Lagrangian tracking of soot particles in LES of gas turbines

doi:10.1016/j.proci.2018.06.013

Proceedings of the Combustion Institute

Volume 37, Issue 4, 2019, Pages 5429-5436

https://doi.org/10.1016/j.proci.2018.06.013 Get rights and content

Abstract

Expected stringent legislation on particulate matter (PM) emission by gas turbine combustors is currently motivating considerable efforts to better understand, model and predict soot formation. This complex phenomenon is very difficult to study in detail with experiment, and numerical simulation is an essential complementary tool. Considering that the chemistry of soot particles strongly depends on their size, the numerical prediction of soot formation requires the description of their size distribution. To do so, either Eulerian methods (sectional or moments), or stochastic Lagrangian approaches are reported in the literature. In the present work a far more simple semi-deterministic Lagrangian approach is proposed. Combined to the semi-empirical model of Leung et al. (1991) for soot chemistry, the Lagrangian approach is first validated on a one-dimensional premixed ethylene-air flame. The model is then applied to a gaseous non-premixed ethylene-air burner measured at DLR and computed with Large Eddy Simulation (LES). The gaseous chemistry is described with an Analytically Reduced Chemistry (ARC) to guarantee a good prediction of combustion and gaseous soot precursors. Results are validated against experiment and compared, in terms of accuracy and CPU cost, to an Eulerian semi-empirical model. To the authors knowledge, it is the first time that such Lagrangian particle tracking approach is used for soot. Results obtained in terms of accuracy and computing time are very encouraging.

Introduction

Particulate Matter (PM) emitted from practical combustion devices contribute to air pollution, which has a strong negative impact on the population health [1] and air quality. This includes soot, which results from a complex gaseous and heterogeneous chemical process. When emitted at high altitude, soot increases significantly the local concentration of aerosols in the atmosphere inducing a possible artificial radiative forcing via the formation of contrails. On the ground, emitted soot particles can be inhaled and, depending on their size, penetrate more or less deeply in the human body where it can trigger specific diseases. In this context, the design of the next generation of combustor devices with limited soot emission has become a major challenge for engine manufacturers. To do so numerical simulation is an essential tool which, if sufficiently accurate, allows a better understanding and control of soot formation.

Soot particle size is not only critical for their toxicity, but also for their formation / destruction processes, as these involve heterogeneous chemistry at the particle surface. The prediction of soot particle formation therefore requires to describe their size distribution. A population of soot particles is then represented by its local and instantaneous Number Density Function (NDF), defined as the number of particles of a given size. The NDF is often bimodal due to the constant inception of very small soot particles and the final large aggregates resulting from successive collisions and surface reactions [2]. The NDF is the solution of the Population Balance Equation (PBE), which is solved using statistical approaches. Three classes of resolution methods of the PBE are commonly used: the Method of Moments (MOM), the Sectional Method (SM), and the Monte Carlo (MC) stochastic Lagrangian approach. The MOM aims at calculating a set of statistical moments of the NDF [3], [4], [5], [6], while SM [7], [8], [9] and MC directly solve the PBE to obtain the NDF. Although they have allowed to obtain very good results [10], [11], these methods are complex, demand specific numerics and are computationally expensive.

An alternative is proposed in the present work, based on a simple semi-deterministic Lagrangian approach. The method is deterministic in the sense that physical particles are tracked, contrary to MC dealing with stochastic particles. It however still includes stochastic processes such as collisions. To limit the computational time, only a subset of particles is computed, representative of all particles possibly present in a control volume. With this strategy, Lagrangian particle tracking becomes affordable in real complex geometries such as aircraft or internal engines. The choice of such a Lagrangian formalism for nano-particles is still on the fringes of the official methods. The reason is to be found in the prohibitive computational cost of the Lagrangian tracking of all physical particles in a 3D complex configuration. As a consequence, most Lagrangian calculations are restricted to the resolution of realizability issues in MOM [12]. An attempt of deterministic Lagrangian calculation of soot has been made very recently by Ong et al. [13] where however the interactions between particles were neglected. This considerably simplified the implementation but also significantly reduced the accuracy as particle interactions are essential. Today, both the progress made in parallel computing and the semi-deterministic Lagrangian concept allow to overcome this computational cost issue, as will be demonstrated in the present paper. This requires however an optimum parallel efficiency of the Lagrangian solver, as well as a careful control of statistical convergence.

In the following, the derivation of the semi-deterministic Lagrangian method is explained in details. Combined to a semi-empirical model for soot evolution [14], it is then validated in a one-dimensional sooting premixed flame. Finally, an experimental gaseous ethylene-air non-premixed burner [15] already investigated with LES and a one-section SM approach [16], [17] is used to assess the computational cost and accuracy provided by the new Lagrangian method.

Section snippets

Lagrangian formalism

The present methodology is based on the Discrete Particle Simulation (DPS), similar to what is used for spray computations. Contrary to dilute sprays, soot particle populations are dense, so that collisions have a high probability and must be accounted for. Indeed, they play an essential role in the soot particles size distribution. The proposed approach, so-called EL POLY, relies on the following assumptions:

•
Dynamics: soot particles are tracers. This means that neither drag nor thermophoresis

Validation in laminar flames

The Lagrangian polydisperse methodology (EL POLY) was implemented in the code AVBP jointly developed by CERFACS and IFPEN. To benefit from the difference between the compressible flow timestep controlled by acoustics, and the particle motion convective timestep which is much larger, Lagrangian iterations are performed only after a number f_s (soot frequency) of flow iterations. This leads to a significant gain of computational cost without loosing accuracy, as illustrated in Table 1 showing the

Configuration and numerical set-up

The configuration studied in this work is an experimental set-up installed at DLR [33] referred to as ISF-3 Target Flame 1. It is one of the target pressurized flame within the International Sooting Flame (ISF) workshop. It is designed to study soot formation in gas turbine combustors under elevated pressure, burning ethylene with or without secondary air dilution. The combustor is presented in Fig. 3, also illustrating the flow topology by displaying the instantaneous axial velocity field. The

Conclusions

A semi-deterministic Lagrangian particle tracking methodology has been introduced and validated for soot prediction in combustion chambers. Validation on a one-dimensional sooting flame and a gaseous non-premixed burner has been performed by comparison with the original Eulerian Leung model and experiment when available. Results confirm that the approach is suitable for soot modeling and provides accurate results in reasonable computing time. Although further validations are required to assess

Acknowledgments

This work was performed using HPC resources from GENCI (Grant no. A0032B10157): CINES, IDRIS and TGCC. Funding from the European Union within the project SOPRANO (Soot Processes and Radiation in Aeronautical innovative combustion) Horizon 2020 Grant agreement no. 690724 is gratefully acknowledged.

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Lagrangian tracking of soot particles in LES of gas turbines

Abstract

Introduction

Section snippets

Lagrangian formalism

Validation in laminar flames

Configuration and numerical set-up

Conclusions

Acknowledgments

Proc. Comb. Inst.

Chem. Eng. Sci.

J. Aerosol Sci.

Combust. Flame

Proc. Combust. Inst.

Combust. Flame

Combust. Flame

Combust. Flame

Comput. Fluids

J. Aerosol Sci.

Combust. Flame

Combust. Flame

Proc. Combust. Inst.

Combust. Flame

Chemical Eng. Sci.

Powder Technol.

Phys. A Stat. Mech. Appl.

J. Comput. Phys.