[american institute of aeronautics and astronautics 46th aiaa aerospace sciences meeting and exhibit...

Control of Emissions and Pulsations in a Premix

Combustor using Fuel Staging

Arnaud Lacarelle∗, Gregor Gelbert†

Rudibert King‡ and Christian Oliver Paschereit§,

Berlin University of Technology, 10623 Berlin, Germany

Extremum seeking control was applied to modify the fuel distribution of a premixedatmospheric swirl stabilized gas combustor to suppress combustion instabilities withoutincreasing NOx emissions. The overall fuel flow was split into one premixed and two sec-ondary injections. Different injection repartitions were tested and the best configurationregarding instability suppression was selected for closed loop control. Two different typesof extremum seeking controllers were implemented and tested on symmetric and asymmet-ric secondary fuel injections at different operating points of the combustion chamber. Toincrease the controller speed, a fast NOx sensor based on chemiluminescence was imple-mented. The controller was able to suppress the instability of two operating points of thecombustion system within a few minutes, mainly limited by the response time of the fuelflow sensors. The control scheme was also able to maintain the combustion stable duringtransients.

Nomenclature

(·)′ dimensionless quantity(·)∗ extremal valuem mass flow(·) amplitude of a harmonic signal〈·〉 mean quantitya amplitude of dithering signal in extremum

seeking loope actuator commandf frequencyF (u) nonlinear static mapp acoustic pressureT temperatureESC extremum seeking controlHP high-pass filter

LP low-pass filter

Subscripts

all overall fuelpre preheaterpre premixed fuelsec secondary fuelsp set point

Symbols

ωp oscillation frequencyφ fuel air equivalence ratioϕ phase of linearly unstable wave

I. Introduction

In order to react to even more stringent emission limitations, lean combustion became the state of theart of modern gas turbines within the last decades as it allows to reduce the flame temperature and hencepollutant emissions like nitrogen oxides (NOx). The main drawback of this technology is the occurrence ofheat release oscillations which can lead to strong combustion instabilities. These instabilities are also calledthermoacoustic instabilities as they occur if the heat release fluctuations are matching with the resonantacoustic modes of the combustion system.

∗PhD student, Chair of Fluid Dynamics, Hermann-Fottinger-Institute, TU-Berlin†PhD student, Chair for Measurement and Control, TU-Berlin‡Professor, Chair for Measurement and Control, TU-Berlin§Professor, Chair of Fluid Dynamics, Hermann-Fottinger-Institute, TU-Berlin

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American Institute of Aeronautics and Astronautics

46th AIAA Aerospace Sciences Meeting and Exhibit7 - 10 January 2008, Reno, Nevada

AIAA 2008-1060

Copyright © 2008 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

Different mechanisms have been identified as possible source of those instabilities (Poinsot et al.1 , Lieuwenet al.2) but one of the dominant mechanisms is equivalence ratio fluctuations (Lieuwen et al.3): pressurefluctuations in low Mach number combustors are causing airflow oscillations at the fuel injection location,thereby creating temporal fuel / air ratio oscillations. These fuel/air ratio oscillations are converted into heatrelease fluctuations at the flame location. If the heat release fluctuations are in phase with the pressureoscillations, the Rayleigh criterion is fulfilled, leading to higher pressure oscillations in the combustionchamber, which may damage the combustor.

Design of modern combustors must prevent the occurrence of those thermoacoustic oscillations over awide range of operating points. This may be achieved by using different strategies to control the mixingprofile. One of the most widespread is the use of a pilot fuel injector (Cohen et al.4 , Paschereit et al.5) ,which creates locally rich zones of fuel and helps to stabilize the flame. If stabilization is reached, NOx

penality may increase very fast with the fuel mass flow through the pilot injector because of the locallynon lean fuel / air ratio and thus can not be used continuously. To reduce the amount of fuel injected,pulsed injection of pilot fuel at the frequency or harmonics of the instability was used in single combustors(Paschereit et al.6). This method appeared to be successful in single combustor in both controlling pulsationsand emissions and showed also good performance in a real gas turbine (Hoffmann7). But the question ofreliability, maintenance intervals and costs of those systems make them less attractive.

