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PROCEEDINGS OF ECOS 2019 - THE 32ND INTERNATIONAL CONFERENCE ON
EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS
JUNE 23-28, 2019, WROCLAW, POLAND
Infrared imaging of a multi-zone condenser for heat
transfer coefficients assessment
R´emi Dickes∗, Olivier Dumont and Vincent Lemort
Thermodynamics Laboratory
Aerospace and Mechanical Engineering Department
University of Li`ege, Li`ege, Belgium
∗Correspinding author (rdickes@ulg.ac.be)
Abstract:
Although crucial for simulations, a proper identification of the convective heat trans-
fer coefficients in multi-zone heat exchangers is a challenging task. While well in-
strumented thermal systems permit to accurately record the energy balance in such
components, the sole knowledge of the global heat transfer rate is not enough to
reliably assess these coefficients. In this work, it is proposed to use the zones spatial
distribution (i.e. the spatial fraction occupied by the liquid phase, the vapour phase
and/or the two-phase regions) as a second identification criteria. An air-cooled
condenser into which flows R245fa is considered as case study and a dedicated in-
frared imaging method is presented to assess the spatial distribution of its different
phases. These new data, combined with standard heat transfer rate measurements,
are exploited to identify the best heat transfer correlations pre-selected from the
scientific literature. In order to further improve the model predictions, the original
heat transfer correlations are ultimately adjusted so as to best fit both the global
heat transfer rate and the zones distribution data.
Keywords:
Infrared camera, Heat Transfer Coefficients, HVAC, ORC, Heat exchangers, Zones
distribution.
1. Introduction
Heat exchangers are crucial components in thermal systems allowing efficient heat transfers
between hot and cold media. In rating problems, the objective is commonly to evaluate the
amount of energy transferred through a specific component based on its geometry and the fluids
supply conditions only. Unlike in steam power plants or higher-capacity systems, small-scale
organic Rankine cycles and HVAC systems often employ single heat exchangers to perform the
complete heating and cooling of their working fluid. While being easier to put in practice,
1
such a simple configuration complicates some modelling aspects. Since the fluid experiences a
phase-change in both evaporators and condensers, several states of fluid (i.e. liquid, two-phase
and/or vapour phases) often coexist in a same component. In order to account for this spatial
division, a common approach is to simulate the heat exchanger with a one-dimensional moving-
boundary method [1]. Each zone iis considered individually and simulated with classic heat
transfer equations, i.e.
Ai=˙
Qi
UiFi∆Tlog,i
(1)
where
1
AiUi
=1
Hh,iAh,i ηs,h,i
+ti
kiAi
+1
Hc,iAc,i ηs,c,i
(2)
and
•Aiis the surface area occupied by the ith zone;
•Uiis the global heat transfer coefficient;
•∆Tlog,i is the zone logarithm mean temperature difference (LMTD) between the two fluids;
•Fiis the LMTD correction factor to apply if the heat exchanger is not of counterflow;
•tiand kiare the wall thickness and conductivity;
•ηs,h,i and ηs,c,i are the surface efficiency on each side (<1 in case of finned geometry, = 1
otherwise);
•Hh,i and Hc,i are the convective heat transfer coefficients (CHTCs) on each side;
The effective heat transfer between the two fluids is thus calculated such as the total surface
area occupied by the different zones corresponds to the actual geometry of the component, i.e.
AHE X =
N
X
i=1
Ai(3)
As highlighted in Equation (2), a proper modelling of the heat exchangers is highly affected
by the ability to characterize the convective heat transfer coefficients (CHTCs) in the different
zones. Although crucial, the identification of these coefficients from experimental measure-
ments is quite challenging. Most test rigs only feature thermo-hydraulic sensors at the inlet
and outlet ports of the heat exchangers which permit “solely” to calculate the global heat
transfer rate within the component (i.e. ˙
Q= ˙m(hsu −hex)). However, such a knowledge of the
global heat transfer is not enough to properly identify these coefficients. Indeed, since several
convective heat transfer coefficients intervene in the computation of the thermal performance,
and because multiple zones coexist in a same component, very different sets of coefficients can
2
0 0.5 1
Temperature [°C]
80
100
120
140 Hh,l = 350 W/(m².K)
Hc,l = 480 W/(m².K)
Hc,tp = 1000 W/(m².K)
Hc,v = 300 W/(m².K)
Set of coefficients #1
0 0.5 1
Temperature [°C]
80
100
120
140 Hh,l = 505 W/(m².K)
Hc,l = 800 W/(m².K)
Hc,tp = 1e+04 W/(m².K)
Hc,v = 50 W/(m².K)
Set of coefficients #2
Spatial fraction [-]
0 0.5 1
Temperature [°C]
80
100
120
140 Hh,l = 100 W/(m².K)
Hc,l = 2000 W/(m².K)
Hc,tp = 2000 W/(m².K)
Hc,v = 120W/(m².K)
Set of coefficients #3
Figure 1: Identical heat transfer in an evaporator with three different sets of convective heat
transfer coefficients (temperature profile vs. normalized length).
