Approximation of joint PDFs by discrete distributions generated with Monte Carlo methods

A new method for the approximation of multivariate scalar probability density functions (PDFs) in turbulent reacting flow by means of a joint presumed discrete distribution (jPDD) is presented. The jPDDs can be generated with specified mean values and variances as well as covariances. Correlations between variables – e.g. fluctuating mixture fractions and/or reaction progress – can thereby be taken into account. In this way the new approach overcomes an important limitation of ordinary presumed PDF methods, where statistical independence between the variables is often assumed. Different methods are presented to generate discrete distributions, based either on biased random number generators or on mixing models familiar from PDF transport models.

The new approach is extensively validated on a turbulent flow configuration with simultaneous mixing and reaction. Large eddy simulation data as well as results from a transported PDF model are used for the validation of the jPDD approach. The comparison shows that in particular distributions generated with mixing models are able to predict mean reaction rates accurately. For the configuration considered, the neglect of correlations results in significant underestimation of reaction rates. Moreover it is found that higher statistical moments (e.g. the skewness) can influence reaction rates. The consequences for the generation of jPDDs are discussed.

In summary, the new jPDD model has the potential to be significantly more accurate than established presumed PDF methods, because correlations between fluctuating variables can be taken into account. At the same time, the new approach is nearly as efficient as standard presumed PDF formulations, since mean rates are computed in a pre-processing step and stored in look-up tables as a function of the first and second moments of the relevant variables.     

Mode-stirred reverberation chambers: A paradigm for spatio-temporal complexity in dynamic electromagnetic environments

We investigate probability distributions in dynamic multi-mode electromagnetic cavities, commonly referred to as mode-stirred reverberation chambers. We show that Bessel K$K$ and Bessel I$I$ distributions play a prominent role when a large but finite number of excited modes, loss of energy (through aperture leakage or dissipation), or nonstationary transient fields are involved. With the aim at reducing the number of simultaneously excited cavity modes as much as possible while maintaining a well-characterizable quasi-random field, measurement results indicate that single-mode stirring is feasible at certain frequencies well below the usual ‘lowest usable frequency’ of the cavity. Distributions for nonstationary fields are shown to allow for improved estimation of the maximum-to-mean ratio of the received power during stepwise rotation of the mode stirrer.     

Information Length Analysis of Linear Autonomous Stochastic Processes

When studying the behaviour of complex dynamical systems, a statistical formulation can provide useful insights. In particular, information geometry is a promising tool for this purpose. In this paper, we investigate the information length for n-dimensional linear autonomous stochastic processes, providing a basic theoretical framework that can be applied to a large set of problems in engineering and physics. A specific application is made to a harmonically bound particle system with the natural oscillation frequency ω, subject to a damping γ and a Gaussian white-noise. We explore how the information length depends on ω and γ, elucidating the role of critical damping γ=2ω in information geometry. Furthermore, in the long time limit, we show that the information length reflects the linear geometry associated with the Gaussian statistics in a linear stochastic process.     

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.     

Monitoring the Structure Evolution of Titanium Oxide Photocatalysts: From the Molecular Form via the Amorphous State to the Crystalline Phase

Amorphous Ti_xO_y with high surface area has attracted significant interest as photocatalyst with higher activity in ultraviolet (UV) light-induced water splitting applications compared to commercial nanocrystalline TiO₂. Under photocatalytic operation conditions, the structure of the molecular titanium alkoxide precursor rearranges upon hydrolysis and leads to higher connectivity of the structure-building units. Structurally ordered domains with sizes smaller than 7 Å form larger aggregates. The experimental scattering data can be explained best with a structure model consisting of an anatase-like core and a distorted shell. Upon exposure to UV light, the white Ti_xO_y suspension turns dark corresponding to the reduction of Ti⁴⁺ to Ti³⁺ as confirmed by electron energy loss spectroscopy (EELS). Heat-induced crystallisation was followed by in situ temperature-dependent total scattering experiments. First, ordering in the Ti−O environment takes place upon to 350 °C. Above this temperature, the distorted anatase core starts to grow but the structure obtained at 400 °C is still not fully ordered.     

