Direct numerical simulation of passive scalar in decaying compressible turbulence

1IntroductionDirectnumericalsimulation(DNS)becomesanimportanttoolinrecentresearchofturbulence[1].DNSofcompressibleturbulenceismoredifficultthanthatoftheincompressibleturbulence.WhentheturbulentMachnumberisgreaterthan0.3theshockletsmayappearinthecompressibleturbulentflowfields.Thereasonandmechanismofshockletsexistencearenotclearyet.TheturbulentMachnumberinDNScannotbeveryhighwiththepresentexistingnumericalmethodsandcomputerresource.Fortheproblemofcompressibleisotropicturbulencewiththeinitia…     

Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a Weakly Imperfect Bose Gas

In the example of a weakly imperfect Bose gas, we discuss the mechanism of establishing thermodynamic equilibrium for a chaotic set of quantum vortex filaments. We assume that the dynamics of the Bose condensate is described by the Gross–Pitaevsky equation with an additional noise satisfying the fluctuation–dissipation theorem. In considering a vortex filament as the intersection line of surfaces on which the real and imaginary parts of the order parameter (x,t) vanish, we obtain an equation of the Langevin type for elements of the vortex filament with an appropriately transformed random force. The Fokker–Planck equation for the probability density has a solution given by the Gibbs distribution at the temperature of the Bose condensate. In other words, when the Bose condensate is in thermal equilibrium and no other random actions exist, the system of vortices is also in thermal equilibrium.     

Flow Structure of Lifted Swirling Jet Flames

Swirling combustion is widely applied in various applications such as gas turbines, utility boilersor waste incinerators. This article contributes to the ongoing research by providing experimentaldata that are gathered in the mixing zone of a lifted swirling premixed natural gas flame. Theobjective of this paper is fivefold: (1) to introduce the lifted swirling flame featuring lowNO _x emissions (2) to provide experimental data such as major species distributions, temperature and streamlines of the flow pattern, (3) to report on velocity bias in probability density function (PDF) distributions and to present PDF sequences of velocities in medium scale swirling flows, (4) to make an assessment on the local small-scale turbulence that is present in the swirling mixinglayer and (5) to provide new experimental data for model verification and development.The PDFs are corrected in order to compensate for the velocity bias phenomenon, which is typicalfor randomly sampled LDA data. Sequences of axial PDF data are presented and measurement locationsof interest are selected to look at the PDF characteristics of the internal and externalrecirculation zones, the mixing layer and the onset of the reacting flow into detail. The mixinglayer PDFs covered a wide velocity range and revealed bimodality; even the concept ofmulti-modality is suggested and explored. Analysis showed that a sum of two Gaussian distributionscan accurately envelop the experimental PDFs. The reason for this broadband turbulence behavior isto be found in combination of precessing and flapping motion of the flow structures, and also incombustion generated instabilities of the lifted flame. As a result, the flame brush is wide (largescale motion) and the mixing (small-scale turbulence) flattens any high temperatures in thecombustion process.The multi-scale turbulence concept is subsequently used to make anassessment of the local turbulence characteristics in the mixing layer.The idea is that the PDFs capture both contributions of the flow-inherent fine grain turbulence (u _l ) which is superposed on slowlarge scale fluctuating structures. It is this u _l that will be of interest in continued research on the classification of the lifted flame into acombustion regime diagram (e.g. Borghi diagram). Finally, the bimodalitycharacter in reacting flows and the prediction of large-scale structuresmay be a challenge for LES researchers.     

