Effective
Moisture Penetration Depth (EMPD) Model[LINK]
Moisture has little effect on heating system performance,
but a profound effect on the performance of air conditioning
systems. In order to accurately describe building performance
during periods when cooling is needed, it is very important to
know the moisture conditions of the building. If one assumes
that all building moisture is contained in the room air, then
one ignores the fact that the materials that bound the room
(e.g. wall surfaces, furnishings, linens, etc.) store and
release moisture. Thus, to assume that the only moisture that
effects cooling system performance is contained in the room
air is a false, and it can lead to significant error in the
prediction of room moisture conditions and cooling system
loads.
The EMPD (Effective Moisture Penetration Depth) model is a
simplified, lumped approach to simulate surface moisture
adsorption and desorption.
EMPD Model Description[LINK]
The EMPD concept assumes that a thin layer (δM)
close to the wall surface behaves dynamically and exchanges
moisture with the air domain when exposed to cyclic air
moisture pulses. For short periods where the cyclic integral
of the total moisture adsorption and desorption is near zero
(i.e. there is no net moisture storage), the EMPD concept has
been shown to be a reasonable approximation of reality
(Kerestecioglu et al, 1989). In other words, the following
constraint must be met:
where, τ2-τ1 denotes the finite time
interval over which the equation holds. The EMPD model assumes
no spatial distribution of moisture content across the
thickness (L) of the solid; rather, a thin layer
(δM) of uniform moisture content (U) is assumed to
represent the total moisture content of the solid. This may be
mathematically stated as:
For most building materials, the equilibrium moisture
sorption isotherm can be defined by the following general
equation (Kerestecioglu et al. 1988):
where
and
Given that U=U(W*,T*), the moisture
content may be differentiated with respect to time in the
following manner:
where AT and Bρ are the isothermal
moisture capacity and thermo-gradient coefficient,
respectively. From Eqs. , and , they can be expressed as:
and
The lumped mass transfer equation for the i-th solid domain
may be written as
Using Eqs. , , and , one obtains the final equation needed
for closure moisture transfer at internal surface.
The energy equation for the envelope contains the surface
temperature and is given by the conduction equation
with the boundary conditions at interior surface
A more detailed account of the numerical solution procedure
can be found in Kerestecioglu et al. (1988).
EMPD Value
Determination[LINK]
An effective moisture penetration depth may be determined
from either experimental or detailed simulation data by using
actual surface areas and moisture vapor diffusivity. An
empirical function derived from the detailed simulation may be
used to determine the EMPD value (Kerestecioglu et al,
1989):
where
Figure 16 gives the EMPD values to be used for various
vapor diffusivities evaluated at different ambient
excitations.
EMPD Nomenclature[LINK]
A= Area [m2]
AT= Isothermal moisture capacity
[m3/kg]
Bρ= Thermo-gradient coefficient [kg/kg-K]
Cp= Specific heat [J/kg.K]
hM= Convective mass transfer coeff.
[kg/m2-s]
hT= Convective heat transfer coeff.
[W/m2-K]
k= Thermal conductivity [W/m-K]
L= Length [m]
q”T= Imposed heat flux [W/m2]
Rv= Ideal gas constant [461.52 J/kg-K]
T= Temperature [K]
U= Moisture content [kg/kg]
W= Humidity ratio [kg/kg]
Greek letters[LINK]
δM= Effective penetration depth for moisture
equation [m]
λ= Heat of vaporization [J/kg]
ρ= Density [kg/m3]
τ= Time [s]
φ= Relative humidity [0 to 1]
ξ= Ambient moisture excitation rate [1/h]
Subscripts and
superscripts[LINK]
a= Air
b= Bulk
* = Surface
i= i-th surface
Kerestecioglu, A., Swami, M., Dabir, R., Razzaq, N., and
Fairey, P., 1988, “Theoretical and Computational Investigation
of Algorithms for Simultaneous Heat and Moisture Transport in
Buildings,” FSEC-CR-191-88, Florida Solar Energy Center, Cape
Canaveral, FL.
Kerestecioglu, A., M. Swami and A. Kamel, 1989,
“Theoretical and Computational Investigation of Simultaneous
Heat and Moisture Transfer in Buildings: Effective Penetration
Depth Theory.” ASHRAE Winter Meeting, Atlanta, GA.
Kerestecioglu, A., M. V. Swami, P. Brahma, L. Gu, P.
