An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators

A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally combines explicit and implicit techniques in order to solve the one-dimensional conjugate heat transfer problem in an accurate and fast manner while ensuring energy conservation. The present model has been thoroughly validated against passive regenerator cases with an analytical solution. Compared to the fully implicit scheme, the proposed scheme achieves more accurate results, prevents numerical errors and requires less computational effort. In AMR simulations the new scheme can reduce the computational time by 89%.     

Two-dimensional mathematical model of a reciprocating room-temperature Active Magnetic Regenerator

A time-dependent, two-dimensional mathematical model of a reciprocating Active Magnetic Regenerator (AMR) operating at room-temperature has been developed. The model geometry comprises a regenerator made of parallel plates separated by channels of a heat transfer fluid and a hot as well as a cold heat exchanger. The model simulates the different steps of the AMR refrigeration cycle and evaluates the performance in terms of refrigeration capacity and temperature span between the two heat exchangers. The model was used to perform an analysis of an AMR with a regenerator made of gadolinium and water as the heat transfer fluid. The results show that the AMR is able to obtain a no-load temperature span of 10.9 K in a 1 T magnetic field with a corresponding work input of 93.0 kJ m⁻³ of gadolinium per cycle. The model shows significant temperature differences between the regenerator and the heat transfer fluid during the AMR cycle. This indicates that it is necessary to use two-dimensional models when a parallel-plate regenerator geometry is used.     

室温磁制冷机主动式回热器强化传热数值仿真

研究了脉冲磁场作用下磁工质粉末与水高热流密度小温差强化传热,提出了在工质轮中嵌入高导热材料强化传热的方法,采用建立理论模型与Ansys软件相结合的方法,对几种典型嵌入形式进行了模拟分析,结果表明,铜丝的交叉排列最有利于温度的均匀分布,在高转速运行下磁制冷机铜丝网的强化换热作用明显。铜丝数量的增加导致Gd工质质量减少,从而导致磁致热效应的减少,铜丝数量、磁热效应以及制冷效率之间存在最优值。     

Static and rotating active magnetic regenerators with porous heat exchangers for magnetic cooling

The operation behaviour of an active magnetic regenerator (AMR) with a wavy-structure, or a honeycomb-like regenerator bed was numerically investigated. The thermodynamic model was applied to a static regenerator and – in a generalized version – to a rotary type. The models take two-dimensional unsteady heat conduction in the magnetic material during the four basic processes of the AMR cycle into account. The numerical results were used to determine optimal arrangements of different magnetic materials in order to obtain larger temperature spans between both ends of the porous beds. Furthermore, a first study of magnetic flux lines in a porous rotary heat exchanger was performed.     

A 2D hybrid model of the fluid flow and heat transfer in a reciprocating active magnetic regenerator

This paper evaluates the thermal behavior of a magnetic-Brayton-based parallel plate reciprocating active magnetic regenerator (AMR). A time-dependent, 2D model of the fluid flow and the coupled heat transfer between the working fluid and the solid refrigerant (gadolinium) is proposed. A hybrid calculation method which consists of an analytical solution for the flow and a numerical solution for the thermal field has been adopted. Results for the cooling capacity as a function of the temperature span and mass flow rate agree well with trends observed in experimental data and other theoretical models available in the literature. The volume of fluid displaced through the channels during the isofield processes influences significantly the AMR performance. For a cycle frequency of 1 Hz, the cycle-averaged cooling capacity reaches a maximum when the utilization factor is 0.1 and the displaced fluid volume equals 62% of the fluid volume of the AMR.     

Review on numerical modeling of active magnetic regenerators for room temperature applications

The active magnetic regenerator (AMR) is an alternative refrigeration cycle with a potential gain of energy efficiency compared to conventional refrigeration techniques. The AMR poses a complex problem of heat transfer, fluid dynamics and magnetic field, which requires detailed and robust modeling. This paper reviews the existing numerical modeling of room temperature AMR to date. The governing equations, implementation of the magnetocaloric effect (MCE), fluid flow and magnetic field profiles, thermal conduction etc. are discussed in detail as is their impact on the AMR cycle. Flow channeling effects, hysteresis, thermal losses and demagnetizing fields are discussed and it is concluded that more detailed modeling of these phenomena is required to obtain a better understanding of the AMR cycle.     

