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Research Article Advances in Modeling and
Simulation Tools
E-mail: 20101@tongji.edu.cn
Integration of moisture effects into urban building energy modeling
Xiaoyu Wang1,2, Pengyu Jie1,2, Ke Zhu1,2, John Grunewald3, Xiaoping Xie3, Xing Jin4, Xin Zhou4, Xing Shi1,2 ()
1. College of Architecture and Urban Planning, Tongji University, No. 1239 Si Ping Road, Shanghai 200092, China
2. Key Laboratory of Ecology and Energy-saving Study of Dense Ha bitat, Ministry of Education, No. 1239 Si Ping Road, Shanghai 200092, China
3. Institute of Building Climatology, Dresden University of Technology, Dresden, 01060, Germany
4. School of Architecture, Southeast University, No. 2 Sipailou, Nanjing 210096, China
Abstract
To address the limitations of current urban building energy modeling (UBEM), which often
neglects moisture effects, we developed a comprehensive roadmap for modeling urban heat and
moisture flows. This effort included developing an urban-scale whole-building heat and moisture
transfer (HAMT) model that considers wind-driven rain, integrated with a microclimate model
known as Urban Weather Generator (UWG). The proposed model was validated through analytical
and comparative cases of whole-building hygrothermal performance analyses from the Annex 41
Project. The integrated whole-building and microclimate HAMT models were applied to a real
urban building to assess the impact of moisture on annual energy predictions in a hot-humid
region of Shanghai. The results show that incorporating moisture effects into the UBEM increases
the annual cooling energy demand by 22.11% (5.92% owing to latent heat loads) and the
annual heating loads by 6.06%, resulting in a 19.73% increase in the total annual energy loads.
Additionally, the outer wall surface temperature decreases during and after rainfall events, with
maximum decreases of 3.23 °C in winter and 8.80 °C in summer. Therefore, integrating moisture
effects into UBEM is crucial, particularly in humid regions.
Keywords
urban building energy modeling
moisture effect
coupled heat and moisture transfer
microclimate
wind-driven rain
Article History
Received: 06 September 2024
Revised: 25 November 2024
Accepted: 05 December 2024
© Tsinghua University Press 2025
1 Introduction
Urban buildings contribute 27% of total greenhouse gas
emissions (IEA 2022). With the carbon neutrality agenda,
cities worldwide are increasingly prioritizing the reduction
of urban building energy demand as a key component of
urban planning, design, and renewal efforts. This heightened
awareness of energy and environmental challenges has
prompted city managers to integrate energy-efficient strategies
into their urban development plans to mitigate the impacts
of building operations on climate change.
In this context, urban building energy modeling (UBEM)
has been attracting increasing attention in recent years
(Ang et al. 2020; Hong et al. 2020a). Various physics-based
UBEM tools have been developed, as illustrated in Figure 1.
Among these UBEM tools, there are primarily two types of
building energy models (BEM): EnergyPlus-based BEM (such
as CityBES (Hong et al. 2016), umi (Reinhart et al. 2013), and
AutoBPS (Deng et al. 2023)) and resistance–capacitance
(RC)-based BEM (such as CitySim (Robinson et al. 2009),
CEA (Fonseca et al. 2016), and UECC (Wang et al. 2024)).
Typical meteorological year (TMY) data are commonly
used as meteorological boundary conditions in these tools.
However, regardless of the specific UBEM tools utilized,
these models typically focus solely on heat flows within
urban buildings while neglecting moisture effects at both
the building and urban microclimate levels.
Comprehensive urban heat and moisture flows within
the UBEM should encompass interactions at both the
building and microclimate levels, as depicted in Figure 2.
At the building level, moisture effects include the coupled
heat and moisture transfer (HAMT) in building walls, internal
moisture sources, indoor moisture exchange through
infiltration and ventilation, wind-driven rain on exterior
surfaces, and moisture exchange between exterior surfaces
and the microclimate. At the microclimate level, moisture
BUILD SIMUL
https://doi.org/10.1007/s12273-025-1226-x
Wang et al. / Building Simulation
2
List of symbols
a matrix coefficients for RH solving
A area (m2)
b matrix coefficients for temperature solving
Cp specific heat capacitance (J·kg−1·K−1)
CL cooling loads (W)
d moisture content of air (kg·kg−1)
Dl liquid water conductivity (s)
DT,T heat transfer coefficient under the effect of
temperature gradient (W·m−1·K−1)
DT,φ heat transfer coefficient under the effect of RH
gradient (W·m−1)
Dφ,T moisture transfer coefficient under the effect of
temperature gradient (kg·m−1·s−1·K −1)
Dφ,φ moisture transfer coefficient under the effect of
RH gradient (kg·m−1·s−1)
g moisture flux (kg·m−2·s −1)
h space mesh size (m)
hfg latent heat of vaporization (J·kg−1)
HL heating loads (W)
MA moisture transmittance (kg·s−1)
Madd humidifying load (kg·s−1)
Mc convective load of internal moisture source
(kg·s−1)
Mde dehumidifying load (kg·s−1)
N air change rate (h−1)
P atmospheric pressure (Pa)
Pc capillary pressure (Pa)
Pv vapor pressure (Pa)
Ps saturation vapor pressure (Pa)
q energy flux (W)
Qir infrared radiation (W·m−2)
QPA constant terms for RH solving
QPB constant terms for temperature solving
Qsun1 energy flux from the sun to the external wall
surfaces (W·m−2)
Qsun2 energy flux from the sun that penetrates into the
zone (W)
Rv specific gas constant of water vapor (J·kg−1·K−1)
Rwdr wind-driven rain (kg·m−2·s−1)
Sc convective load of internal heat source (W)
Sr radiative load of internal heat source (W)
t time (s)
t time step (s)
T temperature (oC)
TK Kelvin temperature (K)
U heat transfer coefficient (W·m−2·K−1)
UA thermal transmittance (W·K−1)
Vzone zone volume (m3)
w mass moisture content of material per volume
(kg·m−3)
wv volumetric moisture content of material per
volume (m3·m−3)
x distance from wall interior surface (m)
Y variable
α convective heat transfer coefficient (W·m−2·K−1)
β convective mass transfer coefficient (s·m−1)
δP water vapor permeability (s)
λ thermal conductivity (W·m−1·K−1)
ξ sorption capacity (kg·m−3)
ρ density (kg·m−3)
τ time step index 1, 2, 3, …
φ relative humidity (—)
Subscripts
a,in indoor air
a,in,dry dry indoor air
a,out outdoor air
cz connected thermal zone
e exterior
g,deep deep ground
i interior
inf infiltration
j space nodes index 0, 1, 2, …
kn total number of nodes for surface n
l liquid water
m material
m,dry dry material
mec mechanical ventilation
n wall surface index 1, 2, 3, …
s,i inner surface
s,i,total total area of inner surface
s,o outer surface
tm total moisture
trans transmittance
v vapor
vent natural ventilation
Abbreviations
AHUs air handling units
BEM building energy model
CFD computational fluid dynamics
CTTC cluster thermal time constant
HAMT coupled heat and moisture transfer
RC resistance–capacitance
RH relative humidity
RMSE root mean square error
SHGC solar heat gain coefficient
TMY typical meteorological year
UBEM urban building energy modeling
UCM urban canopy model
UWG Urban Weather Generator
Wang et al. / Building Simulation
3
effects encompass HAMT in the ground, evapotranspiration
from vegetation, reservoir evaporation, and various moisture
sources, such as traffic exhaust and moisture from air
handling units or central plants (e.g., cooling towers).
