SIMULATION OF NOx FORMATION IN TURBULENT SWIRLINGCOMBUSTION USING A USM TURBULENCE—CHEMISTRY MODEL

A unified second-order moment (USM) turbulence-chemistry model for simulating Nox formation in turbulent combustion is proposed. All of correlations, including the correlation of the reaction-rate coefficient fluctuation with the concentration fluctuation, are closed by the transport equations in the same form. This model discards the approximation of series expansion of the exponential function or the approximation of using the product of several 1-D PDF‘s instead of a joint PDF. It is much simpler than other refined models, such as the PDF transport equation model and the condi-tional moment closure model. The proposed model is used to simulate methane-air swirling turbulent combustion and Nox formation. The prediction results are in good agreement with the experimental results.     

燃烧室两相流场亚网格燃烧模型的研究

在三维任意曲线坐标系下采用不同的亚网格燃烧模型对环形燃烧室火焰筒气液两相湍流瞬态反应流进行大涡模拟．计算中所采用的数学度模型有：k方程亚网格尺度模型估算亚网格湍流黏性；热通量辐射模型估算辐射换热，分别采用亚网格EBU燃烧模型（E-A model）、亚网格二阶矩输运方程模型（SOM）和亚网格二阶矩代数模型（SOM-A）估算化学反应速率．并在非交错网格系统下气相采用SIMPLE算法和混合差分格式求解，液相采用Lagrange处理，并用PSIC算法对其进行求解．通过实验结果和计算结果的比较，表明在三维任意曲线坐标系下对燃烧室火焰简两相湍流油雾燃烧流场进行大涡模拟，3种不同的亚网格燃烧模型都能真实反映两相湍流化学反应流流动及实际燃烧过程，而采用亚网格二阶矩输运方程模型稍优于其他两种亚网格燃烧模型．     

Large-eddy structures of turbulent swirling flows and methane-air swirling diffusion combustion

Turbulent swirling flows and methane-air swirling diffusion combustion are studied by large-eddy simulation (LES) using a Smagorinsky-Lilly subgrid scale turbulence model and a second-order moment (SOM) SGS combustion model, and also by RANS modeling using the Reynolds Stress equation model with the IPCM+wall and IPCM pressure-strain models and SOM combustion model. The LES statistical results for swirling flows give good agreement with the experimental results, indicating that the adopted subgrid-scale turbulence model is suitable for swirling flows. The LES instantaneous results show the complex vortex shedding pattern in swirling flows. The initially formed large vortex structures soon break up in swirling flows. The LES statistical results of combustion modeling are near the experimental results and are as good as the RANS-SOM modeling results. The LES results show that the size and range of large vortex structures in swirling combustion are different from those of isothermal swirling flows, and the chemical reaction is intensified by the large-eddy vortex structures. The project supported by the Special Funds for Major State Basic Research (G-1999-0222-07). The English text was polished by Keren Wang.     

湍流燃烧数值模拟研究的综述

对湍流燃烧数值模拟的研究进行了综合评述,其中涉及直接数值模拟（ＤＮＳ）、大涡模拟（ＬＥＳ）、随机涡模拟、概率密度函数输运方程模拟、条件矩模型、简化概率密度函数模型、关联矩模型以及基于简单物理概念的一些唯象模型等几个重要方面．对全面了解湍流燃烧数值模拟的研究现状及前景提出了看法．     

Analysis of Mixing Models for use in Simulations of Turbulent Spray Combustion

The present study concerns the investigation of different mixing models for use in the transported probability density function (PDF) modeling of turbulent (reacting) spray flows. The modeling of the turbulent mixing and other characteristic scalar variables such as gas enthalpy using transported (joint) PDFs has become an important method to describe turbulent (reacting) spray flows since the evaporation process causes the PDF of the mixture fraction to deviate from the widely used β function, which is typically used in models for turbulent gas flows. In the PDF transport equation, the molecular mixing does not appear in closed form so that modeling strategies are required. For gas combustion, the interaction-by-exchange-with-the-mean (IEM) model, the modified Curl (MC) model, and the Euclidean minimum spanning tree (EMST) models are used. More recently, a new mixing model, the PSP model, which is based on parameterized scalar profiles has been developed. The present study focuses on the use and analysis of the IEM, MC and PSP models for turbulent spray flames. For this purpose, the models are reconsidered with respect to the evaporation process that must be included and evaluated if spray combustion is considered. For model evaluation, turbulent ethanol/air spray flames are simulated, and the results are compared to experimental data by A. Masri, University of Sydney, Australia.     

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.     

