[american institute of aeronautics and astronautics 40th aiaa/asme/sae/asee joint propulsion...

1 American Institute of Aeronautics and Astronautics

40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit AIAA-2004-4034 10-14, July, 2004, Fort Lauderdale, Florida

Dynamics and Control of a High Frequency Fuel Valve and its

Application to Active Combustion Control

+Tongxun Yi, *Michael Cornwell and ++Ephraim J. Gutmark +Department of Aerospace Engineering and Engineering Mechanics

University of Cincinnati, Cincinnati, OH 45220-0070 *Goodrich Aerospace, Delavan Gas Turbine Products,

West Des Moines, IA 50265 Abstract An active combustion control valve capable of high-frequency large-amplitude fuel modulations is presented. This valve utilizes a hydraulic piston-cylinder structure. Mean fuel flow rate is controlled by valve opening via a step motor; and fuel modulation is achieved via the extension and contraction of a Terfenol-D rod. Experiments and low-order modeling are performed to optimize valve performance. Finite compressibility of fuel within the valve is considered based on fuel modulus. A fuel with smaller modulus favors larger fuel modulations. Fuel modulations could be more than 40% of mean flow at 700 Hz. An adaptive controller is developed to track and regulate mean flow. Phase-shift fuel control achieves pressure attenuation up to 27 dB in an unstable atmospheric swirling combustor.

Nomenclature:

mα : Step motor gain;

γ : Fuel kinematic viscosity, sm /2 ;

cA : Cross-section area of valve piston, m2;

43021 ,),(, eemee AAxxAA − : Effective flow area of orifices, m2;

tA : Fuel tube cross-section area, m2;

K : Fuel modulus, Psi;

3,2,1L : Fuel tube length, m;

Q& : Fuel modulation, sm /3 ;

0Q& : Mean flow rate, sm /3 ;

_______________________________________Copyright © by 2004 by Tongxun Yi, Michael Cornwell and Ephraim, J. Gutmark, published by the American Institute of Aeronautics and Astronautics, Inc., with permission. ++AIAA Associate Fellow, Ohio Eminent Scholar and Chaired Professor of Department of Aerospace Engineering at University of Cincinnati, [email protected]. +Graduate Research Assistant. *Senior Research Engineer, Goodrich Aerospace.

T : Fuel modulation period, second;

mx : Length of valve cavity, m;

0xxm − : Valve outlet openness, m;

ep : Dynamic pressure downstream of fuel injector, Pa;

Subscript 0: mean quantities;

1. Introduction

Increasingly strict emission regulations greatly affect gas turbine combustion technology. Lean-premixed-prevaporization (LPP) combustion within a short combustion chamber is a promising low emission approach for aircraft engines. However, LPP combustion is susceptible to several complications, such as combustion instability. For a short combustion chamber, it may be difficult to achieve complete combustion and uniform pattern factor. A possible solution is design combustors emphasizing low emission considerations and implement active control systems to remedy the complications. Active control system also can be used to further reduce emissions.

Fuel modulation is a practical combustion control mechanism, which has been widely used for combustion instability attenuation in laboratories1,2 and several large-scale industrial

40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit11 - 14 July 2004, Fort Lauderdale, Florida