A substantial amount of research has been dedicated to
studying the influence of moisture on energy performance
at the individual building scale (Steeman et al. 2010a, 2010b;
Tariku et al. 2010; Qin and Yang 2016). The previous studies
in the literature can be summarized as the development of
HAMT models based on various moisture driving potentials.
These include material moisture content (Philip and De
Vries 1957), water vapor pressure (Busser et al. 2019), water
vapor density (Talukdar et al. 2007), relative humidity (RH)
(Wang et al. 2020; Wang et al. 2021), and capillary pressure
(Pedersen 1992). Theoretically, models with different moisture
driving potentials could be equivalently transformed based
on their interrelationships. Therefore, the accuracy of the
numerical models with different moisture driving potentials
is theoretically equal. However, those utilizing RH as the
moisture driving potential are particularly favored owing
to the ease of determining RH. Notably, the Künzel model,
which employs the RH as the driving potential, has been
widely implemented in several commercial software packages
for building energy simulations, such as COMSOL, WUFIPlus,
and EnergyPlus. Numerous studies have highlighted the
importance of considering the effects of moisture in building
energy simulations (Liu et al. 2015; Xia et al. 2023; Hu et al.
2024). Liu et al. (2015) indicate that when moisture transfer
is ignored, the total cooling, heating, and yearly energy
load are underestimated by 9.9%–34.4%, 1.7%–4.0%, and
5.2%–6.8%, respectively. In Xia et al. (2023), it is shown that
the cooling and dehumidification energy demands could be
underestimated by 8.4% and 12.4%, respectively, without
considering the HAMT in hot-humid regions. The similar
conclusion was obtained in Hu et al. (2024). Although these
conclusions were drawn at the individual building level,
it could be inferred that the impact of moisture should
not be overlooked when extending to urban-scale building
energy simulations. However, existing BEMs that consider
moisture effects for individual buildings cannot be directly
applied to urban-scale building energy simulations with
moisture effects. These models neglect the interactions
Fig. 2 Schematic diagram of urban heat and moisture flows
Fig. 1 Development timeline of physics-based UBEM tools
Wang et al. / Building Simulation
4
between buildings, such as mutual shading (Wang et al.
2023), and the interactions between buildings and the urban
microclimate (Hong et al. 2020b), as shown in Figure 2.
Three main types of microclimate models exist:
computational fluid dynamics (CFD) (Kubilay et al. 2018;
Toparlar et al. 2018), urban canopy models (UCM) (Fabiani
et al. 2019; Conigliaro et al. 2021; Liu et al. 2020; Wang et al.
2022), and cluster thermal time constant (CTTC) models
(Swaid and Hoffman 1990). Each model handles moisture
effects in the urban microclimate differently. The CTTC
model considers the impact of vegetation evapotranspiration
and water body evaporation on temperature but does not
account for humidity. The UCM, based on Monin-Obukhov
similarity theory, accounts for turbulent heat and moisture
exchange between the air within the urban canopy and
surfaces such as buildings, ground, and vegetation, making
it suitable for rapid microclimate calculations at the
neighborhood scale. The CFD model uses the finite volume
method to iteratively solve for variables such as temperature,
wind speed, and RH, incorporating the effects of vegetation
and water bodies as source terms. This allows accurate
calculation of the urban microclimate with a high spatial
resolution of a few meters. However, integrating CFD
models as meteorological boundary conditions into the
BEM for annual hourly energy predictions is challenging
owing to their high computational costs (Katal et al. 2019).
This could explain why almost all UBEM tools ignore
microclimate effects and instead use TMY as a meteorological
boundary condition (Robinson et al. 2009; Reinhart et al.
2013; Fonseca et al. 2016; Hong et al. 2016; Deng et al. 2023;
Wang et al. 2024)
In summary, the existing UBEMs focus solely on heat
flows within urban buildings, neglecting moisture effects at
both building and urban microclimate levels. Therefore, the
main purpose of this study is to integrate moisture effects
into UBEMs. To the best of our knowledge, this is the first
study to incorporate moisture effects into UBEMs. To achieve
this, a roadmap was developed to comprehensively model
urban heat and moisture flows. This involved developing an
urban-scale whole-building HAMT model integrated with
a microclimate model.
2 Methodology
2.1 Whole-building HAMT model
2.1.1 HAMT model for building envelopes
The governing equations for moisture transfer and heat
transfer in building envelopes, according to the Philipp-De
Vries model (Philip and De Vries 1957), are shown in
Equations (1) and (2), respectively.
()
m
m
tm v l
m
div div
φ
wggg
φt
¶
¶=- =- +
¶¶ (1)
()
()
mm
m,dry p,m,dry m p,l m
fg v
div 0
TT
ρC wC λ
tx x
hg
¶¶ ¶
++-
¶¶ ¶
+=
()
(2)
According to Fick’s law and Darcy’s law, the water vapor
and liquid water fluxes can be expressed as follows :
v
vP
P
gδ
x
¶
=- ¶ (3)
c
ll
P
gD
x
¶
=¶ (4)
The water vapor flux, originally given in Equation (3),
can be reformulated using temperature and RH potentials,
as demonstrated in Equation (5).
m
sm
vPm Ps
K
d
d
φ
PT
gδφ δP
Tx x
¶
¶
=- -
¶¶
(5)
The capillary pressure is dependent on temperature and
relative humidity based on Kelvin’s equation (Equation (6)).
As a result, the liquid water flux represented by Equation (4)
can be reformulated using temperature and RH potentials,
as presented in Equation (7).
()
clvKm
lnPρRTφ=- (6)
()
m
mK
l llv m llv
m
ln φ
TT
gDρRφ DρR
xφ
x
¶
¶
=- -
¶¶
(7)
By substituting Equations (5) and (7) into the governing
equations (Equations (1) and (2)), the novel HAMT model
for building envelopes, utilizing the temperature and RH
potentials, can be derived as shown in Equations (8) and
(9), respectively. Compared to the Künzel model used in
WUFIPlus and EnergyPlus (Künzel 1995), this new model
incorporates a liquid water transfer term driven by the
temperature potential.
