T CETC
B.3 Overall Evaluation of the Entropy Generation
fluid current and the heat absorbed from the environment was considered, and the entropy generation in the CHEx was obtained by Eq. B.21.
S˙gen,CHEx =m˙f
∆hCHEx
TCHEx
− ∆pCHEx
ρTCHEx
f
− Q˙C
Tcab
(B.21) Similarly, the entropy generation in the HHEx was calculated by Eq. B.22.
S˙gen,HHEx =m˙f
∆hHHEx
THHEx
−∆pHHEx
ρTHHEx
f
+ Q˙H
Tamb
(B.22) The entropy generation of the fans was calculated considering only the heat exchange with their respective environments, disregarding the entropy variation of the air currents.
As there were no characterization of the fans, the efficiencies could not be assessed, and were both considered to be 20%. The entropy generation of the cold and hot fans were obtained by Eq. B.23 and Eq. B.24, respectively.
S˙gen,CF = W˙ CF 1−ηCF
Tcab (B.23)
S˙gen,HF= W˙ HF 1−ηHF
Tamb
(B.24)
B.3 Overall Evaluation of the Entropy Generation
With the approximations of the entropy generation of single components from the AMR/Magnet and Cabinet/HEx subsystems, all the subsystems and its components of the prototype were evaluated individually. Fig. 57 presents the evaluation of the contribution of each subsystem to the total entropy generation of the prototype. The Cabinet/HEx subsystem contributes with 20% of the total entropy generation of the magnetic wine cooler, being the second highest contribution. The AMR/Magnet subsystem contributes with 11% of the total entropy generation, representing the subsystem with the least contribution.
In a deeper examination of the entropy generation, Fig. 58 presents the contributions of each component. As it can be seen, the pump contributes with around 45% of the total entropy generation of the prototype, representing a very critical point into the system inefficiency.
The fans, although positively contributing to the external second-law efficiency – as they increase the UA of the HEx, represent the second highest contribution, totalling around 17%.
The valves contribute almost as much as the fans, but as it also carry the entropy generation due to the filter, it cannot be confirmed that the valves represent a third critical contribution to the system inefficiencies, as the filter could represent a high restriction to the fluid flow and therefore a high pressure drop. The driving system of the magnet and the AMR, intrinsically the core of magnetic refrigeration, contribute together in around 12%. The contribution of the auxiliary flow meter is around 8.5%, a high contribution for an auxiliary component but a loss that could be avoided in a final product version of the magnetic wine cooler. Lastly,
ŝŖȱƖ
ŗŘȱƖ
ŗŞȱƖ
¢Ȧ
Ȧ
¡Ȧ
Figure 57 – Percentage of entropy generation of the magnetic prototype subsystems.
the cold and hot HExs contribute very little to the total entropy generation, setting both as optimized points in the prototype in terms of inefficiencies.
Ƹ ¡Ȧ
Ŗ ŗŖ ŘŖ řŖ ŚŖ
S
gerȱǽƖǾFigure 58 – Percentage of entropy generation of each component of the magnetic prototype.
The pump, the fans and the valves should be addressed first when considering the improvement of the inefficiencies of the magnetic wine cooler, as together they represent 78% of the total entropy generation of the prototype. However, with a sized and more efficient pump, the need of a high heat transfer coefficient in the hot side – currently supplying three fans, would naturally decrease, as the heat dissipation in the pump would be lower and the power of the fans could be decreased. Also, the entropy generation of the valves should be evaluated without the influence of the filter, to identify if the valves are indeed one of the
B.3. Overall Evaluation of the Entropy Generation 115
critical points in terms of inefficiencies.
The total entropy generation of the system was then calculated by the sum of the entropy generation of each component and further compared to the entropy generation of the system obtained by Eq. B.1. The result calculated by the sum of the single components underestimated the total entropy generation in around 2.5%, representing a good error given the approximations made. However, the shares of entropy generation of the components and the subsystems could change if the entropy generation evaluation were more accurate. So as to improve the entropy generation calculations, some modifications could be made in the current prototype.
The entropy generation of the magnet could be improved by a better approximation of the magnetic interaction power consumption, with measurements of temperature inside the layers of magnetocaloric material, so as to assess the average temperature of the regenerative matrix in each blow and the respective entropy variation. The entropy generation of the CHEx, HHEx and the fans could be improved with a characterization in a wind tunnel, to assess the air flow rates of the fans and the pressure drops in the fans and the HExs. With the pressure drop and air flow rates, the efficiencies of the fans could also be calculated.
Nevertheless, it is necessary to measure the temperatures in the inlet and outlet of the fans and in the inlet and outlets of the HEx in the air currents, so as to assess the enthalpy and entropy variation.
Besides the changes proposed above, the prototype could be instrumented with ther- mocouples and pressure transducers in the inlet and outlet of each component, so as to separate the entropy generation of the main components from the auxiliary components and from the heat losses due to the tubing.
117
APPENDIX C – E xperimental R esults of the C onventional C haracterization
T ests
Table 26 – Experimental results of the characterization tests of the conventional wine cooler.
TsetTupTlowTavgTambTevap,inTevap,outTcond,in˙W˙QCCOPη2nd [o C][o C][o C][o C][o C][o C][o C][o C][W][W][-][%] 87.78.58.224.9-4.3-1.138.642.829.10.684.0 1211.712.212.024.81.03.934.031.822.30.703.1
119
APPENDIX D – E xperimental R esults of the M agnetic W ine C ooler
C haracterization T ests
Table 27 – Experimental results of the performance tests of the magnetic wine cooler proto- type.
Test point V˙f Tcab Tamb TCHEx,in THHEx,in W˙ Q˙C COP η2nd
[l/h] [oC] [oC] [oC] [oC] [W] [W] [-] [%]
F50V125 124.7 12.5 24.2 11.5 26.9 58.5 24.3 0.41 1.7 F50V150 149.6 11.9 24.8 11.0 27.3 84.8 26.4 0.31 1.4 F50V175 176.1 11.8 24.0 10.7 27.4 115.3 25.3 0.22 0.9 F50V200 199.3 13.0 24.6 12.1 28.0 148.4 24.0 0.16 0.6 F50V225 225.3 15.0 24.3 14.4 29.0 192.9 20.1 0.10 0.3 F75V125 126.0 13.5 25.4 12.7 27.6 63.4 24.7 0.39 1.6 F75V150 149.8 11.6 24.4 10.7 27.2 85.5 26.2 0.31 1.4 F75V175 174.9 11.2 24.3 10.3 27.5 117.3 26.7 0.23 1.0 F75V200 200.9 11.6 24.3 10.7 28.0 155.9 26.1 0.17 0.7 F75V225 224.7 12.4 24.2 11.7 28.6 199.0 24.5 0.12 0.5 F100V125 125.2 13.0 25.3 12.1 27.5 65.6 24.2 0.38 1.6 F100V150 149.3 11.6 24.7 10.7 27.1 88.8 26.7 0.30 1.4 F100V175 174.0 10.8 24.6 9.8 27.7 119.9 27.9 0.23 1.1 F100V200 201.0 11.3 24.7 10.3 28.1 160.6 27.4 0.17 0.8 F100V225 224.8 12.1 24.8 11.3 28.7 200.2 25.9 0.13 0.6