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Modelingandexperimentalvalidationofatube‐in‐tube
refrigerantcooledabsorber
Tommaso Toppi (1), Marcello Aprile, Marco Guerra, Mario Motta
Department of Energy, Politecnico di Milano, 20156 Milano, Italy
Preprint
© 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
http://creativecommons.org/licenses/by-nc-nd/4.0/
Please cite this paper as:
Toppi, T., Aprile, M., Guerra, M., & Motta, M. (2015). Modeling and experimental validation of a
tube-in-tube refrigerant cooled absorber. Applied Thermal Engineering, 80, 374–385.
https://doi.org/10.1016/j.applthermaleng.2015.01.073
Abstract
A model for predicting heat and mass transfer and pressure drops occurring inside a tube-in-tube
refrigerant cooled absorber (RCA) is developed. This heat exchanger is used as a low pressure
absorber in a half-effect water-ammonia absorption chiller. The two-phase stream, resulting from
the mixing at low pressure of the weak solution coming from the generator and the refrigerant
leaving the evaporator, flows in the tube-in-tube annulus, while the stream of condensed refrigerant,
throttled to a pressure level intermediate between condenser and evaporator pressures, flows
counter-current in the internal tube. The RCA model is validated by comparing overall heat transfer
1 Corresponding author
E-mail address: tommaso.toppi@polimi.it
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duty, pressure drops on each stream and temperature axial profile in the annulus with experimental
data. Results are in reasonable agreement with experiments in most of the analyzed cases, although
some deviations exist in off-design operations. A sensitivity analysis of the model has shown that
the measurement uncertainty of the inputs to the model does not affect the validity of the results.
1. Introduction
A refrigerant cooled absorber (RCA) is a heat exchanger where the cooling effect for absorbing
some refrigerant vapor within a solution mixture is provided by the evaporation of a fraction of
liquid refrigerant. Such device can be effectively employed in absorption cycles, although its use is
not common. One example is represented by the prototype of half-effect absorption chiller that has
been recently realized [1], experimentally demonstrated [2] and characterized [3]. The key
operating principle of the cycle (see Fig. 1) consists in utilizing part of the liquid refrigerant leaving
the condenser (CON) to cool, at an intermediate pressure, the solution in which the remaining part
of the refrigerant is absorbed after leaving the evaporator (EVA). Such operation takes place inside
a tube-in-tube counter current refrigerant cooled absorber (RCA). A two-phase water-ammonia
solution (with ammonia mass fraction about 0.55) at low pressure (4.5 - 5 bar) flows in the RCA
annulus, counter-current with respect to the refrigerant (ammonia mass fraction above 0.99 at about
8-10 bar) flowing in the internal tube. In the annulus, the vapor is absorbed in the liquid solution,
while in the internal tube, part of the refrigerant evaporates.
A properly sized RCA is crucial for the cycle operation. At parity of other conditions, an effective
RCA allows increasing the pressure in the air cooled absorber (ABS), which in turn allows keeping
a high ammonia mass fraction at the inlet of the generator (GEN). Thus, the concentration gradient
in the GEN increases, providing a positive effect on cycle performance and capacity.
In the literature, many experimental and numerical studies can be found about tube-in-tube heat
exchangers.
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Fig. 1 – Scheme of the half-effect cycle.
Garimella et al. [4] investigated single-phase heat transfer within coiled annular ducts, finding
higher heat transfer coefficients for the coiled annular ducts compared to the ones for straight
annulus. The augmentation of the Nusselt number is higher in the laminar region than in the
transition region, while the turbulent region is not investigated.
Wongwises and Polsongkram addressed two-phase flow in the internal tube [5, 6], investigating
both evaporation and condensation heat transfer and pressure drop of HFC-134a in a helically
coiled concentric tube-in-tube heat exchanger, with two-phase refrigerant flowing in the inner tube
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and water in the annulus. Focusing on the effects of coiling on the heat transfer coefficient and
pressure drops, they found an increase of both when compared with a straight heat exchanger.
A finite volume numerical model for a tube-in-tube heat exchanger with both smooth and fluted
tube is proposed by Huang et al. [7], with refrigerant flowing in the annulus and cooling or heating
water flowing in the inner pipe. A discussion over the precise and reliable methods for tracking the
phase change location is also proposed, with the purpose of reducing the number of finite volumes
and the computational time.
Concerning the pressure drop, Ekberg et al. [8] experimentally investigated two-phase flow
regimes, void fraction and pressure drop in horizontal concentric annuli, comparing the
experimental results with existing correlations. They verified that the same correlation might either
overestimate or underestimate the experimental data, depending on the flow type.
