Modified relaxation time Monte Carlo method for continuum-transition gas flows

Gas flows in the continuum-transition regime often occur in micro-electro-mechanical systems. The relaxation time Monte Carlo (RTMC) method was modified by using an ellipsoid statistical model and a multiple translational temperature model in the BGK model equation to simulate continuum-transition gas flows. The modified RTMC method uses a simplified form of the generalized relaxation time, which is related to the macro velocity and the local Knudsen number. The results for Couette flow and Poiseuille flow in microchannels predicted using the modified RTMC and the DSMC are in good agreement with the modified RTMC being much faster than the DSMC for continuum-transition gas flow simulations.     

A hybrid particle approach for continuum and rarefied flow simulation

A hybrid particle scheme is presented for the simulation of compressible gas flows involving both continuum regions and rarefied regions with strong translational nonequilibrium. The direct simulation Monte Carlo (DSMC) method is applied in rarefied regions, while remaining portions of the flowfield are simulated using a DSMC-based low diffusion particle method for inviscid flow simulation. The hybrid scheme is suitable for either steady state or unsteady flow problems, and can simulate gas mixtures comprising an arbitrary number of species. Numerical procedures are described for strongly coupled two-way information transfer between continuum and rarefied regions, and additional procedures are outlined for the determination of continuum breakdown. The hybrid scheme is evaluated through a comparison with DSMC simulation results for a Mach 6 flow of N₂ over a cylinder, and good overall agreement is observed. Large potential efficiency gains (over three orders of magnitude) are estimated for the hybrid algorithm relative to DSMC in a simple example involving a rarefied expansion flow through a small nozzle into a vacuum chamber.     

Atomistic hybrid DSMC/NEMD method for nonequilibrium multiscale simulations

A multiscale hybrid method for coupling the direct simulation Monte Carlo (DSMC) method to the nonequilibrium molecular dynamics (NEMD) method is introduced. The method addresses Knudsen layer type gas flows within a few mean free paths of an interface or about an object with dimensions of the order of a few mean free paths. It employs the NEMD method to resolve nanoscale phenomena closest to the interface along with coupled DSMC simulation of the remainder of the Knudsen layer. The hybrid DSMC/NEMD method is a particle based algorithm without a buffer zone. It incorporates a new, modified generalized soft sphere (MGSS) molecular collision model to improve the poor computational efficiency of the traditional generalized soft sphere GSS model and to achieve DSMC compatibility with Lennard-Jones NEMD molecular interactions. An equilibrium gas, a Fourier thermal flow, and an oscillatory Couette flow, are simulated to validate the method. The method shows good agreement with Maxwell–Boltzmann theory for the equilibrium system, Chapman–Enskog theory for Fourier flow, and pure DSMC simulations for oscillatory Couette flow. Speedup in CPU time of the hybrid solver is benchmarked against a pure NEMD solver baseline for different system sizes and solver domain partitions. Finally, the hybrid method is applied to investigate interaction of argon gas with solid surface molecules in a parametric study of the influence of wetting effects and solid molecular mass on energy transfer and thermal accommodation coefficients. It is determined that wetting effect strength and solid molecular mass have a significant impact on the energy transfer between gas and solid phases and thermal accommodation coefficient.     

含振动能激发Boltzmann模型方程气体动理论统一算法验证与分析

为模拟研究高温高马赫数下多原子气体内能激发对跨流域非平衡流动的影响,将转动能、振动能分别作为气体分子速度分布函数的自变量,把转动能和振动能处理为连续分布的能量模式,将Boltzmann方程的碰撞项分解成弹性碰撞项和非弹性碰撞项,同时将非弹性碰撞按一定松弛速率分解为平动-转动能松弛过程和平动-转动-振动能松弛过程,构造了一类考虑振动能激发的Boltzmann模型方程,并证明了其守恒性和H定理.基于内部能量变量对分布函数无穷积分,引入三个约化速度分布函数,得到一组考虑振动能激发的约化速度分布函数控制方程组,使用离散速度坐标法,基于LU-SGS隐式格式和有限体积法求解离散速度分布函数,建立含振动能激发的气体动理论统一算法.通过开展高稀薄流到连续流圆柱绕流问题统一算法与直接模拟蒙特卡罗法模拟结果对比分析,特别是过渡流区平动、转动、振动非平衡效应对绕流流场与物面力热特性的影响机制,证实了所建立的含振动能激发的Boltzmann模型方程及气体动理论统一算法的准确可靠性.     

