FLOW PATTERNS IN THE MAGNETIC NANOFLUID CORE OF A MINIATURE PLANAR SPIRAL TRANSFORMER

Transcription

1 Environmental Engineering and Management Journal June 2013, Vol.12, No. 6, Gheorghe Asachi Technical University of Iasi, Romania FLOW PATTERNS IN THE MAGNETIC NANOFLUID CORE OF A MINIATURE PLANAR SPIRAL TRANSFORMER Alexandru Mihail Morega 1, Jean Bogdan Dumitru 1, Mihaela Morega 1, Lucian Pîslaru-Dănescu 2 1 Politehnica University of Bucharest, Faculty of Electrical Engineering, 313 Splaiul Independenţei, Bucharest, Romania 2 The National Institute for Electrical Engineering, ICPE-CA, Bucharest, Romania Abstract This paper analyses mathematical models and numerical simulation results for a notional miniature, planar, spiral transformer (MPST) fabricated in MEMS technology, for galvanic separation, proposed to equip an electric harvesting device (EHD). Two types of core ferrite and (partially) magnetic nanofluid are considered. We found that magnetization body forces occur in the super-paramagnetic nanofluid core and they result in complex, steady state flows consisting of fully 3D recirculation cells. Key words: energy harvesting device, fluid flow, magnetic nanofluid core, magnetic forces, numerical simulation, planar spiral miniature transformer Received: February 2013; Revised final: June, 2013; Accepted: June, Introduction Innovation and research in power generation is more and more becoming a challenging race to finding and valorizing renewable energy resources, like natural non-fossil sources for electricity production: wind, solar light, water energy (waves, currents and water falls) etc. On a smaller scale, but in a multitude of distributed applications, one could still extract usable electric energy from waste associated to various processes (Everett et al., 2012): - friction, ventilation, heat extraction, furnace from industrial technologies; - mechanical stress and strain, vibration from transportation; - chemical reactions and biological processes supporting organisms life; - heat and motion from human physiology during natural living; - energy loss and inherently wasted emissions from electromagnetic devices etc. All these unconventional solutions are based on sensing, capturing, and conversion to electricity of various environmental energy forms and represent some possibilities of energy harvesting. The energy conversion is usually performed in very small and irregular amounts, but with significant contribution added to the efficiency of the application. Technical solutions make use of advanced technologies, unconventional physical interactions and innovative materials. For instance, recent progress in on-a-chip devices, such as for energy harvesting sources (EHS), rely on the development of micro electro-mechanical systems (MEMS) (Bakkali et al., 2010; Baltes et al., 2005; Lee, 2008). An electronic module is often integrated in an energy harvesting (EH) device to adjust power characteristics (frequency, voltage amplitude) to a storage device, to a local consumer or for transfer in Author to whom all correspondence should be addressed: : amm@iem.pub.ro; Phone: ; Fax:

2 Morega et al./environmental Engineering and Management Journal 12 (2013), 6, another network. The electric transformer is a core component of the device. For instance, EHS are aimed at converting the harvested electrical power, e.g., by solar cells (Morega et al., 2006), to adjustable voltage output for driving multiple loads. The usage of chip embedded MEMS components converge to EHS devices that are overall simpler, smaller in size, with lower power consumption. It is customary for such devices to operate in an independent, maintenance-free and reliable system, for their whole life span. Miniature planar spiral transformers (MPST) with micro-structured coils are found as a core construct in the power supplies and DC/DC converters that equip EHS, where a slim high-power design is crucial (Hogerheiden et al., 1997). The planar structure of the MPST improves its cooling characteristics while providing the device a low profile. Recently, super-paramagnetic (SP) nanofluids were shown to be a convenient replacement of the MPST ferrite core, resulting in higher efficiency power