Several works focused on the effect of coiling, comparing heat transfer coefficients and pressure
drops in coiled and straight pipes. The impact of coiling resulted to be dependent on several
parameters, such as the hydraulic diameter, the Dean number, the presence of spacers, the relative
position of the two pipes (concentric, eccentric, with contact) and the flow type (single-phase or
two-phase flow).
Kumar at al. [9] carried out an experimental and numerical investigation on a single-phase flow in a
tube-in-tube helical heat exchanger, with semicircular plates to support the inner tube and to
provide high turbulence in the annulus region. They pointed out that the heat transfer coefficient
and the friction factor increase for coiled tube compared with straight tube, both in the inner pipe
and in the annulus.
These achievements are confirmed by Aria et al. [10], who investigated heat transfer and pressure
drops on a boiling flow of HFC-134a inside a vertical helically coiled concentric tube-in-tube heat
exchanger.
However, the extension of these results from single-phase to two-phase flow is not straightforward.
In fact, as pointed out by Xin et al. [11], the Lockart-Martinelli parameter appears to be lower for
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coiled than for straight annular pipes. This implies that, even if the single-phase pressure drops
increase from straight to coiled annulus, the same may not apply to two-phase flow.
Louw and Meyer [12] investigated the effects on heat transfer and pressure drops of the contact
between internal and external tube, when no spacers are placed between the internal and external
pipe. According to their findings, with respect to the case of concentric pipes, the Nusselt number
decreases in the internal pipe and increases in annulus, while pressure drops in the annulus increase
because of the tube contact.
To the best knowledge of the authors, a study on a tube-in-tube heat exchanger like the RCA, with
two-phase flow in both the inner tube and the annulus, has not been presented previously.
Thus, the objective of this work is to develop and validate a model for predicting the heat and mass
transfer occurring inside a tube-in-tube RCA, along with pressure drops in the internal pipe and in
the annulus. Besides the validation of heat transfer rate and pressure drops, the calculated
temperature profile in the annulus is compared with the experimental temperature profile, measured
along the heat exchanger length. The validation is carried out for different working conditions (i.e.,
temperatures, pressures, mass flow rates and ammonia mass fractions) on both sides of the RCA,
achieved during the steady-state characterization of the aforementioned half-effect chiller prototype
[3].
Finally, a sensitivity analysis has been carried out to assess the reliability of the validation and to
prove that it is not affected by the measurement uncertainty of the inputs to the model.
2 Model description
In this section the RCA model, based on a finite volume approach, is presented. At first the heat
exchanger geometrical features are described. Then, the set of equation solved for each discrete
segment and the heat transfer and pressure drop correlation used within the model are reported.
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2.1. RCA geometry
The RCA is a coiled tube in tube heat exchanger, where a two-phase water ammonia solution flows
in the annulus and the refrigerant flows counter-current in the internal pipe. The heat transfer is
from the solution to the refrigerant, thus the liquid solution absorbs the vapor, while the refrigerant
partially evaporates.
The heat exchanger is composed by two parts with different internal tube diameter. The reason for
the diameter increase lies in the need of sustaining the solution heat transfer coefficient once the
vapor is fully absorbed and the velocity in the annulus tends to decrease: an increase of the internal
tube diameter reduces the annulus cross section and increases the solution mass flux, maintaining a
good heat transfer coefficient.
The total length of the heat exchanger is 9.36 m, being the two sections (LA and LB) 7.06 m and
2.30 m respectively. The external pipe external diameter is 20 mm. The internal tube external
diameter is 12 mm in the first section (DA) and 15.8 mm in the second (DB). The thickness of both
the internal and the external tube is 1 mm. With reference to Fig. 2, the solution inlet section is at
z=0, while the refrigerant inlet section is at z=LA+LB.
There is not a spacer between the two pipes. This implies that the concentric positioning of the
tubes cannot be assured.
Fig. 2 – Tube-in-tube HX geometry.
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2.2 Model assumption
The heat exchanger is discretized in segments of finite size, each one composed of an inner control
volume, containing refrigerant nearly pure in ammonia (ammonia mass fraction above 0.99), and an
outer control volume, containing water ammonia solution (ammonia mass fraction in the range
0.52-0.55). Mass and energy balances are solved iteratively, starting from the solution inlet section
(z=0) and marching towards the refrigerant inlet section (z=LA+LB).
