U-RANS／PDF方法计算钝体后漩涡脱落

本研究发展了U-RANS/PDF混合算法研究湍流和化学反应相互作用对燃烧稳定性的影响,采用有限体积和Monte Carlo相结合的方法在非结构网格中求解相容的U-RANS方程和脉动速度-湍流频率-标量的联合PDF方程.本文对钝体火焰驻定器后冷态流场进行了计算,结果表明此混合算法能够捕捉流场中非稳态的漩涡脱落现象.着重研究了湍流频率模型系数的改变对漩涡脱落频率以及拟序结构在动量输运中的作用的影响.     

轴对称钝体后湍流扩散燃烧的PDF模拟

在无结构网格中，对轴对称钝体驻定的湍流扩散火焰进行数值模拟．采用有限容积(FV)／Monte Carlo(MC)混合算法求解湍流燃烧问题的混合算法．Monte Carlo法求解脉动速度一标量．频率的联合概率密度函数方程，有限容积法求解平均质量、动量和能量方程．求解的两组方程是相容的，合理的耦合方式可以减少统计偏差，计算精度和效率显著优于单独的颗粒方法．文中对化学反应采用层流火焰面模型，并将数值计算结果与实验结果作了比较和分析．     

两相壁面射流PDF方程有限分析方法及数值模拟

提出求解位置-速度相空间中高维两相流PDF(probability density function)方程的有限分析方法,将位置-速度相空间颗粒PDF方程约化到速度空间,并解析求解,颗粒的位置PDF用轨道方法求解.对壁面射流两相流动进行数值模拟,并与颗粒雷诺应力轨道方法进行比较计算,结果优于颗粒雷诺应力轨道方法.     

变分累积展开方法中确定相变点的新方法

在计算有限温度SU(2)格点规范模型Polyakov线的过程中,考虑到变分累积展开法中有限距离相互作用效应与Monte Carlo中的有限体积效应的相似性,采用了新的方法来确定相变点.与已有的方法以及Monte Carlo模拟给出的结果比较,新方法给出的结果更接近Monte Carlo结果.     

钝体驻定湍流扩散火焰的数值研究——燃烧模型比较

分别采用标量联合的概率密度函数方法、稳态火焰面模型、Euler非稳态火焰面模型和基于有限体积/Monte Carlo混合算法的完备PDF模型对钝体驻定的Sydney湍流扩散火焰HM1进行数值模拟,以比较不同燃烧模型的性能,并比较标量联合的概率密度函数方法和Euler非稳态火焰面模型对氮氧化物排放预测的差异.计算结果和实验数据的比较表明,采用概率密度函数方法计算化学反应可以得到更好的结果但计算量较大,而用火焰面模型求解计算量较小,在接近完全燃烧的情形下,其计算结果比较合理.     

基于Monte Carlo的热脉冲法数据分析

热脉冲法是测量聚合物介质薄膜空间电荷分布的有效方法之一, 其数据的分析涉及第一类Fredholm积分方程, 只能采用合适的数值计算方法进行求解, 而Monte Carlo法是近年来提出的数值求解该方程的方法之一. 本文尝试使用Monte Carlo法在频域内实现热脉冲数据的分析, 通过一系列模拟计算讨论Monte Carlo法的分析效果. 计算结果表明: Monte Carlo法可实现对热脉冲法实验数据的有效分析, 提取被测薄膜内的电场分布, 而且计算的电场分布在整个样品厚度上都与真实分布较好地符合, 可有效地弥补尺度变换法只在样品表面附近获得较高准确度的缺陷. 该方法的局限性在于计算结果存在一定的振荡, 且在噪声和数据误差的影响下, 其准确性很大程度上依赖于奇异值分解过程中容差的选择, 在应用的方便程度方面还有待进一步提升.     

用PDF方法求解平均温度梯度为常数的均匀剪切湍流

本文旨在用求解速度、温度和耗散率联合几率密度函数输运方程的方法研究平均温度梯度为常数的均匀剪切湍流的性质,假定耗散率满足对数正态分布,分别用扩散过程、Langevin模型和混合模型模拟脉动压力和分子输运对耗散率、速度和温度变化的影响。用Monte Carlo求解方法得到了与实验数据基本一致的结果。     

描述离散系统动力学演变的Monte Carlo方法分析

通用动力学方程通过描述离散系统中颗粒尺度分布的演变过程来量化颗粒动力学演变过程,而Monte Carlo(MC)算法是求解通用动力学方程的重要方法.目前几种主流的MC算法为Liffman的直接模拟Monte Carlo算法(DSMC)、阶梯式常体积法、常数目法和多重Monte Carlo(MMC)算法.利用这些MC算法描述理想的纯凝并工况和纯破碎工况,发现:由于避免了多个动力学事件之间的解耦过程,基于事件驱动的MC算法比基于时间驱动的MC算法具有更高的计算精度和更低的计算代价;由于尽量减少对整体系统的扰动,阶梯式恢复模拟颗粒数目的MC算法比连续式恢复模拟颗粒数目的MC算法具有更高的精度;由于始终保持计算区域体积,多重Monte Carlo算法具有更友好的扩展性.     

