Annual Report

2.3 LES of unsteady combustion

Unsteady combustion is now a major field of application for Large Eddy Simulations (LES) of reacting flows. These applications include predictions of combustion instabilities but also of ignition or quenching. In 2004 and 2005, CERFACS has lead multiple investigations around these topics and developed additional tools which are needed for these studies: LES tools but also acoustic analysis and sometimes RANS tools. Configurations computed at CERFACS were tested experimentally at the same time elsewhere in Europe, providing CERFACS with a unique data base for validation of the AVBP code. As a result, multiple papers have been produced since 2004 [Selle, 2004a; Sommerer, 2004; Moureau, 2005; Roux, 2005; Truffin, 2005] and the studies on unsteady combustion are a very important part of the team's work.

LES alone is not sufficient to understand turbulent combustion in confined chambers: theory and experiments show that acoustics play a very important role in many cases, especially in triggering combustion instabilities. Therefore writing codes able to describe the structure of acoustic modes in combustion chambers and their coupling with combustion is required: this is done at CERFACS and discussed in Section 2.3.4 and 2.3.5. In May 2005, CERFACS has organized a workshop in Toulouse on combustion instabilities and LES (with the support of the European Commission) which gatherered almost 100 scientists from 10 countries confirming the importance of this topic.

Section 2.3.1 recalls the submodels used for LES and Section 2.3.2 shows one example of LES validations for non-reacting flows where the CERFACS code AVBP was compared to experiments performed in DLR and with an LES code developed at Stanford. Acoustics are discussed in Sections 2.3.3 to 2.3.5. Ignition, quenching and flashback are discussed in Section 2.3.6 while multiburner computations are presented in Section 2.3.7. Effects of radiation and instability on NOx formation are discussed in a staged burner in Section 2.3.8. A ramjet LES is finally discussed in Section 2.3.9 before presenting LES applications in piston engines (Section 2.3.10).

2.3.1 LES models for combustion at CERFACS

Building an efficient LES tool in complex geometry chambers requires a compromise between precision and complexity: all submodels for turbulence, boundary conditions, turbulence / flame interaction, ignition, flame / wall interaction... are chosen to offer homogeneous performance and implementation costs which are compatible with the use of a compressible explicit solver on very large grids and large number of processors. Most models developed by CERFACS jointly with Institut Francais du Pétrole have been already published by CERFACS and are described in the literature.

The DTF (Dynamically Thickened Flame) model initially written by Colin et al (Phys. Fluids 12, 2000) continues to perform very well in the new configurations and has been used with virtually no modification [Sommerer, 2004; Roux, 2005; Giauque, 2005]. This model initially written for premixed flames is now used for diffusion flames with success. Note however, that many flames studied at CERFACS are categorized as diffusion flames because the fuel is injected through holes inside the chamber. However results show that these flames are usually lifted with significant mixing upstream of the flame so that very few diffusion flamelets are found.

An important submodel is the chemical scheme: initially many computations with the DTF model were performed with one-step schemes. Now two-step and four-step schemes are used and the DTF model has been modified to accomodate these multistep schemes [Truffin, 2005 PhD]. The construction of these schemes is performed by comparing their results on simple laminar premixed flames and using genetic algorithm techniques developed by C. Martin in his PhD [Martin, 2005 PhD] to fit the results of the reduced schemes with the data obtained with full schemes. This was done for methane, propane, heptane, JP10 and kerosene. These schemes have also been extended to include NOx in certain cases. For these cases, simple radiation models have also been developed in AVBP [Schmitt, 2005; Schmitt, 2005 PhD].

Boundary conditions and acoustic wave management of boundaries are still key issues for LES codes in which any error created at boundary will generally amplify in the domain. Selle [Selle, 2004] has shown that the true reflection coefficient of a 'non-reflecting' boundary could be predicted analytically and that correct scalings for relaxation coefficients on non-reflecting boundaries have been proposed.

Important work was also required to extend LES from academic configurations to real combustion chambers. Being able to model multiperforated plates for example is mandatory for many chambers where multiperforation is used on a large portion of the chamber walls [Mendez, 2005]. Cooling films also raise additional difficulties. In most cases, models for these phenomena are based on separate DNS (see Section 2.1).

