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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