Modeling ignition and chemical structure of partially premixed turbulent flames using tabulated chemistry

doi:10.1016/j.combustflame.2007.09.001

Combustion and Flame

Volume 152, Issues 1–2, January 2008, Pages 80-99

https://doi.org/10.1016/j.combustflame.2007.09.001 Get rights and content

Abstract

Correctly reproducing the autoignition and the chemical composition of partially premixed turbulent flames is a challenge for numerical simulations of industrial applications such as diesel engines. A new model DF-PCM (diffusion flame presumed conditional moment) is proposed based on a coupling between the FPI (flame prolongation of ILDM) tabulation method and the PCM (presumed conditional moment) approach. Because the flamelets used to build the table are laminar diffusion flames, DF-PCM cannot be used for industrial applications like Diesel engines due to excessive CPU requirements. Therefore two new models called AI-PCM (autoignition presumed conditional moment) and ADF-PCM (approximated diffusion flames presumed conditional moment) are developed to approximate it. These models differ from DF-PCM because the flamelet libraries used for the table rely on PSR calculations. Comparisons between DF-PCM, AI-PCM, and ADF-PCM are performed for two fuels, n-heptane, representative of diesel fuels, and methane, which does not exhibit a “cool flame” ignition regime. These comparisons show that laminar diffusion flames can be approximated by flamelets based on PSR calculations in terms of autoignition delays and steady state profiles of the progress variable. Moreover, the evolution of the mean progress variable of DF-PCM can be correctly estimated by the approximated models. However, as discussed in this paper, errors are larger for CO and CO₂ mass fractions evolutions. Finally, an improvement to ADF-PCM, taking into account ignition delays, is proposed to better reproduce the ignition of very rich mixtures.

Introduction

Combustion models for industrial applications such as diesel engines or gas turbines require accurate prediction of the ignition and chemical structure of diffusion flames. In this article, several models are proposed and discussed to reproduce diffusion flames under high temperature and pressure, corresponding to typical physical conditions in these applications. Because the combustion of n-heptane and diesel fuel are relatively similar in terms of delays—cetane numbers are approximately 56—and cool flame regime, the fuel considered in this work is n-heptane.

To represent correctly the autoignition delay and reaction rate of n-heptane over the complete range of physical conditions found in industrial applications such as diesel engines, our experience is that complex mechanisms with hundreds of species and thousands of reactions need to be considered, such as the ones developed by Curran et al. [1] or Glaude et al. [2]. As these mechanisms cannot be incorporated directly into CFD codes because of their excessive CPU cost, models need to be developed to reproduce complex chemistry effects. A first solution is to reduce the number of species and consequently the number of reactions of the original kinetic mechanism. Because many chemical species and reactions are not taken into account, this method can only be used over a limited range of physical conditions. This limitation is not acceptable for industrial applications such as piston engines because in a single engine cycle, pressure, temperature, and equivalence ratio, for instance, vary over a wide range of values. For this reason, solving for a reduced mechanism is not a solution in such applications.

In order to account simultaneously for realistic chemistry and heterogeneous combustion, the RIF model (representative interactive flamelet) was developed, based on the direct resolution of the simplified equation of flamelets by Peters [3], [4], [5]. In the case of the unsteady flamelet equation, the autoignition and the transition toward a steady diffusion flame are correctly represented. It was applied with success to diesel engine simulations [6], [7]. The main limitation of this approach is that only a reduced number of flamelets are used to represent combustion over the whole domain. Therefore, it can be anticipated that local combustion effects are omitted. A second limitation is that the flamelet equation cannot handle complex chemistry mechanisms with hundreds of species, due to excessive CPU time. For this reason, the RIF model can only be used with reduced mechanisms, leading to a reduced validity range as discussed previously. Lately, the flamelet equation of the RIF model has been used to generate look-up tables based on two independent variables: the strain rate and the progress variable. This model has been applied to n-heptane injection in a vessel [8].

Recently, the FPI tabulation method (flame prolongation of ILDM—intrinsic low-dimensional manifold) [9], which is similar to FGM (flamelet generated manifolds) [10], has been developed. This method is based on the tabulation of chemistry using laminar premixed flames to generate the table. The chemical transition between fresh gases and burnt products is represented by only one variable, the progress variable, which equals zero in the unburned mixture and one at equilibrium. This FPI table, which can only represent laminar flames [9], is coupled with the PCM approach (presumed conditional moment) [11], [12], [13] for representing turbulent combustion. In this approach, the presumed PDFs (probability density functions) of the progress variable and mixture fraction are used to derive the mean reaction rates and species concentrations. PCM/FPI was first developed to model premixed turbulent configurations [14], [15], [16]. Then partially premixed or nonpremixed flames have been described with FPI in laminar cases [17], [18] and with PCM/FPI in turbulent cases [13]. Following the original FPI method, the table is generated prior to the simulation and consequently the complete range of chemical conditions found during the simulation is required for performing the laminar calculations. Another approach is the dynamic tabulation method ISAT (in situ adaptive tabulation) [19], which can be used without this information: laminar calculations are performed during the simulation to increase the size of the table when the chemical coordinates from the simulation cannot be found in the table.