Numerical simulation and its verification for an active magnetic regenerator

In this study, a one-dimensional model for the active magnetic regenerator (AMR) is established and verified by comparison with the experimental results. Besides four basic governing equations concerning mass and momentum conservation of heat transfer fluid and energy conservation of fluid and magnetic refrigerant, energy conservation of the regenerator wall is considered to achieve high accuracy and generalization. For the verification, a room temperature AMR has been fabricated with Gd and Halbach array. The AMR is operated by helium compressor with a rotary valve so that the effect of gas-compression/expansion also exists. Instantaneous mass flow rate and temperature distributions are measured during the experiment. Measured values are utilized as the boundary conditions and compared with the simulation results. Instead of cooling capacity or COP, simulation results are directly compared with the experimental results by temperature distribution in the AMR. The model and simulation results predict temperature distribution of the AMR properly at cyclic steady-state.     

Design and performance of a permanent-magnet rotary refrigerator

In order to demonstrate the potential of magnetic refrigeration to provide useful cooling near room temperature, Astronautics Corporation of America constructed a rotary magnetic refrigerator (RMR) in 2001. The RMR uses the active magnetic regenerator (AMR) cycle with an aqueous heat transfer fluid. The required change in magnetic field is produced by the rotation of a wheel packed with porous beds of magnetocaloric material through a 1.5 T Nd₂Fe₁₄B permanent magnet with steel flux concentration poles. A pump, and valves mounted to the wheel, control heat transfer fluid flow through the magnetocaloric beds and heat exchangers. This rotary design allows quiet, reliable operation over a range of frequencies (0.5–4 Hz), heat transfer fluid flow rates and cooling power. The performance of the device using Gd and Gd alloy spherical particles is reported and analyzed. We also describe the performance effects of introducing layered beds and an La(Fe_1−xSi_x)₁₃H_y alloy with a first order magnetic transition.     

Thermal investigations of an experimental active magnetic regenerative refrigerator operating near room temperature

In this paper, numerical and experimental investigations on a magnetic refrigeration device based upon the active magnetic regeneration (AMR) cycle operating near room temperature are presented. A numerical 1D model based on the transient energy equations is proposed for modelling the heat exchange between the magnetocaloric material and the carrier fluid in the regenerator bed. The validity of 1D AMR-numerical model is investigated 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 the temperature span, the coefficient of performance and the cooling power are presented and discussed. In general, good agreements have been noted between the experimental and numerical results.     

Design method of the layered active magnetic regenerator (AMR) for hydrogen liquefaction by numerical simulation

The design procedure of an active magnetic regenerator (AMR) operating between liquid nitrogen temperature and liquid hydrogen temperature is discussed with the selected magnetic refrigerants. Selected magnetic refrigerants (GdNi₂, Dy_0.85Er_0.15Al₂, Dy_0.5Er_0.5Al₂, and Gd_0.1Dy_0.9Ni₂) that have different transition temperatures are layered in an AMR to widen the temperature span. The optimum volume fraction of the layered refrigerants for the maximum COP with minimum volume is designed in a two-stage active magnetic regenerative refrigerator (AMRR) using one dimensional numerical simulation. The entropy generation in each stage of the AMR is calculated by the numerical simulation to optimize the proposed design. The main sources of the entropy generation in the AMR are pressure drop, convection and conduction heat transfers in the AMR. However, the entropy generation by the convective heat transfer is mostly dominant in the optimized cases. In this paper, the design parameters and the operating conditions such as the distribution of the selected refrigerants in the layered AMR, the intermediate temperature between two stages and the mass flow rate of heat transfer fluid are specifically determined to maximize the performance of the AMR. The proposed design method will facilitate the construction of AMR systems with various magnetic refrigerants and conditions such as AMR size, operating temperature range, and magnetic field variation.     

