Energy & Buildings 224 (2020) 110176
Contents lists available at ScienceDirect
Energy & Buildings
journal homepage: www.elsevier.com/locate/enb
Thermographic 2D U-value map for quantifying thermal bridges
in building façades
Blanca Tejedor a,⇑, Eva Barreira b, Ricardo M.S.F. Almeida b,c, Miquel Casals a
a
Universitat Politècnica de Catalunya (UPC), Department of Project and Construction Engineering, Group of Construction Research and Innovation (GRIC),
C/Colom, 11, Ed. TR5, 08222 Terrassa, Barcelona, Spain
b
CONSTRUCT-LFC, University of Porto, Faculty of Engineering (FEUP), Civil Engineering Department, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
c
Department of Civil Engineering, Polytechnic Institute of Viseu, Campus Politécnico, 3504-510 Viseu, Portugal
a r t i c l e
i n f o
Article history:
Received 23 January 2020
Revised 24 April 2020
Accepted 21 May 2020
Available online 10 June 2020
Keywords:
Quantitative infrared thermography (IRT)
U-value
Thermal bridges
2D map
SURFER
a b s t r a c t
Thermal bridges accounted for 30% of the impact on the energy performance of European residential
building stock. Nevertheless, European countries and their standards do not take into account the influences of this type of anomaly. Furthermore, current methods for quantifying thermal bridges have three
main drawbacks. Firstly, most of approaches consist of complex models based on fluid dynamics or finite
elements as calculation procedure. Secondly, the disturbances of a thermal bridge can’t be assessed along
the vertical and horizontal axis of a wall surface area, since the current methods only allow to perform
local measurements. Thirdly, the stratigraphy and morphology of wall is unknown in most cases.
Hence, this research proposes the implementation of a 2D U-value map to quantify the influence of thermal bridges in three heavy walls by internal quantitative infrared thermography (QIRT). The measurement campaigns were conducted on a walk-in climatic chamber to monitor and evaluate full-scale
building elements. The results demonstrated that the use of 2D U-value maps could help to delimit
the geometry of a thermal bridge as well as its area of greater influence, to quantify the U-value in
any point of an entire wall with acceptable reliability and, to provide real information about the thermal
behaviour of air voids inside opaque façades. Indeed, the U-value results measured by HFM and QIRT
were similar in the inhomogeneous wall areas (from 0.08 to 8.55% of difference in most cases). In this
way, the operational life of a building could be enhanced with specific refurbishment procedures.
Ó 2020 Elsevier B.V. All rights reserved.
1. Introduction
Buildings can contain anomalies that weaken the construction
and impact on energy demand [1–6]. The impact of thermal
bridges (TB) on the energy performance of European residential
building stock has been estimated at 30% [7–9]. According to
dynamic modelling studies, the multidimensional aspects of a TB
are challenging and could represent from 5 to 39% of heat losses
in highly insulated buildings [10–12]. Thermal bridges also affect
external infrared thermography (IRT) evaluations, since 56% of wall
surface temperature measurement errors could be linked to these
heterogeneities [13]. Despite this, the influence of TB is not taken
into account in all European countries and their respective regulations, since the correct calculation procedure of linear thermal
transmittance is quite laborious (especially for the oldest buildings
that require renovation) [4].
⇑ Corresponding author.
E-mail address: blanca.tejedor@upc.edu (B. Tejedor).
https://doi.org/10.1016/j.enbuild.2020.110176
0378-7788/Ó 2020 Elsevier B.V. All rights reserved.
In terms of methodology, several approaches can be distinguished to define the internal composition of a façade and to
obtain a reference value for experimental campaigns: (i) endoscopic analysis to identify the internal structure; (ii) nominal
design data provided by building material databases from standards (theoretical method); (iii) simulation from historical analysis
or analogous buildings; (iv) in-situ measurements by the common
standard method (heat flux meter) or quantitative thermography
(QIRT) [14–19]. A more detailed explanation of each method is presented, except for the endoscopic analysis that damages the building façade.
The theoretical method is characterized by three potentials: it is
the simplest and most widely applied method to determine the
nominal design value of a wall in various countries, physical testing is not required, and national energy efficiency regulations tend
to be well –known [20,19]. Nevertheless, the standards are limited
to ideal constructions (i.e. ISO 6946), since the calculation procedure does not deal with: ageing of materials, wall morphology
(proportions of stone and mortar, voids etc), detailed hygrothermal
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B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
data to local context, moisture content, thermal bridges or influential factors related to workmanship [21,22,17,23]. However, all of
these issues could potentially affect the U-value of a building element over time [21], especially in heterogeneous specimens (i.e.
stone walls) [17,23]. In fact, the largest discrepancy between theoretical and measured U-value is given when insulation layers’ present substantial gaps with greater width as well as air cavities
where the air is stagnant or moving slowly (external air ingress
behind the plasterboard) [21,22]. This problem could also have
implications in energy audits, building modelling and effectiveness
of energy upgrade measures [23–25]. Even building material databases or simulation could present similar drawbacks, since variations of thermal conductivity values in real operating conditions
may be attributed to: the density of the material [15], moisture
content variations [26,27,28] and climatic variations [19]. For these
reasons, building components should also be characterized using
in-situ measurements techniques such as HFM or QIRT.
