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(PSP) 23-1 Modeling and Control of Combustion Instability using Fuel Injection Jean-Pierre Hathout *, Anuradha Annaswamy, and Ahmed Ghoniem Department of Mechanical Engineering MIT NATO AVT Symposium May 8-11, 2000 * Dr. Hathout joined the Robert Bosch Corporation Research and Technology Center in Pittsburgh, PA, since July 2000. Email: jean-pierre.hathout@rtc.bosch.com

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(PSP) 23-2 Continuous Combustion Processes and Thermoacoustic Instability Power Generation Boilers Burners Gas turbines Propulsion Commercial: Environmentally friendly Military: high power Rockets Shuttle main engine Combustion instability in the form of Screech can be seen in the heat-release signature F-22 Raptor (courtesy of UTC)

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(PSP) 23-3 Overview Model –Heat release –Acoustics –Coupling dynamics; combustion instability due to Area fluctuations due to velocity fluctuations Mixture inhomogeneity Fuel-injector dynamics Model –Proportional actuation –Two-Position actuation Control –No delay control: LQG-LTR –Time-delay control –Posi-cast control Impact of injector dynamics –Bandwidth and authority –Nonlinearities

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(PSP) 23-4 Modeling Acoustics Heat Release Coupling mechanism 1. Organ-pipe combustor (MIT, 1kW) 2. Dump combustor Longitudinal modes Bulk mode Heat-release kinematics Mixture inhmogeneity (UTRC, 100kW)

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(PSP) 23-5 Heat Release Model: Flame Kinematics Kinematics: Linearized PDE Model: r For small, and conical flames reduces to: Flame surface : Propagation delay

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(PSP) 23-6 Acoustics: Longitudinal Modes in an Organ-pipe Combustor Assumptions: –1-D flow, –Inviscid Perfect gas, –Linear model (perturbations around a constant mean) –No velocity and heat release. Using Conservation Equations: PDE Model: ODE Model: p,u Flame MIT combustor

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(PSP) 23-7 Organ-pipe Combustor (MIT): Coupling caused by Velocity Fluctuations Acoustics Heat Release b c Summary of the model predictions: (2-modes) MIT Model prediction: 115.8 620.3 Experimental (Lang et al.87):113 630 Growth rate(1/s) Frequency (Hz) c: fn of velocity mode shape b: fn of pressure mode shape 00.20.40.60.81 -0.5 0 0.5 1 bb cc Three-quarter-wave mode Quarter-wave mode bc>0: system becomes unstable

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(PSP) 23-8 Acoustics Model: Dump Combustor with a Large Bulk Assumptions: –1-D flow, –Incompressible in the ducts, –Volume of cavity>>Volume of ducts, –Inviscid Perfect gas, –Linear model (perturbations around a constant mean) Mass and energy conservation in the cavity: Mass and momentum conservation in the j th duct: Substitute (2) in (1): (assume ducts open to atmosphere; pressure distribution is negligible) Where the effective Helmholtz frequency is Flame surface Reactants inlet Products outlet

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(PSP) 23-9 UTRC Combustor: Coupling caused by Inhomogeneity Dynamics Acoustic velocity perturbation in cavity is small, negligible effect on area perturbation. Only perturbations in the equivalence ratio are important Instantaneous at fuel nozzle due to perturbations in the air flow rate: Recall: effect of on is static, but effect of on is delayed! Can a delay trigger the instability? Delay: Fuel Air

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(PSP) 23-10 01 23 Unstable bands UTRC Combustor: Combustion Instability due to Inhomogeneity Dynamics United Technologies combustor: Instability due to Model prediction: 0.62 UTRC instability Pressure (Pa) Time (s) Unstable: when Stability bands identified in experiments (Putnam 1971, Richards 1995, Zinn 1998)

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(PSP) 23-11 Summary of Instability Models General Model: 01 23 Unstable bands When fluctuations are dominant When u fluctuations are dominant Time-delay instability Phase-lag instability

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(PSP) 23-12 Model Predictions: oscillations (Lieuwen and Zinn et al., 1998) (Richards and Yip, 1997), -- Experiments: - Mongia et. al,1997 - Richards and Yip, 1997 - Lieuwen and Zinn et al., 1998 (Cohen et al., 1998) 0 1 2 3 Unstable bands UTRC (Cohen et al., 1998) Unstable: 0.62 UTRC instability when Heat release Bulk Mode Feed system impedance Time-delay (Similar dynamics also in rockets, Crocco 1960, Tsien 1962)

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(PSP) 23-13 Heat release Longitudinal mode Impedance u MIT Model prediction: 115.8 620.3 Experimental (Poinsot 1989 ):113 630 Growth rate(1/s) Frequency (Hz) Frequency Gain Phase Agrees with Experiments by Bloxsidge et al., 1987 Model Predictions: u oscillations Two-modes simulation Phase-lag instability: - MIT combustor - Poinsot et. al, 1989 - Gulati and Mani, 1992 - Sivasegaram and Whitelaw, 1992 - Seume et. al, (Siemens), 1997 Time-delay instability: - Santavicca et. al, 1998 - Richards, 1999

