Adaptive Intelligent Combustion Control Based on ...

Adaptive Intelligent Combustion Control Based on Data-Driven Low-Order Models Tongxun Yi Domenic Santavicca Penn State University

Presented at the 2009 NASA Propulsion Control and Diagnostics Workshop Cleveland Airport Marriott Hotel, Cleveland, Ohio December 8 – 10, 2009

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STATE *NASA Award No: NNX07C98A

Content 1. Why Data-Driven Model-Based Combustion Control 2. Fuel Modulation Techniques 3. Combustion Sensing Techniques 4. Flame Transfer Functions and Control Design Perspective 5. Conclusions and Suggested Future Work 6. Reference

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STATE NASA Award No: NNX07C98A

1. Why Data-Driven Model-Based Combustion Control

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Necessity of Advanced Combustion Control For gas turbine combustors, the design strategies favoring different performance indices are usually not compatible. Combustion control adds extra freedom to improve and optimize overall performance. A typical example is developing control systems to enhance lean combustion stability so that the engines can operate in clean, safe, and stable manner. ¾ Three adaptive phase-shift controllers (Gatech, UTRC, and Yi&Gutmark). The last one is capable of identifying the dominant frequency within one pressure cycle and a half, with an estimation error within 5 Hz, and is free of stability concerns ¾Mixed control performance has been reported, including insufficient suppression of slightlydamped modes. These are the intrinsic deficiencies of phase-shift control principles.

¾ Model-based control design is a standard routine for control engineers and theorists. Datadriven models are in particular attractive and practical.

¾ Enough evidence suggests that model-based controllers can easily outperform the empirical ones, and for highly nonlinear systems, a simple nonlinear controller can well outperform linear ones.

No knowledge can be certain if it is not based on mathematics. mathematics (Leonardo da Vinci) PENN


Example 1. Empirical Vs. Model-based Control Mean Flow Control of the Goodrich Valve: PD Vs. LQG Control PD Control of Mean Flow

Goodrich Magnetostrictive Valve

12 10 8 6 4 2 0 -2 -4 -6 -8

pressure (kPa)

0

1

2

3

Mean Fuel Flow Rate (-2.5 g/s)

4

5 6 Time (s)

7

8

9

10

LQG Control of Mean Flow System Identification Model

M& 0 0.004198 s 3 − 1389 s 2 − 6.284 E 6 s − 6.431 E10 =− 4 U (s) s + 7287 s 3 + 4.155 E 7 s 2 + 2.744 E11s + 3.033 E 9 & Xˆ = Ac X + Gy u = −BT X

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⎛ 0 . 3067 ⎜ ⎜ 0 . 005 G = 0 . 001 ⎜ − 0 . 0027 ⎜ ⎜ − 0 . 0013 ⎝

⎞ ⎟ ⎟ ⎟ ; B = 1000 ⎟ ⎟ ⎠

⎛ − 7 . 0633 ⎜ ⎜ − 3 . 3158 ⎜ 8 . 3638 ⎜ ⎜ 3 . 4277 ⎝

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠


Example 2. Linear Vs. Nonlinear Control Adaptive control of Large-Vortex Shedding

No Control

N-S Equation: POD-based Model

v v v ⎫ 1 DU = −∇ p + Δ U ; ∇ .U = 0 ⎪⎪ ⎧ X& N × 1 = A Re Dt ⇒ ⎨ N→∞ v v ⎬ v r v ⎩ X(0) = X ⎪ U ( S , t) = U 0 ( S , t) + ∑ x i (t) Φ i ( S ) ⎪⎭ i =1

N×N

X + X T B N×N×N X + D

N ×1

0

Failure of the LQG Controller

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Example 2. Linear Vs. Nonlinear Control (cont.) SISI Reduced-Order Model

a1, a2 , a3 and a4: constant or slow-varying but unknown (a1>0); e: bounded unmodeled dynamics and external disturbance,

a1x& + a2x + a3x + a4 + e = u 2

s &ˆ ˆ − ks;s = x − x ; A = − = − ); Φ = E u = YT A ΓYs ; s s Φsat( d Δ Δ k Φ ~ T ˆ +A YT = (x d x x 2 1); A = A ; A = (a1 a 2 a 3 a 4 )

Adaptive control Law

Stability Proof

1 1 ~ ~ ~ & a1 s Δ2 + A T Γ −1 A ; V& = s Δ (u − Y T A − e ) − Aˆ T Γ −1 A 2 2 s ~ & = − ks Δ2 − ( s ΔY T + Aˆ T Γ −1 ) A − s Δ [ kΦ sat ( ) − e ] ≤ − ks Δ2 Φ

V =

&& V

is bounded, so global stability is guaranteed (Barbalat’s Lemma).

