water vapour production and ventilation regimes in large ... · 2 s-w 5 5 0.633 3 n-w 5 2 0.253 ....

Water vapour production and ventilation regimes in large panel building flats Peter Mihalka, Peter Matiasovsky Institute of Construction and Architecture, Slovak Academy of Sciences, Slovakia Determination of the air change rate and water vapour production courses in residential buildings represents the problem connected with the inhabitants behaviour. The air change rates and vapour productions in the concrete large panel building flats were determined by the analysis of long-term measurements of the indoor and outdoor boundary conditions. The analysis was made with use of the system of equations modelling the hygric balance in the indoor space zone with two hygroscopic surfaces. The hygroscopicity of the flats was expressed by the effective air mass multiplier identified in the hygric balance equations. 1 Introduction

In the hygric performance analysis of building enclosures two main approaches can be distinguished according to the analysis objectives. The first approach is based on the application of a detailed spatial modelling of all relevant water vapour transport processes with use of a system of partial differential equations, with limitations given only by the degree of complexity and dimensions of such a model. The second approach is based on the application of relatively simpler models, limited on the contrary by the neglect of aspects not included into the model. The second approach, in spite of its limits, can enable the simple analysis of a complex hygrothermal zone, mainly in cases of the lack of any detailed information on the material properties of the enclosing structures. The description of such a simple model given by the system of several ordinary differential equations, expressing the hygric balances among the indoor and outdoor environments and the internal surfaces was published in [2], [3]. Some original ideas concerning the model arise e.g. from [6], [7]. The model will be applied in the analysis of the long-term hygric performance of real residential objects. The goal of the analysis is to survey the hygric parameters and indoor boundary conditions of the objects with respect to the behaviour of their inhabitants. Especially the determination of water vapour productions and air change rates will be in focus. 2 Measurements

Measurements of indoor climate parameters and monitoring of the inhabitants ventilation habits were carried out in four identical 5-room flats of the 12-storey multi-family buildings with different orientation in Bratislava - Slovakia during ca 1 year period (October 1991 – December 1992). The hourly courses of indoor climate parameters: air temperature, relative humidity and opening windows were monitored continuously. Simultaneously the hourly values of outdoor climatic elements: the solar irradiation, the air temperature and the relative humidity and the wind velocity were acquired from the local weather station.

The enveloped space of each of the flats is 180 m3 and each flat has 4 windows. All flats are

heated by a collective heating system. Orientation, storey and number of inhabitants of particular flats are shown in table 1. Each of the analysed flats, due to its ground plan and performance, can be considered as one hygric zone, having practically the same temperature, air pressure and relative humidity. Therefore the indoor temperature and relative humidity could be measured only in the hall having the central position in a flat (Fig. 1).

Opening windows was registered using the relay control of the time recording the stays: open-closed at each of the ventilation casements of the particular windows. It was quantified by the relative duration of opening windows [1] defined as:

T

tnn

Tt

to

∑=

=

⋅= 0 (1)

where: T is the duration of the monitored time interval (1 hour), n and t is the number and duration [h] of open windows during the period T. In given cases the values of no can vary in the interval 0 - 4.

Fig. 1. View of building type with analysed flats and ground plan of flat Tab.1. Orientation, storey, number of inhabitants and estimated water vapour production of monitored flats

Flat No

Orientation Floor Household members

Water vapour production

[kg/h] 1 S-E 3 5 0.633 2 S-W 5 5 0.633 3 N-W 5 2 0.253

4 N-E 5 5 0.633

The average water vapour productions in particular flats were estimated from the flats occupancy data (number of occupants, number of children, occupants activities, time spent at home, presence of plants), using the values for evaluation of water production rates in rooms [2]. 3 Analysis

In the analysed flats the direct complex and detailed hygric performance analysis on a hourly basis was not possible as the realised measurements do not provide satisfactory information (hourly values) on the air change rate and the water vapour production. The only information on the vapour production was given by the mean occupancy data and the only information on the air change rate was in a form of the relative open windows duration records. Therefore the determination of a complementary information on these two variables was necessary. 3. 1 Determination of mean weekly air change rates

