FIG. 18--Sheathing moisture content plotted versus sheathing type.
TABLE 2--Properties required for a new material.
Property Description Units
Sorption isotherm
Al~b A 1 = kgd/kg ~ (lbd/lb w)
Y = (1 + Aa~b)(1 - A3q~ ) A 2 = dimensionless A 3 = dimensionless
Liquid diffusivity B 1 = m 2 / s (ftZ/h)
D r = Blexp(B2"y) B 2 = dimensionless
Capillary saturated moisture content, % ,/, = kgw/kg ~ (lbw/lbd)
Thermal Conductivity k d = W/m.~ (Btu/h.fl-~
k = k d + Cr(T - TR) + C n ' y C T = W/m'~ per ~ (Btu/h-ft.~ per ~
C~ = W/m.~ per kgw/kg d (Btu/h'ft.~ per lbw/lbd)
Dry density, Pa Pd = kg/m3 (lb/fl3)
Specific heat, C a C a = J/kg-~ (Btu/lb.~
Vapor permeability C 1 = kg w / s-m.Pa (perm-inch)
= C1 + C2Exp(C3"4~) C2 = k g J s . m - P a (perm-inch) C 3 = dimensionless
Note: The symbol d denotes dry and w denotes wet.
S o r p t i o n C o e f f i c i e n t s
S o r p t i o n i s o t h e r m m e a s u r e m e n t s f o r r o o f i n g f i b e r b o a r d h a v e b e e n r e p o r t e d by B u r c h a n d D e s j a r l a i s [23], a n d t h e y a r e s u m m a r i z e d in Table 3.
T h e m e a n d a t a g i v e n in T a b l e 3 m u s t b e fit to t h e s o r p t i o n i s o t h e r m e q u a t i o n g i v e n i n T a b l e 2. T h e c o n s t a n t s (A1, A2,
TABLE 3 - - S o r p t i o n measurements of roofing fiberboard.
Ambient Relative Equilibrium Moisture Content, %
Humidity, % Adsorption Desorption Mean
11.3 0.63 1.26 0.93
32,9 3.06 4.00 3,54
43.2 4.31 5,53 4.92
58.0 5.74 7.57 6,66
78.7 9.15 12.0 10.58
84.5 11.3 14.6 12.95
93.8 16.4 20.6 18.5
97.4 24.6 28.1 26.4
a n d A3) a r e d e t e r m i n e d f r o m a r e g r e s s i o n a n a l y s i s p r o c e - d u r e , A p l o t o f t h e a b o v e - m e a s u r e d d a t a s h o w i n g t h e r e g r e s - s i o n a n a l y s i s e q u a t i o n is s h o w n in Fig. 19.
In a s i m i l a r f a s h i o n , l i q u i d d i f f u s i v i t y a n d v a p o r p e r m e - a b i l i t y d a t a m u s t b e f o u n d in t h e l i t e r a t u r e a n d c u r v e d f i t t e d to t h e a p p r o p r i a t e e q u a t i o n . A f t e r c u r v e fitting, t h e c u r v e - f i t t e d c o e f f i c i e n t s a n d o t h e r m a t e r i a l p r o p e r t y d a t a m u s t b e e n t e r e d i n t o t h e M O I S T p r o g r a m f o l l o w i n g t h e p r o c e d u r e o u t l i n e d in t h e p r o g r a m u s e r m a n u a l [1].
O R D E R I N G T H E P R O G R A M A N D G E T T I N G H E L P
T h e m o s t c u r r e n t r e l e a s e o f t h e p r o g r a m is p r o v i d e d o n t h e e n c l o s e d CD R o m a n d m a y b e d o w n l o a d e d f r o m t h e M O I S T w e b site at w w w . b f r l . n i s t . g o v / 8 6 3 / m o i s t . h t m l ,
30
A 25
='20
2 1 0
= m o3
9 Measured Mean Sorption Data Regression Equation
0.22a.~
(1 .s.1 ~.$ )(1-0.~m.,)
4,
0 ,It /- I I 1 I
0 20 40 60 80 100
Relative Humidity (%)
FIG. 19---Illustration of fitting sorption isotherm for roofing fiberboard to regression equation.
A P P E N D I X
Mathematical Description of MOIST (Release 3.0)
In the previous version of the MOIST Program (Release 2.1), temperature was used as the potential for heat flow, and moisture content was used as the potential for moisture flow.
In the current release of the program, temperature is used as the potential for heat flow, water-vapor pressure is used as the potential for vapor transfer, and capillary pressure is used as the potential for liquid flow. The new model has the advantage that it uses transport potentials that are every- where continuous, thereby leading to a computationally more efficient solution.
ASSUMPTIONS
Some of more important assumptions of the analysis are:
9 heat and moisture transfer are one dimensional,
9 construction is airtight, and the transport of moisture by air movement is neglected,
9 wetting of exterior surfaces by rain is neglected,
9 snow accumulation on horizontal surfaces, and its effect on the solar absorbance and thermal resistance is ne- glected,
9 transport of heat by liquid movement is neglected, and 9 surface condensation is neglected.