Ada ptive Controller Pe rform ance No Control

10

Adaptive Control

X

8 6 4

No Control

2

729

701

673

645

617

589

561

533

505

477

449

421

393

365

337

309

281

253

225

197

169

141

85

113

57

1

29

0 -2 -4 -6 -8 Tim e (x0.04)

-10 -12

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71% Reduction in Turbulent Kinetic Energy


2. Fuel Modulation Techniques

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The NASA Combustion Rig Quartz Tube Static/Dynamic Pressure Temperature Gas Fuel Bar

Quartz Tube

NASA Venturi

Liquid Fuel Tubing & Injector

Pressure & Ignitor

• Visually-observed axisymmetric flame • Pressure drop within 4% up to 70 SCFM • Nice blue flame below Ф=0.38 • Somewhat red/yellow flame above Ф=0.38

NASA Swirler

NASA Fuel Injector

Preheated Air PENN

• Jet-like flow with vortex breakdown, not easy to ignite • Comparable LBO limits with the previous one • Comparable air pressure drop with the previous one • Large fuel pressure drop, about 4 times larger • Less efficient fuel/air mixing than the previous one which has no red/yellow flame up to Ф=0.60


Experiment Setup ICCD Camera

Rotary Fuel Actuator

Choking Plate

Radial Swirler

1.25 m

Dynamic Pressure

P To Exhaust Fan

0.13 m Liquid Fuel

Fuel Injector

0.15 m

Preheated Air Fuel Pressure Measurement

Dynamic and Static Pressure Ports

0.46 mm 0.56 m 0.36 Quartz Tube

Temperature

Choking Plate

UV-Grade Long Optical Fiber Spherical Lenses

ICCD Camera

Spectrometer

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Motor-Driven High-Frequency Fuel Valve Fuel Outlet

Fuel Inlet

Forcing at 300 Hz

80 70

Rotor (20 teeth equally spaced)

P re s s u re (p s i)

60 50 40 30 20 10 0

Size 2.5’’(Ф)x2; Working up to 1 kHz Motor Shaft

0

0.01

0.02

0.03 Time (s)

0.04

0.05

Fuel Transfer Function

Forcing Input u(t)

Flame Transfer Function P1(t) Pressurized Fuel Tank

0

70

Fuel Actuator

1

225

Measurement Prediction

60

Combustor

Measurement

Prediction

175 125

50 40 30 20

75 25 -25

0

100

200

300

400

500

600

-75

10

-125 -175

0

STATE

Q& ' (t )

m& ' (t )

Fuel Injector

On/Off Valve

0

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P3(t)

Phase(Deg)

Pressure Amplitude (kPa)

Needle Valve

P2(t)

100

200

300 400 Frequency(Hz)

500

600

-225

Frequency(Hz)

NASA Award No: NNX07C98A

Pressure Amp (psi)

Air Out

1.8

0.6

1.5

0.5

1.2

0.4

0.9

0.3

0.6

0.2

0.3

0.1

0.0

0.0 0

100 200 300 400 500 600 700 800 Frequency (Hz)

Air In

Air Flow 60 SCFM Shaft

• Driven by a variable speed DC motor • Modulation frequency up to 900 Hz • Inlet velocity modulations above 50% up to 800 Hz • Size 4’’x4’’x2.5’’

STATE

Pressure Amplitude (P3, psi)

0.9

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Normalized Velcity Ratio

Motor-Driven High-Frequency Air Valve

Prediction

Measurement

0.8 0.7 0.6 0.5 0.4 0.3 550

600

650 700 750 Frequency (Hz)

800

850


Flame Response to Air Modulations 0.7

1 Series1 Series2 Series3 Series4

0.6

0.8

0.4

Gain

P0(psi)

0.5

Series1 Series2 Series3 Series4

0.3

0.6 0.4

0.2 0.2

0.1 0 550

600

650


850

900

950

0 550

600

650


850

900

950

180 Series1 Series2 Series3 Series4

Phase(Deg)

