LES Predictions and Validations of the ExitTemperature Profiles in an Industrial Combustion

ChamberG. Boudier∗1, L.Y.M. Gicquel1, T. Poinsot2, D. Bissieres3 and C. Berat3

1CERFACS, Toulouse, France,2IMFT, Toulouse, France,3TURBOMECA, Bordes, France

Large Eddy Simulations (LES) depict very promising capabilities to predict qualitatively unsteady flow structures andproperly predict mean flow statistics in ever more complex combustion chambers. Prior to the industrialisation of the method,few steps are however still required. Among all the steps to achieve this final goal, gauging of the approach in the indus-trial context with its associated requirements is of the foremost importance. The objective of the present investigation goesin this direction and proposes to assess LES to predict temperature distribution at the outlet section of an industrial combus-tion chamber manufactured by Turbomeca (Group SAFRAN). At this occasion LES results are compared with predictionsprovided by RANS calculations and experimental measurements. A two-step chemical scheme forn-decane is designed andintegrated in the LES code to correctly predict temperature levels in this highly complex geometry. The critical issues ofmulti-perforation and film cooling need to be addressed as they are deemed necessary for proper thermodynamic predictions.The former is taken into account through a simplified effusive wall law with given inflow conditions while the latter makes useof low resolution influx conditions for descent time-step control. Preliminary LES results indicate the proper behaviour of theLES solver and qualitatively agree with RANS and experimental results. Further investigations are undergone to meet theindustrial goal of obtaining a predictive tool to be integrated in the design process for combustion chambers.

IntroductionIndustrialisation of the unsteady numerical approach named Large Eddy Simulations (LES) necessarily needs to beperformed with the industrial partners. Indeed, for this tool to properly enter the design steps of the next generationof aeronautical gas turbines, industrial requirements have to be met. Among all the criteria used daily by the turbinemanufacturer Turbomeca (Group SAFRAN), the capability of predicting the chamber exit temperature profile is ofvaluable interest and remains a key design parameter for the engine specification. The larger are the spatial variationsof temperature prior to the turbine, the shorter is the engine life-time or the lower is the overall performance of theengine.Prospective LES results in laboratory scale combustion chambers proved to yield promising capabilities.1–4 Majorsimplifications were however necessary at these stages. Among the omitted aspects that are relevant to this work, onenotes the use of simple hydrocarbon fuels and the usually neglected fine geometrical details present in a real chamber.If the outlet temperature distribution is to be properly predicted, multi-perforation holes and films need to be addressedfor LES to be applied in industry. These observations infer few necessary conditions that need to be satisfied by LES.First, the overall simulated operating point must be identical to the real chamber, that is the modelled chemistry shouldyield the global thermodynamic behaviours as produced by the complex chemical scheme. Second, heterogeneities inthe exit temperature profiles often result from the imperfect mixing of the fresh gases issued by the cooling system(films, multi-perforations....) with the hot products of combustion. Fresh air injection points are in that respect to beproperly taken into account for the mixing to be well reproduced.4,5 To simulaten-decane combustion, a two-stepmechanism with proper thermodynamic properties at the operating point is constructed and validated for LES based ona detailed scheme. To reproduce the cool air injection through films, influx conditions are used to allow low resolutionmeshes in these regions. Similarly, multi-perforated areas make use of effusive wall laws to at least reproduce theincoming flow of fresh air.The organisation of the paper is as follows: first a brief review of the LES code is given, followed by the list ofmodels employed and the chemical scheme developed. Details of the Turbomeca chamber are then exposed alongwith the various flow parameters necessary for LES: grid, Boundary Conditions (BC’s) ... Finally, preliminary resultsare produced and qualitatively compared to RANS predictions. Specific attention is devoted to the assessment of theLES predictions in terms of the exit temperature distribution for which RANS and experimental profiles are available.Conclusions are drawn and prospective directions are suggested to integrate LES in an industrial design chain.

The LES solver: AVBPThe LES solver AVBP (see www.cerfacs.fr/cfd/avbpcode.php) simulates the fully compressible multi-species (vari-able heat capacities) Navier-Stokes equations. Based on a finite-volume discretization of the governing equations for

∗Guillaume.Boudier@cerfacs.fr

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turbulent / laminar, reacting / non-reacting flows, the solver is able to handle fully unstructured / structured / hybridmeshes. Higher order temporal and spatial schemes6 offer reliable unsteady solutions for complex geometries asencountered in the field of aeronautical gas turbines.