conversion of the transformer (Tsai et al., 2010; Vollath, 2008). Magnetic nanofluids, consisting of tiny magnetized iron oxide nanoparticles dispersed in an oil suspension, are already used in power transformers as cooling and insulating medium (Beitelman et al., 2005; Morega et al., 2010; Raj et al., 1993; Segal et al., 2000). Such magnetic nanofluids with near-zero hysteresis provide for a solution to one of the major causes of energywaste in electric transformers. Magnetic and electric sizing of a notional MPST for galvanic separation fabricated in MEMS technology proposed to equip an EHD device was presented by Morega et al. (2012 a, b). Ferrite and SP nanofluid cores were considered. It was shown that magnetization body forces are responsible for setting in the motion of the fluid core, which proves to be essentially 3D. The flow structure depends of the powering scheme of the MPST. In this paper we extend the study on the numerical simulation of the fluid core motion, and discuss the influence of the core geometry (thickness) and the impact of the gravitational force on the flow, i.e., the changing positioning of the fluid core. No load and nominal (opposite amperturns) working conditions, i.e. powering schemes, are used. 2. The NOTIONAL Miniature planar spiral transformer (MPST) Fig. 1 shows the schematic CAD view of the MPST. The magnetic core is of clad type: the coils are contained in a ferrite made case that provides the return path for the magnetic flux. The two identical (mirrored), planar coils representing the primary and secondary windings of 40 turns each sandwich a block made of either ferrite or SP nanofluid. By (MEMS) technological reasons the micro-structured coils have square turns. The magnetic nanofluid core is a stable, colloidal suspension of magnetic nano-particles of about 100 Å (10 nm), dispersed in a liquid carrier, which behaves macroscopically as a superparamagnetic material (Morega et al., 2012 a, b). From the electrical properties point of view, the electrical impedance and the loss tangent of the magnetic fluid are relatively constant. A stabilizing dispersing agent (surfactant) shells the particles preventing their aggregation even under high nonuniform (high gradient) magnetic field. When the magnetic field is off, the magnetic moments of the nanoparticles redistribute randomly fast enough to yield no net (macroscopic) magnetization of the fluid. Ferrite lid Secondary winding Cermic spacer Superparamagnetic / ferrite nanofluid core Ferrite case Primary winding Ferrite lid Electrical terminals Fig. 1. The MPST for galvanic separation the computational domain. Symmetry about the mid cross sectional (horizontal) plane may be noticed 1172

3 Flow patterns in the magnetic nanofluid core of a miniature planar spiral transformer 2. The mathematical model While either simpler (2D) models or more advanced (3D) models may be used to simulate the stationary magnetic field and the static electric field to compute the MPST circuit (lumped) parameters with satisfactory, comparable degrees of accuracy, the motion within the fluid magnetic core requires a 3D analysis. To solve for the stationary flow, the magnetic field has to be known hence its source, the electrical current in the windings, is needed therefore a stationary (DC) analysis is required in the first place. The electrical currents in the windings are provided by solving for the partial differential equation (PDE) (Eq. 1): V 0 (1) where: V [V] is the electric potential and [S/m] is the electrical conductivity of the coils. The surfaces of the windings are assumed to be electrically insulated (n V = 0, where n is the outward pointing normal). The boundary conditions (BCs) for the terminals of each coil are: specified electrical current, assumed distributed uniform electrical current density (n V = 0, Neumann BC), at one end, and ground (V = 0, Dirichlet BC) at the other end. This problem is solved inside the windings only. The mathematical model for the magnetic field is described by the following PDEs (Eqs. 2-4): inside the windings r A J e (2) inside the ferrite part of the core r A 0 inside the SP nanofluid core (3) 1 0 A M 0. (4) In the equations above, A [T m] is