Numerical investigations on internal temperature distribution and refrigeration performance of reciprocating active magnetic regenerator of room temperature magnetic refrigeration

A two-dimension porous medium model for a reciprocating active magnetic regenerator (AMR) of room temperature magnetic refrigeration has been developed. The thermal diffusion effect, heat flux boundary effect and variable fluid physical properties are considered in the model. In the paper, we compare the numerical results of the porous medium model with the experimental data and the calculation results of one-dimension Schumann model to validate our model. Our model can simulate the operation of the reciprocating AMR effectively. With the present model, the internal heat exchange between the two phases is numerically investigated. The two dimensional temperature distributions of the magnetic refrigerant and the refrigeration performance of AMR are obtained, and the influence of the heat flux boundary effect and the variable fluid properties on them is discussed. AMR can achieve a maximum refrigeration capacity of 293.7 W with a corresponding coefficient of performance (COP) of 5.4.     

Experimental and numerical results of a high frequency rotating active magnetic refrigerator

Experimental results for a recently developed prototype magnetic refrigeration device at the Technical University of Denmark (DTU) were obtained and compared with numerical simulation results. A continuously rotating active magnetic regenerator (AMR) using 2.8 kg packed sphere regenerators of gadolinium (Gd) was employed. With operating frequencies up to 10 Hz and volumetric flow rates up to 600 L h⁻¹, the prototype has shown high performance and the results are consistent with predictions from numerical modelling. Magnetocaloric properties of the Gd spheres were obtained experimentally and implemented in a one-dimensional numerical AMR model that includes also the parasitic losses from the prototype. The temperature span for a thermal load of 200 W as a function of frequency was measured and modelled. Moreover, the temperature span dependence on the cooling capacity as a function of cycle frequency was determined. A detailed study of these parasitic losses was carried out experimentally and numerically.     

Fluid choice and test standardization for magnetic regenerators operating at near room temperature

Numerical simulations are performed to investigate the performance of an active magnetic regenerator (AMR) operating near room temperature. A two-dimensional porous model is established to analyze the impact different heat transfer fluids (HTFs) have on the performance of the AMR. The internal temperature distribution and cooling capacity of the system are analyzed and the influence of the HTF discussed. The simulation results show that when mercury is substituted in place of water as the HTF, the cooling capacity can be enhanced by nearly 600%. A fluid with high conductivity, high density, and low specific heat is most suitable for use as the HTF. Furthermore, as the environmental conditions have a great impact upon the performance of the AMR, three feasible methods of standardization testing are proposed. These involve: the evaluation index under fixed test environment conditions, a maximum exergy method, and a maximum specific exergy method around the Curie temperature.     

An experimental study of passive regenerator geometries

Active magnetic regenerative (AMR) systems are being investigated because they represent a potentially attractive alternative to vapor compression technology. The performance of these systems is dependent on the heat transfer and pressure drop performance of the regenerator geometry. Therefore this article studies the effects of regenerator geometry on performance for flat plate regenerators. This paper investigates methods of improving the performance of flat plate regenerators for use in AMR systems and studies how manufacturing variation affects regenerator performance. In order to eliminate experimental uncertainty associated with magnetocaloric material properties, all regenerators are made of aluminum. The performance of corrugated plates and dimpled plates are compared to traditional flat plate regenerators for a range of cycle times and utilizations. Each regenerator is built using 18 aluminum plates with a 0.4 mm thickness, which allows their performance to be compared directly.     