The model is based on the following simplifying hypotheses:
1. Steady state is achieved;
2. Flow is one-dimensional;
3. Kinetic energy and gravitational potential are negligible;
4. Flow is thermally and hydro-dynamically fully developed;
5. Fluid properties are evaluated at the inlet state of each segment;
6. Thermodynamic equilibrium is imposed at each intermediate section;
7. Equilibrium properties are calculated using the Ziegler-Trepp equations of state [13].
8. Heat losses are negligible;
9. Heat conduction in flow direction is negligible;
10. Pipes are concentric and the influence of coiling is negligible.
Most of these assumptions are commonly adopted in the modelling of tube-in-tube heat exchangers
[7]. Steady state (assumption 1) was essentially verified by looking at the fluctuations of
temperatures and pressures, which were fairly stable. Assumption 6 is introduced in order to keep
consistency with the underlying model in most engineering heat transfer correlations, which will be
commented in Section 2.3.
Hypothesis 7 is reasonable thanks to the low heat transfer coefficient due to free convection
between surface and air, in comparison to the internal heat transfer coefficient with the solution.
Moreover, the heat exchanger is insulated with the purpose of reducing the heat losses towards the
environment.
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Concerning assumption 10, both the coiling and the contact between internal and external pipe
might have an impact on heat transfer and pressure drops. However, even if some trends have been
observed in previous works, generalized correlations, able to deal with both these phenomena, are
not currently available. Nevertheless, in commenting the results of this work, the known trends are
taken into account.
2.3 Model equations
An equal set of governing equations is imposed on both solution and refrigerant control volumes
[14]. For simplicity, only the solution side control volume is detailed in the following (see Fig. 3).
Fig. 3 - Differential control volume (solution).
Overall mass balance across liquid phase:
0 (1)
Overall mass balance across gas phase:
0 (2)
Mass balance of ammonia across liquid phase:
0 (3)
Mass balance of ammonia across gas phase:
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0 (4)
Energy balance across liquid phase:
0 (5)
Energy balance across gas phase:
0 (6)
Thermodynamic equilibrium at the output section:
,
0 (7)
,
0 (8)
Thermal equilibrium between liquid and gas phase:
0 (9)
Heat transfer relationship between wall and fluid:
A
(10)
Pressure drop across the elemental volume:
∆
(11)
The corresponding set of governing equations for the refrigerant domain provides additional 11
equations. System closure is achieved by coupling the heat transfers and through the
conduction across the internal tube wall, . The heat transferred from solution domain to the
environment is neglected.
Heat transfer condition at the inner wall of the internal tube:
0 (12)
Heat transfer condition at the outer wall of the internal tube:
0 (13)
Heat transfer relationship across the internal tube wall:
1
(14)
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2.4. Heat transfer and pressure drop correlations
The equilibrium conditions in Eq. 7 and 8 were determined by the Ziegler-Trepp equations of state.
The heat transfer coefficient between the solution bulk and the outer wall of the inner tube was
calculated according to the Shah correlation for heat transfer during condensation in pipes [15],
which joins up the Dittus-Boelter correlation (DB) in the saturated and subcooled liquid region. The
temperature in the inner tube cross section was supposed uniform and the heat transfer coefficient
on the refrigerant side was calculated according to the flow pattern dependent model of Kattan-
Thome-Favrat (KTF), which was validated against experimental data for pure ammonia [16, 17].
Concerning two-phase pressure drops, the correlation of Friedel [18] was used, which was reported
as one of the most accurate for two-phase flows in annuli [8].
Table 1 – Validity and application range of used correlations.
Correlation Use Validity range Application range
Shah
Solution heat transfer
coefficient (two-
phase)
Re 350
Re 35000
200
Re 1100-1300
Re 85000 90000
150 350
DB
Solution heat transfer
coefficient (single-
phase)
10000 120000
800
0.7 120
1000 1100
0.9 7
KTF Refrigerant heat
transfer coefficient
16.3
500
10.9 16.0
74 Re 20399
20
80
10.0
13.8
Re 2000 6000
Friedel Two-phase pressure
drop
1000
2000
7
annulus
70
150 400
6.0
4.2
internal pipe
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G2080
10.0
13.8
The validity range of the used correlations is substantially satisfied, as summarized in Table 1. The
main constraint that does not seem satisfied is the Reynolds number for the Dittus-Boelter
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correlation. However, as underlined in [19], the Dittus-Boelter correlation can be used at Reynolds
number about 1000 with sufficient accuracy, as in the annulus the transition from laminar to
turbulent flow occurs in the range 800-1200. The second requirement that is not met is the hydraulic
diameter in the annulus, which is lower than what required by the Friedel correlation, both in the
first and the second section of the heat exchanger. Finally, in some operating conditions, the
Reynolds number in the annulus is slightly below the lower limit of the Shah correlation. These
aspects and their possible impacts on heat transfer and pressure drop in the annulus will be
discussed in Section 3.3 and 3.4.
