arXiv subjects

R. Bjørk

Publications and source records attributed to R. Bjørk.

At least 19 recordsLinked to original sources

arXiv2021

MagTense: a micromagnetic framework using the analytical demagnetization tensor

We present the open source micromagnetic framework, MagTense, which utilizes a novel discretization approach of rectangular cuboid or tetrahedron geometry "tiles" to analytically calculate the demagnetization field. Each tile is assumed to be uniformly magnetized, and from this assumption only, the demagnetization field can be analytically calculated. Using this novel approach we calculate the solution to the mmag standard micromagnetic problems 2, 3 and 4 and find that the MagTense framework accurately predicts the solution to each of these. Finally, we show that simulation time can be significantly improved by performing the dense demagnetization tensor matrix multiplications using NVIDIA CUDA.

physics.comp-ph↗

arXiv2020

The magnetic field from a homogeneously magnetized cylindrical tile

The magnetic field of a homogeneously magnetized cylindrical tile geometry, i.e. an angular section of a finite hollow cylinder, is found. The field is expressed as the product between a tensor field describing the geometrical part of the problem and a column vector holding the magnetization of the tile. Outside the tile, the tensor is identical to the demagnetization tensor. We find that four components of the tensor, $N_{xy},N_{xz},N_{yz}$ and $N_{zy}$, can be expressed fully analytically, while the five remaining components, $N_{xx},N_{yx},N_{yy},N_{zx}$ and $N_{zz}$, contain integrals that have to be evaluated numerically. When evaluated numerically the tensor is symmetric. A comparison between the found solution, implemented in the open source magnetic framework MagTense, and a finite element calculation of the magnetic flux density of a cylindrical tile shows excellent agreement.

cs.CE↗

arXiv2019

A topology optimized switchable permanent magnet system

The design of a magnetic field source that can switch from a high field to a low field configuration by rotation by $90^\circ$ of a set of iron pieces is investigated using topology optimization. A Halbach cylinder is considered as the magnetic field source and iron inserts are placed in the air gap of the Halbach cylinder. The ideal shape of these iron inserts is determined as function of the field generated by the Halbach cylinder and as function of the size of the iron segments. The topology optimized structures are parabolic shaped pieces and have a difference in flux density between the high and low positions that is on average 1.29 times higher than optimized regular pole pieces. The maximum increase is a factor of 2.08 times higher than the regular pole pieces.

physics.ins-det↗

arXiv2019

The demagnetization factor for randomly packed spheroidal particles

We investigate if the demagnetization factor for a randomly packed powder of magnetic spheroidal particles depend on the shape of the spheroidal particles and what the internal variation in magnetization is within such a powder. A spheroid is an ellipsoid of revolution, i.e. an ellipsoid with two semi-major axis being equal. The demagnetization factor is calculated as function of particle aspect ratio using two independent numerical models for several different packings, and assuming a relative permeability of 2. The calculated demagnetization factor is shown to depend on particle aspect ratio, not because of direct magnetic interaction but because the particle packing depend on the aspect ratio of the particles. The relative standard deviation of the magnetization across the powder was 3\%-8\%, increasing as the particle shape deviates from spherical, while the relative standard deviation within each particle was relatively constant around 5\%.

cond-mat.mtrl-sci↗

arXiv2017

Topology optimized permanent magnet systems

Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. First, the Halbach cylinder is topology optimized with iron and an increase of 15% in magnetic efficiency is shown, albeit with an increase of 3.8 pp. in field inhomogeneity - a value compared to the inhomogeneity in a 16 segmented Halbach cylinder. Following this a topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111% for the chosen dimensions. Finally, a permanent magnet with alternating high and low field regions is considered. Here a $Λ_\mathrm{cool}$ figure of merit of 0.472 is reached, which is an increase of 100% compared to a previous optimized design.

physics.ins-det↗

arXiv2016

The magnetic properties of the hollow cylindrical ideal remanence magnet

We consider the magnetic properties of the hollow cylindrical ideal remanence magnet. This magnet is the cylindrical permanent magnet that generates a uniform field in the cylinder bore, using the least amount of magnetic energy to do so. The remanence distribution of this magnet is derived and the generated field is compared to that of a Halbach cylinder of equal dimensions. The ideal remanence magnet is shown in most cases to generate a significantly lower field than the equivalent Halbach cylinder, although the field is generated with higher efficiency. The most efficient Halbach cylinder is shown to generate a field exactly twice as large as the equivalent ideal remanence magnet.

physics.ins-det↗

arXiv2016

An analytical model for the influence of contact resistance on thermoelectric efficiency

An analytical model is presented that can account for both electrical and hot and cold thermal contact resistances when calculating the efficiency of a thermoelectric generator. The model is compared to a numerical model of a thermoelectric leg, for 16 different thermoelectric materials, as well as the analytical models of Ebling et. al. (2010) and Min \& Rowe (1992). The model presented here is shown to accurately calculate the efficiency for all systems and all contact resistances considered, with an average difference in efficiency between the numerical model and the analytical model of $-0.07\pm0.35$ pp. This makes the model more accurate than previously published models. The maximum absolute difference in efficiency between the analytical model and the numerical model is 1.14 pp for all materials and all contact resistances considered.

