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- Title
- A Kernel-Free Boundary Integral Method for Two-Dimensional Magnetostatics Analysis
- Creator
- Jin, Zichao
- Date
- 2023
- Description
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Performing magnetostatic analysis accurately and efficiently is crucial for the multi-objective optimization of electromagnetic device designs...
Show morePerforming magnetostatic analysis accurately and efficiently is crucial for the multi-objective optimization of electromagnetic device designs. Therefore, an accurate and computationally efficient method is essential. Kernel Free Boundary Integral Method is a numerical method that can accurately and efficiently solve partial differential equations. Unlike traditional boundary integral or boundary element methods, KFBIM does not require an analytical form of Green’s function for evaluating integrals via numerical quadrature. Instead, KFBIM computes integrals by solving an equivalent interface problem on a Cartesian mesh. Compared with traditional finite difference methods for solving the governing PDEs directly, KFBIM produces a well-conditioned linear system. Therefore, the numerical solution of KFBIM is not sensitive to computer round-off errors, and the KFBIM requires only a fixed number of iterations when an iterative method (e.g., GMRES) is applied to solve the linear system.In this research, the KFBIM is introduced for solving magnetic computations in a toroidal core geometry in 2D. This study is very relevant in designing and optimizing toroidal inductors or transformers used in electrical systems, where lighter weight, higher inductance, higher efficiency, and lower leakage flux are required. The results are then compared with a commercial finite element solver (ANSYS), which shows excellent agreement. It should be noted that, compared with FEM, the KFBIM does not require a body-fitted mesh and can achieve high accuracy with a coarse mesh. In particular, the magnetic potential and tangential field intensity calculations on the boundaries are more stable and exhibit almost no oscillations.Furthermore, although KFBIM is accurate and computationally efficient, sharp corners can be a significant problem for KFBIM. Therefore, an inverse discrete Fourier transform (DFT) based geometry reconstruction is explored to overcome this challenge for smoothening sharp corners. A toroidal core with an airgap (C-core) is modeled to show the effectiveness of the proposed approach in addressing the sharp corner problem. A numerical example demonstrates that the method works for the variable coefficient PDE. In addition, magnetostatic analysis for homogeneous and nonhomogeneous material is presented for the reconstructed geometry, and results carried out from KFBIM are compared with the results of FEM analysis for the original geometry to show the differences and the potential of the proposed method.
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- Title
- Modeling and Optimization of Embedded Active Flow Control Systems
- Creator
- Henry, James M.
- Date
- 2024
- Description
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This thesis presents research focused on the aerodynamic performance of circulation control on two-dimensional and quasi-two-dimensional wings...
Show moreThis thesis presents research focused on the aerodynamic performance of circulation control on two-dimensional and quasi-two-dimensional wings. Aerodynamic loads, namely lift, drag, and moment coefficients, are measured through Reynolds Averaged Navier Stokes (RANS) modeling and wind tunnel experiment. A simplified and parameterized RANS model is presented as a rapidly iterable approach to estimating the performance of trailing-edge circulation control on two dimensional airfoils, with the hypothesis that an optimized airfoil shape can be found which maximizes the lift coefficient increment generated by circulation control, through modification of the wing profile. The simplified modeling setup is compared with more conventional approaches to numerical simulation of circulation control. The performance of the simplified modeling scheme is then compared with wind tunnel studies, for both steady-state and dynamic performance, as functions of both momentum coefficient dCμ and chord-based Reynolds number Re_c. The dynamic performance for the model is studied to find an analog to the theoretical unsteady models of Wagner and Theodorsen. An adjoint optimization framework is used to find an optimal airfoil profile for circulation control. The optimized profile is then compared in both a simulation and a wind tunnel test study against a NACA0015 airfoil. In simulation, improvement between 12% and 15% is seen for the lift control authority for all values of dCμ and Re_c tested. In experiment, the optimized profile demonstrated improvements of up to 28% in lift control authority, dCL/dCμfor values of Cμ, and decreased performance for higher values of Cμ.
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- Title
- Correlating Microstructural Properties to Macroscopic Shear Mechanics to Improve the Understanding of Tissue Biomechanics
- Creator
- Cahoon, Stacey Marie
- Date
- 2023
- Description
-
Understanding tissue biomechanics is of interest for modeling organ injury from external loads, development of tissue surrogate materials, and...
Show moreUnderstanding tissue biomechanics is of interest for modeling organ injury from external loads, development of tissue surrogate materials, and creating new biomarkers for disease. Probing the response of soft tissue in shear can provide information on histopathology, provided a methodology exists that connects the macroscopic mechanical properties with cell-level properties. Two of the available methods to measure the macroscopic shear viscoelastic properties of soft tissue are oscillatory shear rheometry and ultrasound shear wave elastography (SWE). Due to its accuracy, rheometry is the gold standard, but it is destructive, requires excised homogeneous samples, and can only be applied ex-vivo. SWE is an emerging non-invasive imaging technique which requires validation, ostensibly by comparing with rheometry. Histology is the gold standard for providing morphological information on the cell level, which can determine tissue pathology. The challenge is to connect the macroscopic mechanical metrics derived from SWE and rheometry to the tissue microstructure. To address this challenge, mathematical models can be used that employ multiple, judiciously chosen measurements of macroscopic shear properties and histology to estimate intrinsic mechanical properties at the cell level.A class of homogeneous and composite lipid phantoms mimicking the mechanical properties of brain white matter were fabricated to test a novel stereotactic system and an optimized SWE imaging protocol. The shear stiffness measurements obtained with SWE on the whole phantom were validated with rheometry performed on a series of samples made with the same material as the phantoms. The same procedure was applied to porcine brain white matter excised from fresh whole brains (n=3). Cylindrical cores were extracted from the corpus callosum area, sliced into discs and microscopic sections were subsequently removed for histology. Good agreement was found between the SWE and rheometry measurements of shear stiffness, which generally increases with the level of compressive prestress. Immunofluorescence was used to stain separately the axon neurofilaments and myelin sheaths, and digital image analysis of the confocal microscopy images allowed the estimation of axon volume fraction and axon-to-myelin ratio in the corpus callosum. Using these metrics and a composite mechanical model, a connection between the macroscopic shear measurements and the viscoelastic properties of axon and glia matrix was made for porcine brain tissue. Similarly, rheometry was used to measure the macroscopic properties of decellularized porcine myocardium extracellular matrix (ECM) in two different fiber locations, and for three different fiber orientations. The mechanical properties were found to be dependent upon fiber location, but not on fiber orientation. Since collagen is a primary supportive structure for the ECM, several microscopic slices were probed with immunofluorescence to compute the collagen I and collagen IV volume fractions. Another mechanical model was employed to establish a connection between the macroscopic properties and the mechanical properties of the collagen matrix in decellularized porcine myocardial ECM.This dissertation highlights the use and integration of three different experimental techniques (rheometry, ultrasound SWE, and histology) to correlate key microstructural properties of soft, fibrous tissues (ex-vivo healthy porcine brain white matter and myocardium ECM) with macroscopic shear mechanics. The consideration of the effect of compressive prestress is noteworthy. The reported baseline data for the tissues under shear loading and prestress are pertinent to the physiological function of these tissues, and therefore constitute preliminary data and a necessary first step before a systematic study of the biomechanics of the same tissues in vivo is performed.
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