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

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)

3. Overview Model Fuel-injector dynamics Model Control
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

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

5. Heat Release Model: Flame Kinematics
Linearized PDE Model:
Flame surface
: Propagation delay
For small , and conical flames reduces to: r

6. Acoustics: Longitudinal Modes in an Organ-pipe Combustor
MIT 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:
p,u
Flame
ODE Model:

7. Organ-pipe Combustor (MIT): Coupling caused by Velocity Fluctuations
Acoustics
Heat
Release b c
c: fn of velocity mode shape
b: fn of pressure mode shape
0.2
0.4
0.6
0.8 1 -1
-0.5
0.5 b c
Three-quarter-wave mode
Quarter-wave mode
bc>0: system becomes unstable
Summary of the model predictions: (2-modes)
MIT Model prediction:
Experimental (Lang et al.’87):
Growth
rate(1/s)
Frequency
(Hz)

8. Acoustics Model: Dump Combustor with a Large Bulk
Flame surface
Reactants
inlet
Products
outlet
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 jth duct:
Substitute (2) in (1):
(assume ducts open to atmosphere;
pressure distribution is negligible)
Where the effective Helmholtz frequency is

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?
Fuel
Air
Delay:

10. UTRC Combustor: Combustion Instability due to Inhomogeneity Dynamics
United Technologies combustor:
Instability due to
Model prediction:
Pressure (Pa)
Time (s)
Unstable:
when
0.62
UTRC instability 1 2 3
Unstable bands
Stability bands identified in experiments (Putnam 1971,
Richards 1995, Zinn 1998)

11. Summary of Instability Models
General Model:
When u’ fluctuations are dominant
Time-delay instability
Phase-lag instability
When f’ fluctuations are dominant 1 2 3
Unstable bands

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

13. Model Predictions: u’ oscillations
Longitudinal mode
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 u’
Heat
release
Impedance
MIT Model prediction:
Experimental (Poinsot ):
Growth
rate(1/s)
Frequency
(Hz)
Two-modes simulation
Frequency
Gain
Phase
Agrees with Experiments by Bloxsidge et al., 1987

14. Overview Model Fuel-injector dynamics Model Conrol
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

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

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

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

18. Overview Model Fuel-injector dynamics Model Conrol
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

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

20. Using Pulsed-fuel Injection (on flame)
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) f
LQG/LTR
Equivalence ratio f
Pressure p’ (Pa)
Time (ms.)
Control on (f’)

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

22. Pole-Placement Control for a Combustor with a Delayed Control Input
Controller structure: S p’ f’
Closed-loop:
Stabilize!
Cancel!
Stable synthesis (Manitius & Olbrot’79, Ichikawa’85)
Robust (Niculescu & Annaswamy, ACC’99)
Amenable to adaptation with uncertainties (Niculescu & Annaswamy, ACC’99)
Validation in turbulent combustors (Evesque, Annaswamy & Dowling,
NATO Symposium’00)
Properties:

23. Simulation with Time-delay Compensator Control
MIT combustor model: ti ~50tac. (mean velocity <<)
Pressure (Pa)
Time (msec)
Control on
Control input, fc*
Time (msec)

24. Overview Model Fuel-injector dynamics Model Conrol
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

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

26. Impact of Nonlinearities in the Actuator
(PSP)23-26
Impact of Nonlinearities in the Actuator
Acoustics
Combustor dynamics
Controlled (stable) limit cycle
Heat
release
f(.)
nonlinearity u’
pressure
Unstable limit cycle G
Control
Asymptotic stability
Actuator dynamics
% secondary fuel
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.
Unstable
limit-cycle
Open-loop
Stable limit-cycle

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

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