AIAA 2004-4034

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


rigs3,4. Fuel modulation also has potential applications for lean blowout extension, emission reduction and pattern factor optimization. An active combustion control valve for aircraft applications should possess high reliability, wide bandwidth (up to 1000 Hz), large fuel modulation (usually 30% of mean flow suffices), proportionality, small size and weight. Solenoid fuel values widely used in reciprocal engines are not suitable for gas turbine combustion control. Such valves usually could not fully close or open above 75 Hz. Fuel flow rate response to duty cycle is not linear at all. Another disadvantage is the significant change of mean flow when solenoid valves operate. This paper presents an active combustion control valve capable of high-frequency large-amplitude fuel modulations. Experiments and theoretical analysis are performed to optimize valve performance. A simple adaptive controller is developed for mean flow regulations. Closed-loop phase shift fuel forcing achieves pressure attenuation up to 27 dB within an unstable atmospheric swirling combustor. A new generation of active combustion control valve is now under development. 2. Active Combustion Control Valve The active combustion control valve (fig. 1) is designed by Goodrich Aerospace. Fig. 2 is a sketch of the valve system. Fuel supply may be a fuel tank pressurized by nitrogen at 200~500 Psi, or a Parker pump capable of flow 0.9 GPM up to 1220 Psi. Usually the fuel pump is working below 600 Psi. The fuel pipe upstream of the valve is about 5 meters long. Most of the valve tests are done in a non-combustion environment. An orifice with comparable flow resistances to the fuel injector is used instead. Usually a long tube (about 3.7 m) is used to recycle the fuel out of the valve to the fuel tank. Several tests are performed on a combustion rig, where the distance between the valve and the fuel injector is about 1.2 m. Instantaneous fuel flow rate is obtained from the pressure drop across a throttle orifice. Flow rate and pressure drop are related as

5.12

5.01 PCPCQ ∆+∆=& . (1)

1C and

2C are obtained by calibration. Some of the throttle orifices flow resistances are comparable to that of the fuel injector. Thus, valve performance can be conveniently studied

in a non-combustion environment. A differential pressure transducer from Sensotec is used for pressure measurement, which is capable of working up to 2 KHz with error below 0.25%. Mean flow rate is controlled by a stepper motor which is operated by a programmable driver. Precise pulse-width modulation (PWM) at 20-30 kHz is intrinsically set for motion control. Jogging direction is controlled by switching input terminals. Because the stepper motor has a much faster dynamics compared with the fluid circuit, the response of valve opening to PWM control signal is modeled as a proportional unit,

)0()()(

>−= mmm

susx

αα (2)

Fuel modulation is achieved by a Terfenol-D rod (fig. 3) which extends or contacts with external magnetic field generated by an unsteady current through a surrounding coil. Different from mean flow regulation, fuel modulation is achieved by “push” fuel out of the valve. Terfenol-D is a kind of magnetostrictive material, capable of generating large strain and large force within several microseconds5. Thermal strain due to coil dissipation and eddy current is neglected here, due to fuel cooling around the rod and short actuation period (usually within several minutes). Fig. 4 shows the fuel modulation diagram. Forcing signal of ± 0.75 volt is generated from the Dspace Controldesk, and sent out to a Titan oscillator via a D/A port of Dspace board CP1104. The Titan oscillator is a current-limited transformer which amplifies the input voltage and outputs a current below 3.3 Ampere to actuate the Terfenol-D rod. The response of Terfenol-D to current is nonlinear with hysteresis. For simplicity, the response of valve opening to input voltage is modeled as a first order low-pass filter:

)0,,,()()(

43214

3

2

1 >+

⋅+

= βββββ

ββ

βsssu

sY (3).

The first term on the right accounts for the decreasing current with frequency, and the second term on the right accounts for the decreasing displacement of Terfenold-D rod with frequency in the same external magnetic fields.

3. Simplified Analysis of Valve Performance

A schematic fluidic circuit is shown in fig. 5. Fuel flow within tubes is modeled as 1D inviscid flow. This is based on the following assumptions:


• Axisymmetric flow; • Large tube length/diameter ratio; • Ratio of viscous stress to acceleration force

2RTγϕ = is very small (<0.002) for jet-A,

¼’’ tube and forcing frequency above 50 Hz. Fuel flow within tubes can be modeled as compressible based on the definition of modulus

ρρddpK =

:

ρKa

xpau

tp

=

=∂∂

±+∂∂ 0)( (4)

Noticing that fuel flow is usually below 7 m/s and pressure drop mostly occurs across the orifices, it is reasonable to assume incompressible flow within tubes. Thus unsteady Bernoulli’s equation applies. For the piston-cylinder cavity (fig. 6), finite compressibility of fuel is considered. Due to its compact volume, pressure dynamics is modeled as a lump system. Starting from mass conservation and fuel modulus, pressure dynamics within the cavity is derived:

ρ)(2

)(

111

21

ce

mc

mc

c

PPAQ

dtdx

AQQxAK

dtdP

−=

+−=

&

&& (5)

ρ)(2 5

42e

ePPAQ −=&

ρ

ρ

)(2

)(2)(

4332

022

PPAQ

PPxxAQ

e

acme

−=

−−=

&

&

By linearizing and combining the equations for incompressible flow within the tubes and pressure dynamics within the cavity, the response of flow rate to the piston movement is modeled as:

ρψ

β

ζ

ψψζβζ

ρ

0

24

23

200

22

0

21

20

2132

21

0

2

;]11)(

1[

;)11(

)]()[()()(

mc

t

eemet

ett

m

t

m

xAKA

AAxxAAQ

AAAQ

ssLsLLssL

xKA

sxsQ

=

++−

=

+=

++++++

=

&

&

&

(6)

Notice that γβζ <<, , for a certain frequency range, equation (6) can be approximated as:

))(()()(

2132

1

0

2

ψρ ++≈

sLLLsL

xKA

sxsQ

m

t

m

& (7)

Resonant Frequency Equation (7) indicates that system behaves like a Helmoltz resonator, with resonant frequency

1Lsψω = (8)

Resonant frequency sω is affected by the upstream tube length and diameter, volume of valve cavity 0mc xA , fuel modulus K and density ρ . Fig. 7 shows that the largest fuel modulation occurs around 380 Hz. For this test, the mean flow rate is 4g/s, and the fuel supply pressure is 400 Psi. For this setup, tube upstream of the valve is about 5 m and about 3.7 m downstream of the valve, PsiK 51084.1 ×≈ ,

075.0/ ≈ct AA , mxm 005.00 ≈ and 3/800 mkg≈ρ , the predicted resonant frequency is 371 Hz, which is very close to the experimental value. It is expected that higher resonant frequency will occur for a smaller fuel flow rate due to a smaller piston-cylinder cavity. Notice that the frequencies of the quarter and three-quarter wave modes within the upstream tube are about 65 Hz and 195 Hz respectively, which are much lower than the resonant frequency 380 Hz. This also supports the assumption of incompressible flow within the upstream tube. Effects of Upstream Tube As can be inferred from equation (8), the resonant frequency becomes higher by reducing tube length upstream of the valve. This suggests implementing a fuel accumulator just upstream of fuel valve. Effects of Fuel Modulus Equation (8) predicts that fuel with a smaller modulus will have a lower resonant frequency. Experiments show that larger fuel modulation is achieved with paint thinner than jet-A when forcing below the resonant frequency. The main component of paint thinner is turpentine, which has a smaller modulus than jet-A. Effects of Downstream Tube Equation (7) suggests that a shorter tube downstream of the valve improves fuel modulation significantly. It is beneficial to implement the value as closely as possible to the rig. This is verified by experiments. Fig. 8 shows that, with a downstream tube of 1.2 m, fuel