The most widely used procedure for determining real U-value is
the heat flux method (HFM) [29,30,31,18,19]. Nevertheless, several
studies evidenced limitations of the HFM: local measurement
[38,17,18,33]; long measuring time [18,19,31]; low reliability of
the results for lightweight walls or inhomogeneous specimens
[32,17,23,25,33]; damages and marks can be produced on the
surface of the building element during the test [34,33]; difficulties
in walls with internal heat sources such as pipes of cold/hot
water flows [35,33]; metrological errors can be caused by environmental conditions, wall structure, thermal inertia of the wall,
thermal bridges, moisture and partial adhesion of the sensors
[36–38,32,15,39,40,17,41,23,33,19]; the use of the technique is
limited to the winter season [19]; operational conditions related
to the users (i.e. furniture, occupant behaviour) can affect the
measurements [19].
Some of the mentioned sources of inaccuracy for the HFM have
been quantified. The features of the sensors (thermocouples and
heat flux meters) could lead to measurement errors from 6 to
26% [33]. In fact, 30% of the heat flux variations could be caused
by the size of the heat flux plate [42] and 26% of the deviation in
the overall heat transfer coefficient could be attributed to the location of the heat flux plate [43]. The less relevant technical factors of
disturbance were found to be poor contact between the plate and
the wall as well as non-one-dimensional flux, whose estimated
errors range from 2 to 5% and 1 to 5% respectively [15]. Despite
not being directly related to the sensors, the orientation of the wall
could be responsible for an error of up to 37.3% [44] and data processing methods (average or dynamic analysis) could add 20%
[37,45]. Some authors also demonstrated that the deviation
between theoretical and measured U-values was found to be
between 30 and 47% in wall areas with presence of air cavities
[21,46,17,25]. Construction defects are unpredictable within the
theoretical calculations [21] and the range of discrepancy depends
on the standard taken as a reference and the proportion of materials (i.e. ratio stone to mortar) [17].
Concerning the IRT, numerous studies assessed existing walls
with defects due to moisture, thermal bridges (TB), cracks or air
leakages. Nevertheless, there are more qualitative IRT studies
[17,39,47–61] than quantitative [62,10,63–68]. Qualitative IRT
studies were characterized by discovering heterogeneities or damage in the layers below the plaster [48,49,52,54,55], defining geometry of the masonry [17], determining wall surface temperature
profiles at different heights [25,61] or adding a filtering process
to each image for the delimitation of the pathology [61]. In some
cases, surface temperature factor and heterogeneity surface temperature factor were also calculated [39].
Quantitative infrared thermography (QIRT) is an alternative
NDT for the in-situ measurement of thermal transmittances
that solves the limitations of other mentioned methodologies
(i.e. endoscopies, data analysis from simulation or building material databases, HFM) [54,69,70,32,18] and requires shorter test
periods (only 30 min) for homogeneous heavy multi-leaf walls
[71]. In contrast to the HFM, which considers the heat flux due
to conduction, QIRT estimates the effect of radiation and convection processes in a stationary regime to assess the U-value.
However, some problems arise from the IRT: the cost of the
equipment is very high [72,33]; a qualified technician is required
to carry out the inspection and the subsequent data analysis
[72,33]; the technician needs to access to the building interiors
and this can be considered invasive by the occupants [19],climatic
conditions can notably influence the results, since the use of the
method is limited in warm areas or summer [50,33,19]; pollution
and smokes with high emissivity may impact on the results
[49,33]; and misreading information can be taken by the IR camera
when temperatures have very close range [73,33,19]. Hence, in
terms of identification of anomalies, it does not depend only on
the features and depth of the defects. Building components, in
thermal or hygroscopic equilibrium, could be difficult to study
with thermography. Indeed, the thermal gradient between inside
and outside environments as well as the direction of thermal flux
determine when a defect can be visible by a thermogram [74,58].
In recent decades, research efforts were focused on finding an
automatic detection of thermal bridges via quantitative IRT [62].
In fact, research activities to refine the IRT methodologies based
on analysis pixel-by-pixel are still ongoing [75]. Table 1 provides
an overview of the most significant studies on this topic. The following information is given for each one: the reference (authors
and year of publication); the number of samples (1 or 5 specimens
generally tested in laboratory under controlled conditions or
real built environment); the analyzed parameters (including
the linear U-value, heat flux and incidence factor of the thermal
bridge among others); the techniques that were performed
(i.e. HFM –heat flux meter-, IRT –infrared thermography-, CFD
–computational fluid dynamics-, SNR –signal to noise ratio- and
EMD –empirical mode decomposition-); the maximum deviation
between theoretical and measured U-value; and observations.
A detailed analysis of Table 1 is reported below.
As seen, few authors have devoted attention to quantify the
contribution of TB to the deviation of in-situ U-values measured
by internal quantitative infrared thermography (QIRT). The common parameters for quantifying the effect of a TB and associated
dispersions of the U-value were based on at least the following
three parameters (regardless of the technique applied): (i) heat
flux; (ii) linear thermal transmittance; (iii) incidence factor of the
TB. The last parameter is defined as the ratio between the heat flux
obtained under the effect of the TB and the theoretical heat flux
resulting from normal operating conditions through a onedimensional building envelope (without TB) [62]. Nevertheless,
when QIRT was implemented to assess the U-value, all authors
used the average temperature of a line element to quantify the
effect of the TB during data post-processing of the thermograms
[10,64–66,68]. In other words, the measured thermal transmittance was associated with the wall surface temperature of each
pixel that comprised the imaginary line defined by the authors.
Therefore, the 2D effect of the TB was not considered.
Another aspect to pointed out is that most of studies validated
the IRT results by simulation, focusing on: fluid dynamics (CFD),
finite elements (FE) and continuous time stochastic modelling
among others. According to [25], an estimation of the heat losses
in heterogeneous walls needs the use of complex 3D computations.
