Multiple-plane-jet turbulent mixing analysis via a kinetic theory approach

Turbulent mixing of a single jet, twin jets, triple jets and multiple jets is synthetically analysed in this paper. Chung's kinetic theory of turbulence and a modified Green's function are employed to solve this problem. The probability density function of fluid elements in the velocity space of multiple plane jets and the corresponding turbulence correlations are revealed in this analysis. The calculated results are found to be in good agreement with the available experimental data. The internal physical structure of the turbulent mixing mechanism seems better understood via the kinetic theory approach. The present study provides the fundamentals for theoretical understanding of multiple-jet turbulent mixing and further application to multiple-jet turbulent combustion analysis.     

大速差射流预燃室内三维回流两相湍流的数值模拟

本文由多流体两相流模型、气相湍流κ-ε模型和颗粒湍流代数模型出发,成功地模拟了真实形状大速差射流预燃室中三维湍流回流两相流动,得到了这类复杂的气固两相流中不同纵横截面上气相速度场、颗粒速度场及浓度场和两相湍流度场的分布,并且获得了与实验定性一致的合理结果,揭示了预燃室中气固两相流动与混合的主要物理特征,探讨了大速差射流技术稳焰和强化燃烧的两相流动机理。     

大速差射流预燃室内三维回流两相湍流的数值模拟

本文由多流体两相流模型、气相湍流κ-ε模型和颗粒湍流代数模型出发,成功地模拟了真实形状大速差射流预燃室中三维湍流回流两相流动,得到了这类复杂的气固两相流中不同纵横截面上气相速度场、颗粒速度场及浓度场和两相湍流度场的分布,并且获得了与实验定性一致的合理结果,揭示了预燃室中气固两相流动与混合的主要物理特征,探讨了大速差射流技术稳焰和强化燃烧的两相流动机理。     

Conditional Source-Term Estimation as a Method for Chemical Closure in Premixed Turbulent Reacting Flow

A Conditional Source-term Estimation (CSE) model is used to close the mean reaction rates for a turbulent premixed flame. A product-based reaction progress variable is introduced as the conditioning variable for the CSE method. Different presumed probability density function (PDF) models are studied and a modified version of a laminar flame-based PDF model is proposed. Improved predictions of the variable distribution are obtained. The conditional means of reactive scalars are evaluated with CSE and compared to the direct numerical simulation (DNS). The mean reaction rates in a turbulent premixed flame are evaluated with the CSE model and the presumed PDFs. Comparison of the CSE closure method to DNS shows promising results. This paper was presented at the 2nd ECCOMAS Thematic Conference on Computational Combustion.     

An Experimental Investigation of the Turbulence Structure of a Lifted H2/N2 Jet Flame in a Vitiated Co-Flow

Measurements of mean velocity components, turbulent intensity, and Reynolds shear stress are presented in a turbulent lifted H₂/N₂ jet flame as well as non-reacting air jet issuing into a vitiated co-flow by laser doppler velocimetry (LDV) technique. The objectives of this paper are to obtain a velocity data base missing in the previous experiment data of the Dibble burner and so provide initial and flow field data for evaluating the validity of various numerical codes describing the turbulent partially premixed flames on this burner. It is found that the potential core is shortened due to the high ratio of jet density to co-flow density in the non-reacting cases. However, the existence of flame suppressed turbulence in the upstream region of the jet dominates the length of potential core in the reacting cases. At the centreline, the normalized axial velocities in the reacting cases are higher than the non-reacting cases, and the relative turbulent intensities of the reacting flow are smaller than in the non-reacting flow, where a self-preserving behaviour for the relative turbulent intensities exists at the downstream region. The profiles of mean axial velocity in the lifted flame distribute between the non-reacting jet and non-premixed flame both in the axial and radial distributions. The radial distributions of turbulent kinetic energy in the lifted flames exhibit a change in distributions indicating the difference of stabilisation mechanisms of the two lifted flame. The experimental results presented will guide the development of an improved modelling for such flames.     

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.     

Flame propagation in the turbulent flow of a burning mixture

The propagation of a flame in the turbulent flow of a burning mixture is analyzed theoretically. An equation is derived for the gas temperature and velocity probability distributions. The solutions of this equation are analyzed and the rate of flame propagation is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–15, September–October, 1976.The author wishes to thank V. A. Sabel'nikova for critical comments.     

