Large Eddy Simulations for the Flame Describing Function of a premixed turbulent swirling flame Davide LAERA, and Aimee S. MORGANS Department of Mechanical Engineering, Imperial College London, London, UK 7 September 2017
2 Outline Motivations Objectives of the work Numerical and experimental setups Flame Describing Function calculations Preliminary results analysis Conclusions and ongoing works
Flow rate and mixture composition disturbances Thermoacoustic combustion instabilities Heat release rate perturbations Acoustic oscillations Harms of combustion instabilities: Augment noise emission. Increase heat fluxes and thermal fatigue. Cause structural vibrations. Flashback and flame out. Multiple swirled injector combustor and damaged system (Goy et al. (2006)) 3
4 Motivations Many are the theoretical, numerical studies focusing on limit cycles predictions of combustion instabilities in longitudinal and azimuthal combustor Theoretical Acoustic Network Helmholtz Solver Noiray et al. (2011) Bauerheim et al. (2013) Campa and Camporeale (2014)
5 Motivations Many are the theoretical, numerical studies focus on limit cycles predictions of combustion instabilities in longitudinal and azimuthal combustor. These approaches rely on the model for the response of the flame to oncoming acoustic perturbations. Upstream acoustic perturbation Responding flame heat release rate fluctuation (Q 0) In the frequency domain, this correlation is given in terms of the Flame Describing Function F Q ഥQ = F ω, u 1 u 1 Τതu 1 u 1 F ω, u 1 Τ തu = G ω, u 1 Τതu 1 e iφ(ω, u 1 Τ ഥu 1 )
LES approaches for FDF FULLY COMPRESSIBLE LES PROS Acoustic waves are directly simulated Able to capture correctly the interactions between the acoustic waves with the flame and hydrodynamic fluctuations CONS Non-reflective boundary conditions Reduced time step Cannot be used for computation of the entire FDF Bauerheim et al., 2015. Proceedings of the Combustion Institute, vol. 35. 6
LES approaches for FDF INCOMPRESSIBLE LES PROS Increased time step with respect to compressible LES Non-reflective BC not required. Multiple frequencies can be simulated in reasonable time. CONS Mapping of the acoustic fluctuations as hydrodynamic fluctuations Han et al., 2015. Combustion and Flame, vol. 162(10). 7
8 Objectives of the study To perform incompressible LES are able to simulate the flame response of a premixed swirling flame using an incompressible LES: Verify if the proposed methodology is able to predict the dynamic phenomena due to the presence of the swirl. To compute the FDF of the swirled burner developed at NTNU university in a frequency range from 300 Hz to 1900 Hz for two level of velocity amplitudes.
The experimental setup x y Worth and Dawson., 2013. Combustion and Flame, vol. 160. 9
10 The numerical domain b cc =2.2d b chosen in order to have the same flame-wall distance of the annular combustor. h/dt=2.5 Bluff Body + 6 blades swirl of 60 Re ~ 15000 based on d b C 2 H 4 -Air perfectly mixture F=0.7 x y
11 Numerical modelling OpenFOAM C 2 H 4 /air reaction mechanism Combustion model SGS turbulence model Time-step size Convective divergence Time integration Compressibility 1-step global Partially-Stirred Reactor (PaSR) (Chen, CST, 1997) Dynamic Smagorinsky 1 x 10-6 s Second Order central difference scheme + Sweby flux limiter 2nd-order implicit Crank- Nicolson scheme Incompressible (state equation: ρ(t) = p 0 /RT) 9M fully structured mesh with max y+ ~ 1
12 y x u x ( Τ m s) Results: Unforced configuration [1/2] M-flame type Flame is anchored at the shear layers from the wake of the bluff body and the side recirculation zones Flame touches only marginally the adiabatic walls y x T(K) M - Flame
13 Modelling of the acoustic forcing U = U in 1 + Τ u തu sin(2πf) where u Τതu is the velocity fluctuations amplitude, f the forcing frequency and U in is the mean inlet velocity. Analysed Frequencies (Hz) 300 400 500 600 700 800 1000 1150 1300 1450 1600 1750 1900 Analysed Amplitude Levels (-) Τ u തu =0.1 Τ u തu =0.2
Q തሶ Q ሶ Amplitude 14 Signal processing: amplitude Example of heat release rate signals at two different acoustic frequencies from LES simulations: Τ u തu =0.1 f=500 Hz, f=1000 Hz Time signals FFT Time Frequency Frequency f (Hz)
15 Signal processing: amplitude Example of the calculation of the phase-lag between the velocity reference signal and heat release rate signal from the LES: Τ u തu =0.1 f=500 Hz Time signals Cross correlation
16 The Flame Describing Function Fist local minimum at f=800 Hz Gain response of approx. 0.5 in the high frequency region. The present LES simulations are proved to be able to capture the phenomena leading to the presence of local maximum and minimum in the flame response. Increasing the longitudinal forcing amplitude level, the nonlinearity of the gain is clearly evident.
17 The Flame Describing Function Almost a linear variation of the phase is obtained increasing the frequencies with exception of the points where a gain local minimum is predicted where a sudden phase variation is observed
Mode conversion mechanisms: experimental observations @ EM2C Lab. (Paris) 18 Gain Peak Gain Minimum Palies et al., Combustion and Flame, 2010.
19 Preliminary numerical investigations Gain Peak f = 500Hz, Τ u തu = 0. 1 UW Gain Mininum f = 800 Hz, Τ u തu = 0. 1 LW
20 Conclusions and Ongoing Work Incompressible LES have been used to predict the Flame Describing Function of the premised swirling M-type flame featured by an annular combustor developed at NTNU university. Simulations have been performed in a frequency range between 300-1900 Hz considering two amplitude levels u Τതu =0.1 and u Τതu =0.2. Numerical predictions retrieve a FDF with a maximum peak at 500Hz and with a gain of 0.5 at high frequencies, where instabilities phenomena have been observed. The presence of minimum and maximum points have been also observed, proving that incompressible LES are able to capture the mode conversion phenomena featured by this type of flames. Ongoing work: validation of the numerical results with experiments.
Davide Laera* Department of Mechanical Engineering Imperial College London London, UK * d.laera@imperial.ac.uk