Acetone Droplet Behavior in Reacting and Non Reacting Turbulent Flow

Acetone droplet characteristics in reacting and non-reacting turbulent flow are predicted and compared to experimental data. Investigations are conducted to study the effects of surrounding environment properties on the velocities, dispersion, and evaporation of a relatively volatile spray fuel that featured a wide range of Stokes numbers. The simulations are performed in the framework of Reynolds Averaged Navier Stokes equations along with the Eulerian-Lagrangian approach in which 12 different classes of the dispersed phase. The phase transition is modeled by the Langmuir-Knudsen law that accounts for non equilibrium effects based on a consistent determination of the molar mass fraction on the droplet surfaces. For the droplet dispersion, the Markov sequence model is improved by adding a correction drift term to the fluid fluctuation velocity at the parcel position along the droplet trajectory. This correction term aimed at accounting for the non-homogeneity effects in the turbulent flow. The combustion is captured using the Bray-Moss-Libby model that is extended to account for the partially premixed spray combustion. The chemistry is described with the flamelet model using a recent detailed reaction mechanism that involves 84 species and 409 reactions for which the Lewis number is not set to the unity. Mean droplet velocities for reacting and non-reacting test cases are compared with experimental data. Good agreement is observed. The spray is interacting with the nozzle edge developing new classes and relatively dense region. Hence the RMS-velocities close to the nozzle exit plan demonstrate discrepancies. The droplets group combustion effect is found to be important in the modeling of the burning velocity which influences the flame propagation. Reasonable agreements between the numerical and the experimental results are also observed in the spray flux and temperature profiles.     

Partial-average-based equations of incompressible turbulent flow

This paper presents a detailed study of incompressible turbulent flow based on a newly developed statistical partial average scheme. As the ensemble average is taken on two groups of turbulent fluctuations separately, the partial average scheme is able to capture the first-order statistical moment of the fluctuation field, providing valuable information in addition to what have been known in the past from the conventional Reynolds average. The first-order statistical moment serves as the foundation in formulating theories of orthotropic turbulence and a momentum transfer chain in the modeling of second-order correlation terms, and eventually leads to a complete set of equations of incompressible turbulent flow. Without any empirical coefficients, the same set of the equations is used to simulate statistical mean behaviors and coherent structures of various benchmark turbulent flows. The simulated results are in good agreement with experimental data.     

Laminar and turbulent burning velocities of propane in spherical vessels

Laminar and turbulent burning velocities of C₃H₈/air mixtures under moderately elevated temperature and pressure conditions have been determined experimentally using spherical combustion bombs. The results are reported here and the effects of temperature, pressure, turbulence intensity and stoichiometric ratio are included. The results obtained are compared with those of other researchers. The laminar burning velocity obtained from the pressure-time curves without compensation for the reaction zone thickness is lower than those determined using burners. A reaction zone thickness correction which reduces the difference is suggested and this relies on an assessment based on the different histories found experimentally when different initial temperatures were used for the isentrope through the standard state. For mixtures with initially low turbulence levels, both the turbulent burning velocity and the burning velocity ratio, turbulent to laminar, increase as the combustion progresses. The rate of increase becomes larger with increase in the initial and instantaneous turbulence intensity, temperature and stoichiometric ratio. Deviation from the Damköhler relationship is noted.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Three-dimensional Linear Eddy Modeling of a Turbulent Lifted Hydrogen Jet Flame in a Vitiated Co-flow

A new methodology for modeling and simulation of reactive flows is reported in which a 3D formulation of the Linear Eddy Model (LEM3D) is used as a post-processing tool for an initial RANS simulation. In this hybrid approach, LEM3D complements RANS with unsteadiness and small-scale resolution in a computationally efficient manner. To demonstrate the RANS-LEM3D model, the hybrid model is applied to a lifted turbulent N₂-diluted hydrogen jet flame in a vitiated co-flow of hot products from lean H₂/air combustion. In the present modeling approach, mean-flow information from RANS provides model input to LEM3D, which returns the scalar statistics needed for more accurate mixing and reaction calculations. Flame lift-off heights and flame structure are investigated in detail, along with other characteristics not available from RANS alone, such as the instantaneous and detailed species profiles and small-scale mixing.     