Magnetic refrigerator for hydrogen liquefaction

This paper reviews the status of magnetic refrigeration system for hydrogen liquefaction. There is no doubt that hydrogen is one of most important energy sources in the near future. In particular, liquid hydrogen can be utilized for infrastructure construction consisting of storage and transportation. When we compare the consuming energy of hydrogen liquefaction with high pressurized hydrogen gas, FOM must be larger than 0.57 for hydrogen liquefaction. Thus, we need to develop a highly efficient liquefaction method. Magnetic refrigeration using the magneto-caloric effect has potential to realize not only the higher liquefaction efficiency >50%, but also to be environmentally friendly and cost effective. Our hydrogen magnetic refrigeration system consists of Carnot cycle for liquefaction stage and AMR (active magnetic regenerator) cycle for precooling stages. For the Carnot cycle, we develop the high efficient system with >80% liquefaction efficiency by using the heat pipe. For the AMR cycle, we studied two kinds of displacer systems, which transferred the working fluid. We confirmed the AMR effect with the cooling temperature span of 12 K for 1.8 T of the magnetic field and 6 s of the cycle. By using the simulation, we estimate the efficiency of the hydrogen liquefaction plant for 10 kg/day. A FOM of 0.47 is obtained for operation temperature between 20 K and 77 K including LN₂ work input.     

Performance modeling of AMR refrigerators

A system modeling approach for predicting the performance of active magnetic regenerators using a one-phase approximation is presented. The approach is described for an arbitrary AMR device independent of the magnetic refrigerant, thermal losses or magnetic waveform. A general expression for magnetic work is derived which can be used for cycles where the low-field intensity is not zero. Additionally, a means of treating the varying magnetic field waveform as a single high and low field is described. The model is applied to a permanent magnet magnetic refrigerator using water–glycol as the heat transfer fluid. Simulated results are compared to experimental data which vary by heat load, frequency and utilization. A sensitivity analysis is performed using utilization, adiabatic temperature change, effective conductivity and particle size as independent variables. Comparisons to experimental data show that reducing the calculated magnetocaloric effect by 25% provides good agreement between simulations and experimental results.     

Experimental analysis of a two-material active magnetic regenerator

Experimental results of an active magnetic regenerator (AMR) composed of two equal volumes of gadolinium and Gd_0.85Er_0.15 using 2 T and 5 T are reported. Drive forces and system losses are measured as a function of thermal load and magnetic field. Metrics for coefficient of performance and efficiency are defined and used to distinguish between regenerator and device performance. Results suggest the largest temperature spans are expected to occur when each material is operating with its average temperature near their Curie temperatures. Force measurements indicate that mechanical losses and pumping power are the most significant contributions to network while the net magnetic work is too small to be resolved. COP values for the magnetic cycle are as high as 2.4 while efficiencies are all less than 0.15. A maximum exergetic cooling of 1.94 W is estimated with a corresponding specific exergetic cooling power of 23 W T⁻¹L⁻¹.     

Design and performance study of the active magnetic refrigerator for room-temperature application

A room-temperature magnetic refrigerator, consisting of permanent magnet, active magnetic refrigeration (AMR) cycle bed, pumps, hydraulic circuit, active magnetic double regenerator cycle (AM2RC) and control subsystems, has been designed. The magnetic field is supplied by NdFeB permanent magnets. The AMR bed made by stainless steel 304 encloses gadolinium particles as the magnetic working substance. Each part of the refrigerator is controlled by the programmable controller. The different standard heat exchangers are employed to expel heat. The cycle performance of this self-designed facility is analyzed using Langevin theory. The results provide useful data for future design and development of room-temperature magnetic refrigeration.     

Thermodynamics of active magnetic regenerators: Part I

Cycle-averaged relationships for heat transfer, magnetic work, and temperature distribution are derived for an active magnetic regenerator cycle. A step-wise cycle is defined and a single equation describing the temperature as a function of time and position is derived. The main assumption is that the convective interaction between fluid and solid is large so that thermal equilibrium between fluid and solid exists during a fluid flow phase (regeneration). Relations for the temperatures at each step in the cycle are developed assuming small regenerative perturbations and used to derive the net cooling power and magnetic work at any location in the AMR. The overall energy balance expression is presented with transformations needed to relate the boundary conditions to effective operating temperatures. An expression is derived in terms of operating parameters and material properties when each location is regeneratively balanced; this relation indicates needed conditions so the local energy balance will satisfy the assumed cycle. By solving the energy balance expression to determine temperature distribution one can calculate work, heat transfer, and COP.