the total magnetic vector potential, J e [A/m 2 ] is the external electric current density, μ 0 = 4π 10-7 [H/m] is the magnetic permeability of free space, and μ r is the relative permeability for the ferrite (μ r = 1000). The magnetization of the SP nanofluid M [A/m] in (4) is approximated by Eq. (5) (Morega et al., 2012a, b): M arctan H (5) where H [A/m] is the magnetic field strength, and α, β are empiric constants selected to accurately fit the magnetization curve of the magnetic fluid. For the working magnetic nanofluid, α = 3050 A/m, and β = m/a provide the best fitting to the available experimental data. Magnetic insulation BC (n A = 0) on the surface of the computational domain may close the problem. However, in this study we consider only the powering scheme that produces opposite amperturns (nominal working conditions). Then, assuming that the spiral effect of the windings is negligible small (the coils may be seen as concentric, planar, square turns) it may be inferred that the symmetry in the geometry of the MPST and in the electric and magnetic working conditions (identical windings, mirrored with respect to the planar, mid cross section of the MPST) lead to symmetry (with respect to the same planar, mid cross section of the MPST) in the flow. The BC on the symmetry plane is, again, magnetic insulation. The magnetization body forces produced within the SP nanofluid (assumed newtonian) entrain the fluid core in a stationary fully 3D motion. For steady state conditions, the laminar, incompressible flow of the fluid core is described by the momentum conservation law and by the mass conservation law, respectively (Morega et al., 2012b) (Eqs. 6, 7): T f g mg (6) u u pi u u u 0. (7) Here u [m/s] is the velocity, p [N/m 2 ] is the pressure, [kg/m 3 ] is the mass density, [N s/m 2 ] is the dynamic viscosity, f mg M H [N/m 3 ] are the magnetization body forces, and g [m/s 2 ] is the gravity (9.81 m/s). If gravity is neglected the nominal working conditions (compensated amperturns) lead to symmetry in the flow pattern about the MPST mid cross sectional plane too, thus the flow problem may be reduced by half, with a significant gain in storage and CPU time. The boundary conditions for the hydrodynamic problem are then: no slip (zero velocity) at the solid walls, and symmetry (slip) by the symmetry plane. If gravity is accounted for, the entire core has to be considered. 3. Numerical simulation results and discussion The electric field within the windings is obtained by solving problem (1), as it is shown in Fig. 2 through field lines (streamlines) of electrical current density. The problem is solved by the Galerkin finite element (FEM) technique implemented by (Comsol, 2011, 2012, 2013). Tetrahedral, quadratic Lagrange elements are used to model the field. The problem is linear therefore a solver that may take advantage of the symmetry of the algebraic system (SPOOLES) was used. 1173

4 Morega et al./environmental Engineering and Management Journal 12 (2013), 6, Fig. 2. Spectra of electric field by gray boundary map (V) and streamlines (J). All parts of the MPST except for the windings are removed for better viewing. The current is 1 ma Once the magnetic field source is known, the problem (2)-(4) may be solved. Tetrahedral, quadratic vector elements are used in the numerical simulations. The algebraic problem related to the FEM analysis is nonlinear, due to the nonlinear behavior of the SP nanofluid core. Therefore a nonlinear (quasi-newton) solver was used in the second case as inner loop for the FMGRES algorithm with SSOR gauge preconditioning (Comsol, ). Fig. 3 shows the magnetic field spectrum. Fig. 3. Magnetic flux density (tubes) for opposite amperturns. The electric potential (gray map) is plotted to outline the winding. This powering scheme was used to compute the self-inductance of the primary winding (Morega et al., 2012b) The magnetic flux density is presented through flux tubes (their color and size are proportional to the module) and the windings are outlined by the electric potential (surface gray map). All parts of the MPST are removed for better viewing. The color of the tubes and their size are proportional to the local value of the