3. Experimental validation
The numerical model has been validated by means of a comparison with experimental data.
Different operating conditions for the RCA have been achieved by running the low temperature
absorption chiller under different working conditions (air temperature, hot water temperature, hot
water mass flow rate).
In this paper, a selection of eight conditions is presented (see Table 2), with the purpose of
analyzing both cases where the RCA model matches very well the experimental results and others
where the accuracy is lower.
Table 2 – set of appliance working conditions used for the model experimental validation
ID
(°C)
(°C)
(°C)
(kg s-1)
(°C)
(°C)
(kg s-1)(W)
(kW)
(kW) COP COPel
1 30 90 80 0.240 12 7 0.147 287 9.40 2.82 0.300 9.81
2 37 90 80 0.168 12 7 0.079 367 6.73 1.65 0.245 4.50
3 40 90 80 0.147 12 7 0.056 460 5.65 1.12 0.198 2.43
4 35 90 85 0.425 12 7 0.117 366 9.06 2.49 0.275 6.81
5 40 90 85 0.375 14 9 0.080 465 7.34 1.67 0.228 3.59
6 35 93 88 0.486 12 7 0.133 410 9.78 2.74 0.280 6.69
7 38 93 88 0.431 12 7 0.117 465 8.69 2.28 0.262 4.90
8 35 85 80 0.375 12 7 0.097 368 7.49 2.02 0.269 5.48
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The chiller performances have been evaluated over a period of at least 10 minutes of stable
operation, meaning that:
- the air temperature had an instantaneous deviation from the average value lower than 0.1 °C;
- the hot water inlet temperature had a deviation from the average value lower than 0.2 °C
- the chilled water inlet had a deviation from the average value lower than 0.1 °C.
3.1 Input to the numerical model
The numerical model bases the calculation on a set of input data, namely the refrigerant and the
solutions conditions at one of the two ends of the heat exchanger. For what concerns the
temperature and the pressure, the inputs have been directly measured on the heat exchanger. On the
other hand, the ammonia mass fraction, the mass flow rate and the vapor quality on both sides of the
RCA are unknown and difficult to measure. To overcome this problem, the unknown input data
have been identified by means of a steady state model of the appliance, that relies on the pressure
(Px) and temperature (Tx) data collected along the cycle (see Fig. 1) and on the measured heat
transfer rates at the water heated generator and at the evaporator. The details on the identification
procedure and its accuracy can be found in [3].
Temperature and pressure measurements are collected with a sampling period of 12 s. Average
values over the entire data acquisition period are used both to feed the numerical model of the RCA
and the numerical simulation of the appliance.
The inputs to the RCA model for the eight studied conditions are reported in Table 3, with reference
to the heat exchanger section corresponding to the solution inlet and refrigerant outlet.
In tests from 1 to 3 the driving hot water inlet and outlet temperature have been kept at 90 °C and
80 °C respectively. The air temperature was set to 30 °C, 37 °C and 40 °C. Over this temperature
range, maintaining chilled water temperature at 12 °C inlet / 7 °C outlet, the power absorbed at the
generator, the cooling power and the COP decreased. On the RCA, the effects of an increased air
temperature are a higher pressure, a higher temperature and a lower mass flow rate both at the
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solution inlet and at the refrigerant outlet sections (see Table 3). Moreover, the vapor quality at the
refrigerant outlet becomes larger, as a higher fraction is evaporated in the RCA to absorb the vapor
in the solution. At the same time, the amount of vapor that needs to be absorbed in the solution
becomes smaller, as it corresponds to the refrigerant mass flow rate returning from the evaporator.
The same relation can be found in test 4 and 5 with a hot water temperature of 90 °C inlet / 85 °C
outlet and for test 6 and 8, with a hot water temperature of 93 °C inlet /88 °C outlet. In the first case,
the air temperature has been raised from 35 °C to 40 °C, in the latter from 35 to 38 °C. It has to be
noticed that 40 °C was beyond the operating limit of the appliance, at chilled water temperature 12
°C inlet / 7 °C outlet, which has thus been raised to 14 °C inlet / 9 °C outlet. Moreover, condition 8
has been chosen for the lower hot water temperature, which further shifts the RCA operating
conditions.