2.3.2 A small gas turbine burner (G. Lartigue, S. Roux, T. Poinsot)

During the PRECCINSTA EC programme, the accuracy of LES was tested for swirled flows by comparing LES velocity fields with measurements performed at DLR in a swirled premixed injector (Fig. 2.8) where swirl is produced by tangential injection downstream of a plenum. A central hub is used to stabilize the flame. Experiments include velocity measurements for the cold flow as well as a study of various combustion regimes.

Figure 2.8: Configuration (left). Location of cuts for velocity profiles (right).

Figure 2.9: Cold flow: RMS axial velocity profiles. Circles: LDV; solid line: LES (AVBP); dotted line: LES (Stanford).

Cold and reacting premixed flows were computed successfully and published in Comb. and Flame [Roux, 2005]. In 2004 and 2005, this study was used as a benchmark by Stanford and CERFACS to compare their LES codes. A typical example of result for non-reacting flow results is given in Fig. 2.9. The RMS axial velocity fields show very good agreement between the LES codes and the experiment. Even though small differences are observed (near walls for example), it is quite interesting to see that fully different codes lead to very similar accuracy on this configuration.

2.3.3 System identification of combustors (L. Selle , A. Giauque , A. Sengissen , K. Truffin , G. Staffelbach , Y. Sommerer , F. Nicoud, M. Brear, T. Poinsot )

System identification by forcing is a normal procedure during investigations of combustors stability: burners are forced in order to examine their response to acoustic waves entering the air or the fuel inlet. This identification can be performed experimentally or numerically using LES. But the cost of such experiments is high and LES are being developed to replace experiments for this task. At CERFACS, multiple studies of this type were devoted to system identifications in 2004 and 2005:

A theoretical study of how forcing should be performed and postprocessed was done by Truffin and Poinsot [Truffin, 2005] on a laminar premixed flame for which experimental results of the EM2C laboratory in EM2C Paris were available.
Chamber B: forced response of a large scale industrial gas turbine [Giauque, 2005] mounted in a square cross section chamber in Karlsruhe University (bilateral work with Siemens).
Chamber C: an experiment built at Twente Univ. in the DESIRE EC project. The computation includes both mixing from the methane jets and combustion in the chamber. Fluid structure interaction between the oscillating combustion and the chamber wall is one goal of this work [Sengissen, 2005] where wall vibrations can be monitored.

Studying the theoretical aspects of combustor forcing using a simple laminar flame proved to be a useful analysis [Truffin, 2005] which demonstrated that many similar studies (experimental or numerical) lack consistency and may lead to erroneous results when the point used to measure the fluctuating velocity is located too far upstream from the chamber.

Figure 2.10: Chamber B: burner (left) and combustion chamber at ITS Karlsruhe (right).

Applying LES to measure flame response in Chamber B was a difficult challenge because it is a high-power swirled burner. It is installed in two different institutes in Karlsruhe, either in a square (ITS) or a circular (EBI) combustion chamber. Fig. 2.10 shows the main features of the burner in which this identification is performed: a central axial swirler (colored in dark) is used to inject and swirl a mixture of natural gas and preheated air. The main part of the combustion air as well as fuel is injected by the diagonal swirler through holes located on both sides of the vanes in order to achieve swirling. Perfectly mixed gases enter the diagonal swirler while pure air enters the axial swirler: the flame inside the chamber is in a partially premixed regime.

Figure 2.11: Chamber B (Fig. 2.10) with pilot flames on, forced by acoustic excitation. Snapshot of the flame visualized by an isosurface of temperature at T=1000K. The left and right results correspond to different geometries of the swirler.

This burner and many of its evolutions have been analyzed in the PhD thesis of L. Selle (2004), G. Staffelbach and A. Giauque (2006). Comparisons of LES results with other methods and experimental results are given in [Giauque, 2005]. An example of results is presented here to illustrate the power of LES in predicting effects of geometrical changes on the flame response. For this study, the flame is pulsated at various frequencies by modulating the inlet velocity. Two configurations are computed to evaluate the response of the burner as a function of the geometry of the swirler. This response is the building block of acoustic solvers that predict the stability of combustors (see Section 2.3.4). Fig. 2.11 shows an instantaneous view of the flame front for a piloted flame during forcing for two different swirler geometries. The impact of this small geometrical modification on the flame response and shape is very strong.