In order to obtain more information on the air change, as the first step, weekly values of the total air change rates in the flats during the measured period were determined with use of the water vapour as a tracer gas. The average hygric balance of a zone during a longer period (1 week and more) can be represented by the most simple steady-state model containing 5 independent variables: vapour production, ventilation rate, indoor temperature and indoor and outdoor vapour pressures. Assuming that the estimated mean vapour production in particular flats (table 1) represents also an average values for a week period, the weekly means of the air change rate were determined from the steady-state water vapour balance equation for the weekly time intervals:

VppGT

nei

pi

⋅−⋅⋅

=)(

462 (2)

where pi, pe are water vapour pressures of indoor and outdoor air respectively [Pa], Ti is the indoor air temperature [K], Gp is the water vapour production in a flat [kg/h.m3], V is the volume of enveloped space [m3], n is the air change rate [1/h]. 3. 2 Correlation among mean weekly air change rates and other quantities

The problem that the both data – on vapour production and air change rate were available on a weekly basis only was solved by the investigation of the potential correlations among the air change rate and other available data on a weekly basis, assuming that the found correlations could be within certain limits applicable also for the time intervals shorter than 1 week. The multiple linear regression analysis has been applied as a tool for the evaluation of such possible correlations and their significance. The analysis of three expected variables gave significant correlations for flats No 1, 2, 3. The statistical significance was evaluated according the t–value for 0.95 confidence interval. The results for the flat No 4 showed no significant correlation and therefore this flat was rejected from further considerations. A detailed enquiry has showed that the flat does not satisfy the definition of a hygric zone. The significant expressions and

corresponding correlation coefficients are in table 2. Tab. 2 Dependence of air change rate on outdoor temperature - to, opening windows - no and wind velocity - w in particular flats Flat No.

Regression Correlation coefficient

1 n = 0,062.ti + 0.0095.to + 0.168.no - 0.0086.w - 0.733 0.693

2 n = - 0.024.ti + 0,0978.to - 0.463.no - 0.0096.w + 3.154 0.845

3 n = 0.130.ti + 0,039.to + 0.435.no + 0.0112.w + 3.015 0.992

The found relations express, in principle, the fact that the air change rate is dependent on indoor - ti and outdoor - to temperatures, opening windows - no and wind velocity - w. The original assumption was that the air change rate will be proportional positively to all considered independent variables, ever to the outdoor temperature due to a higher number of the simultaneously opened windows and the consequently more effective ventilation at the higher temperatures. However also in some other cases the negative proportionality has occurred. The cases of a negative proportionality of the air change rate to the wind velocity were statistically insignificant and partly they can be interpreted by the tendency of inhabitants to precede the cross ventilation at higher wind velocities (by closing the internal doors and having open less windows simultaneously). The case of negative proportionality of the air change rate to opening windows can be interpreted by the the stack effect at the open windows causing the water vapour inflow into the hall, especially in the flats of leeward orientation at lower storeys. The case of negative proportionality of the air change rate to the indoor temperature was statistically insignificant. In figure 2 there are comparisons of the mean weekly air change rate courses determined from vapour production with the courses obtained by a multiple regression analysis, with and without consideration of opening windows as an indapendent variable. The leeward flat No. 1 shows a significance of opening windows, whilst the windward flats No. 2 and 3 show the negligible influence of opening windows.

Flat No. 1

0

0,2

0,4

0,6

0,8

1

1,2

1 2 3 4 5 6 7 8 9 10

Time [weeks]

Air

chan

ge ra

te [1

/h]

Determined from vapour productionMultiple regressionMultiple regression - opening windows neglected

Flat No. 2

0

0,5

1

1,5

2

2,5

3

1 2 3 4 5 6 7 8 9 10Time [weeks]

Air

chan

ge ra

te [1

/h]

Determined from vapour production

Multiple regression

Multiple regression - opening windows neglected

Flat No. 3

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

1 2 3 4 5 6 7Time [weeks]

Air

chan

ge r

ate

[1/h

]Determined from vapour productionMultiple regressionMultiple regression - opening windows neglected

Fig. 2 Mean weekly courses of air change rate determined from vapour production compared with the courses obtained from multiple regression analysis with and without consideration of opening windows 3. 3 Effective air mass multiplier model With use of the regressions in table 2 the hour-to-hour courses of the boundary conditions in the flats could be analysed, assuming that the obtained relations for the air change rate are valid independently on the considered time interval as the air flows have practically instantaneous character. The analysis was done for a period of one month – November 1991. The objective of the analysis was to determine the hourly water vapour production values from the other measured and approximated hourly data, which required the use of the appropriate non-steady state hygric balance model. In the analysis the two-nodal model of hygric balance, considering the zonal and hygroscopic surface - index 1, balances and described by a second order differential equation [2] was used:

