The Turbulent Schmidt Number for Transient Contaminant Dispersion in a Large Ventilated Room Using a Realizable k-εModel

Buildings with large open spaces in which chemicals are handled are often exposed to the risk of explosions.Computational fluid dynamics is a useful and convenient way to investigate contaminant dispersion in such large spaces.The turbulent Schmidt number(Sc_(t))concept has typically been used in this regard,and most studies have adopted a default value.We studied the concentration distribution for sulfur hexafluoride(SF_(6))assuming different emission rates and considering the effect of Sc_(t).Then we examined the same problem for a light gas by assuming hydrogen gas(H_(2))as the contaminant.When SF_(6) was considered as the contaminant gas,a variation in the emission rate completely changed the concentration distribution.When the emission rate was low,the gravitational effect did not take place.For both low and high emission rates,an increase in S_(ct) accelerated the transport rate of SF_(6).In contrast,for H_(2) as the contaminant gas,a larger S_(ct) could induce a decrease in the H_(2) transport rate.

Numerical Investigations on the Impact of Turbulent Prandtl Number and Schmidt Number on Supersonic Combustion

The flow field inside the combustor of a scramjet is highly complicated and the related turbulent Prandtl and Schmidt numbers have a significant impact on the effective numerical prediction of such dynamics.As in many cases researchers set these parameters on the basis of purely empirical laws,assessing their impact(via parametric numerical simulations)is a subject of great importance.In the present work,in particular,two test cases with different characteristics are selected for further evaluation of the role played by these non-dimensional numbers:Burrows-Kurkov case and DLR case.The numerical results indicate that these parameters influence ignition location.Moreover,the temperature distribution is more sensitive to them than to H2O mass fraction and velocity distributions.

Effects of Reynolds number and Schmidt number on variable density mixing in shock bubble interaction

Effects of Reynolds(Re)number and Schmidt(Sc)number on the flow structures and variable density mixing are numerically investigated through the canonical shock cylindrical bubble interaction.By determining the viscosity and diffusivity within a wide range,the controlling parameters,total vortex circulation,and compression rate,are conservative under a broad range of Re and Sc numbers(Re≈10^(3)-10^(5)and Sc≈0.1-5)in the same shock Mach(Ma)number condition(Ma=2.4).As for the Re number effect,the circulation of secondary baroclinic vorticity(SBV),induced by the main vortex centripetal acceleration,is observed to be higher in high Re number and vice versa.Based on the vorticity transport equation decomposition,a growth-inhibition vorticity dynamics balance mechanism is revealed:the vorticity viscous term grows synchronously with baroclinic production to inhibit SBV production in low Re number.By contrast,the viscous term terminates the baroclinic term with a time lag in high Re number,leading to the SBV production.Since the SBV reflects the local stretching enhancement based on the advection-diffusion equation,mixing is influenced by the Sc number in a different behavior if different Re numbers are considered.The time-averaged variable density mixing rate emerges a scaling law with Sc number asχ^(∗)=β·Sc^(−α),where the coefficientβ∼Re−0.2 and the scaling exponentα∼Re−0.385.The understanding of Re number and Sc number effect on variable density mixing provides an opportunity for mixing enhancement from the perspective of designing the viscosity and diffusivity of the fluid mixture.

Influence of Turbulence Schmidt Number on Exit Temperature Distribution of an Annular Gas Turbine Combustor using Flamelet Generated Manifold

The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS(Reynoldsaveraged Navier–Stokes)simulations,where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer.This concept,applied to a lean premixed combustion system,was assessed in this paper in terms of exit temperature distribution.Because of the isotropic assumption involved in this analogy,the prediction in some flow condition,such as jet cross flow mixing,would be inaccurate.In this study,using Flamelet Generated Manifold as reaction model,some of the numerical results,obtained from an annular combustor configuration with the turbulent Schmidt number varying from 0.85 to 0.2,were presented and compared with a benchmark atmospheric test results.It was found that the Schmidt numberσt in mean mass fraction f transport equation had significant effect on dilution air mixing process.The mixing between dilution air and reaction products from the primary zone obviously improved asσt decreased on the combustor exit surface.Meanwhile,the sensitivity ofσt in three turbulence models including Realizable k-ε,SST(Shear Stress Transport)and RSM(Reynolds Stress Model)has been compared as well.Since the calculation method of eddy viscosity was different within these three models,RSM was proved to be less sensitive than another two models and can guarantee the best prediction of mixing process condition.On the other hand,the results of dilution air mixing were almost independent of Schmidt number Sct in progress variable c transport equation.This study suggested that for accurate prediction of combustor exit temperature distribution in steady state reacting flow simulation,the turbulent Schmidt number in steady state simulation should be modified to cater to dilution air mixing process.

