A PRACTICAL MODEL FOR THE HIGH-ALTITUDE RELIGHT OF A GAS TURBINE COMBUSTOR

Transcription

1 MCS 7 Chia Laguna, Cagliari, Sardinia, Italy, Setember 11-15, 011 A PRACTICAL MODEL FOR THE HIGH-ALTITUDE RELIGHT OF A GAS TURBINE COMBUSTOR A. Neohytou*,1, E. Mastorakos*, E.S. Richardson**, S. Stow*** and M. Zedda*** em57@eng.cam.ac.uk * University of Cambridge, Trumington Street, Cambridge CB 1PZ, UK **Faculty of Engineering and the Environment, University of Southamton, SO17 1BG, UK ***Rolls-Royce, Derby, UK 1: Now at CERFACS, Toulouse, France Abstract A model that simulates the ossible flame trajectories following sark ignition in a generic recirculating flame has been alied to a realistic aero-engine combustor. The model has been reviously validated for gaseous and simle sray flames. It uses a CFD solution of the unignited flow and estimates the volume of the combustor that could be ignited given a articular flow field, sray distribution, and sark location, shae and size, and also rovides a measure of the variability between indeendent sarking events. From this information, the ease of igniting the combustor can be assessed, and hence the combustor and injector geometry and sark lacement decisions can be informed at a very early stage of the design rocess. Results for igniting a Rolls-Royce test combustor run with kerosene at high-altitude relight conditions for which exerimental data are available and for which a RANS CFD solution has been develoed, demonstrate the usefulness of the model's outut. The results are consistent with exeriment and also reveal that the sark characteristics and location used in the exeriments, develoed over a number of years by trial-and-error methods, are indeed close to otimum. 1. Introduction Aircraft engines must satisfy high-altitude relight caability. Inexensive models that estimate the flame roagation following sark ignition are valuable in assisting engineers during the design of combustors. Recently, various fundamental asects of sark ignition of non-remixed systems have been revealed by exeriment and simulation (for both laminar and turbulent flames) and some of the findings are reviewed in Ref. [1] and, for srays in articular, in Ref. []. A hysics-based model with low comutational cost was resented in Ref. [3] that aimed at estimating the growth of a flame following ignition in recirculating flows by interrogating a cold CFD solution. The dominant hysics found by recent exeriments with recirculating flows [, 4-6] were imlemented in the model. The model reroduced the turbulent diffusion and the mean convection of the flame, the flammability limits in srays, and the local extinction due to the turbulent stretch rate. In addition, the randomness of the turbulent transort of flame elements and the randomness of the local mixture fraction was incororated. This led to different realisations of the flame growth with the same initial conditions of sark, as demonstrated in exeriments [, 4]. In Ref. [3], the ignition rogress factor π ign, defined as the volume of flammable mixture that has been ignited, was shown to be an interesting quantity to study and led to a calculation of the ignition robability (i.e. the robability that the whole flame will be ignited from deositing a sark at a given location), which agreed reasonably well with exerimentally-determined distributions. The model therefore is in a state to be used in realistic geometries and sarks.

