条件矩模型模拟湍流扩散燃烧

对条件矩模型模拟湍流扩散燃烧进行了初步的研究.在条件矩模型中,标量的统计是以混合分数为条件的,条件平均使得非线性化学反应源项可以在一阶条件下被封闭.模拟结果和美国Sandia国家实验室的实验结果对比表明:对温度、主要组分浓度的预报结果是令人满意的,NO浓度的预报在趋势上也符合实验结果.误差分析表明,提高标量耗散率的预报精度和二阶条件矩模型都将有助于推动条件矩模型的发展.     

Noise Correction and Length Scale Estimation for Scalar Dissipation Rate Measurements in Turbulent Partially Premixed Flames

A recently developed conditional sampling-based method for correcting noise effects in scalar dissipation rate measurements and for estimating the extent of resolution of the dissipation rate is employed to analyze the data obtained in turbulent partially premixed (Sandia) flames. The method uses conditional sampling to select instantaneous fully resolved local scalar fields, which are analyzed to determine the measurement noise and to correct the Favre mean, conditional, and conditionally filtered dissipation rates. The potentially under-resolved local scalar fields, also selected using conditional sampling, are corrected for noise and are analyzed to examine the extent of resolution. The error function is used as a model for the potentially under-resolved local scalar to evaluate the scalar dissipation length scales and the percentage of the dissipation resolved. The results show that the Favre mean dissipation rate, the mean dissipation rate conditional on the mixture fraction, and dissipation rate filtered conditionally on the mixture fraction generally are well resolved in the flames. Analyses of the dissipation rates filtered conditionally on the mixture fraction and temperature show that the length scale increases with temperature, due to lower dissipation rate and higher diffusivity. The dissipation rate is well resolved for temperatures above 1,300 K but is less resolved at lower temperatures, although the probability of very low temperature events is low. To fully resolve these rare events the sample spacing needs to be reduced by approximately one half. The present study further demonstrates the effectiveness of the new noise correction and length scale estimation method.     

Implementation Issues of the Conditional Moment Closure Model in Large Eddy Simulations

Different ways of transferring information regarding the mixture fraction, its sub-grid scale variance and the scalar dissipation rate are examined in terms of a Large Eddy Simulation (LES)/Conditional Moment Closure (CMC) calculation. In such a simulation, information must be transferred from a fine LES grid to a usually coarser CMC grid. Different options of calculating conditional and unconditional quantities in the CMC resolution are assessed by filtering experimental mixture fraction and scalar dissipation rate data at various resolutions. It was found that when a presumed shape for the Filtered Density Function at the CMC resolution is used, special care must be given to the mixture fraction variance. It was also found that the Amplitude Mapping Closure model can be used for the conditional scalar dissipation rate. LES/CMC with detailed chemistry of a bluff-body stabilised burner was performed using two different ways of calculating the turbulent diffusivity. The structure of the flame is realistic, with little difference noticed when using the two diffusivities.     

A-Priori Validation of Scalar Dissipation Rate Models for Turbulent Non-Premixed Flames

The modelling of scalar dissipation rate in conditional methods for large-eddy simulations is investigated based on a priori direct numerical simulation analysis using a dataset representing an igniting non-premixed planar jet flame. The main objective is to provide a comprehensive assessment of models typically used for large-eddy simulations of non-premixed turbulent flames with the Conditional Moment Closure combustion model. The linear relaxation model gives a good estimate of the Favre-filtered scalar dissipation rate throughout the ignition with a value of the related constant close to the one deduced from theoretical arguments. Such value of the constant is one order of magnitude higher than typical values used in Reynolds-averaged approaches. The amplitude mapping closure model provides a satisfactory estimate of the conditionally filtered scalar dissipation rate even in flows characterised by shear driven turbulence and strong density variation.

     

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.     

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.     