The aim of this paper is to propose new models adapted to the simulation of autoigniting heterogeneous mixtures such as the ones found in diesel engines or turbo machines. As presented above, the coupling between chemistry tabulation and the PCM makes it possible to represent simultaneously complex chemistry effects (necessary to correctly predict autoignition delays) and the progress variable and mixture fraction stratifications (present in stratified mixtures). For this reason, a DF-PCM model (diffusion flames presumed conditional moment) is developed based on the PCM with a table built from laminar diffusion flames. However, the computation of these flames requires large CPU times if the chemical mechanism is large. In the case of detailed mechanisms with hundreds of species, computing a diffusion flame is simply not feasible. Consequently, DF-PCM can be used only if reduced mechanisms are available. In this case, as long as the number of laminar diffusion flames needed for generating the table remains low, DF-PCM can be used. In contrast, if the range of physical conditions requires many laminar diffusion flame calculations, the CPU time needed for generating the table becomes excessive. To sum up, the CPU time strongly limits the use of DF-PCM today. A way to reduce it is to generate tables based on PSR (perfectly stirred reactor) calculations that can be performed very fast even with very large chemical mechanisms. Based on this idea, the models AI-PCM (autoignition presumed conditional moment) and ADF-PCM (approximated diffusion flames presumed conditional moment) are developed in this paper to approximate DF-PCM.

A simplified n-heptane mechanism with 56 species [20] is considered and allows the computation of laminar diffusion flames in a reasonable CPU time, keeping in mind that for industrial applications, much heavier mechanisms are required. Laminar diffusion flames are first compared to the results of the modeled flame elements in terms of autoignition delays and species mass fractions. The mean values predicted by all models are then compared in a priori tests.

In the following section, the DF-PCM model is presented. Then, Section 3 describes the FPI tabulation method and the approximated models developed in this work. This section is followed by comparisons between the models DF-PCM, AI-PCM, and ADF-PCM with two fuels, n-heptane and methane, which does not exhibit a cool flame regime. Then an improvement is proposed to better reproduce the ignition of very rich mixtures. Finally, the discrepancies observed between flamelets in terms of final products and mass fractions are discussed.

Section snippets

The FPI/PCM approach

The idea of the FPI tabulation method proposed by Gicquel et al. [9] and of the FGM approach of Van Oijen et al. [10] is to include the effects of complex chemistry without solving equations for all species. For this purpose, the transition between fresh gases and burnt products is represented by only one variable, the progress variable, which allows other quantities (mass fractions, reaction rates, etc.) to be read from a look-up table. A possible definition of the progress variable is based

Construction of FPI tables

In the initial version of FPI [9], the table was built from laminar-premixed flame calculations. This method has been modified by Vervisch et al. [13] to reproduce the chemical structure of a diffusion flame: a mix of laminar premixed and diffusion flames was used to represent the whole range of progress variable values from zero (not reached by a steady diffusion flame and therefore represented by a premixed flame) to the equilibrium value of the diffusion flame, close to unity. In the models

Ignition phase

In this section laminar diffusion flames presented in Section 2.3 are compared to the simplified laminar flame elements retained in models AI-PCM and ADF-PCM computed with the same chemical mechanism proposed by Tao et al. [20] under the same physical conditions. When comparisons with the three diffusion flames lead to similar conclusions, only the intermediate case DF10 is presented for brevity. Autoignition delays are first compared, followed by flame structures defined as $c (Z, t)$ .

Fig. 8

Description

It was observed previously that ADF-PCM flamelets correctly represent the steady state regime of diffusion flames but underestimate delays in the case of n-heptane, especially for large mixture fractions. This section first analyzes the reason for this phenomenon and then presents an improved version of ADF-PCM leading to better results.

Fig. 15 displays the temperature profile of DF50 at $t = 0$ and $t = 1 ms$ and the corresponding progress variable profiles. The reaction rate profile of DF50 is

Validity of the tabulation method

For n-heptane or methane flames, the progress variable profile in the steady state regime can be correctly estimated by ADF-PCM. However, the differences are stronger for CO and CO₂. Fig. 18 compares the steady state profiles of $Y_{CO}$ and $Y_{{CO}_{2}}$ with Z for ADF-PCM, a diffusion flame (DF10 for n-heptane and DF50 for methane), and the values of these two mass fractions read in the autoignition (FPI) table with the progress variable $c (Z)$ given by the diffusion flame (named DF-AI in this figure). For

Concluding remarks

Different models based on the FPI/PCM approach have been proposed and tested to reproduce the combustion in practical applications characterized by the autoignition of heterogeneous mixtures in Diesel engines or gas turbines. Built from laminar diffusion flames, model DF-PCM (diffusion flame presumed conditional moment) can only be used for practical applications where simplified mechanisms are available. For this reason, approximate models were developed based on homogeneous autoignition

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Modeling ignition and chemical structure of partially premixed turbulent flames using tabulated chemistry

Abstract

Introduction

Section snippets

The FPI/PCM approach

Construction of FPI tables

Ignition phase

Description

Validity of the tabulation method

Concluding remarks

Combust. Flame

Prog. Energy Combust. Sci.

Proc. Combust. Inst.

Combust. Flame

Proc. Combust. Inst.

Proc. Combust. Inst.

Combust. Flame

Combust. Flame

Combust. Flame

Energy Fuels

Proc. Combust. Inst.

Turbulent Combustion