Magnetocaloric effect: From materials research to refrigeration devices

Turbulence in the convective boundary layer (CBL) uniformly heated from below and topped by a layer of uniformly stratified fluid is investigated for zero mean horizontal flow using large-eddy simulations (LES). The Rayleigh number is effectively infinite, the Froude number of the stable layer is 0.09 and the surface roughness height relative to the height of the convective layer is varied between 10−6 and 10−2. The LES uses a finite-difference method to integrate the three-dimensional grid-volume-averaged Navier–Stokes equations for a Boussinesq fluid. Subgrid-scale (SGS) fluxes are determined from algebraically approximated second-order closure (SOC) transport equations for which all essential coefficients are determined from the inertial-range theory. The surface boundary condition uses the Monin–Obukhov relationships. A radiation boundary condition at the top of the computational domain prevents spurious reflections of gravity waves. The simulation uses 160 × 160 × 48 grid cells. In the asymptotic state, the results in terms of vertical mean profiles of turbulence statistics generally agree very well with results available from laboratory and atmospheric field experiments. We found less agreement with respect to horizontal velocity fluctuations, pressure fluctuations and dissipation rates, which previous investigations tend to overestimate. Horizontal spectra exhibit an inertial subrange. The entrainment heat flux at the top of the CBL is carried by cold updraughts and warm downdraughts in the form of wisps at scales comparable with the height of the boundary layer. Plots of instantaneous flow fields show a spoke pattern in the lower quarter of the CBL which feeds large-scale updraughts penetrating into the stable layer aloft. The spoke pattern has also been found in a few previous investigations. Small-scale plumes near the surface and remote from strong updraughts do not merge together but decay while rising through large-scale downdraughts. The structure of updraughts and downdraughts is identified by three-dimensional correlation functions and conditionally averaged fields. The mean circulation extends vertically over the whole boundary layer. We find that updraughts are composed of quasi-steady large-scale plumes together with transient rising thermals which grow in size by lateral entrainment. The skewness of the vertical velocity fluctuations is generally positive but becomes negative in the lowest mesh cells when the dissipation rate exceeds the production rate due to buoyancy near the surface, as is the case for very rough surfaces. The LES results are used to determine the root-mean-square value of the surface friction velocity and the mean temperature difference between the surface and the mixed layer as a function of the roughness height. The results corroborate a simple model of the heat transfer in the surface layer.

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Coherent structure of the convective boundary layer derived from large-eddy simulations

Magnetocaloric materials with a Curie temperature near room temperature have attracted significant interest for some time due to their possible application for high-efficiency refrigeration devices. This review focuses on a number of key issues of relevance for the characterization, performance and implementation of such materials in actual devices. The phenomenology and fundamental thermodynamics of magnetocaloric materials is discussed, as well as the hysteresis behavior often found in first-order materials. A number of theoretical and experimental approaches and their implications are reviewed. The question of how to evaluate the suitability of a given material for use in a magnetocaloric device is covered in some detail, including a critical assessment of a number of common performance metrics. Of particular interest is which non-magnetocaloric properties need to be considered in this connection. An overview of several important materials classes is given before considering the performance of materials in actual devices. Finally, an outlook on further developments is presented.

Materials Challenges for High Performance Magnetocaloric Refrigeration Devices

A stochastic model, implemented as a Monte Carlo simulation, is used to compute statistical properties of velocity and scalar fields in stationary and decaying homogeneous turbulence, shear flow, and various buoyant stratified flows. Turbulent advection is represented by a random sequence of maps applied to a one-dimensional computational domain. Profiles of advected scalars and of one velocity component evolve on this domain. The rate expression governing the mapping sequence reflects turbulence production mechanisms. Viscous effects are implemented concurrently. Various flows of interest are simulated by applying appropriate initial and boundary conditions to the velocity profile. Simulated flow microstructure reproduces the −5/3 power-law scaling of the inertial-range energy spectrum and the dissipation-range spectral collapse based on the Kolmogorov microscale. Diverse behaviours of constant-density shear flows and buoyant stratified flows are reproduced, in some instances suggesting new interpretations of observed phenomena. Collectively, the results demonstrate that a variety of turbulent flow phenomena can be captured in a concise representation of the interplay of advection, molecular transport, and buoyant forcing.

