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Solving Thermal Bridging Problems for Architectural Applications
with OpenFOAM
Patrick Kastner1, Timur Dogan1
1Environmental Systems Lab, Cornell University, Ithaca, NY, USA, pk373@cornell.edu
Abstract
Although recent advancements in computational architecture
show promising capabilities, it remains difficult for architects
to conduct advanced simulations due to the limited software
interoperability. For thermal bridging analyses, the archi-
tectural community traditionally relies on specific software
tools that are not integrated into a CAD environment. To
integrate such analyses into the ongoing design process, we
implement a software tool to run heat transfer simulations
with OpenFOAM from Grasshopper and Rhinoceros. This
paper presents an implementation for box-shaped geometries
and compares its results to a thermal bridge analysis from a
validated simulation engine. We show that OpenFOAM’s
chtMultiregionFoam solver is capable of accurately predict-
ing temperature distributions in a geometry setup with 13
different regions and 8 different materials. In conclusion, we
show that heat transfer studies can be highly automated and
integrated into an iterative design process.
Author Keywords
Thermal Bridging, Grasshopper, Rhinoceros, OpenFOAM,
Parametric Design, Computational Architecture
Introduction
With the onset of CAD tools, which aimed to reduce repeti-
tive tasks in design, the field of computational architecture
evolved. Soon after, parametric software platforms followed
to control the dimensions of digital objects while bringing
rapid variability into design (Picon et al.,2016). With a
growing number of available simulation tools, the problem
of CAD (Computer-Aided Design) software interoperability
for the export and import of geometries between different
software tools increased over time (Pal,2016). Such inter-
operability impedes the use of advanced simulation tools
during the fast-paced, iterative design process as re-applying
geometric changes throughout the project development is
often cumbersome and time-consuming, if not error-prone.
In regard to heat transfer analyses, there are many software
tools available that range from free options such as THERM
1
and an additional GUI for Ladybug Tools
2
, or Elmer
3
to
paid options like Flixo
4
,HTflux
5
,HEAT3
6
,Psi-Therm
7
,
QuickField
8
,SOLIDO
9
, and AnTherm
10
. Yet, most of those
tools use individual file formats and CAD implementation
which impedes the interoperability between architectural
design and analysis. Further, the free options are inherently
limited to two-dimensional (2D) analyses which might not be
sufficient for some problem statements. To overcome those
impediments, this study uses Rhinoceros and Grasshopper, a
software suite that is widely adopted in architectural design,
to establish a coupling with OpenFOAM to run heat transfer
and thermal bridging analyses.
Heat transfer analyses in architecture
Building performance simulations are necessary to obtain
green building certifications (ASHRAE,2007;DIN,2013).
Although the criteria to be eligible for those certifications
vary from country to country, most of them require a detailed
analysis of the building’s envelope to ensure minimized heat
loss due to thermal bridging.
Thermal bridges
Thermal bridges are discontinuities in the building envelope
that cause an increased overall thermal transmittance and
thus unnecessary heat loss. We refer to them as structural
thermal bridges if materials with different heat conductivities
are conjoining. If this does not apply, we refer to them as
1https://windows.lbl.gov/software/therm
2https://www.ladybug.tools/
3https://www.csc.fi/web/elmer
4https://www.flixo.com/
5https://www.htflux.com/en/
6https://buildingphysics.com/heat3-3/
7https://www.psitherm.uk/
8https://quickfield.com/
9http://www.physibel.be/solido.htm
10http://www.antherm.at/antherm/EN/
geometrical thermal bridges. Thermal bridges in the build-
ing envelope increase the risk of interstitial condensation
and mold growth if temperatures drop below the dew point
and condensation occurs as a result. Material and insulation
degradation, as well as discomfort due to temperature asym-
metries, may be implications of interstitial condensation.
Thus, it is recommended to avoid thermal bridges or at least
understand and constrain their severity whenever possible.
The overall quality of a building envelope is ensured by
reporting the average thermal transmittance, also referred to
as the U-value which for a single layer is defined as:
𝑈=𝑘
𝑑=1
𝑅(1)
where
𝑑
is the thickness of the layer,
𝑘
is the conductivity, and
𝑅
is the thermal resistance. More generally, for a composite
wall with
𝑛
layers, we are able to calculate the thermal
transmittance by summing the reciprocal resistance of each
layer and considering internal and external convective heat
resistances:
𝑈𝑤 𝑎𝑙𝑙 =1
𝑅tot
=1
𝑅s,ext.+
𝑛
Í
𝑖=1
𝑑𝑖
𝑘𝑖+𝑅s,int.