浅海相干声场不确定性研究

提出一种采用随机响应面法求解浅海中含不确定参数波动方程的方法.将海洋环境不确定参数表示为标准随机变量,利用Hermite多项展开式表示相干声场的随机响应,用概率配点法求解随机多项式系数后,获得相干声场的近似表达式.通过与Monte Carlo法、声场位移法比较,表明本文方法计算精度和效率较高.     

两相湍流色噪声扩维法PDF模型及数值模拟

由颗粒运动的朗之万方程出发,对流体脉动速度采用扩维方法,得到两个不同层次的PDF输运方程.通过对颗粒运动方程求解和高斯分布假设,解决PDF方程的封闭问题,获得颗粒二阶矩模型,然后将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,对比分析数值结果与实验结果.     

The probabilistic solution of stochastic oscillators with even nonlinearity under poisson excitation

The probabilistic solutions of nonlinear stochastic oscillators with even nonlinearity driven by Poisson white noise are investigated in this paper. The stationary probability density function (PDF) of the oscillator responses governed by the reduced Fokker-Planck-Kolmogorov equation is obtained with exponentialpolynomial closure (EPC) method. Different types of nonlinear oscillators are considered. Monte Carlo simulation is conducted to examine the effectiveness and accuracy of the EPC method in this case. It is found that the PDF solutions obtained with EPC agree well with those obtained with Monte Carlo simulation, especially in the tail regions of the PDFs of oscillator responses. Numerical analysis shows that the mean of displacement is nonzero and the PDF of displacement is nonsymmetric about its mean when there is even nonlinearity in displacement in the oscillator. Numerical analysis further shows that the mean of velocity always equals zero and the PDF of velocity is symmetrically distributed about its mean.     

Filtered density function simulator on unstructured meshes

A new computational filtered density function (FDF) methodology is developed for large eddy simulation (LES) of turbulent reacting flows. This methodology is based on a Lagrangian Monte Carlo (MC) FDF solver constructed on a domain portrayed by an unstructured mesh. The base filtered transport equations on this mesh are solved by a finite-volume (FV) method. The consistency of the hybrid FV-MC solver and the realizability of the simulated results are demonstrated via LES of a temporally developing mixing layer. The overall performance of the model is appraised by comparison with direct numerical simulation (DNS) data. The algorithmic implementation in the commercial software ANSYS-FLUENT facilitates future FDF-LES of turbulent combustion in complex configurations.     

A LES/PDF simulator on block-structured meshes

A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41–63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490–5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896–2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912–2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.     

Comparisons of Lagrangian and Eulerian PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions

Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, Lagrangian particle PDF methods are computationally intensive and are not readily integrated into conventional Eulerian computational fluid dynamics (CFD) codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane–air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method, while MEPDF is the most computationally efficient of the three methods. These and other findings are discussed in detail.     

蒙特卡罗方法在解微分方程边值问题中的应用

介绍了蒙特卡罗方法的基本原理以及随机数的产生方法。基于蒙特卡罗方法的思想,结合有限差分方法,建立了求解微分方程边值问题的随机概率模型,并以第一类边界条件的拉普拉斯方程和一个给定初值及边界条件的非稳态热传导方程为数值算例,研究了蒙特卡罗方法在求解微分方程边值问题中的应用。结果表明:利用蒙特卡罗方法,不仅可以有效解决给定边界条件的微分方程,对于给定初值条件的微分方程,也可以从时域有限差分方程出发,采用蒙特卡罗方法进行求解。数值模拟和对误差的理论分析均表明,增加蒙特卡罗试验中的模拟粒子点数,可以提高计算结果的精度。     

Rarefied Flow Computations Using Nonlinear Model Boltzmann Equations

High resolution finite difference schemes for solving the nonlinear model Boltzmann equations are presented for the computations of rarefied gas flows. The discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model Boltzmann equation in phase space to a set of hyperbolic conservation laws with source terms in physical space. Then a high order essentially nonoscillatory method due to Harten et al. (J. Comput. Phys. 71, 231, 1987) is adapted and extended to solve them. Explicit methods using operator splitting and implicit methods using the lower-upper factorization are described to treat multidimensional problems. The methods are tested for both steady and unsteady rarefied gas flows to illustrate its potential use. The computed results using model Boltzmann equations are found to compare well both with those using the direct simulation Monte Carlo results in the transitional regime flows and those with the continuum Navier-Stokes calculations in near continuum regime flows.