湍流燃烧中的概率密度函数方法

用求解速度和化学热力学参数联合概率密度函数(pdf)输运方程的方法,计算湍流燃烧问题时,湍流输运和化学反应等过程可以精确计算,无须模拟。它还可以提供比统计矩模型方法更多的信息,因此是一个很有潜力的方法。本文给出了湍流燃烧概率密度函数的输运方程,扼要地介绍了目前应用较多的随机过程模型,以及求解概率密度函数方程的Monte Carlo算法。最后引用两个例子说明概率密度函数方法的优越性。      

青藏铁路冻土区环境问题对工程安全可靠性影响

当大涡模拟用于研究化学反应流动时，传统的滤波方法会导致化学反应项不封闭. 为克服这 个困难，发展了条件滤波大涡模拟方法. 在选择适当的条件变量后，条件滤波的化学反 应项可以表达为一个封闭项. 但同时也带来了新的问题：条件滤波耗散或条件滤波扩散项的 不封闭. 为解决这一问题，采用了直接数值模拟方法研究了它们在大小尺度上的统计特 性. 研究结果表明：条件滤波耗散和扩散对于大尺度的依赖主要体现在大尺度标量场中扩散 层结构的影响，同时小尺度脉动的变化几乎与条件滤波扩散无关，而它对条件滤波耗散却显 现出明显的作用. 在构造条件滤波耗散的亚格子模型时，小尺度脉动的作用不容忽视.     

条件矩模型模拟湍流扩散燃烧

对条件矩模型模拟湍流扩散燃烧进行了初步的研究.在条件矩模型中,标量的统计是以混合分数为条件的,条件平均使得非线性化学反应源项可以在一阶条件下被封闭.模拟结果和美国Sandia国家实验室的实验结果对比表明:对温度、主要组分浓度的预报结果是令人满意的,NO浓度的预报在趋势上也符合实验结果.误差分析表明,提高标量耗散率的预报精度和二阶条件矩模型都将有助于推动条件矩模型的发展.     

非结构混合网格化学非平衡粘性绕流数值模拟

在非结构混合网格上对化学非平衡粘性绕流进行了数值模拟。控制方程为考虑了化学非平衡效应的二维Navier-Stokes方程,化学动力学模型为7组元、7反应模型。控制方程中的对流项采用VanLeer逆风分裂格式处理,并应用MUSCL方法及Minmod限制器扩展到二阶精度,粘性项用中心差分格式处理。时间推进采用显式5步龙格-库塔方法。为了适应高超声速流场计算,对VanLeer通量分裂方法进行了改进,并引入了化学反应时间步长。对RAMC-II模型的飞行试验流场进行了数值模拟,计算结果与试验测量数据符合较好,并与参考文献中的数值模拟结果吻合。     

化学反应体系中的孤波

本文研究了化学反应扩散方程的动态行为,对于双分子过程得到了近似的孤波;对三分子过程,求得了扭结状的浓度孤波。 1.化学反应扩散方程可以用来描述许多生物化学过程。文献[1]曾详细讨论了单分     

利用有限差分法求解扩散混合化学反应二维平行流动

利用隐式有限差分方法,对两股平行流的扩散混合、化学反应问题进行了计算。计算中,使用了层流压缩边界层方程并考虑了HF化学激光器的化学反应。计算结果表明:HF(2)振动激发态的浓度要比HF(1),HF(3)、HF(0)的浓度都高,从而获得了粒子数反转条件。另外,在计算中不需要混合长度的假设,就可以求得主流(无化学反应区)与化学反应区的两条界面曲线。当然,本文的计算方法要比直接求解二维Navier-stokes方程要简单得多。     

用物理黏性构建高阶不振荡对流扩散差分格式

利用数值摄动算法, 通过扩散格式数值摄动重构把对流扩散方程的2阶中心差分格式(2-CDS)重构为高精度高分辨率格式, 解析分析和模型方程计算证实了新格式的高精度不振荡性质. 新格式是把物理黏性使流动光滑化的扩散运动规律引入2-CDS 中的结果. 该法显然与构建高级离散格式的常见方法不同. 证实: 数值摄动重构中引入扩散运动规律的结果格式与引入对流运动规律(下游不影响上游的规律)的结果格式一致, 说明对离散方程的数值摄动运算, 在维持原格式结构形式不动的条件下, 不仅能提高格式精度和稳健性, 且可揭示对流离散运动规律与扩散离散运动规律之间的内在关联;同时证实, 文中提出和使用的上、下游分裂方法是构建高精度不振荡离散格式的一个有效方法.     

