the case of common indoor relative humidities, excluding the cases with extreme high humidities of indoor air. Therefore constant material properties could be used in the simulations. 2. Description of complex and approach In the both considered approaches the model of indoor humidity simulation is based on the solution of the water vapour mass balance equation in case of well-mixed air in the single zone space (IEA-Annex XIV 1991):
p 462 Ti { Gp + Gsk [ β j Aj ( pi psat, sj )]} i (1) τ = V + n ( p e p ) Where p i is the indoor air partial vapour pressure [Pa], p e is the outdoor air partial vapour pressure [Pa], τ is the time [s], T i is the indoor air temperature [K], G p is the indoor vapour production [kg.s -1 ], ΣG sk is the sum of the moisture flows from or into the room construction surfaces, V is the volume of the room [m 3 ], β j is the surface film coefficient for water vapour transfer [s.m -1 ], A j is the area of the surface where condensation or drying takes place [m 2 ], p sat,sj is the saturation vapour pressure on that surface [Pa], n is the ventilation rate [s -1 ]. The difference between the approaches is in the way of simulation of the interaction between indoor air and hygroscopic surfaces: The complex model consists in the solution of the equation (1) coupled with 1D numerical simulation of the coupled heat and moisture transport through the room structures. It enables to take into account material parameters moisture dependency. The approach is based on assumption of cyclic variation of vapour pressure at the hygroscopic surface. Then only a thin layer of defined thickness interacts with interior air (Cunningham (2003)). In approach it is moreover assumed that the temperature in this layer can be considered as uniform and material parameters can be considered constant. This approach doesn t simulate in detail the water vapour transmission through the exterior structures. The moisture transfer to/from the hygroscopic surface is then described by the following equation: dp dτ = p sat, d ( t ) ( p p ξ i w, Z ) Where d [m] is thickness of humidity buffering layer, ξ w, is the slope of sorption curve expressed by water content in relation to relative humidity [kg/m 3 ], t is temperature [K] and Z is vapour resistance [m/s], calculated from the relation: i (2) Z 1 a d = + (3) β δ i Where δ is water vapour permeability [s], a is coefficient; in the simulations a = 0.5 was used. The thickness of humidity buffering layer is given by the following relation: δ psat,( t ) T d = (4) ξ π w, Where T is the period of cyclic variations [s]. The d calculated according to the relation (4) represents the thickness of buffering layer, where the relative humidity variation is reduced to ca 27% of the surface variation (Arfvidsson 1999). In reality the assumption of cyclic variation of vapour pressure at the hygroscopic surface is not fulfilled. The deviations from the cyclic variation are caused by variations exterior water vapour partial pressure and by irregularities in moisture production/ventilation. On the other hand in cases when the thickness of the hygroscopic layer interacting with the indoor air is limited as it is in case of vapour barrier application, in case of hygroscopic plasters placed on concrete structures or in case when the prevailing part of indoor air - hygroscopic surface interaction takes place at room equipment surfaces the assumption of constant thickness of interacting hygroscopic material could be considered as an acceptable simplification. The assumption of constant material properties is acceptable for great deal of hygroscopic materials on condition of common indoor climate conditions where the indoor air relative humidity values don t exceed ca 70 %. In case of extreme conditions with high indoor humidities the usability of concept depends on concrete humidity variation interval as well as the hygroscopic layer material properties.