(2)
The influence of thermal bridges on the overall thermal
transmittance of the building envelope can be estimated by
evaluating the Ψ-value which is defined as:
Ψ = Θ
Δ𝑇−
𝑛
Õ
𝑖=1
𝑈𝑖·𝑑𝑖(3)
where
Δ𝑇
is the temperature difference and
𝑑𝑖
is the thickness
of the layer in question. The
Δ𝑇
values used to assess thermal
bridges are usually described in engineering standards such
as DIN, and they are assessed under steady-state conditions.
While the material properties and the temperature in Equa-
tion
(3)
are either given or can easily be chosen, it remains
difficult to estimate the crucial heat flux
Θ
for real-world
geometries without conducting detailed simulations. Thus,
deducing that heat flux via simulations of the goal of this
study. Once the heat flux is known, we are able to report the
reduced thermal transmittance as:
𝑈𝑡𝑜 𝑡 ,𝑟 𝑒𝑑 =Í𝑛
𝑖=1Ψ𝑖·𝑑𝑖
𝐴𝑡𝑜 𝑡
+𝑈𝑤 𝑎𝑙𝑙 ,𝑟 𝑒 𝑓 (4)
Governing equations of heat conduction
The governing equation for heat transfer problems can be
derived from the energy balance over a differential control
volume in Cartesian coordinates
𝑑𝑥 𝑑𝑦 𝑑𝑧
, where
¤
𝐸𝑔
de-
noted the generation term and
¤
𝐸𝑠𝑡
denotes the stored energy
(Bergman et al.,2011):
¤
𝐸𝑖𝑛 +¤
𝐸𝑔−¤
𝐸𝑜𝑢𝑡 =¤
𝐸𝑠𝑡 (5)
Reformulation and simplification yield the “Heat Diffusion
Equation” which can be solved both analytically and numer-
ically.
𝜕2𝑇
𝜕𝑥2+𝜕2𝑇
𝜕𝑦2+𝜕2𝑇
𝜕𝑧2+¤𝑞
𝑘=1
𝛼
𝜕𝑇
𝜕𝑡 , with 𝛼=𝑘
𝜌𝑐 𝑝
(6)
Here,
𝑥, 𝑦,
and
𝑧
are the Cartesian coordinates,
𝛼
is the ther-
mal diffusivity,
¤𝑞
is energy generation rate per unit volume,
and
𝑐𝑝
is the specific heat capacity. While an analytical
solution may be feasible for simple 1D and 2D problems,
3D problems with complex geometries and boundary con-
ditions preclude such approaches. In this study, we use
the open-source software OpenFOAM (Open source Field
Operation And Manipulation) to employ a finite volume
method approach to numerically solving such heat transfer
problems. Although there is a multitude of boundary condi-
tions available in OpenFOAM, we exclusively use Dirichlet
boundary conditions of the form:
𝑇(𝑥, 𝑦, 𝑧)=𝑇𝑠(7)
to specify the surface temperature on boundaries for this
study. These boundary conditions do not account for any
convective heat transfer resistance and are thus considered
to be a simplified approach11, see Equation (2).
Reference case & simulation setup
The reference case simulated in this study stems from an
example project called “Wärmebrücke” (thermal bridge) that
is available in the software tool HTflux
12
. This example
exemplifies a structural thermal bridge due to a wall-to-floor
junction where the insulation material is partly tapered. The
simulation domain consists of 13 adjacent regions with 8
different materials summarized in Table 1. The temperature
boundary conditions were assumed to be steady-state both
internally and externally.
Methodology
Figure 1illustrates the simulation steps that have been
implemented in the Grasshopper C# environment. The steps
necessary to run a simulation can be categorized as pre-
processing (necessary as input by the architect), simulation,
and post-processing. The geometry for this simulation is
modeled in Rhinoceros and is further detailed in Figure 7in
the appendix.
11
For an analysis according to the German DIN/ENEV, one would need
to also specify 𝑅𝑠, 𝑖𝑛𝑡 . and 𝑅𝑠, 𝑒 𝑥𝑡 . .
12
HTflux reports to be “validated under the relevant standards EN ISO
10077-2:2007 and EN ISO 10211-2:2012” (Rüdisser,2018).