台阶式溢洪道的δ-LES-SPH数值模拟

δ-LES-SPH模型较传统SPH,在控制方程里添加了扩散项和粘性项来稳定方程格式,并且这两项的系数均由湍流封闭模型来确定。基于Mascio提出的大涡模型思想,实现了δ-LES-SPH模型的方法,并利用溃坝和宽顶堰进行了算例验证。将δ-LES-SPH的模拟值与已有文献的模拟值以及试验值作对比,验证该算法研究具有高雷诺数湍流流动问题的稳定性和准确性。之后利用δ-LES-SPH模型分析了台阶式溢洪道的水流流态、流速以及消能率的变化规律,结果表明,δ-LES-SPH模型的结果与试验值吻合度较高,优于DualSPHysics方法;31阶和26阶的效能率分别达到了75.89%和74.72%,31阶明显优于26阶,同时充分体现了台阶式溢洪道的消能效果。     

求大规模非线性随机动力系统概率密度函数解的子空间法

论文给出了一个求大规模非线性随机动力系统响应概率密度函数解的新方法,称之为子空间法.考察了此方法在求解大规模带位移项参数激励非线性随机动力系统响应概率密度函数的有效性.这里的概率密度函数解由Fokker-Planck-Kolmogorov(FPK)方程控制.该方法是基于将非线性随机动力系统状态变量空间分成两个子空间,然后在其中一个子空间上对FPK方程进行积分,采取一定措施后得到低维的FPK方程.该低维的FPK方程的维数可以人为确定,也可以取为二维,从而可以用现有的求解低维FPK方程的方法求得所需的概率密度函数解.文中给出了算例,用数值结果验证了子空间法的有效性.论文是采用作者曾提出的指数多项式闭合(EPC)法求解由子空间法降维的FPK方程.     

哑铃式聚合物分子模型流变学数值研究

本文介绍了求解哑铃式分子模型位形空间分布函数扩散方程的数值方法,以及用这种方法计算的若干分子模型的流变性质。在通常情况下,将这一方法与求解流动守恒方程的边界元法相结合,便有可能用一个得不到本构方程的分子模型去代替连续介质力学本构方程,来模拟聚合物流体的复杂流动。本文还讨论了这一方法某些令人感兴趣的特点。      

LES Modeling of the Impact of Heat Losses and Differential Diffusion on Turbulent Stratified Flame Propagation: Application to the TU Darmstadt Stratified Flame

Common combustion chambers often exhibit turbulent flames propagating in partially-premixed mixtures. This propagation is generally governed by aerodynamics, unsteady mixing and chemical processes and may also be affected by conductive heat losses when the reactive zone develops close to the burner lips. The Filtered TAbulated Chemistry for Large Eddy Simulation (F-TACLES) model has been recently developed to include tabulated chemistry in Large Eddy Simulation (LES) of adiabatic stratified flames in flamelet regimes. The present article proposes a modeling approach to account for both differential diffusion and non-adiabatic effects on flame consumption speed following the F-TACLES formalism. The adiabatic F-TACLES model is first detailed using a generalized formalism for diffusive fluxes allowing either to account for differential diffusion or not. The F-TACLES model is then extended to non-adiabatic situations. A correction factor based on the non-adiabatic consumption rate is introduced to recover a realistic filtered flame consumption speed. The objective is here to tackle flame stabilization mechanisms when heat losses affect the reaction zone. The proposed approach is validated through the simulation of the unconfined stratified turbulent jet flame TSF-A for which stabilization process is affected by heat losses. Five simulations are performed for both adiabatic and non-adiabatic flow conditions comparing unity Lewis number and complex diffusion assumptions. The adiabatic F-TACLES model predicts a flame anchored at the burner lip disagreeing with experimental data. The non-adiabatic simulation exhibits local extinction due to heat losses near the burner exit. The flame is then lifted improving the comparison with experiments. Results also show a significant impact of molecular diffusion model on both mean flame consumption rate and angle.     

Conditional Moment Closure for Large Eddy Simulations

A conditional moment closure (CMC) based combustion model for large-eddy simulations (LES) of turbulent reacting flow is proposed and evaluated. Transport equations for the conditionally filtered species are derived that are consistent with the LES formulation and closures are suggested for the modelling of the conditional velocity, conditional scalar dissipation and the fluctuations around the conditional mean. A conventional β-probability density distribution of the scalar is used together with dynamic modelling for the sub-grid fluxes. The model is validated by comparison of simulations with measurements of a piloted, turbulent methane-air jet diffusion flame.     