The geometry of burner C (designed for the EC Desire project, PhD of A. Sengissen) is displayed in Fig. 2.12: for this flame the computation must describe both mixing from the four methane jets with air and combustion in the chamber. This experiment was designed for LES validation: the set up can be meshed and computed entirely with LES. Another specificity of the Twente rig is that forcing is achieved by modulating the fuel flow rate and not the air. LES results predict the mean flow field with great accuracy as well as the flame transfer function over a wide range of forcing amplitudes [Sengissen, 2005]. Unsteady wall pressure fields measured in the LES have also been compared with Twente measurements and shown good agreement, allowing to predict the vibration intensities of the chamber walls.

Figure 2.12: Combustor C. Left: geometry: the whole shaded area is meshed and computed. Right: isosurfaces of Y_CH4=0.1 and isosurface of temperature T=1000 K.

2.3.4 Acoustic / combustion numerical tools (A. Kaufmann , L. Benoit , C. Sensiau , F. Nicoud , T. Poinsot )

Acoustics play a key role in combustion and must be accounted for both experimentally and numerically. To understand confined flames, developing acoustic codes solving the wave equation in complex geometries for reacting flows is therefore a necessary step. CERFACS is developing such tools (PhDs of A. Kaufmann, L. Benoit and C. Sensiau).

The first tool called Soundtube provides the low-frequency longitudinal resonant modes in a network of interconnected ducts with variable sections and temperatures. The second tool is a full three-dimensional Helmholtz solver (called AVSP) solving the Helmholtz equation in the frequency domain. It is coupled to the LES code AVBP: they use the same grids; the mean temperature and mass fraction fields required by AVSP (to know the sound speed) and the flame transfer function (to know the acoustic / flame coupling, see Section 2.3.3) are provided by AVBP.

Figure 2.13: Acoustic analysis in a gas turbine annular chamber. Left: typical geometry for one burner Right: AVSP result for the 2nd annular mode (RMS pressure modulus on walls).

As an example, Fig. 2.13 shows a geometry of a single gas turbine burner and the structure of the second annular mode evidenced by AVSP in a full annular chamber with 18 burners. These modes are often crucial for the stability of the combustor.

2.3.5 Acoustic / combustion theoretical tools (C. Martin , A. Giauque , F. Nicoud , T. Poinsot , M. Brear )

At the moment, predicting at the design stage whether a given combustor will oscillate is still a challenge. If and when it oscillates, measurements and computations sometimes give indications of the reasons of the problem but it is usually too late. Being able to predict these phenomena requires the development of a new approach in which LES and acoustics tools are coupled: the joint usage of LES and Helmholtz solvers offers a new and powerful approach for such phenomena and has been exploited for various geometries in the last two years. In a Siemens case [Giauque, 2005], AVBP and AVSP were used together to understand the response of a chamber to forcing.

Section 2.3.4 has shown how acoustic codes were developed at CERFACS. In parallel, new theoretical tools must be built to analyze results: one approach is to look for proper 'energies' to analyze the growth of modes and to examine all terms in the budget of these energy equations. This method generalizes the usual Rayleigh criterion and was exposed in 2005 in a theoretical paper by Nicoud and Poinsot [Nicoud, 2005] following initial ideas proposed by B.T. Chu in 1965. Among all possible energies tested at CERFACS, a classical choice is the acoustic energy e₁ (Poinsot Veynante, RT Edwards, Chapter 8) which follows a budget equation given by:

where the ⁰ subscript refers to mean quantities and the ¹ to acoustic values. If integrated over the whole volume V of the combustor bounded by the surface A, it yields:

where n is the surface normal vector. The surface A consists of walls, inlet and outlet sections. The RHS source term

corresponds to the well-known Rayleigh criterion and is the source of the oscillations. But there are other terms like acoustic fluxes on outlets and inlets

