Large eddy simulation of flame propagation during the ignition process in an annular multiple-injector combustor

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Large eddy simulation of flame propagation during the ignition process in an annular multiple-injector combustor Dongmei Zhaoa,c, Yifan Xiab, Haiwen Ged, Qizhao Lina, Gaofeng Wangb,

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a

Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230027, China School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, China c School of Computer Science and Technology, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China d Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: LES URANS Ignition dynamics Annular combustor Swirling flame

In the present work, Large Eddy Simulation (LES) coupled with a detailed propane/air mechanism and Adaptive Mesh Refinement (AMR) is employed to simulate the ignition procedure in a laboratory scale annular combustion chamber with sixteen swirling injectors. The numerical results are validated by comparing with the available experimental data, and also compared with previous numerical results of Unsteady Reynolds-Averaged Navier-Stokes (URANS). The main flow structures prior to ignition and flame propagation during the reacting phase are analyzed in detail. Particularly, some important characteristics of the light-round sequence, such as the light-round time, the flame dynamics, the morphology of flame front and the interactions between flame and turbulence, are emphatically analyzed. It is found that the faster light-round time and more wrinkles on the flame surface of calculations by LES compared with URANS. The interactions between flame and turbulence reveal that the moving speed of flame front in the early stage is fast, which is accelerated due to the thermal expansion of burnt gas. When two fronts are close to merge, the reverse flow generated in the burned area decreases the moving speed of flame front. Overall, compared with the previous URANS results, the present numerical calculations of the ignition process by LES show better agreement with experimental results.

1. Introduction Ignition performance of combustion chamber is considered as an important indicator in the aero-engine certification. However, lean premixed combustion as a primary technique to low NOx emissions leads to combustion instability and less favorable conditions for ignition. To improve ignition stability, flame stabilization, and pollutant reduction, swirling flows have been widely used in aero-engine combustors [1]. In aero-engines, ignition is usually triggered by the plasma created by a spark plug [2] or a laser beam [3]. The ignition process can be achieved through three phases [4]: energy deposition; kernel expansion; light-round process. This latter phase in an annular premixed swirling multiple-injector combustor is the main topic of this article. Many studies on the ignition process have been done on simple configurations [5–9]. There are relatively less researches on the ignition process of a full annular combustor due to the complex geometry and huge computational cost. Boileau et al. [10] simulated a complete ignition sequence in a full aeronautical chamber including 18 burners using Large-eddy simulation(LES) firstly. No comparisons have been

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carried out between the predicted data and the experimental data due to the difficulties of the in situ experimental investigations in the real aeronautical chamber in this pioneering work. Results show that the large turbulent structure is the dominant factor to influence the flame propagation. And LES shows a high potential to predict such timevarying phenomena in gas turbine combustors. With the development of laboratory scale annular experimental setup, experimental and numerical investigations of an ignition sequence in a full annular combustor become more feasible [11–15]. Particularly, the research team in EM2C has carried out a series of studies on light-round mechanism based on MICCA experimentally and numerically [16–19,4,20,21]. These investigations focuses on the dynamic behaviors of the flame propagation, including instantaneous flame geometry and flame brush spatial location and flame merging time, and confirmed that LES is a promising method in studying ignition process in the annular combustor for gaseous or two-phase mixture. In recent years, a similar laboratory scale annular combustor with 16 swirling injectors has been developed by Zhejiang University [22–24]. Actually, the combustor is a part of experimental platform TurboCombo [25] focusing on combustor

Corresponding author. E-mail address: [email protected] (G. Wang).

https://doi.org/10.1016/j.fuel.2019.116402 Received 14 July 2019; Received in revised form 6 October 2019; Accepted 9 October 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Dongmei Zhao, et al., Fuel, https://doi.org/10.1016/j.fuel.2019.116402