However, models can’t be normally adopted by not specialized
researchers such as energy auditors, since algorithm implementation and high computation time are required [76,77,17,25]. The
calculation procedure is based on detailed and accurate input data
on stratigraphy, thickness, order of assembly of the building
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B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
Table 1
Literature review on the quantification of thermal bridges and their impact on the determination of in-situ measured U-value by QIRT.
Reference
N# samples
Parameters to be analysed
Techniques
Max.
Deviation
[62]
Laboratory:
window
[10]
1
real
building
1 dynamic
wall
BES
dynamic
calculations
Linear U-value
[63]
Prototype
3 TBs
Linear U-value
Heat flux
(RQ for pixels on IR line)
Incidence factor of TB
[64]
3 samples
TBs
2 samples
no TBs
Laboratory:
2 samples
for 3v
Simulation:
6 samples
for 5v
Energy saving factor
Incidence factor of TB
Heat flux
Linear U-value
Impact of the wind
Heat flux
(RQ for pixels on IR line)
Linear U-value
[66]
Laboratory
3 TBs
Incidence factor of TB
Linear U-value
QIRT (hot side of the wall)
Hot box for the validation (ISO
8990)
52%
[67]
Laboratory
5 samples
Multiple
TBs
Internal QIRT (hot side of the
wall)
Hot box (ISO 8990 & ISO 12567–
1)
Finite elements (FE)
Computational fluid dynamics
(CFD)
9% QIRT
8.5% FE
13% CFD
[68]
2 buildings
Thermal bridges under
different pre-processing
tools
Accuracy
of
defect
detection
Computational
complexity
20–57%
[64]
Linear U-value
Heat flux
(RQ for pixels on IR line)
Incidence factor of TB
Heat flux
(RQ for pixels on IR line)
Linear U-value
(wall & window)
HFM point by point
Active QIRT
2D model by FLUENT
–
Finite elements (THERM, KOBRA,
GAMBIT and FLUENT among
others)
System identification methods
by MATLAB
QIRT
HFM
Finite Elements (THERM)
–
Combination HFM – External
QIRT
Hot box for the validation (ISO
8990)
External QIRT
Hot box for the validation (ISO
8990)
Simulation
Sparse principal component
Thermography (SPCT)
Signal-to-noise-ratio (SNR)
Empirical mode decomposition
(EMD)
material layer and thermal properties of each layer (i.e. conductivity,
density, thermal mass, vapour pressure resistance and emissivity).
Indeed, some of data are related to conservative conditions of the
wall [17]. Furthermore, simulation models are often developed
without considering meteorological observations and the risk of
surface condensation among others aspects [78,79,75]. Rye and
Scott [80] were quite critical and suggested that inaccurate estimation of thermal properties of heavyweight construction resulting
from modelling could be up to 77%.
Regardless the calculation procedure for the thermal transmittance, Table 1 shows a high discrepancy between theoretical and
measured U-values. In fact, the studies from Ireland and Italy
revealed that the maximum deviation ranges from 12% to 73% for
the quantitative IRT [63–68]. It should be noted that [62] only provided the deviation for the incidence factor of the thermal bridge
(5%) and [68] presented the percentage of accuracy for defect
detection and non- quantification of linear thermal transmittance.
Within this context, and according to the literature, the way of
enhancing the accuracy of experimental tests conducted in samples with greater heterogeneity was: (i) to know detailed geometrical characterization of the mock-up (dimensions, thicknesses,
73%
12%
36%
Observations
Use of a climatic chamber to ensure steady-state
conditions
Use of TWALL by a single pixel
Measurement technique for IRT analysis: line
meter
3 possibilities to obtain linear U-values (stationary & transient regimes)
Electric circuit model for the 3 layers of the
equivalent wall
Continuous time stochastic modelling (CSTM)
Use of TWALL by a single pixel
Measurement technique for IRT analysis: line
meter
Comparison numerical data vs. experimental
data
Graph T vs. length specimen
Use of TWALL by a single pixel
Measurement technique for IRT analysis: line
meter
Laboratory: 3 wind velocities (0.1 m/s, 1.5 m/s,
4 m/s) for analyzing the influence of wind speed
Simulation: 6 models for 5 wind velocities to
determine the role of thermal conductivity
Use of TWALL by a single pixel
Measurement technique for IRT analysis: line
meter
Graph T vs cm
Use of TWALL by a single pixel
Technique of measurement for IRT analysis: line
meterstribution of probability for T in thermal
bridge
Indoor IRT is more suitable for thermal bridges
Uncertainty calculated by error propagation rule
Measurement technique for IRT analysis: line
meter
Use of TWALL by a single pixel
Calibration: use of fractions of convective transfer coefficients
Reference value: hot box measurement
Use of a multiscale data analysis method
Solar diurnal cycle as an external stimulus
Both buildings were affected by the 2009
earthquakes
percentages of stone and mortar [77,25]; (ii) to know specific
thermos-physical properties [76,77,25]; (iii) to define the moisture
content of the mock-up [81,25]; (iv) to conduct a specific set-up of
the test [82,25]; (v) to extend the metering section [83,25]; (vi) to
increase the number of measurement points [81,25]; (vii) to
increase the temperature gradient between the hot and cold chambers [77,25]. In the case of the quantitative IRT for a real built environment, the best way of obtaining accurate outcomes could be to
increase both metering section and measurement points. For this
reason, a 2D U-value map could be interesting to be developed.
Considering the above aspects, the aim of the current research
was to implement a thermographic 2D U-value map to quantify
the thermal bridges of opaque façades, allowing clear identification
of the most significant points of damage. Firstly, the background of
the most relevant techniques for determining in-situ U-values was
examined, and the calculation procedures and recommendations
were highlighted. Secondly, to analyze the feasibility of the 2D
U-value maps, three heavy walls were tested in a climatic chamber
by quantitative internal thermography and the heat flux meter
method. Subsequently, the results of all the techniques and their
dispersion were compared.