2 In this aer, this model is alied to a realistic kerosene combustor from Rolls-Royce [5]. Previous exerimental investigations with ignition of generic recirculating sray flames showed that ignition was successful if the flame kernel was convected towards the fuel injector by the flow [, 4-7]. In addition, a focused arametric investigation of the sark osition along the side wall of the burner in Ref. [] reached the imortant conclusion that the best axial location for ignition was at the maximum width of the central recirculation zone. Exeriments done with the articular combustor investigated here showed that ignition has a robabilistic nature, that the time from ignition to overall flame stabilisation is between 30 ms and 50 ms, and that successful ignition is associated with a kernel that moved ustream [5]. The two last findings were also reorted in a LES simulation of this combustor, resented in Ref. [8]. The flow atterns from this simulation are analyzed in the resent ignition model, which intends to reroduce these findings. The statistics of π ign are investigated for different sark configurations, and the location and shae of the sark, for the same sark energy, that lead to the best ignition behaviour are exlored. Firstly, we introduce the mathematical model and the combustor investigated. Then we resent the results comuted with the model. The aer concludes on the otential of the model in assisting the design of combustion chambers.. Numerical Formulation The model was described in detail in Ref. [3], where a detailed comarison with exerimental data on sark ignition with gaseous and sray flames in simle geometries is given. In this section, the main concets of the model are reeated for clarity and the CFD solution of the gas turbine combustor is briefly resented..1 Model descrition: main idea The model aims at reresenting the ossible trajectories of individual flame elements originating from a sark in a generic flow field carrying drolets. A time-averaged CFD solution of the cold flow is needed as an inut to the model. The resent model is based on the following stes: 1. The flow is filled with regular grid cells with an arbitrary size. These grid cells can have two states, cold or burnt. Initially, all grid cells are in the cold state. Cells are laced throughout the combustor volume.. The simulation is initialised by defining a sark volume in the domain. All grid cells that overla with the sark volume are switched to the burnt state and each of them releases a flame article. Any shae of sark can be used. 3. A flame article is tracked with a Langevin model using the cold CFD field. A article can extinguish according to a criterion based on a Karlovitz number, resented below. When a article extinguishes, it is no longer comuted. 4. Every time a article visits a grid cell in a cold state, the grid cell switches to the burnt state, if the Karlovitz number ermits it, and a new article is emitted at its center and follows its own random walk. 5. Throughout the simulation, the number of cells in a burnt state divided by the total number of cells is comuted as a function of time. This ratio is named ignition rogress factor and is given the symbol π ign. 6. The comutation is reeated many times with different realisations. The statistics of π ign for this sark location can be analysed to assess ignition erformance. By reeating this rocedure for different sark locations, sark shaes etc, and comaring the resulting statistics of π ign (for examle, its mean and rms), the relative erformance of the various sarks and of their lacement can be assessed. Good ignition imlies high values of π ign at the end of the simulation, while bad ignition imlies a low value, since the flame

3 would not have travelled much before it is either extinguished or convected out of the combustor. Very reeatable behaviour imlies that every realisation gives similarly good or bad ignition characteristics, i.e. low variability in the final π ign, which gives low rms in the statistics. In contrast, a sark or a articular sark location giving very variable ignition behaviour would be characterised by high rms of π ign. The usefulness of the resulting values of π ign lies more in relative comarisons, than in absolute values. The gas turbine combustor designer must strive to achieve high average and low rms of π ign either by selecting the sark location and characteristics given a flow field, or by altering the flow attern given a sark.. Mathematical formulation The flame article coordinate in direction i evolves according to the stochastic differential equation: dx U dt (1), i =, i