采用双混合分数/概率密度函数方法模拟混煤燃烧

混煤燃烧存在复杂的相互影响,将混煤当成单一煤种并采用单混合分数/概率密度函数(probability density function,PDF)方法计算,意味着忽略了煤种之间的影响,结果会产生很大偏差。而双混合分数/PDF方法可以分别定义各单煤性质并跟踪各单煤的燃烧过程,能够体现煤种之间燃烧特性的影响。利用单、双混合分数/PDF方法对同1台300 MW四角切圆锅炉进行模拟研究,并与实测数据进行对比,结果表明:双混合分数/PDF方法模拟的结果更符合混煤在炉内实际的燃烧情况。同时采用双混合分数/PDF方法模拟某一混煤燃烧过程,得到燃烧煤粉锅炉的流动,温度和烟气分布等特性。

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。

塔河七区溶洞储集体发育特征及物性建模

为解决塔河七区T607单元井资料较少、溶洞储集体内部物性参数分布规律不明的问题,提出了以充填模式为指导的概率函数约束建模方法。在溶洞储集体识别的基础上,分析其充填物特征,总结充填模式,并以此为指导构建概率函数,从而约束孔隙度建模过程。研究结果表明,T607单元共发育地下河型溶洞及孤立型溶洞两类储集体,前者在平面上延伸较长,而后者则在垂向上分布较广;地下河型溶洞主要发育搬运型砾岩、搬运型砂岩等充填物,孔隙度曲线垂向呈现"叠置漏斗型",孤立型溶洞主要发育混杂角砾岩充填物,孔隙度曲线垂向上呈现粗略"箱型";结合建模结果,认为控制洞穴储集体的关键参数为其充填特征及规模。

Spectrum Allocation for Cognitive Radio Networks with Non-Deterministic Bandwidth of Spectrum Hole

The spectrum allocation for cognitive radio networks(CRNs) has received considerable studies under the assumption that the bandwidth of spectrum holes is static. However, in practice, the bandwidth of spectrum holes is time-varied due to primary user/secondary user(PU/SU) activity and mobility, which result in non-determinacy. This paper studies the spectrum allocation for CRNs with non-deterministic bandwidth of spectrum holes. We present a novel probability density function(PDF) through order statistics as well as its simplified form to describe the statistical properties of spectrum holes, with which a statistical spectrum allocation model based on stochastic multiple knapsack problem(MKP) is formulated for spectrum allocation with non-deterministic bandwidth of spectrum holes. To reduce the computational complexity, we transform this stochastic programming problem into a constant MKP through exploiting the properties of cumulative distribution function(CDF), which can be solved via MTHG algorithm by using auxiliary variables. Simulation results illustrate that the proposed statistical spectrum allocation algorithm can achieve better performance compared with the existing algorithms when the bandwidth of spectrum holes is time-varied.

A New Statistical Tool： Scalar Score Function

The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous probability distribution and which is simple. Its simplicity makes it possible to introduce new relevant numerical characteristics of continuous distributions. The t-mean and score variance are descriptions of distributions without the drawbacks of the mean and variance, which may not exist even in cases of regular distributions. Their sample counterparts appear to be alternative descriptions of the observed data. The scalar score itself appears to be a new mathematical tool, which could be used in solving traditional statistical problems for models far from the normal one, skewed and heavy-tailed.

Deduction and Validation of an Eulerian-Eulerian Model for Turbulent Dilute Two-Phase Flows by Means of the Phase Indicator Function-Disperse Elements Probability Density Function

A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced. An extension of the standard k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.

Fatigue reliability for LNG carrier

The procedure of reliability-based fatigue analysis of liquefied natural gas(LNG) carrier of membrane type under wave loads is presented. The stress responses of the hotspots in regular waves with different wave heading angles and wave lengths are evaluated by global ship finite element method(FEM) . Based on the probabilistic distribution function of hotspots' short-term stress-range using spectral-based analysis,Weibull distribution is adopted and discussed for fitting the long-term probabilistic distribution of stress-range. Based on linear cumulative damage theory,fatigue damage is characterized by an S-N relationship,and limit state function is established. Structural fatigue damage behavior of several typical hotspots of LNG middle ship section is clarified and reliability analysis is performed. It is believed that the presented results and conclusions can be of use in calibration for practical design and initial fatigue safety evaluation for membrane type LNG carrier.

Probability analysis of contact forces in quasi-solid-liquid phase transition of granular shear flow

The quasi-solid-liquid phase transition exists widely in different fields,and attracts more attention due to its instinctive mechanism.The structure of force chains is an important factor to describe the phase transition properties.In this study,the discrete element model(DEM) is adopted to simulate a simple granular shear flow with period boundary condition on micro scale.The quasi-solid-liquid phase transition is obtained under various volume fractions and shear rates.Based on the DEM results,the probability distribution functions of the inter-particle contact force are obtained in different shear flow phases.The normal,tangential and total contact forces have the same distributions.The distribution can be fitted as the exponential function for the liquid-like phase,and as the Weibull function for the solid-like phase.To describe the progressive evolution of the force distribution in phase transition,we use the Weibull function and Corwin-Ngan function,respectively.Both of them can determine the probability distributions in different phases and the Weibull function shows more reasonable results.Finally,the force distributions are discussed to explain the characteristics of the force chain in the phase transition of granular shear flow.The distribution of the contact force is an indicator to determine the flow phase of granular materials.With the discussions on the statistical properties of the force chain,the phase transition of granular matter can be well understood.