Direct Monte Carlo simulation of high-temperature chemical reactions in air

A novel approach to modeling high-temperature nonequilibrium dissociation in air at a level of molecular collisions is proposed. Information on the energy dependence of the specific reaction cross sections, which is necessary for such modeling, is determined numerically from available macroscopic information on the dependence of the reaction rate constant on translational and vibrational temperatures. The results of Direct Simulation Monte Carlo (DSMC) computations show that the proposed model yields a correct reaction rate in vibrational-translational nonequilibrium. The use of the new model in DSMC computations of high-altitude aerothermodynamics results in obtaining a noticeably different flow structure and a higher heat flux, as compared to that predicted by standard DSMC models (such as the total collision energy model).     

热化学非平衡流动的DSMC-ME算法研究

将最大熵方法(Maximum Entropy,缩写为ME)引入Direct Simulation Monte Carlo(DSMC)模拟热化学非平衡流动过程中,构造一个计算非平衡条件下化学反应几率和反应碰撞能量分配的最大熵模型.在DSMC-ME的模拟过程中,对分子间的非反应碰撞,采用传统的Larsen-Borgnakke唯象论模型模拟碰撞分子内能的激发与松弛;对分子间反应碰撞,采用最大熵模型模拟分子间的化学反应和能量交换.通过模拟高空高超声速绕圆柱和低密度高焓绕钝头锥体流动,并与DSMC算法和HEG实验结果比较,论证了DSMC-ME算法的有效性.     

微喷管流的连续介质模型及其适用性

基于无滑移和有滑移的连续介质模型,对微喷管内的超声速冷态气体流场进行了二维和三维数值模拟,利用DSMC方法验证微喷管流中的连续介质模型,并重点分析微喷管流的低雷诺数效应、三维端面效应及其推进性能.研究表明,局部流场的模拟对模型和边界条件的要求要高于推进性能的估算,在努森数小于0.03时,可以使用无滑移的N-S方程预测推进性能;雷诺数是表征低雷诺数效应和推进性能的特征参数,提高工作压力可以改善微喷管的粘性损失和推进性能;在雷诺数大于1000时,若蚀刻深度和喉部宽度的比值超过13,微喷管具备很好的二维特性.     

跨流域高超声速绕流环境Boltzmann模型方程统一算法研究

如何准确可靠地模拟从外层空间高稀薄流到近地面连续流的航天器高超声速绕流环境与复杂流动变化机理是流体物理的前沿基础科学问题. 基于对Boltzmann方程碰撞积分的物理分析与可计算建模, 确立了可描述自由分子流到连续流区各流域不同马赫数复杂流动输运现象统一的Boltzmann模型速度分布函数方程, 发展了适于高、低不同马赫数绕流问题的离散速度坐标法和直接求解分子速度分布函数演化更新的气体动理论数值格式, 建立了模拟复杂飞行器跨流域高超声速飞行热环境绕流问题的气体动理论统一算法. 对稀薄流到连续流不同Knudsen数0.002 ≤Kn_∞ ≤1.618、不同马赫数下可重复使用卫星体再入过程(110–70 km)中高超声速绕流问题进行算法验证分析, 计算结果与典型文献的Monte Carlo直接模拟值及相关理论分析符合得较好. 研究揭示了飞行器跨流域不同高度高超声速复杂流动机理、绕流现象与气动力/热变化规律, 提出了一个通过数值求解介观Boltzmann模型方程, 可靠模拟高稀薄自由分子流到连续流跨流域高超声速气动力/热绕流特性统一算法.     