which also have a very strong effect on the instabilities: these terms can not be measured experimentally and most studies consider only the term they can quantify (the Rayleigh term) which is clearly just one part of the problem [Martin, 2004] LES offers a new approach by giving access to all terms of Eq. (2.2). In the PhD of C. Martin [Martin, 2004; Martin, 2005 PhD], a full closure of the acoustic energy equation for a burner developed by Ecole Centrale within the Fuelchief project was performed for the first time (AIAA J. 2006 in press). In the same study LES was used to compute the self-excited unstable modes of the device and AVSP was able to recover these modes and to predict their occurrence. In 2005, Pr M. Brear (Melbourne Un.) has spent 5 months at CERFACS to study energy equations for combustion stability. This study should be continued in 2006 at Stanford during the Summer Program.

2.3.6 Ignition, quenching and flashback (Y. Sommerer , G. Staffelbach , M. Boileau , T. Poinsot )

Unsteady combustion is a major field of research for applications. Igniting a combustor is a central issue for helicopter or aircraft engines. Predicting quenching or flashback is another important issue during transients. By improving mixing upstream of the combustion chamber, many devices used to reduce pollution by increasing mixing can also create the possibility for the flames to propagate upstream of their normal stabilization zone, thereby risking the destruction of the injector or a part of it. Predicting such phenomena is also a challenge for modelling because, during flashback, the flame regime changes considerably from partially premixed to almost purely non premixed flames. CERFACS and EM2C Paris have developed a joint experimental / numerical project which lead to the demonstration that LES can indeed predict quenching and flashback in swirled burners. Results were published in J. of Turb. [Sommerer, 2004].

Figure 2.14: Effects of pilot flame flow rate on flame stabilization in Chamber C. When the pilot fuel flow rate is not adequate (right picture), the flame lifts from the central hub and oscillates.

This study was extended to more complex cases in 2005: Fig. 2.14 shows an example where the effects of piloting on flame stabilization were studied in Chamber B (Fig. 2.10). For this burner, decreasing the fuel flow rate going through the pilot injection (left picture to right picture) leads to a loss of stabilization which is a major problem for operability.

Additional studies of ignition have been performed in helicopter engines for full configurations (Section 2.5) and in spark-ignited piston engines (Section 2.3.10). For these studies, the thickened flame model was coupled to a spark model. At the same time, other models for spark ignition (based on flame surface approaches) have also been coded by IFP in AVBP (PhD of S. Richard), leading to similar results.

2.3.7 Multiburner computations (Y. Sommerer , M. Boileau , G. Staffelbach )

Most academic studies of combustion in gas turbines are performed using a single gas turbine burner and installing it into a laboratory combustion chamber. However real gas turbines use 16 to 24 burners installed in the same annular chamber. In such situations coupling may occur between burners: in regions where the issuing flames from neighbouring burners meet, strong turbulence and heat release can take place and lead to instabilities which cannot be observed in single burners configurations. In cooperation with Siemens PG and DLR, within the EC project DESIRE, CERFACS is studying a chamber equiped with three burners (PhD of G. Staffelbach). This LES has been performed for three burners (5 million cells) and started for the full machine (40 million cells: see Section 2.5). It is the largest computation ever performed with combustion in such a geometry. It requires typically 64 to 128 processors to run efficiently for the 3 burner rig and it was performed with up to 5000 processors on the full geometry on a BlueGene architecture. Fig. 2.15 shows an instantaneous isosurface of temperature.

Figure 2.15: Three-burner combustion chamber of DLR. Isosurface of temperature T=1000 K.

2.3.8 Radiation, instability and pollutants (P. Schmitt , T. Poinsot )

Nitric oxide formation in gas turbine combustion depends on four key factors: flame stabilisation, heat transfer, fuel-air mixing and combustion instability. The design of modern gas turbine burners requires delicate compromises between fuel efficiency, emissions of oxides of nitrogen (NO_X) and combustion stability. Burner designs allowing substantial NO_X reduction are often prone to combustion oscillations. These oscillations also change the NO_X fields. Being able to predict not only the main species field in a burner but also the pollutant and the oscillation levels is now a major challenge for combustion modelling. This must include a realistic treatment of unsteady acoustic phenomena (which create instabilities) but also of heat transfer mechanisms (convection and radiation) which control NO_X generation.