Low frequency active control of the fuel repartition within a single combustor (Kokanovic et al.8) or in gasturbines (Kokanovic et al.8 , Scarinici9) also known as fuel staging was proposed and implemented recentlyin real gas turbines. The main principle relays in the control of the convective time delays of fuel / air ratiofluctuations, without having a negative impact on the fuel / air mixing quality. This method showed goodresults in suppressing instabilities or decreasing NOx emissions without the disadvantages of high actuationfrequencies.

To control the fuel distribution, different methods have already been implemented in combustors. Evo-lutionary algorithms have been used by Paschereit et al.10 to optimize the design of an industrial burnerregarding pulsations and NOx emissions. 16 independent injectors were used to fully control the mixingprofile. Reductions in NOx and pressure pulsations were achieved, but the time needed to obtain an optimalsolution make such control suitable for design optimization and less for real-time closed loop control. Gra-dient based controller are much faster in optimization problems and were successfully used by Kokanovic etal.8 and Samuelson et al.11 . Optimum injections were reached within 10 to 20 minutes, often limited by themeasurement technique response time (particullary emission sensors). Gradient based methods are mostlymoving stepwise on the field to optimize and the choice of the step (often empirical) is critical to reach ina defined time an optimum point, hence smoother changes in the controller output may be needed to avoidabrupt changes in the combustor parameters.

Following this, the fuel staging has been applied in this study on a so-called double-cone premixed swirlburner. The aim of the paper was to show the possibility of controlling pressure pulsations and NOx emissionsby adjusting the mixing profile within the burner. Different secondary fuel injections were fixed on the burnerand their effectiveness in reducing pressure pulsation were tested. An Extremum Seeking Controller (ESC)was applied on the best fuel injection configuration in order to first reach a stable point with low emissionsand secondly maintain the system stable during transient cycles. The ESC allowed for continuous changesin the fuel distribution. To allow for a fast response of the chemistry of the flame, a sensor based on OH-chemiluminescence presented by Samuelson et al.11 was used, as conventional emissions analyzer fail todeliver fast response (dead time more than 1 min) and are thus less appropriate for closed-loop control.

The first part of the paper deals with the experimental setup and measurement technique used for thisstudy. The second part describes the Extremum Seeking Controller and how it was implemented in thetest rig. The open-loop investigations of different injection configurations are then presented and help tochose the injection with the best control authority. In the last part, the ability of the closed-loop control tostabilize the combustion configurations is shown.

II. Experimental Setup

A. Test rig and measurement technique

The investigated premix gas burner was a so-called double-cone burner as shown in Fig. 1. Natural gas wasused as fuel. The geometry of the burner produced a strong swirl of the flow at the entry into the combustionchamber which resulted in a vortex breakdown where the flame stabilized. Further description of the burner

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[email protected] 15 December 2007 41

air

Shear layer

Innerrecirculation zone

Outerrecirculation zone

fuel

Figure 1. Sketch of the swirl burner

may be found in Sattelmayer et al.12

The burner was fitted into a 200mm round quartz glass combustion chamber which allowed for a fulloptical access to the flame (Fig. 2). The temperature of the main air flow Tpre could be increased by apreheater mounted upstream of the burner. A resonance tube was mounted downstream of the combustionchamber to amplify the combustion instabilities corresponding to the quarter wave mode oscillation, makingthe combustion system unstable over a wide operating range. The exhaust gas emissions were measuredin the resonance tube with a linear sampling probe. The continuously sampled exhaust gas was sent to anABB gas analyzer where NOx emissions were measured. Values were corrected on vol. 15% O2 and arecorresponding to the NOx values presented in the paper. A detailed description of the test rig may be takenfrom Albrecht et al.13 . OH-chemiluminescence, a measure of the global heat release14 , was measured witha photomultiplier equipped with a band pass filter centered at 308 nm. A microphone mounted upstreamof the burner measured the pressure oscillations of the system. For the generation of the stability maps,both signals were acquired over a time span of 32 s at a sampling rate of 4096Hz on a separate NationalInstrument DAQ.


