Magnetic cooling machine for domestic application
Summary
This paper presents a new type of alternative magnetic cooler working with high-remanence and permanent magnets as the source of the magnetic field. The simulated and measured magnetic field in the machine's air space is about 1.45 Tesla. Initially, the metal gadolinium (Gd) was used as a magnetocaloric refrigerant. Its magnetocaloric performances and quality were experimentally verified on a test bench developed and confirmed by theoretical calculations based on mid-field theory (MFT). To achieve high values of the temperature difference between heat and cold sources (temperature range), a new type of Magnetic Cooling Active (AMR) cycle was carried out. However, in order to reduce energy consumption and then increase the thermodynamic performance of the magnetic system, a special configuration of magnetocaloric materials is developed. The numerical results of the magnetic forces applied in the new configuration are given and analyzed in detail. The developed machine is designed to produce a cooling power between 80 and 100 Watts with a temperature range of more than 20°C. The results obtained show that magnetic cooling is a promising alternative to replace traditional systems.
Keywords: magnetic cooling, magnetocaloric effect, magnetic cooling system, system optimization, active magnetic cooling,
1. Introduction
The impact of synthetic refrigerants on the environment, as well as legal certainty obligations drive the refrigeration industry to look for new ways to completely eliminate greenhouse gases or to reduce their load in numerous facilities. In order to get rid of synthetic refrigerants, industries are continuously looking for new environmentally friendly and suitable technologies that will allow high energy savings, thus reducing indirect CO2 emissions. Over the past fifteen years, both, namely reducing the load of refrigerants on the premises and using refrigerants natural, non-flammable, environmentally friendly resources have been the preferred options for many end users. Research on refrigeration technologies of the future is focused on indirect cooling technology such as Grout Phase Change (PCS), CO2 steam compressor technology, thermoelectric cooling, thermo-acoustic cooling and magnetic cooling (RM).
Since the discovery of the high polarization of permanent magnets of Nd-Fe-B, the giant magnetocaloric effect in Gd5Ge2Si2 and the evolution of the superior performance of magnetic cooling systems close to the temperature of the room, intensive studies were motivated on magnetocaloric materials and magnetic cooling devices. Magnetic cooling (MRI) is based on the magnetocaloric effect (MCE). This intrinsic property of some magnetic materials was discovered by Warburg in 1881 [1]. It is defined as the response of some magnetic materials to a variable magnetic field that manifests itself as the change of isothermal entropy _s and change in adiabatic temperature _Tad (see Fig. 1). When a magnetic field is applied to magnetic material near the transition phase region, magnetic moments change their order state and consequently magnetic entropy. Under adiabatic conditions, this change in magnetic entropy is compensated by a modification in part of the lattice (vibration of atoms) of the total entropy that increases or decreases the temperature of the material depending on the sign of the applied field and the nature of magnetic order in the refrigerant.
Figure 1: Adiabatic temperature change with magnetization by pure gadolinium
The origin of THE CEF was explained independently by Debye and Giauque [2, 3], and noted that low temperatures could be achieved by a paramagnetic salt. In 1933 [4], Giauque and MacDougall have successfully achieved temperatures below 1 Kelvin by using refrigeration degaussing. Brown was the first to demonstrate the viability of MRI near room temperature [5]. In 1976, he obtained a temperature difference of 46 K between the hot and cold end of a simple refrigerator with using 158 g of metal gadolinium and an applied field of 7 Tesla. The carrier fluid consisting of a mixture of 80% water and 20% ethyl alcohol solution was used as a heat transfer fluid. Compared to classical refrigeration, magnetic cooling is an environmentally safe technique (absence of CFCs and HCFCs) with many advantages, such as high efficiency, low noise, low pressure and compact configuration.
Modern magnetic cooling technology was born when Zimm et al developed machines that operated successfully demonstrating that this technology is viable and competitive for large-scale domestic and industrial applications. The first (alternative) test operated with a magnetic field of 5 Tesla with a superconducting magnet [6]. With 10 K of temperature range (between 281 and 291 K), he achieved a cooling power of 600 W, a coefficient of performance (COP), of 10 and maximum of 60% of Carnot's performance. The COP represents a ratio between the cooling energy (Qcool) and the total energy input (W). It is worth noting that the COP of the traditional refrigerator is 30 to 40% Carnot efficiency [7, 8 and 9].
The second prototype developed by Zimm et al [10] was a rotating machine working with some rare ground-based compounds as magnetized and demagnetized magnetocaloric refrigerant through a 1.5 Tesla magnetic field produced by a magnetic source based on permanent Nd-Fe-B (PM) magnets. The cooling power obtained was 50 W to 0 K temperature range and 25 K as the maximum temperature difference between the hot and cold source. Later, several protesters were reported in the literature. For more information, see Gschneidner et al [11].