Fairey, and S. Chandra, 1989, “FSEC 1.1 User’s Manual,”
Florida Solar Energy Center, Cape Canaveral, FL
Effective Moisture Penetration Depth (EMPD) Model[LINK]
Overview[LINK]
Moisture has little effect on heating system performance, but a profound effect on the performance of air conditioning systems. In order to accurately describe building performance during periods when cooling is needed, it is very important to know the moisture conditions of the building. If one assumes that all building moisture is contained in the room air, then one ignores the fact that the materials that bound the room (e.g. wall surfaces, furnishings, linens, etc.) store and release moisture. Thus, to assume that the only moisture that effects cooling system performance is contained in the room air is a false, and it can lead to significant error in the prediction of room moisture conditions and cooling system loads.
The EMPD (Effective Moisture Penetration Depth) model is a simplified, lumped approach to simulate surface moisture adsorption and desorption.
EMPD Model Description[LINK]
The EMPD concept assumes that a thin layer (δM) close to the wall surface behaves dynamically and exchanges moisture with the air domain when exposed to cyclic air moisture pulses. For short periods where the cyclic integral of the total moisture adsorption and desorption is near zero (i.e. there is no net moisture storage), the EMPD concept has been shown to be a reasonable approximation of reality (Kerestecioglu et al, 1989). In other words, the following constraint must be met:
where, τ2-τ1 denotes the finite time interval over which the equation holds. The EMPD model assumes no spatial distribution of moisture content across the thickness (L) of the solid; rather, a thin layer (δM) of uniform moisture content (U) is assumed to represent the total moisture content of the solid. This may be mathematically stated as:
For most building materials, the equilibrium moisture sorption isotherm can be defined by the following general equation (Kerestecioglu et al. 1988):
where
and
Given that U=U(W*,T*), the moisture content may be differentiated with respect to time in the following manner:
where AT and Bρ are the isothermal moisture capacity and thermo-gradient coefficient, respectively. From Eqs. , and , they can be expressed as:
and
The lumped mass transfer equation for the i-th solid domain may be written as
Using Eqs. , , and , one obtains the final equation needed for closure moisture transfer at internal surface.
The energy equation for the envelope contains the surface temperature and is given by the conduction equation
with the boundary conditions at interior surface
A more detailed account of the numerical solution procedure can be found in Kerestecioglu et al. (1988).
EMPD Value Determination[LINK]
An effective moisture penetration depth may be determined from either experimental or detailed simulation data by using actual surface areas and moisture vapor diffusivity. An empirical function derived from the detailed simulation may be used to determine the EMPD value (Kerestecioglu et al, 1989):
where
Figure 16 gives the EMPD values to be used for various vapor diffusivities evaluated at different ambient excitations.
EMPD Nomenclature[LINK]
A= Area [m2]
AT= Isothermal moisture capacity [m3/kg]
Bρ= Thermo-gradient coefficient [kg/kg-K]
Cp= Specific heat [J/kg.K]
hM= Convective mass transfer coeff. [kg/m2-s]
hT= Convective heat transfer coeff. [W/m2-K]
k= Thermal conductivity [W/m-K]
L= Length [m]
q”T= Imposed heat flux [W/m2]
Rv= Ideal gas constant [461.52 J/kg-K]
T= Temperature [K]
U= Moisture content [kg/kg]
W= Humidity ratio [kg/kg]
Greek letters[LINK]
δM= Effective penetration depth for moisture equation [m]
λ= Heat of vaporization [J/kg]
ρ= Density [kg/m3]
τ= Time [s]
φ= Relative humidity [0 to 1]
ξ= Ambient moisture excitation rate [1/h]
Subscripts and superscripts[LINK]
a= Air
b= Bulk
* = Surface
i= i-th surface
References[LINK]
Kerestecioglu, A., Swami, M., Dabir, R., Razzaq, N., and Fairey, P., 1988, “Theoretical and Computational Investigation of Algorithms for Simultaneous Heat and Moisture Transport in Buildings,” FSEC-CR-191-88, Florida Solar Energy Center, Cape Canaveral, FL.
Kerestecioglu, A., M. Swami and A. Kamel, 1989, “Theoretical and Computational Investigation of Simultaneous Heat and Moisture Transfer in Buildings: Effective Penetration Depth Theory.” ASHRAE Winter Meeting, Atlanta, GA.
Kerestecioglu, A., M. V. Swami, P. Brahma, L. Gu, P. Fairey, and S. Chandra, 1989, “FSEC 1.1 User’s Manual,” Florida Solar Energy Center, Cape Canaveral, FL
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