U, i where is the article velocity in direction i. follows a simlified Langevin model U, i [9] and consists of a linear drift towards the local Favre averaged velocity of the flow and an added isotroic diffusion term: 1 3 ~ 1/ du, i = ( + C0 ) ω ( U, i U i ) dt + ( C0ε dt) N, i () 4 where U ~ is the local Favre averaged velocity in direction i, is a normally distributed i N, i variable (with mean zero and variance unity), C0 is a constant assumed equal to.0 [9], ε is the turbulent dissiation at the article location and ω is the inverse turbulent timescale at the article location ω = u / Lturb,, u = (/3k ) with k the local turbulent kinetic energy and ε = k ω. The random variable for one article is indeendent from N, i another (the velocity correlation between articles is ignored). Hence, articles are simly convected by the turbulent flow and undergo random walk to model their disersion. Equations (1) and () are the standard formulations of simulating turbulent disersion in a Lagrangian framework. The initial velocity of each article is a random Gaussian variable with a mean equal to the local Favre mean and an rms equal to the local turbulent intensity. Different realisations are obtained by setting different random distributions. At the end of each time ste dt, a criterion based on a Karlovitz number is used to assess if the flame article extinguishes. A Karlovitz number Ka is defined for each article and is comared to a critical value Kacrit. If Ka > Kacrit, the article extinguishes. Ka is defined as the ratio between the chemical time and the recirocal eddy lifetime [10]: 3 ( u ) 1 Ka = ν (3) L turb, S L, where ν is the mixture kinematic viscosity of air at the conditions studied and is the laminar flame seed, detailed below. The critical value Ka crit was found by Abdel-Gayed and Bradley to be 1.5 for remixed flows [10], and the same critical value is used here in view of the lack of corresonding data for the extinction of turbulent sray flames. Each article begins its random walk from a mixture fraction samled from a β function df based on the mean and the rms of the mixture fraction from the CFD solution. The stochastic differential equation for the mixture fraction of a article assuming interaction by exchange with the mean [9], and alying the mean evaoration rate from the local CFD cell, is given by: 1/ 1/ S L,

4 1 ~ Γm dξ = Cξω( ξ ξ ) dt + (1 ξ ) dt (4) ρ where ρ is the mean local density while Γ m is the mass source term due to evaoration, ξ is the article mixture fraction and ~ ξ is the local Favre averaged mixture fraction in the flow. Cξ is a constant taken equal to.0 [9]. Knowledge of ξ enables the calculation of and in turn of Ka. The comutation of the laminar flame seed as a function of the local mixture fraction for a gas flame is trivial, while in a sray is more comlicated and the S L, S L, method used is resented in Section.3. As discussed in Ref. [3], validation of the resent model against exeriments [,4] shows that it is valid only for high values of u /S L, where turbulent disersion dominates, which is obviously the case in gas turbine combustors. S L,.3 Laminar flame seed for kerosene srays The value of S L, needed for the evaluation of the local Karlovitz number of the article, must be given for srays as a function of overall equivalence ratio φ 0 (i.e. using both the gaseous fuel vaour and the liquid fuel), the vaour fraction Ω, and the drolet diameter a d. Such information can be rovided exerimentally or numerically. For the case of altitude relight, we need S L at low ressure and low temerature conditions. Laminar remixed sray flame calculations with detailed chemistry that can rovide the S L needed have been erformed already [11]. The results of Ref. [11] are correlated here by:.5 ( φ0 μ) S L = S L, max ex (5) π σ The flame seed is determined by the three arameters S,, μ and σ. is the gaseous L max laminar flame seed at stoichiometry, μ = 1.07 and σ = If φ 0.5, the flame seed g g 0 S L,0 is set to zero; this reresents the lean flammability limit. For very small drolets ( a d 5μm ), the simulations of Ref. [11] show that the sray flame seed is virtually identical to the gaseous one, S L, max = SLg, max, μ = μg and σ = σ g. For ure gas, S Lg, max = 1.01SL,0. For larger drolets ( a d > 5μm ), we use the following exressions. For n-decane at atmosheric conditions: S 3 L, max ( = 0)/ SL,0 = (ln( ad )) Ω 0.430(ln( a d )) 6.87(ln( a )) μ Ω = 0) = 0.64(ln( a )) 0.31(ln( a d )) (ln( a )) ( d 3 σ Ω = 0) = 0.41(ln( a )) 1.994(ln( a d )) (ln( a )) ( d For n-decane at high altitude relight conditions ( =41.37 kpa, T =65 K): S 3 L, max ( = 0)/ SL,0 = 0.04(ln( ad )) P0 0 Ω 0.859(ln( a d )) (ln( a )) μ Ω = 0) = 0.974(ln( a )) 30.89(ln( a d )) 3.963(ln( a )) ( d 3 σ ( Ω = 0) = 0.566(ln( ad )) (ln( a d )) (ln( ad )) (11) The coefficients vary linearly between Ω = 0 and Ω = 1 (ure gas): S ( S S ( Ω = 0)) Ω + S ( = 0) (1) L, max = Lg, max L, max L, max Ω d d d d d (6) (7) (8) (9) (10) μ = ( μg μ( Ω = 0)) Ω + μ( Ω = 0) (13) σ = ( σ g σ ( Ω = 0)) Ω + σ ( Ω = 0) (14)