lead to the exact same heat transfer predictions. Such a situation is illustrated in Figure 1 with
an evaporator. As evidenced with three different scenarios, the same heat transfer rate (i.e.
the outlet temperatures are identical) is retrieved with significantly different combinations of
CHCTs. Therefore, unless the experimental data features single-zone conditions (i.e. operating
conditions with only a liquid-phase, a vapour-phase or a two-phase flow in the HEXs), the
identification of the CHTCs based only on heat transfer rate measurements will more likely
lead to wrong results since there is an infinity of solutions. Alternatively, one may use heat
transfer correlations found in the literature to estimate the coefficients Hh,i and Hc,i. How-
ever, these correlations are generally purely empirical and calibrated to fit experimental data
gathered on specific test rigs. Their extrapolability to other fluids, geometries or operating
conditions is often controversial and multiple candidates can be considered to simulate a same
situation. While these correlations provide good guesses to estimate the CHTCs, they generally
need some adjustments to better fit another case study, which leads to the same identification
issue as mentioned above. An interesting solution to this problem appears by looking back to
Figure 1. As evidenced with the temperature profiles, the heat transfer coefficients do not only
play a role on the thermal performance, they also impact the spatial distribution of the different
zones. This observation is extremely important and has one crucial outcome: any knowledge
about the zones distribution in a heat exchanger can help to identify the convective heat trans-
fer coefficients. This work aims to illustrate how an infrared camera can be exploited to this end.
The paper is organized as follows. The heat exchanger considered as case study is first presented
in Section 2. Then Section 3 describes the infrared imaging method developed to record the
3
zones distribution. This method, combined with standard global heat transfer measurements,
are ultimately exploited to identify the convective heat transfer coefficients in Section 4.
2. Case study description
In order to illustrate this work, an air-cooled condenser integrated in a 2 kWeORC system is
taken as case study. Depicted in Figure 2a, it is a fin coil heat exchanger developed by Alfa
Laval (model Solar Junior 121) made of 13 parallel channels, each effectuating 12 passes in a
matrix of plain fins. Condensing R245fa is pumped across the tubes while ambient air is pulsed
with a variable-speed fan placed at the top of the condenser. As shown in Figure 2b, the test rig
is fully monitored with thermocouples, flow meters and pressure sensors so the condenser heat
transfer rate can be evaluated accurately. An extensive experimental campaign was conducted
with the ORC system which led to a complete database including more than 300 steady-state
points 1. The condenser heat transfer performance (i.e. ˙
Qcd) is thus fully characterized over a
wide range of conditions. As mentioned in the introduction, however, these global heat transfer
data are not enough to reliably identify the convective heat transfer coefficients. In parallel to
these thermo-hydraulic measurements, the following IR imaging method was applied.
(a) Photo of the system.
P: pressure sensor - T: thermocouple
m: mass flow meter - V: volumetric flow meter
TV
P
m
T
P
T
T
(b) Scheme of the condenser.
Figure 2: Fin coil condenser of an ORC system taken as case study.
3. Infrared imaging method
In order to perfectly assess the zones distribution, the ideal solution would be to continuously
record the fluid temperature all along its path in the condenser. In practice, the tubes into
1The work presented in this paper is part of more general investigation focusing on the charge distribution in
ORC systems. The experimental campaign did not aim to characterize the condenser only, but also all the other
components and the ORC charge inventory. For any further detail regarding the ORC unit, the experimental
campaign or the results, please refer to the author’s PhD thesis [2].