135 90

Flame Transfer Function:

CH * ( s ) G ( s) = P 0 (s)

Air modulations above 900 Hz 45 0 550 -45 -90

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Air: 40 SCFM; Preheat Temperature: 373 K

600

650

700

750

800

850

900

950

Nonlinearity in terms of the forcing amplitude, in particular around the one-wave resonant frequency Quite some details need to be figured out

Frequency (Hz)


3. Combustion Sensing Techniques

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Background of Combustion Sensing • The instantaneous heat release rate and equivalence ratios are two key parameters for combustion analysis and control. Chemiluminescence-based sensors are practical solutions. • For premixed gas-fueled combustion, linearity between chemiluminescence yield and heat release is valid for slightly turbulent or wrinkled flamelet region. But in the corrugated and broken flamelet region, nonlinearity cannot be ignored. • In combustion instability analysis, it is usually assumed that chemilumienscence is proportional to the instantaneous heat release rate, which in fact, suffers from several major deficiencies. • Reported is an accurate correlation-function-based method for real-time combustion sensing, based on chemiluminescence measurements using PMTs. For the first time in combustion literature, the nonlinearity among heat release, chemiluminescence, equivalence ratios, and acoustics effects is taken into account

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CH* Chemiluminescence(A.U.)

Phi=0.51 Phi=0.45 Phi=0.39 Phi=0.33

10o

30 25 20

100o

190o

15 5

290

320

350 380 410 Wavelength(nm)

440

0 260 285 310 335 360 385 410 435 460 485 Wavelength(nm)

470

CO2* Chemiluminescence (A.U.)

Curve-Fitting

6 4 2 0

11 10 9 8 7 6 5 4 3 2 1 0

35

10

8

100

200

300

Measurement

400 500 600 700 Experiment Index

800

12

300

8 6 4 2

0

Curve-Fitting

I 430 200


800

900 1000 1100

Curve-Fitting

0

900 1000 1100

I 365

100

Measurement

10

I 307

0

STATE

40 Phi=0.54 Phi=0.48 Phi=0.42 Phi=0.36

Measurement

10

Unstable Combustion

45

12

0

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Stable Combustion Intensity(A.U.)

11 10 9 8 7 6 5 4 3 2 1 0 260

OH* Chemiluminescence(A.U.)

Intensity(A.U.)

UV and VIS Flame Spectra

100

200

300


Ti ⎞ ⎛ ⎜φ + ⎟ 2000 ⎠ ⎝

nm

~ = 94 . 61 m& 1a . 7558 φ

2 . 2280

nm

~ = 115 . 85 m& 1a .. 3637 φ

3 . 0735

nm

~ = 212 . 05 m& 1a . 6627 φ

2 . 1369

800

900

1 . 1060

1000 1100

~ p

Ti ⎞ ⎛ ⎜φ + ⎟ 2000 ⎠ ⎝

0 . 8217

Ti ⎞ ⎛ ⎜φ + ⎟ 2000 ⎠ ⎝

1 . 4352

− 0 . 4522

~ p − 0 . 2183 ~ p − 0 . 4045

Average Error: 2.4% for OH*; 2.0% for CO2*; 3.8% for CH*.


Combustion Sensing Strategy The above correlation functions are mostly developed from stable combustion, thus they can be used to determine the mean heat release rate and the mean equivalence ratio (See JPP, Vol.129, No.5).

~ 1.4747 (I 365nm (t ) )0.7294 (I 430 nm (t ))−1.5540 ( ~p (t ) )0.1974 m& (t ) = 0.1571(I 307 nm (t ) ) −1.2966 (I (t ) )1.4942 (I (t ) )0.1437 ( ~p (t ) )−0.2021 φ (t ) = 0.1392(I (t ) ) 307 nm

365 nm

⎛ m& f ~ & & QR (t ) = 0.1ΔH R m(t )φ (t )⎜ ⎜ m& ⎝ a

430 nm

⎞ ~ ~ ⎟ = 0.00674ΔH R m& (t )φ (t ) = 281.7 m& (t )φ (t )(kW ) ⎟ ⎠ stoichiometry

They are obtained by eliminating the term of flame temperature from the three correlation functions.