Construction
geometry
Boundary conditions ψ-Value estimation
Domain Builder:
Box-shaped domain
with imposed
boundary conditions
Temperature
distribution
Materials
Meshing
Inputs Toolkit
Numerical
simulation
Output
Pre-processing Simulation Post-processing
Figure 1: Flow chart of the simulation steps that have been implemented in the Grasshopper C# environment.
Table 1: Construction material properties used for the
simulation domain illustrated below. The data was taken
from the demo example “Wärmebrücke” (thermal bridge)
that ships with the commercial software tool HTflux (Rüdisser,
2018).
Construction materials 𝑘W
m K 𝑐𝑝hJ
kg K i𝜌hkg
m3i
Concrete (1 % steel reinf.) 2.30 1000 2300
Brick 0.08 920 710
Insulation 0.039 1450 35
Plaster (inside) 0.7 1000 1400
Plaster (outside) 0.87 1100 1800
Perimeter isolation strip 0.87 1100 1800
Cement screed 1.33 1080 2000
Impact sound insulation 0.041 1450 15
Boundary conditions 𝑇[°𝐶]BC type
Inside temperature 20 fixedValue
Outside temperature -5 fixedValue
𝑥
𝑧
Figure 2: Imposed simulation boundaries for the background
mesh (blue) and the internal fixed-temperature boundary
conditions (red).
Pre-processing
During pre-processing, the materials the corresponding prop-
erties from Table 1are chosen and assigned to each region
via user dictionaries. All regions (including air) are modeled
as extrusions with conjoining faces parallel to the x, y, and z-
axis. In other words, every volume in the simulation domain
has to be assigned to either a material with its corresponding
boundary conditions or to air. However, it is not neces-
sary to split the regions into sub-regions with congruent
conjoining surfaces which means that some surfaces may
have multiple adjacent zones (or faces), whereas other zones
might exhibit one adjacent zone per surface. For instance,
the zone with the material Plaster (outside) is adjacent to
3Brick zones along the positive x-direction whereas the
brick zone is adjacent to 1 Plaster (outside) zone along the
negative x-direction, see Table 1. The flexible modeling
of multi-adjacent zones simplifies both the modeling of the
geometry in question and reduces the number of subregions
and faces that need to be created during pre-processing. To
create and export this zonal adjacency graph necessary to
specify all boundary conditions between those zones, Open-
FOAM features the tool changeDictionary which is capable
of testing and reporting the “connectedness” between each
zone. By coupling Rhinoceros and Grasshopper, however,
we solve the cross-reference of all internal geometries from
which OpenFOAM retrieves the combinations needed for
the internal zonal adjacency graph. As a result, there is no
need to make use of changeDictionary.
A unified boundary representation (Brep) of all 13 regions
defines the dimensions for the background mesh. To create
the background mesh, we use the blockMesh tool to create a
voxelized mesh for the highlighted zone in blue in Figure 2.
The resulting structured mesh consists of
1.9 ×106c
ells and
is refined in the x and z-direction. As OpenFOAM inherently
operates on 3D simulation domains, this setup is to be seen as
a section of a wall with symmetry boundary conditions in the
y-direction, and as such representing a quasi-2D case setup.
This quasi-2D case setup was chosen to allow for comparison
against the validated tool HTflux. On all surfaces dashed in
red, a “fixedValue” boundary condition was imposed which
implies that the convective heat transfer resistance between
wall and air on both sides was neglected.
Simulation
For the numerical simulation, we use the chtMultiRegion-
Foam solver from the latest OpenFOAM 6.0
13
release which
is capable of solving “steady or transient fluid flow and
solid heat conduction, with conjugate heat transfer between
regions, buoyancy effects, turbulence, reactions, and radia-
tion modeling.” (Weller et al.,2018). The simulation was
run in a steady-state mode for 200 iterations until sufficient
convergence was reached.
13https://github.com/OpenFOAM/OpenFOAM-6
Post-processing
For post-processing purposes, the case was sampled with
OpenFOAM’s internal postProcess utility and a “cellPoint”
interpolation and plotted along the x-axis for
𝑧=1.58 m
and
𝑧=2.2 m
, see Figure 3. Finally, to calculate the heat
fluxes for each region
𝑖
in Figure 4, Fourier’s law of heat
conduction was used for which
∇𝑇
was sampled from the
simulation results.
