Premixed Turbulent Combustion Modelling Using Level Set Approach

The paper deals with a level set approach application to SI engine combustion modelling, which is based on solving an additional transport equation to determine the flame front propagation. The presented work is an extension of the paper [6]. The influence of engine speed, air excess, swirl number, engine load as well as application of different turbulence model, in.uence of mesh coarseness and model fine-tuning constants are investigated and the results are presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Mathematical Model and Research Progress of the Boundary Layer Flashback in Premixed Combustion北大核心CSCD

Flashback is a key problem influencing the normal operation of power equipment such as gas turbines. As one of the main mechanisms that cause flashback, the boundary layer flashback has an important effect on the design and operation of gas turbine combustors and other combustion devices. Since the critical gradient model for the boundary layer flashback was put forward by Lewis et al. in 1945, the theoretical models for the boundary layer flashback, such as the Peclet number model, the Damköhler number model and the flame angle theory, were developed one after another. However, these theoretical models still need improvements. Until now, the theoretical models for the boundary layer flashback are still in continuous development and modification. The history of the boundary layer flashback was reviewed, and the background, pertinence and shortcomings of the theoretical models were elucidated in the order of the model establishment time. In addition, the development status and research progress of the theoretical models for the boundary layer flashback in recent years were summarized, especially the progress made with new methods such as numerical simulation and statistical analysis. Further, the theoretical research direction and breakthrough points of the combustion boundary layer flashback at present and in the future were put forward. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Influence of the Propagation Direction for an Acoustic Wave Interacting with a Turbulent Premixed Flame

We investigate in this work the conditions leading to amplification or damping of a planar, Gaussian acoustic wave interacting with a CO/H₂/Air turbulent premixed flame. We examine in particular the influence of the direction of propagation. In a first case the acoustic wave is coming from the right direction (starting in burnt gas zone), while it propagates from the left direction (starting in fresh gas zone) in the second case. This investigation is based on fully compressible Direct Numerical Simulation (DNS) results. Chemical processes are computed using a complete reaction scheme and accurate transport properties are taken into account. A local version of the classical Rayleigh's criterion is used to analyze the results, based on the single assumption that the celerity of sound is independent of time and only function of the spatial coordinates. We observe that, after the interaction, the wave is wrinkled leading to a non-planar geometry, similar to that of the initial flame front. For both cases the heat release fluctuation is concentrated in very small zones, associated either with positive or negative values. Rayleigh's criterion is then used to localize large positive and negative values (amplification resp. damping conditions). This criterion shows that wave amplification occurs only inside well-located small zones in the two cases. The propagation direction has no influence on these results, confirming that amplification or damping is mainly controlled by a coupling process between pressure and heat release fluctuations through the chemical reactions. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于浸入边界-有限元法的流固耦合碰撞数值模拟方法

针对流固耦合碰撞问题,建立了流体中固体与固体碰撞界面解析直接模拟方法,采用清晰界面浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时网格出现负体积的问题,采用基于罚函数的有限元方法对固体的运动和碰撞进行求解,以分域耦合方式实现流体域和固体域的耦合求解.通过与静止流体中球形颗粒与壁面正碰撞和斜碰撞的实验数据对比,验证了建立的数值模拟方法对流体中固体与固体碰撞数值模拟的正确性,获得了流体域流场在碰撞前后随时间的变化,同时通过该文建立的数值模拟方法也获得了固体域中固体的碰撞力和应力.未来,将把该数值模拟方法应用到流体流动环境中,如固体颗粒对管道的冲蚀、流体诱导海洋立管之间的碰撞、坠物对海底管道的撞击等.     

虚拟解法分析浸入边界法的精度

浸入边界法是对流固耦合系统进行建模和模拟的有效工具,在生物力学领域的应用尤为广泛．该文的工作主要包含两个部分:程序验证和精度分析．前者证明了程序的正确性,后者给出了浸入边界法的精度．两部分工作均使用虚拟解法作为研究工具．在程序验证部分,使用二阶空间离散格式进行数值计算,通过分析各种变量的离散误差,得到的程序计算精度阶是二阶,与理论精度阶一致,证明了数值计算所使用程序的正确性．精度分析部分工作在此基础上展开．引入压强跳跃,在动量方程中加入相应源项,通过分析带有源项的控制方程中各物理量的离散误差,证明浸入边界法只具有一阶精度．同时可以得出以下结论:粗网格无法敏感地捕捉浸入边界的影响;当Euler网格固定时,增加Lagrange标志点的数目并不会改善计算误差．     

湍流边界层内准流向发卡涡生成的数值模拟

采用根据共振三波理论模型建立的初始准二维流场和直接数值模拟方法,对湍流边界层近壁区流向涡的生成进行了研究．计算得到了准流向发卡涡和次生准流向涡结构的生成过程及其主要特征,讨论了它们的产生机理．作为相干结构的主要特征,利用共振三波理论模型对流向涡结构生成与演化过程的研究为湍流边界层内相干结构的研究与流动控制提供了新的途径和思路．     

湍流边界层中固体小颗粒湍流运动的Lagrangian模型

给出了固体小颗粒在边界层中的Lagrangian运动方程,方程中包括受壁面影响的粘性阻力,Saffman升力及Magus升力等.使用频谱法,得到了颗粒响应流体的Lagrangian能谱的表达式,使用这些结果研究了各种响应特性.本文的结果清楚地表明了固体个颗粒在湍流扩散过程中,其湍流扩散是可能大于流体的.     

