15
Investigation of the effect of demagnetizing field on magnetic refrigeration devices
Y. Chiba 1*, A. Smaïli 2 and O. Sari 3†
1 Département de Génie Mécanique, Faculté des Sciences et de la Technologie Université de Médéa, 26 000, Médéa, Algeria
2 Laboratoire de Génie Mécanique et Développement
Ecole Nationale Polytechnique, P.B. 182, El-Harrach, 16200 Algiers, Algeria 3 University of Applied Sciences of Western Switzerland Avenue des sports 20, 1400, Yverdon-Les-Bains, Switzerland
Abstract - This paper presents a study of the effect of demagnetizing magnetic field on magnetic refrigeration device performances operating near room temperature. The test bench developed at HE-SO has been used for direct measurements of the magneto-caloric effect of Gadolinium under applied magnetic field of 2 T. For this purpose, a magnetic refrigeration device based upon the active magnetic regeneration (AMR) cycle has been used. To determine thermal performances of the cycle, a numerical 1D model based on the transient energy equations is used for modeling the heat exchange between the magneto-caloric material and the carrier fluid in the regenerator bed. The obtained results including the temperature span, the coefficient of performance and the cooling power are presented and discussed.
Keywords: Magneto-caloric effect, Demagnetization field, Numerical simulation, Thermal analysis.
1. INTRODUCTION
The magnetic refrigeration is based on the magneto-caloric effect, which consists in the entropy change of a magneto-caloric material when adiabatically magnetized or demagnetized, resulting respectively in heat absorption or rejection of magneto-caloric material. The phenomenon has been discovered by Warburg in 1881 [1].
Several works and numerical methods to predict the performance of the active magnetic regeneration, ‘AMR’ have been investigated previously [2-6]. These researches, however, were performed with different conditions and assumptions. For more applications of the magnetic refrigeration near room temperature, Kitanovski et al., [2] have reported in detail recent developments on magnetic refrigeration devices.
In this paper, investigations of the effect of demagnetizing field on magnetic refrigeration devices have been carried out through the recently developed magnetic cooling demonstrator by Clean Cooling Systems SA, ‘CCS’ at the University of Applied Sciences of western Switzerland, ‘HES−SO’. The obtained results including magneto-caloric effect, the coefficient of performance and the cooling power are presented and discussed.
2. DESCRIPTION OF AMR CYCLE
Figure 1 shows a schematic of an the active magnetic regeneration, ‘AMR’ device, which is constituted of (i) a two block AMR bed (i.e. solid magnetic material which can act as refrigerant and regenerator media), (ii) a blower to force the flow throughout the
*achiba.younes@ univ-medea.dz , [email protected] arezki
16
regenerator at convenient velocity, (iii) a circulating heat transfer fluid (i.e. in this study water). The AMR cycle consists of four processes, namely, magnetization / demagnetization steps, by application and removal of a magnetic field (through adiabatic or isothermal steps; in this study, only adiabatic steps, are considered), as well as cold and hot blows (i.e. cooling and heating the circulating fluid).
Fig. 1: Schematic diagram of the active magnetic refrigeration refrigerator setup [3]
The AMR thermodynamic cycle can be described as follows [4]:
Adiabatic magnetization process: The bed is magnetized adiabatically when the magnetic field increases from zero to B, without flow.
Hot blow at applied field: The fluid is then forced by the pump to move from the cold to the hot ends, entering the bed, the fluid temperature rises along the flow direction, and it leaves the bed at the average hot outlet temperature higher than the hot reservoir temperature, TH. Passing through the hot heat exchanger, the fluid temperature drops to TH by rejecting an amount of heat rate.
Adiabatic demagnetization process: By reducing magnetic field from given strength B to zero with no flow.
Cold blow at zero field: The fluid is then forced by the pump to move from the hot to the cold reservoirs. Upon entering the bed, the fluid temperature is equal to the hot reservoir temperature, TH, exchanging heat with the bed it drops to the average cold outlet temperature lower than the cold reservoir temperature, TC, at the cold end. Going through the cold heat exchanger, the fluid absorbs an amount of cold rate.
3. THERMODYNAMIC APPROACH AND NUMERICAL MODEL
The measurement of magneto-caloric effect has been performed directly by using the test bench developed at Heig-VD.
For this purpose, the data of magnetization measured at different field within Grenoble laboratory (INTERREG Iva France-Suisse Program). Therefore, one can quantify the effect of demagnetizing field as follows [8]:
M N B
Beff ext d (1)
where, Beff is effective magnetic field, Bext is external magnetic field, Nd is demagnetizing factor, and M is adiabatic magnetization.
The mathematical model of AMR includes the following assumptions:
-Losses such as those due to eddy current and magnetic hysteresis are neglected -The fluid is incompressible.
-Radiation heat transfer process within the regenerator has been neglected.
Under these considerations, the 1D energy conservation equations for solid and fluid circulating through regenerator are given as follows:
2 2 r r r
r
2 h f 2 f
3 f 2
2 f f f
f f
f
x k . A ) T ( A . t h V C . ) 1 (
D . A 2
m f x
k T . A ) T ( A . x h C T . t m V T C .
.