A unified gas-kinetic scheme for continuum and rarefied flows

With discretized particle velocity space, a multiscale unified gas-kinetic scheme for entire Knudsen number flows is constructed based on the BGK model. The current scheme couples closely the update of macroscopic conservative variables with the update of microscopic gas distribution function within a time step. In comparison with many existing kinetic schemes for the Boltzmann equation, the current method has no difficulty to get accurate Navier–Stokes (NS) solutions in the continuum flow regime with a time step being much larger than the particle collision time. At the same time, the rarefied flow solution, even in the free molecule limit, can be captured accurately. The unified scheme is an extension of the gas-kinetic BGK-NS scheme from the continuum flow to the rarefied regime with the discretization of particle velocity space. The success of the method is due to the un-splitting treatment of the particle transport and collision in the evaluation of local solution of the gas distribution function. For these methods which use operator splitting technique to solve the transport and collision separately, it is usually required that the time step is less than the particle collision time. This constraint basically makes these methods useless in the continuum flow regime, especially in the high Reynolds number flow simulations. Theoretically, once the physical process of particle transport and collision is modeled statistically by the kinetic Boltzmann equation, the transport and collision become continuous operators in space and time, and their numerical discretization should be done consistently. Due to its multiscale nature of the unified scheme, in the update of macroscopic flow variables, the corresponding heat flux can be modified according to any realistic Prandtl number. Subsequently, this modification effects the equilibrium state in the next time level and the update of microscopic distribution function. Therefore, instead of modifying the collision term of the BGK model, such as ES-BGK and BGK–Shakhov, the unified scheme can achieve the same goal on the numerical level directly. Many numerical tests will be used to validate the unified method.     

微通道内气体流动的DSMC方法

基于压力边界条件开展了微尺度低速流动DSMC方法的研究, 定义了两个无量纲参数作为微尺度DSMC方法下网格尺寸与时间步长的约束条件, 通过微尺度Poiseuille流进行了方法的验证与比较, 获得了网格尺寸与时间步长的一般原则。在此基础上, 对变截面的单孔和双孔模型的微通道气体流动进行DSMC模拟, 结果表明, 通道几何形状对微尺度气体流动具有显著影响, 孔口后由于通道收缩, 产生压降, 导致气流加速, 并在孔口下游拐角处发生分离; 双孔口模型的流动结构与单孔口模型相似, 且在相同压差情况下, 经双孔口后的气体流速低于经单孔口后的气体流速; 随着入口压力的增加, 经过孔口压缩后的速度越大, 分离区尺寸也越大。      

稀薄气体流动非线性耦合本构关系研究进展

临近空间高超声速飞行器流场蕴含着复杂的非线性流动机理与丰富的热化学非平衡流动现象, 基于Newton摩擦定律和Fourier热传导定律的Navier-Stokes(N-S)方程不足以描述高超声速飞行器从连续流到稀薄流的多尺度非平衡现象。非线性耦合本构关系(nonlinear coupled constitutive relations, NCCR)作为一种全新的本构方程体系, 在严格满足热力学熵条件的基础上, 巧妙地构建了应力与热流的非线性表达形式。然而, NCCR方程的强非线性耦合特性是求解过程的一大难题。为了克服这一技术瓶颈, 提出了混合迭代算法, 为实现NCCR方程的高效稳定求解提供了坚实的理论基础。在该理论研究的基础上, 考虑到原始NCCR方程对热通量演化方程的简化处理, 降低了方程的计算精度, 提出了改进的NCCR+方程。该方程在强激波压缩区域和膨胀区域表现出比传统NCCR方程更高的计算精度与更强的非平衡流动模拟能力。同时, 为了解决临近空间高超声速空气动力学的多尺度与多物理效应耦合难题, 提出了NCCR与转动非平衡的耦合计算模型, 拓展了NCCR方程在双原子气体中的模拟能力。为了揭示稀薄气体效应与真实气体效应的耦合作用机理, 进一步建立了NCCR与热化学反应的耦合计算方法。大量研究结果表明, 考虑多物理效应的NCCR方程在低Kn下能够恢复到与N-S方程一致的解。随着Kn的增加, 流场的非平衡程度逐渐增强, 其结果与N-S方程差异显著, 而与DSMC方法计算结果和实验数据具有更好的一致性。      