Table 3 – Mass flow rate and thermodynamic properties at RCA solution inlet/refrigerant.
ID
refrigerant side solution side
(kg h-1)
(kg h-1)
(-)
(-)
(°C)
(bar)
(kg h-1)
(kg h-1)
(-)
(-)
(°C)
(bar)
1 8.64 13.96 0.996 1.000 21.4 8.9 68.98 8.64 0.490 0.996 35.3 4.4
2 5.19 9.81 0.995 1.000 23.7 9.6 71.17 5.19 0.509 0.995 37.9 4.6
3 3.61 8.07 0.995 1.000 24.5 9.8 71.75 3.61 0.522 0.995 39.5 4.7
4 7.85 13.42 0.995 1.000 24.3 9.7 71.58 7.85 0.498 0.995 39.1 4.7
5 5.42 10.71 0.994 1.000 26.1 10.3 72.86 5.42 0.517 0.994 42.5 5.1
6 8.64 14.51 0.995 1.000 24.5 9.8 72.42 8.64 0.487 0.995 40.0 4.7
7 7.27 12.83 0.994 1.000 25.9 10.2 73.40 7.27 0.497 0.994 41.6 4.9
8 6.32 11.04 0.996 1.000 23.3 9.5 68.92 6.32 0.519 0.996 37.2 4.8
3.2 RCA temperature profile measurement
Ninety-four thermocouples have been placed on the external surface of the heat exchanger, spaced
by 10 cm, covering the entire length of the RCA (see Fig. 4 and Fig. 5). The thermocouples have
been insulated in order to reduce the disturbance of the external conditions, so that, neglecting the
thermal resistance of tube, the measured value was reasonably close to the solution temperature.
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An error has been found for few thermocouples, whose reading was affected by the proximity of the
frame supporting the RCA coils, which created a sort of thermal bridge across the insulation layer.
Figure 4 – Thermocouples positioning along the RCA.
Fig. 5 – Thermocouples placed on the RCA before insulation.
3.3 Metrological analysis
The experimental data have been collected running the absorption chiller in a climatic chamber,
connected with external water circuits with controlled temperature and mass flow rate. The air and
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water temperature were measured with thermo-resistance Pt100, while the water mass flow rates
were measured with magnetic flow meters. Sensors with a suitable operating range and properly
calibrated were used. The temperature influence on the water properties (density and specific heat
capacity) was considered in the calculation of uncertainties.
The meters used for each variable and the related measure uncertainty are reported in Table 4. The
values include both the sensor uncertainty and the digitalization of the signal. The uncertainties
expressed in terms of percentage refer to the read value.
Table 4 – Uncertainty assessment of measured quantities.
Quantity Meter Range Uncertainty
Pt100 23‐40°C ±0.10°C
Pt100 70‐90°C ±0.10°C
∆Pt100 5‐10°C ±0.15°C
magneticflow
meter 500‐1800kg/h 1.0‐2.0%
Pt100 7‐12°C ±0.10°C
∆
Pt100 5‐10°C ±0.15°C
magneticflow
meter 280‐500kg/h 1.5‐2.5%
calculated 5‐10kW 1.8‐3.2%
calculated 1‐3kW 3.2‐3.4%
profile thermocouples 25‐40°C ±0.4°C
∆
capacitiveP
probe 15‐25kPa 0.5‐0.8%
∆
capacitiveP
probe 1.5‐5.0kPa 2.5‐8.0%
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3.4 Results on the heat transfer rate
The RCA model has been run based on both measured and calculated inputs to replicate the
experimental conditions. A reasonable agreement with the experimental data has been found for all
the operating conditions. A first qualitative evaluation of the match between numerical and
experimental results can be found in Figure 6, where each sub-plot is related to a specific operating
condition. The measured value of each thermocouple is displayed with a dot, while the straight line
represents the temperature profile obtained by means of the numerical calculation. As the charts are
plotted with the same scale, it is possible to appreciate the different temperature profiles achieved
and used for the model validation.
A more quantitative evaluation of the agreement between numerical and experimental results can be
found in Table 5, where the average deviation, the root mean square deviation (RMSD) and the
maximum and minimum difference between numerical and experimental data are reported.
These parameters confirm that the results related to condition 3 and condition 6 are the least and the
most accurate respectively.
Table 5 – Difference between numerical and experimental temperature profile along the RCA.