VGT

TTTp

TTp

dtdp

TTTdtpd pieiii ⋅⋅

⋅+⋅

=⋅

+⎟⎟⎠

⎞⎜⎜⎝

⎛+++

4621111

331313212

2

(3)

with the time constants given by:

nT 1

1 = (4)

1

12 462 AT

VZT

i

p

⋅⋅⋅

= (5)

11111

3 CZpsat

dZT p

p ⋅=⋅⋅

=ρξ

(6) The possible three-nodal model with two hygroscopic surfaces – indices 1, 2 is described by a third order differential equation was taken into consideration:

VGT

TTTTTp

TTTp

dtdp

TTTTTTTTdtpd

TTTTTdtpd

piei

iii

⋅⋅⋅

⋅+

⋅⋅=

⋅⋅+

+⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛++⎟⎟

⎠

⎞⎜⎜⎝

⎛++⎟⎟

⎠

⎞⎜⎜⎝

⎛+++++

4621

111111111111

53531531

532154132

2

543213

3

(7)

with the further time constants:

2

24 462 AT

VZT

i

p

⋅⋅⋅

= (8)

22222

5 CZpsat

dZT p

p ⋅=⋅⋅

=ρξ

(9)

where: Zp is the diffusion resistance of the hygroscopic surface [m/s], A is the hygroscopic surface area [m2], ρξ is volumetric moisture capacity - the slope of the linear central part of the suction curve of the surface material [kg/m3] , d is the surface effective penetration depth [m], psat is the partial water vapour saturation pressure [Pa], C is the hygroscopic capacitance [kg/Pa]. The diffusion resistances and the hygroscopic capacitances are lumped parameters determined by the effective penetration depth cencept. The analytical solution of the differential equations (3) and (7) for a time step excitation has in general the character of the sum of exponential functions in time. However in cases when only one exponential term of the solution is significant, the second or third order differential equations can be reduced to a first order differential equation:

( ) ( )V

GTppn

dtdp

TT

TT

TTn piie

i ⋅⋅+−⋅=⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+++⋅+

4621

4

5

2

353 (10)

In equation (10) the time constants can be grouped into the effective air mass multiplier – Em, [2] consisting of a linear and constant terms (Em = n.A + B):

( )V

GTppn

dtdpE pi

iei

m

⋅⋅+−⋅=

462 (11)

The minimum possible real value of Em is 1, in a case of the zero zonal hygric inertia. The finite difference approximation of equation (11) solution for a time step is:

⎥⎦

⎤⎢⎣

⎡⋅⋅⋅

+⋅∆⋅+⋅∆⋅

−⋅∆⋅

+= )

462()

2(

2

101 Vn

GTptnptnEtnE

p pieim

m

i (12)

Knowing the values of Em, with use of relation (12), the hourly values of water vapour production from the values of air change rate, and water vapour pressures can be calculated. Simultaneously the long-term (at minimum weekly) means of the calculated water vapour production hourly values should be identical with the mean values estimated from the flat occupancy, presented in table 1. The fulfillment of this condition is dependent on the correctness of the effective air mass multiplier – Em, value. 4 Results

The hygric performances of particular analysed flats were various, given by their occupancy, heating system state and the properties of finishing materials. This is noticeable in figure 2 describing the monthly courses of indoor vapour pressure in the flats. In table 3 there is a basic information on the indoor climatic parameters in the analysed period. The outdoor temperature varied in the interval from 13.3 to –6.6 °C. At the locations of all flats the prevailing winds orientation was NW. The relation (12) has one unknown variable – the water vapour production and one unknown parameter - the effective air mass multiplier and the correctness of both of them is checked by the condition of the equality of expected and calculated vapour production means in a considered period. In figure 3 there is the hypothetical dependences of calculated mean vapour production on the linear – A and constant – B effective air mass multiplier terms for identical indoor vapour pressure and air change rate courses in particular flats. The limit combination A = 0, B = 1 represents the case of a zone without hygroscopicity. The calculated vapour production increases with the increase of both effective air mass multiplier terms. The increase of vapour production is caused by the fact that with the assumed increase of hygric inertia the measured vapour pressures courses can be obtained only with the simultaneous assumption of a vapour production increase. For a determination of the actual effective air mass multiplier values the information on the hygroscopic surfaces parameters in the analysed flats was necessary. In all flats two types of significant hygroscopic surfaces were supposed: the wallpaper finish of walls and ceilings and the textile materials, mainly carpets. In table 4 there are areas of the internal surfaces supposed to be active in a zonal hygric balance in particular flats.