Setup Symmetric Injection

b mpremix

Injectors

Flame front

Combustion chamber

Gas sampling probe

Photomultiplier

tRound silica

iup

id

AirPremixFuel

SecondaryFuel

Microphone

Figure 2. Schematic of the symmetric injection configurations on the burnermounted in the combustion chamber. b, m, t: gas injection positions (bot-tom, middle, top)


1,0E+05

1,1E+05

1,2E+05

1,3E+05

1,4E+05

1,5E+05

1,6E+05

0 50 100 150 200

Massflow flux CH4 [kg/s.m²]U

pstr

eam

Pre

ssur

e [P

a] Slot InjectionBurner 0,7mm holesBurner 1,0mm holes

m m_flux Pu, mod inj m_flux Pu, Burner Pu, Burner[kg/h] [kg/m².s] [Pa] [kg/m².s] 0.7mm holes 1mm holes

20 114,1 1,15E+0512 605 4,73E+05 139,6 1,23E+05 68,45 1,05E+05

9 454 2,87E+05 104,7 1,13E+05 51,34 1,03E+057 353 2,06E+05 81,5 1,08E+055 252 1,51E+05 58,21 1,04E+053 151 1,18E+05 34,92 1,01E+052 101 1,08E+05 23,28 1,01E+05

1,5 75 1,04E+05 17,475 1,00E+051 50 1,02E+05 11,65 1,00E+05

0,5 25 1,00E+05 5,825 1,00E+050,25 12,5 1,00E+05 2,913

0,1 5 1,00E+05

Figure 3. Schematic of the sec-ondary injectors (top) and asym-metric injection (bottom)

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B. Staged burner injection

1. Symmetric and asymmetric injection

In Figure 2, the concept of the symmetric secondary fuel injection of the burner is presented. To control thefuel distribution, the main fuel supply was split in three parts: the premix part (gray), the upstream injection(iup, green) and the downstream injection (id, red). The premix part corresponded to the standard injectionof the burner. The downstream and upstream injections together formed the secondary gas injection. Thethree injections were controlled by proportional valves and two Coriolis mass meters were used to monitorthe fuel mass flow through the premix and the secondary pipings. The maximal gas mass flow injectedthrough each secondary valve was 6.8 kg/h for a pressure drop of two bar. The control scheme of these valveswas built in Simulink and ran on a DS1103 PPC control board (dSPACE).

An asymmetric fuel injection was also tested. For this injection type, the fuel of one of the secondaryvalves was injected at two different injector positions, one injection on each side of the burner. The remainingsecondary valve was connected to the two other injectors left. A sketch of this connection is shown in Fig. 3.

2. Injector description

The secondary injectors were built from small cylindrical pipes (diameter 4 mm) with a slot of about 5.5mmwidth and 1mm height at the injector side (e.g. Fig. 3). A higher jet momentum, which is assumed to improvethe mixing, was achieved with this geometry compared to a circular outlet of 4 mm diameter. Furthermore,the elliptic geometry increased the pressure loss across the secondary injectors, making the fuel mass flowless prone to oscillate when combustion instabilities occur. This assumption is only valid if sufficient fuelmass flow through the injector is considered. The injectors were fixed on the side of the premix gas injection,injecting at an angle of 30 degrees with respect to the burner axis. The injection angle was chosen so that ahigh momentum injection would bring the fuel faster to the flame front, reducing the convective time delaysto stabilize the flame.

3. Notations and list of the performed investigations

In order to compare different operating points of the burner two dimensionless parameters α and β weredefined to characterize the fuel distribution. α describes the ratio premix gas to overall gas mass flow and βcharacterizes the ratio upstream injection to total secondary gas mass flow. They were defined as follows:

α =mpre

mallwith 0 ≤ α ≤ 1 (1)

β =mup

(1− α)mallwith 0 ≤ β ≤ 1 (2)

with mall = mpre + msec. α = 1 corresponded to the full premixed injection and β = 1 to a secondary fuelinjected through the iup pipings only.

Three operating points of the burner were investigated and are listed in Table 1. At these operatingpoints and when only premix fuel was injected, the combustion chamber showed a very strong instability .

OP mair in kg/h φ Tpre in KA 240 0.64 298B 220 0.56 423C 210 0.64 298

Table 1. Operating points of the burner (OP). The points are defined with an air mass flow mair, a fuel / airratio φ and a preheating temperature Tpre.