,
mm
m
m,T
φφφ
φφ
T
ξD D
tx x x x
¶¶
¶¶ ¶
=+
¶¶ ¶ ¶ ¶
()()
(8)
()
mm
m,dry p,m,dry m p,l T,T
m
T,φ
TT
ρC wC D
tx x
φ
D
x
x
¶¶¶
+=
¶¶ ¶
¶
¶
+¶¶
()
() (9)
where:
()
s
,T P m l l v m
K
dln
d
φ
P
Dδφ DρRφ
T
=+
K
,Psllv
m
φφ
T
DδPDρR
φ
=+
Wang et al. / Building Simulation
5
s
T,T fg P m m
K
d
d
P
Dhδφ λ
T
=+
T, fg P sφ
DhδP=
2.1.2 Indoor humidity and energy balance
The indoor humidity and energy balance equations are
expressed in Equations (10) and (11), respectively. The
humidity balance equation considers the moisture buffering
effects of the building envelope; moisture exchange through
air changes from ventilation, infiltration, and mechanical
ventilation; internal moisture sources; as well as moisture
supply and removal by the equipment. The sorption capacity
of indoor air is defined as the derivative of the moisture
content of air with respect to RH. The moisture content
of air and the sorption capacity of indoor air are given in
Equations (12) and (13), respectively. The total moisture
exchange rates due to air changes from venting, infiltration,
and mechanical ventilation are represented by Equation (14).
The indoor energy balance equation considers several
factors: convective heat exchange between the indoor air and
interior surfaces, heat exchange with the external environment
through transparent envelopes, and heat exchange due to
venting, infiltration, and mechanical ventilation. It also
includes internal heat sources, the latent heat associated with
indoor moisture movement, and the heating and cooling loads
managed by the air-conditioning system. Additionally, the
moisture effect on the air’s heat capacity is also considered.
The total indoor–outdoor heat exchange rates through
windows, venting, infiltration, and mechanical ventilation
are represented by the parameter UA, as specified in
Equation (15).
()
()
a,in
a,in zone i, s,i, s,s,i, a,in s,a,in
surf
a,out a,in c add de
d
d
MA
nn n n
n
φ
ξV βAφ P φP
t
φφ MMM
=
=-
+-++-
å
(10)
()
()
() ( )
()
()
a,in
p,a,in a,in p,v zone a,in i, s,i, a,in
surf
a,out a,in fg c c fg a,out a,in
fg i, s, i, s,s, i, a, in s,a,in fg add de
surf
d
d
UA MA
HL CL
nn n
n
nn n n
n
T
CdCVρ αATT
t
TT hMSh φφ
hβAφPφP hMM
=
=
+=-
+-+++ -
+-+-
+-
å
å
(11)
()
a,in a,in s,a,in a,in a,in s,a,in
0.622dφPPφP=-
(12)
()
()
a,in
a,in a,in,dry
a,in
2
s,a,in a,in a,in s,a,in a,in s,a,in
a,in,dry 2
a,in a,i n s,a,in
0.622 0.622
d
ξρ φ
PP φP φP
ρPφP
¶
=¶
-+
=-
(13)
()
a,in zone vent inf mec
MA 3600ξV N N N=++
(14)
()
()
trans trans
zone a,in p,a,in vent inf mec
UA
3600
UA
VρC N N N
=
+++
å
(15)
2.1.3 Boundary conditions
The Robin boundary condition (i.e., convective boundary
condition) is adopted for interior surfaces of the building.
The moisture and heat balance equations for interior surfaces
are expressed in Equations (16) and (17), respectively. The
convective moisture exchange between indoor air and
interior surfaces is considered to account for the moisture
buffering effects of the interior lining materials. For the
heat flux across the interior surfaces, convective heat exchange,
latent heat due to moisture movement, transmitted solar
radiation and internal heat sources absorbed by the interior
surfaces, and longwave radiation exchange (Yan et al. 2022)
are considered. The transmitted solar radiation and longwave
radiation exchange of each interior surfaces are calculated
based on the method developed in our previous work
(Wang et al. 2024).
()
m
m
surf,i ,T , i, a,in s,a,in s,i, s,s,i,
ii
φφφn nn
φ
T
gD D βφPφP
xx
¶
¶
=- - = -
¶¶
(16)
()( )
()
m
m
surf,i T,T T,
ii
i, a,in s,i, fg i, a,in s,a,in s,i, s,s,i,
sun2 r s,i,total ir,i,
φ
nnn nn
n
φ
T
qD D
xx
αT T hβφP φP
QSA Q
¶
¶
=- -
¶¶
=-+ -
++ + (17)
Different building construction categories exhibit
specific exterior boundary conditions. For the exterior walls,
roofs, and raised floors, factors such as wind-driven rain,
solar radiation, and longwave radiation exchange should be
considered, as shown in Equations (18) and (19). In urban
environments characterized by mutual shading among
buildings, the calculation of direct solar radiation incorporates
shading effects from sun shields, the buildings themselves,
and neighboring buildings, following the methodologies
established in our previous research (Wang et al. 2023).
Regarding the rainfall load and moisture absorption capacity
of building surfaces, if a surface becomes completely wet
(i.e., saturated), its RH will reach 100%. If the surface is not
fully wet and is exposed to the windward side (cosθ < 0), the
wind-driven rain is calculated using the method specified
in ASHRAE 160, as detailed in Equation (20).
()
m
m
surf,e ,T ,
ee
e, a,out s,a,out s,o, s,s,o, w dr,
φφφ
nnnn
φ
T
gD D
xx
βφP φP R
¶
¶
=+
¶¶
=-+
(18)
Wang et al. / Building Simulation
6
()( )
()
m
m
surf,e T,T T,
ee
e, a,out s,o, fg e, a,out s,a,out s,o, s,s,o,
sun1, ir,e, wdr p,l wdr s,o,
φ
nnn nn
nn n
φ
T
qD D
xx
αT T hβφP φP
QQRCTT
¶
¶
=+
¶¶
=-+ -
+++ -
(19)
()
wdr E D L wind,out h
cosRFFFv θR= (20)
where, FE is the rain exposure factor, recommended value
is 1.5; FD is the rain deposition factor, recommended value
is 0.5; FL is the empirical constant, recommended value is
0.2 kg·s/(m3·mm); vwind,out is the reference outside wind speed,
m/s; Rh is horizontal rainfall intensity, mm/s; θ is the angle
between wind direction and the normal to the wall.
The boundary conditions on the outside surfaces of
internal walls, floors, and ceilings are similar to the interior
boundary conditions, as specified in Equations (21) and (22).
()
m
m
surf,e ,T ,
ee
i, ,cz a, ,cz s,a, ,cz s,o, s,s,o,
φφφ
nnn nn
φ
T
gD D
xx
βφP φP
¶
¶
=+
¶¶
=-
(21)
()( )
()
m
m
surf,e T,T T,
ee
i, ,cz a, ,cz s,o, fg i, ,cz a, ,cz s,a, ,cz s,o, s,s,o,
sun2,,cz r,,cz s,i,total,,cz ir,i,,cz
φ
nn n n nn nn
nn n n
φ
T
qD D
xx
αT T hβφP φP
QSA Q
¶
¶
=+
¶¶
=-+ -
++ +
(22)
For slab-on-ground construction, the exterior boundary
conditions are represented by a constant deep-ground
temperature and RH as follows:
s,o, g,deepn
φφ= (23)
s,o, g,deepn
TT= (24)
2.2 Microclimate HAMT model
TMY data are commonly utilized as meteorological boundary
conditions in existing UBEMs, which neglect the effects of
microclimate and moisture. To incorporate moisture effects
into the UBEM, a microclimate HAMT model is essential to
substitute TMY data as meteorological boundary conditions.