Vapour pressure

0

200

400

600

800

1000

1200

1400

1600

1800

1.11 3.11 5.11 7.11 9.11 11.11 13.11 15.11 17.11 19.11 21.11 23.11 25.11 27.11 29.11 1.12

Time [days]

Vapo

ur p

ress

ure

[Pa]

OutdoorFlat No.1Flat No.2Flat No.3

Fig. 3 Indoor vapour pressure courses in particular flats in November 1991 Tab. 3 Indoor climatic parameters in particular flats during analysed period

Flat No. 1 Flat No. 2 Flat No. 3 Parameter Max Min Aver Max Min Aver Max Min Aver

Temperature [°C] 25 21 22.8 25 20 22.7 23 18 21 Relative humidity [%] 56.5 38 49.1 58 29.5 37.4 52 28.5 41.3

Flat No.2

0,7

0,71

0,72

0,73

0,74

0,75

0,76

0,77

0,78

0,79

1 2 3 4 5 6 7 8B

Moi

stur

e pr

oduc

tion

[kg/

h]

A=0A=1A=2A=3Computed aver.production (a)A=1,257 (b)A=0,153 ( c)A=1,024 (d)A=0,153 (e)A=1,024 (f)A=1,071 (g)A=1,593 (h)A=1,039 (i)

Flat No.3

0,24

0,25

0,26

0,27

0,28

0,29

0,3

0,31

1 2 3 4 5 6 7 8B

Moi

stur

e pr

oduc

tion

[kg/

h]

A=0A=1A=2A=3Computed aver.production (a)A=1,378 (b)A=0,168 ( c)A=1,123 (d)A=0,168 (e)A=1,123 (f)A=1,175 (g)A=1,746 (h)A=1,139 (i)

Flat No.1

0,646

0,648

0,65

0,652

0,654

0,656

0,658

0,66

0,662

0,664

1 2 3 4 5 6 7 8B

Moi

stur

e pr

oduc

tion

[kg/

h]

A=0A=1A=2A=3Computed aver.production (a)A=1,219 (b)A=0,149 ( c)A=0,994 (d)A=0,149 (e)A=1,039 (g)A=0,994 (f)A=1,545 (h)A=1,008 (i)

Fig. 4 Dependence of calculated mean vapour production on linear – A and constant – B terms of effective air mass multiplier Tab. 4 Supposed active hygroscopic surfaces areas in particular flats

The supposed material parameters of the considered hygroscopic surfaces are in table 5. The penetration depth was calculated under consideration of the 4 hours cycle period, as daily in average 6 oscillations of indoor vapour pressure were observed in all flats. Besides these parameters also the possible variations of the vapour resistance factor, hygroscopic surface areas and surface transfer coefficients from the expected parameters were taken into consideration. The case with the supposed the material properties in tables 3 and 4 is marked as the combination a in table 6. The varied combinations are marked as b – i in the same table. The mean vapour productions calculated for the supposed parameters and their variations are depicted in figure 3. The results of vapour production calculation were compared with the vapour productions estimated in particular flats. Considering the condition that the long-term means of the calculated water vapour production should be identical with the estimated mean values the optimum parameters combinations represented by the cases giving the vapour production values closest to the estimated ones. It results from the analysis of the mean vapour production dependence on the supposed and varied terms of the effective air mass multiplier that following calculated vapour productions are closest to the expected vapour productions: 0.647 → 0.633 in flat No. 1, 0.707 → 0.633 in flat No. 2 and 0.252/0.254 → 0. 253 in flat No. 3. The parameters of optimum cases for all 3 flats are in table 7. In the flats No. 1 and 2 the optimum combinations e and c are different from the supposed ones. The hygric inertia is represented only by the wallpaper in these flats the influence of textile surfaces is negligible. In the flat No. 3 also the hygroscopicity of textile surfaces plays a role. In all cases the supposed zonal hygroscopicity - combination a was overestimated. The comparison of calculated and estimated vater mean weekly vapour productions and corresponding air change rates in particular November weeks is in figure 4. In figures 5 – 13 there are results of the final calculations for the parameters and boundary conditions determined from a previous analysis. The monthly courses of indoor and outdoor vapour pressures, ventilation rate and vapour production in particular flats during the analysed period are in figures 5, 8 and 11. The more detailed indoor water vapour pressure courses in the flats, compared with the calculated cases not considering the hygric inertia are in figures 6, 9 and 12. In figures 7, 10 and 13 there are the calculated average daily courses of vapour production and air change rate during the weekdays and weekends together with 0.68 probability bands for individual daily time values. A different behaviour of the inhabitants during weekends is evident. In flat No 1 there is a visible difference between the inhabitants behaviour at weekdays and weekends. The vapour production and air change rate maxima occur at morning during weekdays and at noon during weekends. The increased variation of the vapour production at noon is characteristic for this flat. As the air chage rate is influenced by opening windows (Fig. 2) during the weekends the correlation between vapour production and air change rate as well as between their variations is apparent. In flat No 2 there are small differences between weekdays and weekends. The maximum variation of vapour production is about at noon/afternoon. The air change rate maxima and minima track the everage autumn daily wind velocity courses in a given location. In flat No 3 there are differences between weekdays and weekends, in the vapour