Numerical Simulations of Unsteady Flows from Rarefied Transition to Continuum Using Gas-Kinetic Unified Algorithm

Numerical simulations of unsteady gas flows are studied on the basis of Gas-Kinetic Unified Algorithm (GKUA) from rarefied transition to continuum flow regimes. Several typical examples are adopted. An unsteady flow solver is developed by solving the Boltzmann model equations, including the Shakhov model and the Rykov model etc. The Rykov kinetic equation involving the effect of rotational energy can be transformed into two kinetic governing equations with inelastic and elastic collisions by integrating the molecular velocity distribution function with the weight factor on the energy of rotational motion. Then, the reduced velocity distribution functions are devised to further simplify the governing equation for one- and two-dimensional flows. The simultaneous equations are numerically solved by the discrete velocity ordinate (DVO) method in velocity space and the finite-difference schemes in physical space. The time-explicit operator-splitting scheme is constructed, and numerical stability conditions to ascertain the time step are discussed. As the application of the newly developed GKUA, several unsteady varying processes of one- and two-dimensional flows with different Knudsen number are simulated, and the unsteady transport phenomena and rarefied effects are revealed and analyzed. It is validated that the GKUA solver is competent for simulations of unsteady gas dynamics covering various flow regimes.     

Two-dimensional direct simulation Monte Carlo (DSMC) of reactiveneutral and ion flow in a high density plasma reactor

We present a two dimensional direct simulation Monte Carlo (DSMC) study of the rarefied reactive flow of neutrals and ions in a low pressure inductively coupled plasma reactor. The spatially-dependent rate coefficients of electron impact reactions and the electrostatic field were obtained from a fluid plasma simulation. Neutral and ion etching of polysilicon with chlorine gas was studied with emphasis on the reaction uniformity along the wafer. Substantial gradients in total gas density were observed across the reactor invalidating the commonly made assumption of constant gas density. The flow was nonequilibrium with differences in the species translational temperatures, and 100 K temperature jumps near the walls. When etching was limited by ions the etch rate was highest at the wafer center. When etching was limited by neutrals, the etch rate was highest at the wafer edge. In such case, the etch uniformity changed significantly depending on the reactivity of the ring surrounding the wafer. The ion angular distribution was several degrees off normal and it was different at the wafer edge compared to the rest of the wafer     

High-order shock-fitting methods for direct numerical simulation of hypersonic flow with chemical and thermal nonequilibrium

In recent years, much progress has been made in the direct numerical simulation of laminar-turbulent transition of hypersonic boundary layer flow. However, most of the efforts at the direct numerical simulation of transition previously have been focused on the idealized perfect gas flow or “cold” hypersonic flows. For practical problems in hypersonic flows, high-temperature effects of thermal and chemical nonequilibrium are important and cannot be modeled by a perfect gas model. Therefore, it is necessary to include the real gas models in the numerical simulation of hypersonic boundary layer transition in order to accurately predict flow field parameters. Currently most numerical methods for hypersonic flow with thermo-chemical nonequilibrium are based on shock-capturing approach at relatively low order of accuracy. Shock capturing schemes reduce to first-order accuracy near the shock and have been shown to produce spurious oscillations behind curved strong shocks. There is a need to develop new methods capable of simulating nonequilibrium hypersonic flow fields with uniformly high-order accuracy and avoid spurious oscillations near the shock. This paper presents a fifth-order shock-fitting method for numerical simulation of thermal and chemical nonequilibrium in hypersonic flows. The method is developed based on the state-of-the-art real gas models for thermo-chemical nonequilibrium and transport phenomena. Shock-fitting approach is used because it has the advantage of capturing the entire flow field with high-order accuracy and without any oscillations near the shock. The new method has been tested and validated for a number of test cases over a wide span of free stream conditions. The developed method is applied for the study of receptivity of free stream acoustic waves over a blunt cone for hypervelocity flow. Some preliminary results of the computations of the high order shock fitting method for the above mentioned study have also been presented.     