Magnetocaloric material is an important key to the development of magnetic cooling technology. However, until today the main material used in magnetic cooling prototypes is gadolinium metal (Gd) and its alloys. This is essentially attributed to its good magnetocaloric performance at room temperature, good mechanical properties, low hysteresis, market availability and its ability to respond to various engineering needs. However, high cost and chemical instability limit the use of Gd as a refrigerant in a large-scale application. In order to replace Gd, a giant MCE was discovered in first-order transition materials Gd5(Ge1-xSix)4 [12]. A few years later, several other families of MCmaterials were reported and found presenting high levels of MCEs in large temperature ranges: from room temperature to low temperatures. These include series such as MnAs1-xSbx [13] MnFeP1-xAsx [14], LaFe13-xSix [15, 16] and their derivatives. From a practical point of view, LaFe13-xSix materials appear to be the most promising in magnetic cooling systems due to their high MCE, low cost and low hysteresis. In our laboratory, many efforts are focused on the development, improvement and application of this family, in collaboration with industrial and academic partners. This paper presents the initial results of a pre-industrial magnetic cooling system. This machine was designed and developed with design, market and thermodynamic performance requirements in mind.
2. Source of the magnetic field
In addition to magnetic refrigerants, optimizing permanent magnets to generate a high magnetic field is an important key to the development of magnetic cooling technologies. In magnetic cooling systems, the source of the magnetic field is equivalent to the compressor in conventional compression cycle systems. In magnetic systems, the greater the magnetic field generated, the higher the temperature and entropy change of the working substance and as a consequence the more powerful system can be. Considering the magnetocaloric performance of the available materials, an applied magnetic field greater than 1 Tesla is necessary.
Figure 2: Distribution of the magnetic field along the axis of the given magnetic source for different empty air height values.
For industrial applications, i.e. supermarket refrigerators, building air conditioning, gas liquefaction, etc., superconducting magnets can be used to reach the induction level up to 8-10 Tesla with the restriction of using liquid helium or a cryocooler to keep the superconducting coil, about 4 K. However, as noted by Gschneidner et al [11] for domestic applications and small cooling systems, the superconducting magnet is out of the question and the design of low-cost permanent magnet arrays with high induction is an important aspect of the commercialization of MRI in the consumer market. With PM machines, thermal energy is induced without electricity consumption, only one actuator is required to magnetize and demagnetize magnetocaloric materials. In the literature, various types of magnetic flux sources will be reported [17, 18]. For what was developed by Lee et al [17], the magnetic field of a PM with lateral aperture can assist 3 T with an air gap of 5.8 mm.
For the machine presented here, an innovative magnetic source is developed and designed. The latter is based on a rotation theorem modified by Halbach and can be used for both alternative and rotating magnetic systems. In the first step of the process, we start the optimized design of the geometry of the new source theoretically strung this structure as a function of air space, magnets, remanence flow density, etc.
Due to the complexity of the geometric structure and the presence of different soft magnetic materials, analytical formulations are out of the question. To this end, numerical simulations of the generated magnetic field were carried out. In this work, the Finite Element Flux3D program was used to simulate the magnetic field in the PM circuit. Flux3D is based on Fortran code that runs on both Unix and Windows operating systems. He uses Maxwell's equations as the basis for determining magnetic potential under static conditions on the basis of this equation:
Where μ is relative magnetic permeability and Mr is remanence. The magnetic potential obtained allows the calculations of all magnetic quantities at any point in space.
Figure 3: Distribution of the magnetic field along the axis of the magnetic source as a function of length magnet.
Figure 4: Magnetic field calculated and measured
along the magnetic source axis
(L = 120 mm, h = 12 mm)
In this study, the magnetic field has been calculated based on the length and height of the air space of the magnetic source. The structure of the magnet is designed on the basis of Nd-Fe-B. Permanent magnets have a higher remanence of around 1.45 Tesla. In order to study and optimize the structural parameters, the height h of the air space was varied between 10 mm to 22 mm for a fixed length L = 120 mm and the latter was changed from 120 mm to 200 mm for h = 12 mm. The force of magnetic induction along orientation and in the center of the air space is given in Figures 2 and 3. As shown in the figures, the geometric structure of permanent magnets can be easily adapted depending on the required application. The induced magnetic field is very sensitive to the height of the air space and increases almost linearly as h decreases. Meanwhile, the length of the magnetic source slightly influences the magnetic field in the air space. For the prototype developed here, the approved air space field source has a cross of 12 mm x 50 mm and a length of 120 mm. The induction calculated at the center of the magnet by the Flux 3D is about 1.44 Tesla. To check the validity of the magnetic fields obtained by 3D simulations, we have measured the magnetic flux density generated with the Hall probe. The results of the measurements will be compared with the numerical data shown in Figure 4. The comparison indicates the very good agreement of results that confirms the ability of Flux3D to evaluate the magnetic field in the same systems.
