On the Effect of Vortex Grid Density in the Vortex-in-cell Simulation of Mixing Layers

The two-dimensional vortex-in-cell method is used in the simulation of a spatially growing mixing layer at a high Reynolds number. Criteria, showing that the vortex grid density plays a role in obtaining a converged solution, are presented. Numerical experiments are conducted to test the criteria by varying the number of vortices and the grid sizes. The effects on the momentum thickness and on the peak values of the root-mean-square velocity fluctuations, and negative cross-stream correlation are discussed in terms of the vortex grid density.     

Large Eddy Simulation (2D) of a Reacting Plane Mixing Layer Using Filtered Density Function Closure

The filtered density function (FDF) is implemented for a two-dimensional, large eddy simulation (LES) of a gas phase, spatially developing, reacting and non-reacting, constant-density, plane mixing layer in a flow regime prior to the mixing transition where the flow is mainly two-dimensional. The unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities following the FDF approach. In the derived FDF transport equation, the effect of chemical reactions appears in a closed form. The Lagrangian Monte Carlo scheme is used to solve the FDF transport equation. The applicability and performance of the FDF for LES of a reacting plane mixing layer are assessed by comparisons with experimental measurements. In non-reacting flow, the calculated mean streamwise velocity profiles and mean mixture fraction profiles relax to self-similarity, which is in satisfactory agreement with the measurements. In reacting flow, the FDF calculation provided a satisfactory accuracy in comparison with measurements of mean reactant and product concentration. The increase in the total amount of product formation in the flip case demonstrates the asymmetric characteristics of the entrainment and mixing characteristics in the mixing layer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Passive Scalar Transport in a Turbulent Mixing Layer

This paper describes a combined experimental and numerical study of scalar transport in spatially developing, two-stream, turbulent mixing layers with velocity ratios of approximately 2:1. The experimental mixing layer was created by an S-shaped splitter plate mounted in a wind tunnel, and the concentration field was realized by releasing incense smoke into the high-speed side boundary layer above the splitter plate. Simultaneous measurements of the velocity and concentration fields were performed. A 12-sensor hot-wire probe was used to measure the velocity field and its gradients, while the concentration field was recorded with digital photographs of the laser-illuminated smoke. In parallel, a large-eddy simulation (LES) of the spatially developing mixing layer was carried out. Auxiliary turbulent boundary layer LES were used to provide high quality inflow boundary conditions for the velocity and concentration fields. By synchronizing the velocity and concentration measurements, concentration fluxes were also determined. Octant analysis based on the sign combinations of the velocity and concentration fuctuations was performed on the flux data to investigate the scalar transport processes. It was found that octants compatible with mean gradient transport of the scalar contribute most to the scalar fluxes. Conditional planar averages of scalar and momentum fluxes were obtained to determine their spatial distribution with respect to the organized roller and rib vortices of the mixing layer, and distinct patterns were observed. The simulation provided additional insight about the flow and scalar flux distribution topology. This topology was found to be partially compatible with simple models of roller and rib vortices that transport the scalar in a mean gradient sense.     

Mixing in Isotropic Turbulence with Scalar Injection and Applications to Subgrid Modeling

A new technique for injecting scalar fluctuations in a DNS of isotropic turbulence is presented. It is used to study statistically steady states associated with different levels of mixing. The results are analysed in terms of spectra and PDF, and they are used as a database to investigate the effect of the filtering operation that is performed in LES. It is shown that the PDF of the scalar is substantially affected by the filtering operation. It is also shown that the Cook and Riley [1] subgrid model allows reconstruction of a PDF which is in fairly good agreement with the unfiltered DNS results. The consequences of estimating the scalar subgrid variance by scale similarity assumptions are investigated. It is found that the results are improved by a local determination of the model constant. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling of the Joint PDF of a Scalar and Its Gradient in Turbulent Mixing

A joint probability distribution function of a conservative scalar (mixture fraction) and its gradient is predicted numerically. Statistical moments of this function are compared to their approximations, direct numerical simulation data, and also to the results obtained by simplified models for a conditional rate of scalar dissipation, the surface density function, and the one-point PDF of scalar fluctuation under homogeneous isotropic turbulence. The results allow to evaluate the performance of existing statistical micromixing models.     