视密度加权的时平均统一二阶矩两相湍流模型

在气粒两相湍流的双流体模型中,颗粒相的视（表观）密度是有脉动的,在时平均的统一二阶矩（USM）模型中出现了和颗粒数密度或视密度脉动有关的项和方程,使模型方程比较复杂。实际上,用LDV或PDPA测量的流体（用小颗粒代表）和颗粒速度都是颗粒数加权平均的结果。因此,在视密度加权平均基础上推导两相湍流模型更为合理。通过推导和封闭了视密度加权平均的统一二阶矩模型（MUSM）方程组,改进了两相速度脉动关联的封闭,并引入了颗粒遇到的气体脉动速度及其输运方程。MUSM模型可以减少所用方程数,节省计算量。视密度加权平均的统一二阶矩两相湍流模型是一种对原有时间平均的统一二阶矩模型和改进和发展。     

Subgrid Modeling of Turbulent Premixed Flames in the Flamelet Regime

Large eddy simulation (LES) models for flamelet combustion are analyzed by simulating premixed flames in turbulent stagnation zones. ALES approach based on subgrid implementation of the linear eddy model(LEM) is compared with a more conventional approach based on the estimation of the turbulent burning rate. The effects of subgrid turbulence are modeled within the subgrid domain in the LEM-LES approach and the advection (transport between LES cells) of scalars is modeled using a volume-of-fluid (VOF) Lagrangian front tracking scheme. The ability of the VOF scheme to track the flame as a thin front on the LES grid is demonstrated. The combined LEM-LES methodology is shown to be well suited for modeling premixed flamelet combustion. The geometric characteristics of the flame surfaces, their effects on resolved fluid motion and flame-turbulence interactions are well predicted by the LEM-LES approach. It is established here that local laminar propagation of the flamelets needs to be resolved in addition to the accurate estimation of the turbulent reaction rate. Some key differences between LEM-LES and the conventional approach(es) are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamic coefficient evaluation for an algebraic subgrid stress model

Static model coefficients for an algebraic subgrid stress (SGS) model are determined using a dynamic approach, based on results from simulations of isotropic decaying turbulence. The study was motivated by the discrepancies in energy transfer predictions using the previously documented coefficients (Bhushan and Warsi, Int. J. Numer. Meth. Fluids 2005; 49 : 489–519). The discrepancies are identified to be due to inconsistent filter functions used in the analytic estimates and the simulations. The study emphasizes that SGS model development should use filter functions compatible with those inherent in CFD application solvers. The dynamic approach predicts consistent model and transfer coefficients for different grid resolutions and is judged to be a reliable basis for model coefficient adjustments. The predicted Leonard's stress coefficient and associated energy transfer coefficients agree very well with the analytic estimates using a Gaussian/cutoff combination filter. This suggests that the modeling of Leonard's stress term using a truncated Taylor series expansion is robust and may not benefit significantly from dynamic modeling. Validation simulations were performed for turbulent channel flow at Re_τ = 180 and 590. The dynamic approach was found to be reliable only for the lower log‐layer of the Re_τ = 590 case, where the scale invariance condition was satisfied. Nonetheless, in this narrow range, the model and transfer coefficients compare well with the isotropic case. The static coefficient algebraic model with new adjusted coefficients shows improved predictions compared with the previous coefficients, for both isotropic decaying turbulence and channel flow cases. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling of a Bluff-Body Nonpremixed Flame using a Coupled Radiation/Flamelet Combustion Model

A coupled radiation/flamelet combustion modelling technique is applied to the simulation of a bluff-body flame. Radiation heat transfer is incorporated into the laminar flamelet model for turbulent combustion through the enthalpy defect. A new method is developed for generating flamelet library with enthalpy defect. The radiation within the flame is modelled using a raytracing approach based on the discrete transfer method. The predicted results are compared with the reported experimental data. Comparison shows that the effects of radiative heat transferr on the temperature and major species are small for the flame considered. However, a significant improvement in the prediction of OH is achieved when radiation heat transfer is included. This revised version was published online in July 2006 with corrections to the Cover Date.     

Validation of a novel very large eddy simulation method for simulation of turbulent separated flow

The paper describes the validation of a newly developed very LES (VLES) method for the simulation of turbulent separated flow. The new VLES method is a unified simulation approach that can change seamlessly from Reynolds‐averaged Navier–Stokes to DNS depending on the numerical resolution. Four complex test cases are selected to validate the performance of the new method, that is, the flow past a square cylinder at Re = 3000 confined in a channel (with a blockage ratio of 20%), the turbulent flow over a circular cylinder at Re = 3900 as well as Re = 140,000, and a turbulent backward‐facing step flow with a thick incoming boundary layer at Re = 40,000. The simulation results are compared with available experimental, LES, and detached eddy simulation‐type results. The new VLES model performs well overall, and the predictions are satisfactory compared with previous experimental and numerical results. It is observed that the new VLES method is quite efficient for the turbulent flow simulations; that is, good predictions can be obtained using a quite coarse mesh compared with the previous LES method. Discussions of the implementation of the present VLES modeling are also conducted on the basis of the simulations of turbulent channel flow up to high Reynolds number of Re_τ = 4000. The efficiency of the present VLES modeling is also observed in the channel flow simulation. From a practical point of view, this new method has considerable potential for more complex turbulent flow simulations at relative high Reynolds numbers. Copyright © 2013 John Wiley & Sons, Ltd.     