One-dimensional turbulence: model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows

Using direct simulations of the incompressible Navier-Stokes equations with rigid upper and lower boundaries at fixed temperature and periodic sidewalls, scaling with respect to Rayleigh number is determined. At large aspect ratio (6:6:1) on meshes up to 288 × 288 × 96, a single scaling regime consistent with the properties of ‘hard’ convective turbulence is found for Pr = 0.7 between Ra = 5 × 104 and Ra = 2 × 107. The properties of this regime include Nu ∼ RaβT with βT = 0.28 ≈ 2/7, exponential temperature distributions in the centre of the cell, and velocity and temperature scales consistent with experimental measurements. Two velocity boundary-layer thicknesses are identified, one outside the thermal boundary layer that scales as Ra−1/7 and the other within it that scales as Ra−3/7. Large-scale shears are not observed; instead, strong local boundary-layer shears are observed in regions between incoming plumes and an outgoing network of buoyant sheets. At the highest Rayleigh number, there is a decade where the energy spectra are close to k−5/3 and temperature variance spectra are noticeably less steep. It is argued that taken together this is good evidence for ‘hard’ turbulence, even if individually each of these properties might have alternative explanations.

Rayleigh number scaling in numerical convection

Turbulence in thermal convection is investigated for flows in which the production of turbulence energy is due solely to buoyancy, and the statistics of the flow are homogeneous in horizontal planes. New experimental results for high Rayleigh number unsteady turbulent convection in a horizontal layer heated from below and insulated from above are presented and compared to turbulent Rayleigh convection, convection in the planetary boundary layer, and laboratory penetrative convection. Mean temperature fields are correlated in terms of wall layer scales and convection scales. Joint statistics of turbulent temperature and horizontal velocity and vertical velocity through fourth order are presented for the core region of the convection layer.

Turbulent thermal convection in wide horizontal fluid layers

The present paper describes the design, operation and preliminary results of an active magnetic regenerator test machine The regenerator consists of twenty eight 085 mm thick parallel gadolinium (Gd) plates that form 01 mm thick parallel channels with an effective length of 126 mm The working fluid is water and the magnetic field source is a Halbach array with a maximum flux density of 165 T A maximum temperature span between the hot and cold ends of the regenerator ( ∆T REG ) of 445 K and a maximum cooling capacity of 39 W were measured in tests without and with a thermal load, respectively The behavior of ∆T REG as a function of the utilization factor and of the temperature of the hot source is explored in the manuscript The experimental results are discussed in the light of the fluid flow and heat transfer phenomena taking place in the regenerator

Experimental evaluation of a Gd-based linear reciprocating active magnetic regenerator test apparatus ☆

The primary objective of this paper is to quantify the impact of the internal magnetic field and reversibility of the magnetocaloric effect on the numerical evaluation of the thermal performance of a parallel-plate active magnetic regenerator. To this end, direct measurements of the adiabatic temperature change of commercial-grade gadolinium samples were carried out for an applied field change of 1.65 ± 0.03 T (for both magnetization and demagnetization) and temperatures between 283 and 303 K. The tests were carried out in a specially constructed apparatus and the results were in good agreement with the literature. The data were incorporated into a mathematical model for solving the fluid flow and conjugated heat transfer in the parallel-plate regenerator. It was found that if demagnetization phenomena (i.e., the demagnetization factor and the reversibility of the magnetocaloric effect) are not take properly into account, the thermal performance of the regenerator can be severely over-predicted.

Assessment of demagnetization phenomena in the performance of an active magnetic regenerator

This paper describes the design, operation and preliminary results of an active magnetic regenerator test machine. The regenerator consists of 28 parallel Gd plates (126 mm long, 0.85 mm thick) which form 0.1 mm-thick parallel channels. The working fluid is water and the magnetic field source is a Halbach array with a maximum flux density of 1.65 T. A maximum temperature gradient of 4.45 K and a maximum cooling capacity of 3.9 W were measured in tests without and with a thermal load, respectively. The results show trends of the maximum temperature gradient as a function of the utilization factor and of the temperature of the hot source which are in line with those presented in the literature.

Rogério T.S. Ferreira

Papers

Turbulent thermal convection in wide horizontal fluid layers

Experimental evaluation of a Gd-based linear reciprocating active magnetic regenerator test apparatus ☆

Assessment of demagnetization phenomena in the performance of an active magnetic regenerator

Design and preliminary results of a Gd-based linear reciprocating active magnetic regenerator test apparatus.