5 In the above curve-fits, a d is to be used in microns. The original data and the above curve fits are shown in Fig. 1, where it is evident that the laminar flame seed for a sray can be high even in very rich situations, which has been exlained by the fact that the flame consumes only the fuel that is available in vaour form; this could be close to stoichiometry even if there is overall much more fuel in the liquid hase. Note that the data for n-decane can be used instead of kerosene, which is the fuel of relevance to aviation gas turbines, because the two fuels have reasonably similar flame seeds [1]. Note also that the laminar flame simulations [11] show very small changes in the flame seed between atmosheric and the used relight conditions, ossibly due to the detrimental effect of the low temerature being balanced by the beneficial effect of the low ressure. Therefore, to a good aroximation, the data in Fig. 1 are sufficient for a range of altitudes. However it is very imortant to use laminar flame seed data for flames in srays, and not in revaourized fuels, since the SMD and φ 0 can affect S L in a major way, as Fig. 1 demonstrates. (a) (b) Figure 1: Laminar flame seed in srays against the overall equivalence ratio φ 0 for different initial drolet diameters for (a) n-decane at atmosheric conditions and (b) n-decane at high altitude ( relight ) conditions ( P0 =41.37 kpa, T0 =65 K). Plain lines corresond to the detailed chemistry simulation data [11], while dashed lines are comuted using Eq. (5) with Ω = 0. (a) (b) Figure : (a) Geometry of the test combustor [5,8]. The black iso-surface shows qualitatively the fuel lacement from the CFD solution of the un-ignited flow. (b) Plane y = 0 mm contains the axis of the cylindrical sarks studied. The two arrows show qualitatively the sray angle. The shaes of sarks A, B and C are reresented.

6 The CFD solution (resented later) includes sray, and so the Sauter Mean Diameter (SMD), the fuel vaour mass fraction, and the fuel in liquid hase are available at every grid node, and hence S L can be calculated. Since the turbulent kinetic energy and dissiation rate are also available from the CFD solution, the Karlovitz number of every flame article and at every oint during the article's trajectory can be evaluated and hence the ossibility of quenching is included for all times during the flame article s evolution..4 Combustor investigated and model settings The combustion chamber is shown in Fig. a. The downstream direction is aligned with the x -axis. The high-altitude test rig is a two-sector rig, one sector (the left-hand sector when looking downstream) being fitted with a lean-burn injector (Rolls-Royce Deutschland Ltd & Co KG), and the other having an un-fuelled dummy injector. The fuel injected is liquid kerosene. A RANS solution of a cold flow field of this geometry was erformed in the Rolls- Royce laboratories using the in-house code PRECISE (see [8] and references therein). The oerating conditions chosen are given in Table 1. The RANS solution rovides the three comonents of the mean velocity, the turbulent kinetic energy and dissiation rate, the fuel and liquid fuel mass fractions, and the Sauter Mean Diameter at every CFD grid cell. Due to the low volatility of kerosene and the cold conditions, there is virtually no fuel in vaour form in the combustor and hence Ω = 0 in Eq. (1). The flame article tracking is erformed on a rectangular Cartesian grid (which can be larger than the CFD domain). Each of these cells is initially deemed cold. The time ste in the flame article tracking is dt = 0.5 ms, smaller than the estimated turbulent timescale L turb /u = ms in the flow. The simulations stos after 60 ms, which has been found to be long enough for the flame articles to have exerienced all their ossible histories. 1/ The quantity ( C0 ε dt) dt is the maximum sacing for tracking the flame, as suggested in Ref. [3]. The volume-averaged turbulent dissiation rate in the domain was about m /s 3, the number of grid cells for the flame tracking model was 67,87, and the grid sacing was mm, which satisfies this criterion. 