SGER: Three-Dimensional PCMRI-Based Rheometry

ABSTRACTPROPOSAL没有。该探索性研究将侧重于使用三维相衬磁共振成像（PCMRI）测速数据来确定实际流动几何中的流体力学特性。PCMRI能以20微米的精度测量全三维流场，提供丰富的信息。以前的研究使用了简单的流动，并进行了一维分析，但没有尝试过三维计算。向三维扩展的关键是用计算流体力学方法代替一维的解析方法。通过求解一般粘性流体的Stokes流反问题，采用有限元最小二乘方法确定粘度作为位置的函数。由于模型系统包含三个方程（对应三个动量平衡）和两个未知数（粘度和压力），因此它是过确定的，将以最小二乘的方式求解。一旦粘度-位置关系已知，就有可能将粘度与应变速率张量的不变量联系起来，而无需预先选择本构方程。这将代表在复杂环境中研究流动行为能力的重大进步。该项目具有很强的探索性，计算分析方法新颖，而PCMRI的使用还相对较新。该勘探项目将侧重于获得一套良好的PCMRI数据和同一流体的经典流变学数据进行比较。如果成功，将研究更复杂的系统和瞬态效应。由于流变学与生理学（例如血液流动）高度相关，并且更好的流变学方法将改善工程研究和设计的基础设施，因此该项目具有显著的广泛影响。

ABSTRACTPROPOSAL NO.: CTS-0618811PRINCIPAL INVESTIGATORS: V. BAROCASINSTITUTION: UNIVERSITY OF MINNESOTASGER: Three-Dimensional PCMRI-Based Rheometry This exploratory research will focus on using three-dimensional phase-contrast magnetic resonance imaging (PCMRI) velocimetry data to determine fluid mechanical properties in realistic flow geometries. PCMRI can measure the full three-dimensional flow field with 20 micron accuracy, giving a rich supply of information. Previous studies have used simple flows and have performed one-dimensional analysis, but no three-dimensional calculations have been attempted. The key to the extension to three dimensions is to replace the analytical methods suitable for one dimension with a computational fluid dynamics approach. A finite-element least-squares approach will be used to determine the viscosity as a function of position by solving the inverse problem associated with Stokes flow of a general viscous fluid. Since the model system contains three equations (corresponding to three momentum balances) and two unknowns (viscosity and pressure), it is over determined and will be solved in a least-squares sense. Once the viscosity-position relation is known, it will be possible to relate viscosity to the invariants of the rate-of-strain tensor without preselection of a constitutive equation. This will represent a significant advance in the ability to study flow behavior in complex environments. The project is highly exploratory in that the computational analysis method is novel, and the use of PCMRI is still relatively new. The exploratory project will focus on getting a good set of PCMRI data and classical rheological data for the same fluids for comparison. If successful, more complex systems and transient effects will be investigated. The project has significant broader impact since rheology is highly relevant to physiology (e.g. blood flow) and since better rheological methods will improve the infrastructure for engineering research and design.