Families of Schmidt-number witnesses for high dimensional quantum states

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

基于微震监测的地下采场稳定性分析

微震监测技术已经成为深部地压研究和管理的一个基本手段。基于IMS微震监测系统,对中色白音诺尔铅锌矿地下采区采掘过程引起的岩体微破裂进行监测,可有效反映目标区域内采空区及生产作业采场的稳定性。数据分析表明:1)通过微震事件时空分布分析、b值法和能量指数EI、施密特数Scs与累计视体积CAV关系法,结合现场施工情况可更加准确地分析微震数据,有效评价地下采场的整体稳定性,得出合理结论;2)在EI降低的前提下,CAV曲线在拐点处斜率降低对应微震事件发生的概率或事件数较近前值降低,反之亦然;在Scs降低的前提下,无论CAV曲线在拐点处斜率增减,微震事件发生的概率或事件数较近前值均减小;3)该有色金属矿山地下采区大爆破余震事件发生频率显著降低,该生产采场稳定性较好。该系统的应用对中色白矿地下矿床开采中的防震减灾和安全生产将起到积极的作用。

湍流标量输运过程中的Schmidt数识别

湍流Schmidt数是湍流传质过程中的关键控制参数,为了准确识别输运过程的湍流Schmidt数,提出基于Metropolis-Hastings算法和有限单元法的湍流Schmidt数识别算法。湍流求解采用稳态标准k-ε模型,浓度场求解采用非稳态无源对流扩散方程。算例计算结果表明,基于Metropolis-Hastings算法和有限单元法的参数识别算法对湍流Schmidt数的识别精度较高。

关于矩阵Schmidt分解的注记

研究矩阵Schmidt分解、Schmidt系数及Schmidt数的特性。通过偏迹、矩阵拉直运算之间的关系与矩阵的纯化工具,推广了矩阵的Schmidt分解,给出了两个矩阵Schmidt系数相等的充要条件,获得矩阵Schmidt数的有关结果。

Analysis of a Stagnation Point Flow with Hybrid Nanoparticles over a Porous Medium

The unsteady stagnation-point flow of a hybrid nanofluid over a stretching/shrinking sheet embedded in a porous medium with mass transpiration and chemical reactions is considered.The momentum and mass transfer problems are combined to form a system of partial differential equations,which is converted into a set of ordinary differential equations via similarity transformation.These ordinary differential equations are solved analytically to obtain the solution for velocity and concentration profiles in exponential and hypergeometric forms,respectively.The concentration profile is obtained for four different cases namely constant wall concentration,uniform mass flux,general power law wall con-centration and general power law mass flux.The effect of different physical parameters such as Darcy number Da^(1-1),mass transpiration parameter V_(C),stretching/shrinking parameter (d),chemical reaction parameter(β)and Schmidt number (Sc)on velocity and concentration profile is examined.Results show that,the axial velocity will decreases as the shrinking sheet parameter increases,regardless of whether the suction or injection case is examined.The concentration decreases with an increase in the shrinking sheet parameter and the chemical reaction rate parameter.

湍流模型和施密特数对街谷内污染扩散模拟的影响

选取不同的湍动施密特数,分别采用标准κ-ε模型和realizableκ-ε模型对孤立街道峡谷内的气流运动和污染物扩散进行了数值模拟.计算得到的气流速度场和污染物浓度分布表明,标准κ-ε模型和realizableκ-ε模型预测出极为相似的气流旋涡结构,即在峡谷内生成一个中心大致位于峡谷中央的顺时针大旋涡,并在此大旋涡的作用下污染物往峡谷的背风侧积聚.通过对比分析峡谷迎风面和背风面上的无量纲污染物浓度计算结果与风洞试验数据表明,湍动施密特数的改变并不影响计算空气流场,但改变污染物扩散方程中的湍动扩散率,增大湍动施密特数将减弱污染物的湍动扩散作用,使得峡谷顶部污染物外溢减少,从而导致峡谷内的污染物浓度计算值增大;只要给定合适的计算参数,标准κ-ε模型和realizableκ-ε模型均能预测出峡谷内的污染物扩散分布,标准κ-ε模型合适的湍动施密特数为0.4～0.6,而realizableκ-ε模型则为0.3～0.5;当取湍动施密特数为0.7（Fluent软件系统中的默认值）时,标准κ-ε模型的计算精度高于realizableκ-ε模型的计算精度.