𝑞𝑖=−𝑘𝑖∇𝑇(8)
Results
Figure 3shows the temperatures plotted at
𝑧=1.58 m
and
𝑧=2.2 m
for simulations conducted with both OpenFOAM
and Htflux. Similarly, the 2D temperature distributions are
illustrated in Figure 6. For
𝑧=2.2 m
, we predict a piece-
wise linear temperature progression as one would expect
for a steady-state case. For
𝑧=1.58 m
, we predict a piece-
wise, partly non-linear progression due to the difference
in thermal conductivity for floor and ceiling materials. It
is evident that OpenFOAM accurately predicts both the 1-
and 2D temperature changes compared to the validated data
simulated with HTflux for 𝑇𝐻𝑡 𝑓 𝑙𝑢𝑥 ,ℎ =0.
Figure 4depicts the heat flux through the wall-ceiling junc-
tion. This visual representation indicated the effectiveness
of the low-conductive insulation material which insulates
the concrete from the outside. We also see the asymmetric
temperature distribution in the ceiling and floor layers and
the resulting asymmetric heat fluxes towards the insulation
material. To calculate the final
Ψ
value,
𝑞
may be integrated
over the outside boundary and normalized by its length in
m
. The resulting
Θ
in
W m−1
may the be used as input for
Equation (3).
The temperature plots denoted with
𝑇𝐻𝑇 𝑓 𝑙𝑢 𝑥
in Figure 3
depict the temperature distributions for which external and
internal heat transfer coefficients
ℎ
are considered which
was not part of this study. The additional heat transfer
resistances imposed are
𝑅𝑠,𝑒𝑥 𝑡 . =0.04 m2K W−1
for the
external boundary condition and
𝑅𝑠,𝑖 𝑛𝑡 . =0.13 m2K W−1
for the internal boundary conditions. For comparison, taking
into account both additional resistances leads to a temperature
difference of 2°Cat 𝑥=0.25 m.
Figure 5shows the temperature residuals in all zones.
Discussion
The results show that it is possible to use Rhinoceros and
Grasshopper to streamline the pre- and post-processing of
multi-zone architectural heat transfer studies.
The study focused on a linear thermal bridge, that is rep-
resented by a 2D box-shaped problem discretized with
blockMesh. Only a limited number of real-world prob-
lems, however, may be represented with such simplified
box-shaped geometries. OpenFOAM comes with meshing
tools (snappyHexMesh/cfMesh) to produce high-quality, 3D,
(a)
-5
0
5
10
15
20
0 0.2 0.4 0.6 0.8 1
Temperature [°C]
x [m]
T (HTflux)
T (HTflux, h = 0)
T (OpenFOAM)
CAD model
(b)
-5
0
5
10
15
20
0 0.2 0.4 0.6 0.8 1
Temperature [°C]
x [m]
T (HTflux)
T (HTflux, h = 0)
T (OpenFOAM)
CAD model
Figure 3: Temperature plot at z = 2.20 m (a) and z = 1.58 m (b). The plots
𝑇ℎ=0
refer to the variant for which the heat transfer
coefficient was neglected. For the
𝑇𝐻𝑇 𝑓 𝑙𝑢 𝑥
plots,
𝑅𝑠,𝑒𝑥 𝑡 . =0.04 m2K W−1
for the external boundary condition and
𝑅𝑠,𝑖 𝑛𝑡 . =
0.13 m2K W−1for the internal boundary condition was assumed.
unstructured meshes by snapping arbitrary geometries to
the background mesh that has already been used in this
study. This may either be achieved by using the internal
OpenFOAM tools or by importing meshes from other en-
gines as there is an abundance of conversion algorithms
available. While the possibility to produce such meshes
exists, it should be noted that the snapping procedure adds a
level of complexity. We mentioned that all regions need to
constitute extrusions with conjoining faces along the three
axes to ensure a robust convergence. As such, the usage
of snappyHexMesh may likely introduce irregularities at
conjoining surfaces of extrusions that in turn might lead to a
significant decrease in simulation robustness.
Further, we have shown how the heat fluxes can be calculated
by probing
∇𝑇
from the simulation results The necessary
integration to compute the final
Ψ
values could be done
either with OpenFOAM function objects or by manually
probing and integrating
Θ
during post-processing. This
could easily be extended to 3D cases to estimate the thermal
transmittance 𝜒of point thermal bridges.
Finally, we showed that imposing an additional convective
heat transfer coefficient leads to a temperature difference of
2°C
at the internal wall of the wall-ceiling junction. In colder
climates, sub dew point temperature levels may be reached
at internal walls with unfortunate material configurations.
In such cases, the simplified approach presented would
significantly underestimate the temperature distributions.
Apart from that, condensation in insulation materials might
degrade their thermal resistance over time. A fully transient
approach that takes into account moisture transfer should be
considered to be the gold standard.
