Collaborative Research: Multiphysics modeling and analysis of thermo-visco-acoustic equations with applications to the design of trace gas sensors

合作研究：热粘声方程的多物理场建模和分析及其在痕量气体传感器设计中的应用

• 批准号: 1620222
• 负责人: Robert Kirby
• 金额: $ 9万
• 依托单位: Baylor University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-15 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620222&HistoricalAwards=false
• 关键词: Collaborative; Research; Multiphysics; modeling; analysis

Trace gas sensors can be used to detect and identify very small quantities of gases for applications in such diverse fields as atmospheric chemistry, environmental and industrial emissions monitoring, explosives detection, industrial process control, and non-invasive medical diagnostics. The large-scale adoption of trace gas sensors requires sensor systems that are compact, portable, efficient, sensitive, cost-effective and highly reliable. Quartz Enhanced Photoacoustic Spectroscopy (QEPAS) sensors hold promise as a technology that may achieve many of these goals. In particular, QEPAS sensors can be as small as several cubic millimeters, whereas sensors based on other sensitive spectroscopic techniques require large cell volumes of tens to hundreds of cubic centimeters. QEPAS sensors use a quartz tuning fork to detect weak sound waves that are generated when a beam of light from a laser interacts with a trace gas. A major engineering challenge to overcome before QEPAS sensors can be widely deployed is to increase their sensitivity and lower their production cost. The overall goal of this project is to develop a computational model for QEPAS sensors that is a significant enhancement over existing models, and to then use this model to determine cost-effective designs that increase the sensitivity of QEPAS sensors. The major mathematical challenge of the project is to develop efficient computational methods to solve the multiphysics equations that form the basis of the model. The project will provide broad training in computational science for two mathematics graduate students from faculty mentors with complementary expertise in the physics and engineering of the application, mathematical modeling, numerical analysis, and parallel computing.QEPAS sensors employ a resonantly vibrating quartz tuning fork to detect weak acoustic pressure waves and thermal disturbances which are generated when optical radiation from a laser beam interacts with a trace gas. The project will involve the development and analysis of computational methods to solve a system of Helmholtz equations that describes the interaction between a thermo-visco-acoustic fluid and a resonantly vibrating mechanical structure (a quartz tuning fork). The model will be used to numerically optimize the QEPAS signal as a function of the geometric parameters of the sensor. The cumulative effect of the damping of the tuning fork by the viscous fluid will be computed in terms of the geometric parameters of the system and physical constants. Consequently, the model will allow for realistic optimization of QEPAS sensors by varying the tuning fork geometry. Furthermore, in some situations, the thermal diffusion wave can dominate the acoustic pressure wave on the surface of the tuning fork, in a phenomenon known as Resonant Opto-Thermo-Acoustic DEtection (ROTADE). Current mathematical descriptions of these sensors cannot capture both QEPAS and ROTADE phenomena simultaneously, although experimental data indicates that depending on the position of the laser beam along the tuning fork axis, both types of trace gas sensing may occur. The new model will allow for simultaneous simulation of both types of sensor systems. Preliminary analytical and computational results show that standard finite element methods for solving the equations in the model are ineffective due to small parameters in the equations and the high wave number of the solution. The small parameters produce an ill-conditioned linear system resulting from the finite element discretizations of the equations, while the high wave numbers can cause large phase errors in the computed solution (pollution error). This project will advance knowledge in computational mathematics by developing and analyzing block preconditioners for the multiphysics Helmholtz system. In addition, methods for reducing the pollution error will be developed by extending higher-order finite element and interior penalty stabilization methods originally proposed for scalar Helmholtz equations to the multiphysics Helmholtz system. The techniques developed will be relevant for more general coupled Helmholtz systems such as those which arise in the study of thermal phenomena near thin bodies, the design of hearing aid transducers and micro-electrical-mechanical devices.

痕量气体传感器可用于检测和识别非常少量的气体，用于各种领域，如大气化学，环境和工业排放监测，爆炸物检测，工业过程控制和非侵入性医疗诊断。痕量气体传感器的大规模采用要求传感器系统紧凑、便携、高效、灵敏、成本效益高且高度可靠。石英增强光声光谱（QEPAS）传感器有望成为实现许多这些目标的技术。特别是，QEPAS传感器可以小到几立方毫米，而基于其他敏感光谱技术的传感器需要几十到几百立方厘米的大单元体积。QEPAS传感器使用石英音叉来检测激光器发出的光束与痕量气体相互作用时产生的微弱声波。在QEPAS传感器可以广泛部署之前，需要克服的一个主要工程挑战是提高其灵敏度并降低其生产成本。该项目的总体目标是为QEPAS传感器开发一个计算模型，这是对现有模型的显著增强，然后使用该模型来确定提高QEPAS传感器灵敏度的成本效益设计。该项目的主要数学挑战是开发高效的计算方法来求解构成模型基础的多物理场方程。该项目将提供广泛的培训，在计算科学的两个数学研究生从教师导师与互补的专业知识，在物理和工程的应用，数学建模，数值分析，QEPAS传感器采用共振石英音叉来检测弱声压波和热扰动，当来自激光束的光辐射与来自石英音叉的光辐射相互作用时，一种微量气体该项目将涉及开发和分析计算方法，以求解描述热粘声流体与共振机械结构（石英音叉）之间相互作用的亥姆霍兹方程组。该模型将用于数值优化QEPAS信号作为传感器的几何参数的函数。由粘性流体阻尼音叉的累积效应将根据系统的几何参数和物理常数来计算。因此，该模型将允许通过改变音叉几何形状来现实地优化QEPAS传感器。此外，在某些情况下，热扩散波可以主导音叉表面上的声压波，这是一种被称为共振光-热-声检测（ROTADE）的现象。这些传感器的当前数学描述不能同时捕获QEPAS和ROTADE现象，尽管实验数据表明取决于激光束沿着音叉轴的位置，两种类型的痕量气体感测都可能发生。新模型将允许同时模拟两种类型的传感器系统。 初步的分析和计算结果表明，标准的有限元方法求解方程的模型是无效的，由于小参数的方程和高波数的解决方案。小的参数产生一个病态的线性系统，从有限元离散方程，而高波数可能会导致大的相位误差的计算解决方案（污染误差）。本项目将通过开发和分析多物理场亥姆霍兹系统的块预处理器来提高计算数学的知识。此外，减少污染误差的方法将通过扩展高阶有限元和内部惩罚稳定化方法最初提出的标量亥姆霍兹方程的多物理场亥姆霍兹系统。开发的技术将是相关的更一般的耦合亥姆霍兹系统，如那些出现在薄体附近的热现象的研究，助听器换能器和微机电设备的设计。