BASIC TRANSPORT EQUATIONS
Within each material layer of the construction, the moisture distribution is governed by the following conservation of mass equation:
The first term of the left side of Eq A-1 represents water- vapor diffusion, whereas the second term represents capil- lary transfer. The right side of Eq A-1 represents moisture storage within the material. The potential for transferring water vapor is the vapor pressure (Pv), with the permeability (ix) serving as a transport coefficient. The potential for trans- ferring liquid water is the capillary pressure (Pl), with the hydraulic conductivity (K) serving as the transport coeffi- cient. The potentials p,, and p] were assumed to be contin- uously consistent with the theory of IEA Annex 24 [4]. The signs on the first two terms are different because water vapor flows in the opposite direction of the gradient in water vapor pressure, and capillary water flows in the same direction as the gradient in capillary pressure. Other symbols contained in the above equation include the dry density of the material
C H A P T E R 8 - - M O I S T : A N U M E R I C A L M E T H O D F O R D E S I G N 1 3 3 (Pd), moisture content (y), distance (y), a n d time (t). The
sorption i s o t h e r m 7 (i.e., the relationship between equilib- r i u m moisture content a n d relative humidity) and the cap- illary pressure curve (i.e., the relationship between capillary pressure and moisture content) were used as constitutive re- lations in solving Eq A-1.
I n the c o m p u t e r algorithms, Eq A-1 was recast into two finite-difference e q u a t i o n s - - o n e for the vapor phase a n d the other for the liquid phase. I n the vapor phase equation, the diffusion transport is treated in an implicit way, and the liq- uid t r a n s p o r t is treated in an explicit way. The sorption iso- t h e r m is used as an equation of state. In the liquid t r a n s p o r t equation, the liquid t r a n s p o r t is treated in an implicit way, a n d the v a p o r t r a n s p o r t is treated in an explicit way. The suction pressure curve serves as an equation of state. During each time step, these two equations are solved for the water vapor pressure (Pv) a n d the capillary pressure (Pl). A n e w moisture content is subsequently calculated f r o m these two potentials. This a p p r o a c h was developed by Carsten Peder- sen (now Carsten Rode) a n d is described in Ref 5.
The hydraulic conductivity (K) in Eq A-1 is related to the liquid diffusivity (Dr) by the relation:
K odD~ (A-2)
Opl 0"1
where the t e r m in the d e n o m i n a t o r of the right side of the equation is the derivative of the capillary pressure with re- spect to moisture content. W h e n the t e m p e r a t u r e is below freezing, the liquid diffusivity is taken to be zero.
The t e m p e r a t u r e distribution is calculated f r o m the fol- lowing conservation of energy equation:
( ,
The first t e r m on the left side of Eq A-3 represents c o n d u c - tion, whereas the second t e r m is the latent heat transfer derived f r o m phase change associated with the m o v e m e n t of moisture. The right side of Eq A-3 represents the storage of heat within the material and a c c u m u l a t e d moisture. Sym- bols in the above equation include t e m p e r a t u r e (T), the dry specific heat of the material (ca), the specific heat of water (cw), a n d the latent heat of vaporization (hl~).
I n E q A-l, the water vapor permeability (Ix) a n d the hy- draulic conductivity (K) are strong functions of moisture content. In E q A-3, the t h e r m a l conductivity (k) is also a function of t e m p e r a t u r e a n d moisture content.
A D J A C E N T LAYER
B O U N D A R Y C O N D I T I O N S
The temperature, water-vapor pressure, and capillary pres- sure are c o n t i n u o u s at adjacent material layers.
7In this paper, the sorption isotherm was assumed to be independent of temperature. This is consistent with other heat, air, and moisture transfer models cited in IEA Annex 24 [4]. Some researchers have reported a small effect of temperature on the sorption isotherm [24,29,30].
I N D O O R B O U N D A R Y C O N D I T I O N S
At the i n d o o r b o u n d a r y of the construction, the moisture transfer t h r o u g h an air film and paint layer (or wallpaper) at the i n d o o r surface is equated to the diffusion transfer into the solid material surface, or:
Me.i(Pv,i - Pv) = - ~ - - Opv (A-4)
~v
where the quantities are evaluated at the i n d o o r boundary.
Here, an effective c o n d u c t a n c e (Me.i), defined by:
1
Me'i 1 1 (A-5)
- - + Mt,i Mp,i
has been introduced. The effect of a thin paint layer is taken into a c c o u n t as a surface c o n d u c t a n c e (Mp,i) in series with the convective mass transfer coefficient (Mr:i) associated with the air film.