3. Comparison of and complex simulation results 3.1 Presentation of simulated case With the aim to compare and analyse the results of indoor humidity simulation by complex and approach the simulation of the resultant indoor air relative humidity were done for the chosen simply object. The code PenDepth (Mihalka, Matiasovsky and Drzik 2007) was used for the calculations and NPI code (Koronthalyova 2006) was used for complex model calculations. The calculations were done for the case when water vapour transmission through the structure could be neglected. The indoor humidity values corresponded to common indoor climate conditions and therefore constant material properties were used also in NPI calculations. The aim of the simulations was to quantify the effect of limited thickness of hygroscopic layer, moisture production/ventilation regimes irregularities and presence of temperature gradient in hygroscopic layer on the ability of approach. The calculations were done for the simply 1-zone space with the hygroscopic surfaces area S = 64.49 m 2 (walls and ceiling) and the volume V = 49 m 3. For the simplicity it was assumed that the room walls and ceiling have the same composition. The considered structure composition was (from interior): 12.5 mm thick layer of gypsum board, plaster (0.02 m), brick (0.24 m), PPS insulation (0.07 m) and plaster (0.02 m). In case of the limited thickness of hygroscopic layer the gypsum board was separated from the outer part of structure by water vapour barrier. The total thermal resistance of the structure was R = 2.4 m 2 K/ W. The used material properties of gypsum board are presented in Table 1. The thickness of humidity buffering layer used in PenDepth code for considered period T = 12 h was d = 9 mm. The effect of moisture production/ventilation irregularities was tested by simulation of two different cases of moisture production/ventilation regimes: - Regular moisture production and ventilation regimes. The moisture production and ventilation schedule was the same during the whole simulated period and corresponded to the working day regime (Table 2). - Irregular moisture production and ventilation. The irregularities were caused by different moisture production and ventilation regime during the working days and weekends, representing the case that the room was not occupied during weekends (Table 2). Table 1. Material properties of gypsum board. Thermal conductivity [W/(m.K)] Density [kg/m 3 ] Specific heat capacity [J/(kg.K)] Moisture content at 80% RH [kg/m 3 ] Vapour resistance factor [-] 0.3 710 850 9.5 8 Table 2. Moisture production and air change rate schedule used in simulations. Working days Weekends Hour 0-6 6-8 8-16 16-21 21-24 22-24 0-24 Air change rate [1/h] 0.45 1.2 0.45 1.0 1.0 0.45 0.1 Moisture production [kg/h] 0.025 0.4 0.025 0.2 0.2 0.025 0.025 With the aim to evaluate the effect of temperature gradient on the resultant indoor humidity the NPI calculations were done for two cases: In the first case it was assumed that all structures were inner structures and therefore their temperature was the same as the temperature of interior. In the second case all structures were considered as envelope ones, changing their temperature profile in concordance with the outdoor conditions.
The comparison of the calculation results was done for the period from 14th February to 22nd April. The outdoor clima parameters were taken from the Holzkirchen data for the year 2005 (Lenz, Holm 2005). Indoor air temperature was considered constant t i = 20 C. 3.2 Results and discussion In Table 3 the average and the maximum differences between indoor air relative humidities calculated by NPI and PenDepth are presented for all considered cases. The comparison of the simulation results for two chosen week periods are presented in Figures 1 5. The period from 16 th to 23 rd March was characterised by significant changes of exterior partial vapour pressure (between 450 and 1100 Pa) (Figures 1 4). The period from 21 st to 28 th February was characterised by extreme low temperatures of outdoor air (between 3 and -24 C), but due to the temperature decrease also exterior vapour pressure decrease took place (Figure 5). In the Figures 1 4 the effect of sudden increase of external vapour pressure during 1802 nd - 1866 th and 1924 th 19 th hours can be observed. The sudden significant change of exterior water vapour pressure was the main reason of differences between the calculated humidities in case of hygroscopic layers placed on inner structures and regular moisture production/ventilation regime. In case of external structures the effect of temperature gradient in the structures on resultant indoor humidity was noticeable in spite of their relatively good thermal insulation. Therefore in Figures 1 5 also the NPI results corresponding to case when half of hygroscopic surfaces were placed on inner structures and half on exterior ones - which is closer to common sitting of hygroscopic surfaces in interior are shown (NPI inner + envelope). The effect of temperature gradient in external walls can be seen in Figure 5. It resulted in relatively high difference between the NPI results for case of inner structures and case of half inner/half exterior structures. The differences between NPI and PenDepth results were not so high during the period because the effect of temperature gradient was partly compensated by coupled phenomenon of exterior water vapour pressure decrease. As can be seen from results in Table 3 the results of the complex and approach were in satisfactory agreement in case of limited thickness of hygroscopic layer (presence of vapour barrier) and regular moisture production/ventilation regime or in case that hygroscopic layers belonged to internal structures. In case without water vapour barrier the differences between the NPI and PenDepth results were significant. The highest differences between the and NPI simulation results were achieved in case of unlimited thickness of the hygroscopic layer and coupled effect of moisture production irregularity and temperature gradient in the structure. TABLE. 3: Differences between he the results of complex (NPI) and (Pen Depth) model during the considered period Hygroscopic layer Limited Unlimited Moisture production regime Structure RH difference between and complex model [%RH] Average Maximum Regular Inner 1 3 Envelope 2.3 4.6 Irregular Inner 1 3 Envelope 3.8 10.1 Regular Inner 2.5 10.1 Envelope 3.7 10.3 Irregular Inner 2.6 11.6 Envelope 6.1 17.8
64 60 Relative humidity [%] 56 52 48 NPI inner NPI inner + envelope 32 1798 1822 1846 1870 1894 1918 1942 1966 FIG. 1: Comparison of the calculated indoor air relative humidity courses for 1-week period from 16 th to 23 rd March: Vapour barrier and regular moisture production/ventilation regimes. 64 60 Relative humidity [%] 56 52 48 32 NPI inner NPI inner + envelope 28 1798 1822 1846 1870 1894 1918 1942 1966 FIG. 2: Comparison of the calculated indoor air relative humidity courses for 1-week period from 16 th to 23 rd March: Regular moisture production/ventilation regimes without vapour barrier.