Condition
ID
Average RMSD Min Max
°C
1 0.43 0.50 -0.22 1.17
2 0.76 0.83 -0.30 1.72
3 1.16 1.21 0.09 2.22
4 0.35 0.46 -0.25 1.19
5 0.22 0.43 -1.06 1.18
6 0.31 0.41 -0.35 1.07
7 0.50 0.54 -0.18 1.34
8 0.67 0.73 -0.53 1.47
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Figure 6 – Comparison between the calculated (straight line) and measured (dotted line) RCA
temperature profile.
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As the RCA is an internal heat exchanger, with two-phase flow on both the sides, a reliable measure
of the heat transfer rate was not possible, thus, the experimental value, used as reference, is the
calculated heat transfer obtained from the chiller numerical model. The RCA model proves to be
rather accurate in predicting the heat transfer rate (see Table 6).
Table 6 – Heat transfer in the RCA: comparison between RCA model and experimental results.
Condition
ID
QRCA (kW)
Numerical Experimental Difference
1 4.17 3.99 4.7%
2 3.70 3.64 1.7%
3 2.02 2.30 -12.0%
4 4.52 4.41 2.4%
5 3.79 3.79 0.0%
6 2.82 3.01 -6.4%
7 3.19 3.20 -0.4%
8 3.98 3.85 3.5%
For both the solution temperature profile and the heat transfer rate, the model accuracy decreases
when the heat exchanger works outside the design conditions (as in condition 3). In these cases, a
root mean square deviation up to 1.2 °C can be found in the calculation of the temperature profile
and up to 12% in the heat transfer rate. A clear influence of the RCA load on the model accuracy
can be found in Figure 7, where the RMSD is plotted against the RCA heat transfer rate for a large
set of conditions, including some not presented in detail within this work. A possible reason, which
is not taken into account in the model, is an increase of the heat transfer coefficient due to the coiled
shape of the RCA. In single-phase flows, this effect appears to have a larger impact at low Reynolds
numbers [4]. Even if not directly applicable for two-phase flow, a similar behavior would justify the
larger difference between experimental and numerical data at low (~150 kg m-2 s-1) than at high
(~400 kg m-2 s-1) mass fluxes. However, in [5] an increase of the heat transfer coefficient during
condensation is reported also for mass fluxes in the range 400-800 kg m-2 s-1, making this
explanation less certain.
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A more convincing explanation might lie in the use of the Shah correlation for mass fluxes below
the lower limit of applicability. This is the case for the conditions at low heat transfer rates, which
show the largest deviations from the experimental data. The explanation is coherent with the results
at high heat transfer rates, which show the smallest deviations from experimental data and have a
mass flux within the range of validity for the Shah correlation.
Figure 7 – RMSD plotted against the RCA heat transfer rate.
3.5 Results on the pressure drops
On the annulus side, the calculated pressure drops generally underestimate the measured values,
which range between 17 and 40 kPa, with a deviation between 10% and 25% (see Table 7).
Table 7 – Pressure drop in the annulus: comparison between RCA model and measured data.
ID Numerical
(kPa)
Experimental
(kPa) Difference
1 23.42 28.27 -17.2%
2 18.07 23.82 -24.1%
3 15.95 20.45 -22.0%
4 25.10 28.28 -11.3%
5 18.59 23.26 -20.1%
6 22.53 28.75 -21.6%
7 19.66 26.32 -25.3%
8 20.26 24.20 -16.3%
20
The hydraulic diameter lower than the lower limit required by the Friedel correlation does not seem
to be a valid reason for the higher than expected pressure drop. In fact, experiments on two-phase
flow in straight small diameter circular pipes (D≤2.3 mm) proved that the Friedel correlation
overestimates the actual pressure drop, especially at small mass flux [20].
Concerning the refrigerant side, values between 1.5 kPa and 5 kPa have been found for the pressure
drop. The simulated values are found to be in the same range, but, even if in some conditions the
pressure drop is predicted with a rather good accuracy (±20%.), others experimental results show
errors up to ±50%. In this case, a clear systematic error has not been found, as the deviation is much
sparser.
Besides these errors, it can be considered that the model provides reasonable prediction of the
pressure drops. In fact, the errors in both the annulus and in the internal pipe are in the range of
accepted deviations, as it is normally expected that not more than 80% of the experimental data are
predicted with accuracy better than ±30% by correlations [21].
