Optimization of Viscous Mixing in a Two-Dimensional Cavity Transfer Mixer

Following up ideas put forward by J.M. Ottino and colleagues, the possibility of designing a computational tool to optimize the mixing of viscous fluids in industrial devices is studied. It is shown that an efficient method to characterize and quantify a mixing process is to apply the statistical measures introduced by Danckwerts (e.g., intensity of segregation and scale of segregation) on the coarse-grained density distribution of points in Poincaré sections and advection patterns, that can be obtained by tracking the positions of marked fluid elements numerically. This method is not computationally excessively costly and, as is demonstrated here, can be applied easily to experimental dye advection studies. The model system used is the Stokes flow in a two-dimensional cavity transfer mixer: two rectangular cavities which are periodically driven by a solid wall and by the passage of the cavities over each other. This system shares with many industrial devices the complexity that the geometry of the flow is time-dependent. These changes in the geometry of the flow impose difficulties on the techniques of calculating the fluid velocity field (a boundary element method) and the advection of marked fluid elements. Ways of overcoming these difficulties are described.     

Experimental 3D Analysis of the Large Scale Behaviour of a Plane Turbulent Mixing Layer

A new structure education method is proposed for representing the three dimensional large scale structures from hot wires measurement data. Due to the limited number of hot wire probes that can be used simultaneously, we firstly have to optimise the spatial location of sensors in order to detect large scale coherent structures. For such a purpose a detailed analysis of the 3D space-time flow organisation is given with particular emphasis on the full two point correlation tensor of the velocity field. Secondly, several procedures are developed in order to reconstruct instantaneous 3D velocity field on any finer and larger mesh than the experimental one from the limited available experimental information. The particular case of a spatially developing turbulent plane mixing layer is investigated. We then show that Stochastic Estimation and Proper Orthogonal Decomposition lead to a satisfactory reconstruction preserving the 3D coherent character of the flow. Finally, this reconstructed velocity field provides a 3D space-time representation of the large scale structures in a streamwise section of the flow and can then be used as realistic turbulent inflow condition for Large Eddy Simulations.     

Mixing of hot gases in an axisymmetric channel with a pre-swirled flow

The problem of the mixing of hot turbulent gases in an axisymmetric channel with a lateral surface of arbitrary shape and a pre-swirled flow is considered. The flowfields and the temperature and concentration distributions are calculated for various inlet conditions.     

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.     

Computational Modelling of Turbulent Mixing in Confined Swirling Environment Under Constant and Variable Density Conditions

A high-intensity swirling flow in a model combustor subjected to large density variations has been examined computationally. The focus is on the Favre-averaged Navier–Stokes computations of the momentum and scalar transport employing turbulence models based on the differential second-moment closure (SMC) strategy. An updated version of the basic, high-Reynolds number SMC model accounting for a quadratic expansion of both the pressure–strain and dissipation tensors and a near-wall SMC model were used for predicting the mean velocity and turbulence fields. The accompanied mixing between the annular swirling air flow and the central non-swirling helium jet was studied by applying three scalar flux models differing mainly in the model formulation for the pressure-scalar gradient correlation. The computed axial and circumferential velocities agree fairly well with the reference experiment [So et al., NASA Contractor Report 3832, 1984; Ahmed and So, Exp. Fluids 4 (1986) 107], reproducing important features of such a weakly supercritical flow configuration (tendency of the flow core to separate). Although the length at which the mixing was completed was reproduced in reasonable agreement with the experimental results, the mixing activity in terms of the spreading rate of the shear/mixing layer, that is its thickness, was somewhat more intensive. Prior to these investigations, the model applied was validated by computing the transport of the passive scalar in the non-swirling (Johnson and Bennet, Report NASA CR-165574, UTRC Report R81-915540-9, 1981) and swirling (Roback and Johnson, NASA Contractor Report 168252, 1983) flow in a model combustor.     

三维动态混合过程界面追踪模拟与表征

建立了振动力场作用下单螺杆挤出机计量段物理模型,在Stokes假设基础上,得到了螺槽内牛顿流体速度分布的解析解。采用自适应步长4阶Runge-Kutta方法,对动态混合过程进行三维数值模拟追踪,计算了示踪剂构形依时演变及界面拉伸速率,对动态混合过程进行了实时表征。结果表明,低频振动时,螺槽内的混合仍然是规则的层流混合,混合效果有待于进一步提高,指出了进一步提高混合效果的措施。     

DNS of Mixing and Reaction of Two Species in a Turbulent Channel Flow: A Validation of the Conditional Moment Closure

