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Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts

机译：在确定性和随机背景下使用Boltzmann方程的微系统中热驱动流量的定量

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摘要

When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls separated by a few mean free paths, induces a gas flow-an observation attributed to the thermostress convection effects at the microscale. The dynamics of the overall thermostress convection process is governed by the Boltzmann equation-an integrodifferential equation describing the evolution of the molecular distribution function in six-dimensional phase space-which models dilute gas behavior at the molecular level to accurately describe a wide range of flow phenomena. Approaches for solving the full Boltzmann equation with general intermolecular interactions rely on two perspectives: one stochastic in nature often delegated to the direct simulation Monte Carlo (DSMC) method and the others deterministic by virtue. Among the deterministic approaches, the discontinuous Galerkin fast spectral (DGFS) method has been recently introduced for solving the full Boltzmann equation with general collision kernels, including the variable hard/soft sphere models-necessary for simulating flows involving diffusive transport. In this work, the deterministic DGFS method, Bhatnagar-Gross-Krook (BGK), Ellipsoidal statistical BGK (ESBGK), and Shakhov kinetic models, and the widely used stochastic DSMC method, are utilized to assess the thermostress convection process in micro in-plane Knudsen radiometric actuator-a microscale compact low-power pressure sensor utilizing the Knudsen forces. The BGK model underpredicts the heat-flux, shear-stress, and flow speed; the S-model overpredicts; whereas, ESBGK comes close to the DSMC results. On the other hand, both the statistical/DSMC and deterministic/DGFS methods, segregated in perspectives, yet, yield inextricable results, bespeaking the ingenuity of Graeme Bird who laid down the foundation of practical rarefied gas dynamics for microsystems. Published under license by AIP Publishing.
机译：当流被充分稀薄，温度梯度，例如介于两个壁相隔几平均自由路径，诱导归因于在微尺度的thermostress对流效果的气体流的观察。整体thermostress对流过程的动力学是由波尔兹曼方程-一个积分描述的分子分布函数的演化方程支配六维相空间内，这模型在分子水平稀释气行为准确地描述的宽范围的流量的现象。途径解决全玻耳兹曼方程与一般的分子间的相互作用依靠两个方面：在自然界中一个随机经常下放给直接模拟蒙特卡洛（DSMC）方法和其他人凭借确定性。之间的确定性的方法中，间断Galerkin快速光谱（DGFS）方法是最近引入的用于解决全波尔兹曼方程与一般的碰撞内核，包括可变硬/软球模型-必要用于模拟流动涉及扩散传输。在这项工作中，确定性DGFS方法，纳加尔-格罗斯 - 克鲁克（BGK），椭球统计BGK（ESBGK），和Shakhov动力学模型，和广泛使用的随机DSMC方法，被用来评估在微IN-的thermostress对流过程平面辐射克努森致动器 - 一个利用克努森力微尺度紧凑低功率压力传感器。该模型BGK的underpredicts热通量，剪切应力和流动速度;在S-模型overpredicts;然而，ESBGK接近的DSMC结果。在另一方面，无论是统计/ DSMC和确定性/ DGFS方法，在隔离的观点，但是，产生无法摆脱的结果，bespeaking格雷姆·伯德谁放下实际稀薄气体动力学微系统的基础上匠心。通过AIP发布在许可证下发布。

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