50 indeendent sark events were simulated. Under those conditions, the CPU time to comute a single sark event was about 30 min in a deskto PC. The different sarks studied are summarised in Table. All sarks investigated are cylindrical, the cylinder axis being aligned with the z -axis, and have the same volume (i.e. same energy). Sarks are located on the uer wall on the line y = 0 mm and a arametric investigation is carried out on the sark shae (length Ls and diameter ds of the cylinder), and the location of the sark axis x s. The sarks studied are illustrated in Fig. b. The length and diameter of sark A are based on flame imaging immediately after the energy deosition [5, 6] and the cylindrical shae was chosen as reresentative of the enetrating sarks created by the surface discharge igniters used in gas turbines. Sarks B and C are used as a sensitivity study. At t = 0, all model grid cells intersecting the sark are deemed burnt and a random walk of one flame article starts from each of these burnt cells. Large sarks, therefore, emit more flame articles than small sarks. However, since the model allows for flame article quenching if the article is found with Ka > Ka crit, it is ossible that not all of these flame articles will evolve and hence the size of the sark, er se, does not guarantee good ignition. According to the resent model, the imortant oint is whether the sark has intersected sray with SMD and overall equivalence ratio aroriate to give a high S L and fluid with the correct velocity. As will become evident later, this is crucial for ignition success.

7 Table 1: Oerating conditions used in the CFD RANS simulation. Air ressure (bar) 0.55 Air temerature (K) 78 Fuel temerature (K) 88 Normalized air mass flow 0.38 Normalized fuel-air ratio 0.56 Table : Different cases studied in the simulations (sark osition along centerline, Sark sark diameter d, sark length L ). s x (mm) L (mm) (mm) s s s d s A [0,100] B C x s 3. Results and Discussion 3.1 Effect of sark location Figure 3a shows the time evolution of π ign for all events for sark A at x s = 47.5 mm. In all events, π slowly increases until t =10 ms, then raidly increases until t = 40 ms and ign finally stabilises to a constant value. The slow initial increase is fully consistent with exeriment in both simlified [, 4] and comlex geometries [5-7]. The time duration needed to reach a stabilized value for π rovides an estimate of the time needed to ignite the whole ign combustor. For the resent results, this time is close to the ignition timescale, about 50 ms, reorted in the exeriment [5] and the LES simulation of Ref. [8]. This constitutes an imortant validation test of the resent model and suggests that the underlying hysics of flame exansion for this flow is reasonably accurately included by the combination of the Langevin random walk, the generation of new flame articles from flammable regions reached by a travelling article, and the use of a local Karlovitz number criterion. The simulations also reroduce the stochasticity of ignition since each event results in different values of π ign. Considering the values of π ign for each event at the end of the simulation ( t = 60 ms), a mean and a rms can be calculated, see Fig. 3a. These two quantities reveal the mean amount of burned material and the variability of ignition associated with the articular sark center and the sark shae. In Fig. 3a, the average and the rms of π ign are resectively 0.19 and The low value of the rms suggests that different events lead to fairly similar final values of burned volume. The df of the final π ign comiled over the 50 realisations is shown in the inset. Figure 3d shows the evolution of the mean and the rms of π ign with x s (i.e. for different sark locations) for sark A. The final mean π ign first increases with x s, stabilises to a relatively high value in the range 0 mm < xs 60 mm, then decreases with x s and stabilises to a relatively low value in the range 80 mm < x s 100 mm. Close to the injector, mm < x 0 mm, the sark is located in a region ustream of the recirculation 0 s