LES closures

The concept of LES introduces the notion of spatial filtering to be applied to the set of governing equations usuallyused to simulate turbulent reacting flows.7,8 Resulting from this operation, are unclosed terms issued from the non-linear character of the Navier-Stokes equations. In order to solve numerically the filtered Navier-Stokes equations,Sub-Grid Scale (SGS) models need to be supplied to mimic the turbulent scale effects on the resolved field.9

I this work, SGS stresses are described using the classical Smagorinsky10 model. When dealing with wall boundedflows, wall functions are introduced and yield results comparable to the dynamic model.11 SGS turbulent mixingappearing in the species and temperature transport equations are modelled through the gradient hypothesis alongwith the turbulent Schmidt, Prandtl numbers. Finally, filtered source terms resulting from the change in compositiondue to chemical reaction need also to be closed. This flame / turbulence missing information is obtained by use ofthe Dynamically Thickened Flame (DTF) model12 which allows to handle both mixing (which is crucial in partiallypremixed flames) and combustion.

n-decane two-step chemical scheme

The required accuracy of the exit temperature levels imposes the use of a precise chemical scheme which correctlymodels burnt gas temperatures. The chemical scheme developed for this work is obtained for gaseousn-decaneformally denoted bynC10H22. A two-step scheme is retained to take into account dissociation and re-association ofthe carbon oxides. The set of governing reactions reads:

nC10H22 +212

O2 → 10CO + 11H2O (1)

CO +12O2 ⇀↽ CO2 (2)

The first reaction in Eq. (1) is an irreversible reaction decomposing the complex hydrocarbon into carbon monoxideand water. The second reaction in Eq. (2) is the re-combination of the carbon monoxide in carbon dioxide and allowsthe control of the heat release issued by the first reaction. It is governed by an equilibrium process. Reaction constantssuch as the pre-exponential constants have been fitted using the Sandia’s chemistry code CHEMKIN along with thedetailed chemical scheme used by Turbomeca in the RANS code.

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Fig. 1 Two-step chemical scheme forn-decane: Validation against the detailed scheme as used in RANS by Turbomeca for(a) the temperature of the burnt gases and (b) the flame speed as functions of the equivalence ratio.

Figure 1 shows equilibrium temperatures and flame speeds as predicted by the reduced two-step scheme and comparedto the detailed mechanism for fully premixed combustion. Although differences appear for the highest values of theequivalence ratio (rich sides of the diagrams), the good overall behaviour of the equilibrium temperature ensuresthat the thermodynamic behaviour is expected to be well reproduced at least in a global sense. That is, if the meanequivalence ratio defining the operating point to be simulated is below1.2, the developed scheme ensures proper meantemperature predictions at the exit of the chamber. Spatial and temporal deviations from the mean temperature mayhowever be affected by the differences observed. In particular, if local values reach the rich sides of the diagrams, the

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observed differences infer poor predictions of the flame positioning and hot gas distributions prior to the exit. Thisshortcoming is however limited for the geometry targeted as large values of the equivalence ratio are restricted to localarea and far from the exit of the chamber.

Turbomeca target configurationThe computational domain is a36 degree section of an annular inverted-flux combustion chamber designed by Tur-bomeca (Group SAFRAN). A premixed gaseous mixture ofn-decane enters the chamber through the prevaporiser.Fresh gases are consumed in the primary zone, delimited by the chamber dilution holes (see Fig. 2). This region ofthe chamber is fed with air by the primary holes located on the inner liner of the chamber (see Fig. 2). Burnt gases arethen cooled in the remaining part of the chamber thanks to the dilution holes and cooling films located on the innerand outer liners as well as on the return bend of the combustion chamber. Multi-perforated plates ensure local wallcooling in the region pointed out on Fig. 2.

Fig. 2 Turbomeca chamber considered for LES in an industrial context.