On the Relationship Between the Statistics of the Resolved and True Rate of Dissipation of Mixture Fraction

The relationship between the one-point probability-density-function (PDF) of the dissipation rate of mixture fraction fluctuations and the corresponding resolved quantity available in large eddy simulation (LES) is analyzed. The investigation pursues two fronts: an a priori study using direct numerical simulation (DNS), and an analytic development that, using common turbulence physics simplifications, relates the one-point statistics of the resolved and true scalar dissipations. Particularly, the analysis reveals the connection between the multi-point correlations of the mixture fraction gradient and the one-point PDF of the resolved scalar dissipation. A DNS of a temporally evolving shear layer with and without heat release is used to quantify the accuracy of the analytical result. It is verified, both by filtering the DNS and from the theory, that increasing the filter cutoff width reduces the magnitude of the resolved scalar dissipation fluctuations, as expected and observed experimentally. Comparison with DNS indicates that the analytical relationship predicts the behavior of the resolved scalar dissipation PDF well at the center planes of the shear layer, where turbulence is locally more isotropic and homogeneous. Large-scale anisotropy and inhomogeneities in the DNS degrade the accuracy of the approximate analytical result close to the edges of the shear layer. These results may be improved with future investigations to account fully for the missing statistics in LES, which have the potential to allow a more accurate quantification of finite-rate chemistry effects in reacting flows.     

Measurements of the Statistical Distribution of the Scalar Dissipation Rate in Turbulent Axisymmetric Plumes

In this paper we reconsider the high resolution Planar Laser-Induced Fluorescence (PLIF) mixing measurements that were presented in Markides and Mastorakos (Chem. Eng. Sci. 61:2835–2842, 2006). The PLIF experiments were performed in flows created by the continuous injection, with various velocity ratios, of a passive scalar (acetone) from a finite sized round nozzle, into uniform turbulent co-flows confined within a cylindrical tube with a range of turbulent Reynolds numbers. Here, we extend our study of these flows to include an investigation of the Probability Density Functions (PDFs) of the scalar dissipation rate (χ), as well as of the scalar dissipation rate conditional on mixture fraction (χ|ξ). To this effect, we have further processed the resulting data from the earlier work, including an additional correction for density variations in the flow. The results were then reprocessed for the accurate recovery of the spatial gradients of the normalized scalar concentration (ξ), which resulted in direct measurements of χ. All results that are presented in this paper involve the two-dimensional scalar dissipation rate (χ _2D ) evaluated in the plane of imaging, and furthermore, results are only shown and discussed along the centreline of our axisymmetric configuration. The PDFs of χ were calculated and found to deviate slightly from a lognormal distribution, consistent with other published work. Moreover, the PDFs of χ|ξ followed a similar distribution, and showed a similar deviation. This deviation was more pronounced closer to the source and decayed downstream. The ratio of the standard deviation over the mean of χ and χ|ξ increased with streamwise distance and reached values of 2.8 and 1.2 respectively.     

Structure of nonpremixed reaction zones in numerical isotropic turbulence

Results from direct numerical simulation of low heat release, turbulent nonpremixed reacting flows modeled using single-step reactions with constant and temperature-dependent rate laws are discussed, and compared with laminar predictions. The mixture fraction and its dissipation rate are statistically independent in regions of intense reaction, partially supporting a commonly made assumption in flamelet-based models. In the presence of a finite rate reverse reaction, the reaction zone spans the entire range of mixture fraction. The joint pdf of the reactive scalars evolves to an equilibrium that is dictated by a balance between the reactive and mixing fluxes in composition space. When the temperature-dependent rate law is implemented, strain-induced extinction is observed for a Zel'dovich (modified) number of 10. As the ratio of local flow to chemical time scale is decreased below unity, a larger fraction of the flow field experiences this mode of extinction. The critical turbulent scalar dissipation rate is compared with laminar values and asymptotic predictions.The first two authors express their acknowledgment to the donors of The Petroleum Research Fund, administered by the American Chemical Society for partial support of this work through a type G grant. We also acknowledge the Council for Research and Creative Writing at the University of Colorado for providing partial financial support.     

Simulations of Turbulent Non-Premixed Counterflow Flames with First-Order Conditional Moment Closure

Simulations of turbulent CH₄-air counterflow flames are presented, obtained in terms of zero and two-dimensional first-order Conditional Moment Closure (CMC) to study the flame structure and extinction limits. The CMC equation with detailed chemistry is solved without the need for operator splitting, while the accompanying flow field is determined using a commercial CFD software employing a Reynolds stress turbulence model and additional transport equations for the turbulent scalar flux and for the mean scalar dissipation rate. Two detailed chemical mechanisms and different conditional scalar dissipation rate models have been examined and small differences were found.The first-order CMC captures the overall structure of the counterflow flame accurately for the unconditional averages. The calculated conditional averages behave as if the scalar dissipation rate were under-predicted, although a comparison with measurement of the conditional scalar dissipation rate is reasonable. The calculated extinction velocity is found to be much higher than the experimental value, but the trend of increasing extinction velocity with air dilution of the fuel stream is captured well. The discrepancies with the data are mostly attributed to the neglect of conditional fluctuations.     