physics.ins-det↗

arXiv2016

A thermoelectric power generating heat exchanger: Part I - Experimental realization

An experimental realization of a heat exchanger with commercial thermoelectric generators (TEGs) is presented. The power producing capabilities as a function of flow rate and temperature span are characterized for two different commercial heat transfer fluids and for three different thermal interface materials. The device is shown to produce 2 W per TEG or 0.22 W cm$^{-2}$ at a fluid temperature difference of 175 $^\circ$C and a flow rate per fluid channel of 5 L min$^{-1}$. One experimentally realized design produced 200 W in total from 100 TEGs. For the design considered here, the power production is shown to depend more critically on the fluid temperature span than on the fluid flow rate. Finally, the temperature span across the TEG is shown to be 55% to 75% of the temperature span between the hot and cold fluids.

physics.ins-det↗

arXiv2016

The lifetime cost of a magnetic refrigerator

The total cost of a 25 W average load magnetic refrigerator using commercial grade Gd is calculated using a numerical model. The price of magnetocaloric material, magnet material and cost of operation are considered, and all influence the total cost. The lowest combined total cost with a device lifetime of 15 years is found to be in the range \$150-\$400 depending on the price of the magnetocaloric and magnet material. The cost of the magnet is largest, followed closely by the cost of operation, while the cost of the magnetocaloric material is almost negligible. For the lowest cost device, the optimal magnetic field is about 1.4 T, the particle size is 0.23 mm, the length of the regenerator is 40-50 mm and the utilization is about 0.2, for all device lifetimes and material and magnet prices, while the operating frequency vary as function of device lifetime. The considered performance characteristics are based on the performance of a conventional A$^{+++}$ refrigeration unit. In a rough life time cost comparison between the magnetic refrigeration device and such a unit we find similar costs, the former being slightly cheaper, assuming the cost of the magnet can be recuperated at end of life.

physics.ins-det↗

arXiv2016

Modeling the microstructural evolution during constrained sintering

A numerical model able to simulate solid-state constrained sintering is presented. The model couples an existing kinetic Monte Carlo (kMC) model for free sintering with a finite element model (FEM) for calculating stresses on a microstructural level. The microstructural response to the local stress as well as the FEM calculation of the stress field from the microstructural evolution is discussed. The sintering behavior of a sample constrained by a rigid substrate is simulated. The constrained sintering results in a larger number of pores near the substrate, as well as anisotropic sintering shrinkage, with significantly enhanced strain in the central upper part of the sample surface, and minimal strain at the edges near the substrate. All these features have also previously been observed experimentally.

cond-mat.mtrl-sci↗

arXiv2015

The performance of a combined solar photovoltaic (PV) and thermoelectric generator (TEG) system

The performance of a combined solar photovoltaic (PV) and thermoelectric generator (TEG) system is examined using an analytical model for four different types of commercial PVs and a commercial bismuth telluride TEG. The TEG is applied directly on the back of the PV, so that the two devices have the same temperature. The PVs considered are crystalline Si (c-Si), amorphous Si (a-Si), copper indium gallium (di)selenide (CIGS) and cadmium telluride (CdTe) cells. The degradation of PV performance with temperature is shown to dominate the increase in power produced by the TEG, due to the low efficiency of the TEG. For c-Si, CIGS and CdTe PV cells the combined system produces a lower power and has a lower efficiency than the PV alone, whereas for an a-Si cell the total system performance may be slightly increased by the TEG.

physics.ins-det↗

arXiv2015

The universal influence of contact resistance on the efficiency of a thermoelectric generator

The influence of electrical and thermal contact resistance on the efficiency of a segmented thermoelectric generator is investigated. We consider 12 different segmented $p$-legs and 12 different segmented $n$-legs, using 8 different $p$-type and 8 different $n$-type thermoelectric materials. For all systems a universal influence of both the electrical and thermal contact resistance is observed on the leg's efficiency, when the systems are analyzed in terms of the contribution of the contact resistance to the total resistance of the leg. The results are compared with the analytical model of Min and Rowe (1992). In order for the efficiency not to decrease more than 20%, the contact electrical resistance should be less than 30% of the total leg resistance for zero thermal contact resistance, while the thermal contact resistance should be less than 20% for zero electrical contact resistance. The universal behavior also allowed the maximum tolerable contact resistance for a segmented system to be found, i.e. the resistance at which a leg of only the high temperature thermoelectric material has the same efficiency as the segmented leg with a contact resistance at the interface. If e.g. segmentation increases the efficiency by 30% then an electrical contact resistance of 30% or a thermal contact resistance of 20% can be tolerated.