On the origin of nonequilibrium radiation from iodine molecules at the shock wave front

The direct simulation Monte Carlo (DSMC) method is used for modeling the problem on the shock wave front in the 0.7%I₂-99.3%He mixture for a shock wave Mach number of 4.85. The choice of this system is due to the fact that intense radiation peaks have been observed experimentally precisely in such systems and it has been convincingly proven that this effect is induced by high-energy collisions between I₂ molecules. The results of simulation provide additional sound arguments in favor of the conclusion that the translational nonequilibrium state at the shock wave front in a light gas with a small admixture of heavy nonreacting molecules may cause the experimentally observed nonequilibrium radiation peaks.     

信息保存方法在微尺度变温流场中的应用研究

在信息保存法(IP)方法的基础上，提出了一个简单易行的温度模型，该模型可以有效模拟计算有温度变化的流动.此外研究发现，在用IP方法模拟计算的流场局部密度变化很大时，如果采用质量守恒方程的二阶中心差分格式更新信息密度时会使计算发散，因此建议采用一阶迎风格式更新信息密度. 关键词： IP方法 低速流动 微尺度 变温流动     

矩形微槽道气体流动的速度分布

矩形微槽道的各个流向截面可以局部近似为平面Poiseuille流动,应用信息保存(IP)方法和直接模拟Monte Carlo(DSMC)方法计算了从连续介质区到自由分子流区的平面Poiseuille流动,利用其结果对Beskok-Karniadadis公式和质量流率动理论因子进行修正和重新拟合,给出在整个稀薄气体流动领域都适用的微槽道气体流动速度分布.     

Particle-in-cell plus direct simulation Monte Carlo (PIC-DSMC)approach for self-consistent plasma-gas simulations

The particle-in-cell (PIC) and direct simulation Monte Carlo (DSMC) approaches have been combined into a PIC-DSMC model for self-consistent simulations of low-temperature collisional plasmas and the background gas. This novel approach is based on the weighting collision simulation scheme allowing for disparate number densities and time scales of different species. The applicability of the developed algorithm is illustrated by simulations of one-dimensional direct current and two-dimensional magnetron sputtering discharges in argon. An appreciable effect of the energetic discharge species on the density, temperature, and flow field of the background gas shows the importance of the coupled plasma-gas simulation for such technologies as sputtering, dry etching, plasma enhanced vapor deposition, etc     

Variance-reduced DSMC for binary gas flows as defined by the McCormack kinetic model

A variance-reduced direct simulation Monte Carlo method is presented for binary gas flows as defined by the McCormack kinetic model. Two types of flow configuration, namely pressure driven flow between two parallel plates and through rectangular channels, are considered. The kinetic model is transformed into one- and two-dimensional projected formalisms. Both cases are modeled by the variance-reduced DSMC. Simulations are performed to compare the method to the analytical discrete ordinate and discrete velocity methods. For both flow configurations, very good agreement is obtained between the results of different approaches. The results of the approach are also compared to the prediction of the moment method and the results of hard-sphere gases. The model can be beneficial for computing slow rarefied gaseous mixture flows, especially in nano- and microscale devices.     

非定常粘性空化流动模型及其数值计算

基于气液两相当地均相介质模型,本文给出了一种模拟非定常粘性空化流动的计算模型。认为空化绕流流场中流动介质是一种当地均匀的气液混相物。控制方程采用了应用两相流模型的N-S方程。基于液相和气相的状态方程推导了混合介质密度的表达式。为了保证数值计算的稳定性,控制方程的数值求解采用了TVD-MacCormack格式。为了评价计算模型的可靠性,分别计算了绕台阶和管道水锤的空化流动,所得结果是合理的,说明该方法可以用于空化流动的数值计算。