SGER: Three-Dimensional PCMRI-Based Rheometry

摘要提案编号：CTS-0618811主要制造商： 五、巴罗莎机构： 明尼苏达大学：基于三维PCMRI的流变学这项探索性研究将集中在使用三维相衬磁共振成像（PCMRI）测速数据，以确定在现实的流动几何形状的流体力学性能。PCMRI能够以20微米的精度测量全三维流场，提供丰富的信息。以前的研究都是使用简单的流动，并进行了一维的分析，但没有尝试三维的计算。将计算流体力学方法推广到三维的关键是用计算流体力学方法取代适用于一维的解析方法。有限元最小二乘方法将被用来确定作为位置的函数的粘度，通过求解与一般粘性流体的斯托克斯流相关的逆问题。 由于模型系统包含三个方程（对应于三个动量平衡）和两个未知量（粘度和压力），因此它是超定的，将在最小二乘意义下求解。一旦知道了粘度-位置关系，就有可能将粘度与应变率张量的不变量联系起来，而不需要预先选择本构方程。这将代表在复杂环境中研究流动行为的能力方面的重大进步。该项目是高度探索性的，因为计算分析方法是新颖的，PCMRI的使用仍然是相对较新的。探索性项目将集中于获得一组良好的PCMRI数据和相同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（例如血流）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，因此该项目具有更广泛的影响。

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.