4
which flows the working fluid are placed in a matrix of plain fins and most of them are invisible
from the outside. However, by removing the side plates of the condenser, one can visualize
the end-tips of these tubes. If the end-tips are observed with an infrared camera as shown in
Figure 3, the temperature evolution along the channels can be reconstructed. Although the
temperature profile is not continuously monitored (i.e. the temperature is rated at 13 discrete
points), these infrared (IR) data help to more precisely localize the frontiers between the liquid,
the vapour and the two-phase zones.
(1)
(2)
(4)
(6)
(8)
(10)
(12)
(3)
(5)
(7)
(9)
(11)
(13)
Front side Back side
Figure 3: Configuration and position numbering for one channel in the condenser.
For every operational point tested with the ORC system, a set of 4 infrared (IR) photos is
captured with a FLIR E50 camera. Each photo is shot from a specific point of view (two at
the front, two at the back) in order to fully monitor the condenser temperature profile. For
instance, the photos collected for one operating point are given in Figure 4. The IR photos #1
and #4 offer an overview of the temperature distribution in the complete tubes bank, while
photos #2 and #3 focus on a specific channel. After verifying that the temperature distribution
along the heat exchanger is quasi-homogeneous (i.e. that there is no significant discrepancies
between the different channels), the temperature profile along one typical path is extracted.
To this end, a semi-automated algorithm is run to quickly locate the end-tips of this particular
channel on the different photos (i.e. the red crosses in Figure 4). The temperatures are then
retrieved from the IR data corresponding to the selected pixels. In order to avoid any viewing
angle effect [3], the pixels locations are selected so the tube outer surface is always normal to
the IR camera. A post-treatment algorithm is then applied to merge the temperature profiles
identified on the front side (i.e. from photo #2) and the back side (i.e. from photos #3 and
#4) of the condenser. Because the tube emissivity is not perfectly known and because the
photos are not taken from the same distance, the two temperature profiles cannot be simply
superposed. Indeed, each photo gives an image of the relative temperature gradient seen from
a specific point of view, but they do not share the same absolute reference. To overcome this
issue, the temperatures profiles are shifted and combined so as to comply with the saturation
temperatures gathered by the pressure sensors. More specifically, the merging algorithm relies
in two main steps, i.e.
5
IR photo #1
26
28
30
32
34
36
38
40
42
44
IR photo #2
IR photo #3 IR photo #4
T [°C]
Figure 4: Example of IR photos taken for one operational point (the red crosses correspond to
the locations where the temperatures are evaluated).
1. to identify the pseudo-isothermal region in which occurs the condensation process on both
front and back sides;
2. to merge the front and the back temperature profiles assuming a continuity in the two-
phase region.
For instance, the temperature profile identified for the previous example is depicted in Figure 5.
As discussed in the next section, such a result offers very valuable information to better identify
the convective heat tranfer coefficients. However, the proposed infrared imaging method has
two important limitations that must be pointed out:
- Because the temperature profile is not continuously recorded but evaluated at 13 discrete
points, the zones distribution is known with a limited accuracy. In the example given
in Figure 5, the boundary between the two-phase and the vapour zones is not perfectly
assessed. Indeed, it can be located at any place between positions #1 and #2. Similarly,
the frontier between the liquid and the two-phase regions is located anywhere between
positions #7 and #8. Combining these two uncertainties, the spatial fraction occupied by
the two-phase region is known with an absolute accuracy of ±16.7%. The spatial fraction
of the single-phase zones, however, is estimated within an error of ±8.3%.
- The IR photos record the external wall temperature of the tubes which can significantly
differ from the bulk conditions of the fluid. The difference between these two values
not only depends on the ambient conditions, but also on the convective heat transfer
coefficients of the fluid. In two-phase regions, the external wall temperature is close to
the internal conditions because the condensing heat transfer coefficient is very high. In
single-phase regions, however, the heat transfer coefficient is much lower and a larger
6
Discrete position
1 2 3 4 5 6 7 8 9 10 11 12 13
Temperature [°C]
25
30
35
40
45 Two-phase Liquid
Vap
Saturation T
T from IR #2
T from IR #3
T from IR #4
Final T profile
Thermocouples
Tsat (Psu)
Tsat (Pex)
Figure 5: Temperature profiles identify for the example case in Figure 4.
temperature gradient appears between the external wall and the bulk. Such a situation
is observable in Figure 5 at the condenser inlet. Because of these radial gradients, the
temperature profiles identified with the IR data should only be used for qualitative and
not quantitative purposes. The IR observations help to identify the zones boundaries
but should not be considered as an exact measurement of the working fluid temperature
profile.