In this study, the Urban Weather Generator (UWG) (Bruno
2010; Bruno et al. 2013) is adopted as the microclimate
HAMT model because of its efficiency in microclimate
calculation at the neighborhood and urban scales. This
makes it suitable for use as a meteorological boundary
condition in the UBEMs. The schematic of UWG is shown
in Figure 3. The UWG plugin in Grasshopper is used to
update temperature and RH within TMY data for each
district. Input parameters include the geometric model of
buildings and vegetation, traffic sensible heat, vegetation
latent heat fraction, vegetation albedo, terrain albedo,
terrain thickness, and terrain conductivity. UWG converts
the inputted actual models in GIS into several geometric
parameters, including average height, footprint density,
façade-to-site ratio, tree cover, and grass cover. These five
geometry-related parameters in the UWG are derived from
real geometric models as follows: Average height is derived
from the average height of buildings in the area, typically
extracted from 3D building models. Footprint density is
calculated by dividing the total footprint area of all buildings
by the total site area. Façade-to-site ratio is computed by
dividing the total façade area of all buildings by the total
site area, considering all building façades. Tree cover is the
ratio of tree-covered area to the total site area, often obtained
from remote sensing or GIS data. Grass cover is the ratio of
grass-covered area to the total site area, also derived from
remote sensing or GIS data. This approach allows for the
Fig. 3 Schematic diagram of UWG
Wang et al. / Building Simulation
7
modeling of urban heat island effects, considering the impacts
of vegetation and traffic exhaust at the neighborhood scale
(Xu et al. 2024). It can efficiently generate annual hourly
meteorological EPW data for each district (Yang et al. 2023;
Xu et al. 2024).
2.3 Solution method
The HAMT model for building envelopes, along with the
indoor humidity and energy balance equations, were
discretized using the finite difference method and the
implicit Euler method for the time derivative. The resulting
discretized equations are expressed in Equations (25)–(28).
One must note that, in the nodal equations of heat balance,
the humidity terms (i.e., φτ) are included in the constant
term on the right-hand side of the equation. Similarly, in
the nodal equations of moisture balance, the temperature
terms (i.e., Tτ) are included in the constant term on the
right-hand side of the equation. Although this decouples
the heat and moisture transfer, it can be recoupled through
iterative solving to achieve convergence.
1111
1
,, 1 ,, 1 ,, 1 ,, 1
m
11
222
111
m11 1
,, 1 ,, 1
22
ττττ
τ
φφ j φφ j φ φ j φφ j
τττ
j
jj
ττ ττ
τjj jj
ττ τ
jφTj φTj
DDDD
ξ
φφφ
t
hhh
TT TT
ξφD D
thh
----
-
-+-+
-+
-+-
-- -
+-
+
-++ -
--
=+ -
()
(25)
1111
T,T, 1 m,dry p,m,dry m p,l T,T, 1 T,T, 1
1
22
11
T,T, 1 m,dry p ,m,dry m p,l 1
11
1T,,1
2 2
1
1
T, , 1 2
ττττ
jjj
τ τ
j
j
ττττ
j
jj
τττ
jjφj
ττ
jj
τ
φj
DρCwCDD
TT
t
hh
DρCwC φφ
TTD
t
hh
φφ
Dh
----
-+-
-
--
+ +
--
++
-
-
-
++
-+ +
+-
-= +
-
-
()
(26)
1
a,in zone 1
i, s,a,in a,in
surf
1
a,in zone
11
i, s,0, 0 , a,in
surf
a,out c add d e
MA
MA
τ
ττ ττ
nn
n
τ
τττ τ
nn nn
n
ττ τ τ τ
ξV βAP φ
t
ξV
βAPφ φ
t
φMMM
-
-
=
-
--
=
++
-=
+++-
å
å
()
(27)
()
()
()
a,in
1
p,a,in p,v zone a,in 1
i, a,in
surf
1
p,a,in a,in p,v zone a,in
11
i, 0, a,in
surf
1
a,out fg i, 0, s,0 , a,in s,a,in
surf
fg a,out a,
UA
UA
MA
τ
τττ
nn
n
τ
ττ τ
nnn
n
ττ τ τ τ τ τ
nn n n
n
ττ
CdCVρ αAT
t
CdCVρ
αAT T
t
ThβAφPφP
hφφ
-
-
=
-
--
=
-
=
+++
+
-=
++ -
+-
å
å
å
()
() ( )
in fg c fg add de
cHL CL
ττττ
τττ
hM h M M
S
++ -
++ - (28)
The supplementary boundary node method was
adopted to establish boundary nodal equations to achieve
second-order accuracy. A schematic of the supplementary
boundary node method is shown in Figure 4. The resulting
discretized equations for the interior and exterior surface
nodes are as follows:
1
,,1
11
i, s,a,in a,in 1, i, ,0 0,
1
,,1 1, 1,
1
1, ,T ,1
2
22
τ
φφ
τττ τ τττ
nnnsn
τττ
φφ nn
ττ
nφ
D
βPφ φ βPφ
h
DTT
φD
hh
-
--
-
-
-
-
-++
-
-= (29)
()
()
11
T,T,1 T,T,1
11
i, a,in 1, i, 0, 1,
1, 1,
11
T, ,1 fg i, a,in s,a,in 0 , s ,0,
sun2 r s,i,total ir,i,
22
-
2
ττ
ττ τ ττ τ
nnnnn
ττ
nn
ττττττ
φnnn
ττ τ
n
DD
αT T αT T
hh
φφ
DhβφPφP
h
QSA Q
--
--
-
-
--
-+ +-
-
=+
++ + (30)
11
,, 1 ,, 1
1
1e,s, 1
11
11
,T, 1 e, a,out s,a,out wdr,
22
2
nn
nnn n
nn
n
ττ
φφk φφk
ττττ τ
knkk k
ττ
kk
τττττ
φk n n
DD
φβPφ φ
hh
TT
DβφPR
h
--
++
-
-+
+-
--
+
-++
-
=- + + (31)
()
()
11
T,T, 1 T,T, 1
1
-1 e , wdr p ,l 1
1-1
11
T, , 1 e, a,out
1
fg e, a,out s,a,out s,
sun1, ir,e, wdr p,l wdr
22
2
n n
nnn
nn
n
nn
ττ
kk
τττ τ τ
kn k k
ττ
kk
τττ
φk n
τττ ττ
nkk
ττττ
nn
DD
TαRCT T
hh
φφ
DαT
h
hβ φ P φ P
QQRCT
--
++
-
+
+
--
+
-
-+++
-
=- +
+-
+++ (32)
Fig. 4 Schematic diagram of supplementary boundary node
method
Integrating all the nodal equations (Equations (25)–(32)),
two solving matrices are derived for each thermal zone:
one for the temperature nodes of indoor air and building
envelopes, and the other for the RH nodes of indoor air and
building envelopes, as presented in Equations (33) and (34),
respectively.
Wang et al. / Building Simulation
8
A flow diagram of the numerical calculation process for
the whole-building HAMT model is shown in Figure 5.