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B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
2. Methodology
This study proposes to compute a 2D U-value map for quantifying thermal bridges of entire façades by means of quantitative
internal thermography. To achieve this objective, the research
methodology was divided into two steps: (i) measurements setup; (ii) data treatment. In the first step, a climatic chamber was
used to impose a temperature gradient between the two sides of
three case studies (heavy walls) and the procedures required to
assess the U-value by HFM and QIRT were implemented. In the second step, the data collected were analyzed with two goals. Initially,
the U-value of undisturbed zones was calculated using QIRT and
the results were compared with the HFM (standardized method).
Afterwards, the 2D U-value map with SURFER software was computed. A detailed explanation of both steps is presented in Sections
2.1 and 2.2. Subsequently, the measuring equipment and the case
studies are briefly described in Sections 2.3 and 2.4.
2.1. Measurement set-up
The measurements were carried out in a walk-in climatic chamber (FITOCLIMA 1000, EDTU) in the Laboratory of Building Physics,
Faculty of Engineering of the University of Porto (FEUP). The chamber allows to assess full-scale components (1.90 1.90 m2) under
controlled conditions of temperature and humidity (Fig. 1). It consists of two fans, three resistances, one compressor, several sensors
and a display to configure the equipment. Besides this, the climatic
chamber presents an attachment of another chamber (2.00 1.0
0 m2) where the technician can access through a door (2.00 0.
80 m2). For this reason, the technician can perform internal quantitative IRT tests. The technical features of the climatic chamber are
shown in Table 2 (Section 2.3).
Before implementing the experimental techniques, the theoretical method was applied to estimate the nominal design value of
the specimens, according to the country’s technical building code
and the European Standards UNE-EN ISO 6946:2012 [84] and
UNE EN-ISO 10456:2012 [85]. In this way, it was possible to have
a reference value. The theoretical U-value Ut [W/(m2K)] can be
expressed by Eq. (1).
Ut ¼
RSi þ
Pn
1
Dxi
i¼1 ki
þ RSe
ð1Þ
where Rsi and Rse denotes the theoretical thermal resistances of the
outer and inner surfaces [(m2K)/W]; Dxi is the thickness of the
layer in metres; and ki is the thermal conductivity of the layer
[W/(mK)].
Subsequently, the U-value of the specimens was determined by
HFM using the procedure indicated in ISO 9869-1:2014 [86]. As
seen in Eq. (2), this standardized non-destructive test (NDT) consists of determining the thermal transmittance UHFM [W/m2K] as
the quotient between the specific heat flux by conduction across
the wall qcond [W/m2] measured using a transducer and the temperature gradient (TIN -TOUT) [K] measured by thermocouples [86].
Pn
ðq
Þ
U HFM ¼ Pn i¼1 condi
ð
T
T
IN
OUT
i
iÞ
i¼1
ð2Þ
In recent years, some researchers established a set of recommendations about execution criteria of HFM. These are briefly
described below: (i) the transducer should be located at 1.5 m
above the floor [87] and at least 1.3 m from heating systems (fan
coils or radiators) [35]; (ii) thermocouples for assessing air temperature should be installed at 0.30–0.40 m (horizontally) from the
façade [88]; (iii) HFM tests should be repeated in different positions of the specimen [15]; (iv) the temperature gradient should
range between 10 and 15 °C [54,31]), but over 19 °C could be
required for walls with low U-values [41]; (v) the data acquisition
interval needs to be long enough (considering a test duration
between a minimum of 72 h and a maximum of 1 week), to ensure
reliable outcomes [54,15,19].
Taking into account the above aspects, the boundary conditions
were configured to ensure an indoor controlled space for the application of the HFM and the quantitative IRT. Each test specimen was
placed in the structure of the metering box. The inner air temperature (TIN) and relative humidity (RH) were set to be 35 °C and 50%
respectively. To avoid possible disturbances due to temperature
peaks, air currents throughout the vertical surface of the specimen
and reflections, the internal walls of the climatic chamber were
entirely covered with a black cardboard. The outer air temperature
and the relative humidity were by default 18–20 °C and 40%
respectively. For all case studies, the walls were pre-conditioned
in the climatic chamber for 72 h to ensure a stable temperature
gradient and homogeneity of the heat flux.
A qualitative IRT survey was also performed following the procedures indicated in ISO 6781:2015 [89] and UNE EN 13187:1998
[90], to define the position of the sensors in order to avoid any possible unknown heterogeneity in the specimens. The sensor layout
included two heat flux meters installed inside the climatic chamber at 1.5 m above the floor (Fig. 2). The duration of the HFM tests
was 72 h with a data acquisition interval of 10 min.
Fig. 1. Image of the climatic chamber.
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B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
Table 2
Main technical specifications of the equipment.
