ASME Turbo Expo, Charlotte, NC, USA June 29, 2017 GT2017-63247 Predicting Thermoacoustic Instability in an Industrial Gas Turbine Combustor: Combining a Low Order Network Model with Flame LES Yu Xia, Aimee S. Morgans, William P. Jones Dept. of Mechanical Engineering, Imperial College London, UK. Jim Rogerson, Ghenadie Bulat Siemens Industrial Turbomachinery Ltd., Lincoln, UK. Xingsi Han Nanjing University of Aeronautics and Astronautics, PR China. ASME Turbo Expo, Charlotte, NC, USA June 29, 2017

Outline Background & Motivation Methodology – Combined prediction approach Low-order network modelling of acoustic waves Flame describing functions via incompressible flame LES Results – Predicting thermoacoustic instability Conclusions and future work

Thermoacoustic instability Excessive heat transfer Background Traditional fossil fuels (e.g. coal, oil) will remain popular in the next decade*. NOx emissions from fuel combustion must be controlled due to stricter environmental policies in power and aviation industries. Lean premixed combustion (LPC) is widely used, but is highly susceptible to thermoacusitc instability – an extremely undesirable phenomenon. Fatigue failure of turbine blades Thermoacoustic instability Excessive heat transfer to melt burner Damaged turbine blades Melted burner *International energy agency. 2014 key world energy statistics.

Thermoacoustic instability Background Thermoacoustic instability is caused by an in-phase, two-way interaction between linear acoustic wave perturbation (𝒑′) and unsteady flame heat release fluctuation ( 𝑸′ ): Limit cycles: fixed amplitude and frequency p’ Q’

Motivation Project aim: Predicting thermoacoustic instability in an adapted Siemens SGT-100 gas turbine combustor (single burner) Built in DLR Stuttgart; Fuel: German natural gas (98.97% CH4) . Air/fuel technically premixed; Tair = 685 K, Tfuel = 305 K Uair =~5 m/s, Ufuel = ~60 m/s Lean combustion (∅=0.60) Mach number 0.02 ~ 0.28 Reynolds number 104 ~ 105 Two operating pressures (3 bar & 6 bar)

Methodology Combined Prediction Approach Low order network acoustic modelling Flame describing function (FDF) 1. Geometry simplified into network 3. Simulate flame-acoustic interaction Upstream forced velocity u1’ Downstream heat release rate Q’ 2. Wave-based acoustic modelling 4. Construct numerical FDFs 5. Combine into OSCILOS* and calculate thermoacoustic modes *J. Li, D. Yang, C. Luzzato, A. S. Morgans, OSCILOS Long technical report, 2014.

Network simplification of combustor geometry Step 1: simplify combustor geometry into a network of connected modules: Complex combustor geometry Swirler entry Simplified network of connected modules Inlet Thin flame sheet Exhaust cooling pipe Air passage Outlet Combustion chamber

Wave-based modelling of acoustic waves Step 2: model plane acoustic modes using wave-based method Cold module Wave-based equations (k=1, …, 𝑁) Hot module Flame jump conditions* *A. Dowling, S.R. Stow, J. Propulsion and Power 2003

Establishment of network transfer matrix Last module 1st module BC: damped open-outlet BC: fully-closed inlet 1-D acoustic wave modes are obtained without flame-acoustic interaction:

Simulation of flame response to acoustic forcing To include the flame-acoustic interaction, an additional “flame model” is needed. Upstream forced velocity perturbation u’1 Responding flame heat release rate fluctuation (Q’ ≠ 0) (Hydrodynamic disturbance excited by acoustics) Flame model Small u1’ Large u1’ Linear flame transfer function (FTF) Weakly non-linear flame describing function (FDF) E.g. classical 'n−τ’ model* Simulated by faster incompressible LES solvers *Crocco L, Proc. Symp. Int. Combust., 1969

Computational domain for LES simulations Step 3: Simulate flame response to acoustic forcing via incomp. LES: Mesh cells in the whole domain Measurement Location @ x = 28. 7 mm x = 0 mm Computational domain (7.0 million structured mesh cells) B.C.s: velocity inlet, zero-gradient outlet, adiabatic non-slip walls. Mesh cells in the refined flame region