At the same boundary, the heat transferred t h r o u g h the air film, ignoring the thermal resistance of the paint layer, is equated to the heat c o n d u c t e d into the i n d o o r boundary, giv- ing:
(h,,, + hcs)(T i -- T ) = --k - - OT (A-6) Oy
where all quantities are evaluated at the i n d o o r surface.
O U T D O O R B O U N D A R Y C O N D I T I O N S
At the o u t d o o r b o u n d a r y of the construction, a similar equa- tion is applied to c o m p u t e the moisture transfer. The heat c o n d u c t e d into the o u t d o o r b o u n d a r y and the absorbed solar radiation is set equal to the heat loss to the o u t d o o r air by convection and radiation, or:
- k O T + a H,o l = hc,o(T - To) + hr.o(T - T, ky) (A-7) oy
where all quantities are evaluated at the o u t d o o r surface.
Here hr,o is the radiative heat transfer coefficient defined by the relation:
hr, o = Ecr(T, + Tsky)(Z 2 + rs2y) (A-S) where E is the emittance factor which includes the surface emissivity and the view factor f r o m the o u t d o o r surface to the sky, T s is the surface temperature, a n d Tsky is the sky temperature. The solar radiation (Hsoz) incident onto exterior surfaces having arbitrary tilt a n d orientation was predicted using algorithms given in Duffle and B e c k m a n [15]. The sky t e m p e r a t u r e was calculated using an equation developed by Bliss [16].
V A R I A B L E I N D O O R H U M I D I T Y M O D E L W h e n the interior of a residential building can be m o d e l e d as a single zone with a u n i f o r m t e m p e r a t u e a n d relative hu- midity, the p r o g r a m has an option to permit the i n d o o r rel-
ative humidity to vary during the winter. The variable indoor relative humidity feature is only applicable to residential build- ings and should not be applied to non-residential buildings.
When this option is selected, the indoor conditions are de- termined in the following fashion.
Space Heating Operation
When the daily average outdoor temperature is less than or equal to the balance point temperature for space heating, the house operates in a space-heating mode. The indoor tem- perature is taken to be equal to the heating set-point tem- perature. The indoor relative humidity is permitted to vary and is calculated from an indoor humidity model developed by TenWolde [17].
The rate of moisture production by the occupants is equal to the rate of moisture removed by natural a n d / o r forced ventilation plus the rate of moisture storage at interior sur- faces and furnishings, or:
W = paIJh,t(oJi -b COo) -b K Af(qb i - qbi,x) (A-9) Using the psychometric relationship between humidity ratio (~0) and relative humidity (+) as a constitutive relationship, the above equation may be solved for the indoor relative hu- midity.
The hygroscopic memory (4)i,~) is computed from the scan- ning function:
N - 1
Y, Z(n)+i(n)
n=N 4"r (A-10)
(~i,-r ---~ N - 1
z(n)
n=N-4*
In the above equation, the hygroscopic memory at the cur- rent time step N is found from a past-history relative humidity time series. The time series is evaluated over four time constants (-r). The exponential weighing factors Z(n) are defined as:
Z(n) = e -(N-n)/" (A-11) TenWolde [17] has conducted experiments and determined the sorption constant per unit floor area (K) and the time constant (x) for several manufactured and site-built houses.
The natural ventilation rate for the house is predicted by the single-zone Lawrence Berkeley Laboratory (LBL) infil- tration model developed by Sherman and Grimsrud [18] and described by ASHRAE [2] which is given by:
(/h,, = Lh [CarJTi - To] + Cv V2] ~ (A-12) When mechanical ventilation Vh,m is present, the total ven- tilation rate Vh, t in Eq A-9 is determined by the relation de- veloped by Palmiter and Bond [19]:
IfrVh,~ < 2 rVh,~,r~h,t = r~h,~ + 0.S Vh, m
If (/h..~ >- 2 gh.,,, (/I,,t = 12<m (A-13) It should be noted that in Eq A-13. V<., is the actual mechanical ventilation rate produced by the ventilation equipment installed in the house, as opposed to the rated value. The actual value is typically about half of the rated value (see Tsongas [20]).
In the hourly calculations, the dew-point temperature of the indoor air is compared with the temperature of the in- side glass surface to determine if window condensation oc- curs. When condensation occurs, the vapor pressure of the indoor air is taken to be equal to the saturation pressure at the inside glass surface. The indoor relative humidity is cal- culated from the indoor temperature and vapor pressure us- ing psychrometric relationships.
Space Cooling Operation
When the daily average outdoor temperature is greater than or equal to the balance point temperature for space cooling, the house operates in a space cooling mode. The indoor tem- perature and relative humidity are maintained at constant specified values.
Window Opened Operation
When the daily average outdoor temperature is greater than the balance point for space heating but less than the balance point for space cooling, then neither space heating nor space cooling are required. It is assumed that the windows are opened and the indoor temperature and relative humidity are equal to the outdoor values. When the space cooling equipment is turned off, it was assumed that the occupant will open the windows, and the building again operates in an opened window mode.