Keeping these limitations in mind, this IR imaging method is applied for every point of the
experimental campaign conducted with the ORC system. Ultimately, a complete database
of temperature profiles and global heat transfer performance is gathered to characterize the
condenser operation. As discussed in the next section, these data provide valuable information
to identify the various convective heat transfer coefficients.
4. Identification of the convective heat transfer coefficients
The convective heat transfer coefficients can either be fully re-identified from the experimental
data but best practice is to exploit state-of-the-art correlation as initial guesses. For the present
case study, the coefficients of three flow regimes must be assessed, namely for single-phase and
condensing conditions of the working fluid, so as for the air flow across the plain fins and the
tubes bank. Single-phase flows inside smooth horizontal tubes constitutes probably the best
known situation in the literature. In this work, a single correlation is considered given the large
credit recognized for its heat transfer predictions and its wide range of validity. This model
is the one of Gnielinski [4]. For each of the other flow regimes (i.e. the condensation of the
working fluid and the air flow), two candidates are selected from well-quoted correlations in
the literature, namely the models of Shah [5] and of Cavallini et al. [6] for the condensation,
and the models of Wang et al. [7] and of the VDI [4] for the air flow. Ultimately, four different
models of the condenser are considered (i.e. every combination between the two condensing
models and the two air-flow correlations) and compared to the experimental data. To assess
7
N RM S E _
Q[!]
0
0.01
0.02
0.03
0.04
0.05 VDI + Shah
Wang + Shah
VDI + Cavallini
Wang + Cavallini
(a) Fitting of the global heat transfer rate.
N RM S E/[!]
0
0.5
1
1.5
2
2.5
3VDI + Shah
Wang + Shah
VDI + Cavallini
Wang + Cavallini
(b) Fitting of the zones spatial distribution.
Figure 6: Comparison of the four set of correlations to simulate the condenser.
the validity of the different models, their predictions are discussed both in terms of global heat
transfer rate and zones spatial distribution. In order to quantify the compliance between the
simulation results with the experimental data, normalized root mean square errors (NRMSEs)
are computed for each criteria, i.e. one for the global heat transfer predictions
NRM S E ˙
Q=v
u
u
t
N
X
i=1 ˙
Qsim,i −˙
Qexp,i
˙
Qexp,max −˙
Qexp,min !2
(4)
and one for the zones spatial distribution i.e.
NRM S Eδ=v
u
u
t
N
X
i=1 |δAv,i |2+|δAl,i|2+|δAtp,i|2
3!2
(5)
where
δAv,i =Av ,sim,i −Av,I R,i
Acd,tot
(6)
δAl,i =Al,sim,i −Al,I R,i
Acd,tot
(7)
δAtp,i =Atp,sim,i −Atp,I R,i
Acd,tot
(8)
and Acd,tot is the total surface area of the condenser and Aj,sim,i/Aj,I R,i are the areas predicted
and experimentally monitored for the different zones for the ith point. The results gathered for
the four models are depicted in Figure 6. For the sake of convenience, these models are referred
to as model A,B,Cand Din the following discussion. Comparing the different NRMSE
factors, the model demonstrating the poorest fit is the model A. In comparisons to the three
others, this model leads to the largest residuals for both the global heat transfer and spatial
8
zone distributions. The models Band Cshow antagonist benefits. While the first one much
better replicates the condenser heat transfer rate, the model Chas a better compliance with
the zones spatial distribution. The best candidate among the four options investigated appears
to be the model D, i.e. the one coupling the correlations of Wang et al. [7], of Cavallini et al. [6]
and of Gnielinski [4]. A good starting point is thus to consider these correlations to calculate
the convective heat transfer coefficients. In order to further improve the model predictions,
these CHTC correlations can be adjusted so as to better comply with the experimental data.
To this end, each correlation is simply scaled by a constant factor cjas proposed in [8], i.e.