Numerical settings of LES solvers Two incompressible LES solvers, BOFFIN and OpenFOAM, are used BOFFIN (in-house) OpenFOAM (open-source) CH4/air reaction mechanism 15-step + 19 species* (3 & 6 bar) 4-step + 7 species** (3 bar) 2-step + 7 species*** (3 bar & 6 bar) Combustion model Stochastic field method (Valino, FTaC, 1998) Partially-Stirred Reactor (PaSR) (Chen, CST, 1997) SGS turbulence model Dynamic Smagorinsky Constant Smagorinsky Time-step size 5 x 10-7 s 5 x 10-6 s Time integration 2nd-order Crank-Nicolson scheme Spatial discretisation 2nd-order Central Difference scheme Compressibility Incompressible (state equation: 𝜌(𝑇)= 𝑝 0 /𝑅𝑇) *Sung et al. Combust. Flame, 2001. **A. Abou-Taouk, et. al. Combust. Sci. Technol. 2016. *** Westbrook & Dryer, Prog. Ener. Combust. Sci., 1984.

Simulation results for an unforced case Contours of flow variables simulated by OpenFOAM with 2-step reaction @ 3 bar Axial velocity (m/s) Static temperature (K) Heat release rate per unit volume (W/m3) 3D contour of axial velocity (40 m/s)

Validation of LES predictions: mean flow variables LES and measurements match quite well for mean flow variables Comparison between LES and exp. data @ 3 bar (mean var. @ x = 28.7mm)

Validation of LES predictions: RMS flow variables LES and measurement also match well for RMS flow variables (small errors exist) Comparison between LES and exp. data @ 3 bar (RMS var. @ x = 28.7mm)

Modelling of acoustic forcing Step 4: Determine flame describing functions (FDFs) 4.1. Define a harmonic forcing velocity 𝑼 𝒂𝒊𝒓 at swirler air-entry: 𝑈 𝑎𝑖𝑟 = 𝑈 𝑎𝑖𝑟 ∙ 1+ 𝐴 𝑈 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡 𝑚/𝑠 Mean inflow Velocity ~5m/s Velocity forcing amplitude [-] Velocity forcing frequency [Hz] By controlling both 𝐴 𝑈 and 𝑓 𝑈 , a total of 16 forcing cases (see below) are performed by each LES solver at each pressure.

Calculation of total heat release rate fluctuation (calculated at each time-step) Local Q ′(x,y,z) spatially integrated over domain volume V 𝑄 = 𝑄′ x,y,z 𝑑𝑉 𝑉 4.2. Approximate total heat fluctuation 𝑸 by a harmonic expression: Heat responding amplitude [-] Heat responding phase [rad] The values of unknown 𝑨 𝑸 and ∅ 𝑸 are calculated for each forcing case. 𝑄 = 𝑄 ∙ 1+ 𝐴 𝑄 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡+ ∅ 𝑄 (𝑊/ 𝑚 3 )

Heat responding amplitude 𝑄 = 𝑄 ∙ 1+ 𝐴 𝑄 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡+ ∅ 𝑄 (𝑊/ 𝑚 3 ) Heat responding phase Heat responding amplitude Power spectra of 𝑼 𝒂𝒊𝒓 Power spectra of 𝑄 𝑨 𝑸 = 0.124 Spectral peak at forcing frequency Power spectra via FFT (AU = 0.1, fU = 200 Hz) Cross-correlation between 𝑼 𝒂𝒊𝒓 and 𝑄 Location of maximum cross-correlation magnitude ∅ 𝑸 = -1.906 rad Cross-correlation (AU = 0.1, fU = 200 Hz)

