3D simulation of magneto-mechanical coupling in MRI scanners using high order FEM and POD

Magnetic Resonance Imaging (MRI) scanners have become an essential tool in the medi-cal industry due to their ability to produce high resolution images of the human body. To generate an image of the body, MRI scanners combine strong static magnetic fields with transient gradient magnetic fields. The interaction of these magnetic fields with the con-ducting components present in superconducting MRI scanners gives rise to an important problem in the design of new MRI scanners. The transient magnetic fields give rise to the appearance of eddy currents in conducting components. These eddy currents, in turn, result in electromagnetic stresses, which cause the conducting components to deform and vibrate. The vibrations are undesirable as they lead to a deterioration in image quality (with image artefacts) and to the generation of noise, which can cause patient discomfort. The eddy currents, in addition, lead to heat being dissipated and deposited into the cryo-stat, which is filled with helium in order to maintain the coils in a superconducting state. This deposition of heat can cause helium boil off and potentially result in a costly magnet quench. Understanding the mechanisms involved in the generation of these vibrations and the heat being deposited into the cryostat are, therefore, key for a successful MRI scanner design. This involves the solution of a coupled magneto-mechanical problem, which is the focus of this work.In this thesis, a new computational methodology for the solution of three-dimensional (3D) magneto-mechanical coupled problems with application to MRI scanner design is presented. To achieve this, first an accurate mathematical description of the magneto-mechanical coupling is presented, which is based on a Lagrangian formulation and the assumption of small displacements. Then, the problem is linearised using an AC-DC splitting of the fields, and a variational formulation for the solution of the linearised prob-lem in a time-harmonic setting is presented. The problem is then discretised using high order finite elements, where a combination of hierarchical H1 and H(curl) basis func-tions is used. An efficient staggered algorithm for the solution of the coupled system is proposed, which combines the DC and AC stages and makes use of preconditioned iter-ative solvers when appropriate. This finite element methodology is then applied to a set of challenging academic and industrially relevant problems in order to demonstrate its accuracy and efficiency.This finite element methodology results in the accurate and efficient solution of the magneto-mechanical problem of interest. However, in the design stage of a new MRI scanner, this coupled problem must be solved repeatedly for varying model parameters such as frequency or material properties. Thus, even if an efficient finite element solver is available for the solution of the coupled problem, the need for these repeated simulations result in a bottleneck in terms of computational cost, which leads to an increase in design time and its associated financial implications. Therefore, in order to optimise this process, the application of Reduced Order Modelling (ROM) techniques is considered. A ROM based on the Proper Orthogonal Decomposition (POD) method is presented and applied to a series of challenging MRI configurations. The accuracy and efficiency of this ROM is demonstrated by performing comparisons against the full order or high fidelity finite element software, showing great performance in terms of computational speed-up, which has major benefits in the optimisation of the design process of new MRI scanners

Numerical Study of Interfacial Flow using Algebraic Coupled Level Set-Volume of Fluid (A-CLSVOF) Method

Solving interfacial flows numerically has been a challenge due to the lack of sharpness and the presence of spurious currents at the interface. Two methods, Algebraic Coupled Level Set-Volume of Fluid (A-CLSVOF) method and Ghost Fluid Method (GFM) have been developed in the finite volume framework and employed in several interfacial flows such as Rayleigh-Taylor instability, rising bubble, impinging droplet and cross-flow oil plume. In the static droplet simulation, A-CLSVOF substantially reduces the spurious currents. The capillary wave relaxation shows that this method delivers results comparable to those of more rigorous methods such as Front Tracking methods for fine grids. The results for the other interfacial flows also compared well with the experimental results. Next, interfacial forces are implemented by enlisting the finite volume discretization of Ghost Fluid Method. To assess the A-CLSVOF/GFM performance, four cases are studied. In the case of the static droplet in suspension, the combined A-CLSVOF/GFM produces a sharp and accurate pressure jump compared to the traditional CSF (continuum surface force) implementation. For the linear two-layer shear flow, GFM sharp treatment of the viscosity captured the velocity gradient across the interface. For a gaseous bubble rising in a viscous fluid, GFM outperforms CSF by almost 10%. Also, a Decoupled Pressure A-CLSVOF/GFM method (DPM) has been developed which separates pressure into two pressure components, one accounting for interfacial forces such as surface tension and another representing the rest of flow pressure. It is proven that the DPM implementation results in more efficiency in PISO (Pressure Implicit with Splitting of Operators) loop. A two-phase solver is used to study buoyant oil discharge in quiescent and cross-flow ambient. Different modes of breakup including dripping, jetting (axisymmetric and asymmetric) and atomization for cross-flow oil jet are captured