Initially, matrix coefficients a and b in Equations (33) and
(34) are updated at each time step based on the temperature
and RH from the previous time step. Following this, the
temperature and RH are iteratively calculated without
111
111
111
11
1,1 1,2 1, 3 1, 4 1, 1 1, 1, 1 1, 1 1, 1, 1
2,1 2,2 2,3 2,4 2, 1 2, 2, 1 2, 1 2, 2, 1
3,1 3,2 3,3 3,4 3, 1 3, 3, 1 3, 1 3, 3, 1
4,1 4,2 4,3 4,4 4, 1 4, 4,
nnn
nnn
nnn
kkk kkk
kkk kkk
kkk kkk
kk
aaa a a a a a a a
aaa a a a a a a a
aaa a a a a a a a
aaaa a a a
-+- +
-+- +
-+- +
-
1
1 1 1 1 11 11 11 1 1 1
1 1 1 1 11 11 11 1 1 1
11
1 4, 1 4, 4, 1
1,1 1,2 1, 3 1, 4 1, 1 1, 1, 1 1, 1 1, 1, 1
,1 ,2 ,3 ,4 , 1 , , 1 , 1 , , 1
1,1 1
nnn
nnn
nnn
kkkk
k k k k kk kk kk kk kk kk
k k k k kk kk kk kk kk kk
kk
aaa
aaaa a a a a a a
aaa a a a a a a a
aa
+- +
--- - --- -+ --- -+
-+- +
++
1 1 11 11 11 1 1 1
111
,2 1, 3 1, 4 1, 1 1, 1, 1 1, 1 1, 1, 1
1,11,21,31,4 1,11, 1,1 1,11, 1,1
,1 ,2 ,3 ,4
...
...
nnn
nnn n n n n nnnnnn
nnn n n
k k kk kk kk kk kk kk
k k k k kk kk kk kk kk kk
kkk k k
aa a a a a a a
aaa a a a a a a a
aaa a a
++ +-+ ++ +-+ ++
--- - --- -+ --- -+
111
111
a,in
1,1
0,1
,1 , , 1 ,1 , , 1
1,1 1,2 1, 3 1, 4 1, 1 1, 1, 1 1, 1 1, 1, 1
...
n n nn nn nn
nnn n n n n nnnnnn
τ
τ
τ
kkkkk kkkkkk
k k k k kk kk kk kk kk kk
φ
φ
φ
φ
aa a aa
aaa a a a a a a a
-
-+- +
+++ + +-+ ++ +-+ ++
é ù
ê ú
ê ú
ê ú
ê ú
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ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ë û
1
1
1
PA,a,in
PA, 1,1
PA,0,1
PA,1,1
1,1
PA
1,1
,1
1,1
1,2
0,2
1,2
1,
0,
1,
1,
,
1,
n
n
n
τ
τ
k
τ
k
τ
k
τ
τ
τ
τ
n
τ
n
τ
n
τ
kn
τ
kn
τ
kn
Q
Q
Q
Q
Q
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
-
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+
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ëû
1
1
1
,1,1
PA, ,1
PA, 1,1
PA, 1,2
PA,0,2
PA,1,2
PA, 1,
PA,0,
PA,1,
PA, 1,
PA, ,
PA, 1,
n
n
n
k
k
k
n
n
n
kn
kn
kn
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
-
+
-
-
-
+
é
ù
ê
ú
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(33)
111
111
111
11
1,1 1,2 1, 3 1, 4 1, 1 1, 1, 1 1, 1 1, 1, 1
2,1 2,2 2,3 2,4 2, 1 2, 2, 1 2, 1 2, 2, 1
3,1 3,2 3,3 3, 4 3, 1 3, 3, 1 3, 1 3, 3, 1
4,1 4,2 4,3 4,4 4, 1 4, 4,
nnn
nnn
nnn
kkk kkk
kkk kkk
kkk kkk
kk
bbbb b b b b b b
bbb b b b b b b b
bbb b b b b b b b
bbb b a b b
-+- +
-+- +
-+- +
-
1
1 1 1 1 11 11 11 1 1 1
11 1 1 11 1111 1 1 1
11
1 4, 1 4, 4, 1
1,1 1,2 1, 3 1,4 1, 1 1, 1, 1 1, 1 1, 1, 1
,1 ,2 ,3 ,4 , 1 , , 1 , 1 , , 1
1,1 1
nnn
nnn
nnn
kkkk
k k k k kk kk kk kk kk kk
k k k k kk kk kk kk kk kk
kk
bbb
bbbb b b b b b b
bbbb b b b b b b
bb
+- +
-- -- --- -+ --- -+
-+- +
++
1 1 11 11 11 1 1 1
111
1
,2 1, 3 1, 4 1, 1 1, 1, 1 1, 1 1, 1, 1
1,1 1,2 1, 3 1, 4 1, 1 1, 1, 1 1, 1 1, 1, 1
,1 ,2 ,3 , 4 ,
nnn
nn n n n n n nnnnnn
nn n n n
k k kk kk kk kk kk kk
k k k k kk kk kk kk kk kk
kk kk kk
bb b b b b b b
bbbb b b b b b b
bbbb b
++ +-+ ++ +-+ ++
-- -- --- -+ --- -+
-
11
111
a,in
1,1
0,1
1,1
1, ,1 ,1, ,1
1,1 1,2 1, 3 1, 4 1, 1 1, 1, 1 1, 1 1, 1, 1
n n nn nn nn
nnnn n n n nnnnnn
τ
τ
τ
τ
kk kk kk kk kk
k k k k kk kk kk kk kk kk
T
T
T
T
T
bb b bb
bbbb b b b b b b
-
+- +
+++ + +-+ ++ +-+ ++
é ù
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1
1
1
1
PB,a,in
PB, 1,1
PB,0,1
PB,1,1
PB, 1,
1,1
,1
1,1
1,2
0,2
1,2
1,
0,
1,
1,
,
1,
n
n
n
τ
k
k
τ
k
τ
k
τ
τ
τ
τ
n
τ
n
τ
n
τ
kn
τ
kn
τ
kn
Q
Q
Q
Q
Q
T
T
T
T
T
T
T
T
T
T
T
-
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1
1
1
PB, ,1
PB, 1,1
PB, 1,2
PB,0, 2
PB,1,2
PB, 1,
PB,0,
PB,1,
PB, 1,
PB, ,
PB, 1,
n
n
n
k
k
n
n
n
kn
kn
kn
Q
Q
Q
Q
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+
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(34)
Wang et al. / Building Simulation
9
heating/cooling loads to achieve a convergence error of
1e−4. Next, the computed indoor air temperature and RH
are compared with the set-point values. Following this, the
sensible and latent loads are determined by recalculating
Equations (33) and (34) using the indoor air temperature
and RH as known variables. A sensitivity analysis indicated
that using a uniform grid size of 1 mm and a time step
of 100 s achieved the optimal balance between calculation
accuracy and efficiency for the cases studied in this paper.
To enhance the efficiency of matrix solving, the TensorFlow
library in Python was used to execute parallel matrix
operations on the GPU. The entire program was written in
Python.