70 Air Flow Rate (g/s)

Equivalence Ratio

0.40 0.35 0.30 Measurement Prediction

0.25

60 Measurement Prediction

50 40

Error: 1.4% 0.20

Error: 1.9%

30

1

3

5


15

17

1

3

5


15

17

The estimated mean air consumption rate and the mean equivalence ratio. The air flow rate is 66.7g/s, the preheat temperature is 373 K, and the equivalence ratio is decreased from 0.41 to 0.31.

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Combustion Sensing Strategy (Cont.) Self-Excited Combustion Oscillations 8

CO2*(A.U.)

CH*(A.U.)

OH*(A.U.)

Combustor Pressure(x0.1, kPa)

7 CH*(A.U.) Estimated Air Consumptiion Rate(x0.05,g/s) Estimated Heat Release(x0.05, kW)

6

7 6

5

5

4

4

Combustor Pressure(x0.1, kPa) Estimated Equivalence Ratio(x10)

3

3

2 2

(b)

1

(a)

1

0

0 0

0.005

0.01

0.015 Time(s)

0.02

0.025

0

0.005

0.01

0.015 Time(s)

0.02

0.025

(a) Time traces of chemiluminescence and combustor pressure; (b) The estimated instantaneous air consumption rate, the estimated instantaneous equivalence ratio, and the estimated instantaneous heat release rate.

Fuel Forcing Induced Combustion Oscillations 0.40

Normalized CH* Chemiluminescence Normalized Equivalence Ratio Normalized Fuel Pressure

0.32

Normalized Air Consumption Rate Normalized Heat Release Rate

0.60

Normalized CH* Chemiluminescence Normalized Equivalence Ratio Normalized Fuel Pressure

0.50

0.24

0.40

0.16

0.30

Normalized Air Consumption Rate Normalized Heat Release Rate

0.20

0.08

0.10 0.00 0

0.005

0.01

0.015

-0.08

0

0.001

0.002

0.003

0.004

0.005

0.006

-0.20 -0.30

-0.24 Time(s)

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0.00 -0.10

-0.16

-0.32

0.02

Forcing at 296 Hz

-0.40 Time(s) -0.50

Forcing at 874 Hz


4. Flame Transfer Functions and Control Design Perspective

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Background • Combustion instability and lean blowout are major technical challenges for liquid-fueled DLE combustion. Both phenomena can be attributed to the increased sensitivity in heat release to external disturbances or intrinsic acoustic oscillations at very lean conditions. • First-principle low-order modeling is challenging. The measured flame transfer functions (FTFs), i.e. heat release responses to inlet air and/or fuel modulations, provides an accurate description of combustion dynamics around the working conditions where they are derived. • Active control of both phenomena can be achieved using small-amplitude fuel modulations, employing the same control hardware and fuel actuators. However, major differences exist.

• Acoustic responses are system- and geometry-dependent, but heat-release-based openloop FTFs can be used for different types of engines employing the same type of burners.

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Flame Transfer Functions Gain(A.U.) Phase(Deg)

0.08

0.0035

200

150

0.0030

150

100 50

0.05

0

0.04

-50

0.03

Gain(A.U.)

0.06

0.01 0.00 0

200


800

0 0.0015 -50

-150

0.0005

-200 1000

0.0000

-100 -150

0

200

CH * ( s ) / Pf ( s )

0.3

20

100

6.0

0

50

5.0

-20

4.0

-40

3.0

-60

-100

2.0

-80

-150

1.0

-100

-200 1000

0.0

-120 1000

-50

0.1 0.0

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7.0

0

0.2

STATE

Q& R ( s) Pf ( s)

800

Phase(Deg)

150

Gain(A.U.)

Gain(A.U.) Phase(Deg)


-200 1000

40 Gain(A.U.)

Phase(Deg)

Gain(A.U.)