Equipment
Output
Measuring range
Resolution
Accuracy
Climatic Chamber
–
Heat flux sensor TPD TND-TH
QCOND
0.1
0.1
–
±0.5 °C
±2%
±5%
Infrared camera
NEC TH9100MR
TWALL
TREF
320 240 pixels
±2 °C or ± 2% reading
Integrated T & RH sensors
HOBO UX100
Emissometer
D&S, Model AE1
TIN
TOUT
Temperature: 50 °C to 180 °C
Humidity: 10 < RH < 98%
Maximum temperature: 90 °C
Temperature correction: + 0.10%/K
Thermal conductivity: 0.25 W/(mK)
Internal electrical resistance: 445–450 Ohm
Constant of calibration: 17
Temperature: 20 °C to + 100 °C
FOV: 21.7 16.4°; IFOV: 1.2 mrad
Spectral Range: 8–14 lm
Thermal sensitivity: 0.04 °C at 30 °C
Sensor: FPA, uncooled microbolometer
Temperature: 20 °C to 70 °C
Humidity: 1 < RH < 95%
–
0.024 °C
0.05%
–
±0.21 °C
±2.5%
±0.01
eWALL
of 5.67 108 [W/m2K4]; air thermal conductivity (kair) measured
in [W/m K]; wall height (L) seen from inside the building in [m];
and dimensionless parameters Rayleigh (Ra) and Prandtl (Pr) numbers (assuming Pr = 0.73 for dry air under atmospheric pressure
and TIN = 20–25 °C). For Eq. (4), the total number of thermograms
(n) are considered.
The equipment for the QIRT included an IR camera, temperature
sensors with data loggers and a crinkled sheet of aluminum foil.
Figs. 3 and 4 show a schematic representation of the experimental
set-up and a real image of the execution of the method respectively. All the equipment was placed at 1.5 m above the floor and
the distance between the IR camera and the target was established
at 1 m. In addition, the angle of tilt of the IR camera was 5° from
the horizontal to avoid reflections. The walls were monitored for
4 h with a data acquisition interval of 1 min. Only the last 2 h were
used to determine the U-value, to ensure the stability of the system
and avoid the effects of opening and/or closing the climatic chamber to position the equipment. Once the measurements had been
Fig. 2. Sensors layout for the execution of the HFM method inside the climatic
chamber.
Regarding the quantitative IRT, the method proposed by [18]
was applied to determine the influence of thermal bridges on the
accuracy of in-situ measurements of thermal transmittance UQIRT
[W/m2K]. The recommendations in [91] and [71] were also considered, in terms of: (i) operating conditions; (ii) thermophysical
properties (i.e. kappa value); (iii) time series analysis for data
post-processing. The instantaneous and average measured Uvalues [W/m2K] were determined according to Eqs. (3) and (4)
respectively.
8
>
>
<
>
>
:
0:825þh
1
^
0:387AR
a6
9
1þ 0:492 16
Pr
ð
Þ
L
U QIRT i ¼
92
>
>
=
i278 >
>
;
kair
h
i
^ rA
^ T REF 4 T WALL 4
½T IN T WALL þ eWALL A
ðT IN T OUT Þ
ð3Þ
U QIRT av g
Pn
Pn
W
ðq þ qc i Þ
U QIRT i
¼ Pn i¼1 r i
¼ i¼1
^ K
n
ð
T
T
Þ
IN
OUT
m2 A
i
i
i¼1
ð4Þ
The parameters presented in Eq. (3) are: inner and outer air
temperatures (TIN and TOUT) in [K]; wall surface temperature (TWALL)
in [K]; reflected ambient temperature (TREF) in [K]; wall surface
emissivity (eWALL); Stefan–Boltzmann’s constant (r) with a value
Fig. 3. Position of the measuring equipment in relation to the wall (lateral side of
the climatic chamber).
6
B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
Fig. 4. Execution of the quantitative internal IRT inside the climatic chamber.
carried out, the dimensionless approach (based on the Nusselt
number for vertical surfaces in laminar flux regime) was used to
estimate the in-situ measured U-value (Eqs. (3) and (4)).
2.2. Data-treatment
The first step of the data treatment was the calculation of the Uvalue of the undisturbed zones based on the results attained by
HFM and QIRT, following the procedures in Sections 2.1. Afterwards, to create the 2D U-value map with SURFER [Golden [92],
the thermal images of the QIRT tests were subdivided using an
n-elements (i j) mesh. In these case studies, 1600 elements were
considered, each one with 8 6 pixels, to maintain the initial
width/height ratio of the thermal image.
The U-value of each element of the mesh was then computed
using the formulation presented in Eqs. (3) and (4), considering
TWALL as the average temperature of the element. The resulting n
U-values were then plotted in a 2D colour map. A computer program was developed to automatize this procedure. Fig. 5 shows a
schematic representation of this methodology.
Fig. 5. Schematic representation of the development of the 2D U-value map.
7
B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
2.3. Measuring equipment
The main technical specifications of the equipment used for
HFM and QIRT are shown in Table 2. For the HFM, two transducers
(TPD TND-TH PU3.2) and two temperature and relative humidity
sensors (HOBO Temp/RH data logger UX100) were used, as presented in Fig. 2 (Section 2.1). Quantitative infrared data (instantaneous TWALL and TREF values) were acquired with a resolution of
320 240 pixels by means of an IR camera (NEC TH9100MR).
The wall surface emissivity (eWALL) was found to be 0.93 for all
walls, according to the readings obtained with an emissometer
(D&S Model AE1). The hygrothermal variables of the inner and
outer environments were monitored by means of the same integrated sensors of HFM (HOBO Temp/RH data logger UX100).
2.4. Case studies
Three heavyweight walls were prepared for this research
(Fig. 6), since they are common construction solutions in southern
European countries. W1 was a single-leaf wall in which the possible effect of air voids and gaps in the internal structure of the brick
required evaluation. W2 was a heavyweight multi-leaf wall comprised of small defects (0.06 0.06 m2) of varying depths
(0.025 m, 0.050 m and 0.065 m). W3 was also a heavyweight
multi-leaf wall, but with a large internal horizontal thermal bridge
(0.88 0.20 m2). The details of each specimen are given below,
with information on the complete configuration and the technical
features (Table 3) as well as a schematic representation (Fig. 7).