Presumed Mapping Functions for Eulerian Modelling of Turbulent Mixing

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for a range of initial conditions common for turbulent combustion applications, e.g. for binary or trinary mixing. The purpose of this paper is to investigate the possibility of making this solution a presumed mapping function (PMF) for inhomogeneous flows. The PMF in turn will imply a presumed mixture fraction PDF that can be used for a wide range of models in turbulent combustion, e.g. flamelet models, the conditional moment closure (CMC) or large eddy simulations. The true novelty of the paper, though, is in the derivation of highly efficient, closed algebraic expressions for several existing models of conditional statistics, e.g. for the conditional scalar dissipation/diffusion rate or the conditional mean velocity. The closed form expressions nearly eliminates the overhead computational cost that usually is associated with nonlinear models for conditional statistics. In this respect it is argued that the PMF is particularly well suited for CMC that relies heavily on manipulations of the PDF for consistency. The accuracy of the PMF approach is shown with comparison to DNS of a single scalar mixing layer to be better than for the β-PDF. Not only in the shape of the PDF itself, but also for all conditional statistics models computed from the PDF.     

A Generalised Multiple Mapping Conditioning Approach for Turbulent Combustion

This paper follows the evolution in understanding of the multiple mapping conditioning (MMC) approach for turbulent combustion and reviews different implementations of MMC models. As the MMC name suggests, the original version represents a consistent combination of CMC-type conditional equations (conditional moment closure) and generalised mapping closure. It seems that the strength of the MMC model, and especially that of its stochastic version, lies in a more general (and much more transparent) interpretation. In this new generalised interpretation, we can replace complicated derivations by physical reasoning and the model appears to be a natural extension of modelling approaches developed in recent decades. MMC can be seen as a methodology for enforcing certain known characteristics of turbulence on a conventional mixing model. This is achieved by localising the mixing operation in a reference space. The reference space variables are selected to emulate the properties of a turbulent flow which have a strong effect on reactive quantities. The best and simplest example is an MMC model which has a single reference variable emulating the mixture fraction. In diffusion flames turbulent fluctuations of reacting quantities are strongly correlated with fluctuations of the mixture fraction. By making mixing local in the reference mixture fraction space a CMC-type mixing closure is enforced. In the original interpretation of MMC the reference variables are modelled as Markov processes. Since the reference variables should emulate properties of turbulent flows as realistically as possible the next step, and the basis of generalised MMC, is to remove the Markovian restriction and set reference variables equal to traced Lagrangian quantities within DNS or LES flow fields. Indeed, no Markov value can emulate the mixture fraction better than the mixture fraction itself. (Using a Markov vector process of dimension higher than the number of conditioning variables represents a more economical alternative for producing reference variables in generalised MMC.) The generalised MMC approach effectively incorporates the mixture fraction-based models, the PDF methods and LES/DNS techniques into a single methodology with possibility of blending useful features developed previously for conventional models. The generalised approach to MMC stimulates a more flexible understanding of simulations using sparsely placed Lagrangian particles as tools that may provide accurate joint distributions of reactive scalars at relatively low computational cost. The physical reasoning behind the new interpretation of MMC is supported by example computations for a partially premixed methane/air diffusion flame (Sandia Flame D). The scheme utilises LES for the dynamic field and a sparse-Lagrangian filtered density function method with MMC mixing for the scalar field. Two different particle mixing schemes are tested. Simulations are performed using only 35,000 Lagrangian particles (of these only 10,000 are chemically active) on a single workstation. The relatively low computational cost allows the use of realistic chemical kinetics containing 34 reactive species and 219 reactions. Intended for publication in the special issue of Flow, Turbulence and Combustion arising from the 2nd ECCOMAS Thematic Conference on Computational Combustion held at Delft in mid-2007.     