On the Decay of Turbulence in the 20-Liter Explosion Sphere

The transient flow field in the standard 20-liter explosion sphere was investigated by means of laser Doppler anemometry. Velocities were measured at various locations within the flow field, and this information was used to quantify the transient behavior of the root-mean-square of the velocity fluctuations and to investigate the spatial homogeneity and the directional isotropy of the turbulence. The investigation involved the transient flow fields generated by the three most widely used dust dispersion systems, namely, the Perforated Dispersion Ring, the Rebound Nozzle, and the Dahoe Nozzle. With all three dispersion dust devices, the decay of turbulence could be correlated by a decay law of the form

Bilinear estimates and applications to 2d NLS

The three bilinearities for functions are sharply estimated in function spaces associated to the Schrödinger operator . These bilinear estimates imply local wellposedness results for Schrödinger equations with quadratic nonlinearity. Improved bounds on the growth of spatial Sobolev norms of finite energy global-in-time and blow-up solutions of the cubic nonlinear Schrödinger equation (and certain generalizations) are also obtained.

     

Basis Problem for Turbulent Actions II: c0-Equalities

Let (Xⁿ,dⁿ) be a sequence of finite metric spaces of uniformlybounded diameter. An equivalence relation D on the product defined by if and only if is a c₀-equality.A systematic study is made of c₀-equalities and Borel reductionsbetween them. Necessary and sufficient conditions, expressedin terms of combinatorial properties of metrics d_n, are obtainedfor a c₀-equality to be effectively reducible to the isomorphismrelation of countable structures. It is proved that every Borelequivalence relation E reducible to a c₀-equality D either reducesa c₀-equality D' additively reducible to D, or is Borel-reducibleto the equality relation on countable sets of reals. An appropriatelydefined sequence of metrics provides a c₀-equality which isa turbulent orbit equivalence relation with no minimum turbulentequivalence relation reducible to it. This answers a questionof Hjorth. It is also shown that, whenever E is an F-equivalencerelation and D is a c₀-equality, every Borel equivalence relationreducible to both D and to E has to be essentially countable.2000 Mathematics Subject Classification: 03E15.     

Probabilistic Estimates for the Two-Dimensional Stochastic Navier–Stokes Equations

We consider the Navier–Stokes equation on a two-dimensional torus with a random force, white noise in time, and analytic in space, for arbitrary Reynolds number R. We prove probabilistic estimates for the long-time behavior of the solutions that imply bounds for the dissipation scale and energy spectrum as R.     

一种新型的空气扰动探测方法

基于光折变材料的二波耦合特性提出了一种新型的空气扰动探测方法。空气中的微扰导致入射到光折变材料中两束光的光程差发生改变，干涉条纹随之发生变化。由于光折变体相位栅建立时间比较长，体相位栅不能及时跟随干涉条纹发生变化，导致干涉条纹与体相位栅间的相移将随空气扰动信息的变化而变化。相移角的改变将导致瞬态能量转移，输出两束光的能量在瞬态能量转移作用下将实现对空气扰动信息的光调制，并且这种调制过程是一种差分调制方式。在接收端采用电差分检测方法便可解调出空气扰动信息。这种利用光折变体相位栅的差分探测方法在未来的探测领域将有广泛的应用前景。     

柴油机氮氧化物的特征时间模型

本文综合考虑湍流混合、分子扩散的作用,提出了一个新的NO生成计算模型.该模型采用化学动力学时间尺度和湍流时间尺度来考虑化学动力学和湍流混合对NO生成的影响.文中模拟了一台浅盆形燃烧室柴油机,对计算结果和实测结果进行了对比分析.研究表明,新模型计算的NO生成速率与实测结果有较好的一致性.     

弱湍流大气激光通信中的光强闪烁研究

大气激光通信中，湍流引起的光强闪烁严重影响通信系统的性能指标（误码率）。通过对湍流条件下光强分布的数值仿真，得出弱湍流时接收光强服从对数正态分布，与Rytov理论一致。用随机过程分析的方法给出了系统误码率与光强闪烁的关系，并进行MATLAB数值模拟。研究表明误码率随对数振幅方差（湍流强度）的增加而上升，且当对数振幅方差在0～0．02时，误码率随对数振幅方差的变化较快，近似呈线性递增。在工程中，可采用自适应光学或多发射机等技术抑制湍流对大气激光通信的影响。