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and turbine interactions. Based on this setup, the researchers have conducted some experimental investigations on the ignition process in the annular combustor. These researches have revealed some important factors affecting the key characteristic values including light-round time and flame propagation speed in the light-round sequence, such as different geometry of injector and various operation parameters (bulk velocity, thermal power and equivalence ratio). We have further analyzed the ignition process through numerical simulations using URANS [26]. The flow structure of cold flow and the light-round sequence are involved in the analysis. Despite overall good agreement with experimental results, several differences have been found in terms of lightround time (22% slower than experiment) and flame surfaces (less wrinkled than experiment) between URANS results and experimental data. In order to better characterize the cold flow field and understand the interactions between flame and turbulence, LES is conducted in the present work. Besides, a detailed chemical kinetic mechanism-UCSD propane/air mechanism-is used, which is much more comprehensive than the two-step reduced scheme used by Philip et al. [18,19,4] AMR is adopted to maintain reasonable computational times. The LES results are validated by comparing with the experimental data and numerical results of URANS [26]. In the following, Sections 2 and 3 describe the experimental and numerical setups, respectively. The numerical results including the flow field before ignition, the flame topology evolution, the light-round sequence, the light-round time and the interaction between the flow field and flame propagation are discussed respectively in the subsequent sections before concluding.

Table 1 Experimental conditions. Parameters

ṁ air (g / s )

ṁ C3 H8 (g / s )

Φ

Ub (m/ s )

Re

Values

6.910

0.310

0.67

4.87

3166

experimental methods can be found in Ref. [22]. The parameters of experimental condition including the mass flow rate of air ṁ air and fuel ṁ C3 H8 , the bulk velocity Ub , and the equivalence ratio Φ are listed in Table 1. Bulk velocity Ub is calculated at the outlet of the swirling injectors. The corresponding Reynolds number is about Re = 3166, which is defined based the bulk velocity Ub and the diameter of the swirling injector. 3. Numerical setup 3.1. Computational domain, numerical algorithms and turbulence model In the present work, a commercial computational fluid dynamics program CONVERGE [27,28] is employed to simulate the three-dimensional, compressible, transient chemically reacting flow in the complex geometry described in experimental setup. The main components of the experimental rig shown in Fig. 1 are included in the computational domain. As shown in Fig. 2(a), the whole computational domain is divided into two regions, i.e., the swirling injectors and the annular combustor chamber. The detailed structure of the swirling injector is illustrated in Fig. 2(b). The dynamic structure model, which is a one-equation non-viscosity [29,28] LES model, is adopted to account for effects of turbulence on the momentum, energy, and species transport fields. This model estimates the actual stress tensor using the dynamic methodology to obtain a tensor coefficient and from a transport equation for the sub-grid kinetic energy. The compressible momentum equation in LES framework is given by

2. Experimental setup The annular combustor with multiple swirling injectors is shown in Fig. 1. The combustor features 16 straight-installed swirling injectors equally arranged on the annular plate. The combustor chamber is made of two transparent cylindrical concentric quartz tubes. The inner diameter and the outer diameter of the chamber are 200 mm and 300 mm , and the hight is 300 mm . Air and propane are fully premixed and then conveyed into the plenum through 8 supplying pipes. The mixture is fed to the chamber through 16 swirling injectors, whose swirl number is 0.82 , on the plenum. The ignition process is initiated by an electric spark plug. The ignition sequences are recorded with a high speed camera (Phantom M110), which captures gray-scale experimental images of 1280 × 800 pixel. The frame rate and shutter time are set at 1000 Hz and 500 μs , respectively. Details about the combustor and

¯ i ̃ uj ̃ ∂τij ∂σ¯ij ∂ρu ¯ ĩ ∂ρu ∂P¯ − . =− + + ∂x j ∂x j ∂x j ∂x i ∂t

(1)

Here, ρ is density; ui is velocity; P is pressure; σij is the viscous stress tensor, τij is the sub-grid stress tensor and is given by ∼∼  τij = ρ (u i uj − ui uj ) . In the dynamic structure model, the sub-grid stress tensor is modeled by

Lij τij = 2k ⎛ ⎞, ⎝ Lii ⎠ ⎜

⎟

(2) 1 (ui ui 2

− u¯ i u¯ i ), Lij is the where k is the sub-grid kinetic energy, k = Leonard stress term given by the Germano identity[30]:

   Lij = (u ¯ i u¯ j − u ¯i u ¯ j ).