Surface area [m2] Flat No. Wallpaper Wool carpet

1 145.1 27.9 2 268.2 50.8 3 185.1 24.6

production mainly. The vapour production is practically constant and vapour production maxima are at afternoon during weekdays. During weekends the air change rates shift towards morning and the vapour production has visible minima at noon. The coefficient of variation of air change rate in flat No 3 is higher then in the other flats, which can be explained by the fact that the air change rate in this flat is practically dependent more on a weather situation than on opening windows (Fig. 2). Generally the variation of air change rate is lower than the variation of vapour production at particular hours of day. The maxima of vapour production variation are about at noon. The maxima of air change rate variation are at night. A futher analysis showed that the daily variations are relatively lower than the interdiurnal variations. The daily variations can be characterised by the probability function and autocorrelation. They can be modelled by means of the hourly values generator consisting of the “pseudo random number generator” and the autocorrelation procedure based on the assumption that the coherence is more defined by the way the values succeed each other than by the values themselves [8]. This simple model was applied for flat No 3 and is displayed in figure 14. Tab. 5 Hygric properties of finishing materials

Material

Thickness

[m]

Penetration depth

[-]

Vapour resistance

factor [-]

Bulk density

[kg/m3]

Specific moisture capacity

[kg/kg] Wallpaper 0.00028 0.00102/0.00076 50/90 570 0,080

Textile 0.00500 0.00400/0.00281 7/14 300 0,072 Tab. 6 Considered combinations of parameters of hygroscopic surfaces

Wallpaper Textile Combination

Area [m2]

Diffusion resistance factor [-]

Area [m2]

Diffusion resistance factor [-]

Convective surface heat

transfer coefficient [W/m2 K]

a supposed 50 supposed 7 4 b supposed 90 supposed 7 4 c supposed 50 0 - 4 d 0 - supposed 7 4 e sum of both surfaces 50 0 - 4 f 0 - sum of both surfaces 7 4 g supposed 50 supposed 14 4 h supposed 50 supposed 7 2 i supposed 50 supposed 7 6

Tab. 7 Values of time constants, effective air mass multiplier terms and average effective air mass multiplier for optimum combination of hygroscopic surfaces parameters for particular flats

Flat No - combination

T1 [h]

T2 [h]

T3 [h]

T4 [h]

T5 [h]

A [h-1]

B [-]

Em [-]

1 – e 1/n 0.269 0.149 - - 0.149 1.552 1.641 2 – c 1/n 0.174 0.153 - - 0.153 1.881 2.126

3 – d/g 1/n 0.253 0.168 1.897 1.123 1.291 2.255 3.030

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2

1 2 3 4

Time [weeks]

Air

chan

ge r

ate

[1/h

]

Flat No.1,average of values obtained from regression Flat No.1, from vapour productionFlat No.2,average of values obtained from regression Flat No.2, from vapour productionFlat No.3,average of values obtained from regression Flat No.3, from vapour production

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1 2 3 4

Time [weeks]

Vap

our

prod

uctio

n [k

g/h]