A Non-Adiabatic Flamelet Progress�CVariable Approach for LES of Turbulent Premixed Flames

A progress variable/flame surface density/probability density function method has been employed for a Large Eddy Simulation of a CH₄/Air turbulent premixed bluff body flame. In particular, both mean and variance of the progress variable are transported and subgrid spatially filtered gradient contributes to model the flame surface density (that introduces the effect of the subgrid flame reaction zone) and to presume a probability density function (that introduces the effect of subgrid fluctuations on chemistry). Chemistry is preliminarly tabulated in terms of laminar premixed flames and enthalpy is included as a new coordinate in their tabulation to take into account heat losses in the flowfield. Then, the PDF is used to build a turbulent flamelet library. The filtered mass, momentum, enthalpy and scalar equations mentioned above are integrated by an explicit scheme using finite differences, 2nd?Corder accurate in space and third order in time, over a cylindrical non-uniform grid using a staggered mesh. The bluff-body geometry is modelled by using the Immersed Boundary Method. The numerical predictions are compared with the available experimental data.     

Large eddy simulation of vertical turbulent jets under JONSWAP waves

The effect of random waves on vertical plane turbulent jets is studied numerically and the mechanism behind the interaction of the jet and waves is analyzed. The large eddy simulation method is used and the σ-coordinate system is adopted. Turbulence is modeled by a dynamic coherent eddy model. The σ-coordinate transformation is introduced to map the irregular physical domain with a wavy free surface and an uneven bottom onto a regular computational domain. The fractional step method is used to solve the fil...     

Application of PDF Modeling to Swirling and Nonswirling Turbulent Jets

The turbulence modeling in probability density function (PDF) methods is studied through applications to turbulent swirling and nonswirling co-axial jets and to the temporal shear layer. The PDF models are formulated at the level of either the joint PDF of velocity and turbulent frequency or the joint PDF of velocity, wave vector, and turbulent frequency. The methodology of wave vector models (WVMs) is based on an exact representation of rapidly distorted homogeneous turbulence, and several models are constructed in a previous paper [1]. A revision to a previously presented conditional-mean turbulent frequency model [2] is constructed to improve the numerical implementation of the model for inhomogeneous turbulent flows. A pressure transport model is also implemented in conjunction with several velocity models. The complete model yields good comparisons with available experimental data for a low swirl case. The individual models are also assessed in terms of their significance to an accurate solution of the co-axial jets, and a comparison is made to a similar assessment for the temporal shear layer. The crucial factor in determining the quality of the co-axial jet simulations is demonstrated to be the proper specification of a parameter ratio in the modeled source of turbulent frequency. The parameter specification is also shown to be significant in the temporal shear layer.     

Analysis of high-order velocity moments in a strained channel flow

In the current study, model expressions for fifth-order velocity moments obtained from the truncated Gram-Charlier series expansions model for a turbulent flow field probability density function are validated using data from direct numerical simulation (DNS) of a planar turbulent flow in a strained channel. Simplicity of the model expressions, the lack of unknown coefficients, and their applicability to non-Gaussian turbulent flows make this approach attractive to use for closing turbulent models based on the Reynolds-averaged Navier-Stokes equations. The study confirms validity of the model expressions. It also shows that the imposed flow deformation improves an agreement between the model and DNS profiles for the fifth-order moments in the flow buffer zone including when the flow reverses its direction. The study reveals sensitivity of particularly odd velocity moments to the grid resolution. A new length scale is proposed as a criterion for the grid generation near the wall and in the other flow areas dominated by high mean velocity gradients when higher-order statistics have to be collected from DNS.     

Method for verification of the self-consistency of experimental data for free turbulent flows of an incompressible liquid

A direct method is proposed for verification of the quality of the method of measurements of the characteristics of free self-similar turbulent flows (the longitudinal mean velocity and the components of the tensor of the turbulent stresses), consisting in the direct substitution of experimentally obtained distributions of the longitudinal mean velocity and the turbulent stresses into the Reynolds equations. Using the proposed method, a lack of consistency is observed in the experimental data for the self-similar sections of plane [1] and axisymmetric [2] jets in a flooded space.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–164, November–December, 1978.The authors thank V. L. Zimont for his useful evaluation of the results of the work and for his advice, which were used in preparing this article for publication.     

入口速度比对射流拟序结构的影响

为了深入了解湍流流动机理以及湍流拟序结构发现过程的影响因素，本文采用大涡模拟方法对不同入口射流伴流速度比的平面湍射流流动进行了数值模拟。采用分步投影法求解动量方程，亚格子项采用标准Smagorinsky亚格子模式模拟，压力泊松方程采用修正的循环消去法快速求解，空间方程采用二阶精度的差分格式，在时间方向上采用二阶精度的显式差分格式。模拟结果给出了平面射流中湍流拟序结构的瞬态发展演变过程，分析了入口速度比对射流拟序结构发展演化过程及宏观流场形态的影响。为进一步研究射流拟序结构及其在湍流流动中的作用提供了基础。     

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.     