0.5

200

800

8.0

200

0


φ ( s ) / Pf ( s )

0.6

0.4

50

0.0020

0.0010

-100

0.02

100

Gain(A.U.) Phase(Deg)

0.0025 Phase(Deg)

0.07 Gain(A.U.)

200

0

200


800

Phase(Deg)

0.09

Phase(Deg)

0.10

Q& R ( s) CH * ( s)


Control-Oriented Low-Order Modeling The measured flame transfer function provides an accurate description of combustion dynamics. 3.3

3.0

2.1

2.0

1.9

1.0

1.7

0.0

-60

500

400

100

600 6.0

500

200 300 400 Frequency(Hz)

500

-200

400

500

600

500

600

Frequency(Hz)

600 -300 0 0

473 K 423 K 373 K

4.0

-90

300

75.1 g/s 66.7 g/s 58.4 g/s

-150

Preheat Temperature

600

Measurement Model

200

-100

5.0

300

100

-250

0

400 Frequency(Hz)

0 -50

4.0

2.3

300

Equivalence Ratio Phase(Deg)

Gain

5.0

2.5

0 200 -30

75.1 g/s 66.7 g/s 58.4 g/s

6.0

2.7

1.5 200

Phase(Deg)

7.0

Gain

Amplitude

2.9

0

Measurement Model

100

200

300

400

-45 Phase(Deg)

3.1

3.0

-90

-135

2.0

473 K 423 K 373 K

-180

1.0 -225

0.0

-120

0

-150 -180

Frequency(Hz)

CH * ( z −1 ) − 0.4213 z −2 + 1.604 z −3 − 1.147 z −4 W ( z −1 ) = = P0 ( z −1 ) 1 − 1.952 z −1 + 1.525 z − 2 − 0.5222 z −3

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100

200


500

600

-270

Frequency(Hz)

Examination of the gain and phases of the measured FTFs at different working conditions sheds insight on adaptive robust control design.


Fast Control of LBO LBO limits can be extended by increasing the amount of pilot fuel. But this approach is too slow, not suitable for transient LBO. In addition, locally hot regions form and exacerbate emissions. Small-amplitude fuel modulations, based on a feedback controller, are capable of quickly attenuating small deviations from the equilibrium points within a small fraction of a second. Also detection of incipient LBO is not needed. The spatial fuel distribution is not modified, thus favoring low emissions. Near-LBO combustion dynamics is rather slow, typically below 200 Hz. Thus the requirements of the actuator bandwidth and challenges associated with time delay are no longer major technical challenges. 1.2 Measurement

0

Model

0

50

100

150

200

250

-20

1.0

Phase(Deg)

Amplitude

1.1

0.9 0.8

-40

Measurement Model

-60 0.05

Closed-loop output

Control signal

Open-loop output

-80 0.03

0.7

-100 0

50


200

250

37.2618( s + 9793)( s + 1262) W (s) = (s + 26.7) (s 2 + 6.6s + 2.119e6)

Frequency(Hz)

0.01 -0.010.00

0.04

0.06

0.08

0.10

-0.03 -0.05

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0.02

Time(s)


FTFs around Resonant Frequencies The FTFs around the acoustic resonant frequencies are no longer open-loop and linear. In this figure, off the resonant frequencies, i.e. around 340 Hz and 670 Hz, differences in both the gain and phases are rather small. Considerable differences exit around the acoustic resonant frequencies. 5

180 Gain(No Baffle) Gain(Baffle) Phase(No Baffle) Phase(Baffle)

90 45

Gain

3

0 2

-45

Phase(Deg)

4

135

-90

1

-135 0

-180 0

150

300


750

900

1050

Ф=0.40 , the air flow rate of 44.5 g/s, and Ti=373 K. Stable combustion is achieved by inserting three baffle plates inside the combustion chamber.

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Nonlinear Responses of Combustion Instability Shown here are the quenching and entrainment of self-excited combustion instability with fuel modulation approaching the unstable frequency. 2.5

2.0 CH* (A.U.) Pressure(psi)

CH* (A.U.) Fuel Pressure (x0.2, psi)

Amplitude

1.6

1.5

Baseline Spectrum 1.0

1.2 0.8 0.4

0.0

0.0 650

100

2.0

400

Forcing at 661 Hz

1300

1600

670 680 Frequency (Hz)

Forcing at 666 Hz

1.2 0.8 0.4

690

700

CH* (A.U.) Pressure (psi)

3.2

Fuel Pressure (x0.2, psi)

0.0 650

660

4.0

CH* (A.U.) Pressure (psi)

1.6 Amplitude


Pressure (psi)

Forcing at 655 Hz

0.5

Amplitude

Amplitude

2.0

Fuel Pressure (x0.2, psi)

2.4 1.6 0.8

660


690

700

0.0 650

660


690

700

Unstable combustion occurs at Ф=0.40 , the air flow rate of 44.5 g/s, and Ti=373 K. The fundamental resonant frequency is 672 Hz, corresponding to one-wave mode of the combustion chamber, 1.05-m-long.

