Incorporation of Hysteretic Effects in Model-Order Reduction Analysis of Magnetic Devices

The ability to predict the properties of magnetic materials in a device is essential to ensuring the correct operation and optimization of the design as well as the device behavior over a wide range of input frequencies. Typically, development and simulation of wide-bandwidth models requires detailed, physics-based simulations that utilize significant computational resources. Balancing the trade-offs between model computational overhead and accuracy can be cumbersome, especially when the nonlinear effects of saturation and hysteresis are included in the model. This study focuses on the development of a system for analyzing magnetic devices in cases where model accuracy and computational intensity must be carefully and easily balanced by the engineer. A method for adjusting model complexity and corresponding level of detail while incorporating the nonlinear effects of hysteresis is presented that builds upon recent work in loss analysis and magnetic equivalent circuit (MEC) modeling. The approach utilizes MEC models in conjunction with linearization and model-order reduction techniques to process magnetic devices based on geometry and core type. The validity of steady-state permeability approximations is also discussed.

Studies of turbulent flows in continuous casting of steel with and without magnetic field

This thesis develops and tests various transient and steady-state computational models such as direct numerical simulation (DNS), large eddy simulation (LES), filtered unsteady Reynolds-averaged Navier-Stokes (URANS) and steady Reynolds-averaged Navier-Stokes (RANS) with and without magnetic field to investigate turbulent flows in canonical as well as in the nozzle and mold geometries of the continuous casting process. The direct numerical simulations are first performed in channel, square and 2:1 aspect rectangular ducts to investigate the effect of magnetic field on turbulent flows. The rectangular duct is a more practical geometry for continuous casting nozzle and mold and has the option of applying magnetic field either perpendicular to broader side or shorter side. This work forms the part of a graphic processing unit (GPU) based CFD code (CU-FLOW) development for magnetohydrodynamic (MHD) turbulent flows. The DNS results revealed interesting effects of the magnetic field and its orientation on primary, secondary flows (instantaneous and mean), Reynolds stresses, turbulent kinetic energy (TKE) budgets, momentum budgets and frictional losses, besides providing DNS database for two-wall bounded square and rectangular duct MHD turbulent flows. Further, the low- and high-Reynolds number RANS models (k-ε and Reynolds stress models) are developed and tested with DNS databases for channel and square duct flows with and without magnetic field. The MHD sink terms in k- and ε-equations are implemented as proposed by Kenjereš and Hanjalić using a user defined function (UDF) in FLUENT. This work revealed varying accuracies of different RANS models at different levels. This work is useful for industry to understand the accuracies of these models, including continuous casting. After realizing the accuracy and computational cost of RANS models, the steady-state k-ε model is then combined with the particle image velocimetry (PIV) and impeller probe velocity measurements in a 1/3rd scale water model to study the flow quality coming out of the well- and mountain-bottom nozzles and the effect of stopper-rod misalignment on fluid flow. The mountain-bottom nozzle was found more prone to the longtime asymmetries and higher surface velocities. The left misalignment of stopper gave higher surface velocity on the right leading to significantly large number of vortices forming behind the nozzle on the left. Later, the transient and steady-state models such as LES, filtered URANS and steady RANS models are combined with ultrasonic Doppler velocimetry (UDV) measurements in a GaInSn model of typical continuous casting process. LES-CU-LOW is the fastest and the most accurate model owing to much finer mesh and a smaller timestep. This work provided a good understanding on the performance of these models. The behavior of instantaneous flows, Reynolds stresses and proper orthogonal decomposition (POD) analysis quantified the nozzle bottom swirl and its importance on the turbulent flow in the mold. Afterwards, the aforementioned work in GaInSn model is extended with electromagnetic braking (EMBr) to help optimize a ruler-type brake and its location for the continuous casting process. The magnetic field suppressed turbulence and promoted vortical structures with their axis aligned with the magnetic field suggesting tendency towards 2-d turbulence. The stronger magnetic field at the nozzle well and around the jet region created large scale and lower frequency flow behavior by suppressing nozzle bottom swirl and its front-back alternation. Based on this work, it is advised to avoid stronger magnetic field around jet and nozzle bottom to get more stable and less defect prone flow.