Flat No.1,average calculated Flat No.1,assumedFlat No.2,average calculated Flat No.2,assumedFlat No.3,average calculated Flat No.3,assumed

Fig. 5 Comparison of expected and calculated mean weekly values of air change rate and vapour production in particular flats

Flat No.1

300400500600700800900

10001100120013001400150016001700180019002000

1.11 3.11 5.11 7.11 9.11 11.11 13.11 15.11 17.11 19.11 21.11 23.11 25.11 27.11 29.11 1.12

Time [days]

Vap

our

pres

sure

[Pa]

0

0,5

1

1,5

2

2,5

3

Air

chan

ge r

ate

[1/h

]V

apou

r pr

oduc

tion

[kg/

h]

Indoor vapour pressure

Outdoor vapour pressure

Air change rate

Vapour production

Fig. 6 Monthly courses of indoor and outdoor vapour pressures, air change rate and vapour production in flat No 1

Flat No.1

300400500600700800900

10001100120013001400150016001700180019002000

12.11.91 0:00 12.11.91 12:00 13.11.91 0:00 13.11.91 12:00 14.11.91 0:00Time [days]

Vapo

ur p

ress

ure

[Pa]

0

0,5

1

1,5

2

2,5

3

Air

chan

ge r

ate

[1/h

]Va

pour

pro

duct

ion

[kg/

h]

Indoor vapour pressureVapour pressure without inertiaOutdoor vapour pressureAir change rateVapour production

Fig. 7 Indoor water vapour pressure course in flat No 1 calculated without and with assumption of hygric inertia

Flat No 1 - Weekdays

0,2

0,30,4

0,5

0,6

0,70,8

0,9

1

0 2 4 6 8 10 12 14 16 18 20 22 24Time [h]

Vap

our

prod

uctio

n [k

g/h]

MeanMean + SDMean - SD


0,20,30,40,50,60,70,80,9

1

0 2 4 6 8 10 12 14 16 18 20 22 24Time [h]

Air

chan

ge ra

te [1

/h]


Flat No 1 - Weekends

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6 8 10 12 14 16 18 20 22 24Time [h]

Vapo

ur p

rodu

ctio

n [k

g/h]



0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 2 4 6 8 10 12 14 16 18 20 22 24

Time [h]

Air

chan

ge ra

te [1

/h]


Fig. 8 Average daily courses of vapour production and air change rate with 0.68 probability bands characteristic for weekdays and weekends in flat No 1

Flat No.2

300400500600700800900

100011001200130014001500160017001800

1.11 3.11 5.11 7.11 9.11 11.11 13.11 15.11 17.11 19.11 21.11 23.11 25.11 27.11 29.11 1.12

Time [days]

Vap

our

pres

sure

[Pa]

0

1

2

3

4

5

6

Air

cha

nge

rate

[1/h

]V

apou

r pr

oduc

tion

[kg/

h]



Air change rate

Vapour production


Flat No.2

300400500600700800900

100011001200130014001500160017001800

12.11.91 0:00 12.11.91 12:00 13.11.91 0:00 13.11.91 12:00 14.11.91 0:00

Time [days]

Vapo

ur p

ress

ure

[Pa]

0

1

2

3

4

5

6

Air

chan

ge r

ate

[1/h

]Va

pour

pro

duct

ion

[kg/

h]

Iindoor vapour pressureIndoor vapour pressure without inertiaOutdoor vapour pressureAir change rateVapour production

Fig. 10 Indoor water vapour pressure course in flat No 2 calculated without and with assumption of hygric inertia


0,2

0,4

0,6

0,8

1

1,2

1,4

0 2 4 6 8 10 12 14 16 18 20 22 24Time [h]

Vapo

ur p

rodu

ctio

n [k

g/h]



0,2

0,7

1,2

1,7

2,2

2,7

0 2 4 6 8 10 12 14 16 18 20 22 24Time [h]

Air c

hang

e ra

te [1

/h]



0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 2 4 6 8 10 12 14 16 18 20 22 24

Time [h]

Vapo

ur p

rodu

ctio

n [k

g/h]



0,2

0,7

1,2

1,7

2,2

2,7

0 2 4 6 8 10 12 14 16 18 20 22 24Time [h]

Air

chan

ge ra

te [1

/h]


Fig. 11 Average daily courses of vapour production and air change rate with 0.68 probability bands characteristic for weekdays and weekends in flat No 2