Notably, the characterization of this kind of walls can be quite
challenging due to their heterogeneous nature, roughness of the
block surface and the wet construction type [83].
3. Discussion of results
All the 2D U-value maps (Figs. 9–11) were developed by SURFER
[Golden [92] through a TWALL processed image (1600 elements that
contain 8 6 pixels). To interpret them, an interval scale of 0.2 W/
m2 K was used and the same palette colour as the original thermogram. The Rainbow High Contrast Palette allows detection of slight
temperature changes even in low-contrast conditions (the red colour referred to warmer areas and the blue colour corresponded to
colder areas with greater disturbance of the reference value).
Hence, this could help to better understand the distribution of
the U-value.
The comparative analysis of techniques for determining thermal transmittance is presented in Table 4, highlighting: (i) the
Fig. 6. Single-leaf wall (W1) and heavy multi-leaf walls (W2 and W3).
Table 3
Configuration and technical features of the façades (from outside to inside).
N#
Material layer
Dxi [m]
ki
W1
1
Lightweight concrete
0.25
W2 (without TB)
1
2
3
4
5
Lightweight concrete
Lightweight mortar
Projected thermal plaster
Bonding mortar with fiberglass
Mineral mortar
0.25
0.01
0.065
0.005
0.01
W2 (with TB)
1
2
3
4
5
Lightweight concrete
Lightweight mortar
Projected thermal plaster
Bonding mortar with fiberglass
Mineral mortar
W3 (without TB)
1
2
3
4
W3 (with TB)
1
2
3
4
Rt I [(m2K)/W]
L [m]
Ut [W/(m2K)]
–
1.36
1.9
0.654
–
0.61
0.042
0.45
0.61
1.36
–
–
–
–
1.9
0.32
0.25
0.01
0.04/0.015/0
0.005
0.01
–
0.61
0.042
0.45
0.61
1.36
–
–
–
–
1.9
(a) 0.396
(b) 0.518
(c) 0.635
Lightweight concrete
Lightweight mortar
Insulation EPS
Plasterboard
0.25
0.01
0.06
0.005
–
0.61
0.037
0.21
1.36
–
–
–
1.9
0.313
Lightweight concrete
Lightweight mortar
Insulation EPS
Plasterboard
0.25
0.01
–
0.005
–
0.61
–
0.21
1.36
–
–
–
1.9
0.637
[W/(mK)]
Dxi: thickness of the layer; kl: thermal conductivity of the layer; Rt i: theoretical thermal resistance of the layer; L: height of the wall; Ut: theoretical thermal transmittance of
the building façade.
8
B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
Fig. 7. Schematic representation of the case studies.
Fig. 8. Influence of the internal thermal bridge.
theoretical U-value; (ii) the U-value measured by HFM; (iii) the
U-value measured by QIRT in the same area of the HFM; (iv) the
2D U-value map results. The following parameters were calculated: the average, minimum and maximum values of thermal
transmittance [W/m2K)]; the standard deviation (SD) [W/m2K)]
and the coefficient of variation (CV) [%] of the measurements.
When the area was not large enough to implement the HFM, only
the theoretical U-value and 2D map results were provided.
Table 4 shows that the existence of air voids and gaps in the
internal structure of the brick with lightweight concrete (Fig. 8)
could have affected the thermal performance of the building components. Generally speaking, and in terms of reliability, the outcomes were comparable with previous studies. Focusing the
attention in the HFM, some authors stated that the deviation
between theoretical and measured U-values ranged between 30
and 47% in wall areas with presence of air cavities [21,46,17,25].
B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
In this research, the discrepancy was from 7.29 to 26.84% for the
undisturbed wall areas. As regards quantitative IRT, the literature
showed that the maximum percentage of deviation was estimated
to be 12–73% for walls with thermal bridges [63–68]. In the case of
the thermographic 2D U-value map, the deviation was found to be
between 7.83 and 27.80% for moderate inhomogeneous walls. In
both experimental techniques, the deviation between the theoretical and the measured U-values was > 50 when the specimens did
not have EPS insulation or projected thermal plaster. However, the
U-value results measured by HFM and QIRT were similar (from
0.08 to 8.55% of difference in most cases). Hence, it could be concluded that the nominal design value is not suitable for materials
with several heterogeneities and the characterization of the specimen should only be based on in-situ measurements.
Fig. 9 presents the 2D U-value map of W1. As can be observed,
the distribution of the U-value went from the centre of the brick to
9
the sides like an expansive heat wave that ranged from 0.9 to 2 W/
(m2K). The U-values measured by HFM and QIIRT were found to be
1.308 and 1.307 W/m2K. Despite being really equal, the internal
thermography results had a lower degree of dispersion than those
obtained by the HFM. Specifically, the coefficients of variation of
the QIRT and 2D U-value map were 6.47% and 10.48% respectively,
compared to the 37.43% of the HFM (Table 4). Hence, this aspect
demonstrated that the 2D U-value map is especially useful in
specimens with greater heterogeneity. As regards the internal TB
and the junctions among bricks using lightweight mortar, these
parts contributed significantly to increase the dispersion of the
heat flux across the material (U2D map = 2.5–3 W/m2K).
Fig. 10 corresponds to W2. The small defects described in Section 2 were clearly detected through the 2D U-Value map. When
defects are of small dimensions and depths, it can be assumed that
their influence from the delimitation of the holes to the rest of the
Fig. 9. 2D U-value map for W1.
Fig. 10. 2D U-value map W2.
10
B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
Fig. 11. 2D U-value map W3.
Table 4
Comparative analysis of techniques for determining thermal transmittance.