(2)
Specific heat of the magneto-caloric material can be determined by using mean field theory [3]. The convection heat transfer coefficient, h, and the friction coefficient, f have been estimated according to empirical correlations proposed for fully developed laminar flow [9]. Since the regenerator bed passages consist in parallel plates, the coefficients h and can be calculated by the following relationships respectively:
54 . 7
Nu (3)
Re 24
f (4)
The coefficient of performance and exergy can be determined by using the equations (5) and (6) respectively
P M
C W W COP Q
(5)
1
T . T Q x E
C
H
(6))
To solve the resulting energy equations the finite difference implicit scheme method has been used, the initial and the boundary conditions are reported in detail in the paper [3].
4. RESULTS AND DISCUSSION
Figure 2 shows adiabatic temperature change under 2T for Gadolinium (Gd) obtained from direct measurement by using test bench developed at Heig-VD. The obtained results have been normalized and fitted by using Gaussian approach. As it can be seen, differences can be noticed between measurement and normalized data of Gd;
shift up to 10% can be noted by considering the effect of demagnetizing field.
Figure 3 shows the evolution of coefficient of performance as function of cold temperature under magnetic field of 2T and the cycle operating parameters, namely, mass flow rate of 0.01 kg/s and temperature of hot exchanger of 22 °C. As it can be seen, differences between normalized and measured value can also be noticed, especially at higher temperature spans. Thus, the impact of demagnetizing field on the resulting COP values seems to be significant.
18
Fig. 2: Variation of the magneto-caloric effect measured and normalized as function of temperature of Gd under 2 T
Fig. 3: Evolution of coefficient of performance as function of temperature
span
Figure 4 and figure 5 show respectively cooling power and exergy as function of cold temperature under magnetic field of 2T and operating parameters; namely, mass flow rate of 0.01 kg/s and temperature of hot exchanger of 22 °C. As it can be seen, differences up to 15% have been noted between measurements and normalized data.
Fig. 4: Evolution of cooling power as function of cold temperature
Fig. 5: Evolution of exergy as function of cold temperature
Fig. 6: Evolution of exergy as function of temperature span
Figure 6 shows exergy as function of temperature span under magnetic field of 2T and operating parameters; mass flow rate of 0.01 kg/s and temperature of hot exchanger of 22 °C. Also differences up to 15 % have been noted between measurements and normalized data.
5. CONCLUSION
The main objective of this work presented in this paper, is to study and clarify the impact of demagnetizing field on magnetic refrigeration devices presented by Aharoni in 1998 and Kitanovski et al., 2015. The magneto-caloric effect normalized and measured values have been used, in order to investigate AMR device thermal performances. It has been concluded that the use of magneto-caloric effect normalized provides a high thermodynamic efficiency in magnetic refrigeration demonstrator operating near room temperature, especially at higher temperature spans.
NOMENCLATURE
A, Heat transfer area, (m2) B, Magnetic field, (T)
C, Specific heat, (J/kg.K) COP, Coefficient of performance Dh, Hydraulic diameter, (m) C, Cold, f, Fluid, r, regenerator f , Friction coefficient k, Thermal conductivity, (W/K.m-1)
L, Length, (m) , Porosity
, Density, (kg/m3) , Solid temperature, (°C) h, Heat transfer coefficient of convection, (W/m-2.K-1)
REFERENCES
[1] E. Warburg, ‘Magnetische Untersuchungen’, Annalen der Physik und Chemie, Tome 13, pp. 141 - 164, 1881.
[2] A. Kitanovski, J. Tusek, U. Tomc, U. Plaznik, M. Ozbolt, A. Poredos, ‘Magneto- caloric Energy Conversion: From Theory to Applications’, Springer International Publishing. 2015.
[3] Y. Chiba, A. Smaïli, C. Mahmed, M. Balli and O. Sari, ‘Thermal Investigation of an Experimental Active Magnetic Regenerative Refrigerator Operating Near Room Temperature’, International Journal of Refrigeration, Vol. 37, pp. 36 – 42, 2014.
[4] A. Smaïli, S. Ait-Ali and R. Chahine, ‘Performance Predictions of First Stage Magnetic Hydrogen Liquefier’, International Journal of Hydrogen Energy, Vol. 36, N°6, pp. 4169 – 4177, 2011.
[5] Y. Chiba, O. Sari, A. Smaïli, C. Mahmed and P. Nikkola, ‘Progress in Clean Energy, Volume 1, Chapter 16: Experimental Study of a Multilayer Active Magnetic Regenerator Refrigerator Demonstrator’, Springer International Publishing Switzerland, 2015.
[6] Y. Chiba, A. Smaïli, O. Sari and J. Hu, ‘Composite Material Based on Lafe (Co, Si) for Active Magnetic Regenerator Operating Near Room Temperature’, International Renewable Energy Congress, ‘IREC’, IEEE, Conference Publications, 2015, p.1-4 [7] A. Smaïli and R. Chahine, ‘Thermodynamic Investigations of Optimum Active
Magnetic Regenerators’, Cryogenics, Vol. 38, N°2pp. 247 – 252, 1998.
20
[8] A. Aharoni, ‘Demagnetizing Factors for Rectangular Ferromagnetic Prisms’, Journal of Applied Physics, Vol. 83, N°6, pp. 3432 – 3434, 1998.
[9] A. Bejan and A.D. Kraus, ‘Heat Transfer Handbook’, John Wiley and Sons, Inc., Hoboken, New Jersey, 403 p., 2003.