3 Case studies
3.1 Case 1: analytical verification case
The analytical verification cases from the Annex 41 Project,
known as “Moisture BESTEST” Case 0A and Case 0B (Ruut
and Rode 2004, 2005; Rode et al. 2006; Tariku et al. 2010),
were used to validate the proposed whole-building HAMT
model. Figure 6 shows the schematic of these verification
cases. The building is designed without windows, and all
external surfaces are exposed to outdoor conditions
with a temperature of 20 °C and a RH of 30%. The initial
conditions are set at 20 °C and 30% RH. The entire building
envelope is constructed from a 150 mm thick layer of aerated
concrete, with material properties including a density of
650 kg/m, thermal conductivity of 0.18 W/(m·K), heat
Fig. 6 Schematic diagram of analytical verification cases
capacity of 840 J/(kg·K), vapor permeability of 3e−11 s, and
a sorption curve defined as wv = 0.042965φ m/m. The
infiltration rate is kept at a constant of 0.5 ACH throughout
the day. The indoor moisture source is 500 g/h from 9 a.m.
to 5 p.m.
In Case 0A, there are no moisture exchanges between the
wall surfaces and air, meaning that the moisture buffering
effects of the building envelope are not considered. In
contrast, Case 0B includes moisture exchange between the
indoor air and the interior wall surfaces, accounting for the
moisture buffering effects of the interior lining materials.
It should be noted that these moisture exchange processes
occur under isothermal conditions of 20 °C, with the
moisture transfer coefficient for the interior surfaces set at
2e−8 s/m.
3.2 Case 2: comparative case—whole building
hygrothermal analysis
A comparative case study of the whole-building hygrothermal
Fig. 5 Flow diagram of numerical calculation process for whole building HAMT model
Wang et al. / Building Simulation
10
performance among various HAMT models was conducted
to further validate the novel model. This comparative
case, known as the Common Exercise (Case 3) in the
Annex 41 project (Ruut and Rode 2004, 2005; Rode et al.
2006; Tariku et al. 2010), features a building with two
south-facing windows, unlike the analytical verification
cases, as depicted in Figure 7. The entire building envelope
is also made of a 150 mm thick layer of aerated concrete, but
the hygrothermal properties of the material are more realistic
compared with analytical cases, as listed in Table 1.
In this case, the building’s exterior surfaces are exposed
to actual weather conditions, with both shortwave and
longwave radiation taken into account. The weather data
is based on conditions in Copenhagen, Denmark (55.37° N,
12.4° E), using information from IWEC weather files. Heat
and moisture exchanges occur at both interior and exterior
surfaces. The heat and moisture transfer coefficients for
interior surfaces are 8.3 W/(m·K) and 2e−8 s/m, respectively,
while for exterior surfaces, they are 29.3 W/(m·K) and
6.25e−8 s/m. Both convective and longwave radiation
Fig. 7 Schematic diagram of comparative case
exchanges are included in the heat exchange coefficients.
The window’s solar heat gain coefficient is set to 1, with
a U-value of 3 W/(m·K), and the solar absorptance of
exterior surfaces is 0.6. Initial conditions are set to 20 °C
and 80% RH. The infiltration rate remains constant at 0.5
ACH throughout the day. Heat and moisture sources are
maintained at 800 W and 500 g/h, respectively, from 9 a.m.
to 5 p.m. The indoor temperature is consistently regulated
between 20 and 27 °C throughout the day.
3.3 Case 3: real urban building case
The integrated whole-building and microclimate HAMT
models was applied to a real urban network at Tongji
University to assess the impact of moisture on annual
building performance, as shown in Figure 8. This city block
is located on No. 1239 Si Ping Road, Shanghai (31.285° N,
121.498° E), China. The sample building, highlighted in
green, is an office building measuring 21.5 m × 13 m × 10 m
with three floors. The first layer is 4 m and the remaining
two layers are 3 m. The effects of vegetation (represented
by a white square in the model) on the microclimate are also
incorporated in this case. The sample building faces south,
with a window-wall ratio of 0.5, for each exterior wall, and
large isometric windows centrally located on each floor’s
exterior walls. The zoning algorithm designates one thermal
zone per floor, resulting in three thermal zones.
The construction details of the building envelope and
the fundamental hygrothermal properties of the materials
are provided in Tables 2 and 3, respectively. The hygrothermal
properties are obtained from the Delphin material database.
Table 1 Hygrothermal properties of aerated concrete in comparative case
Conductivity
(W·m−1·K−1)
Density
(kg·m−3)
Specific heat
(J·kg−1·K−1)
Sorption isotherm
(m3·m−3)
Vapor permeability
(s)
0.18 600 840 11.99
v
ln
0.3 1 0.0011
φ
w-
=-()
(
)
11 2
vv
P23
v
vv
1 10 51.00426 5192.35845 450032.86298
19.32674 794.93556 55114.8639 62770.85367
ww
δww w
-
⋅-+
=-+ -
Fig. 8 Urban building case of Tongji University in real city block
Wang et al. / Building Simulation
11
Table 2 Building envelope construction and fundamental material properties
Element
Conductivity
(W·m−1·K−1)
Thickness
(m)
Density
(kg·m−3)
Specific heat
(J·kg−1·K−1)
Solar
absorptance
Lime cement mortar 0.546·wv+0.803 0.02 1876.1 757.9 0.75
Mineral foam insulation board 0.564·wv+0.045 0.043 125.7 968.4 —
Concrete B25 0.556·wv+2.100 0.1 2320.2 850 —
Exterior wall
(inside to outside)
Lime cement mortar 0.546·wv+0.803 0.025 1876.1 757.9 0.75
Lime cement mortar 0.546·wv+0.803 0.02 1876.1 757.9 0.75
Extruded polystyrene board 0.560·wv+0.030 0.046 40 1500 —
Textile reinforced concrete 0.560·wv+0.804 0.1 1945.4 829.2 —
Roof
(inside to outside)
Lime cement mortar 0.546·wv+0.803 0.02 1876.1 757.9 0.75
Lime cement mortar 0.546·wv+0.803 0.02 1876.1 757.9 0.75
Raised ground
(inside to outside) Cellular concrete 0.560·wv+0.100 0.15 414.6 850 —
Lime cement mortar 0.546·wv+0.803 0.025 1876.1 757.9 0.75
Textile reinforced concrete 0.560·wv+0.804 0.15 1945.4 829.2 —
Interior floor
(inside to outside)
Lime cement mortar 0.546·wv+0.803 0.02 1876.1 757.9 0.75
Lime cement mortar 0.546·wv+0.803 0.02 1876.1 757.9 0.75
Textile reinforced concrete 0.560·wv+0.804 0.15 1945.4 829.2 —
Interior ceiling
(inside to outside)
Lime cement mortar 0.546·wv+0.803 0.025 1876.1 757.9 0.75
Gypsum board 0.56·wv+0.177 0.16 745.1 1825.9 0.70
Wall air gap 0.56·wv+0.138 0.025 1.3 1050 —
Internal wall/mass
Gypsum board 0.56·wv+0.177 0.16 745.1 1825.9 0.70
U (W·m−2·K−1) Solar heat gain coefficient (SHGC)
Exterior window 2.4 0.35
UA infiltration (h−1) UA ventilation (m3·h−1·person−1)
UA infiltration and
ventilation 0.5 25.4844
Table 3 Hygroscopic and moisture transfer properties of construction materials
