Mixing time-history effects in Large Eddy Simulation of non-premixed turbulent flames: Flow-Controlled Chemistry Tabulation

doi:10.1016/j.combustflame.2011.06.005

Combustion and Flame

Volume 159, Issue 1, January 2012, Pages 336-352

https://doi.org/10.1016/j.combustflame.2011.06.005 Get rights and content

Abstract

The time history of mixing is known to play a crucial and non-trivial role in non-premixed turbulent combustion. In a first part, Eulerian balance equations are derived for both a flow residence time and a characteristic time of the mixing which the particles gathered in a fluid element have been subjected to in their flow histories. These equations are analyzed and solved in a Large Eddy Simulation (LES) context for a fuel jet mixing with an oxidizer co-flow. Typical responses of filtered mixture fraction versus flow residence time are highlighted. In a second part, a Flow-Controlled Chemistry Tabulation (FCCT) is devised in which the effects of unresolved fluctuations of thermochemical variables in LES are simulated, combining partially stirred reactors with tabulated chemistry. The reactor evolutions are organized to mimick flow engulfment and micro-mixing, so as to reproduce the observed filtered mixture fraction versus residence time response. This allows for dynamically building subgrid scale joint probability density functions, and thereby the subfilter response of the non-premixed flames, according to four control parameters: the filtered mixture fraction, the progress of reaction, the flow residence time, and a mixing time. Finally, LES of the Cabra et al. [Combust. Flame 143 (2005) 491–506] fuel-jet lifted-flame developing in a vitiated oxidizer environment is performed and results are compared against measurements.

Introduction

The time history of mixing is usually considered as central to turbulent flames, where large-scale unsteady flow motion leads to an imperfect mixing of the reactants, while micro-scale molecular diffusion brings chemical species in contact within thin reaction zones [1]. In this context, Large Eddy Simulation (LES) has flourished to simulate the large-scale mixing, while smallest scales are modeled [2]. However, LES must address the turbulent structures at a resolution fine enough to allow for a reliable prediction of the subgrid-scale (SGS) mixing dynamics [3], specifically when scalar fields are concerned [4].

Accounting for time-history effects in the evaluation of the SGS statistics, while dealing with the double challenge of accuracy and computational cost, is not straightforward. A large set of methods tackle this issue in different ways. The transported probability density function (pdf) and transported mass-weighted pdf methods [5] are formulated precisely to follow the individual history of fluid elements. In their Lagrangian formulation, the evolution of stochastic particles are subjected to chemical sources and turbulent transport, the interaction between mixing and chemistry is reproduced throughout the evolution of particles [6], [7]. It was shown that equivalent averaged results may be obtained with an Eulerian formulation, by the computation of several stochastic fields [8], [9], [10]. Obviously, the numerical accuracy of these methods is directly sensitive to the number of stochastic particles, or fields, used in the computations.

Fully prescribing the SGS statistics with presumed pdfs oversimplifies the history of fluid parcels. The Presumed Conditional Moments (PCM) formulation [11], [12], [13], [14] is such an approach; it relies on estimating low-order statistical properties of the distributions, like averages and variances. The pdfs are then assumed to take a specific shape, parameterized by these quantities. In the presumed pdf approach, the history of the flow is only taken into account through its effect on these statistical properties and it is the local result of history that is described, not its dynamics. Complex correlations between chemical and mixture parameters cannot be accounted for, and strong hypotheses must often be framed, such as statistical independence between mixture fraction and progress of reaction. Moreover, the transport of statistical higher moments, like scalar variances, is subject to inaccuracies as soon as the filter size – in most cases the mesh – is not sufficiently refined [4]. On the other hand, the filtered flame response may be tabulated with a reduced number of controlling parameters. A lookup table, computed prior to the LES, is then accessed from the simulation, making the additional cost due to chemistry marginal. Methods based on direct computations of conditional means, as Conditional Moment Closure (CMC), have also being explored in the literature [15], [16], [17], [18].

The work presented in this paper proposes an alternative parameterization of the flow for non-premixed jet flames, which enables a tabulation of turbulent chemistry, but avoids presuming joint pdfs. The idea is to describe not the results of flow mixing history, but properties of this history itself. Previous attempts to enable the description of history through conditioning scalars have been made: age-related markers were introduced in premixed flames [19], [20] and a flamelet lifetime was used for an interactive computation of unsteady diffusion flamelets [21]. In a tabulated chemistry approach for RANS [22], a residence time was also formerly introduced as a conditioning variable to replace the reaction progress variable.

A multi-scale approach is followed [23] that is summarized in Fig. 1: In the LES, in addition to usual continuity, momentum and energy budgets, four quantities are resolved: $\tilde{Z}$ , the filtered mixture fraction; ${\tilde{Y}}_{c}$ , the progress of reaction used to tabulated detailed chemistry; ${\tilde{τ}}_{res}$ , the time duration over which mixing has been acting on a fluid particle, and τ_mix, an evaluation of the characteristic turbulent mixing time along the fluid particle trajectory. From two of these quantities $({\tilde{τ}}_{res}, \tilde{Z})$ , a distribution of mixture fraction versus residence time is found, which is representative of the unsteady mixing dynamics.

Aside from the flow solution, time sequences of a stochastic reactor are considered under the mixing constraint given by the mixture fraction versus residence time distribution, which is fulfilled by monitoring reactor injection. In this reactor, at the micro-scale level, the balance between molecular diffusion and chemistry is described by a flamelet hypothesis [24], [25], and chemistry is thus retrieved from the mixture fraction Z and a progress of reaction Y_c. At an intermediate scale, which is still at the subgrid level in the LES, these flamelets interact with turbulence according to a mixing closure in the stochastic reactor and with the mixing time scale τ_mix.