Parameters
Ut [W/(m2K)]
W1
W2
W3
Without TB
With TB
Without TB
TB (a)
z = 0.025 m
TB (b)
z = 0.050 m
TB (c)
z = 0.065 m
Without TB
With TB
0.654
–
0.320
0.396
0.518
0.635
0.313
0.637
Statistical Parameters for each NDT (HFM, IRT, 2D MAP)
UHFM_avg [W/(m2K)]
1.308
–
UHFM_min [W/(m2K)]
0.777
–
2
UHFM_max [W/(m K)]
2.639
–
SD UHFM [W/(m2K)]
0.683
–
CV UHFM [%]
37.43
–
UIRT_avg [W/(m2K)]
1.307
–
UIRT_min [W/(m2K)]
1.023
–
UIRT_max [W/(m2K)]
1.610
–
2
SD UIRT [W/(m K)]
0.084
–
CV UIRT [%]
6.47
–
U2DMAP_avg [W/(m2K)]
1.250
1.962
U2DMAP_min [W/(m2K)]
1.002
1.501
U2DMAP_max [W/(m2K)]
1.499
3.381
SD U2DMAP [W/(m2K)]
0.131
0.375
CV U2DMAP [%]
10.48
19.11
0.297
0.212
0.417
0.058
19.43
0.306
0.240
0.387
0.029
9.70
0.280
0.168
0.400
0.051
18.26
–
–
–
–
–
–
–
–
–
–
0.427
0.400
0.896
0.122
22.30
–
–
–
–
–
–
–
–
–
–
0.562
0.400
1.192
0.150
26.66
–
–
–
–
–
–
–
–
–
–
2.570
1.002
4.976
1.111
43.19
0.397
0.292
0.647
0.086
21.66
0.370
0.258
0.484
0.070
18.78
0.400
0.335
0.500
0.045
11.28
1.102
0.893
1.626
0.188
17.06
1.294
0.807
1.695
0.316
24.42
1.229
0.505
2.201
0.486
39.52
Deviation between theoretical and measured U-values
DUHFM/Ut [%]
>50
–
DUIRT/Ut [%]
>50
–
DU2DMAP/Ut [%]
>50
–
7.29
4.43
12.59
–
–
7.83
–
–
8.49
–
–
>50
26.84
18.21
27.80
>50
>50
>50
Deviation among NDT
DUIRT/UHFM [%]
DU2DMAP/UHFM [%]
DU2DMAP/UIRT [%]
3.09
5.72
8.55
–
–
–
–
–
–
–
–
–
6.80
0.76
8.11
17.42
11.52
5.02
0.08
4.43
4.36
–
–
–
wall area are more isolated. In this case study, delimitations with a
depth between 0.025 m and 0.005 m did not derive to a significant
alteration in terms of thermal behaviour, since U2D map = 0.2 to
0.4 W/m2K from the top to the middle of the 2D map. The theoretical U-value and the measured U-values (HFM and QIRT) were
inside the above range for the undisturbed wall area
(Ut = 0.320 W/m2K; UHFM avg = 0.297 W/m2K; UQIRT avg = 0.306W/m2K). Concerning the internal area of the second TB (b), the
fluctuations in thermal transmittance went from the borderlines
to the centre of the anomaly (1–1.2 W/m2K). Indeed, and according to Table 4, the minimum U2D map was the same for both depths,
at 0.400 W/m2K. However, the maximum values were quite
different (0.896 W/m2K vs. 1.192 W/m2K). In terms of deviations
between the theoretical U-value and the average readings of the
2D U-value map, the TB with z = 0.025 m presented a deviation
of 7.83% and the TB with z = 0.050 m had a value of 8.49%. For
depths of 0.065 m, the impact of the anomaly could be estimated
at least 8 times higher than the reference value (Ut = 0.320
W/m2K vs. U2D map, = 2. 570 W/m2K), reaching a peak of
4.976 W/m2K. This also implied a higher degree of dispersion of
the measurements for the areas around and inside the defect, since
the coefficients of variation were 18.26% and 43.19% respectively.
The third case study was distinguished from the others by a
horizontal internal thermal bridge that was specifically executed
B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
for the research. As shown in Fig. 11, the 2D U-value map provided
information on the evolution of the thermal property as the effect
of the TB increased. In fact, a minimum of five regions could be
highlighted: 0.3–0.5 W/m2K corresponding to the undisturbed
area located on top of the thermogram; 0.7–0.9 W/m2K from the
area without any influence of the TB to the area where the TB
began; 0.9–1.3 W/m2K for the junctions among bricks using lightweight mortar; 1.3–1.5 W/m2K for the top area of the TB; 1.5–
2.3 W/m2K with intervals of 0.2 W/m2K referring to the area with
greater disturbance of the measured U-value. Notably, the attachment of the last material layer (EPS) was not totally airtight, since
the insulation was assembled after building the internal horizontal
thermal bridge. Hence, the wall could have had air infiltrations
from inside the climatic chamber in different directions or air voids
between the insulation and the structure.
The results of the 2D map were corroborated by a comparative
analysis of Table 4 and Lucchi’s study [25]. Lucchi et al. [25]
defined a procedure to assess inhomogeneous walls by means of
hot box apparatus and supported by qualitative IRT surveys and
dynamic simulations. They demonstrated that the deviation for
monolithic stone walls with air cavities (area influenced by thermal bridging) was 33–36% and 23–26% for the same wall with
injected aerogel (‘‘moderate inhomogeneous” areas with a good
thermal stability). As regards the U-values in the area of the thermal bridge without and with the application of aerogel in stationary regime, the measurements of the HFM were 1.26 W/m2K and
0.43 W/m2K respectively. In the homogeneous thermal area, the
readings were 1.06–1.10 W/m2K without aerogel and 0.32–
0.35 W/m2K with aerogel. Values of the same order were obtained
in the current research for W3.