modulation at 700 Hz is about 40% of mean flow, which is two times larger than for a downstream tube of 3.7 m. Here fuel modulation percentage is defined as the ratio of fuel modulation amplitude to mean flow. For this test, mean flow is 2.5g/s. Upstream tube length is 5 m, and fuel supply pressure is 400 Psi. Forcing amplitude is 0.3 volt. Other experiments show that fuel modulation can be up to 80% of mean flow at 800 Hz using shorter tubes with larger diameters6. Effects of Tube Diameter Equation (8) also suggests that tubes with larger diameters will result in a higher resonant frequency. Experiments using a 3/8’’ tube achieve larger fuel modulation than a ¼’’ tube6. Effects of Fuel Supply Pressure Fuel supply pressure affects fuel modulations, as shown in fig. 9. It seems that above 500 Hz, higher fuel supply pressure leads to larger fuel modulation, up to 40% of the mean flow at 600 Hz. For this test, the downstream tube is 3.7 m. Mean flow rate is 2.5 g/s. A Jet-A tank pressurized with nitrogen is located 5 m upstream of the valve. Again, the peak frequency is observed around 380 Hz. Effects of Forcing Input The Titan oscillator is a current-limited transformer whose gain is not constant except for a smaller forcing voltage at higher forcing frequency, due to current saturation. Fig. 10 shows that larger input generates larger fuel modulation above 200 Hz, and fuel modulation is almost the same around 100 Hz for forcing amplitude above 0.3 volts. This test is done on a combustion rig with mean fuel flow rate 2. 5g/s, fuel supply pressure 300 Psi. The distance between the valve and fuel injector is 1. 2 m with a ¼’’ tube 0.7 m and a 1/8’’ tube about 0.5 m. A fuel accumulator is located 1.2 m upstream of the valve. Very large fuel modulations occur around 700 Hz due to a shorter tube upstream of the valve. Effects of Downstream Pressure Strong pressure oscillations downstream of the fuel injector may introduce fuel flow rate perturbations. Coupling between fuel injections and pressure oscillations is a common mechanism for combustion instability. To model this effect, pressure dynamics within the piston-cylinder cavity is neglected. Since the Terfenol-D rod is not actuated, there is no fast

change of the cavity volume. The response of flow rate to downstream pressure perturbations is derived as:

)11)(

111(

1)()(

24

23

200

22

21

204

321

eemeettt

e

AAxxAAAQs

AL

AL

ALsP

sm

++−

+++

++

−=

&

&

(9) It is clear that, almost all the factors favoring larger fuel pulsations can not suppress downstream disturbances except the valve inlet orifice. Increasing flow resistance at the valve inlet necessitates a higher fuel supply pressure for the same flow rate. Flow response to downstream pressure pulsations in an unstable atmospheric combustor will be shown in section 5. Bubble Effects It is necessary to keep bubbles out of the fuel system in order to achieve larger fuel modulations. Air bubbles may form within the fuel system if it is not purged out before starting the valve. If a fuel tank is pressurized with nitrogen, nitrogen bubbles may form within the fuel system due to substantial pressure drop across the valve. Assume a nitrogen bubble with mass bbbb TRm ρ=& resides within the valve, and

the bubble temperature bT is assumed to be a constant. Further assume a big fuel source at constant pressure just upstream of the valve and fuel is ejected directly to the atmosphere. The response of fuel modulation to valve movement is derived as:

]1)(

[2)()(

200

22

2100

0

+−

+

−=

xxAAPmsTRM

sPAsxsm

me

ecbbb

cc

m

ρ&

& (10)

It is clear that fuel modulation gain will decrease with more air or nitrogen bubbles. Fig. 11 shows that fuel modulation level is reduced by more than 12 times because of bubbles with forcing input amplitude 0.3 volt at 300 Hz. With bubbles, a substantial phase-lag exists between forcing input and fuel modulation. Effects of Other Geometric Factors For shorter tubes upstream and downstream of the valve, equation (6) shows that larger fuel modulation is favored for a larger valve outlet orifice, larger throttle orifice, larger cylinder cross-section, larger tube diameter and larger fuel injection ports. Effect of valve inlet orifice

1eA on fuel modulation is somewhat complex. It


seems that, for shorter tubes, a smaller valve inlet orifice 1eA favors fuel modulation. This may be because more fuel will be pushed downstream than upstream if the inlet orifice has a larger flow resistance. 4. Mean Flow Rate Regulation Mean flow rate regulation is necessary in order to follow the flow command and counteract various disturbances such as fuel supply pressure variations, rearrangement of fuel systems such as tubes with different length and diameters, orifices with different flow resistances and so on. Terfenol-D actuation also affects mean flow. Because of the very small gap between the piston and cylinder, the high-frequency high-speed motion of Terfenol-D rod introduces large viscous stresses on the cylinder, thus the cylinder may be forced to move with the piston during the contraction period. This will result in a smaller valve outlet orifice and a smaller mean flow. The stepper motor is used to regulate the mean flow rate by controlling the valve opening. Accuracy and fast response are the basic requirements for flow regulation. The latter is especially important for combustion instability control. A simple adaptive controller is developed for mean flow regulation. The control design is based on the following models:

ssusx

AAxxAAm

sA

LLLxxA

m

sxsm

mm

eemett

me

m

αρ

ρ

=

++−

++++

=

)()(

]11)(

11[

)()()(

24

23

200

22

20321

200

22

20

&

&

& (11)

mα is the stepper motor gain. Here the dynamics of the stepper motor is neglected due to the very small time constant. For convenience, equation (11) is rewritten as:

]11)(

111[)(

)()(

0,1)()(

24

23

200

22

21

2321

012

20

3212

0022

1

212

21

eemeet

t

mt

me

AAxxAAALLLAmAm

LLLxxA

sssusm

++−

++++

=

++−=

>+

=

ρα

α

αρ

α

αααα

&

&

&

(12)

In the time domain, equation (12) is formulated as: u

dtmd

dtmd

=+&&

22

2

1 αα (13)

A stable adaptive control design is performed without knowing detailed values for coefficients

1α and 2α :

0,ˆˆ)(

21

1221

>−+∆−∆−=

ααλαα mamasignu && (14)

mdtad

mm

&&

&

1

1

0

Γ∆

=

>+=∆

λλλ

m

dtad

&&

2

2

Γ∆

−=

Closed loop system response is affected by parametersλ , 1Γ and 2Γ . Usually larger λ and smaller 1Γ and 2Γ improve dynamic response. Lyapunov function-based stability proof:

0

0,

)ˆ(21)ˆ(

21

21

22

1

21

2222

2111

21

≤∆−∆−=

>ΓΓ

−Γ+−Γ+∆=

ααE

aaaaaE

&

(15)

Step response of the control system is shown in fig. 12. Within half a second, flow rate can be changed by 100%. 5. Fuel Modulation for Combustion Control Phase-shift fuel modulation is applied to stabilize an unstable atmospheric swirling combustor fueled with turpentine. The combustion rig features a triple annular research swirler (TARS) with distributed fuel injections. The combustion chamber is a stainless-steel pipe 26’’ long with inner diameter 4’’, supporting unstable longitudinal quarter wave mode between 200 and 325 Hz7. Effects of Pressure Pulsations on Fuel Flow Rate Strong pressure pulsations up to 6 kPa occurs at air flow rate 116 SCFM, equivalence ratio 0.44 and power 88 kW. Fig. 13 shows that dominant frequency is at 265 Hz, with a much stronger third harmonics at 800 Hz than the second harmonics at 531 Hz. Fuel flow rate is affected by pressure pulsations, and is out of phase with pressure oscillations, as shown in fig. 14. However, fuel flow rate oscillation is about 0.003 g/s, less than 0.1% of mean flow. Such a small fuel oscillations suggests that equivalence ratio variation may not be the dominant mechanism for combustion instability in this test. One possible mechanism is that oscillations of vortex breakdown, corner


recirculation zone and swirling shear layers, and their interactions with flame structure, as suggested by the phase-locked images in the reference7. Detailed study of the instability mechanism will be done later. Effects of Fuel Modulation on Heat Release Fig. 15 shows the spectrum of a CH optical fiber with sinusoidal forcing at 800 Hz with amplitude 0.3 volt. The CH optical fiber is embedded in the inner swirler of TARS. For this test, combustion is stable with equivalence ratio 0.28 and power 56.7 kW. Detailed studies of heat release response to fuel modulation will be done later. Phase-Shift Combustion Control Fig. 16 shows the phase-shift control diagram. Pressure is sampled by a water-cooled microphone PCB106B conditioned by a signal conditioner 482A22. Voltage from the conditioner is sampled by a PC using Dspace board CP1104, then it is filtered (150-325Hz), delayed, amplified and magnitude-limited, and finally it was sent to the Titan oscillator for fuel modulation. The control signal is limited within ± 0.3 volt. Fig. 17 shows that pressure is damped by 27 dB within 162 ms. Fuel modulation about 2% of mean fuel is required at the initial stage of pressure attenuation. After that, 0.2% of mean fuel is enough to prevent instability from reoccurring.