A spray flamelet/progress variable approach combined with a transported joint PDF model for turbulent spray flames

A spray flamelet/progress variable approach is developed for use in spray combustion with partly pre-vaporised liquid fuel, where a laminar spray flamelet library accounts for evaporation within the laminar flame structures. For this purpose, the standard spray flamelet formulation for pure evaporating liquid fuel and oxidiser is extended by a chemical reaction progress variable in both the turbulent spray flame model and the laminar spray flame structures, in order to account for the effect of pre-vaporised liquid fuel for instance through use of a pilot flame. This new approach is combined with a transported joint probability density function (PDF) method for the simulation of a turbulent piloted ethanol/air spray flame, and the extension requires the formulation of a joint three-variate PDF depending on the gas phase mixture fraction, the chemical reaction progress variable, and gas enthalpy. The molecular mixing is modelled with the extended interaction-by-exchange-with-the-mean (IEM) model, where source terms account for spray evaporation and heat exchange due to evaporation as well as the chemical reaction rate for the chemical reaction progress variable. This is the first formulation using a spray flamelet model considering both evaporation and partly pre-vaporised liquid fuel within the laminar spray flamelets. Results with this new formulation show good agreement with the experimental data provided by A.R. Masri, Sydney, Australia. The analysis of the Lagrangian statistics of the gas temperature and the OH mass fraction indicates that partially premixed combustion prevails near the nozzle exit of the spray, whereas further downstream, the non-premixed flame is promoted towards the inner rich-side of the spray jet since the pilot flame heats up the premixed inner spray zone. In summary, the simulation with the new formulation considering the reaction progress variable shows good performance, greatly improving the standard formulation, and it provides new insight into the local structure of this complex spray flame.     

电纸书PDF阅读器的设计与实现

设计了电纸书平台上的PDF阅读器,探讨建立在嵌入式Linux上的电纸书软件体系,并对PDF的文件结构及文字信息读取流程进行分析,最终实现了以Qt/Embedded设计的PDF阅读器.     

基于大涡模拟的湍流非预混燃烧混合分数概率密度函数

混合分数概率密度函数(probability density function,PDF)反映了湍流对燃料和氧化剂混合过程的影响,在湍流非预混燃烧的理论研究和数值模拟中有非常重要的作用。该文基于大涡模拟(large eddy simulation,LES)对非预混火焰中的混合分数PDF进行了研究。利用LES预测的SandiaFlame D的速度和温度的均值和均方根分布与实验结果符合很好,瞬态温度场显示了合理的湍流火焰形态。混合分数PDF在反应区为钟形分布,在贫燃侧和富燃侧为钟形分布或单调形分布,取决于当地流场状态。对简化PDF模型的研究表明:β函数模型对钟形PDF和单调形PDF的预测效果都很好;截尾Gauss函数模型只能较好地预测钟形分布PDF;多点δ函数模型的预测能力与截尾Gauss函数模型的预测能力类似;双δ函数模型的预测结果偏差较大。     

PDF417条形码在航材管理中应用的可行性研究

为了实现航材信息的自动识别录入和准确监控，将PDF417条形码技术引入到航材管理领域。通过分析和论证，认为将该技术应用于航材管理领域是可行的，而且可以极大地提高航材管理的工作效率和准确性。     

PDF对Hg2+、Pb2+、Cd2+的吸附机理及动力学研究

利用马铃薯提取淀粉后的废弃物——马铃薯渣制成的新型纤维(PDF)对重金属离子Hg^2 、Pb^2 、Cd^2 单组分水溶液进行吸附研究，对吸附模型、吸附时间、不同吸附剂用量、pH值、温度等给予表征。结果表明：PDF对Hg^2 、Pb^2 、Cd^2 的吸附是化学与物理吸附的综合结果。物理吸附中，对Hg^2 、Pb^2 的吸附既符合Langmuir吸附模式，又符合Freundlich吸附模式，而对Cd^2 的吸附仅符合Langmuir吸附模式。