The thermal transmittances with and without TB were found to
be really similar among HFM and quantitative IRT techniques. On
the top of the specimen, the average U-Value for the 2D map was
equal to 0.400 W/m2K while the HFM and QIRT in the same area
of execution provided a value of 0.397 and 0.370 W/m2K respectively. As seen, the deviation among NDT ranged from 0.76 to
8.11% for the area without TB. In the area with disturbance, the
outcomes were as follows. The average U-value of the 2D map
was found to be 1.229 W/m2K, showing a contour line from 0.9
to 1.3 W/m2K; UHFM = 1.102 W/m2K and UQIRT = 1.294 W/m2K.
Hence, the deviation among NDT oscillated between 5.02 and
17.42%. As regards the dispersion of the readings, the coefficients
of variation were also affected by the TB, giving higher percentages
for the internal thermography than the HFM. For example, the CV
for the 2D U-value map with and without anomaly was 11.28 and
39.52% respectively, while the HFM presented 18.78 and 24.42%
but worked with a minor study area. In addition, the minimum
and maximum values for each technique were approximately four
times higher when the readings were undertaken in the air cavity.
Taking into account these aspects, it could be assumed that the
measurements clearly depended on the air cavity (volume of moving fluid), instead of the workmanship (correct execution of the
assembly).
4. Conclusions
The main contribution of this research is the quantification of
thermal bridges by a thermographic 2D U-value map for façades
in operative conditions, without requiring additional equipment
or simulation techniques (such as FLUENT, THERM and MATLAB).
The review of the scientific literature highlighted several problems related to theoretical and experimental techniques to determine the thermal transmittance of building elements with
anomalies, especially thermal bridges or air cavities. The results
of this research demonstrated the 2D U-value map could help to
11
solve some of these issues, as shown below. However, the proposal
is a preliminary study that needs further research.
In the last decade, some authors pointed out that complex models are not adopted by energy auditors [76,77,17,25]. The 2D Uvalue map could reduce the complexity of the calculation procedure as well as time of data post-processing, since it allows
to carry out an automated analysis pixel-by-pixel.
The influence of thermal bridges is not considered in all European countries and their respective regulations [4]. In fact, some
drawbacks are constantly repeated over time: the standards are
limited to ideal constructions [21,22,17,23], the stratigraphy
and morphology of wall is unknown in most cases of the real
built environment [25] and construction project documents
for existing buildings are not available (especially the oldest
buildings) [18]. The 2D U-value map could help to provide real
information about the thermal behaviour of the air inside opaque façades as well as variations in the thermophysical property
along the vertical and horizontal axis of the wall surface. This
means that an entire inhomogeneous wall could be assessed
without requiring to install a large number of sensors to measure wall surface temperatures and heat flux at different points
of the building element. Until now, the metering section of
heterogeneous specimens contained between 21 and 35 sensors
[93,25]. Consequently, the cost of the equipment could be notably reduced.
The results of the current research are in line with previous
quantitative IRT studies from Ireland and Italy which revealed
that the maximum deviation between theoretical and measured
U-value ranges from 12% to 73% [63–68]. Construction defects
are unpredictable [21]as well as the range of discrepancy
mainly depends on the standard taken as a reference and the
proportion of materials (i.e. ratio stone to mortar) [17]. Indeed,
low reliability of the HFM results was also found for lightweight
walls or inhomogeneous specimens [32,17,23,25,33].
Some authors suggested a total of six ways to enhance the accuracy of experimental tests conducted in samples with greater
heterogeneity [82,76,77,25]. In the case of quantitative IRT,
the best option of achieving accurate outcomes could be to
extend the metering section and to increase the number of measurement points. Hence, the 2D U-value map allows to perform
both aspects at the same time, facilitating: (i) the delimitation
of the most significant areas of the thermal bridge, to identify
the geometry of the thermal bridge as well as its area of impact
in 2D; (ii) the quantification of the measured thermal transmittance at any point of the wall surface. Particularly, the 2D Uvalue map is especially useful in specimens with greater heterogeneity, with small defects and internal air voids. Until now, the
presence of substantial gaps and air cavities behind the plasterboard caused the largest deviation between theoretical and
measured U-value [21,46].
In terms of applicability, the quantification of thermal bridges
by a 2D U-value map could provide enough information to enhance
the operational life of the structure with economical refurbishment
procedures. Future steps in the research should include the application of the presented transmittance thermographic mapping to
detect and quantify dampness in a whole building façade. It could
also be recommendable to assess the influence of different climates. According to Genova et al. [23], tests executed in the summer are less reliable than those conducted in winter for the
Mediterranean climate. Hence, it could be interesting to compare
the proposed procedure in existing buildings of north-east Spain
(Mediterranean Climate) and northern Portugal (an Atlantic climate with high humidity and more probability of intensive rain
and wind).
12
B. Tejedor et al. / Energy & Buildings 224 (2020) 110176
CRediT authorship contribution statement
Blanca Tejedor: Methodology, Investigation, Formal analysis,
Writing - original draft, Writing - review & editing. Eva Barreira:
Conceptualization, Resources, Visualization. Ricardo M.S.F.
Almeida: Conceptualization, Software, Formal analysis. Miquel
Casals: Supervision, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared
to influence the work reported in this paper.
Acknowledgements
This work was financially supported by: Base Funding UID/
ECI/04708/2019 of the CONSTRUCT - Instituto de I&D em Estruturas e Construções- funded by national funds through the FCT/
MCTES (PIDDAC).
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