Flat No.3

300400500600700800900

100011001200130014001500160017001800

1.11 3.11 5.11 7.11 9.11 11.11 13.11 15.11 17.11 19.11 21.11 23.11 25.11 27.11 29.11 1.12

Time [days]

Vap

our

pres

sure

[Pa]

0

0,5

1

1,5

2

2,5

3

Air

cha

nge

rate

[1/h

]V

apou

r pr

oduc

tion

[kg/

h]



Air change rate

Vapour production


Flat No.3

300400500600700800900

100011001200130014001500160017001800

12.11.91 0:00 12.11.91 12:00 13.11.91 0:00 13.11.91 12:00 14.11.91 0:00

Time [days]

Vap

our p

ress

ure

[Pa]

0

0,5

1

1,5

2

2,5

3

Air

chan

ge r

ate

[1/h

]V

apou

r pro

duct

ion

[kg/

h]

Indoor vapour pressureIndoor vapour pressure without inertiaOutdoor vapour pressureAir change rateVapour production

Fig.13 Indoor water vapour pressure course in flat No 3 calculated without and with assumption of hygric inertia


00,050,1

0,150,2

0,250,3

0,350,4

0,450,5

0 2 4 6 8 10 12 14 16 18 20 22 24Time [h]

Vapo

ur p

rodu

ctio

n [k

g/h]

Mean

Mean + SD

Mean - SD

Random


0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6 8 10 12 14 16 18 20 22 24

Time [h]

Air

chan

ge ra

te [1

/h]

MeanMean + SDMean - SDRandom


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 2 4 6 8 10 12 14 16 18 20 22 24

Time [h]

Vapo

ur p

rodu

ctio

n [k

g/h]

MeanSeries2Mean - SDRandom


0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6 8 10 12 14 16 18 20 22 24

Time [h]

Air

chan

ge ra

te [1

/h]

MeanMean + SDMean - SDRandom

Fig. 14 Average daily courses of vapour production and air change rate with 0.68 probability bands characteristic for weekdays and weekends in flat No 1, compared with generated random courses 5 Conclusions

The courses of the characteristic indoor relative humidity and open windows duration were analysed in the flats of identical type, during a selected period of a year The relative humidity responses to moisture production and ventilation excitations in particular flats were analysed with use of a simple hygric balance model based on the effective air mass multiplier concept. The derivation and interpretation of the concept in the system of limited number of ordinary differential equations enabled its application for the assessment of the hygric properties of the internal surface finish materials. The obtained air mass multiplier values indicate an influence of hygroscopicity in the analysed flats. The approach enables to estimate/analyse the characteristic ventilation and moisture production variations, simultaneously with the estimation of the hygric properties of internal surfaces. The daily courses can be modelled by the part represented by mean characteristic daily courses and the part satisfying a given probability function and autocorrelation function. Acknowledgement

Financial support of the project APVT-51-030704 is gratefully acknowledged.

References [1] IEA-Annex VIII. 1987.Inhabitants Behaviour with Respect to Ventilation, Final Report. [2] IEA-Annex XIV. 1991.Condensation and Energy. Source Book. [3] de Wit M. H. IEA-Annex XIV report NL-T4-02/1988 A Second Order Model for the

Prediction of Indoor Air Humidity [4] Koronthályová O. 1994. Evaluation of contribution of ventilation by opening windows to

total air change rate based on one year period measurements. In Vnútoná klíma budov. SSTP Bratislava, p. 129-133. (In Slovak)

[5] de Wit M. H. 2006 Hambase Heat, Air and Moisture Model for Building and Systems Evaluation. Bouwstenen series No 100, Eindhoven University Press

[6] Stehno V. 1982. Praktische Berechnung der instationären Luftzustandsänderungen in Aufenthaltsräumen yur raumbegrenyenden Bauteile. In Baupysik, Vol. 4, p. 128-134

[7] Kuenzel H. 1960. Die klimaregelnde Wirkung von innenputzen. Gesundheits-Ingenieur, Vol. 81, p. 196-201

[8] Van Passen A. H. C. 1979 The Syntetical Reference Outdoor Climate. In Energy and Buildings, Vol 2, p. 151-161

water vapour production and ventilation regimes in large ... · 2 s-w 5 5 0.633 3 n-w 5 2 0.253 ....

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