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.     

Effects of the Similarity Model in Finite-Difference LES of Isotropic Turbulence Using a Lagrangian Dynamic Mixed Model

A Lagrangian dynamic formulation of the mixed similarity subgrid (SGS) model for large-eddy simulation (LES) of turbulence is proposed. In this model, averaging is performed over fluid trajectories, which makes the model applicable to complex flows without directions of statistical homogeneity. An alternative version based on a Taylor series expansion (nonlinear mixed model) is also examined. The Lagrangian models are implemented in a finite difference code and tested in forced and decaying isotropic turbulence. As comparison, the dynamic Smagorinsky model and volume-averaged formulations of the mixed models are also tested. Good results are obtained, except in the case of low-resolution LES (32³) of decaying turbulence, where the similarity coefficient becomes negative due to the fact that the test-filter scale exceeds the integral scale of turbulence. At a higher resolution (64³), the dynamic similarity coefficient is positive and good agreement is found between predicted and measured kinetic energy evolution. Compared to the eddy viscosity term, the similarity or the nonlinear terms contribute significantly to both SGS dissipation of kinetic energy and SGS force. In order to dynamically test the accuracy of the modeling, the error incurred in satisfying the Germano identity is evaluated. It is found that the dynamic Smagorinksy model generates a very large error, only 3% lower than the worst-case scenario without model. Addition of the similarity or nonlinear term decreases the error by up to about 50%, confirming that it represents a more realistic parameterization than the Smagorinsky model alone.     

Modeling and Simulation of Effects of Turbulence on Vaporization, Mixing and Combustion of Liquid-Fuel Sprays

The objective of this work is twofold. Firstly, the effects of turbulence intensity variations on the turbulent droplet dispersion, vaporization and mixing for non-reacting sprays (with and without swirl) are pointed out. Secondly, the effects of the coupling of the turbulence modulation with external parameters, such as swirl intensity, on turbulent spray combustion are analyzed in configurations of engineering importance. This is achieved by using advanced models for turbulence, evaporation and turbulence modulation implemented into FASTEST-LAG3D-codes: (1) To highlight the influence of turbulence modulation on some spray properties, a thermodynamically consistent modulation model has been considered besides the standard assumption and the well known Crowe's model. For turbulent droplet dispersion, we rely on the Markov-sequence formulation. (2) In order to characterize phase transition processes ongoing on droplets surfaces, a non-equilibrium evaporation model shows better agreement with experiments in comparison with the quasi-equilibrium-based evaporation models often used. (3) The results of turbulence intensity variations reveal the existence of a limited range out of which the increase or decrease of the turbulence intensity affects no more the efficiency of the heat and mass transfer. A derived characteristic number, a vaporization Damkhöler number, possesses a critical value which separates two different behavior regimes with respect to the turbulence/droplet vaporization interactions. (4) Under reacting conditions, it is shown how the evaporation characteristics, mixing rate and combustion process are strongly influenced by swirl intensity and turbulence modulation. In particular, the turbulence modulation modifies the evaporation rate, which in turn influences the mixing and the species concentration distribution. In the case under investigation, it is demonstrated that this effect cannot be neglected for low swirl intensities (Sw.Nu. ≤ 1) in the region far from the nozzle, and close to the nozzle for high swirl number intensities. In providing these particular characteristics, a reliable control of the mixing of gaseous fuel and air in evaporating and reacting sprays, and a possible optimization of the mixing process can tentatively be achieved.     

Vortex-In-Cell and Probability Density Function Approach for a Passive Scalar Field in a Mixing Layer

A Reynolds-averaged simulation based on the vortex-in-cell (VIC) and the transport equation for the probability density function (PDF) of a scalar has been developed to predict the passive scalar field in a two-dimensional spatially growing mixing layer. The VIC computes the instantaneous velocity and vorticity fields. Then the mean-flow properties, i.e. the mean velocity, the root-mean-square (rms) longitudinal and lateral velocity fluctuations, the Reynolds shear stress, and the rms vorticity fluctuations are computed and used as input to the PDF equation. The PDF transport equation is solved using the Monte Carlo technique. The convection term uses the mean velocities from the VIC. The turbulent diffusion term is modeled using the gradient transport model, in which the eddy diffusivity, computed via the Boussinesq's postulate, uses the Reynolds shear stress and gradients of mean velocities from the VIC. The molecular mixing term is closed by the modified Curl model.