基于流场验证的紊流施密特数对街道峡谷污染物扩散数值模拟的影响

以城市街道峡谷的水槽和风洞试验数据为依据,利用ANSYS Fluent软件,数值模拟了街道峡谷内的流场(包括时均流动和紊流强度)及污染物浓度。结果表明:标准k-ε紊流模型、RNG k-ε紊流模型和标准k-ω紊流模型均能基本正确地模拟街道峡谷内的流场和浓度场;紊流施密特数Sct对浓度值有明显的影响,街道峡谷内的浓度值随Sct的增加而变大,当Sct取1.3时,浓度值和试验值吻合最好;由于标准k-ω模型对流场的模拟结果相对最好,其模拟的浓度场也与试验值吻合最佳。街道峡谷内的浓度分布由时均流输运和紊流扩散共同决定,因此,合理的Sct数不能仅仅依据浓度值与试验值的吻合度来选取,而应首先保证流动模拟的准确性。

挥发性化合物的分子结构对水-气界面传质的作用

利用能精确捕获水自由液面的VOF(Volume of fluid,体积百分比)法,建立挥发性化合物在无化学反应条件下的耦合扩散时空模型.用W*(分子拓扑指数)表征化合物分子结构,将化合物传质系数——Schmid数与W*进行关联,结合亨利常数、Schmidt数与W*的关联式,预测乙醇、苯、己醛与2,2,4-三甲基戊点源泄漏后的质量浓度时空分布,预测结果与试验吻合较好.烷基苯、醇、醛、烃类化合物的Schmidt数与W*0.25成线性关系.Schmidt数随分子间距减小而增大,烷基苯、醇、醛、烃类化合物在水中的Schmidt数约为空气中的600倍以上.相同W*的化合物,Schmidt数随分子量增加而增大.泄漏初期,亨利常数的作用高于Schmidt数,挥发强度随亨利常数的增加而增大,水中乙醇峰值浓度下降的平均速率仅是苯的45.1%;泄漏后期,Schmidt数起主要作用,挥发强度随Schmidt数减少而增大,苯的峰值浓度下降平均速率降低,乙醇峰值浓度下降平均速率比苯高120.0%.己醛的W*是2,2,4-三甲基戊的16.27倍,但二者的亨利常数和Schmidt数很接近,挥发迁移过程极其相似.

基于GS正交投影快速估计信源个数的方法

经典估计信源个数的Akaike信息论准则(Akaike information criterion,AIC)和最小描述长度(Minimum description length,MDL)方法需要特征分解,运算量较大且需要较多快拍数,为了便于工程实现,在传统的针对数据域Gram-Schmidt(GS)正交投影算法估计信源个数的基础上,提出了一种对协方差矩阵进行GS正交化来估计信源个数新方法,并推导出这种算法的自适应门限。仿真结果表明,该算法和AIC及MDL算法相比,虽然估计性能有所下降,但性能下降幅度不大,且其运算量小、所需快拍数少;与传统GS算法相比,运算量增加不大,但估计性能有较大提高。

标量图像测速原理及数值检验

标量图像测速是一种新型的能够测量微小结构的湍流实验测量系统,其理论依据是Schmidt(Sc)数>1的标量湍流里,标量场脉动的时间尺度和空间耗散尺度要小于对应的速度场脉动的时间尺度和空间耗散尺度,标量脉动比速度脉动具有更强的间歇性,标量场所含信息大于速度场所含信息,从高Sc数标量场提取速度场是可能的。笔者详细介绍了标量图像测速原理,并在积分最小化法思想指导下根据标量输运守恒方程及限定条件,建立了积分最小化标量图像测速的数学表示。通过变分法,获得了积分空间每个点的三个速度分量的欧拉特征方程,对欧拉特征方程离散化即可在积分空间建立一线性稀疏方程组。采用变分迭代法对此线性稀疏方程组进行求解即可获得三维速度场,据此采用积分最小化法建立了标量图像测速图像处理系统。还介绍了四维标量场(三维空间加一维时间)的图像采集原理,并采用DNS数据对标量图像测速处理系统进行了数值检验,检验结果表明标量图像测速技术所求解的速度场和DNS精确解之间在结构上是十分相似的,标量图像测速可以正确地提取速度场。