In the end, a four-dimensional lookup table $(\tilde{Z}, {\tilde{Y}}_{c}, τ_{mix}, {\tilde{τ}}_{res})$ resulting from the Monte-Carlo simulations of the Flow-Controlled Chemistry Tabulation (FFCT) model is built, which supplies the unclosed Eulerian source terms. This features similarities with presumed pdf approach with tabulated chemistry, however, here the subfilter joint pdf is not imposed a specific shape but built according to flow mixing dynamics.

In a first section, the mentioned flow timescales are introduced and their role in describing the turbulent mixing properties is analyzed. The FCCT method is then presented in detail, specifications of the PaSR model are given, and the table generation technique is described. A last part illustrates the implementation of the method in the LES; the results of a simulation of a lifted methane–air jet flame in a vitiated co-flow are compared with experiments [26], after studying the output table properties.

Section snippets

Residence time

Let a scalar ϕ be defined by the Lagrangian equation $\frac{d ϕ}{d t} = S .$ It may be seen as the property of a single, identifiable particle, and measures the accumulation of the source field S on its trajectory $T : t \mapsto \underset{̲}{x} (t)$ ; for an initial value $ϕ_{0}, ϕ = ϕ_{0} + \int_{T} S (\underset{̲}{x} (t), t) d t$ . Considering now ϕ(x,t) as an Eulerian field, defined on any test volume of the flow as its ensemble average value on the enclosed particles, it satisfies the following conservation equation: $\frac{\partial ρ ϕ}{\partial t} + \underset{̲}{\nabla} \cdot (ρ \underset{̲}{u} ϕ) = \underset{̲}{\nabla} \cdot (ρ D \underset{̲}{\nabla} ϕ) + ρ S .$ Interactions with particles

Modeling strategy

The mass-weighted space filtering operation is defined in Large Eddy Simulation as: $\tilde{Q} ({\underset{̲}{x}}_{0}, t) = \frac{\int_{\underset{̲}{x}} ρ (\underset{̲}{x}, t) Q (\underset{̲}{x}, t) G_{Δ} (\underset{̲}{x} - {\underset{̲}{x}}_{0}) d \underset{̲}{x}}{\int_{\underset{̲}{x}} ρ (\underset{̲}{x}, t) G_{Δ} (\underset{̲}{x} - {\underset{̲}{x}}_{0}) d \underset{̲}{x}},$ where $G_{Δ}$ is a filter function used to damp fluctuations at lengths smaller than Δ. Assuming that Q is a unique function of the set of parameters $\underset{̲}{ϕ}, \tilde{Q}$ may be computed from the joint pdf p(ϕ; x, t): $\tilde{Q} ({\underset{̲}{x}}_{0}, t) = \int_{\underset{̲}{ϕ}} Q (\underset{̲}{ϕ}) p (\underset{̲}{ϕ}; {\underset{̲}{x}}_{0}, t) d \underset{̲}{ϕ} .$

The Flow-Controlled Chemistry Tabulation approach stems from the idea that the residence time ${\tilde{τ}}_{res} (\underset{̲}{x}, t)$ and mixing

Jet flame LES using FCCT

Large Eddy Simulation of the vitiated-air jet flame [26] is now performed, the simulation follows the procedure reported in Ref. [12], in which the flamelet presumed pdf lookup table has been replaced by the FCCT one. Along with the Navier–Stokes equations in their fully compressible form, Eqs. (9), (10) are solved for ${\tilde{τ}}_{res}$ and $\tilde{Θ}$ , and relation (11) provides τ_mix. A usual convection–diffusion equation is solved for the mixture fraction $\tilde{Z}$ ; in the Eulerian balance equation for the progress of

Summary

A novel chemistry tabulation approach for LES has been presented that is based on properties of the flow history. It is formulated through probability density functions which are not presumed, but generated in Monte-Carlo simulations of a Partially-Stirred Reactor that models three processes: turbulent mixing, chemical reaction, and inflow/outflow (engulfment). The result is a lookup table accessed from the flow solver with the following input parameters: a residence time and a mixing

Acknowledgments

This work is co-funded by ADEME and Air Liquide through the SAFIR (Simulation Avancée de Foyers Industriels avec Recycle) project. This work was granted access to the HPC resources of CRIHAN and IDRIS under the allocation 2009-020152 made by GENCI (Grand Equipement National de Calcul Intensif).

References (70)

K.N.C. Bray
Proc. Combust. Inst.
(1996)
P. Moin
Int. J. Heat Fluid Flow
(2002)
L. Vervisch et al.
Combust. Flame
(2010)
M.R.H. Sheikhi et al.
Proc. Combust. Inst.
(2005)
M. Yaldizli et al.
Int. J. Heat Mass Transfer
(2010)
W.P. Jones et al.
Combust. Flame
(2010)
P. Domingo et al.
Combust. Flame
(2008)
V. Subramanian et al.
Combust. Flame
(2010)
J.-B. Michel et al.
Combust. Flame
(2008)
A.Y. Klimenko et al.
Progr. Energy Combust. Sci.
(1999)

B. Merci et al.

Combust. Flame

(2006)

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Mixing time-history effects in Large Eddy Simulation of non-premixed turbulent flames: Flow-Controlled Chemistry Tabulation

Abstract

Introduction

Section snippets

Residence time

Modeling strategy

Jet flame LES using FCCT

Summary

Acknowledgments

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