Figure 2.16: LES of combustion in a staged burner.

Figure 2.17: Comparison of LES and experiment: mean axial (left) and radial (right) velocity fields on transverse axis for various distances to inlet. Circles: experiments (DLR), solid line: LES.

In this study, LES was applied to a realistic gas turbine combustion chamber configuration where pure methane is injected through multiple holes in a cone-shaped burner. Mixing and combustion are handled simultaneously using the DTF model and a two-step chemical scheme. Simulations have shown the impact of cooling air and heat transfer on nitric oxide emissions as well as the effects of combustion instability on nitric oxide emissions. Additionally, the combustion instability is analysed in detail, including the evaluation of the terms in the acoustic energy equation and the identification of the mechanism driving the oscillation. Fig. 2.16 shows the geometry of the burner and a typical flow snapshot during combustion instability displaying an isosurface of fuel mass fraction (0.1) (showing the methane jets) and an isosurface of reaction rate (showing the flame position). This regime corresponds to a pulsating flame. The comparison of the LES data with experiments is also good as shown in Fig. 2.17 (J. Fluid Mech. 2006; paper under revision).

2.3.9 Ramjet (Y. Sommerer , L. Gicquel , A. Roux , T. Poinsot )

Combustion instabilities are common in ramjet engines: they can lead to vehicle damage and still remain a difficult problem to solve at the design stages. The LES tools of CERFACS allow to investigate flame dynamics and predict combustion instabilities for highly compressible flows as found in ramjet engines. The research ramjet studied for MBDA is a two-inlet side-dump ramjet combustor experimentally investigated by ONERA and the flight case corresponds to a high-altitude flight condition. Boundary conditions are 'exact' because the inlet is perfectly non-reflecting and the outlet is a choked nozzle. Fig. 2.18 shows the complexity of the flame topology. Two distinct flames are observed and stabilized by different processes: the first flame is located in the head-end and anchored by the recirculation zone due to jet impingement while the second flame is located in the combustion chamber and fed by hot rich burned gases coming from the head end and fresh gases directly coming from the air intakes. Comparisons between LES and LDV fields are good both for mean and RMS fields. LES reveals a high frequency 'screech-like' mode often observed in such side-dump configurations. The frequency observed by LES matches exactly the second transverse mode of the chamber predicted by AVSP suggesting that this oscillation is probaly due to thermo-acoustic resonances.

Figure 2.18: Ramjet configuration and instantaneous visualization of the flame (white iso-surface). x-plane: fuel mass fraction ; z-plane: pressure field.

2.3.10 LES in piston engines (L. Thobois , O. Vermorel , T. Poinsot )

Another field where LES is developing fast is flow in piston engines. Together with IFP, CERFACS has extended its LES tools to piston engines. Two main directions have been pursued: computing multiple successive cycles and computing steady flow with LES through valves. Of course, being able to develop high-fidelity computations on moving grids and managing grid displacements in complex geometries were the major difficulties in this task: AVBP was modified in depth to allow moving mesh computations and new numerical techniques were required to handle these problems. Solutions used now in AVBP are described in a JCP paper published in 2005 [Moureau, 2005].

With this tool, for the first time, CERFACS and IFP have produced in 2005 a computation of all phases of combustion in engines (intake, compression, combustion and exhaust) over multiple cycles with LES. Results open a path which has never been followed before: investigate cycle-to-cycle variations in engines. Fig. 2.19 shows an example of the flame front position in an engine at the same crank angle for four successive cycles. Obviously LES does capture variations between cycles.

Figure 2.19: Fields of reaction rate (marking the flame position) in a plane normal to cylinder axis for four cycles at the same crank angle: all cycles are different (LES with AVBP).

Figure 2.20: LES of the flow field in a steady bench for 4 valve engine tests.

LES was also used to predict pressure losses and flow structure during intake in a joint study with PSA and Ford (Fig. 2.20). It was shown to be much more accurate than RANS for this type of flow [Thobois, 2004; Thobois, 2005]. This configuration was run on CERFACS computers but was also tested with a 20 million cell grid on a BlueGene configuration (Section 2.5).

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