Uncertainty analysis of correlated non-normal geotechnical parameters using Gaussian copula

Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for modelling the joint probability distribution of bivariate uncertain data.First,the concepts of Pearson and Kendall correlation coefficients are presented,and the copula theory is briefly introduced.Thereafter,a Pearson method and a Kendall method are developed to determine the copula parameter underlying Gaussian copula.Second,these two methods are compared in computational efficiency,applicability,and capability of fitting data.Finally,four load-test datasets of load-displacement curves of piles are used to illustrate the proposed method.The results indicate that the proposed Gaussian copula-based method can not only characterize the correlation between geotechnical parameters,but also construct the joint probability distribution function of correlated non-normal geotechnical parameters in a more general way.It can serve as a general tool to construct the joint probability distribution of correlated geotechnical parameters based on incomplete data.The Gaussian copula using the Kendall method is superior to that using the Pearson method,which should be recommended for modelling and simulating the joint probability distribution of correlated geotechnical parameters.There exists a strong negative correlation between the two parameters underlying load-displacement curves.Neglecting such correlation will not capture the scatter in the measured load-displacement curves.These results substantially extend the application of the copula theory to multivariate simulation in geotechnical engineering.

Performance analysis of relay-aided free-space optical communication system over gamma-gamma fading channels with pointing errors

The average bit error rate(ABER) performance of a decode-and-forward(DF) based relay-assisted free-space optical(FSO) communication system over gamma-gamma distribution channels considering the pointing errors is studied. With the help of Meijer's G-function, the probability density function(PDF) and cumulative distribution function(CDF) of the aggregated channel model are derived on the basis of the best path selection scheme. The analytical ABER expression is achieved and the system performance is then investigated with the influence of pointing errors, turbulence strengths and structure parameters. Monte Carlo(MC) simulation is also provided to confirm the analytical ABER expression.

Macro and micro issues in turbulent mixing

Numerical prediction of turbulent mixing can be divided into two subproblems: to predict the geometrical extent of a mixing region and to predict the mixing properties on an atomic or molecular scale, within the mixing region. The former goal suffices for some purposes, while important problems of chemical reactions(e.g. flames) and nuclear reactions depend critically on the second goal in addition to the first one. Here we review recent progress in establishing a conceptual reformulation of convergence, and we illustrate these concepts with a review of recent numerical studies addressing turbulence and mixing in the high Reynolds number limit. We review significant progress on the first goal, regarding the mixing region, and initial progress on the second goal, regarding atomic level mixing properties. New results concerning non-uniqueness of the infinite Reynolds number solutions and other consequences of a renormalization group point of view, to be published in detail elsewhere, are summarized here.The notion of stochastic convergence(of probability measures and probability distribution functions) replaces traditional pointwise convergence. The primary benefit of this idea is its increased stability relative to the statistical "noise" which characterizes turbulent flow. Our results also show that this modification of convergence, with sufficient mesh refinement, may not be needed. However, in practice, mesh refinement is seldom sufficient and the stochastic convergence concepts have a role.Related to this circle of ideas is the observation that turbulent mixing, in the limit of high Reynolds number, appears to be non-unique. Not only have multiple solutions been observed(and published) for identical problems, but simple physics based arguments and more refined arguments based on the renormalization group come to the same conclusion.Because of the non-uniqueness inherent in numerical models of high Reynolds number turbulence and mixing, we also include here numerical examples of validation. The algorithm we use here has two essential components. We depend on Front Tracking to allow accurate resolution of flows with sharp interfaces or steep gradients(concentration or thermal), as are common in turbulent mixing problems. The higher order and enhanced algorithms for interface tracking, both those already developed, and those proposed here, allow a high resolution and uniquely accurate description of sample mixing problems. Additionally, we depend on the use of dynamic subgrid scale models to set otherwise missing values for turbulent transport coefficients, a step that breaks the non-uniqueness.

Isotopic Effects on Stereodynamics of the C^+ + H_2→CH^+ + H Reaction

The effects of isotope substitution on stereodynamic properties for the reactions C^+ + H_2/HD/HT →CH^+ + H/D/T have been studied applying a quasi classical trajectory method occurring on the new ground state CH_2^+ potential energy surface [J. Chem. Phys. 142(2015) 124302]. In the center of mass coordinates applying the quasi classical trajectory method to investigate the orientation and the alignment of the product molecule. Differential cross section and three angle distribution functions P(θ_r), P(ф_r), P(θ_r, ф_r) on the potential energy surface that fixed the collision energy with a value is 40 kcal/mol have been studied. The isotope effect becomes more and more important with the reagent molecules H_2 changing into HD and HT. P(θ_r, ф_r) as the joint probability density function of both polar angles θ_r and ф_r, which can illustrate more detailed dynamics information. The isotope effect is obvious influence on the properties of stereodynamics in the reactions of C^+ + H_2/HD/HT → CH^+ + H/D/T.