球形封闭容器内一个简单的煤粉燃烧爆炸模型

在分析了大量球形封闭容器内煤粉燃烧爆炸实验数据基础上，考虑了煤粉燃烧爆炸机理所涉及的湍流燃烧、相变、各种化学反应动力学过程等复杂因素，并且对球形封闭容器内由于煤粉混合不均匀造成的燃烧不充分给予了考虑，得到了球形封闭容器内煤粉燃烧爆炸特征的数值计算结果，计算的压力－时间曲线与实验结果符合较好。     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

Development of an Analytical <Emphasis Type="Italic">β</Emphasis>-Function PDF Integration Algorithm for Simulation of Non-premixed Turbulent Combustion

Among many presumed-shape pdf approaches for modeling non-premixed turbulent combustion, the presumed β-function pdf is widely used in the literature. However, numerical integration of the β-function pdf may encounter singularity difficulties at mixture fraction values of Z = 0 or 1. To date, this issue has been addressed by few publications. The present study proposes the Piecewise Integration Method (PIM), an efficient, robust and accurate algorithm to overcome these numerical difficulties with the added benefit of improving computational efficiency. Comparison of this method to the existing numerical integration methods shows that the PIM exhibits better accuracy and greatly increases computational efficiency. The PIM treatment of the β-function pdf integration is first applied to the Burke–Schumann solution in conjunction with the k − ε turbulence model to simulate a CH₄/H₂ bluff-body turbulent flame. The proposed new method is then applied to the same flow using a more complex combustion model, the laminar flamelet model. Numerical predictions obtained by using the proposed β-function pdf integration method are compared to experimental values of the velocity field, temperature and species mass fractions to illustrate the efficiency and accuracy of the present method.     

Flow Physics of a Bluff-Body Swirl Stabilized Flame and their Prediction by Means of a Joint Eulerian Stochastic Field and Tabulated Chemistry Approach

In the frame of this work a transported joint scalar probability density function (PDF) method is combined with the flamelet generated manifolds (FGM) tabulated chemistry approach for large eddy simulation (LES) modeling of a three-dimensional turbulent premixed swirl burner. This strategy accounts for the turbulence-chemistry interaction at reasonable computational costs. At the same time, it allows the usage of detailed chemistry mechanisms for the creation of the chemical database. The simulation results obtained are comparatively assessed along with complementary measurements. Furthermore, transient and time-averaged data are used to provide insight into the flow physics of the bluff-body swirl stabilized flame considered. The sensitivity of the results to different modeling approaches regarding the predicted flame shape and its dynamics is also investigated, where the implemented approach is compared with the well-established artificially thickened flame (ATF) combustion model. Consequently, the investigation conducted in this work aims to provide a complete picture on the ability of the proposed combustion model to reproduce the flow conditions within complex bluff-body swirl stabilized flames.     

Application of the PITM Method Using Inlet Synthetic Turbulence Generation for the Simulation of the Turbulent Flow in a Small Axisymmetric Contraction

We investigate the turbulence modeling of second moment closure used both in RANS and PITM methodologies from a fundamental point of view and its capacity to predict the flow in a low turbulence wind tunnel of small axisymmetric contraction designed by Uberoi and Wallis. This flow presents a complex phenomenon in physics of fluid turbulence. The anisotropy ratio of the turbulent stresses τ ₁₁/τ ₂₂ initially close to 1.4 returns to unity through the contraction, but surprisingly, this ratio gradually increases to its pre-contraction value in the uniform section downstream the contraction. This point constitutes the interesting paradox of the Uberoi and Wallis experiment. We perform numerical simulations of the turbulent flow in this wind tunnel using both a Reynolds stress model developed in RANS modeling and a subfilter scale stress model derived from the partially integrated transport modeling method. With the aim of reproducing the experimental grid turbulence resulting from the effects of the square-mesh biplane grid on the uniform wind tunnel stream, we develop a new analytical spectral method of generation of pseudo-random velocity fields in a cubic box. These velocity fields are then introduced in the channel using a matching numerical technique. Both RANS and PITM simulations are performed on several meshes to study the effects of the contraction on the mean velocity and turbulence. As a result, it is found that the RANS computation using the Reynolds stress model fails to reproduce the increase of anisotropy in the centerline of the channel after passing the contraction. In the contrary, the PITM simulation predicts fairly well this turbulent flow according to the experimental data, and especially, the “return to anisotropy” in the straight section of the channel downstream the contraction. This work shows that the PITM method used in conjunction with an analytical synthetic turbulence generation as inflow is well suited for simulating this flow, while allowing a drastic reduction of the computational resources.