Lagrangian model simulations of molecular mixing, including finite rate chemical reactions, in a temporally developing shear layer (original) (raw)
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Journal of Fluid Mechanics, 1982
Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows a t high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale inviscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.
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Physical Review E, 2017
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Physics of Fluids, 2001
Understanding the passive reaction of two chemical species in shear-free turbulence with order unity Schmidt number is important in atmospheric and turbulent combustion research. The canonical configuration considered here is the reacting scalar mixing layer; in this problem two initially separated species mix and react downstream of a turbulence generating grid in a wind tunnel. A conserved scalar in this flow is, with some restrictions, analogous to temperature in a thermal mixing layer, and considerable laboratory data are available on the latter. In this paper, results are reported from high resolution, direct numerical simulations in which the evolution of the conserved scalar field accurately matches that of the temperature field in existing laboratory experiments. Superimposed on the flow are passive, single-step reactions with a wide range of activation energies and stoichiometric ratios (r). The resulting data include species concentrations as a function of three spatial dimensions plus time, and statistical moments and spectra of all species. Several aspects of the flow are investigated here with the conclusions that ͑1͒ reactions in which r 1 are more accurately modeled by frozen and equilibrium chemistry limits than are reactions in which rϭ1, ͑2͒ an existing definition of a reduced Damköhler number that includes temperature and stoichiometry effects is a useful measure of reaction rate, and ͑3͒ existing theoretical models for predicting the coherence and phase of fuel-oxidizer cross-spectra and the spectrum of the equilibrium fuel mass fraction when rϭ1 yield accurate predictions.
Proceedings of the Combustion Institute, 2020
For general reacting flows the numerical simulation faces two main challenges. One is the high dimensionality and stiffness of the governing conservation equations due to detailed chemistry, which can be solved by using simplified chemical kinetics. The other one is the difficulty of modeling the coupling of turbulence with thermo-chemical source term. The probability density function (PDF) method allows to calculate turbulent reacting flows by solving the thermal-chemical source term in closed form. Usually, the PDF method for turbulent processes such as mixing processes and the reduction method for chemical kinetics are developed separately. However, coupling of both processes plays an important role for the numerical accuracy. To investigate the importance of coupling between turbulence and simplified chemistry, two different coupling strategies for mixing and reduced chemistry are discussed and tested for the well-known Sandia Flames E and F, in which there is a strong interaction between turbulence and chemical kinetics. The EMST mixing model is chosen for turbulent mixing, while the Reaction-Diffusion Manifolds (REDIMs) is used as simplified chemistry. However, the proposed strategies are also valid for other mixing models and manifold based simplified chemistry.
Direct numerical simulation of a statistically stationary, turbulent reacting flow
Combustion Theory and Modelling, 1999
An inhomogeneous, non-premixed, stationary, turbulent, reacting model flow that is accessible to direct numerical simulation (DNS) is described for investigating the effects of mixing on reaction and for testing mixing models. The mixture-fraction-progress-variable approach of Bilger is used, with a model, finite-rate, reversible, single-step thermochemistry, yielding nontrivial stationary solutions corresponding to stable reaction and also allowing local extinction to occur. There is a uniform mean gradient in the mixture fraction, which gives rise to stationarity as well as a flame brush. A range of reaction zone thicknesses and Damkohler numbers are examined, yielding a broad spectrum of behaviour, including thick and thin flames, local extinction and near equilibrium. Based on direct numerical simulations, results from the conditional moment closure (CMC) and the quasi-equilibrium distributed reaction (QEDR) model are evaluated. Large intermittency in the scalar dissipation leads to local extinction in the DNS. In regions of the flow where local extinction is not present, CMC and QEDR based on the local scalar dissipation give good agreement with the DNS.
Chemical Engineering and Processing: Process Intensification, 2011
a b s t r a c t The way in which reagents are mixed can have a large influence on the product distribution of chemical reactions. To model effects of mixing on various scales on the course of chemical reactions the method of Large Eddy Simulation (LES) of non-premixed, turbulent reactive flows of incompressible fluids is considered in this work. The subgrid modeling of chemical reaction is based on a beta distribution of the mixture fraction in combination with a conditional moment closure based on linear interpolation of local instantaneous reactant concentration values. The predictions obtained with LES are compared with experimental data for fast parallel chemical reactions, the fluid velocity measured using Particle Image Velocity (PIV) technique and the passive tracer concentration measured using the Planar Laser Induced Fluorescence (PLIF) technique. Predictions of the model based on LES are compared as well with results obtained using the non-equilibrium multiple-time-scale mixing model combined with a standard k-ε model and employing similar conditional moment closure as LES, applied, however, at larger scale. All comparisons show a very good performance of the model based on LES.