Relative humidity [%] 68 64 60 56 52 48 32 NPI inner+envelope NPI inner 28 1798 1822 1846 1870 1894 1918 1942 1966 FIG. 3: Comparison of the calculated indoor air relative humidity courses for 1-week period from 16 th to 23 rd March: Irregular moisture production/ventilation regimes without vapour barrier. 68 64 Relative humidity [%] 60 56 52 48 NPI inner+envelope NPI inner 1798 1822 1846 1870 1894 1918 1942 1966 FIG. 4: Comparison of the calculated indoor air relative humidity courses for 1-week period from 16 th to 23 rd March: Vapour barrier and irregular moisture production/ventilation regimes.
48 Relative humidity [%] 32 28 24 20 NPI inner+envelope NPI inner 16 12 1268 1292 1316 13 14 1388 1412 FIG. 5: Comparison of the calculated indoor air relative humidity courses for 1-week period from 21 st to 28 th February: Irregular moisture production/ventilation regimes without vapour barrier. 4. Conclusions The conditions for reliable using simplified EPMD concept were analysed for the case of 1-zone space by the comparison with the complex model. The analysis dealt with cases when the assumption of well-mixed air was acceptable and water vapour transmission through the building envelope was negligible in comparison to the convective transfer by ventilation. The analysis was also limited to the case of common indoor relative humidities, excluding the cases with extreme high humidities of indoor air. In spite of relatively good thermal insulation of the considered structures the influence of temperature gradient in the envelope structures on resultant indoor humidity was noticeable. In case of limited thickness of the hygroscopic layer the results of PenDepth code were in good agreement with the complex model results on condition that the moisture production and ventilation could be described as regular cyclic process or in case that the most of the hygroscopic surfaces was placed on inner structures and therefore the influence of temperature gradient in the structures was negligible. The most significant differences between the and NPI simulation results were achieved in the case of unlimited thickness of the hygroscopic layer and coupled effect of moisture production irregularity and temperature gradient in the structure. Acknowledgements: The financial support of Slovak Science and Technology Assistance Agency under number APVT-51-030704 and of Slovak Grant Agency VEGA (Grant No 2/7113/27) was gratefully acknowledged. 5. References Arfvidsson J. (1999) A New algorithm to Calculate the Isothermal Moisture Penetration for Periodically Varying Relative Humidity at the Boundary. Nordic Journal of Building Physics. Vol. 2
Cunningham M. J. (1992). Effective Penetration Depth and Effective Resistance in Moisture Transfer. Building and Environment. Vol. 27, p. 379-386. Cunningham M. J. (2003). The building volume with hygroscopic materials: an analytical study of a classical building physics problem. Building and Environment. Vol. 38, p. 329-337. IEA-Annex XIV (1991), Condensation and Energy, Source Book, 1991. Janssens A., De Paepe M. (2005) Effect of moisture inertia models on the predicted indoor humidity in a room. In Proceedings of 26 th AIVC Conference. Koronthalyova O. (2006) Determination of moisture buffer ability of 1-zone space. Building Research Journal. Vol. 54, Number 3-4, p. 221-232. Lenz K., Holm A. (2005) Annex 41 subtask1. Common Exercise 3: Whole building heat and moisture analysis. Fraunhofer Institute for Building Physics, Holzkirchen Branch. Mihalka P., Matiasovsky P. and Drzik, M. (2007). Numerical modelling of local convective internal surface heat transfer coefficient. IEA ANNEX 41 Paper A41-T3-Sl-07-2. Rode C. et al. (2005). Moisture Buffering of Building Materials. Report BYG DTU R-126. Department of Civil Engineering, Technical University of Denmark