magnetic flux density. Similarly, the self-inductance of the secondary winding may be found. Finally, the flow problem in the fluid core described by (5) and (6) may be approached. In this study we are concerned with the influence of fluid core thickness and the position (i.e., the gravity) upon the flow pattern. The numerical simulations were performed for the reference case (100%, i.e., 2 mm fluid core thickness), and 75%, 50%, 25%, for 1 ma. Gravity is neglected here. Fig. 4 shows flow patterns seen from above (negative Oz direction). The flow field is presented by streamtubes and their color and size are proportional to the velocity module. The windings are outlined by the electric potential through surface gray map. Apparently, the slimmer and more constrained the core the slower the motion is. Also, even if symmetry about Oz axis (perpendicular to the figures) is manifest, the flow structures differ substantially. It should be noticed that the volumes of the fluid cores are different (hence the electric and magnetic lumped parameters of the MPST are expected to differ) therefore the magnetization body forces that entrain the flow are different. Fig. 5 shows 3D views of the flows presented in Fig. 4. Next, the effect of gravity was studied, for the fluid core of nominal size (thickness). The entire fluid core is considered when g acts in negative Oz direction because the xoy mid cross sectional plane is no longer a symmetry plane for the flow. Figure 5 depicts the flows for g in Oz direction, when the body magnetic forces are produced by opposite electrical currents of 1 ma (at the terminals). However, further numerical simulation results suggest that the structure of the forced flow entrained by these forces is practically independent of gravity. (a) 25% core thickness the maximum velocity is of the order O(25 nm/s) (b) 50% core thickness the maximum velocity is of the order O(65 nm/s) 1174

5 Flow patterns in the magnetic nanofluid core of a miniature planar spiral transformer (c) 75% core thickness the maximum velocity is of the order O(0.1 mm/s) (d) 100% core thickness the maximum velocity is of the order O(10 mm/s) Fig. 4. Streamtubes showing the flow field from above (above the mid cross section plane) (a) 25% core thickness the maximum velocity is of the order O(25 nm/s) (b) 50% core thickness the maximum velocity is of the order O(65 nm/s) (c) 75% core thickness the maximum velocity is of the order O(0.1 µm/s) (d) 100% core thickness the maximum velocity is of the order O(10 µm/s) Fig. 5. 3D views of the flow field through streamtubes of flow field Fig. 6 presents the flows for three cases: a. no gravity; b. gravity acts in negative Oz direction; c. gravity acts in negative Oy direction. The flow morphologies resemble, and it is the pressure field that evidences discrepancies, as the gray maps indicate (light grey means higher pressure, darker gray indicates lower pressure). When gravity acts in Oz direction higher and lower pressure regions are horizontally stratified. If g is oriented in Oy direction the higher and lower pressure regions are vertically stratified. 1175

6 Morega et al./environmental Engineering and Management Journal 12 (2013), 6, Fig. 5. The flow in the fluid core for 1 ma. The effect of gravity is negligibly small (a) No gravity. The pressure drop is of the order O(10-3 ) Pa g (b) Gravity is in negative Oz direction. The pressure drop is of the order O(20) Pa g (c) Gravity is in negative Oy direction (from right to the left, in plane). The pressure drop is of the order O(60) Pa Fig. 6. The effect of gravity upon the flow for 1 ma. Lighter grey indicates higher pressure regions 1176