Mixing of a conserved scalar in a turbulent reacting shear layer
Journal of Fluid Mechanics, 2003
Mixing of a conserved scalar representing the mixture fraction, of primary importance in modelling non-premixed turbulent combustion, is studied by direct numerical simulation (DNS) in strongly turbulent planar shear layers both with and without heat release at a reaction sheet. For high heat release, typical of hydrocarbon combustion, the mixing is found to be substantially different than without heat release. The probability density function of the scalar and the conditional rate of scalar dissipation are affected by the heat release in such a way that the heat release substantially decreases the overall reaction rate. To help clarify implications of the assumptions underlying popular models for interaction between turbulence and chemistry, the local structure of the scalar dissipation rate at the reaction sheet is extracted from the DNS database. The applicability of flamelet models for the rate of scalar dissipation is examined. To assist in modelling, a characteristic length scale is defined, representing the distance around the reaction sheet over which the scalar field is locally linear, and statistical properties of this length scale are investigated. This length scale can be used in studying values of the rate of scalar dissipation that mark the boundary between flames that feel a constant scalar dissipation field and those that do not.
Contribution of different turbulent scales to mixing and reaction between unpremixed reactants
Chemical Engineering Science, 1994
The quality of prediction of the reaction rate from models based on the assumption of a single controlling stage for mixing has been tested by comparison with experimental data concerning the neutralization of NaOH with HCI in a tubular reactor with coaxial feeds. The reactor was operated both in isokinetic and in jet-flow configuration and it was equipped with a fiber-optic spectrophotometer to measure the axial concentration profile of NaOH. A numerical code based on orthogonal collocation along the axis and finite difference along the radius has been developed for efficient simulations.
Discrete dynamical system models of turbulence-chemical kinetics interactions
… Conference, 2002. IECEC'02. 2002 37th …, 2004
A new approach to subgrid-scale (SGS) modeling for large-eddy simulation of turbulent non-premixed combustion is proposed and tested against experimental data. The model is composed of three specific factors: an amplitude, an anisotropy correction and a temporal fluctuation to be evaluated at each discrete point, during each time step, of resolved-scale calculations. We employ discrete dynamical systems (DDSs) for the third factor and in the present work focus on construction of these for a reduced kinetic mechanism and compare results with experimental data from the Technische Universität Darmstadt H2/N2−air jet diffusion flame H3. The DDS model is derived as a single-mode Galerkin approximation (with the mode left arbitrary) of the governing partial differential equations, but with the mode number and normalization(s) incorporated into bifurcation parameters. Such algebraic systems are capable of producing the full range of temporal behaviors of the original differential equations (while being very efficient to evaluate) and, in particular, can exhibit the chaotic behavior of fractal (strange) attractors that can be associated with turbulence. Moreover, they are able to mimic specific reaction pathways for any given kinetic mechanism on the subgrid scales. We compare computed results from the SGS model with the above mentioned data, both qualitatively (appearance of the time series) and quantitatively (rms fluctuation levels) and show reasonable agreement, especially for the former.
Large-eddy simulation of a reacting scalar mixing layer with arrhenius chemistry
Computers & Mathematics with Applications, 2003
method for predicting filtered chemical species concentrations and filtered reaction rates in large-eddy simulations ofnonpremixed, nonisothermal, turbulent reacting flows has been previously demonstrated to be.quite accurate for higher Damkohler numbers and simple chemistry. The method extends quasi-steady flamelet concepts to model reactions that occur at lengths smaller than those resolved on the numerical grid. In this paper, the method is more fully tested using predictions of filtered mass fractions, temperatures, and reaction rates in an incompressible scalar mixing layer. One-and two-step reactions are considered, with activation temperatures and stoichiometric mixture fractions typical of reactions that occur in natural and engineering processes. The predictions for the mass fractions and temperatures are excellent in all csses considered for which quasi-steady flamelet modelling is appropriate. The predictions of the filtered reaction rates are also very good, even for cases where the reaction zones are very thin. Also demonstrated is a one-parameter model for the probability density of the subgrid-scale dissipation rate that significantly improves the predictions of the filtered reaction rates.