The computational results were compared with two-dimensional experimental results for passive scalar. The predicted turbulent flow characteristics, i.e. mean velocity and rms longitudinal fluctuations in the self-preserving region, show good agreement with the experimental measurements. The profiles of the mean scalar and the rms scalar fluctuations are also in reasonable agreement with the experimental measurements. Comparison between the mean scalar and the mean velocity profiles shows that the scalar mixing region extends further into the free stream than does the momentum mixing region, indicating enhanced transport of scalar over momentum. The rms scalar profiles exhibit an asymmetry relative to the concentration centerline, and indicate that the fluid on the high-speed side mixes at a faster rate than the fluid on the low-speed side. The asymmetry is due to the asymmetry in the mixing frequency cross-stream profiles. Also, the PDFs have peaks biased toward the high-speed side.     

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.     

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.     

Report on Turbulence and Mixing in Geophysical Flows II

We describe the presentations at the international meeting/workshop on Mixing in Geophysical Flows that took place at Vilanova i la Geltru, near Barcelona during the 20, 21 and 22nd of March 1997. There were more than 100 participants from 20 countries with 66 oral and poster presentations covering experimental and theoretical aspects of rotating and stratified fluids as well as field observations. The main topics discussed at the workshop were stratified flows, rotating stratified flows, gravity waves, instabilities and mixing, convection, experiments and numerical simulations of Geophysical flows and turbulent mixing. The papers are summarised in this report giving a state-of-the-art overview of present research in geophysical turbulent mixing.     

Modeling of the turbulent motion of particles in a vertical channel

The results of modeling of the statistical parameters of a turbulent particle motion in a vertical plane channel are presented. The model is based on a kinetic equation for the particle velocity probability density function. The results are compared with direct numerical simulation.     

Particle Clustering in Isotropic Turbulent Flow

A kinetic statistical model for describing the dispersion and clustering of heavy particles in homogeneous isotropic turbulence is presented. The model developed is used for calculating the relative velocities and the radial distribution function of a pair of particles in a steady suspension. The results obtained are compared with the known data obtained by direct numerical simulation.     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 2. Flows with heat transfer and combustion

The objective of this part of the paper is to summarize the information concerning the authors' works in the field of simulation of two-phase gas-particle turbulent flows with heat transfer and combustion. A kinetic equation had been derived for the probability density function (PDF) of the particle velocity, temperature, and mass distributions in turbulent flows. This PDF equation is used for the construction of the governing conservation equations of mass, momentum, and heat transfer in the dispersed particle phase.The numerical scheme incorporates two-phase fluid dynamics, convective and radiative heat transfer, and combustion. The proposed models have been applied to the calculation of various particle-laden turbulent flows in jets, combustion and gasification chambers, and furnaces.     

Modeling of Liquid Fuel Injection, Evaporation and Mixing in a Gas Turbine Burner Using Large Eddy Simulations

The interaction of turbulence, temperature fluctuation, liquid fuel transport, mixing and evaporation is studied by using Large Eddy Simulations (LES). To assess the accuracy of the different components of the methods we consider first isothermal, single phase flow in a straight duct. The results using different numerical methods incorporating dynamic Sub-Grid-Scale (SGS) models are compared with DNS and experimental data. The effects of the interactions among turbulence, temperature fluctuation, spray transport, evaporation and mixing of the gaseous fuel are studied by using different assumptions on the temperature field. It has been found that there are strong non-linear interactions among temperature-fluctuation, evaporation and turbulent mixing which require additional modeling if not full LES is used. The developed models and methods have been applied to a gas turbine burner into which liquid fuel is injected. The dispersion of the droplets in the burner is described. This revised version was published online in July 2006 with corrections to the Cover Date.     