Sensitivity analysis of LES–CMC predictions of piloted jet flames

The sensitivity of Large Eddy Simulation with Conditional Moment Closure (LES–CMC) simulations of the Sandia piloted jet Flames D and F to various parameters have been investigated. It was found that while an LES grid may sufficiently resolve velocity fields, the conditional scalar dissipation rate obtained may still be affected by grid size due to the calculation of sub-grid scalar dissipation rate, and this can affect the degree of localised extinction predicted. A study of the relative size of the terms in the CMC equation during an extinction/reignition event showed that transport, including in the cross stream direction, plays a key role. The results are sensitive to the choice of inlet boundary conditions as extinction is only observed when the inert-mixing distributions in mixture fraction space are used as inlet conditions for the CMC equation in the primary jet and air jets.     

Some Aspects of Scalar Dissipation

Scalar dissipation is of great importance in the theory and modelling of combustion and other reacting turbulent flows. Measurements of scalar dissipation are found to lack the quality assurance of checks available from the conservation equations. Conditional averages of the scalar dissipation, so important in turbulent reacting flow theory and modelling, have qualitative and quantitative dependences that are very dependent on the details of the flow and mixing conditions. Accordingly, effort needs to focus on viable means of modelling it. Fluctuations of the scalar dissipation about the conditional mean are also important. Research results in this area need to be made more accessible to the combustion scientist. Heat release effects, so important in turbulent premixed combustion, are found to be much less important in non-premixed combustion.     

Lower Bounds on Scalar Dissipation in Bounded Rectilinear Flows

Lower bounds on the scalar dissipation rate in rectilinear flows are found for three sets of constraints. The bounding dissipation rates provide upper bound estimates of the scalar concentration variance. One of the lower bounds on the dissipation rate is close to the dissipation rate assessed from detailed numerical simulation. This proximity enables a simplified model of concentration variance. For a pulse input of solute, the predictions of concentration variance by the simplified model are in agreement with the results of detailed simulation. The large-time bimodality of the concentration variance and its rate of decay observed in the detailed numerical simulations is predicted by the simplified model.     

Possible Effects of Small-Scale Intermittency in Turbulent Reacting Flows

It is now well established that quantities such as energy dissipation, scalar dissipation and enstrophy possess huge fluctuations in turbulent flows, and that the fluctuations become increasingly stronger with increasing Reynolds number of the flow. The effects of this small-scale “intermittenc” on various aspects of reacting flows have not been addressed fully. This paper draws brief attention to a few possible effects on reaction rates, flame extinction, flamelet approximation, conditional moment closure methods, and so forth, besides commenting on possible effects on the resolution requirements of direct numerical simulations of turbulence. We also discuss the likelihood that large-amplitude events in a given class of shear flows are characteristic of that class, and that, plausible estimates of such quantities cannot be made, in general, on the hypothesis that large and small scales are independent. Finally, we briefly describe some ideas from multifractals as a potentially useful tool for an economical handling of a few of the problems touched upon here.     

Measurements of Scalar Variance, Scalar Dissipation, and Length Scales in Turbulent Piloted Methane/Air Jet Flames

One-dimensional (line) measurements of mixture fraction, temperature, and scalar dissipation in piloted turbulent partially premixed methane/air jet flames (Sandia flames C, D, and E) are presented. The experimental facility combines line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence. Simultaneous single-shot measurements of temperature and the mass fractions of all the major species (N₂, O₂, CH₄, CO₂, H₂O, CO, and H₂) are obtained along 7 mm segments with a nominal spatial resolution of 0.2 mm. Mixture fraction, ξ, is then calculated from the measured mass fractions. Ensembles of instantaneous mixture fraction profiles at several streamwise locations are analyzed to quantify the effect of spatial averaging on the Favre average scalar variance, which is an important term in the modeling of turbulent nonpremixed flames. Results suggest that the fully resolved scalar variance may be estimated by simple extrapolation of spatially filtered measurements. Differentiation of the instantaneous mixture fraction profiles yields the radial contribution to the scalar dissipation, χ _r = 2D _ξ(?ξ/?r)², and radial profiles of the Favre mean and rms scalar dissipation are reported. Scalar length scales, based on autocorrelation of the spatial profiles of ξ and χ _r , are also reported. These new data on this already well-documented series of flames should be useful in the context of validating models for sub-grid scalar variance and for scalar dissipation in turbulent flames.     