Flame describing functions (FDFs) Forced harmonic velocity 𝑼 𝒂𝒊𝒓 𝑈 𝑎𝑖𝑟 = 𝑈 𝑎𝑖𝑟 ∙ 1+ 𝐴 𝑈 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡 𝑚/𝑠 Velocity forcing amplitude Velocity forcing frequency Responding total heat release rate fluctuation 𝑄 𝑄 = 𝑄 ∙ 1+ 𝐴 𝑄 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡+ ∅ 𝑄 (𝑊/ 𝑚 3 ) Heat responding amplitude Heat responding phase The FDF is finally defined in frequency domain as: FDF-Gain: G = A Q / AU FDF-Phase: ∅ = ∅ Q ±𝑛∙2𝜋 (n: an appropriately selected integer)

AU = 0.1 (lower forcing amplitude) AU = 0.2 (higher forcing amplitude) Flame describing functions (FDFs) Completed FDFs by polynomially-fitting gain G and phase ∅ over frequency. @ 3 bar pressure @ 3 bar pressure AU = 0.1 (lower forcing amplitude) AU = 0.2 (higher forcing amplitude)

AU = 0.1 (lower forcing amplitude) AU = 0.2 (higher forcing amplitude) Flame describing functions (FDFs) At both pressures, the fitted FDFs have small mismatches in FDF-gains, and have generally linearly-distributed FDF-phases. @ 6 bar pressure @ 6 bar pressure AU = 0.1 (lower forcing amplitude) AU = 0.2 (higher forcing amplitude)

Methodology Combined Prediction Approach Low order network acoustic modelling Flame describing function (FDF) 1. Geometry simplified into network 3. Simulate flame-acoustic interaction Upstream forced velocity u1’ Downstream heat release rate Q’ 2. Wave-based acoustic modelling 4. Construct numerical FDFs 5. Combine into OSCILOS* and calculate thermoacoustic modes *J. Li, D. Yang, C. Luzzato, A. S. Morgans, OSCILOS Long technical report, 2014.

Predicting thermoacoustic instability using OSCILOS Step 5: use the open source software OSCILOS (www.oscilos.com) to combine acoustic modes and FDFs to predict thermoacoustic modes. 5. Calculate thermoacoustic modes 1. Build network geometry 2. Calculate mean flow properties 3. Import and fit numerical FDFs 4. Define acoustic B.C.s

Measured thermoacoustic modes from DLR DLR measurement Pressure sensor installed on the top-inner wall @ x = 273 mm 6-bar Measured modes 3-bar Time-series of measured pressure signals Power spectra magnitude of pressures

Thermoacoustic prediction by OSCILOS OSCILOS defines a complex plane (X: growth rate, Y: frequency); Predicted modes are marked by white stars at plane minima; The frequencies of measured modes are marked by black dash lines. White stars: predicted modes by BOFFIN-FDFs @ 3 bar, AU = 0.1 Dashed lines: frequencies of measured modes at 3 bar. A total of 10 predictions cases are completed by OSCILOS

Predicted thermoacoustic modes via OSCILOS: 3 bar BOFFIN @ 3 bar, AU = 0.1 OpenFOAM @ 3 bar, AU = 0.1 (left) 4-step (right) 2-step BOFFIN @ 3 bar, AU = 0.2 OpenFOAM @ 3 bar, AU = 0.2 (left) 4-step (right) 2-step

Predicted thermoacoustic modes via OSCILOS: 6 bar BOFFIN @ 6 bar, AU = 0.1 OpenFOAM @ 6 bar, 2-step, AU = 0.1 BOFFIN @ 6 bar, AU = 0.2 OpenFOAM @ 6 bar, 2-step, AU = 0.2

Comparison of modal frequencies: prediction vs. measurement The errors for all predicted modal frequencies are <17%. Modal frequencies @ 3 bar Exp. data Modal frequencies @ 6 bar PSDs of pressure signals measured at x = 231 mm at 3 bar (solid) and 6 bar (dashed-dotted).

Comparison of modal growth rates: prediction vs. measurement The growth rate of the ~368 Hz mode is over-predicted, while the real unstable ~215 Hz mode is under-predicted. Unstable mode Modal growth rates @ 3 bar Exp. data Unstable mode Modal growth rates @ 6 bar PSDs of pressure signals measured at x = 231 mm at 3 bar (solid) and 6 bar (dashed-dotted).