7 Flow patterns in the magnetic nanofluid core of a miniature planar spiral transformer 5. Conclusions This study was concerned with the mathematical models and numerical simulation of the magnetic field and the flow in the fluid core of a notional MPST fabricated in MEMS technology for galvanic separation, proposed to equip EHD devices. The core is made of ferrite (case) and superparamagnetic (SP) nanofluid (the core space between the windings). The magnetic nanofluid core is a stable, colloidal suspension of magnetic nano-particles dispersed in a liquid carrier, which behaves as an SP material. When the coils are powered, the magnetic field produces magnetization body forces inside the fluid core, which entrain the fluid core in a stationary flow. The flow pattern depends on the structure of the magnetic field, and proves to be complex, fully 3D, with four lobbed trefoil pattern, which drives external, smaller, inner, recirculation cells. Besides the direct effect upon the lumped circuit electric and magnetic parameters (not addressed in this study), the fluid core thickness is related to the flow pattern. It is less so for the gravity that seems to have a minute influence (if any) upon the flow, commonly consistent with forced type of flows. For the cases considered in this study (vertical and horizontal direction of g) the effect of gravity is best evidenced by the pressure field that approaches hydrostatic-like stratified structures. Acknowledgments The work was conducted in the Laboratory for Multiphysics Modeling at UPB. The author J.B. Dumitru acknowledges the support offered by the Sectorial Operational Programme Human Resources Development of the Romanian Ministry of Labor, Family and Social Protection through the Financial Agreement POSDRU/107/1.5/S/ References Bakkali M., Carmona-Galan R., Rodriguez-Vazquez A., (2010), A Prototype Node for Wireless Vision Sensor Network Applications Development, 5th International Symposium on I/V Communications and Mobile Network (ISVC), September 30-October 2, Rabat, Maroc, 1-4, DOI: /ISVC Beitelman L., Segal V., Curran C.P., (2005), Cooling Electromagnetic Stirrers. USA Patent No. 6, 927, 510 B1. Baltes H., Brand O., Fedder G.K., Hierold C., Korvink J., Tabata O., (2005), Advanced Micro & Nanosystems, Vol. 2, CMOS-MEMS, Wiley-VCH Verlag, GmBH & Co. KGaA, Meinheim. COMSOL, (2010), COMSOL Multiphysics, Vesion 3.5a, On line at: COMSOL, (2011), COMSOL Multiphysics, Vesion 4.2a, On line at: Multiphysics.pdf. COMSOL, (2013), COMSOL Multiphysics, Vesion 4.3a, On line at: Everett R., Boyle G., Peake S., Ramage J., (Eds.), (2012), Energy Systems and Sustainability: Power for a Sustainable Future, 2nd edition, Oxford University Press, Oxford, UK. Hogerheiden J., Ciminera M., Jue G., (1997), Improved planar spiral transformer theory applied to a miniature lumped element quadrature hybrid, IEEE Transactions on Microwave Theory and Techniques, 45, Lee D., (2008), Energy harvesting chip and the chip based power supply development for a wireless sensor, Sensors, 8, Morega A.M., Ordonez J.C., Negoias P.A., Morega M., Hovsapian R., (2006), Optimal Electrical Design of Spherical Photovoltaic Cells, COMSOL Conference, Congress Center of the Czech Technical University, Prague, October 26, On line at: ega.pdf. Morega A.M., Morega M., Pîslaru-Dănescu L., Stoica V., Nouraş F., Stoian F.D., (2010), A Novel, Ferrofluid- Cooled Transformer. Electromagnetic Field and Heat Transfer by Numerical Simulation, Proc. of the 12th International Conference on Optimization of Electrical and Electronic Equipment (OPTIM), May, Brasov, Romania, , DOI: /OPTIM Morega A.M., Pîslaru-Dănescu L., Morega M., (2012a), A Novel Nanoparticles Magnetic Fluid Microactuator Device, Proc. of the 13th International Conference on Optimization of Electrical and Electronic Equipment (OPTIM), May 2012, Brasov, Romania, , DOI: /OPTIM Morega A.M., Morega, M., Dumitru, J.B., Pîslaru-Dănescu L., (2012b), Magnetic and Electric Sizing of a Miniature Planar Spiral Transformer, Proc. of International Conference and Exposition on Electrical and Power Engineering (EPE),, October, Iaşi, Romania, , DOI: /ICEPE Raj K., Moskovitz R., (1993), Ferrofluid, Cooled Electromagnetic Device and Improved Cooling Method. USA Patent No. 5,462,685. Segal V., Rabinovich A., Nattrass D., Raj K., Nunes A., (2000), Experimental study of magnetic colloidal fluids behavior in power transformers, Journal of Magnetism and Magnetic Materials, , Tsai T.H., Kuo L.S., Chen P.H., Lee D.S., Yang C.T., (2010), Applications of ferro-nanofluid on a microtransformer, Sensors, 10, Vollath D., (2008), Nanomaterials. An Introduction to Synthesis, Properties and Application, WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim, Germany. 1177