3. Magnetocaloric refrigerant: gadolinium
The choice of magnetocaloric refrigerant is of great importance as it strongly influences the thermodynamic performance of the cooling machine. Pure Gadolinium is the only material used in most magnetic cooling prototypes. This is essentially attributed to its important CEF, its ability to respond to various engineering requirements and availability in the market.
First of all, we have used Gd refrigerant flat plates in our machine. The hermomagnetic properties of Gd such magnetization, entropy, adiabatic temperature change and specific heat will be studied extensively and reported in the literature [19]. However, before placing the material in the machine, we have measured the magnetocaloric performance under practical operating conditions with a set-up developed in our laboratory. This system allows the measurement of the change of the near temperature of the ambient temperature in a magnetic induction around 2 Tesla.
The measurement results are given in Figure 5 (Gd: 2 mm). The normalized T_ obtained with respect to the magnetic field is approximately 2 K / T which is comparable with what is reported in the literature [19].
In order to study the demagnetization effect of the magnetocaloric properties of Gd several measurements _T were made on the gadolinium leaves with different thicknesses and the magnetic field was applied perpendicular to the surface of the plates. The temperature change of three plates with a thickness of 0.3 mm, 1 mm and 2 mm is compared in Figure 5. We can observe that the MCE of Gd is drastically reduced by decreasing the thickness of the sheet from 2 to 0.3 mm.
Figure 5: Effect of the demagnetization field of the magnetocaloric properties of Gd (less than 2 T).
This difference is attributed to the demagnetization effect due to the shape of the sample. The application of a field perpendicular to the surface of the material induces an internal field in the reverse direction called the demagnetization field. The latter cancels a part of the applied field which reduces the total internal field of the magnetocaloric material and consequently decreases magnetocaloric actions. To avoid the degaussing effect on our machine, the plates were placed parallel to the applied field.
4. Description of the magnetic refrigerator and preliminary results
An overview of the designed magnetic cooling machine is presented in Figure 6. The experimental apparatus consists of two permanent magnetic sources producing about 1.45 Tesla, two regenerators with Gd plates, four heat exchangers.
The regenerator is divided into two parts, each part contains flat Gd plates 1 mm thick and 100 mm long, corresponding to about 400 grams of gadolinium.
Figure 6: A view of the developed magnetic cooling machine.
Figure 7: The magnetic forces calculated for blocks 1 and 2 in the regenerator
Magnetic work makes up a large part of the energy fully absorbed by the magnetic cooling system. In addition, the reduction of magnetic forces is of great importance for the development of high-efficiency machines. To do this and with the aim of compensating for the magnetic forces, the regenerator was divided into two parts separated by a distance of about 30 mm. Figure 7 shows the difference between the magnetic forces calculated numerically for 1 and 2 blocks of Gd.
As shown in Figure 7, the magnetic force can be drastically decreased when using a bed consisting of two blocks of Gd. The numerical calculations developed in Figure 7 were confirmed experimentally by measurements made on the machine reported here. A detailed study of magnetic forces in magnetic cooling systems will be published in an upcoming communication.
The temperature range between the cold and hot ends was amplified by special thermodynamic cycles called active magnetic cooling regeneration (AMR) [19]. These cycles are divided into four steps:
magnetization of magnetic materials inducing heating;
flow of a liquid from the cold source to the heat source to evacuate heat: the flow temperature increases and the heat generated by the MC material is removed and evacuated in the direction of the hot end;
demagnetization of the material when removed from the magnetic field, which leads to the potential increase in magnetic entropy, decreasing the temperature of the refrigerant;
flow of the heat transfer fluid to the cold source in order to evacuate the cooling energy.
The operating process of the AMR can be controlled by adjusting the movement of the actuator and valve. The operating frequency of the cycle was 0.5 Hz.
Figure 8 shows an example of the results of the experimental data. At each heat source, the temperature progressively changes to a limit value in the steady state. After several CYCLES of AMR, the maximum temperature range reached between the cold and hot ends is about 12°C.
The relatively low temperature range is essentially attributed to the poor thermal properties of the heat transfer fluid. Basylon was specially used to protect the Gd bed from corrosion and oxidation.
Figure 8: Temperature range: experimental results for f = 0.5 Hz and Basylon as a heat transfer fluid.
However, preliminary results show that by using water or Zitrec as heat transfer fluids, a temperature difference of around 22°C can be achieved. More details about the machine with optimized parameters will be communicated in the future.
5. Conclusions and future work
A linear alternative permanent magnetic cooling system has been designed and built. Gadolinium is used as the first magnetocaloric test material, but other materials are considered for testing, in particular, NaZn13-based compounds. However, much effort was put into making the developed machine more compact, to obtain sufficient magnetic induction in the air chamber (1.45 Tesla) and reduce the magnetic forces acting on the magnetocaloric refrigerant during the magnetization-demagnetization process. Preliminary tests of the machine were carried out and encouraging results were obtained. To investigate the device, more experiences will be run and a detailed report about the machine with the optimized parameters will be communicated in the future.
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