The combination of secondary injector positions bottom, middle and top with the two mass flows mup

and md allows for three distinct injection cases which are listed in Table 2. The different configurationstested in this study for the three cases (operating point, open-loop / closed-loop, Symmetric or Asymmetricinjection) are also listed.

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Case mup md Operating Points Open Loop/Closed Loop Symmetric/Asymmetric1 b m A-B-C OL/CL Sym./Asym.2 m t B OL Sym.3 b t B OL Sym.

Table 2. List of the tested injection configurations and of the tests performed

C. Fast NOx - Sensor based on chemiluminescence

If the response time of a pressure sensor may be considered as immediate, this is not the case of conventionaland accurate emission analyzers. The latter have a high delay in their response (superior to 30 s) which doesnot satisfy continuous control applications. Thus, to increase the speed of the Extremum Seeking Controller(ESC) described later, a fast NOx sensor was needed. As NOx emissions in premixed flames scale with thelocal temperature of the flame, and as the OH-chemiluminesence of the flame scales with the equivalenceratio and thus with the flame temperature (Haber et al.14) , the OH signal of the photomultiplier was used asa sensor. Such a sensor have already been successfully implemented in model and industrial combustors bySamuelson11 . The response of the sensor used there to symmetric and asymmetric fuel repartitions for theworking points A and B are presented in Fig. 4. As expected for the case B, an increase of the OH - Signalwas linked to an increase of the NOx emissions, and a linear approximation was appropriate to describe therelationship betweenNOx and the OH-chemiluminescence. This relationship could not be found back for thecase A, as the chemiluminescence did not show significant tendency with changes in the fuel repartition forthis operating point. The response of the OH sensor was thus depending on the operating point chosen.


Calibration OH = f(NOx)

Fuer 9kg/h

Phi = Cste, 9kg/h

0

2

4

6

8

10

12

0.00 0.20 0.40 0.60 0.80OH in V

NO

x in

ppm

Phi = Cste, All

y = 12.6x + 4.8

0

2

4

6

8

10

12

-0.2 -0.1 0 0.1 0.2 0.3 0.4OH in V

NO

x in

ppm

Figure 4. Correlation between the OH Signal and NOx Emissions for the operating points A (φ = 0.64,left)and B (φ = 0.56, right) for symmetric and asymmetric fuel injections

0 50 100 150time in s

Jump 2

fuel split command

NOx

⟨OH⟩1

OH

Figure 5. OH and Gas Anlayzer response to a step signal of the burner fuel repartition at constant φ, mair,Tpre

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Unlike conventional emission analyzers, the sensor response time may be considered as immediate as canbe seen in Fig. 5. The fuel mass flow was kept constant but the fuel repartition was changed following a stepfunction at t=20 s. The response of the OH-Photomultiplier, even strongly noisy, was almost instantaneous,while the NOx analyzer needed about 80 s to stabilize to its end value. Because of the high level of noisepresent in the OH signal, particulary during stable combustion, a 1 s moving average filter was applied onthe OH signal to feed the controller with a smoothed signal. After this Low Pass filter, the level of noise wasstrongly reduced and could be used as a control signal of the emissions. This filtered signal will be referredto in the next parts as 〈OH〉1

III. Feedback control by extremum seeking

A. Principle of the controller on a single-input/single-output (SISO) system

tt

t

t

y = F (u)

a sin ωt

a sin ωt a sin ωt

− sin ωt

HP

LPu0 u

u

u

y

u∗

y∗

∫

F (u)

K

Figure 6. Block diagram of a SISO extremum seeking feedback scheme for minimization of the output y (fromMoeck et al.15)

In order to find the optimal values for α and β an extremum seeking control algorithm is used. Extremumseeking control (ESC) is an adaptive, closed-loop control scheme with the purpose to find an extremum inan unknown field of parameters. A major advantage of ESC is that no plant model is required for controllersynthesis. Furthermore, the algorithm guarantees closed-loop stability, if designed properly (see Krsticand Wang16 and Ariyur and Krstic17 for details). The method has been used in recent years in variousapplications (pressure rise maximization in an axial flow compressor18 or separation control of a high-liftaifoil19). The basic principles of ESC are shortly explained here, based on the example of a minimum searchof a single-input/single-output system (see Fig. 6). The plant is considered as a block with a static nonlinearinput-output-map y = F (u). The idea is to perform a gradient based online optimization in order to findthe control input u∗, such that the minimal steady-state system output y∗ is achieved. The steady-stateinput-output-map F (u) and especially its extremum y∗ = min (y) = F (u∗) are unknown and/or changing intime due to variations in the operating conditions.