Solid-liquid interactions in microscale structures and devices

Liquid-solid interactions become important as dimensions approach mciro/nano-scale. This dissertation focuses on liquid-solid interactions in two distinct applications: capillary driven self-assembly of thin foils into 3D structures, and droplet wetting of hydrophobic micropatterned surfaces. The phenomenon of self-assembly of complex structures is common in biological systems. Examples include self-assembly of proteins into macromolecular structures and self-assembly of lipid bilayer membranes. The principles governing this phenomenon have been applied to induce self-assembly of millimeter scale Si thin films into spherical and other 3D structures, which are then integrated into light-trapping photovoltaic (PV) devices. Motivated by this application, we present a generalized analytical study of the self-folding of thin plates into deterministic 3D shapes, through fluid-solid interactions, to be used as PV devices. This study consists of developing a model using beam theory, which incorporates the two competing components — a capillary force that promotes folding and the bending rigidity of the foil that resists folding into a 3D structure. Through an equivalence argument of thin foils of different geometry, an effective folding parameter, which uniquely characterizes the driving force for folding, has been identified. A criterion for spontaneous folding of an arbitrarily shaped 2D foil, based on the effective folding parameter, is thus established. Measurements from experiments using different materials and predictions from the model match well, validating the assumptions used in the analysis. As an alternative to the mechanics model approach, the minimization of the total free energy is employed to investigate the interactions between a fluid droplet and a flexible thin film. A 2D energy functional is proposed, comprising the surface energy of the fluid, bending energy of the thin film and gravitational energy of the fluid. Through simulations with Surface Evolver, the shapes of the droplet and the thin film at equilibrium are obtained. A critical thin film length necessary for complete enclosure of the fluid droplet, and hence successful self-assembly into a PV device, is determined and compared with the experimental results and mechanics model predictions. The results from the modeling and energy approaches and the experiments are all consistent. Superhydrophobic surfaces, which have unique properties including self-cleaning and water repelling are desired in many applications. One excellent example in nature is the lotus leaf. To fabricate these surfaces, well designed micro/nano- surface structures are often employed. In this research, we fabricate superhydrophobic micropatterned Polydimethylsiloxane (PDMS) surfaces composed of micropillars of various sizes and arrangements by means of soft lithography. Both anisotropic surfaces, consisting of parallel grooves and cylindrical pillars in rectangular lattices, and isotropic surfaces, consisting of cylindrical pillars in square and hexagonal lattices, are considered. A novel technique is proposed to image the contact line (CL) of the droplet on the hydrophobic surface. This technique provides a new approach to distinguish between partial and complete wetting. The contact area between droplet and microtextured surface is then measured for a droplet in the Cassie state, which is a state of partial wetting. The results show that although the droplet is in the Cassie state, the contact area does not necessarily follow Cassie model predictions. Moreover, the CL is not circular, and is affected by the micropatterns, in both isotropic and anisotropic cases. Thus, it is suggested that along with the contact angle — the typical parameter reported in literature quantifying wetting, the size and shape of the contact area should also be presented. This technique is employed to investigate the evolution of the CL on a hydrophobic micropatterned surface in the cases of: a single droplet impacting the micropatterned surface, two droplets coalescing on micropillars, and a receding droplet resting on the micropatterned surface. Another parameter which quantifies hydrophobicity is the contact angle hysteresis (CAH), which indicates the resistance of the surface to the sliding of a droplet with a given volume. The conventional methods of using advancing and receding angles or tilting stage to measure the resistance of the micropatterned surface are indirect, without mentioning the inaccuracy due to the discrete and stepwise motion of the CL on micropillars. A micronewton force sensor is utilized to directly measure the resisting force by dragging a droplet on a microtextured surface. Together with the proposed imaging technique, the evolution of the CL during sliding is also explored. It is found that, at the onset of sliding, the CL behaves as a linear elastic solid with a constant stiffness. Afterwards, the force first increases and then decreases and reaches a steady state, accompanied with periodic oscillations due to regular pinning and depinning of the CL. Both the maximum and steady state forces are primarily dependent on area fractions of the micropatterned surfaces in our experiment. The resisting force is found to be proportional to the number of pillars which pin the CL at the trailing edge, validating the assumption that the resistance mainly arises from the CL pinning at the trailing edge. In each pinning-and-depinning cycle during the steady state, the CL also shows linear elastic behavior but with a lower stiffness. The force variation and energy dissipation involved can also be determined. This novel method of measuring the resistance of the micropatterned surface elucidates the dependence on CL pinning and provides more insight into the mechanisms of CAH.