Numerical characteristics

A fully unstructured mesh is produced with286, 500 nodes and1, 550, 000 tetrahedric elements resulting in an explicittime step of about0.13µs. The mesh is refined in the vicinity of the fuel injector outlets, the primary holes and thedilution holes, Fig. 3. Special attention is devoted to the control of the grid spacing in the region of the films so asto ensure a manageable time step for LES to be performed with a tractable computer cost. In general, the height ofthe film inlets is represented by one face of a single element which imposes the manipulation of the fluxes throughthis face to enforce the BC’s. The same approach is used for the specification of the cooling air effusing from themulti-perforated walls. All other inlet and outlet BC is treated with the NSCBC characteristic boundaries13 whichallows to take under control the acoustic behaviour of the system. Side boundaries are considered as periodic. Theoperating point is set to the real operating point.

ResultsThis section presents the LES results as obtained for the target geometry from Turbomeca (Group SAFRAN) anddescribed previously. Focus is made on the temperature field as obtained instantaneously by LES so as to illustrate theunsteady nature of the flow. Assessment of the mean temperature field and mean exit temperature profiles are obtainedby comparisons against RANS results as well as experimental measurements. The planes for which the comparisonsare illustrated, are identified on Fig. 4. In particular, quantification of the radial variations of the mean temperature,denoted by the non-dimentionalized parameterRTDF , is investigated for plane4. Qualification of the approach interms of industrial requirements is assessed at this occasion.

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Fig. 3 Fully unstructured mesh as considered for the geometry of the Turbomeca chamber.

Fig. 4 Cutting planes position: 1 Symmetry plane, 2 Prevaporiser outlet plane, 3 Periodicity plane, 4RTDF plane.

Unsteady LES temperature fields

Figure 5 shows instantaneous temperature distributions within the combustion chamber in the planes identified inFig. 4. Fresh gases exiting from the prevaporiser with an equivalence ratioφ > 1 are burnt through a rich premixedflame attached to the pre-evaporator outlet sections. The remaining unburnt gases, composed of puren-decane mixedwith combustion products, are consumed by a diffusion flame front located in the vicinity of the chamber head coolingfilms and the primary holes. The maximum value of the instantaneous temperature field corresponds to the stoechio-metric temperature.Note that combustion is restrained to the primary zone of the chamber as designed initially by Turbomeca. Primaryholes feed the diffusion flame with oxygen, Fig. 5(b), while dilution holes confine the chamber’s primary region bydramatically cooling the gas mixture and partially contributing to the combustion of the fresh gases. Cooling films areobserved to largely contribute to the overall wall cooling process by shielding the walls from the hot gases.

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(a) (b)

(c) (d)

Fig. 5 Instantaneous temperature fields as obtained by LES: (a) plane 1, (b) plane 2, (c) plane 3, (d) plane 4.

Spatial variations of the instantaneous temperature field is evidenced by Fig. 5(d) for plane4. At this location, regionsof cool air are clearly separated from the zone with large values of the temperature. Significant diminution of thepeak temperature is however achieved when compared to the instantaneous field ofT as obtained within the com-bustion chamber. Such results underline the potential of LES to reproduce temporal and spatial evolutions of highlyunsteady reacting flows which constitutes a valuable information for design purposes . Assessment of the predictionsin terms of industrial critieria is however still needed. This is the aim of the following section where mean temporalLES predictions are gauged against RANS results andRTDF ’s are evaluated by comparisons against experimentalmeasurements.

Validation of the LES mean temperature predictions

Mean temporal values of the LES temperature fields are obtained through Reynolds average of the instantaneous LESpredictions. Integration is here performed for roughly one flow-through time in order to ensure convergence of atleast the first moments. Further investigations are currently conducted to assess stationarity of the higher order flowstatistics. Non-stationary information is however accessible by LES; it will be retrieved in future work but will not beaddressed in this work although very valuable for design purposes..Figure 6 depicts the mean temperature fields as obtained by LES (left column) and by RANS for the same configuration(right column). Mean temperature distributions, in the various planes of interest, are seen to be much sharper in LESand reacting regions reach larger values of the temperature when compared to the RANS predictions. Such differencesare explained through the theoretical differences inferred by the two approaches and the well known smearing effect ofRANS modelling (here a classicalk− ε model for turbulence). Also at the origin of these differences are the chemicalschemes which differ as underlined above. Note that the RANS turbulent combustion model is CLE model14 whichcorresponds to a mixed-is-burnt model limited by equilibrium. It is complemented by a detailed chemical schemewhile LES use only a two-step reaction. Because of these modelling differences, the overall flame position is seento differ when comparing the two methods. If identified by the peak of the mean temperature, the LES mean flame