Lime cement mortar Mineral foam insulation board
Sorption isotherm
(m3/m3)
3
v2
10
0.005 0.052 0.052
φ
wφφ
-
=+- 3
v2
10
6.765584 13.227541 6.469674
φ
wφφ
-
=-+
Vapor
permeability (s)
11
p5.467 10δ-
=⋅
11
p3.05699 10δ-
=⋅
Liquid
conductivity (s)
()
23
v
vv
10 l 23
vv v
46.207978 1050.741736 8104.243861 8615.095664
log 1.859623 42.483922 326.469608 126.533989
ww w
Dwwww
-+ - +
=-+ +
()
23
v
vv
10 l 23
vvv
0.01007 1.624773 25.951626 106.881423
log 0.0004756 0.130162 2.066877 8.684261
ww w
Dwww
-- + -
=+-+
Concrete B25 Extruded polystyrene board
Sorption isotherm
(m3/m3)
523
v23
2.425142 10 4.982037 12.62385 17.488207
17.145343 510.462604 803.365401 276.66111
φφ φ
wφφφ
-
⋅+ + -
=+- + 23
v23
0.0025035 0.02691 0.0613424 0.038721
1.438759 7.234284 11.326834 5.528985
φφφ
wφφφ
-+- +
=-+ -
Vapor
permeability (s)
11
p2.1 10δ-
=⋅ 11
p1.1 10δ-
=⋅
Liquid
conductivity (s)
()
23
vv
10 l 23
vv v
2.461127 322.562514 11306.582918 30731.707955
log 0.081153 11.370181 392.591075 1023.355465
v
www
Dww w
-+ -
=-+ - - 0
Textile reinforced concrete Cellular concrete
Sorption isotherm
(m3/m3)
523
v23
5.086029 10 0.0166235 0.170211 0.152665
0.118469 0.516584 1.883283 1.481291
φφ φ
wφφ φ
-
⋅- + -
=-+ - 11.99
v
ln
0.3 1 0.0011
φ
w
-
=-()
Vapor
permeability (s)
11
p1.92 10δ-
=⋅ 11
p4.16 10δ-
=⋅
Liquid
conductivity (s)
()
23
v
vv
10 l 23
vv
130.483882 2440.170214 14865.911486 29106.452163
log 6.467766 116.292484 667.936354 1185.751095
v
www
Dww w
-+ -
=-+ - +
()
23
v
vv
10 l 23
vv v
0.279391 76.570908 1225.390616 5058.129909
log 0.01397 4.249561 96.517713 373.363814
ww w
Dww w
-- +
=-+ + -
Gypsum board Soil (clayey sandy)
Sorption isotherm
(m3/m3)
23
v23
0.0001637 25.540153 116.0672 88.169691
395.416272 869.969393 10921.675947 9645.326045
φφ φ
wφφφ
-+ - +
=+- + 23
v23
0.0208427 0.0551403 0.0473684 0.0130398
4.258289 13.178838 13.595685 4.674989
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Vapor
permeability (s)
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p1.522 10δ-
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Liquid
conductivity (s)
()
23
v
vv
10 l 23
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22.046983 5096.148312 1692.705614 883.330083
log 1.102349 339.294062 1282.434036 1162.417918
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23.836138 1345.284471 32465.485112 70761.696427
log 1.191868 66.113729 1780.722845 1818.720049
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Wang et al. / Building Simulation
12
The occupancy rate, equipment usage rate, and lighting
usage rate are set to 0.7 from 8 a.m. to 9 p.m. Each person
occupies a floor area of 10 m. The heat dissipation rates
are 134 W/person, 5 W/m for the equipment, and 8 W/m
for lighting. The moisture emission rate per person is 70 g/h.
The heat and moisture transfer coefficients for interior
surfaces are 8.3 W/(m·K) and 2e−8 s/m, respectively, while
for exterior surfaces, these values are 29.3 W/(m·K) and
6.25e−8 s/m. These coefficients include convective and
longwave radiation exchanges. Heating is required from
January 1 to March 15 and from December 1 to December 31,
with the indoor temperature set to 20°C during working
hours. Cooling is required from June 1 to September 30,
with the indoor temperature set to 26°C during working
hours. During transitional seasons, the air-conditioning
system is switched off. Initial conditions are set to 20°C
and 60% RH.
4 Model validation and analyses
4.1 Model validation
Figure 9 depicts the hourly average RH of the indoor air
after reaching a quasi-steady state in Case 1. The numerical
predictions of the novel whole-building HAMT model
show excellent agreement with the analytical solutions for
both Cases 0A and Case 0B obtained from Refs. (Ruut
and Rode 2004, 2005; Rode et al. 2006; Tariku et al. 2010).
In Case 0A, the maximum calculation error of the novel
model was 4.05% RH compared with the analytical results,
whereas in Case 0B, this error was reduced to 0.75%. To
further quantify the discrepancies in RH between the novel
model and the analytical results, the root mean square
error (RMSE) is employed, as shown in Equation (35). The
RMSE values for the novel model, when compared to the
analytical results for Case 0A and Case 0B, are 2.07% and
0.37% RH, respectively, thereby confirming the model’s
accuracy. The fluctuation amplitude of the indoor RH
decreased significantly in Case 0B compared to Case 0A
(from 39.47% to 8.83%), which can be attributed to the
moisture buffering effects of the interior building envelope
components. The increase in indoor humidity at 9 a.m.
was due to moisture generation, whereas the decrease after
5 p.m. resulted from infiltration and the absence of indoor
moisture sources.
()
NewModel, B mark,
RMSE
ii
Y
24 2
ench
1
-
24
i
Y
=
=å (35)
For Common Exercise (Case 3) of the Annex 41 project
(referred to as Case 2 in this paper), the model outputs
including indoor temperature/RH, heating and cooling loads,
and roof exterior surface temperature/RH of our model on
a typical day (July 5th) were compared with those of other
models referenced in Tariku et al. (2010); Ruut et al. (2005);
Rode et al. (2006), as shown in Figure 10. The numerical
results from our model are highlighted in red, whereas all
other models are depicted as black and gray curves. As
illustrated in Figure 10, the numerical results from our model
aligned closely with a cluster of models whose solutions
were in close proximity to one another. The RMSE was
also used to quantify the discrepancies in the numerical
results of the novel model, using the HAMFitPlus model
(Tariku et al. 2010) as the benchmark. The HAMTFitPlus
model is selected as the benchmark in this study due to
its comprehensive consideration of both vapor and liquid
transfer effects on building energy performance, aligning
closely with the influencing factors addressed in our
model. Furthermore, HAMTFitPlus has undergone rigorous
validation using both analytical and observed data,
establishing its reputation as one of the most accurate
whole-building HAMT models. The Finite Element Method
Fig. 9 Hourly average RH of indoor air with quasi-steady state
Wang et al. / Building Simulation
13
in COMSOL was utilized to solve the model. Detailed
information about the solution method can be found in
Tariku et al. (2010). The RMSE values for indoor temperature
and RH of the novel model, when compared to the
HAMFitPlus model, are 0.29°C and 1.78% RH, respectively,
while for the roof’s exterior surface temperature and RH,
the RMSEs are 0.66 °C and 1.07% RH. Additionally, the
RMSE values for heating and cooling loads are 0.068 kWh
and 0.24 kWh, respectively. These results demonstrate that
the proposed whole-building HAMT model is accurate and
suitable for the comprehensive evaluation of whole-building
hygrothermal performance and energy predictions.