physics.ins-det↗

arXiv2015

The efficiency and the demagnetization field of a general Halbach cylinder

The maximum magnetic efficiency of a general multipole Halbach cylinder of order $p$ is found as function of $p$. The efficiency is shown to decrease for increasing absolute value of $p$. The optimal ratio between the inner and outer radius, i.e. the ratio resulting in the most efficient design, is also found as function of $p$ and is shown to tend towards smaller and smaller magnet sizes. Finally, the demagnetizing field in a general $p$-Halbach cylinder is calculated, and it is shown that demagnetization is largest either at $\cos 2pϕ=1$ or $\cos 2pϕ=-1$. For the common case of a $p=1$ Halbach cylinder the maximum values of the demagnetizing field is either at $ϕ= 0,π$ at the outer radius, where the field is always equal to the remanence, or at $ϕ= \pm π/2$ at the inner radius, where it is the magnitude of the field in the bore. Thus to avoid demagnetization the coercivity of the magnets must be larger than these values.

physics.ins-det↗

arXiv2014

The influence of the magnetic field on the performance of an active magnetic regenerator (AMR)

The influence of the time variation of the magnetic field, termed the magnetic field profile, on the performance of a magnetocaloric refrigeration device using the active magnetic regeneration (AMR) cycle is studied for a number of process parameters for both a parallel plate and packed bed regenerator using a numerical model. The cooling curve of the AMR is shown to be almost linear far from the Curie temperature of the magnetocaloric material. It is shown that a magnetic field profile that is 10% of the cycle time out of sync with the flow profile leads to a drop in both the maximum temperature span and the maximum cooling capacity of 20-40\% for both parallel plate and packed bed regenerators. The maximum cooling capacity is shown to depend very weakly on the ramp rate of the magnetic field. Reducing the temporal width of the high field portion of the magnetic field profile by 10% leads to a drop in maximum temperature span and maximum cooling capacity of 5-20%. An increase of the magnetic field from 1 T to 1.5 T increases the maximum cooling capacity by 30-50% but the maximum temperature span by only 20-30%. Finally, it was seen that the influence of changing the magnetic field was more or less the same for the different regenerator geometries and operating parameters studied here. This means that the design of the magnet can be done independently of the regenerator geometry.

physics.ins-det↗

arXiv2014

Determining the minimum mass and cost of a magnetic refrigerator

An expression is determined for the mass of the magnet and magnetocaloric material needed for a magnetic refrigerator and these are determined using numerical modeling for both parallel plate and packed sphere bed regenerators as function of temperature span and cooling power. As magnetocaloric material Gd or a model material with a constant adiabatic temperature change, representing a infinitely linearly graded refrigeration device, is used. For the magnet a maximum figure of merit magnet or a Halbach cylinder is used. For a cost of \$40 and \$20 per kg for the magnet and magnetocaloric material, respectively, the cheapest 100 W parallel plate refrigerator with a temperature span of 20 K using Gd and a Halbach magnet has 0.8 kg of magnet, 0.3 kg of Gd and a cost of \$35. Using the constant material reduces this cost to \$25. A packed sphere bed refrigerator with the constant material costs \$7. It is also shown that increasing the operation frequency reduces the cost. Finally, the lowest cost is also found as a function of the cost of the magnet and magnetocaloric material.

physics.ins-det↗

arXiv2014

Metamaterial anisotropic flux concentrators and magnetic arrays

A metamaterial magnetic flux concentrator is investigated in detail in combination with a Halbach cylinder of infinite length. A general analytical solution to the field is determined and the magnetic figure of merit is determined for a Halbach cylinder with a flux concentrator. It is shown that an ideal flux concentrator will not change the figure of merit of a given magnet design, while the non-ideal will always lower it. The geometric parameters producing maximum figure of merit, i.e. the most efficient devices, are determined. The force and torque between two concentric Halbach cylinders with flux concentrators is determined and the maximum torque is found. Finally, the effect of non-ideal flux concentrators and the practical use of flux concentrators, as well as demagnetization issues, is discussed.

physics.ins-det↗

arXiv2014

Comparison of adjustable permanent magnetic field sources

A permanent magnet assembly in which the flux density can be altered by a mechanical operation is often significantly smaller than comparable electromagnets and also requires no electrical power to operate. In this paper five permanent magnet designs in which the magnetic flux density can be altered are analyzed using numerical simulations, and compared based on the generated magnetic flux density in a sample volume and the amount of magnet material used. The designs are the concentric Halbach cylinder, the two half Halbach cylinders, the two linear Halbach arrays and the four and six rod mangle. The concentric Halbach cylinder design is found to be the best performing design, i.e. the design that provides the most magnetic flux density using the least amount of magnet material. A concentric Halbach cylinder has been constructed and the magnetic flux density, the homogeneity and the direction of the magnetic field are measured and compared with numerical simulation and a good agreement is found.

physics.ins-det↗

arXiv2014

Improving magnet designs with high and low field regions

A general scheme for increasing the difference in magnetic flux density between a high and a low magnetic field region by removing unnecessary magnet material is presented. This is important in, e.g., magnetic refrigeration where magnet arrays has to deliver high field regions in close proximity to low field regions. Also, a general way to replace magnet material with a high permeability soft magnetic material where appropriate is discussed. As an example these schemes are applied to a two dimensional concentric Halbach cylinder design resulting in a reduction of the amount of magnet material used by 42% while increasing the difference in flux density between a high and a low field region by 45%.

physics.ins-det↗