基于修正Hung-Turner投影的快速信源数检测算法

空间信源数检测是阵列信号处理的关键问题之一,常用的信源数检测算法需要计算采样协方差矩阵的特征值,该文提出一种基于改进Hung-Turner投影的多目标信源数快速检测算法,该算法根据采样协方差矩阵估计误差的渐进分布特性确定一个判断门限,利用该门限实现GS正交化次数的自动确定,从而完成对信源数的检测。该算法无需对采样协方差矩阵的特征值分解运算,计算复杂度低,检测性能好,计算机仿真证明了算法的正确性和有效性。

基于前后向协方差矩阵投影的信源数估计算法

针对均匀线阵的信源数估计问题,提出了一种基于前向-后向采样协方差矩阵正交投影的多目标信源数快速估计算法。该算法将经过酉变换后的前向-后向采样协方差矩阵的列矢量做Gram-Schmidt(GS)正交化,并将正交化后矢量的模值与一个自适应判决门限做比较来估计信源个数。该判决门限根据阵列采样协方差矩阵估计误差的渐近分布特性推导得到。计算机仿真证明了该算法的正确性和有效性。

城市大气中污染物扩散的施密特数研究

借助反问题方法对风洞实验工况选取不同施密特数进行数值模拟试验，分析比较了不同施密特数时街道峡谷内各个观测点的数值模拟数据和风洞实验数据．研究结果表明，城市街道内大气污染物扩散的施密特数为0．7～0．8．

自然通风建筑内空气流动和污染物扩散的数值模拟

数值模拟了单体自然通风建筑模型内的空气流动和污染物扩散,考察了紊流施密特数Sct对污染物模拟值的影响。结果表明,选取的3种紊流模型对时均流速和紊动能的模拟值和风洞试验值基本一致,标准k-ε模型与realizable k?ε模型模拟的流场较相似,其浓度场结果也基本相同,当Sct为0.8~1.0时,模拟值和试验值吻合得最好。由于RNG k-ε模型对地面污染源附近的时均流动模拟不准确,导致其浓度模拟值和试验值相差较大,因此,选取合理的Sct时,应基于准确的流动模拟,而不能仅考察浓度模拟值和试验值的吻合程度。

正交混合态的局域分辨

考虑混合态的局域精确分辨,利用混合态的Schmidt数分析混合态的局域分辨,证明正交混合态为乘积态或Schmidt数之和不大于整个Hilbert空间的维数是局域分辨的必要条件及任意两个混合正交乘积态可以局域分辨.

固体火箭高温高压复杂燃气系统的扩散系数及其相似准则数计算

为了解决固体火箭推进剂高温高压燃气输运系数难以实验测量和理论预估的实际问题,考虑燃气中含有H_(2)O、HCl、SO_(2)等强极性组分和H_(2)等轻质组分,通过大量文献实例验证,归纳了适于上述组分及其混合物在高温高压条件下的扩散系数计算方法,并计算了典型双基推进剂、复合改性双基推进剂和复合推进剂三种主要固体推进剂燃气在不同温度(1500~3800 K)和压强(8~20 MPa)下的扩散系数和输运准则数(施密特数和路易斯数),得到了固体火箭发动机燃气扩散系数随温度和压强变化的幂指数函数规律(典型双基推进剂燃气的扩散系数随温度变化的幂指数为1.64655、典型复合改性双基推进剂和典型复合推进剂为1.62952),以及路易斯数、施密特数的典型取值(典型双基推进剂燃气的施密特数为0.772、路易斯数为0.91,典型复合改性双基推进剂燃气的施密特数为0.675、路易斯数为0.9,典型复合推进剂燃气的施密特数为0.74、路易斯数为0.83)。这对于促进高温高压气体混合物输运性质的深入研究、火箭发动机燃烧及其内外流动仿真,均具有重要的实际应用意义。该方法没有考虑凝聚相对输运性质的影响。