Simulation of Dilute Acetone Spray Flames with LES-CMC Using Two Conditional Moments

Large-eddy simulations (LES) have been coupled with a conditional moment closure (CMC) method for the computation of a series of turbulent spray flames. An earlier study by Ukai et al. (Proc. Combust. Inst. 34(1),1643–1650, 2013) gave reasonable results for the prediction of temperature and velocity profiles, but some limitations of the method became apparent. These limitations are primarily related to the upper limit in mixture fraction space. In order to enhance the applicability of the LES-CMC model, this paper proposes a two-conditional moment approach to account for the existence of pre-evaporated fuel by introducing two sets of conditional moments based on different mixture fractions. The two-conditional moment approach is first tested for a non-reacting test case. The results indicate that the spray evaporation induces relatively large conditional fluctuations within a CMC cell, and one set of conditional moments might not be sufficient. The upper limit of the mixture fraction space is dynamically selected for the solution of the second set of conditional moments, and the corresponding CMC solution in a CFD cell is estimated by interpolation between the two conditional moments weighted by the amount of vapour emitted within the domain. The cell-filtered value is given by integration of the conditional moment across mixture fraction space using a bounded β-FDF for the distribution of the scalar. As a result, the fuel concentration profiles given by LES and the two-conditional moment approach are shown to agree well. Then, the two-conditional moment approach is applied to four different flame configurations. The comparison of LES cell quantities and conditionally averaged moments indicates that the two sets of conditional moments are necessary for accurate predictions in zones where gas phase mixture fraction is significantly increased by droplet evaporation within the computational domain. The unconditional temperature profiles clearly show that the new approach improves the predictions of mean temperature especially along the centerline. Also, the better predictions of the temperature field improve the accuracy of the predicted mean axial droplet velocities. Overall, good agreement with the experimental results is found for all four cases, and the methodology is shown to be applicable to flames with a relatively wide range of fuel vapour concentrations.     

LES of the Sandia Flame D Using Laminar Flamelet Decomposition for Conditional Source-Term Estimation

A variation of the Laminar Flamelet Decomposition (LFD) method for the Conditional Source Term (CSE) model developed by Bushe and Steiner (Phys Fluids 15:1564–1575, 2003) is implemented into an existing LES code. In this approach, the set of basis functions, on which the decomposition is based, is reduced using the mixture fraction dissipation rate as external parameter for the selection. It was found that reducing the basis improves and stabilises the inversion, resulting in reasonably accurate approximation for the average conditional quantities. Some modifications have been introduced to improve the inversion process by reducing the number of flamelets. This modification is found to help stabilize the inversion and keep the dimension of the linear system small. The model is used to simulate the turbulent non-premixed piloted SANDIA Flame D. Reasonably good predictions for conditional and unconditional average variables were found for different planes and at centreline of the flow field. However, an over prediction of the consumption rate in the near field of the flame is found, which may be partially attributed to the use of the Steady Laminar Flamelets (SLF) as functions for the decomposition and the use of a constant boundary condition for the species mass fractions in solving the flamelets. The present simulation of a turbulent reacting jet is the first test of the LFD approach in a realistic scenario using only the temperature field to calculate the inversion. The model is found to be computationally inexpensive.     

A fast image encryption scheme with a novel pixel swapping-based confusion approach

In traditional permutation-diffusion type image cipher, the confusion and diffusion are two independent procedures. In general, several overall rounds are required to achieve a satisfactory security level, which downgrades its advantage in online image protection. In this paper, a novel plain pixel-related swapping confusion approach that can contribute considerable diffusion effect in the permutation procedure is proposed. By employing the self-related non-linear pixel swapping confusion approach, a tiny difference between two plain images can bring about completely different confused images. Therefore, the spreading process of the cryptosystem is significantly accelerated, and the workload of the time-consuming diffusion part will be reduced. Moreover, an improved image encryption architecture is proposed in conjunction with the pixel swapping-based confusion approach. Compared with the typical permutation-diffusion structure, the new architecture well addresses the weakness of confusion key sensitivity in the first encryption round. Simulation results and numerical analyses justify the higher efficiency and sufficient strength of the proposed image encryption scheme.     

Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.     

Effects of the method of identification of the diffusion coefficient on accuracy of modeling bound water transfer in wood

An alternative approach to determining the bound water diffusion coefficient is proposed. It comprises a method for solving the inverse diffusion problem, an improved algorithm for the bound-constrained optimization as well as an alternative submodel for the diffusion coefficient’s dependency on the bound water content. Identification of the diffusion coefficient for Scots pine wood (Pinus sylvestris L.) using the proposed inverse approach is presented. The accuracy of predicting the diffusion process with the use of the coefficient values determined by traditional sorption methods as well as by the inverse modeling approach is quantified. The similarity approach is used and the local and global relative errors are calculated. The results show that the inverse method provides valuable data on the bound water diffusion coefficient as well as on the boundary condition. The results of the identification can significantly improve the accuracy of mass transfer modeling as studied for drying processes in wood.