Computational Modeling of Transport Phenomena and Electro- mechanical Dynamics in Microscales

1)微通道中的输运现象——带滑移边界条件的过渡流耦合Navier-Stokes和能量方程的谱元法的发展微通道中低克努森数流的直接模拟蒙特卡罗方法将被执行。非矩形几何，如梯形截面，将被研究。2)微电机静电力计算-微扰法将扩展到求解三维静电力场计算。电阻率对材料的影响也将包括在内。计算将执行各种微电机几何形状，以优化设备设计。3)微动力装置中的挤压膜阻尼——求解雷诺方程，了解微板间不同间隙距离下挤压膜的流体动力学。该结果将与(2)的结果相结合，并与我们使用静电悬浮微孔板获得的独特实验数据进行比较。将确定有效阻尼特性。阶段II 1)微通道中的传输现象- (I.I)的结果将扩展到包括通道几何形状的缺陷，这在微加工中是不可避免的。将采用混合光谱/有限差分离散方法。（I.I）和本任务的结果将进行总结，以提供一个全面的微通道流量数据库。2)微电机的静电力计算-(1.3)的结果将被扩展到在Macintosh II系列计算机上执行静电力计算。该规范将得到扩展，以便在从CAD程序导入的图纸上执行静电力计算。3)微电机及其他微结构中的流体动力阻力和升力——谱元法将用于研究具有等截面转子的微电机的详细流场。该结果将与（I.2）和（II.2）的结果相结合，并与最近报道的测量微电机瞬态动力学的频闪实验工作进行比较。第三阶段1)微动力装置的流体动力轴承- (I.1-3)和（II.1-3）的综合结果将用于研究减少微动力装置阻力和增加微动力装置升力的方法。本文还将研究在外加静电场作用下，利用水动力使微电机转子居中的问题。2)降阶模型开发- (I.1-3)和（II.1-3）的综合结果将被仔细制表，以开发微动力设备和系统的科学数据库。将为输运现象和机电动力学发展简化的方程组，它们的相对准确性将通过与（I.1-3）和（II.1-3）的结果进行比较来确定。降阶模型将有助于开发硬件制造前进行设计优化研究的手段，以及微动力设备和系统的闭环控制策略。

Phase I 1) Transport Phenomena in Microchannels - Development of Spectral Element Method for the coupled Navier-Stokes and Energy Equation with slip boundary conditions for transition flows, and Direct Simulation Monte Carlo Method for low Knudsen number flows in microchannels will be performed. Non-rectangular geometries, such as trapezoidal cross sections, will be investigated. 2) Electrostatic Force Calculations for Micromotors - Perturbation Method will be extended to solve three-dimensional electrostatic force field calculations. The effects of resistivity in the materials will also be included. The calculations will be performed for various micromotor geometries to optimize device designs. 3) Squeeze Film Damping in Microdynamical Devices - Reynold's Equation will be solved to understand fluid dynamics of squeeze film between microplates at various gap distances. The results will be integrated with the results of (2) and compared to our unique experimental data obtained using electrostatic levitation microplates. The effective damping characteristics will be determined. Phase II 1) Transport Phenomena in Microchannels - Results from (I.I) will be extended to include the imperfections of channel geometries, which are unavoidable in micromachining. Hybrid Spectral/Finite Difference Discretization Method will be used. The results of (I.I) and this task will be summarized to provide a comprehensive data base for microchannel flows. 2) Electrostatic Force Calculations for Micromotors - The results of (1.3) will be extended to perform electrostatic force calculations on the Macintosh II family of computers. The code will be extended such that electrostatic force calculations will be performed on drawings imported from CAD programs. 3) Hydrodynamic Drag and Lift in Micromotors and Other Microstructures - Spectral Element Method will be applied to study the detailed flow field of micromotors with uniform cross section rotors. The results will be combined with the results of (I.2) and (II.2) and compared to the recently reported stroboscopic experimental work measuring the transient dynamics of a micromotor. Phase III 1) Hydrodynamic Bearings for Microdynamical Devices - The comprehensive results of (I.1-3) and (II.1-3) will be applied to investigate the methods of reducing drag and increasing lift of microdynamical devices. The use of hydrodynamic forces to center the rotor of micromotors under the applied electrostatic field will also be investigated. 2) Reduced Order Model Development - The comprehensive results of (I.1-3) and (II.1-3) will be carefully tabulated to develop a scientific data base for microdynamical devices and systems. Simplified sets of equations will be developed for both transport phenomena and electromechanical dynamics, and their relative accuracy will be determined by comparing the results to those from (I.1-3) and (II.1-3). The reduced order models will be useful for developing means to conduct design optimization studies before hardware fabrication, as well as closed loop control strategies for microdynamical devices and systems.