微纳通道内流动与传热的基础研究

As pressure-driven micro/nano flows are inherently complex, there currently is no widely agreed, sufficiently accurate, and computationally efficient model. This work will significantly extend previous studies to the whole range of the Knudsen number from continuum, through the slip and transition regimes up to the free molecular regime to bridge kinetic theory and conventional fluid dynamics. A simple unified analytical model with appropriate second-order slip boundary conditions will be proposed. The developed unified models can be used to predict the velocity distribution, Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution and pressure drop of gaseous flow in various noncircular microchannels and nanochannels by the research community for the practical engineering design. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. The appropriate or effective second-order slip boundary conditions include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation. The proposed unified models will be compared with numerical and experimental data in the literature. The compressibility and rarefaction effects will be analyzed. Compressibility may depend on a new dimensionless parameter and a fresh general pressure drop model for isothermal low Mach number compressible flow in microchannels and nanochannels will be proposed. This study also deals with issues of hydrodynamic flow development and the effects between entrance region and rarefaction will be studied. The coupled effects between rarefaction and surface roughness will be investigated as well. It is significant to develop an expression for the rarefaction correction to the continuum solution for heat transfer. An analogy for slip and transition flow heat transfer in microchannels and nanochannels will be proposed. The analogy can be utilized to obtain an initial engineering approximation of the Nusselt number in the whole range of the Knudsen number.

由于微纳通道流动问题固有的复杂性，当前还没有广泛接受的、充分准确的和计算有效的模型存在。扩展纳维斯托克斯方程的应用范围无疑是非常理想的，因为连续介质模型具有显著的计算效率。本项目研究将显著扩展过去的研究到整个克努森数范围，以便架起分子运动论与传统流体力学之间的桥梁。我们将发展一个包含克努森层影响的统一二阶滑移边界条件模型。对于各种形状微纳通道内的气体流动，研究和设计界可以应用这个模型来预计速度分布、泊肃叶数、质量流率、压力分布和压降。本项目提出的跨尺度统一模型将用数值数据、实验数据和理论结果来验证。我们将分析压缩性和稀薄性的影响并提出判断压缩性影响的新的无量纲数和一个低马赫数可压缩层流的压降模型。本项目将研究进口地区发展流与稀薄性的相互影响、表面粗糙度与稀薄性的耦合影响。本项目将提出新的动量与能量传递比拟来发展一个相对于连续流解的修正模型，以便在整个克努森数范围内得到努谢尔数的估计值。

由于微纳通道流动问题固有的复杂性，当前还没有广泛接受的、充分准确的和计算有效的模型存在。扩展纳维斯托克斯方程的应用范围无疑是非常理想的，因为连续介质模型具有显著的计算效率。本项目研究显著扩展过去的研究到广泛的克努森数范围，以便架起分子运动论与传统流体力学之间的桥梁。我们发展了一个包含克努森层影响的统一二阶滑移边界条件模型。对于各种形状微纳通道内的气体流动，研究和设计界可以应用这个模型来预计速度分布、泊肃叶数、质量流率、压力分布和压降。本项目提出的跨尺度统一模型已用数值数据、实验数据和理论结果验证。我们分析了压缩性和稀薄性的影响并提出判断压缩性影响的新的无量纲数和一个低马赫数可压缩层流的压降模型。本项目研究了进口地区发展流与稀薄性的相互影响、表面粗糙度与稀薄性的耦合影响。本项目提出新的动量与能量传递比拟来发展一个相对于连续流解的修正模型，以便在广泛的克努森数范围内得到努谢尔数的估计值。