Correlation coefficients of the fluctuating density in turbulent premixed flames

 Two-point density measurements by laser induced Rayleigh scattering are used in this study to fully characterise the scalar field in a Bunsen type turbulent premixed flame. The two points are separated within the flame brush in the axial or radial directions. Correlation coefficients are obtained by comparing the evolution of one-point density fluctuations in time or the two-point density fluctuations in both space and time. Time and length scales of the scalar field, and the mean convection velocity of the turbulent scalar structures are deduced from these correlation coefficients. Time scales are calculated from the auto-correlation coefficients, length scales are determined from the space correlation coefficients and the mean convection velocity of the scalar structures in the axial direction is deduced from the space–time correlation coefficients. The relevance of these results for analysing and modelling the structure of turbulent premixed flames is discussed. Received: 30 April 1996 / Accepted: 2 September 1997     

Large Eddy Simulations of the Darmstadt Turbulent Stratified Flames with REDIM Reduced Kinetics

Turbulent stratified combustion is often found in practical combustion devices, however, for large eddy simulations (LES) of it is still a challenge. In the present work, LES of the Darmstadt turbulent stratified flame (TSF) cases are conducted. In total, one isothermal flow case A-i2 and four reacting cases with different combinations of stratification and shear, i.e., A-r, C-r, E-r, G-r cases, are simulated. The employed sub-grid scale (SGS) combustion model is the REDIM-PFDF model, in which the chemical kinetics is reduced into a two-dimensional chemistry look-up table by the reaction-diffusion manifolds (REDIM) method, which performs a model reduction based on the coupling of the chemical kinetics with molecular transport. The fluctuation of scalars within the LES filter volume is modeled by the presumed filtered density function (PFDF). The overall good agreement of the statistics of velocity, temperature and species with the experimental data demonstrates the capability of the REDIM-PFDF model for TSF. Additionally, the probability distributions of the alignment angle, α, between the reaction layer and mixing layer, are analyzed in detail. It is shown that the probability distributions of the alignment angel vary with the axial distance from the jet nozzle. It also reveals that, with a stronger turbulence, the stratification effect can be weakened and the probability difference for finding ‘back-supported’ and ‘front-supported’ flame modes tends to decrease.     

Experimental study of an impinging jet with different swirl rates

A stereo PIV technique using advanced pre- and post-processing algorithms is implemented for the experimental study of the local structure of turbulent swirling impinging jets. The main emphasis of the present work is the analysis of the influence of swirl rate on the flow structure. During measurements, the Reynolds number was 8900, the nozzle-to-plate distance was equal to three nozzle diameters and the swirl rate was varied from 0 to 1.0. For the studied flows, spatial distributions of the mean velocity and statistical moments (including triple moments) of turbulent pulsations were measured.

The influence of the PIV finite spatial resolution on the measured dissipation rate and velocity moments was analyzed and compared with theoretical predictions. For this purpose, a special series of 2D PIV measurements was carried out with vector spacing up to several Kolmogorov lengthscales.

All terms of the axial mean momentum and the turbulent kinetic energy budget equations were obtained for the cross-section located one nozzle diameter from the impinging plate. For the TKE budget, the dissipation term was directly calculated from the instantaneous velocity fields, thereby allowing the pressure diffusion term to be found as a residual one. It was found that the magnitude of pressure diffusion decreased with the growth of the swirl rate. In general, the studied swirling impinging jets had a greater spread rate and a more rapid decay in absolute velocity when compared to the non-swirling jet.     

Properties of vortices in the self-similar turbulent jet

Instantaneous, two-dimensional velocity measurements were conducted in the axial plane of a self-similar turbulent axisymmetric jet. The velocity fields were high-pass filtered to expose the vortical structures. An automated method was used to identify the radial and axial coordinates of the vortex centers and rotational sense, and to measure their size, circulation, vorticity, and energy. New insights into turbulent jets are obtained by plotting statistical distributions for vortex properties as functions of Reynolds number and radial position. While the probability of finding a vortex is uniform up to the edge of the jet, the strongest eddies in the high-pass filtered field occur near the jet axis. The average circulation is directly proportional to the vortex size. The Reynolds number strongly affects the average vorticity, circulation, and energy of the eddies. However, the normalized curves show a good collapse implying that the jet is indeed self-similar. Results for the left and right half-planes of the jet are also presented. Interestingly, we find that contrary to customary drawings of jet flows, a substantial number of both clockwise and counter-clockwise rotating eddies exist on both sides of the jet axis, with almost equal numbers of oppositely rotating vortices close to the jet axis. Further, the disparity in the number of oppositely rotating eddies in each half-plane increases with the eddy size. Nevertheless, these results are consistent with the well-known radial vorticity distribution of axisymmetric jets.     

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.