8 zone, in the corner (Fig. b). The low value of the average of π ign at x s = 0 mm indicates that in most cases, the flame does not sread and raidly extinguishes. In addition, the high rms of π shows that ignition there is very robabilistic so that in some events, a large ign volume is ignited while in others the kernel raidly extinguishes. In this zone, there is virtually no fuel. However, due to the large sark size, some flammable material is ignited, albeit very little. Moreover, the mean convection there is ositive while the turbulent kinetic energy and the turbulent dissiation are relatively high. Therefore, the ignited articles can either be brought downstream to ignite regions with more fuel or they can be transorted ustream where there is no fuel leading to extinction. Hence, different realisations can lead to successful ignition events or to quickly quenched kernels. For = 0 mm, the average of π ign becomes 0.19 while its rms decreases to (Fig. 3d). This means that for a sark at =0 mm, most of the events ignite a relatively large volume of the combustor with a low x s variability. This is because there is a great overla between the sark and the recirculation zone, see Fig. b. In the recirculation zone more fuel exists and ignited flame articles are easily catured by the recirculating flow and brought to the flammable region, as suggested by the exeriments with recirculating srays of Ref. []. x s (a) (b) (c) (d) Figure 3: Time evolution of π ign of individual sark events for x s = 47.5 mm and (a) sark A, (b) sark B and (c) sark C. The inset show the PDF of π ign at the end of the simulation. (d) Average and rms of π ign comuted at the end of the simulation over all events vs. sark location along the uer wall x s for sark A. In the region 0 mm < xs 50 mm, Fig. 3d shows that the average and the rms of π ign remain almost constant. This imlies that any sark in this region will have similar ignition

9 erformance, and that all events lead to a relatively large volume of the burner ignited. Note that this region corresonds to the maximum width of the recirculation zone. In Ref. [], with exeriments with sarks along the side wall, the best sark lacement corresonded to the maximum width of the recirculation zone. Since the highest mean π ign was redicted from sark locations close to where the recirculation zone is widest, the exerimental recommendation has been accurately reroduced by the resent model alied to realistic combustors. This rovides a further validation of the usefulness of the results achieved. Finally, in the region 50 mm < xs 80 mm, the average of π ign decreases with x s while its rms first increases with xs, reaches a eak at x s = 70 mm and then decreases to a relatively low value. As x s increases from 50 mm, the sark center moves further away from the maximum width of the recirculation zone and in turn the overla between the sark and the recirculation zone is less, see Fig. b. Therefore, the ignited flame articles are more likely to be convected downstream by the mean flow although the random turbulent motion can occasionally bring them towards the recirculation zone. It is thus exected that the mean π ign becomes lower with xs. The increase of the rms of π ign is due to the increased variability. In some events all articles are convected downstream, leading to a low π ign while in others turbulence moves flame articles in the recirculation zone, leading to a high π ign. The location x s = 90 mm corresonds to the stagnation oint of the recirculation zone, see Fig. b. Beyond this value, there is no overla between the sark and the recirculation zone and there is little chance that the turbulent motion brings the ignited articles in the recirculation zone. The ignited flame articles are all convected downstream and never make it to the recirculation zone. Hence, they can only ignite material on their way downstream but not ustream. This leads to a low average of π ign and a low rms of π ign (little variability). We conclude that the model reroduces the exerimentally-observed timescale of fullflame establishment, the exerimentally-determined best ignitor location, and rovides useful insights concerning the stochasticity of individual ignition events. It can therefore be used by the engine designer to assist the analysis of a combustor in terms of its relight caability. 3. Effect of sark shae Figure 4: Average and rms of π ign comuted at the end of the simulation over all events with sark location x s = 47.5 mm for sark A (normal), B (long and thin) and C (short and wide). In this section, the sark axis is fixed at xs = 47.5 mm and the statistics of π ign are comared between sarks A, B and C. Note that this sark location is in the best ignition