A Preliminary Study of Acoustic Prediction Technology Based on Detached Eddy Simulations for Supersonic Jets Impinging on Flat Plates

An application of an existing industry tool to study supersonic jets impinging on at plates is shown. This industry tool is the commercially available CFD package ANSYS FLUENT. The supersonic jet studied is perfectly expanded with a Mach number of 1.5, and it impinges on a flat surface 4 nozzle throat diameters from the jet exit. All turbulence modeling is done using a hybrid RANS/LES technique known as Delayed Detached Eddy Simulation (DDES). A transient solution is calculated using the pressure-based coupled solver formulation with the second-order bounded central-upwind spatial discretization and second-order implicit time marching scheme. Flow features like the stagnation bubble, wall jet and feedback mechanism were studied using contour plots. An examination was also done into the mean flow fields of the jet core. The acoustics of the case were studied using two dierent techniques, direct measurement and the use of a acoustics source surface method. Using limited computational power, reasonable agreement between simulation and experimental data was found for the mean flow field and acoustics. Thus, it was demonstrated that ANSYS FLUENT can be used for this problem to provide good preliminary results in an industry setting with limited computational power

Towards Adaptive and Grid-Transparent Adjoint-Based Design Optimization Frameworks

With the growing environmental consciousness, the global perspective in energy production is shifting towards renewable resources. As recently reported by the Office of Energy Efficiency & Renewable Energy at the U.S. Department of Energy, wind-generated electricity is the least expensive form of renewable power and is becoming one of the cheapest forms of electricity from any source. The aeromechanical design of wind turbines is a complex and multidisciplinary task which necessitates a high-fidelity flow solver as well as efficient design optimization tools. With the advances in computer technologies, Computational Fluid Dynamics (CFD) has established its role as a high-fidelity tool for aerodynamic design.In this dissertation, a grid-transparent unstructured two- and three-dimensional compressible Reynolds-Averaged Navier-Stokes (RANS) solver, named UNPAC, is developed. This solver is enhanced with an algebraic transition model that has proven to offer accurate flow separation and reattachment predictions for the transitional flows. For the unsteady time-periodic flows, a harmonic balance (HB) method is incorporated that couples the sub-time level solutions over a single period via a pseudo-spectral operator. Convergence to the steady-state solution is accelerated using a novel reduced-order-model (ROM) approach that can offer significant reductions in the number of iterations as well as CPU times for the explicit solver. The unstructured grid is adapted in both steady and HB cases using an r-adaptive mesh redistribution (AMR) technique that can efficiently cluster nodes around regions of large flow gradients.Additionally, a novel toolbox for sensitivity analysis based on the discrete adjoint method is developed in this work. The Fast automatic Differentiation using Operator-overloading Technique (FDOT) toolbox uses an iterative process to evaluate the sensitivities of the cost function with respect to the entire design space and requires only minimal modifications to the available solver. The FDOT toolbox is coupled with the UNPAC solver to offer fast and accurate gradient information. Ultimately, a wrapper program for the design optimization framework, UNPAC-DOF, has been developed. The nominal and adjoint flow solutions are directly incorporated into a gradient-based design optimization algorithm with the goal of improving designs in terms of minimized drag or maximized efficiency