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front is essentially encompassing most of the primary zone of the combustion chamber. RANS results seem to predictan overall shorter flame front limited to the lower par of the primary zone of the combustion chamber. Providedthe various differences issued from the LES approach and the RANS method, the gross agreement between the LEStemperature field and the RANS predictions constitutes a qualitative validation of the developments performed in LESand for this configuration (at least from an engineering point of view). The other noticeable differences appear in the

(a) (b)

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Fig. 6 LES and RANS comparisons for different planes within the chamber (cf. Fig. 4). The mean temperature fields in theplanes of interest and as issued by LES are illustrated on the left column while RANS predictions are shown on the rightcolumn.

jet trajectories within the chamber. In general, LES jet penetrations are less pronounced than the one obtained with

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RANS. Such observations are expected to be a major source of differences when assessing the mean exit temperatureprofiles.Figure 7 assesses the LES results in terms of the industrial design criterion that is theRTDF . The primary aim of thisparameter is to quantify the radial variations of the mean temporal temperature from its mean planar value. It indicatesthe degree of heterogeneity to be seen by the turbine blades. Of course, one tends to control theRTDF profile inregards to the mechanical constraints. Mixing of the cool gases with the hot products issued from the combustion, ishenceforth critical to properly predict this quantity and the associated design.RTDF profiles for plane4 as obtainedfrom LES are shown on Fig. 7 for the exact integration of the numerical model (solid black line) and experimentalmeasures obtained for four radial positions on the real engine (open diamonds). Due to experimental uncertainties, adiscrete treatment approaching the experimental approach is performed on the LES and added to Fig. 7 (solid circles).This diagnostic aims at recovering the low spatial experimental discretization which may bias the measures to becompared to LES.

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Fig. 7 LES validation in terms of RTDF profile for plane 4.

Overall agreement between measured data and LES results is very encouraging. Differences in theRTDF profilesessentially appear for low values of the radial position. In this region, cool gases are expected to be present forboth LES and the real chamber. LES however predict more mixing with the hot gases when compared to the data.Poor discretization of the experimental measurements is observed to be an important issue when applied to LES orexperiment. Its impact may not be negligible on the expected results especially in regions of enhanced heterogeneities(bottom of the vein). Comparisons with the measurements and RANS results nonetheless confirm the potential of LESas a design tool for industry.

ConclusionApplication of LES to industrial configurations is of great interest for design purposes. Indeed, because of capacity ofthe approach to predict unsteady turbulent reacting flows, LES yield information that is not accessible with conven-tional numerical approaches. Among the potential mechanisms grasped by LES and of great importance to industry,one retains: Flame turbulence interactions, flame acoustic coupling and all the large scale temporally dependent flowfeatures such as mixing. Validation of the approach when applied to industrial configurations is however still needed.In an attempt to assess LES with an industrial design criterion, predictions of a Turbomeca chamber is performed inthis work. Comparisons against RANS results underline the potential differences inferred by the different approaches.In that respect, LES mean temperature fields within the chamber are observed to be sharper and to reach larger values.Assessment of the predictions in term ofRTDF profiles, a design parameter quantifying the mean exit temperatureheterogeneities seen by the turbine, proves LES to yield very promising results. Among the numerically importantparameters evidenced by this work on LES, one stresses the necessity of dealing with the cooling system as often

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encountered in real gas turbine engines. To properly take into account film cooling as well as multi-perforated plates,specific treatment is implemented to reduce computational costs imposed by such geometrical details. Likewise, atwo-step chemical scheme forn-decane is obtained and validated for the operating point dealt with. Formal validationof these developments is obtained in light of the quality of the LES predictions for the Turbomeca chamber.On-going investigations are currently been performed to improve the treatment of the cooling system which is found tobe a critical parameter for temperature heterogeneity predictions. More specifically, the proper integration of the multi-perforated wall is being addressed for LES within the INTELLECT DM European project. Likewise film cooling mightbe improved at this occasion. Finally, developments of higher order chemical schemes may be of interest if propertemperature and flame position is deemed critical to assess next generation of aeronautical gas turbine engines.

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