(3)

In this simulation, the flow solver is based on an implicit first-order time advancement and second-order central scheme. The pressure-velocity coupling is achieved using a modified Pressure Implicit with Splitting of Operators (PISO) [31] scheme. The point-wise successive over-relaxation (SOR) was used per PISO loop. The modified Rhie-Chow [32] interpolation scheme is employed to maintain collocated variables and eliminate the undesirable odd-even decoupling. The convective term is discretized by the second-order central scheme with monotonic limit. When the ratio of gradients on either side of a cell face exceeds the monotonic tolerance (1e−05), the spatial discretization method is switched to a first-order upwind. The method for setting the time-step is a variable time-step that is calculated internally. 3.2. Combustion modeling Fig. 1. Schematic illustration of the annular combustor. (1) Quartz tube wall, (2) Swirling injector, (3) Supplying pipe, (4) Plenum.

Combustion is modeled using SAGE detailed chemical kinetics 2

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Fig. 2. (a) The whole computational domain; (b) The detailed structure of the swirling injector.

calculations by grouping similar computational cells and invoking the chemistry solver once per group rather than once per cell. The detailed chemical kinetic mechanism of complete San Diego mechanism [39] is applied to model the chemical reactions, which has 57 species and 268 reactions. More detail of the reaction mechanism can be seen in our previous work [26].

solver [33]that assumes each computational cell is a perfectly stirred reactor, i.e., there is no explicit turbulence chemistry interaction (TCI) models in the present simulations. Recently, Dahms et al. [34]conducted an asymptotic analysis that showed there is implicit TCI in the multi zone SAGE model. The implicit TCI means that the performance of the combustion model depends on grid size, numeric, etc. The TCI can be fully recovered by SAGE model when the grid size and time step approaches the size of DNS. Although the present grid size and time step are not small enough to fully recover the TCI, local mesh refinement near the flame front can largely recover the TCI. The SAGE solver reads in CHEMKIN-formatted detailed chemical kinetics. There are two options to solve the systems of ordinary differential equations: the CVODE solver which is a part of the SUNDIALS (SUite of Nonlinear and Differential/Algebraic equation Solvers) package [35] and SuperLU (Sparse Linear Equation Solver) as a preconditioner of GMRES [36]. In this simulation, CVODES with preconditioned iterative solver with SuperLU are used. The modeled species LES transport equation is given by

∼  ∼ ∼   j ̃ Y ∂τY−j ∂ρ u ∂ρ Ym ∂ ⎛  ∂Ym ⎞ ̃ m = + + ω̇m + ρ Dt ⎜ ⎟ ∂x j ∂x j ∂x j ∂x j ∂t ⎝ ⎠

3.3. Adaptive mesh refinement (AMR) During the simulation, fixed embedding and AMR tools based on a modified cut-cell Cartesian grid generation method [27] are used to control the grid size. The grids at the specific cylinder area of the energy source are refined using embedding scale of 2. AMR is used to automatically refine other regions of the computational domain to achieve a well resolved simulation and still maintain reasonable computation times. In the domain, the size of base grid is specified as Δx 0 . Then the grid_scale is used to change the local grid size Δx according to Δx = Δx /2 grid _ scale (7) 0

The grid resolution (embedding) is increased by the AMR algorithm where the flow field is most under-resolved or where the curvature of a specified field variable is the highest [27]. For a scalar ϕ′, the sub-grid field is the difference between the actual field ϕ and the resolved field ϕ¯

(4)

where ω̇m is the net production rate of species m and ∼ ∼   j ̃ Y τY−j = ρ (uj ̃ Ym − u m ) is the sub-grid species unclosed term that should be modeled. The net production rate of species m is given by

as

ϕ′ = ϕ − ϕ¯

R

ω̇m =

∑

vm, r qr

r=1

for m = 1, 2, ….M .