Nu∗
j=cjNuj(9)
where Nujis the original Nusselt number predicted by the correlation. To ensure the most reli-
able model, the calibration of the cjfactors is conducted by minimizing the residuals committed
on both the heat transfer rate and the zones repartition predictions, i.e.
min
cj F= Ψ v
u
u
t
N
X
i=1 ˙
Qsim,i −˙
Qexp,i
˙
Qexp,max −˙
Qexp,min !2
| {z }
NRMSE ˙
Q
+Ω v
u
u
t
N
X
i=1 |δAv,i |2+|δAl,i|2+|δAtp,i|2
3!2
| {z }
NRMSEδ
(10)
where Ω and Ψ are two scaling values giving the same weight at both criteria. The correction
factors identified by this optimization are specified in Table 1 and the results gathered with
the adjusted correlations are depicted in Figure 7. As demonstrated, a good agreement is now
observed for both heat transfer and spatial distribution predictions.
Experimental power [W]
0 10 20 30
Simulated power [W]
0
5
10
15
20
25
30
RMSE = 260 W
X=Y
± 10%
(a) Experimental vs. simulated heat
transfers
Spatial deviation /A [-]
-1 -0.5 0 0.5 1
Number of points
0
50
100
150
200
250
300
350 2-phase
Liquid
Vapour
(b) Histogram on spatial distribution er-
rors
Figure 7: Predictions after tuning of the best predictive model.
9
Figure 8: Compact condenser for an automotive application.
5. Conclusion
Although crucial for simulations, a proper identification of the convective heat transfer coef-
ficients in multi-zone heat exchangers is a challenging task. While well instrumented systems
permit to accurately record the energy balance in such components, the sole knowledge of the
global heat transfer rate is not enough to reliably assess these coefficients. In this work, it is
proposed to use the zones spatial distribution (i.e. the spatial fraction occupied by the liquid
phase, the vapour phase and/or the two-phase regions) as a second identification criteria. An
air-cooled condenser placed in a 2kWe ORC unit is considered as case study and a dedicated
IR imaging method is presented to assess the spatial distribution of the different zones. These
new data, combined with standard heat transfer rate measurements, are exploited to identify
the best heat transfer correlations pre-selected from the scientific literature. Ultimately, it is
shown that for the present case study, the correlations of Wang et al. [7], Gnielinski [4] and
Cavillini et al. [6] best replicate the experimental observations. In order further improve the
model predictions, the original heat transfer correlations are tuned so as to better fit both data
on the global heat transfer rate and zones repartition.
The methodology proposed here above is not restricted to the present case study and can be
re-applied to many other heat exchanger (HEX) technologies. As long as the temperature
evolution can be recorded with an IR camera (as shown in Figure 8 for another example),
the zones spatial distribution can be reconstructed and exploited effectively. This method is
particularly suited for heat exchangers implying two-phase conditions inside tubes (e.g. finned-
tube HEXs, tube-in-tube HEXs, helocoidal HEX, etc.) but could also be extended to other
common technologies, like plate heat exchangers (e.g. as demonstrated in [9]).
10
Appendix
The coefficients identified by minimizing (10) are reported in Table 1. Constitutive equations
of the heat transfer correlations are accessible in the corresponding references.
Table 1: Adjusting coefficients of the heat transfer correlations
Zone Heat transfer correlation Tuning coefficient
Air-side flow Wang et al. [7] c= 0.8719
Liquid flow Gnielinski [4] c= 0.7868
Condensing flow Cavallini et al. [6] c= 1.6
Vapour flow Gnielinski [4] c= 2.45
Nomenclature
CHTC Convective Heat Transfer Coefficient ˙
QHeat power [W]
HEX Heat Exchanger tthickness [m]
HVAC Heating Ventilation Air Conditioning UHeat transfer coefficient [W/m2.K]
LMTD Logarithmic Mean Temp. Difference Ttemperature [K]
NRMSE Normalize Root Mean Square Error
ORC Organic Rankine Cycle c cold
cd condenser
Asurface [m2] ex exhaust
ccoefficient [−] exp experimental
∆TTemperature difference [K] h hot
ηFin efficient [−] l liquid
FLMTD factor [−] log logarithmic
HConvective Heat Transfer Coeff. [W/m2.K] sat saturation
kConductivity [W/K] sim simulated
˙mmass flow [kg/s] su supply
Nu Nusselt number [−] tp two-phase
PPressure [P a] v vapour
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