Thermodynamic analysis on a magnetic refrigeration system

Magnetic refrigeration utilizes the magnetocaloric effect of a magnetic material, whose temperature changes according to the change of magnetic field strength. It is regarded as an eco-friendly refrigeration technology in that it uses magnetic materials as refrigerants instead of CFC, HCFC, and HFC refrigerants used in vapor compression refrigeration. It is also regarded as an energy-efficient refrigeration technology in that it does not use noisy and power-consuming compressors. This paper presents thermodynamic analysis on a magnetic refrigeration system using experimental results obtained from a magnetic refrigeration apparatus. The magnetic refrigeration apparatus was built using two sets of concentric Halbach cylinders consisting of permanent magnet segments. Specifically the coefficient of performance (COP) of the magnetic refrigeration system was calculated using the energy removed from the working fluid across an AMR bed and the work input to run electric motors.


Introduction
Hydrofluorocarbons (HFCs), which were commonly used as refrigerants in air conditioners and refrigeration systems, have been targeted for phase-out due to their high global warming potential (GWP).International agreements like the Kigali Amendment to the Montreal Protocol aim to reduce the production and consumption of HFCs to mitigate climate change.The transition away from HFCs has led to the adoption of low-GWP refrigerants such as hydrofluoroolefins (HFOs), hydrocarbons (HCs), and natural refrigerants like carbon dioxide (CO 2 ) and ammonia (NH 3 ).These alternatives are more environmentally friendly and have lower GWPs.Many countries have enacted regulations and standards to promote the use of low-GWP refrigerants and restrict the use of high-GWP options.These regulations are often aligned with the goals of the Paris Agreement to mitigate climate change.The refrigeration industry continues to invest in research and development to find even more sustainable and efficient refrigerant options.This includes exploring new materials and technologies for refrigeration systems.Ongoing research and development efforts are focused on creating new refrigerants with even lower GWP and improved energy efficiency.Additionally, scientists and engineers are working on developing more sustainable refrigeration technologies, such as magnetic cooling and solid-state cooling.
Magnetic refrigeration is an emerging, environmentfriendly technology based on a magnetic solid that acts as a refrigerant by magnetocaloric effect (MCE).Many magnetic refrigeration prototypes with different designs and software models have been built in different parts of the world.The most important advantage offered by the magnetic system is that it gets rid of the refrigerants present in the vapor compression system, which are mainly Chlorofluorocarbons (CFCs) and HFCs, which is responsible for the destruction of Ozone layer.Instead, it utilizes magnetocaloric material and a heat transfer fluid such as water, which is environmentally friendly and does not have Ozone Depleting Potential (ODP).Another important advantage offered by the magnetic system is the high thermodynamic efficiency as compared with the conventional system.A compressor brings a few disadvantages to the conventional system such as the noise and vibrations.In a magnetic system the compressor is absent and is replaced by a magnet, which does not involve any noise or vibrations.Magnetic refrigeration setup ensures economical running and negligible maintenance [1].The history of magnetic refrigeration is over 140 years old, and it can be said that it began in 1881 when Warburg [2] first discovered the magnetocaloric effect of iron near its Curie temperature.In 1976, Brown [3] first reported a magnetic refrigerator operating at room temperature.He could obtain a temperature difference of 47℃ (46℃ in high temperature and -1℃ in low temperature) in a large magnetic field of 7 T(tesla) by regenerating fluids (80% water and 20% ethyl alcohol) using gadolinium(Gd) as a magnetic refrigerant.Two important advances were made in magnetic refrigeration in 1997: (1) A joint research team from Astronautics Corporation of America and Ames Laboratory announced a proof-of-principle magnetic refrigerator operating continuously at room temperature (reciprocating apparatus using two magnetocaloric beds filled with Gd spheres having diameter of 150 to 300 μm and magnetic field of 1.5 to 5 T by a superconducting magnet) [4], (2) They also reported the discovery of a new material, Gd 5 (Si x Ge 1-x ) 4 , which exhibited greater magnetocaloric effect than those of existing magnetocaloric materials [5,6].Since then, interest in magnetic refrigeration at room temperature has increased a lot and research and development on magnetic materials and magnetic refrigeration systems have increased accordingly.
The Gd 5 (Si x Ge 1-x ) 4 compound (0 ≤ x ≤ 0.5) not only shows a huge magnetocaloric effect, but also can adjust the Curie temperature to 30 to 275 K according to the change in the x value [7].It has been announced that this compound has a magnetocaloric effect twice as great as gadolinium, which is known to be the best magnetic refrigerant at room temperature [8].Afterwards research has been actively conducted on materials that have greater or comparable magnetocaloric effect than this compound, and are more inexpensive and suitable for magnetic refrigerants [9].
Because the temperature change obtained by the magnetocaloric effect of a magnetic material is not very large, an appropriate heat exchange method is required to obtain a sufficient temperature difference needed for refrigeration.An active magnetic regenerator (AMR) is adopted so that a magnetic material is used as a refrigerant as well as a regenerator of the heat transfer fluid.