Here, the sub-grid value is approximated as

(5)

where M is the total number of species and R is the total number of reactions, vm, r = vm″ , r − vm′ , r . Here, vm′ , r and vm″ , r are the stoichiometric coefficients for the reactants and products, respectively, for species m and reaction r. The turbulent diffusivity Dt is computed from the Schmidt number[37]:

Dt = μt / Sct

(8)

ϕ′ = −α[k]

∂2ϕ¯ , ∂xk ∂xk

α[k] is dxk2/24

k = 1, 2, 3

(9)

for a rectangular cell and the bracket [] indicates no where summation. To test the grid convergence, three different mesh resolutions are used in the non-reacting single injector domain with AMR. In these mesh resolutions, the absolute value of the velocity sub-grid field is used to determine where embedding is added. The mesh convergence could be achieved when AMR minimum cell size dx is equal to 0.25 mm in the swirling pipe region. In more detail, the AMR embed scales based on the velocity sub-grid value are listed in Table 2 In the present work, there are two stages for the simulation. The sub-grid velocity is used as the criteria parameter of AMR algorithm in

(6)

A constant Prandtl number Pr0 = 0.9 and Schmidt number Sc0 = 0.78 are assumed. The chemical reactions are solved in each cell based on the temperature, pressure, and species mass fractions. Based on the reaction rates, the species mass fractions are then updated accordingly. The cell temperature is updated on the basis of the predicted species concentrations. Adaptive zoning [38] is used to accelerate the chemistry 3

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4. Results and discussion

Table 2 AMR embed scales. Embed Scale Base gird size, dx 0 (mm) AMR minimum cell size, dx (mm)

1 1 0.5

2 1 0.25

4.1. Flow field before ignition

3 1 0.125

Comparison of time-averaged streamlines in the X-clip plane of the annular combustor configuration between URANS and LES is shown in Fig. 4. Two simulation results can capture the features of the main flow regions. The flow forms two swirling jets at the outlet of the injector. The CRZ and IRZ are separated by the SWJ and the velocity of the interface between the SWJ and the two recirculation zones is high. The CRZ locates around the SWJ and the IRZ spreads from the exit of the injector to downstream in the combustion chamber. The height of the two recirculation zones is 5D and 10D respectively. Meanwhile, it can be seen that the flow field near the inner wall is different from that near the outer wall. In URANS results, only one obvious CRZ is formed near the inner wall. In LES results, there are two CRZ near the outer wall and one CRZ near the inner wall. The flow structures are quite different, because the URANS and LES are different turbulence models to resolve the velocity field. The mean velocity field is an ensemble time average by URANS. This differs from LES approach, where the resolved velocity field is defined as a spatial average of the actual velocity field. The actual turbulence characteristics such as the interrupted and stochastic can not be captured by URANS. So the streamline of the IRZ is almost regular and symmetric about the axis as shown in Fig. 4(a). In addition, LES can capture more vortex information. This is also the reason for the different structure of flow field. The time-averaged top-view flow structures before ignition at various position from the exit of injectors by LES are shown in Fig. 5. Sixteen similar symmetric swirling flows centered at the outlet of the injectors are observed in Fig. 5(a)–(c). With the flow developing downstream, the magnitude of the velocity in the center region of the swirling flows decreases gradually. At z = 10D, the symmetrical swirling structures have been transformed into large-scale circulation. The clockwise circumferential motion alongside the inner wall and the counter-clockwise circumferential motion alongside the outer wall are observed in Fig. 6. As can be seen from the figure, the flow field calculated by URANS almost only consists of large-scale vortex, while the LES flow field has smaller scale and more vortex. The reason for the difference is that the processes of swirling weakening and turbulent vortex dissipation are also faster in URANS results. Many small scale motions and fluctuations have been smoothed out due to time-averaging. Thus, only large-scale circulation remains in URANS results, but