正则化δ函数对浸入边界法精度的影响

浸入边界法是对流固耦合系统进行数学建模和数值模拟的有效工具,在生物力学领域的应用尤为广泛．正则化δ函数对精度的影响是研究浸入边界法本身性质的一个重要课题．采用虚拟解法对此展开分析．首先使用光滑虚拟解证明程序的正确性,然后使用压力存在跳跃的虚拟解研究浸入边界法的精度．通过分析使用4种不同的正则化δ函数时整个流场的离散误差,得到以下结论:浸入边界法只具有1阶精度;选用不同的正则化δ函数,不能提高浸入边界法的精度,但会影响整个流场的离散误差值．     

湍流边界层底层相干结构的一个理论模型*

本文采用非线性稳定性分析方法,研究了湍流边界层底层相干结干结构的成因.计算得到的增长最快的不稳定波的展向尺度与纵向尺度都与实验相符.这一分析的特点是采用了不同于湍流平均速度剖面的更合理的速度剖面作为稳定性分析的基础,并采用了新的非线性理论.文中结果有助于理解湍流边界层底层相干结构的拟有序现象.     

Inflow Treatment for the Simulation of Subsonic Jets with Turbulent Nozzle Boundary Layers

The state of the boundary layer at the nozzle exit of a circular nozzle-jet configuration has an important influence on the development of the shear layer and the emitted sound. Of special interest is the acoustic near-field obtained when the nozzle exit boundary layer is fully turbulent. The turbulent inflow generation and the inflow boundary treatment are important issues to be addressed. We use the Synthetic Eddy Method (SEM) to generate a turbulent inflow which reproduces mean flow and Reynolds stress profiles of specified reference data. The spatially and temporally varying synthetic fluctuations are imposed in the simulation by a forcing term added to the governing equations which is active in a small region downstream of the inflow boundary. This forcing in combination with characteristic boundary conditions allows for passing of upstream-propagating acoustic waves and avoids an uncontrolled drift of mean-flow quantities. We employ this inflow boundary treatment for a subsonic nozzle-jet flow simulation at a Reynolds number of ∼ 9500 and Mach number of 0.9. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solvability of the Stokes Immersed Boundary Problem in Two Dimensions

We study coupled motion of a 1-D closed elastic string immersed in a 2-D Stokes flow, known as the Stokes immersed boundary problem in two dimensions. Using the fundamental solution of the Stokes equation and the Lagrangian coordinate of the string, we write the problem into a contour dynamic formulation, which is a nonlinear nonlocal equation solely keeping track of evolution of the string configuration. We prove existence and uniqueness of local-in-time solution starting from an arbitrary initial configuration that is an H^5/2-function in the Lagrangian coordinate satisfying the so-called well-stretched assumption. We also prove that when the initial string configuration is sufficiently close to an equilibrium, which is an evenly parametrized circular configuration, then a global-in-time solution uniquely exists and it will converge to an equilibrium configuration exponentially as t → + ∞. The technique in this paper may also apply to the Stokes immersed boundary problem in three dimensions. © 2018 Wiley Periodicals, Inc.     

The Set of Pre-Ends and the Ideal Boundary of a Manifold without Boundary

Relations between prime pre-ends and elements of the ideal boundary of a manifold without boundary are studied. The cases of a manifold with Mazurkiewicz or Riemannian intrinsic metric and of a manifold with quasihyperbolic metric are considered.     

用Level Set算法模拟孤立波与前台阶的相互作用

进一步研究了Level Set方法的数学基础,研究了求解有自由水面水动力学问题的具体方法。并在此基础上,对孤立波与前台阶相互作用这一问题进行了计算及研究,取得了与实验结果相符合的计算结果。     

Mathematical Simulation of Turbulent Combustion of Carbon in the Problems of White Dwarf Mergers and Explosions of Type Ia Supernovae

Journal of Applied and Industrial Mathematics - Type Ia supernovae play a key role in astrophysics, but the study of the mechanisms of their explosion is still incomplete. The mathematical...     

Coupling Boundary Elements to a Raytracing Procedure using the Singular Indirect Method

The coupling of Boundary Elements and a raytracing procedure is presented here. Such a hybrid method is best suited to the study of realistic outdoor sound propagation problems: The noise often acts in a domain where many objects like buildings or sound insulation walls scatter the sound. Thus, diffraction has to be taken into account. BEM is well suited. To study the effects of this noise on a sound receiver far away, raytracing may be preferable for such application, because refraction can be implemented more easily. Hence, a Boundary Element Analysis is performed in noisy nearfield regions, a raytracing procedure at a larger distance from the sound sources. First, the direct Boundary Element algorithm is applied to determine the sound pressure at interface points. Second, a singular indirect Boundary Element formulation is used to find intensities of point sources on the same interface which produce the previously determined sound pressure. Finally, these sound intensities are the input data for the raytracing procedure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Level Set of the Asymptotic Rate of Convergence for the Method of Steepest Descent

Ukrainian Mathematical Journal - The asymptotic rate of convergence of the method of steepest descent is regarded as a function of the initial approximation. We study the level set of this rate,...     

基于集对分析的一种优选模型确定水库正常蓄水位

针对鲁皂水库正常蓄水位优选中各指标不相容问题,利用集对分析理论构建正常蓄水位优选模型,将参选水库正常蓄水位方案的多个指标合成为一个与标准评价集的优越度,用来描述水库正常蓄水位方案的总体综合优越性.研究结果表明,鲁皂水库正常蓄水位为1386m,采用对立与同一优选模型确定水库特征水位合理可行,模型结构简洁,计算量小.