6. Conclusions

An active combustion control valve capable of high-frequency large-amplitude fuel modulation is presented. Qualitative predictions of low-order models fit the experiment results, and shed insight to fuel system optimization. Experiments and theoretical analysis show that by implanting a fuel accumulator just upstream of the valve and implementing the valve just nearby the combustion rig will improve fuel modulation, especially for high frequency forcing. Fuel modulus, tube diameters, effective flow areas of orifices, downstream pressure and forcing input affect fuel modulation. To achieve the maximum fuel modulations, it is necessary to purge the bubbles out of the fuel system before starting it. A simple adaptive controller is developed for mean flow regulation. Phase-shift fuel forcing using this valve achieves pressure attenuation 27 dB within an atmospheric swirling combustor.

Reference:

1. Mcmanus, K.r., Poinsot, T. and Candel, S.M., “Review of Active Control of Combustion Instabilities,” Progress in Energy and Combustion Science, Vol.19, No.1, pp.1-29.

2. Kailasanath, K. and Gutmark, E.J., “Combustion Instability,” Propulsion Combustion: Fuels to Emission (chapter 5), Washington DC., Taylor and Francis, 1998.

3. Hibshman, J.R., Cohen, J.M., Banaszuk, A., Anderson, T.J. and Alholm, H.A, “Active Control of Combustion Instability in a Liquid-Fueled Sector Combustor,” ASME 99-GT-215.

4. Johnson, C.E., Neumeier, Y., Neumeier, M. and Zinn, B.T., “Demonstration of Active Control of Combustion Instabilities on a Full-Scale Gas Turbine Combustor,” ASME 2000-GT-79.

5. Kondo, K, “Dynamic Behavior of Terfenol-D,” Journal of Alloys and Compounds, 258 (1997), pp.56-60.

6. Cornwell, M., private communication.

7. Yi, T. and Gutmark, E.J., “Combustion Instabilities and Control of a Multi-Swirl Atmospheric Combustor,” AIAA 2004-635.


Fig. 1 Active Combustion Control Valve

Fig. 2 Sketch of Valve System

Fig. 3 Structure of Terfenol-D Rod

Fig. 4 Schematic of Fuel Modulation


Fig. 5 Schematic of Fluidic Circuit

Fig. 6 Piston-Cylinder Structure

Fuel Modulation with Forcing Frequency

0

0.5

1

1.5

2

100 200 300 400 500 600

Frequency (Hz)

Fuel

Mod

ulat

ion

(g/s

)

Fig. 7 Fuel Modulation with Forcing Frequency

Fig. 8 Effects of Downstream Tube Length on Fuel Modulation


Effects of Upstream Pressure on Fuel Modulation

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

100 200 300 400 500 600

Frequency (Hz)

Flow

Mod

ulat

ion

(g/s

)

200 Psi300 Psi500 Psi

Fig. 9 Effects of Fuel Supply Pressure on Fuel Modulation

Effects of Forcing Magnitude and Frequency

00.05

0.10.15

0.20.25

0.30.35

0.40.45

0 100 200 300 400 500 600 700

Frequency (Hz)

Fuel

Mod

latio

n (g

/s)

V=0.7V=0.6V=0.5V=0.4V=0.3

Fig. 10 Effects of Forcing Amplitude on Fuel Modulation

Fig. 11 Effects of Bubble on Fuel Modulation


Fig.12. Step Response

Fig. 13 Pressure Spectrum at Equivalence Ratio 0.44 and Power 88 KW

Fig. 14. Flow Rate Oscillations due to Pressure Pulsation


Fig. 15. CH Spectrum with Fuel Modulation at 800 Hz

Fig. 16 Schematics of Phase-Shift Fuel Modulation

Fig. 17 Pressure Stabilization With Fuel Modulation

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