A Field Monte Carlo Formulation for Calculating the Probability Density Function of a Single Scalar in a Turbulent Flow

The probability density function (PDF) formulation of one scalar field undergoing diffusion, turbulent convection and chemical reaction is restated in terms of stochastic fields. These fields are smooth in space as they have a length scale similar to that of the PDF. Their evolution is described by a set of stochastic partial differential equations, which are solved using a finite volume scheme with a stochastic source term. The application of this methodology to a particular flow is shown first for a linear source term, with exact analytical solution for the mean and standard deviation, and then for a nonlinear reaction.     

Non-Equilibrium Mixing of Turbulence Scales Using a Continuous Hybrid RANS/LES Approach: Application to the Shearless Mixing Layer

A new subgrid-scale (SGS) model based on partially integrated transport method (PITM) is applied to the case of a turbulent spectral non-equilibrium flow created by the mixing of two turbulence fields of differing scales: the shearless mixing layer. The method can be viewed as a continuous hybrid RANS/LES approach. In this model the SGS length scale is no longer given by the size of the discretization step, but is dynamically estimated using an additional transport equation for the dissipation rate. The results are compared to those corresponding to the classical model of Smagorinsky and to the experimental data of Veeravalli and Warhaft. A method for creating an anisotropic analytical pseudo-random field for inflow conditions is also proposed. This approach based on subgrid-scale transport modelling combined with anisotropic inlet conditions gives better results for the prediction of the shearless mixing layer.     

可压缩混合层中细光束畸变效应的实验研究

利用双曝光CCD相机成像技术,对小直径光束穿越可压缩混合层流场存在的大尺度结构特性及其引起的气动光学效应进行了实验研究。实验研究结果表明:在不同对流马赫数(Mc=0.17,0.45)下,可压缩混合层中的大尺度结构形状不同,因而具有不同的折射率分布场,从而导致光束投影发生了不同程度的变形和偏移。利用光束质心的概念定量分析了不同对流马赫数下光束偏移和抖动的统计特性。统计结果表明在高对流马赫数下光束投影的偏移量减小,光束沿流场展向的平均偏移角度减小,但摆动幅度加大。     

Study of a Mixing Layer Formed by a Supersonic Main Stream of Air and a Co-Flowing Supersonic Helium Jet

The development of large-scale organised motions in a compressible mixing layer is studied experimentally using holographic interferometry, pressure and turbulence measurements. The mixing layer was formed behind the base of a parallel strut with a Mach 2 air main stream and a co-flowing two-dimensional slot jet (aspect ratio = 45) of helium at a Mach number of 1.2. The mixing layer exhibited highly organised vortical structures which were elongated and inclined approximately 45–50° to the flow direction. The mixing layer showed a linear growth and the mean velocity data indicated self-similar behaviour at sufficiently downstream distances. The results have shown that the thickness of the primary boundary layer has a strong influence on the growth and structure of the mixing layer. This revised version was published online in July 2006 with corrections to the Cover Date.     

气固两相混合层二维涡配对的数值研究

采用双向耦合模型中的速度耦合模型,数值模拟了气固两相混合层中涡的配对、合并过程,文中采用拟谱方法对流场进行了直接数值模拟,用Lagrange模型跟踪固粒,结果发现,在双向耦合过程中Stokes数仍然是重要的参数,但不是唯一影响流场的参数,流场的发展还与固粒的体积浓度、固粒的相对密度以及固粒大小等因素有关。固粒抑制流场的发展,阻碍涡的配对、合并,加快了涡量的扩散;小St数的固粒仍然跟随流体运动,大St数的固粒趋向于低涡量区的趋势减弱。     

Linear-Eddy Model Formulated Probability Density Function and Scalar Dissipation Rate Models for Premixed Combustion

A tabulated, pseudo-turbulent Probability Density Function (PDF) model for premixed combustion is proposed. The Linear-Eddy Model (LEM) is used to construct the PDFs for a temperature-based progress variable in a premixed, turbulent methane/air V-flame produced by the Cambridge slot burner. As a second case study, the LEM PDFs are similarly compared to PDFs extracted from Direct Numerical Simulations (DNS) of a turbulent premixed flame. LEM demonstrates the ability to reproduce the salient features from experimental and DNS PDFs; moreover, it is able to better capture turbulent effects than previously suggested laminar flamelet PDF models. The Scalar Dissipation Rate (SDR) for premixed combustion is likewise investigated. The stochastic nature of LEM enables it to mimic the overall behaviors of turbulent reactions inexpensively and qualitatively. Crucially, LEM appears to be well suited for the preprocessing tabulation of PDF and SDR models for a number of premixed combustion simulation strategies.     