White in Time Scalar Advection Model as a Tool for Solving Joint Composition PDF Equations

A rapidly decorrelating velocity field model is used to derive stochastic partial differential equations (SPDE) allowing one to compute the modeled one-point joint probability density function of turbulent reactive scalars. Those SPDEs are shown to be hyperbolic advection/reaction equations. They are dealt with in a generalized sense, so that discontinuities in the scalar fields can be treated. The Eulerian Monte Carlo (EMC) method thus defined is coupled with a RANS solver and applied to the computation of a turbulent premixed methane flame over a backward facing step.     

扩展重要抽样法及其在平尾转轴可靠性分析中的应用

提出了扩展重要抽样法，用以计算结构系统的多个失效模式中含有不全相同基本随机变量时的系统失效概率。通过构造扩展重要抽样法的抽样密度函数，给出该方法失效概率的估计值，以及其方差和变异系数的计算公式。并将此方法用于某型飞机平尾转轴的可靠性分析，算例结果表明其优越性。     

壁面湍流标度律的PIV实验研究

利用高分辨率、高帧率PIV系统对湍流边界层内的自相似标度律在不同的壁面距离的具体表达形式进行了实验研究。在动量损失雷诺数（Reθ=2167）下测量平板湍流边界层内的二维瞬时速度场。应用小波分析和传统统计学方法,在垂直于平板的平面内,对不同法向位置的自相似的标度律的具体形式及其随尺度的变化情况进行考察,并与已知的She-leveque（简称SL）标度律进行比较分析。结果表明,越接近壁面,结构函数的概率密度曲线尾部越宽,表现出逐渐增强的间歇性;并且随着壁面距离的减小,ESS标度律曲线与SL标度律曲线之间的差别也就越大,而新形式标度律曲线则与SL标度律曲线的差别逐渐减小。在提取的结构尺度一样时,结构函数的标度指数随法向位置的不同变化不大,但是随着提取结构尺度的增加,两种形式的标度律适用的尺度范围也在逐渐增大。     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows

This paper presents a review of authors' collective works in the field of two-phase flow modeling done in the past few decades. The paper is aimed at the construction of mathematical models for simulation of particle-laden turbulent flows. A kinetic equation was obtained for the probability density function (PDF) of the particle velocity distribution in turbulent flows. The proposed kinetic equation describes both the interaction of particles with turbulent eddies of the carrier phase and particle-particle collisions. This PDF equation is used for the derivation of different schemes describing turbulent momentum transfer in the dispersed particle phase. The turbulent characteristics of the gaseous phase are calculated on the basis of the k - turbulence model with a modulation effect of particles on the turbulence.

The constructed models have been applied to the calculation of various two-phase gas-particle turbulent flows in jets and channels as well as particle deposition in tubes and separators. For validating the theoretical and numerical results, a wide range of comparisons with experimental data from Russian and foreign sources has been done.     

Statistical model of collisions of bidisperse particles in an anisotropic turbulent flow

A statistical model for describing the motion and collisions of a bidisperse mixture of particles in anisotropic turbulent flows is presented. The model is based on a kinetic equation for the particle velocity probability density function (PDF). The results are compared with the data of a direct numerical simulation of the sedimentation of a bidisperse mixture of particles under the action of the gravity force.     

Differential and algebraic models for the second moments of particle velocity and temperature fluctuations in turbulent flows

Differential and algebraic models are constructed for the dispersed-phase turbulent stresses and heat fluxes and for the mixed moments of the velocity and temperature fluctuations in the continuous and dispersed phases. The models are based on a kinetic equation for the joint probability density of the particle velocity and temperature in an anisotropic turbulent flow. The results are compared with the available direct numerical simulation (DNS) data.     

Transition to Turbulence in the Boundary Layer on a Plate in the Presence of a Negative Free-Stream Pressure Gradient

Transition to turbulence in the boundary layer on a flat plate is investigated numerically for an incompressible fluid flow with a given negative free-stream pressure gradient. The transition is investigated using the three-parameter turbulence model developed by the authors. The calculation results are compared with the available experimental data.