two stages in the simulation. For the non-reacting stage, only the subgrid velocity value is used and is equal to 0.01. The maximum embedding scale is 2 and 1 for the swirling pipe region and annular chamber region respectively. As shown in Fig. 3(a), the smallest cell is 0.25 mm in the swirler pipe and 0.5 mm at its exit during the nonreacting stage. For hot flow, AMR is used for the temperature and velocity fields in the region of the annular chamber. The maximum embedding scale and sub-grid value for temperature are 3 and 2.5 K. To properly capture the flame propagation on the grid, the AMR minimum cell size dx is equal to 0.125 mm across the flame front in the combustor chamber as shown in Fig. 3(b). The mesh counts 120–150 million cells of Cartesian grid cells in overall computational domain.

3.4. Simulation procedure The details of the simulation methodology and procedure of URANS can be found in our previous work [26]. For the present simulation, there are two stages. Firstly, the quasisteady of non-reacting flow and the unsteady ignition process. Considering the cost of time, the stable state is obtained by restarting from the existing steady solution. It takes a period of time (0.5 s) to ensure the flow is fully developed and the annular chamber is full of proper equivalent ratio fresh mixture at 298 K. Then, a cylindrical energy source is placed at the exact location of the electric spark plug in the experiment, to mimic the early development of the ignition kernel (t = 0.501 s). The radius and height of cylinder is 2 mm and 5 mm . The total discharged energy is 0.1 J . The duration to release energy is 0.5 ms . Then, the process of burner to burner flame propagation occurs. The walls of the injectors are set as no-slip and 298 K. The inner and outer walls of the annular chamber are set as no-slip and adiabatic. The outlet of the chamber is set as pressure outlet (1 atm).

Fig. 3. Mesh in X-clip plane of the computational domain. (a) Mesh scale for the cold flow; (b) Mesh scale for the hot flow. 4

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Fig. 4. The time-averaged streamlines in the X-clip plane: (a) URANS; (b) LES.The main flow regions are identified: Swirled Jet(SWJ),Inner Recirculation Zone(IRZ) and Corner Recirculation Zone(CRZ). Black lines indicate various distances from the exit of the injector.

Fig. 5. The time-averaged top-view flow structure before ignition at various position by LES: (a) Z = 0.5D; (b) Z = 1D; (c) Z = 5D; (d) Z = 10D. 5

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Fig. 6. The time-averaged top-view flow structure before ignition at 10D position: (a) URANS; (b) LES.

Circumferential flame propagation speed Sc directly influences the light-round time τ . And Sc mainly depends on turbulent flame speed ST and thermal volumetric expansion effect. In general, ST is simply defined as ST = ΞSL , where Ξ is wrinkling factor and SL is laminar flame speed. Unlike URANS, LES can resolve Kolmogorov length scales by refining the computational grid. The turbulence levels are accurately estimated by LES. Appropriate turbulence can corrugate and stretch the flame surface area where reactions occur, which leads to faster burning due to increased flame surface. So the Sc predicted by LES is faster than that by URANS. However, the present SAGE model that does not consider the additional turbulence chemistry interaction model can lead to underestimate the wrinkling of the flame surfaces. Therefore, the Sc for the experiment is faster than that by LES. The light-round sequence can also be compared quantitatively. As illustrated in Fig. 9, the curves of flame position θ versus ignition time during the light-round process is given. In Fig. 9, the annular combustor is considered as a 0°~ 360° circumference in counter-clockwise direction and 0° corresponds to the No. 0♯ injector. Since there are 16 injectors equally arranged, the adjacent injectors are 22.5° aparted. The ignition occurrence of each injector is identified by its value of azimuthal angle θ . The initial flame kernel forms at t = 0 ms, representing the starting point. The intercepts of t axis means the No. 0♯ injector has been ignited, and the moment of all injectors have been ignited means the ending point.It can be seen from the Fig. 9 that except the last three nozzles, the LES results match the measurements very well. Under-prediction of the flame speed for the last three nozzles leads to the result that the ending point of experiment is shorter than that of LES as well as URANS. It is consistent with the visual comparison of the ignition sequence. One potential reason of under-predicting the flame propagation speed is that the present model doesn’t fully consider the turbulence-chemistry interaction. In the future, other turbulent combustion models such as level-set G-equation model and Extended Coherent Flame Model (ECFM) will be considered. Fig. 10 shows the merging time (light-round time) τ compared to the results of Bourgouin’s work [16]. The red solid line presents the experimental results and the red dashed line presents the estimated values based on the following Bourgouin’s empirical equation