10 region as shown in the revious section. Figures 3a, b and c show the evolution of π ign with time for all events, resectively for sark A, B and C. Events for sark A and B both lead to relatively high values of π ign. However, the variability is larger with sark B (thin and long) than with sark A. In addition, it is clear that sark C (wide and short) results in very low values of π ign with all events behaving in the same way (i.e. a very narrow df of the final π ign ). Figure 4 shows the average and the rms of π ign calculated over all events at the end of the simulation for sarks A, B and C. Sark A leads to the highest value of the average of π and a low value of the rms. Sark B has a slightly lower mean and a higher rms. Thus, ign events in sark A reeatedly ignite a larger volume of the combustor than sarks B and C. The behaviour of sark A is thus referred. In the resent combustor, the overall equivalence ratio is much higher on the sides of the recirculation zone than in the center (not shown here, but see Fig. 30 of Ref. [11]). Since in sark A, the sark volume is concentrated to a region of high equivalence ratio, more articles samle flammable mixtures than in sark B, where a substantial art of the sark is in the center of the recirculation zone where there is almost no fuel. The larger mass of flammable material ignited by sark A can then sread and ignite further material. This leads to higher π ign. Moreover, it is ossible that since sark B exeriences a larger range of mean velocities and turbulence intensities than sark A, see Fig. b, the variability and in turn the rms of π ign is higher for sark B. With sark C, the mean and the rms of π ign are both low. This imlies that little material is ignited in all events. This is attributed to the shae of the sark that results in little enetration in the recirculation zone, see Fig. b. Although the sark overlas with flammable material, the flow tends to convect all ignited articles downstream. The results show that a given sark energy (in the resent model, sark energy is associated with the initial volume that releases flame articles; sarks A-C have the same volume) can have different ignition behaviour deending on the initial kernel s shae relative to the recirculation zone and the fuel lacement. This observation is consistent with exeriments [] that showed that successful ignition from a reetitive sark in a lab-scale atmosheric sray flame haened when the turbulence haened to stretch the sark to reach inside the recirculation zone where the overall equivalence ratio was close to stoichiometric and the velocity towards the sray atomizer. Sark A is the one used in the exeriments. Its location was selected emirically in Rolls- Royce over a number of years to rovide good and reeatable ignition characteristics for injectors having similar aerodynamic features to the one used here. It is interesting to note that this sark and this location was also found by the model to give the best ignition erformance. This gives further credence to the techniques roosed here. 3.3 Visualization of ignition events In this section, we show the evolution of flame articles with sark A for two different events. In the first event, x s = 47.5 mm and a relatively large volume of the burner is ignited. In the second event, the sark is further downstream at x s = 100 mm, and much less material is ignited. These two locations are reresentative of the best and a bad sark lacement for ignition, resectively. Figures 5a and 5b shows the evolution of the comuted articles for the first and the second event resectively. The green sheres denote articles that are active (i.e. have Ka < Ka crit ) at the instant shown, while red sheres denote articles that have already extinguished. Note that the longer the model runs the higher the

11 ossibility that all articles will eventually extinguish, as they will eventually obtain high Ka or they will be convected out of the domain. The imortant outut of the model is how much of the combustor has been visited by flame articles, i.e. how high π becomes before it stabilises to a constant value. In Fig. 5a, some articles are convected downstream just after ignition. On their ath out of the combustor, they ignite many grid cells, and hence many more articles are emitted. Moreover, some articles from the sark are brought towards the recirculation zone where they ignite further grid cells. The ignition occurring in the recirculation zone contributes to a large extent to the large value of π ign achieved here, see Fig. 3d. In contrast, Fig. 5b shows that in the second event, all articles are convected downstream. They ignite only grid cells on their ath away from the injector, which leads to low values of π ign. Hence, these two resent simulations show that π ign is high when flame articles are convected ustream by the recirculating turbulent flow. This is consistent with the finding that ignition with this articular combustor was successful when the kernel moved ustream towards the fuel injector [5,6]. The article visualizations also agree with the more general