4.2 Model analyses
The annual total and hourly peak energy loads with and
without moisture effects in a real urban building were
compared, as shown in Table 4. Shanghai experiences a
hot-humid climate with a plum rain season from the 25th
week to the 29th week, making it suitable for analyzing
moisture effects including wind-driven rain. As shown in
Table 4, incorporating moisture effects in the UBEM results
in a 22.11% increase in annual cooling energy demand
compared with the UBEM that only considers heat transfer,
with 5.92% of this increase attributed to latent heat loads.
Fig. 10 Comparisons of indoor air, roof and energy demand on July 5 with other models
Wang et al. / Building Simulation
14
Additionally, the annual heating loads increased by 6.06%
when moisture effects were considered. Overall, these
changes led to a 19.73% increase in the annual total energy
load after considering moisture effects in the UBEM. The
annual peak hourly heating and annual peak hourly cooling
loads increased by 5.7% and 13.53%, respectively. Several
factors have contributed to these results. First, the increased
thermal conductivity due to moisture effects leads to greater
heat loss. Second, the higher heat capacity resulting from
the effects of moisture requires more energy to maintain the
desired temperature. In addition, the latent heat generated
by moisture movement further increases the overall energy
demand. Compared to the increase in heating loads, the
cooling loads showed a greater magnitude of increase after
considering the effects of moisture. This is because lower
winter temperatures reduce moisture evaporation, resulting
in lower latent heat. Additionally, summer is more humid
than winter owing to continuous rainfall from the 25th to the
29th week in Shanghai. In conclusion, integrating moisture
effects into UBEM is crucial, particularly in humid regions.
Figure 11 compares the outer surface temperature of
the roof with and without moisture effects from February
24 to March 3 in winter and from June 23 to June 30 in
summer. As shown in Figure 11, the outer surface temperature
of the roof decreased during and after the rainfall events.
This is due to the cooling effect of rain during precipitation
and the subsequent evaporative cooling effect. The annual
maximum wall outer temperature decreases after considering
moisture effects are 3.23 °C in winter and 8.80 °C in summer.
These decreases occurred at 2 p.m. on February 15 and
11 a.m. on August 25, respectively, when the evaporative
cooling effect was strongest owing to high solar radiation
and temperature. The greater temperature reduction in
summer compared to winter was due to more intense rainfall
and more significant cooling effects after rainfall events.
5 Conclusions and future work
Moisture effects are often neglected in existing UBEMs at
both building and urban microclimate levels. To address
this limitation, we developed a comprehensive roadmap to
model urban heat and moisture flows. This effort included
the development of an urban-scale whole-building HAMT
model integrated with a microclimate HAMT model, known
as UWG. To the best of our knowledge, this is the first
study to incorporate the effects of moisture into UBEMs.
The proposed model was validated through both analytical
verification and comparative cases of whole-building
hygrothermal performance from the Annex 41 Project. The
integrated whole-building and microclimate HAMT models
were applied to a real urban building at Tongji University
to assess the impact of moisture on annual building
energy predictions. The main conclusions of this study are
summarized as follows.
Table 4 Energy load comparisons with and without moisture effects in real urban building case
Only heat
HAMT
(sensible heat)
HAMT
(latent heat)
HAMT
(total)
Percentage
variation*
Annual heating loads (GJ) 25.097 26.617 0 26.617 +6.06%
Annual cooling loads (GJ) 144.299 167.659 8.538 176.197 +22.11%
Total energy loads (GJ) 169.396 194.276 8.538 202.814 +19.73%
Annual hourly peak heating loads (kW) 51.906 54.866 0 54.866 +5.70%
Annual hourly peak cooling loads (kW) 50.586 54.110 3.319 57.430 +13.53%
* Compared with heat transfer alone, the percentage variation in total loads when considering HAMT.
(a) Winter (February 24 to March 3) (b) Summer (June 23 to June 30)
Fig. 11 Comparisons of roof outer surface temperature with and without moisture effects in real urban building case
Wang et al. / Building Simulation
15
(1) In the analytical and comparative cases from the Annex
41 project, the proposed whole-building HAMT model
aligned well with the analytical results and other
hygrothermal models. It accurately predicted the indoor
temperature, indoor RH, heating/cooling loads, exterior
surface temperature, and RH.
(2) In a real urban building case conducted in the hot-humid
climate of Shanghai, incorporating moisture effects in
the UBEM resulted in a 22.11% increase in the annual
cooling energy demand compared to the UBEM, which
only considers heat transfer, with 5.92% of this increase
attributed to latent heat loads. Additionally, the annual
heating loads increased by 6.06% when moisture effects
were considered. Overall, these changes led to a 19.73%
increase in the annual total energy load after considering
moisture effects in the UBEM. The annual peak hourly
heating and annual peak hourly cooling loads increased
by 5.7% and 13.53%, respectively. Therefore, integrating
moisture effects into UBEM is crucial, particularly in
humid regions.
(3) In the real urban building case conducted in the
hot-humid climate of Shanghai, the wall outer surface
temperature decreases during and after rainfall events.
The annual maximum wall outer temperature decreases
after considering moisture effects are 3.23 °C in winter
and 8.80 °C in summer.
However, these detailed whole-building HAMT models
are complex, making it challenging to predict the energy
usage of hundreds to thousands of urban buildings at a
city scale. To address this issue, we adopted parallel GPU
operations in this study to solve the UBEM matrix. To
further reduce the computational costs, we will explore a
novel whole-building HAMT model based on the RC
method, which we hope will be published in the near future.
Additionally, cases with different envelope components and
climate zones from various countries will be considered to
further capture the effects of moisture in different climate
regions. In our future work, the microclimate HAMT model
will also be improved to consider more moisture sources,
such as water bodies, moisture released from buildings,
based on the urban canopy model.
Data availability
The computational code and data are available from the
corresponding author for academic purposes upon
reasonable request.
Acknowledgements
This paper has received financial support from the National
Natural Science Foundation of China (52478031).
Declaration of competing interest
The authors have no competing interests to declare that are
relevant to the content of this article. Xin Zhou is a Subject
Editor of Building Simulation.
Ethical approval
This study does not contain any studies with human or
animal subjects performed by any of the authors.
Author contribution statement
All authors contributed to the study conception and design.
Material preparation, data collection and analysis were
performed by Xiaoyu Wang, Pengyu Jie, Ke Zhu, John
Grunewald, Xiaoping Xie, Xing Jin, Xin Zhou, Xing Shi.
The first and revised draft of the manuscript was written
by Xiaoyu Wang and all authors commented on previous
versions of the manuscript. All authors read and approved
the final manuscript.
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