A deeper investigation of the topic is outside the scope of this work. Nevertheless, the model can be
improved in the future by taking into consideration the effects of the heat exchanger coiled shape
[9, 10] and the contact between internal and external tube [12]. Unfortunately, comprehensive
correlations are not available for two-phase flow. Finally, the flow regime could be another aspect
to be considered for better predictions of pressure drops. In fact, according to [8], the Friedel
correlation overestimates pressure losses in the annulus under certain flow regimes (plug, stratified
and annular-plug) and underestimates them in others (bubbly, churn). In some of the flow regimes,
the deviation seems to depend on the annulus thickness (annular, bubbly-plug).
4. Sensitivity analysis
In this section a sensitivity analysis is presented, with the purpose of discussing the influence of
input data on the model results and validation. Each input is varied, maintaining the other
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parameters of the set constant. Then, the numerical model is run to underline the effects of each
variation.
The results of the sensitivity analysis are presented for two test conditions: the least and the most
accurate (conditions 3 and 6, based on Table 5). Nevertheless, the analysis and the discussion can
be extended to all the test conditions included in this work.
The solution temperature profiles obtained within the sensitivity analysis are reported in Figure 8
and Figure 9 for condition 6 and Figure 10 and Figure 11 for condition 3. In the charts the
temperature profiles, obtained from the measured and calculated inputs, are represented with a
continuous line (base). The two dashed lines correspond to the temperature profiles obtained
modifying one of the inputs; each hollow circle represents a thermocouple measurement, while the
black dotted line is the refrigerant side temperature profile with the base inputs.
Each figure shows the resulting variation of the temperature profile, when one of the inputs is
changed as follows:
- Refrigerant mass flow rate: increased and decreased by 5% (mr +5%, mr -5%);
- Refrigerant vapor quality: increased and decreased by 5%, maintaining constant total mass flow
rate (xr +5%, xr -5%);
- Liquid phase ammonia mass fraction in the refrigerant: increased and decreased by 1%, making
sure that it never exceeds 1 (CrL +1%, CrL -1%);
- Refrigerant pressure: increased and decreased by 0.5% (Pr +0.5%, Pr -0.5%);
- Solution mass flow rate: increased and decreased by 5% (ms +5%, ms -5%);
- Solution vapor quality: increased and decreased by 5%, maintaining constant total mass flow rate
(xs +5%, xs -5%);
- Liquid phase ammonia mass fraction in the solution: increased and decreased by 1% (CsL +1%,
CsL -1%);
- Solution pressure: increased and decreased by 0.5% (Ps +0.5%, Ps -0.5%).
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The analysis on both condition 3 and 6 shows little influence on the shape of the solution
temperature profile and on the heat transfer rate when an input related to the refrigerant side is
modified. Variations of inputs on the refrigerant side modify the temperature profile mostly on the
last part of the RCA, where the inner tube diameter is larger and the solution is sub-cooled liquid.
This can be explained looking at the heat transfer coefficients in the annulus and in the internal
pipe. In the first section of the RCA, the internal and external heat transfer coefficients are about of
the same magnitude and none of the two is dominating over the other. On the contrary, in the
second section, the heat transfer is dominated by the heat transfer coefficient in the internal pipe,
which is about three times smaller than the one in the annulus. Thus, a variation of one of the inputs
related to the internal pipe has a stronger impact on the second section than on the first one.
Moreover, in the second part of the RCA, the solution completes the absorption of the vapor and
becomes fully liquid. In a liquid flow, a variation on the heat transfer conditions may cause larger
temperature variations than in a two-phase flow.
Regarding the annulus, the solution mass flow rate and the vapor quality at the RCA inlet have little
influence on the calculations and, again, the variations are mainly located at the last part of the heat
exchanger. Larger impact is found for variation of the solution pressure and concentration: a higher
concentration or a lower pressure shift down the temperature profile, while lower concentration or
higher pressure move it up. The effects of a variation of one of these two inputs are found along all
the RCA length.
In subplots (b), (c) and (d) of Figure 9 and Figure 11, the lines cross in the final section of the RCA.
This behavior may seem unexpected and deserves a case-by-case explanation. Considering subplot
(b), if the inlet solution vapor is increased (red line), a larger amount of vapor has to be absorbed
along the RCA. Keeping constant the other parameters, the length of heat exchanger needed for the
absorption process increases. On the other side, higher vapor quality means also higher pressure
losses, which reduce the solution pressure and thus the temperature at the final section of the heat
exchanger.