For highly-accurate results, it is, therefore, necessary to
consider the full spectrum of heat transfer modes (conductive,
convective and radiative) with a transient approach coupled
with moisture transport.
Conclusion
In this study, Rhinoceros and Grasshopper were used as a
pre-/post-processing interface to use OpenFOAM for heat
transfer studies of box-shaped, multi-zone architectural ge-
ometries. By comparison with an example case from a
well-established and validated software tool, it was shown
that OpenFOAM’s chtMultiregionFoam solver is capable of
accurately predicting temperature distributions in a geome-
Figure 4: Heat flux through center regions calculated with
OpenFOAM. It is evident how the insulation material impedes
the heat flux from in the concrete from penetrating the outside
layers of the building envelope.
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0 20 40 60 80 100 120 140
Residual
Iteration
TZone13
TZone10
TZone9
TZone0
TZone1
TZone2
TZone3
TZone4
TZone5
TZone6
TZone7
TZone8
Figure 5: Temperature residuals of all zones.
try setup with 13 different regions and 8 different materials.
In conclusion, heat transfer analyses with OpenFOAM can
be highly automated and integrated into an iterative archi-
tectural design process. Although we were able to show
excellent agreement of simulation results for a simplified set
of boundary conditions, it is worth noting the limitations
of the current implementation: thus far, only box-shaped
geometries and fixed-temperature boundary conditions have
been presented and compared to validated data which does
not necessarily represent the temperature distribution that
would occur in presence of convective and radiative heat
losses/gains.
The chtMultiRegionFoam solver is not only equipped with
transient simulation capabilities but also supports conjugate
heat transfer. These capabilities should be explored to vali-
date both the transient behavior and the interplay of conjugate
heat transfer phenomena. Further, the illustration of heat
flux through the wall-ceiling junction in Figure 4was created
manually by applying Fourier’s law of heat conduction to
every zone in the simulation domain. Since the heat flux is
necessary to calculate the
Ψ
values, more time should be
spent on automatically extracting the heat flux from the sim-
ulation domain and the subsequent calculation of
Ψ
values.
Moreover, future work should focus on the implementation
of convective and radiative boundary conditions as well as
complex 3D, non-orthogonal geometries.
Nomenclature
𝛼Thermal diffusivity, m2s−1
𝑐𝑝Specific heat capacity, Jkg−1K−1
𝑑Length, m
𝐸Energy, J
ℎHeat transfer coefficient, W m−2K−1
𝑘Thermal conductivity, W m−1K−1
ΨLinear thermal transm. coeff., W m−1K−1
ΘHeat flux, W m−1
𝑞Heat flux density, Wm−2
¤𝑞
Energy generation per unit volume,
W m−3
𝑡Time, s
𝑅Thermal resistance, m2K W−1
𝑇Temperature, °C
𝑈Thermal transmittance, W m−2K−1
𝜒Point thermal transmittance, W K−1
𝑥, 𝑦, 𝑧 Cartesian coordinates, m
References
ASHRAE (2007). Ashrae standard 90.1.
Bergman, T. L., A. S. Lavine, F. P. Incropera, and D. P.
Dewitt (2011). Fundamentals of heat and mass transfer.
DIN (2013). Din en 4108-2:2013.
Pal, S. (2016). Is the CAD Interoperability Prob-
lem Over? URL: https://www.engineersrule.com/is-the-cad-
interoperability-problem-over/. Last visited on 2018/10/12.
Picon, A., A. Menges, and F. Aish (2016). Advancements in
Design Computation. URL: https://www.aaschool.ac.uk/VIDEO/
lecture.php?ID=3376. Last visited on 2018/10/12.
Rüdisser, D. (2018). HTflux: Hygric and thermal simulation.
https://www.htflux.com.
Weller, H., C. Greenshields, and C. de Rouvray (2011-
2018). Openfoam - The OpenFOAM Foundation. https://
openfoam.org/.
Appendix
(see following pages)
Simulated temperature distributions
(a)
(b)
(c) (d)
Figure 6: Temperature distributions of the analyzed geometry simulated with both HTflux (left) and OpenFOAM (right): (a)
Overview HTflux; (b) Overview (OpenFOAM); (c) Geometric detail with isotherms (HTflux); (d) Geometric detail with isotherms
(OpenFOAM). As can be seen by comparing left and right, OpenFOAM is able to accurately predict the reference temperature
distribution.
CAD model
Figure 7: CAD model