more scales of turbulent vortexes appear in LES results at the same distance from the injector (10D). Fig. 7 shows the distribution of turbulent velocity u′ at various position from the exit of injectors in LES calculation. The turbulent velocity is mainly induced by the swirling flow of the swirler. Near the exit of the injector, the turbulent fluctuation is strong. And the distribution of turbulent fluctuation is characterized by high central area and low surrounding area of the injector. With the increasing distance from the injector outlet, the turbulent fluctuating gradually weakens and disperses towards the radial expansion. At down stream of the annular chamber, the turbulence velocity dissipated gradually, from Z = 5D to Z = 10D. 4.2. Flame front dynamics The light-round process predicted by LES is compared with results of URANS and experiment in Fig. 8. The flame surface is presented by the iso-surface of temperature (T = 1781 K). The results given by LES in the present work are improved a lot compared to previous URANS results. Firstly, the flame surface resolved by LES is more wrinkled than URANS, which suggests that the LES can capture more details of the interaction between turbulence and flame surface. The flame front predicted by LES is closer to the experimental images than the one predicted by URANS. Four phases in the ignition process can be identified: Phase (I) An initial flame kernel is generated in the vicinity of the energy source (Fig. 8a); Phase (II) After the formation of the first stable swirl flame, the flame front splits into two parts and propagates oppositely to the neighboring injector in an arch form(Fig. 8b); Phase (III) The flame fronts in two opposite directions gradually ignite the neighboring burners(Fig. 8c); Phase (IV) The two flame fronts propagate along the circumferential direction until merge(Fig. 8d, e). During the Phase I, the flame is dominated by the Joule heating of the plasma and thermal expansion. With the growth of the flame kernel, the distance between the flame front and arc path increases. Accordingly, the influence of the joule heating decreases quickly, since its influence on flame kernel growth is proportional to r 2 (r is the distance between the flame front and arc path) [40]. During the Phase II to IV, the flame propagation is driven by the chemical kinetics and fluid dynamics. Relatively, the effect of the wall is insignificant during the Phase II, since the flame front has not reached the solid wall yet. The light-round time τ defined in the previous work [26] between simulations and the experiment has some discrepancies. The lightround time τ for experiment is about 85 ms. For URANS and LES simulations, τ is about 104 ms and 96 ms respectively. Obviously, the light-round time τ of LES is closer to the experimental results.

τm = 0.2v −0 0.38.

(10)

Here, the τm is the merging time and the v0 is the magnitude of the bulk velocity. The purple diamond and the green pentagon present two simulations based on the URANS and LES, respectively. The blue triangle presents the experimental results in our work. As shown in Fig. 10, the order of magnitude and the trend show an overall agreement between present experimental results in this article and the estimated values 6

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Fig. 7. The distribution of turbulent velocity before ignition at various position by LES: (a) Z = 0.05D; (b) Z = 0.5D; (c) Z = 1D; (d) Z = 2D; (e) Z = 5D; (f) Z = 10D.