A magnetic refrigerant is used as a regenerator and the working fluid circulates inside the regenerator to transfer heat.In the study of room-temperature magnetic refrigerators, a method of magnetizing or demagnetizing magnetic refrigerants is generally realized by reciprocating permanent magnets or magnetic materials relatively.Among domestically constructed magnetic refrigeration systems, relative reciprocating motion was achieved in the perpendicular direction [10] or in the parallel direction [11] to the AMR bed length.
Besides the reciprocating system, there are other methods such as a rotating system [12][13][14][15][16] that changes the magnetic field as the AMR bed or permanent magnet rotates and a concentric cylindrical system [17][18][19][20][21][22] that fixes the AMR bed to the center and rotates the cylindrical permanent magnet around the bed.Bohigas et al. [12] constructed a room temperature magnetic refrigeration device using a permanent magnet was configured to obtain a temperature difference of 1.6 K between a high temperature part and a low temperature part under a magnetic field of 0.3 T. They used gadolinium ribbons as the magnetic refrigerant and olive oil as the heat transfer fluid, which was able to obtain a temperature difference of 5 K by increasing the intensity of the magnetic field to 0.95 T. Zimm et al. [13] presented the structure and performance of rotary magnetic refrigerators.Rotary magnetic refrigerators have been tested by the company since 2001, maintaining the concept of a four-stroke cycle reciprocating magnetic refrigerator built in 1997, increasing the operating frequency and reducing the bed to the size of a compact disk (CD).Increasing the operating frequency can be said to have an important meaning in terms of practical use because increasing the operating frequency can obtain the same refrigeration capacity even with less magnetic materials.
Jacobs et al. [14] constructed a large-scale rotary magnetic refrigerator which was designed to provide 2 kW of cooling power over a temperature span of 12 K with Electrical Coefficient of Performance (COPe) > 2. The system used a NdFeB magnet assembly with peak field of 1.44 T which rotates over twelve beds arranged circumferentially.Each bed was packed with six layers of LaFeSiH of different Curie temperatures, chosen to optimize system performance over the desired span.Eriksen et al. [15] built a rotary AMR prototype with the focus on enhanced performance in terms of efficiency and compact design at temperature spans and cooling powers relevant for commercial applications.They obtained promising experimental results, including a temperature span of 10.2 K at a cooling load of 103 W and a COP of 3.1.Lozano et al. [16] designed and built a novel rotary magnetic refrigerator.They used a two-pole system in a rotor-stator configuration with flux density of 1 T.They obtained the maximum no-load temperature span of 12 K at 1.5 Hz and 150 L/h, and the maximum zero-span cooling power of 150 W at 0.8 Hz and 200 L/h.For a thermal load of 80.4 W, at 0.8 Hz and 200 L/h, the device generated a temperature span of 7.1 K, with a COP of 0.54.
A research team at Victoria University in Canada reported the performance of systems in which concentric cylindrical magnets were used in double [17] and triple [18].They also examined the total cost of cooling provided by an idealized dual-regenerator concentric Halbach design.The objective function was the capital and operating cost rate based on a 10 years life cycle, and the constraints were set to be minimum cooling power, maximum pressure drop, and maximum peak field.Under the presented constraints and configuration, they showed that cost limiting factors were the permanent magnet size and pressure drop, while, surprisingly, power requirements were achieved with a relatively low magnetic field, operating frequency, and utilization factor [19].
Gangneung-Wonju National University's research team reported experimental results using a pump-driven type magnetic refrigeration apparatus with single refrigerant [20] and layered refrigerants [21], and experimental results using a piston-driven type magnetic refrigeration apparatus [22].Permanent magnets were used in form of concentric Halbach cylinders for both types.Lee et al. [20] measured temperature changes in real time at inlet and exit of two AMR beds.In the absence of a cooling load, the maximum temperature difference between high and low temperatures was 30.9 °C when the heat exchange time was 2 s. Lee [21] compared the performance of the magnetic refrigeration system using a single refrigerant Gd and a mixture of Gd and GdTb.The average temperature difference in the steady state was about 29 °C for a single refrigerant and about 26 °C for layered refrigerants, respectively.The main reason for the lack of better performance in layered refrigerants was that there was a dead zone in the joint of the layered-refrigerant bed, and the mass of the magnetic material used was reduced by 93 g (550 g -457 g).
Bjørk et al. [23] investigated five different variable permanent magnet designs, the concentric Halbach cylinder, the two half Halbach cylinders, the two linear Halbach arrays and the four and six rod mangles.They concluded that the best performing design, i.e. the design that provides the highest magnetic flux density using the least amount of magnet material, was the concentric Halbach cylinder design.A concentric Halbach cylinder was constructed and the magnetic flux density, the homogeneity and the direction of the magnetic flux density were measured to be in good agreement with numerical simulation.
This paper attempts to perform a thermodynamic analysis using experimental results [22] obtained using a piston-driven type magnetic refrigeration apparatus.In particular, coefficient of performance (COP) representing the performance of a refrigeration system is calculated using the experimental results obtained by varying the piston stroke (moving distance) and the piston speed (moving speed) that determine the circulated amount and flow rate of the heat exchange fluid.

