Three-dimensional direct simulations and structure of expanding turbulent methane flames

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Abstract

Direct numerical simulations (DNS) are ideally suited to investigate in detail turbulent reacting flows in simple geometries. For an increasing number of applications, detailed models must be employed to describe the chemical processes with sufficient accuracy. Despite the huge cost of such simulations, recent progress has allowed the direct numerical simulation of turbulent premixed flames while employing complete reaction schemes. We briefly describe our own developments in this field and use the resulting DNS code to investigate more extensively the structure of premixed methane flames expanding in a three-dimensional turbulent velocity field, initially homogeneous and isotropic. This situation typifies, for example, the initial flame development after spark ignition in a gas turbine or an internal combustion engine. First investigation steps have been carried out at low turbulence levels on this same configuration in the past Symposium, and we build on top of these former results. Here, a considerably higher Reynolds number is considered, the simulation has been repeated twice in to limit the possibility of spurious, very specific results, and several complementary post-processing steps are carried out. Characteristic features concerning the observed combustion regime are presented. We then investigate in a quantitative manner the evolution of flame surface area, global stretch-rate, flame front curvature, flame thickness, and correlation between thickness and curvature. The possibility of obtaining reliable information on flame front curvature from two-dimensional slices is checked by comparison with the exact procedure.

Introduction

Localized ignition of a reactive mixture and later flame development in a turbulent flow represents a very important combustion process, found in many practical applications. Current understanding is still unsatisfactory and severely limits prediction capabilities, and thus achievements concerning the control of pollutant emissions or improvement of the global efficiency.

Direct numerical simulations (DNS) have been known for over 10 years to be ideally suited to study turbulent premixed flames [1], [2], [3] because they do not require any particular assumption concerning the turbulence. Due to the huge cost of direct simulations, strong hypotheses have generally been introduced to reduce the requested computing times [4]. Despite these simplifications, like, for example, constant-density combustion [5] or single-step chemistry [1], [6], [7], many interesting results have been obtained over the years.

When considering quantitative problems like predictions of intermediate radicals, pollutant emission or ignition/extinction limits, the reaction processes should be described using detailed models [2], [8], [9], [10], [11], [12]. This leads to a more faithful representation of the combustion processes, as explained in a recent review paper [13].

Very often, such computations relying on detailed models have been limited to 2D. Three-dimensional direct simulations including detailed reaction schemes are fairly recent. Associated computing times are huge and limit the possible use of such simulations to investigate turbulent combustion. Nevertheless, several such publications have appeared in the last three years concerning premixed as well as non-premixed combustion [14], [15], [16], [17], [18], [19], [20], [21], [22].

The present work builds on top of our recent efforts to carry out three-dimensional direct simulations of reacting flows at reasonable computing costs, while keeping a realistic description of chemical processes. Such computations are clearly required, since: (1) turbulence is intrinsically three-dimensional, and the behavior of 2D-turbulence is very different; (2) reducing chemical processes to a single-step reaction is a crude approximation, very useful to get global trends but often too limited when quantitative results are needed, as shown in [13].

Concerning previous simulations on the same configuration, two-dimensional DNS of spark ignition in a turbulent flow using single-step chemistry are reported in [4], [9], [23], where the emphasis is laid on flame initiation and on modeling issues. Two-dimensional direct simulations using detailed chemistry are presented in [11]. High-resolution three-dimensional simulations relying on single-step chemistry have also been presented at the last Symposium [7], where the emphasis was laid on flame curvature.

In the last Symposium volume, we published a study dealing with the comparison of such two-dimensional and three-dimensional direct simulations, showing large discrepancies between both [16]. A three-dimensional DNS code, called π3 and written in Fortran 95, has been specifically developed for this purpose. This same code is again used in the present study.

Physical models and numerical methods employed in π3 are first briefly recalled. Afterwards, results of three-dimensional direct simulations are described. We first analyze our results in the light of turbulent combustion regimes. Many quantities, in particular flame surface area, stretch-rate, flame front curvature, and flame thickness, are then extracted from numerical data. For flame curvature, we compare the results obtained using a full three-dimensional treatment with those of post-processing methods working on 2D slices. Impact of turbulence on flame thickness is finally investigated, partly supporting some recent findings [24].

Section snippets

Physical models and numerical methods

Our latest DNS code, called π3, has been already described in previous publications, e.g. [16], [22]. We therefore only consider briefly two specific aspects of this code.

First, our code relies on a low-Mach number approximation and not on a fully compressible formulation. For most applications of interest, the maximum Mach number is generally quite small, at least in the region where combustion takes place. It is then unnecessary and computationally inefficient to employ a fully compressible

Direct simulations and results

Fully premixed methane/air flames at an equivalence ratio of ϕ = 1.59, atmospheric pressure, and fresh gas temperature of 298 K are considered. This high value of ϕ has been retained to facilitate the computations, and in particular to get a larger flame thickness and lower density jump through the flame, leading to a smoother time- and space-integration. Moreover, previous studies tend to show that differences with single-step chemistry are considerably larger for rich flames [8], [13]. These

Conclusions

We have successfully developed a three-dimensional direct simulation code relying on the low-Mach number approximation and on the FPI chemistry reduction technique. The obtained tool is computationally very efficient and allows three-dimensional DNS of turbulent flames at moderate Reynolds numbers on a standard PC. This code has been used to investigate the development of a premixed methane/air flame in a turbulent flow, as observed after ignition. Evolutions of the flame surface area, of the

Acknowledgments

Many people have participated in the development of the code π3. We in particular thank O. Gicquel, J. de Charentenay, and R. Hilbert for their contributions.

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