front and flow field in phase I to phase II, i.e., the process from the initial flame kernel to the formation of a stationary single swirling flame. As shown in Fig. 11(b), the flame front breaks up and forms a new isolated flame front when the expanding flame kernel encountering the swirling flow of adjacent injector and the original flame front is maintained at the periphery of the swirling injector. At the same time, the flame develops along the normal direction of its own surface and along with the overall counter-clockwise flow in the zone where swirl is weak. For the flow field near the flame front, the direction of flow across the flame front is the same as that of the flame front because of the influence of thermal expansion of the burned gases. The interaction between flame front and flow field in the phase III, when the two separate flame fronts progressing in Fig. 12. In this phase, for the first time, the flow across the flame front on the clockwise propagation is

from Bourgouin’s work. Particularly, the merging time of our experiment is almost consistent with the estimated value when the magnitude of bulk velocity is between 4 and 6 m/s. In addition, the merging time based on the LES is better than the URANS in the same magnitude of bulk velocity although both simulations overestimate the merging time. It is interesting that all the simulations in this plot over-predict the merging time. 4.3. Flame-flow interactions Figs. 11–13 show the flame front interaction with the flow field in four phases of the ignition process. The red solid lines denote the flame front (T = 1781 K). The black dash lines denote the direction of flow across the flame front. Fig. 11 shows the interaction between flame 7

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Fig. 8. Comparison of the ignition sequences. Left: Expreimental images represented in false colors; Middle and right: Respectively LES and URANS simulations. The flame fronts are both represented by isosurface of temperature T = 1781 K, both colored by axial velocity.

Fig. 10. Present values compared with Bourgouin’s work. The Merging time deduced from experimental results (red) and from simulations based on the Gequation (black) in the Bourgouin’s work [16] and the present values in this article. Fig. 9. Flame positions θ vs. time. The experiment value is the average of several independent experiments.

Fig. 14 shows the distribution of the mass fraction of OH* during the ignition process. It is found that the peak concentration of OH* is located in the narrow area where severe chemical reactions are happening. This ignition case is a typical premixed flame and the regime of the turbulent flame fronts can be identified based on Karlovitz number (Ka) and Damkolher number(Da) [41,42]. In this case, Ka < 4 and Da > 16 are calculated following the expressions in Ref. [43]. In more detail, the predicted and the measured turbulent flames in the Peters-

opposite to the moving direction of the flame front, which partially pushes back the flame front and reshapes the flame topology. It slows down the flame propagation on clockwise direction and eventually causes asymmetric behavior in the light-round process. Fig. 13 shows the interaction between the flow and the flame in the phase IV. In this phase, it can be clearly seen that the reverse flow across the flame front appears in both clockwise and counter-clockwise directions. 8

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Fig. 11. The front with the streamline(Z = 0.5D) in the phase I II.

5. Conclusions

Borghi’s diagram [44] are depicted in Fig. 15. The diagram defines the regimes of premixed turbulent combustion using the velocity fluctuation (u′/ SL0 ) and the length scale (l 0/ δL ) ratios. Here, SL0 and δL are the laminar flame speed and thickness, respectively. The velocity fluctua2 2 2 + vrms + wrms )/3. Here, urms , vrms , wrms are tion u′ is defined as u′ 2 = (urms the RMS velocities of the axial, radial and tangential direction, respectively [22]. In present work, the u′ at 25 mm downstream is applied to approximate the level of velocity fluctuation as described in Ref. [22]. The average velocity fluctuation value is selected, for example, u′ = 0.953 m/s for the experiment [22]. The flames locate nearby the critical value Ka = 1. The Ka number of the LES result is closer to the experiment than that of URANS, because the URANS under-estimated the velocity fluctuation of the flow field.

In present work, the LES of ignition process of the annular combustor is conducted to investigate the characteristics of flame propagation. Detail propane/air reaction mechanism is implemented through SAGE model, which better reproduces the effects of chemical kinetic. LES gives better agreements with experiments in term of the light-round time and more wrinkled flame surface compared with previous URANS results. In addition, more informations on transient flow field are captured by LES. The process of swirling flow development and turbulence dissipation is described. Qualitative analysis of the interactions between flame and turbulence show that swirling flow in the center of injectors is the main factor causing flame surface fragmented. With

Fig. 12. The front with the streamline(Z = 0.5D) in the phase III. 9

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Fig. 13. The front with the streamline(Z = 0.5D) in the phase IV.