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Characterization of Combustion Instability

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Characterization of Combustion Instability (Cont.)

Phase Portrait of Self-Excited Combustion Instability

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STATE

Probability Density Function of Pressure Amplitude and Period


5. Conclusions and Suggested Future Work

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Conclusions • Performed systematic investigations of flame response to fuel modulations up to 1 kHz and to air modulations up to 900 Hz. • Developed strategies for accurate determination of the instantaneous heat release rate and equivalence ratios, which take into account of the nonlinearity among heat release, chemiluminescence, equivalence ratios, and acousticsinduced chemiluminescence oscillations. • Proposed that a single adaptive robust controller be used for simultaneously control of both combustion instability and lean blowout.

Suggested Future Work • Development of high-frequency fuel-modulation technologies • Quantification of flame response within a large range of working conditions • Implementation of combustion control experiments

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Reference 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

12.

13.

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T. Yi and D. A. Santavicca, “Flame Spectra for Turbulent Liquid-Fueled Swirl-Stabilized LDI Combustion,” Journal of Propulsion and Power, Vol.25, No.5, pp.1058-1067, 2009. T. Yi and D. A. Santavicca, “Forced Flame Response of Turbulent Liquid-Fueled Swirl-Stabilized LDI Combustion to Fuel Modulations,” Journal of Propulsion and Power, Vol.25, No.6, pp.1259-1271, 2009. T. Yi and D. A. Santavicca, “Combustion Instability in a Turbulent Liquid-Fueled Swirl-Stabilized LDI Combustion,” under review at Journal of Propulsion and Power (similar to AIAA2009-5014). T. Yi and D. A. Santavicca, “Determination of Instantaneous Fuel Flow Rates out of a Fuel Injector,” ASME Journal of Engineering for Gas Turbines and Power, Vol.132, No.2, 2010. T. Yi and D. A. Santavicca, “Flame Transfer Functions for Turbulent Liquid-Fueled Swirl-Stabilized LDI Combustion,” ASME Journal of Engineering for Gas Turbines and Power, Vol.132, No.2, 2010. T. Yi and E. J. Gutmark, “Stability and Control of Lean Blowout in Chemical-Kinetics-Controlled Combustion Systems,” Combust. Sci. and Technol., Vol.181, No.2, pp.226-244, 2009. T. Yi and E. J. Gutmark, “Adaptive Control of Combustion Instability Based on Dominant Acoustic Modes Reconstruction,” Combust. Sci. and Technol., Vol.180, No.2, pp.249-263, 2008. T. Yi and E. J. Gutmark, “Online Prediction of the Onset of Combustion Instability based on the Computation of Damping Ratios,” Journal of Sound and Vibration, Vol.310, No.1-2, pp.442-447, 2008. T. Yi and E. J. Gutmark, “Real-Time Prediction of Incipient Lean Blowout in Gas Turbine Combustors,” AIAA Journal, Vol.45, No.7, pp.1734-1739, 2008. T. Yi and E. J. Gutmark, “Dynamics of a High Frequency Fuel Actuator and its Applications for Combustion Instability Control,” ASME J. Eng. Gas Turbines Power, Vol.129, pp. 648-654, 2007. D. Wee, T. Yi, A. M. Annaswamy, and A. F. Ghoniem, “Self-Sustained Oscillations and Vortex Shedding in Backward-Facing Step Flows: Simulation and Linear Instability Analysis,” Physics of Fluids, Vol. 16, No. 9, pp. 3361-3373, 2004. T. Yi, D. Wee, A. M. Annaswamy, and A. F. Ghoniem, “Self-Sustained Oscillations in Separating Flows I: Stability Analysis and Reduced-Order Modeling,” Proceedings of the International Symposium on Combustion Noise and Control, pp. 214-220, Cranfield University, 2003. T. Yi, A. M. Annaswamy, and A. F. Ghoniem, “Self-Sustained Oscillations in Separating Flows II: Reduced-Order Modeling and Control,” Proceedings of the International Symposium on Combustion Noise and Control, pp. 221-227, Cranfield University, 2003.


Thanks ! PENN