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Moving to subplot (c), where the influence of different solution concentrations is reported, when the
liquid solution concentration decreases, the two-phase solution temperature increases. This provides
a larger temperature difference between the solution and the refrigerant, which improves the heat
transfer and anticipates the completion of the absorption process. Once the vapor has been
absorbed, the liquid solution temperature drops rapidly. On the contrary, a higher concentration
reduces the solution temperature and extends the absorption phase.
The same discussion can be made for subplot (d), where the pressure variation at constant
concentration gives the same effects.
Looking at the charts, it seems clear that an error on one of the inputs of the refrigerant side have a
little effect on the results of the RCA model. The same can be stated about the solution mass flow
rate or vapor quality.
More interesting is the sensitivity analysis on the solution ammonia mass fraction and pressure.
Looking at condition 6, variation on the solution ammonia mass fraction or pressure may slightly
improve the model accuracy, which is however already good with the original inputs. On the other
side, looking at condition 3, where the model results to be less accurate, a variation of one of these
inputs may improve the match between numerical and experimental results, but it does not seems
enough to reach the accuracy found for condition 6.
On the basis of these considerations, it can be stated that any modification on the model input can
hardly move very accurate RCA model results to less accurate ones and vice versa. This means that
errors in the determination of the RCA inputs due to measurement uncertainty or to imprecise
identification of chiller states, if within reasonable values, may slightly improve or deteriorate the
model validation, but cannot modify its conclusions.
24
Figure 8 – Sensitivity analysis on the inputs for test condition 6, refrigerant side.
25
Figure 9 – Sensitivity analysis on the inputs for test condition 6, solution side.
26
Figure 10 – Sensitivity analysis on the inputs for test condition 3, refrigerant side.
27
Figure 11 – Sensitivity analysis on the inputs for test condition 3, solution side.
5. Conclusions
The heat and mass transfer occurring inside a tube-in-tube counter current refrigerant cooled
absorber (RCA) has been investigated by numerical simulations and the overall heat exchanger
performance has been validated against experimental data. In particular, the calculated temperature
profile of the solution flowing in the annulus has been compared with experimental data, finding
that the model predictions are in reasonable agreement with the experiments. Moreover, it has been
found that the calculated heat transfer rate matches the experimental value with accuracy better than
12%. From an analysis on the model accuracy, it appears that the higher the load at the RCA, the
28
better the model accuracy. The most convincing explanation for the lower accuracy at low heat
transfer rate is the use of the Shah correlation for mass fluxes below its lower limit of applicability.
A deviation of 0-20% has been found for the calculation of pressure drop in the annulus. Even if
within the typical range of accuracy of pressure drop correlations, the values show that the model
tends to underestimate the experimental data. Some possible reasons have been discussed, but none
of them has been found convincing. Among the considered issues there are the coiled shape of the
heat exchanger, the contact between the two pipes and the use of the Friedel correlation slightly
outside the validity range. Concerning the pressure drops in the internal tube, a deviation between
calculated and measured value of ±50% has been found.
Finally, a sensitivity analysis has been carried out on the inputs to the RCA, finding that errors in
the measured or calculated inputs may improve or reduce the match between numerical and
experimental results, without modifying the overall conclusions of the validation.
Nomenclature
A heat transfer area, m2
C ammonia mass fraction, kg kg-1
D diameter, m
Dhyd hydraulic diameter, m
E electrical power, W
G mass flux, kg m-2 s-1
h heat transfer coefficient, W m-2 K-1
i enthalpy, J kg-1 K-1
L axial length, m
mass flow rate, kg s-1
P pressure, Pa
Pr Prandt number, -
29
Q heat transfer rate, W
thermal resistance for cylindrical pipe, K W-1
Re Reynolds number, -
T temperature, K
x vapor quality, kg kg-1
z axial coordinate, m
m dynamic viscosity, Pa s
P pressure difference, Pa
T temperature difference, °C
z finite element length, m
Subscripts
1 finite volume inlet section
2 finite volume outlet section
A first section of the RCA
a ammonia
B second section of the RCA
c chilled water
el electrical
eq equilibrium
G vapor phase
h hot water
in inlet
L liquid phase
LG liquid to vapor phase
out outlet
30
r refrigerant
s solution
w water
W wall
Abbreviations
ABS absorber
CON condenser
COP coefficient of performance
EVA evaporator
GEN generator
HX heat exchanger
RCA refrigerant cooled absorber
REC rectifier
RHE refrigerant heat exchanger
RMSD root mean square deviation, -
RS restrictor
SEP separator
SHE solution heat exchanger
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