approaching the merging point, the jagged flame front becomes relatively regular and decelerates due to the large adverse flows in the burned area. At last, the qualitative analysis of morphology and structure of flame front show that the flame fronts are not far from the flamelet regime. The turbulent flames locate approaching the critical value Ka = 1 in the Peters-Borghi’s diagram. Thus, light-round simulations will be interesting to perform with different turbulent combustion

models in order to quantify their impact. Constrained by the grid mesh and the present combustion model due to the available computational power, which is about 2 million CPU hour for the simulation of light-round procedure in 100 ms physical time, some differences between calculations and measurements have been identified in terms of flame propagation speed and flame surfaces despite LES shows more advantages to capture the transient

Fig. 14. The top-view Z-clip plane YO H at various time: (a) t = 0 ms; (b) t = 58 ms; (c) t = 78 ms; (d) t = 96 ms. 10

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Fig. 15. Numerical and experimental data in Peters-Borghi’s diagram.

information. The differences (about 10% over-estimated) in light-round time might come from the uncertainties due to initial instantaneous turbulent fields or wall temperature of combustion chamber. Multiple running of light-round simulations are of course very interesting to check the impact of these uncertainty parameters on the accuracy of the calculation in future. In addition, error analysis and quantitative comparisons on the flow fields for LES are scheduled when more experimental measurements are available in future work. Acknowledgments The authors acknowledge the support of Convergent Science Inc. to this research by providing the free academic license. The authors acknowledge the High-Performance Computing Center (HPCC) at Texas Tech University at Lubbock for providing HPC resources that have contributed to the research results. This research was funded by the Natural Science Foundation of China (No. 51976184 and 91541108) and the Fundamental Research Funds for the Central Universities (No. 2019FZA4025). References [1] Ji J, Gore JP. Flow structure in lean premixed swirling combustion. Proc Combust Inst 2002;29(1):861–7. [2] Lefebvre AH. Gas turbine combustion. 2nd ed. CRC Press; 1998. [3] Bradley D, Sheppard CGW, Suardjaja IM, Woolley R. Fundamentals of high-energy spark ignition with lasers. Combust Flame 2004;138(1):55–77. [4] Philip M, Boileau M, Vicquelin R, Schmitt T, Durox D, Bourgouin J-F, Candel S. Simulation of the ignition process in an annular multiple-injector combustor and comparison with experiments. J Eng Gas Turb Power 2015;137(3):031501. [5] Ahmed SF, Balachandran R, Marchione T, Mastorakos E. Spark ignition of turbulent nonpremixed bluff-body flames. Combust Flame 2007;151(1–2):366–85. [6] Mastorakos E. Ignition of turbulent non-premixed flames. Prog Energy Combust Sci 2009;35(1):57–97. [7] Cordier M, Vandel A, Cabot G, Renou B, Boukhalfa AM. Laser-induced spark ignition of premixed confined swirled flames. Combust Sci Technol 2013;185(3):379–407. [8] Bulat G, Jones W, Marquis A. Large eddy simulation of an industrial gas-turbine combustion chamber using the sub-grid pdf method. Proc Combust Inst 2013;34(2):3155–64. [9] Jones W, Prasad V. Les-pdf simulation of a spark ignited turbulent methane jet. Proc Combust Inst 2011;33(1):1355–63. [10] Boileau M, Staffelbach G, Cuenot B, Poinsot T, Bérat C. LES of an ignition sequence in a gas turbine engine. Combust Flame 2008;154(1–2):2–22. [11] Fanaca D, Alemela PR, Ettner F, Hirsch C, Sattelmayer T, Schuermans B. Determination and comparison of the dynamic characteristics of a perfectly premixed flame in both single and annular combustion chambers. ASME turbo expo 2008: power for land, sea, and air. American Society of Mechanical Engineers; 2008. p. 565–73. [12] Fureby C. LES of a multi-burner annular gas turbine combustor. Flow Turb Combust 2010;84(3):543–64. [13] Machover E, Mastorakos E. Spark ignition of annular non-premixed combustors.

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