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(PSP) 23-14 Overview Model –Heat release –Acoustics –Coupling dynamics; combustion instability due to Area fluctuations due to velocity fluctuations Mixture inhomogeneity Fuel-injector dynamics Model –Proportional actuation –Two-Position actuation Conrol –No delay control: LQG-LTR –Time-delay control –Posi-cast control Impact of injector dynamics –Bandwidth and authority –Nonlinearities

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(PSP) 23-15 Fuel-Injector Dynamics Proportional Injection Electro-magnetic and mechanical components dynamics: Fluid dynamics - Fuel inlet choked: - armature Magnetic coil spring poppet x E

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(PSP) 23-16 Fuel-injector Dynamics Two-position (on-off) injection Dynamics: Same as proportional + effect of physical stops (saturation) + Dead-zone E(s) Driver gain + 1 s on off Dead-zone Hysteresis On: Off:

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(PSP) 23-17 model experiment 100 Hz, 50% duty cycle Two-position (on-off) injection: Velocity Response model experiment 100-Hz sweep model experiment 50 Hz, 50% duty cycle model experiment 50-Hz sweep

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(PSP) 23-18 Overview Model –Heat release –Acoustics –Coupling dynamics; combustion instability due to Area fluctuations due to velocity fluctuations Mixture inhomogeneity Fuel-injector dynamics Model –Proportional actuation –Two-Position actuation Conrol –No delay control: LQG-LTR –Time-delay control –Posi-cast control Impact of injector dynamics –Bandwidth and authority –Nonlinearities

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(PSP) 23-19 Model: 2 Acoustics modes, and flame dynamics Fuel Injector: - Proportional - 200 Hz bandwidth - 1st order dynamics 5th order model Controller: LQG/LTR (5th order) Using Pulsed-fuel Injection (on flame) LQG/LTR Control on ( ) Equivalence ratio Pressure p,(Pa)

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(PSP) 23-20 Using Pulsed-fuel Injection (on flame) Equivalence ratio Pressure p (Pa) Time (ms.) Control on ( ) Model: 2 Acoustics modes, and flame dynamics Fuel Injector: - Two-position (on-off) - 200 Hz bandwidth - 1st order dynamics 5th order model Controller: LQG/LTR (5th order) LQG/LTR

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(PSP) 23-21 Time-delay Control (injection at main fuel supply) Idea: cancel the perturbations in the main fuel causing the instability, stability depends on natural damping in the combustor. Choose control: Pressure (Pa) Control input, c * Time (s) Secondary fuel Primary fuel UTRC combustor Experimental results ( UTRC, Cohen et al.98 ): c Stable and unstable zones, model predictions unstable stable

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(PSP) 23-22 Cancel! Stabilize! Pole-Placement Control for a Combustor with a Delayed Control Input Controller structure: p Closed-loop: Stable synthesis(Manitius & Olbrot79, Ichikawa85) Robust(Niculescu & Annaswamy, ACC99) Amenable to adaptation with uncertainties(Niculescu & Annaswamy, ACC99) Validation in turbulent combustors(Evesque, Annaswamy & Dowling, NATO Symposium00) Properties:

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(PSP) 23-23 Simulation with Time-delay Compensator Control MIT combustor model: i ~50 ac. (mean velocity <<) Time (msec) Control on Control input, c * Pressure (Pa) Time (msec)

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(PSP) 23-24 Overview Model –Heat release –Acoustics –Coupling dynamics; combustion instability due to Area fluctuations due to velocity fluctuations Mixture inhomogeneity Fuel-injector dynamics Model –Proportional actuation –Two-Position actuation Conrol –No delay control: LQG-LTR –Time-delay control –Posi-cast control Impact of injector dynamics –Bandwidth and authority –Nonlinearities

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(PSP) 23-25 Actuator Limitations (Sec. Injector) p (Pa) Time (ms.) Control on ( ) Time (ms.) p (Pa) Higher authority, sec. Fuel flow rate Faster settling time Time (ms.) p (Pa) Lower bandwidth Unsuccessful control Results similar to observations in Yu (1997)

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Impact of Nonlinearities in the Actuator Heat release Acoustics f(.) nonlinearity u Control Saturated/on-off injectors: limited control authority Stability (asymptotic, or stable limit-cycle) depends on control authority Stable solutions depend on Initial conditions, define an unstable limit-cycle In agreement with K. Yu 1997. Controlled (stable) limit cycle Unstable limit cycle Asymptotic stability pressure % secondary fuel G Actuator dynamics Combustor dynamics Open-loop Stable limit-cycle Unstable limit-cycle (PSP)23-26

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(PSP) 23-27 Summary Reduced-order models for combustion instability Heat release Acoustics Coupling dynamics; combustion instability due to Area fluctuations due to velocity fluctuations Mixture inhomogeneity Model-based control Optimal Accommodates large time-delays Injection dynamics Bandwidth and authority limiations Nonlinearities

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(PSP) 23-28 Current Work Open-loop subharmonic control using fuel injection Richards et al., 1999 Time(sec) Normalized pressure, Prasanth,Annaswamy, Hathout and Ghoniem, 2000 Visit us at http://centaur.mit.edu/rgd for further details Extend models to turbulent combustion System ID Models

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