Summary on OSCILOS predictions Based on the thermoacoustic predictions by OSCILOS: A total number of 7 thermoacoustic modes are predicted for all cases, matching the measured number; All the predicted modal frequencies accurately match the measured values, with an error less than 17%; The change of FDFs will considerably modify the mode distribution; The change of forcing amplitude does not highly affect the mode distribution; The change of operating condition (e.g., pressure) also has some effects; The most dynamic predicted mode occurs at ~380 Hz for all cases, mismatching the most dynamic measured mode at ~215 Hz.

Conclusion & Future work This work predicted the thermoacoustic instability in a real industrial gas turbine combustor with complex geometry, having: Low computational costs (Analytical acoustic modelling + Flame LES); High prediction accuracy (on frequencies of all thermoacoustic modes); Convenient prediction process (offered by open source OSCILOS); Future work will focus on: Using a refined mesh to study the mesh sensitivity of LES and FDFs; Studying the mismatch of FDFs and modal growth rates at low frequencies (e.g., adding an upstream air plenum, using a Helmholtz solver, etc.); Using a simpler reaction mechanism (e.g., 4-step) for BOFFIN LES

Acknowledgement Siemens Industrial Turbomachinery (UK) UK National Supercomputing Service Centre for Doctoral Training in Fluid Dynamics, Imperial College London European Research Council

Imperial College London Thank you very much! And any questions? YU XIA Imperial College London yu.xia13@imperial.ac.uk

A1. Mesh sensitivity analysis on SGT-100 combustor Same fixed mass inflow rates for fuel CH4 Coarse mesh: 7.0 m structured cells Refined mesh: 14.3 m unstructured cells

A1. Mesh sensitivity analysis on SGT-100 combustor The OpenFOAM-FDFs obtained by refined mesh (14M) have close gains and phases compared to BOFFIN & OpenFOAM-FDFs obtained by coarse mesh (7M) BOFFIN & OpenFOAM-FDFs @ 3bar pressure (left) AU = 0.1, (right) AU = 0.2

A2. Effect of chemical reaction steps on BOFFIN-FDFs Comparison between 4-step and 15-step chemistry using BOFFIN 4-step chemistry (Abou-Taouk et al) 15-step chemistry (Valino) Fuel Methane (CH4), 3 bar pressure, equivalence ratio = 0.6 Compressibility Incompressible (with BOFFIN) Combustion Model Stochastic field method SGS model Dynamic Smagorinsky model Time integration 2nd-order Crank-Nicolson scheme Spatial discretisation 2nd-order central difference scheme

A2. Effect of chemical reaction steps on BOFFIN-FDFs 2 spot-check cases @ A=0.1, f =600 Hz & A=0.2, f =600 Hz both show close FDF gain and phase BOFFIN-FDF @ 3bar pressure (left) AU = 0.1, (right) AU = 0.2

A3. Effect of stochastic field numbers on BOFFIN-FDFs Comparison between one and eight stochastic fields using BOFFIN One stochastic field Eight stochastic field Fuel Methane (CH4), 3 bar pressure, equivalence ratio = 0.6 Compressibility Incompressible (with BOFFIN) Combustion Model Stochastic field method SGS model Dynamic Smagorinsky model Time integration 2nd-order Crank-Nicolson scheme Spatial discretisation 2nd-order central difference scheme

A3. Effect of stochastic field numbers on BOFFIN-FDFs BOFFIN-FDFs are insensitive to the number of stochastic fields BOFFIN-FDF @ 3bar pressure (left) AU = 0.1, (right) AU = 0.2

A4. Comparison between Helmholtz and OSCILOS Geometry Swirler + Combustor + Exhaust Pipe Highly simplified Slightly modified Air plenum Flame region Swirler Combustor Exhaust pipe Exhaust pipe Swirler Combustor Air plenum Helmholtz solver (COMSOL) OSCILOS Acoustic boundary conditions: Fully closed inlet R1(s) = 1 Open outlet with damping

A4. Comparison between Helmholtz and OSCILOS With BOFFIN-FDFs (A=0.1) 3 bar pressure Most unstable mode correctly captured All modal frequencies match well Thermoacoustic modal frequency Thermoacoustic modal growth rate