Computational Acoustic Beamforming of Noise Source on Wind Turbine Airfoil

A new method, Computational Acoustic Beamforming, is proposed in this thesis. This novel numerical sound source localization methodology combines the advantages of the Computational Fluid Dynamics (CFD) simulation and experimental acoustic beamforming, which enable this method to take directivity of sound source emission into account while maintaining a relatively low cost. This method can also aid the optimization of beamforming algorithm and microphone array design. In addition, it makes sound source prediction of large structures in the low frequency range possible. Three modules, CFD, Computational Aeroacoustics (CAA) and acoustic beamforming, are incorporated in this proposed method. This thesis adopts an open source commercial software OpenFOAM for the flow field simulation with the Improved Delayed Detached Eddy Simulation (IDDES) turbulence model. The CAA calculation is conducted by an in-house code using impermeable Ffowcs-Williams and Hawkings (FW-H) equation for static sound source. The acoustic beamforming is performed by an in-house Delay and Sum (DAS) beamformer code with several different microphone array designs. Each module has been validated with currently available experimental data and numerical results. A flow over NACA 0012 airfoil case was chosen as a demonstration case for the new method. The aerodynamics and aeroacoustics results are shown and compared with the experimental measurements. A relatively good agreement has been achieved which gives the confidence of using this newly proposed method in sound source localization applications

Fast, Adaptive Algorithms for Flow Problems

Time-accurate simulations of physical phenomena (e.g., ocean dynamics, weather, and combustion) are essential to economic development and the well-being of humanity. For example, the economic toll hurricanes wrought on the United States in 2017 exceeded $\$200$ billon dollars. To mitigate the damage, the accurate and timely forecasting of hurricane paths are essential. Ensemble simulations, used to calculate mean paths via multiple realizations, are an invaluable tool in estimating uncertainty, understanding rare events, and improving forecasting. The main challenge in the simulation of fluid flow is the complexity (runtime, memory requirements, and efficiency) of each realization. This work confronts each of these challenges with several novel ensemble algorithms that allow for the fast, efficient computation of flow problems, all while reducing memory requirements. The schemes in question exploit the saddle-point structure of the incompressible Navier-Stokes (NSE) and Boussinesq equations by relaxing incompressibility appropriately via artificial compressibility (AC), yielding algorithms that require far fewer resources to solve while retaining time-accuracy. Paired with an implicit-explicit (IMEX) ensemble method that employs a shared coefficient matrix, we develop, analyze, and validate novel schemes that reduce runtime and memory requirements. Using these methods as building blocks, we then consider schemes that are time-adaptive, i.e., schemes that utilize varying timestep sizes. The consideration of time-adaptive artficial compressibility methods, used in the algorithms mentioned above, also leads to the study of a new slightly-compressible fluid flow continuum model. This work demonstrates stability and weak convergence of the model to the incompressible NSE, and examines two associated time-adaptive AC methods. We show that these methods are unconditionally, nonlinearly, long-time stable and demonstrate numerically their accuracy and efficiency. The methods described above are designed for laminar flow; turbulent flow is addressed with the introduction of a novel one-equation unsteady Reynolds-averaged Navier-Stokes (URANS) model with multiple improvements over the original model of Prandtl. This work demonstrates analytically and numerically the advantages of the model over the original

Large eddy simulation of acoustic propagation in turbulent flow through ducts and mufflers

This research involves study of acoustic propagation of pulse in a simple expansion muffler, which is very often used in HVAC or automotive exhausts. A hybrid pressure-based compressible solver is developed and validated for a low Mach number flow simulation of acoustic pulse. This new solver is developed using C++ based OpenFOAM toolkit and further tested for low Mach number flow test case. The analysis of simple expansion muffler for various structures, frequency ranges and numerical schemes is performed and results are summarized. RANS simulation of duct and muffler with mean flow is conducted and results are presented with inherent limitations associated with the method. Further, a mixed synthetic inflow boundary condition is also developed and validated for LES of channel flow. The mixed synthetic boundary is then used for LES of a simple expansion muffler to analyse the flow-acoustic and acoustic-pulse interactions inside the expansion muffler. The improvement in the prediction of tonal noise and vortex shedding inside the chamber is highlighted in comparison to the RANS method. Further, the effect of forced pulsation on flow-acoustic is observed in regard to the shift in Strouhal number inside the simple expansion muffler. Finally, a set of benchmark results for experimental analysis of the simple expansion muffler both, with and without flow is obtained to compare attenuation in forced pulsation for various mean-flow velocities. These experimental results are then used for validation of the proposed pressure-based compressible solver