青藏铁路冻土区环境问题对工程安全可靠性影响

当大涡模拟用于研究化学反应流动时，传统的滤波方法会导致化学反应项不封闭. 为克服这 个困难，发展了条件滤波大涡模拟方法. 在选择适当的条件变量后，条件滤波的化学反 应项可以表达为一个封闭项. 但同时也带来了新的问题：条件滤波耗散或条件滤波扩散项的 不封闭. 为解决这一问题，采用了直接数值模拟方法研究了它们在大小尺度上的统计特 性. 研究结果表明：条件滤波耗散和扩散对于大尺度的依赖主要体现在大尺度标量场中扩散 层结构的影响，同时小尺度脉动的变化几乎与条件滤波扩散无关，而它对条件滤波耗散却显 现出明显的作用. 在构造条件滤波耗散的亚格子模型时，小尺度脉动的作用不容忽视.     

Conditional Moment Closure for Large Eddy Simulations

A conditional moment closure (CMC) based combustion model for large-eddy simulations (LES) of turbulent reacting flow is proposed and evaluated. Transport equations for the conditionally filtered species are derived that are consistent with the LES formulation and closures are suggested for the modelling of the conditional velocity, conditional scalar dissipation and the fluctuations around the conditional mean. A conventional β-probability density distribution of the scalar is used together with dynamic modelling for the sub-grid fluxes. The model is validated by comparison of simulations with measurements of a piloted, turbulent methane-air jet diffusion flame.     

Investigation of Mixing Models and Conditional Moment Closure Applied to Autoignition of Hydrogen Jets

The present paper is focused on performing a thorough investigation of first order Conditional Moment Closure (CMC) including an inhomogeneous turbulent mixing model for the conditional scalar dissipation rate to predict autoignition. Autoignition of a hydrogen and nitrogen fuel mixture in a heated coflow of air is examined. A sensitivity analysis is proposed for the autoignition length with respect to the mixing field, as well as a comparison of the effects of the inhomogeneous turbulent and Amplitude Mapping Closure (AMC) mixing models. The choice of turbulence constants only change predicted ignition length by approximately 5 % when applied to the AMC mixing model. Predictions of ignition length performed by the inhomogeneous model are lower than that of the AMC model by up to 15 %. The current ignition predictions are in reasonable agreement with the experimental data and previous simulation results. Two of the four regimes observed experimentally are reproduced qualitatively. Further improvement may be gained by using large eddy simulation and a gradient model for the conditional velocity in the inhomogeneous turbulent mixing model.     

Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames

The effect of spatial averaging is important for scalar gradient measurements in turbulent nonpremixed flames, especially when the local dissipation length scale is small. Line imaging of Raman, Rayleigh and CO-LIF is used to investigate the effects of experimental resolution on the scalar variance and radial gradient in the near field of turbulent nonpremixed CH₄/H₂/N₂ jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and B) and in piloted CH₄/air jet flames at Reynolds numbers of 13,400, 22,400 and 33,600 (Sandia flames C/D/E). The finite spatial resolution effects are studied by applying the Box filter with varying filter widths. The resulting resolution curves for both scalar variance and mean squared-gradient follow nearly the same trends as theoretical curves calculated from the model turbulence kinetic energy spectrum of Pope. The observed collapse of resolution curves of mean squared-gradient for nearly all studied cases implies the shape of the dissipation spectrum is approximately universal. Fluid transport properties are shown to have no effect on the dissipation resolution curve, which implies that the dissipation length scale inferred from the square gradient is equivalent to the length scale for the scalar dissipation rate, which includes the diffusion coefficient. With the Box filter, the required spatial resolution to resolve 98% of the mean dissipation rate is about one−two times of the dissipation cutoff length scale (analogous to the Batchelor scale in turbulent isothermal flows). The effects of resolution on the variances of mixture fraction, temperature, and the inverted Rayleigh signal are also compared. The ratio of the filtered variance to the true variance is shown to depend nearly linearly on the probe resolution. The inverted Rayleigh scattering signal can be used to study the resolution effect on temperature variance even when the Rayleigh scattering cross section is not constant. The experimental results also indicate that these laboratory scale turbulent jet flames have small effective Reynolds numbers, such that there is some direct interaction of the large (energy containing) and small (dissipative) scalar length scales, especially for the near field case at x/d = 7.5 of the piloted Sandia flames C/D/E.