Piston-driven type magnetic refrigeration apparatus
Figure 1 shows the piston-driven type magnetic refrigeration apparatus having two sets of concentric Halbach cylinders used in the current study.The magnetic refrigeration apparatus consists of cylindrical magnets, AMR beds filled with magnetic materials, heat exchangers and heat exchange fluid circulation system, and temperature measurement and control systems.In the concentric cylindrical magnet set, two Halbach cylinders with different diameters are combined as one assembly.The outer Halbach cylinder with a large diameter is fixed while the inner Halbach cylinder rotates [20].The AMR bed is placed in the middle of the cylindrical magnet assembly, and gadolinium spheres (Fig. 2) of about 250 μm in diameter are filled inside the AMR bed.Gadolinium was used in this study, because it is the established benchmark material for magnetocaloric cooling, even though there are better materials.Dzekan et al. [24] compared the performance of a state of the art thermomagnetic generator using gadolinium and La-Fe-Co-Si as thermomagnetic material, which exhibit strong differences in thermal conductivity and type of magnetic transition.La-Fe-Co-Si outperforms gadolinium in terms of voltage and power output.Their analysis revealed the differences in thermal conductivity are less important than the particular shape of the magnetization curve.
Figure 3 shows two AMR beds used in this apparatus (PVC pipes with 25 mm inner diameter and 32 mm outer diameter).550 g of Gd spheres with a Curie temperature of 20°C were filled in each bed. Figure 4 shows cross-sectional views of a concentric cylindrical magnet assembly with arrows in magnet segments showing directions of magnetic field.When the magnetic fields of two Halbach cylinders are in the same direction, the magnetic field of the assembly is maximized (a), and when the magnetic fields are opposite to each other, the magnetic field is minimized (b).The magnetic field strength inside the Halbach cylinder was simulated in the axial direction, which was the largest at the middle and became smaller outwards [25].
Figure 5 is a schematic diagram of the piston-driven type magnetic refrigeration apparatus, which shows two AMR beds placed in the middle of concentric cylindrical magnets, high-temperature and low-temperature heat exchangers, and a motor reciprocating two pistons within cylinders.The inner Halbach cylinder is periodically rotated 180 degrees by an electric motor to maximize and minimize the magnetic field of the system.The direction of the fluid flow is controlled by two three-way valves located between both sides of the high-temperature heat exchanger.In the magnetic refrigeration apparatus used for this study, the maximum magnetic field strength was measured as 1.6 T [22].
The cylinder-piston assembly is used to circulate the heat exchange fluid in the piston-driven type apparatus, as shown in Fig. 5.The piston in the cylinder reciprocates by a servo motor that drives a screw bar connecting two pistons.The specifications of the cylinder used in this experiment are 32 mm inner diameter and 100 mm length, in which 80 cc of water is contained.The moving distance of the piston can be adjusted by the number of rotations of the servo motor, and the amount of water, which is a heat exchange fluid circulating in proportion thereto, is determined.Therefore, it is possible to move up to 80 cc of water with a stroke of 100 mm.The moving speed of the piston may be adjusted by the rotation speed of the servo motor, and thus flow rate of the heat exchange fluid may be determined.When the speed of the piston varies by 10 mm/s, flow rate of the heat exchange fluid varies by 8 cc/s [22].
The piston stroke and speed were varied to investigate the performance according to the circulated amount and flow rate of the heat exchange fluid.The piston stroke (moving distance) was varied from 60 to 100 mm by the amount of 10 mm (water circulation is 48 to 80 cc, by 8 cc), and the piston speed (moving speed) was varied from 10 to 40 mm/s by the amount of 10 mm/s (water flow rate is 8 to 32 cc/s, by 8 cc/s), and the thermodynamic analysis was conducted using the experimental results.