We consider the chemical reaction in a turbulent flow for the case that the time scale of turbulence and the time scale of the reaction are comparable. This process is complicated by the fact that the reaction takes place intermittently at those locations where the species are adequately mixed. This is known as spatial segregation. Several turbulence models have been proposed to take the effect of spatial segregation into account. Examples are the probability density function (PDF) and the conditional moment closure (CMC) models. The main advantage of these models is that they are able to parameterize the effects of turbulent mixing on the chemical reaction rate. As a price several new unknown terms appear in these models for which closure hypothesis must be supplied. Examples are the conditional dissipation 〈 χ ∣ φ 〉, the conditional diffusion 〈 κ ∇² φ ∣ u, φ 〉 and the conditional velocity 〈 u ∣ φ 〉. In the present study we investigate these unknown terms that appear in the PDF and CMC model by means of a direct numerical simulation (DNS) of a fully developed turbulent flow in a channel geometry. We present the results of two simulations in which a scalar is released from a continuous line source. In the first we consider turbulent mixing without chemical reaction and in the second we add a binary reaction. The results of our simulations agree very well with experimental data for the quantities on which information is available. Several closure hypotheses that have been proposed in the literature, are considered and validated with help of our simulation results. 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．     

在ESS中嵌入滤波器实现转子电场恒速的系统设计方法

对于空心大球转子静电陀螺仪,转速接近静电支承系统(ESS)的剪切频率,一般采用磁场恒速控制方法,因而介绍了一种电场恒速控制方法,通过在支承电路中加入滤波器,来提高支承系统的力矩系数,从而利用支承系统构成了恒速控制系统。实验结果表明,系统的稳定性满足要求,恒速精度优于0.1Hz。     

Effect of Streamline Curvature on Intensity of Streamwise Vortices in the Mixing Layer of Supersonic Jets

The structure of supersonic nonisobaric jets with Mach numbers M_a = 1 and 2 is considered experimentally to find the effect of streamline curvature on the evolution of streamwise vortices in the mixing layer. The spatial development of steady streamwise vortices in the mixing layer of supersonic jets is considered. A method for generation of steady streamwise vortices by applying microroughness elements of controlled size onto the inner surface of the nozzle is developed. Radial profiles and azimuthal variations of total pressure are obtained; the mixinglayer thickness and the curvature of streamlines in supersonic jets are determined. A significant effect of microroughness elements of prescribed shape located on the nozzle surface on the behavior of total pressure in the mixing layer of supersonic jets, as compared to natural disturbances, is obtained.     

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。     

弹性接触问题的常刚度迭代方法及其加速

通过引入接触间隙荷载，在荷载项中反映接触状态变化的影响，避免了重新形成接触刚度矩阵，构造了弹性接触问题的常刚度迭代格式。然后借助于不动点迭代的Steffensen加速技术给出了一种求解弹性接触问题的常刚度迭代加速算法。文中最后给出两个算例表明了本文方法的有效性。     

次谐波对混合层中拟序涡合并过程影响的数值研究

本文用拟谱方法对混合层二涡、三涡的合并规律进行了数值研究,分析了基波和交谐波之间相位差对涡合并过程的影响,并对此进行了解释。计算结果表明：二涡合并有配地和撕裂两种形式,且涡的完全通过撕裂合并的现象仅在相位差为π/2时出现;三涡合并有三种形式。通过计算可见,通过施加多级次谐波并改变它们之间的相位差可以主动控制拟序涡的发展和演变。     

Mixing Layer on the Lee Side of an Obstacle

Twolayer miscible flow above an uneven bottom is considered. A mathematical model in the shallowwater approximation is constructed for the development of a turbulent layer between homogeneous layers of different density in a twolayer channel flow over a local obstacle. The influence of the mixing process on the formation of an initial segment of the steadystate densitystratified flow on the leeward side of the obstacle is studied.     

Research on Coherent Structures in a Mixing Layer of the Fene-P Polymer Solution

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An Experimental Study of the Near-Field Mixing Characteristics of a Swirling Jet

The present experimental investigation is devoted to the mixing characteristics of a passive scalar in the near-field region of a moderately swirling jet issuing from a fully developed axially rotating pipe flow. Instantaneous streamwise and azimuthal velocity components as well as the temperature were simultaneously accessed by means of a combined X-wire and cold-wire probe. The results indicate a modification of the turbulence structures to that effect that the swirling jet spreads, mixes and evolves faster compared to its non-swirling counterpart. The high correlation between streamwise velocity and temperature fluctuations as well as the streamwise passive scalar flux are even more enhanced due to the addition of swirl, which in turn shortens the distance and hence time needed to mix the jet with the ambient air.     

Investigation of the Nitrogen Shock Wave Structure on the Basis of Trajectory Calculations of the Molecular Interaction

The shock wave structure in a diatomic gas is investigated using the direct statistical simulation (Monte-Carlo) method. The energy exchange between translational and rotational degrees of freedom (TR-exchange) is calculated by solving the dynamic problem of the interaction between rigid-rotator molecules within the framework of classical mechanics. The density profiles calculated are compared with the experimental data and on this basis the nitrogen rotational relaxation time is estimated. The possibility of using simplified intermolecular interaction models, namely, the variable-diameter sphere model employed together with a phenomenological consideration of the TR-exchange, is studied. Gasdynamic parameter profiles in the shock wave are analyzed. Simple approximations of the velocity gradient and translational and rotational temperature profiles are obtained on the basis of a parametric calculation of the shock wave structure. This makes it possible approximately to describe the gasdynamic parameter profiles in terms of elementary functions.