Decomposition of Mixing Layer Turbulence into Coherent Structures and Background Fluctuations

The eduction of coherent structures from cross-wire rake data in a fully turbulent incompressible mixing layer confirms the feasibility of a decomposition of a turbulent flow field, first suggested by Farge, as non-periodic non-equilibrium coherent structures interacting with a ‘thermalized’ broad-band turbulence. A simple wavelet coefficient decimation algorithm and orthogonalization yields non-periodic dominant flow structures and a background field that has a Gaussian distribution of velocities at the centerline. The coherent structures are classified in terms of their topology. The non-coherent background field has flat energy spectra and normal distribution of velocity components. Most background field statistics depend only weakly on the type of structure on which they are superposed. It may be possible to adapt existing subgrid scale models to this decomposition. This revised version was published online in July 2006 with corrections to the Cover Date.     

混合层中粒子扩散的实验研究

本文应用流动显示和LDA测量,对混合层中粒子的扩散问题进行了实验研究。结果表明：粒子的扩散强烈地依赖于St数,具有较小St的粒子的扩散近似地与流体示踪粒子相同,随着St的增大,扩散角度增大,也就是说粒子扩散加快,并且随着粒子惯性的增大,它对湍流脉动的响应将会减弱。     

添加聚合物对混合层流场特性影响的实验研究

叙述了适用于粘弹性流体混合层流场的实验装置的设计和研制．采用二维激光多普勒系统对混合层流场进行了测量，得到了平均速度剖面、动量厚度、湍流脉动强度、雷诺应力等一些流场的基本特征量．结果表明，混合层中加入聚合物后流场将有较大的变化，同时也说明本文所研制的实验装置满足实验的要求．     

混合层中柱状粒子取向分布函数的研究

数值模拟了平面流固混合层中柱状粒子在平面取向的分布函数，提出了描述流场中某点直粒子取向占优程度的参数Dψ的分析，说明在混合层中心区域粒子的取向排列是有序的，在混合层相邻两个大涡之间的区域，是粒子最可几角占优程度最高的地方，而且最可几取向就是沿流场的拉伸方向，说明流场的拉伸作用及方向对粒子的取向排列具有重要影响。与其它模型相比，粒子取向的分布函数模型能定量反映流场大涡对粒子取向控制的强弱程度。     

Mixing Measurements in a Supersonic Expansion-Ramp Combustor

This paper reports results on molecular mixing for injection via an expansion-ramp into a supersonic freestream with M ₁ = 1.5. This geometry produces a compressible turbulent shear layer between an upper, high-speed “air” stream and a lower, low-speed “fuel” stream, injected through an expansion-ramp at α = 30° to the high-speed freestream. Mass injection is chosen to force the shear layer to attach to the lower guide wall. This results in part of the flow being directed upstream, forming a recirculation zone. Employing the hypergolic hydrogen-fluorine chemical reaction and pairs of “flip” experiments, molecular mixing is quantified by measuring the resulting temperature rise. Initial experiments established the fast-chemistry limit for this flow in terms of a Damköhler number (Da). For Da ≥ 1.4, molecularly mixed fluid effectively reacts to completion. Parameters varied in these experiments were the measurement station location, the injection velocity of the (lower) “fuel” stream, the stoichiometry for the flip experiments, and the density ratio of the fuel and air streams. As expected, mixing increases with increasing distance from the injection surface. The mixed fluid fraction increases by 12% when changing the fuel-to-air stream density ratio from 1 to 0.2. Comparisons with measurements at subsonic (high-speed) “air” stream velocities show that the trend of decreasing mixing with increasing speed documented in free-shear layer flows is also encountered in these flows. The current geometry produces higher mixing levels than do free shear layers.     

随机振动载荷作用下结构Von Mises应力过程的研究

随机振动载荷作用下结构的多轴疲劳分析非常复杂，利用Von Mises应力准则将多轴应力响应转换为单轴应力是一条简单而有效的途径，其关键问题是Von Mises应力概率密度函数的确定。本文提出了Von Mises应力过程近似服从Weibull分布的假设，同时给出了确定Weibull参数的方法，为进一步直接利用Von Mises应力进行结构多轴疲劳分析创造了条件。