Thermodynamic analysis
In the current study, variations of temperature in the high-and low-temperature sides of the magnetic refrigeration apparatus were measured in the absence of refrigeration loads.During the experiment, the lowtemperature part was insulated to prevent heat exchange with the surroundings, and the high-temperature part was open to the surroundings so that the heat was released.
Experiments were conducted for the piston stroke of 60 to 100 mm varying by 10 mm and the piston speed of 10 to 40 mm/s varying by 10 mm/s for each stroke.The average temperature changes through AMR beds at 40 min after the experiment is summarized in Table 1.The largest temperature difference was observed when the piston speed was 20 mm/s for most piston strokes.Temperature variations at the entrance and exit of the AMR bed were measured in real time using Pt100Ω, whose specifications are given in Table 2 with measurement uncertainty of 0.2℃ after temperature calibration.
Figure 6 shows the results of real-time measurement of temperature variations at inlets and outlets of two AMR beds for the piston stroke of 80 mm.The piston speed was varied from 10 to 40 mm/s by 10 mm/s.There is a   difference in the high and low temperatures of two AMR beds (A and B), but the temperature difference shows similar values.About 40 min after starting the experiment, it seemed to reach a steady-state when the piston speed was 10 to 20 mm/s.However, when the piston speed was 30 to 40 mm/s, temperatures at inlets and outlets continued to rise.This is thought to be due to the fact that as the piston moves faster, a lot of frictional heat is generated.Thermodynamic analysis was performed using temperature differences across AMR beds when the piston stroke was held as 80 mm and the piston speed was varied from 10 to 40 mm/s by 10 mm/s.The performance of the refrigerator is represented by coefficient of performance (COP), and COP is calculated by Eq. 1 using the symbol shown in Fig. 7.
where Q L is the amount of heat removed from the low- temperature part and W is the work required, and QL and Ẇ represents the rate of heat removed and the power, respectively.In this study, since the experiment was conducted under no load, it was decided to calculate the amount of heat removed from the AMR bed instead of the amount of heat removed from the low temperature part.As the experimental apparatus repeats the fourstroke cycle, a temperature gradient as shown in Fig. 8 is formed in the AMR bed.The temperature drops when water passes through the AMR bed from the hightemperature side to the low-temperature side, and this amount of heat was calculated using Eq. 2.
where ṁ is the mass flow rate of water, c is the specific heat of water, and T is the temperature drop of water.
When the piston stroke is 80 mm, 64 cc of water is transferred, approximately equal to 63 cc of water inside the AMR bed.As water flows inside the AMR bed, water temperature drops from high-temperature side (T H ) to low-temperature side (T L ), and the average temperature drop between the inlet and exit of the AMR bed becomes Tspan/2.The required work was calculated by multiplying the power for the motor (200 W) reciprocating the piston and the motor (750 W) rotating the inner Halbach cylinder by their operating times.The power required for (2) Q = ṁc T solenoid valves was ignored.Table 3 summarizes the process of calculating COP using the experimental data, and Fig. 9 shows COP versus piston speed for the piston stroke of 80 mm.As the piston speed varies from 10 to 40 mm/s, COP tends to increase.

Conclusions
Experiments were performed using the piston-driven type magnetic refrigeration apparatus with concentric Halbach cylinder magnets by varying piston stroke (moving distance of the piston) and piston speed (moving speed of the piston) to investigate the performance according to the circulated amount and flow rate of heat exchange fluid.

6Fig. 7
Fig. 7 Energy flow in a refrigerator

( 1 )Fig. 8
Fig. 8 Temperature distribution in an AMR bed AMR bed and the work (power × operating time) required to operate pistons and inner Halbach cylinders were used.(4) When the piston stroke was 80 mm, as the piston speed increased from 10 to 40 mm/s, COP increased accordingly.The amount of heat removed from the AMR bed was the largest at 20 mm/s with the maximum temperature difference.However, as the piston speed increased, the amount of heat removed per stroke decreased little by little, while the amount of work required decreased, resulting in a gradual increase in COP.

Table 1
Average temperature changes through AMR beds (Unit: ℃)

Table 2
Specifications of the temperature measurement device

Table 3
COP calculation using temperature changes through AMR beds when the piston stroke is 80 mm