revious finding with gaseous and sray recirculating flames where ignition occurred when the sark kernel was convected by the gas towards the fuel injector [,4]. ign (a): 0 ms ms 4 ms 6 ms 8 ms 60 ms (b): 0 ms ms 4 ms 6 ms 8 ms 60 ms Figure 5: Evolution of articles with sark A. (a) Good ignition event ( oor ignition event ( x s =47.5 mm); (b) =100 mm). Green sheres reresent articles that are still in motion (i.e. have Ka Ka ). Red sheres reresent extinguished articles ( Ka > Ka ). < crit x s crit 4. Conclusions A model, develoed to calculate the flame sread following the generation of a kernel given a cold CFD solution, has been alied to a realistic aero-engine kerosene combustion chamber. A arametric study on the characteristics and location of the cylindrical sark was erformed by varying the location of the sark axis x, the sark length L and the sark diameter d s. For each configuration, 50 sark events were calculated and statistics on the ignition rogress factor π ign, i.e. the relative volume of the burner that has ignited, were comiled. The aim of the model is to enable an assessment of ignitability of different flow atterns and of various sark locations and roerties without having to erform a full CFD calculation of the ignition transient. The simulation reroduced the stochastic nature of ignition and the timescale for the flame sread, the former in qualitative and the latter in quantitative agreement with exeriment with this combustor [5]. Furthermore, high values of π ign were associated with s s

12 flame articles moving towards the injector, consistent with exeriment [5] and revious work on recirculating gaseous and sray flames [,4]. The region of best sark location was shown to be at the maximum width of the recirculation zone, in excellent agreement with exeriments on a simlified sray burner []. Moreover, the otimum sark shae was suggested to be a sark volume that has a great overla with the side of the recirculation zone, where the mixture is flammable and the recirculating flow catures the flame. It is interesting to note that the sark location that gives the best ignition erformance according to the model is the one selected for injectors with similar aerodynamics after years of in-house ractical exerience. Although the model has limitations and should not be considered as an exact descrition of the flame motion following ignition, it can be used to study qualitatively the ignition rocess in aero-engine combustors. Since the simulations are relatively chea, the model can be used to carry out arametric investigations of ignition, e.g. with different sark ositions, air flow rate, or fuel-air ratio, rovided a reliable CFD solution of the un-ignited flow is available. Such investigations can hel the designer select the sark energy, orientation and location given a articular injector early in the design rocess. Acknowledgments The work at the University of Cambridge has been funded by the Rolls-Royce Grou and the Euroean Commission through roject TECC-AE (ACP7-GA ). The work in Rolls-Royce has been funded by the Euroean Commission through roject TIMECOP-AE (AST5- CT ). The aer reflects only the authors views and the Community is not liable for any use that may be made of the information contained therein. References [1] E. Mastorakos, Prog. Energy Combust. Sci., 35:57-97, 009. [] Marchione, T., Ahmed, S. F. and Mastorakos, E. Combust. Flame, 156: , 009. [3] Neohytou, A. (010) PhD Thesis, University of Cambridge. Available from htt://www-diva.eng.cam.ac.uk/theses.html [4] Ahmed, S. F. and Balachandran, R. and Marchione, T. and Mastorakos, E. Combust. Flame, 151: , 007. [5] Mosbach, T. and Sadanandan, R. and Meier, W. and Eggels, R. L. G. M. Exerimental Analysis of Altitude Relight Under Realistic Conditions Using Laser and High-Seed Video Techniques. In: Proc. ASME Turbo Exo 010, Glasgow, UK, June, 010. ASME Paer GT [6] Read, R. W. and Rogerson, J. W. and Hochgreb, S. Flame imaging of gas turbine relight. AIAA Journal, 48: , 010. [7] Naegeli, D. W. and Dodge, L. G. Combust. Sci. Technol., 80: , [8] Stow, S. and Zedda, M. and Triantaffylidis, A. and Garmory, A. and Mastorakos, E. and Mosbach, T. Conditional Moment Closure LES modelling of an aero-engine combustor at relight conditions. In: ASME Turbo Exo 011, Vancouver, Canada, 6-10 June, 011. Paer GT [9] Poe, S. B. Turbulent Flows. Cambridge University Press, London, 000. [10] Abdel-Gayed, R. G. and Bradley, D. Combust. Flame, 6:61-68, [11] Neohytou, A. and Mastorakos, E. Combust. Flame, 156: , 009. [1] Franzelli, B. and Riber, E. and Sanjose, M. and Poinsot, T. Combust. Flame, 157: , 010.