The initial control input u0 is superimposed by a small amplitude sine signal a sinωt. With the pre-requisite that the period of the harmonic perturbation is larger than the largest plant time constant, anapproximately sinusoidal output y will be obtained, initially oscillating around y0 = F (u0). To achieve agradient based optimization, the output signal is passed through a high-pass filter (HP), which removes themean value but not the sinusoidal perturbation. Information about the slope of F is obtained by multiplyingthis zero-mean signal with a negative sine of the same perturbation frequency ω. The product of the filteredoutput and the sine signal has a non-zero mean component as long as the minimum is not attained. If theplant is initially right to the minimum, the input and output perturbations are in phase, and hence theproduct will be negative. Conversely, an anti-phase relation, giving a positive product, will be an indicationof being located to the left of the minimum. The subsequent low-pass filter (LP) smoothes the signal, whichis then integrated and multiplied with K yielding an additional term u. As long as the output of the LP ispositive, i.e., the system is on the left side of the minimum, an increasing value u is obtained, thus movingu = u + u0 + a sinωt closer to the optimal value u∗. For a negative output of the LP, the opposite is true.19

The choice of certain design parameters is dependent on the dynamics of the plant. The overall feedback

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system has a fast, a medium and a slow time scale corresponding to the plant dynamics, the periodicperturbation and the filters in the extremum seeking scheme, respectively. If the plant behavior variesdue to uncertainties, the time scale of the perturbation signal needs to be larger than the slowest possibleplant dynamics. Cut-off frequencies of the HP and the LP need to be lower than the frequency ω of theperturbation signal. For these reasons, the speed of the algorithm is limited. The permanent harmonic inputand output perturbations are another disadvantage.

B. DIDO / SIDO Controller


ESC1

Valves &Massmeters

SignalProcessing

ESC2

Combustionchamber

(a)


Functional

ESC

Valves &Massmeters

SignalProcessing

Combustionchamber

(b)

Figure 7. Implementation of the DIDO (a) and SIDO (b) ESC controller in the test rig

1. Signal processing of pressure and OH signals

Two different types of ESC were used to control pressure pulsations and NOx emissions: a dual-input/dual-output (DIDO) controller and a single-input/single-output (SIDO) controller. A schematic of their imple-mentation in the test rig is shown in Fig. 7. The two control inputs of the combustion chamber were theparameters αis and βis and its two outputs OH and p were continuously recorded.

As presented in the previous part, a linear relationship existed between NOx and the mean signal 〈OH〉of the photomultiplier for low fuel air ratios (operating point B). Thus, reduction of the NOx emissions wasequivalent to a reduction of 〈OH〉 or 〈OH〉1.

The detection of the pulsation amplitude p was done using the scheme described by Wang and Kristic.18

The measured pressure signal was of the form p = y1 = p cos(ωpt+ϕ)+ b. This signal was sent first througha HP-Filter (ωe,HP = 1/10 ωp) to subtract the possible offset b. The resulting signal was then squared, givingy2 = p2cos2(ωpt + ϕ). This signal oscillated with the frequency 2ωp and the application of a LP filter with(ωe,LP ≤ 2 ωp) yield to the signal y3 oscillating then with low amplitude around 1/2p2. Multiplying by twoand taking the square root gave the desired amplitude p. As changes in the fuel repartition occurred witha frequency at least two magnitude order lower than the instable frequency, the cut-off frequency could bechosen small enough to dampen the oscillations of y3. For the algorithms considered here, the frequency waschosen to be (ωe,LP = 2/10 ωp).

2. DIDO Controller

The obtained values p and 〈OH〉1 were used in two different ways to feed the DIDO and SIDO controllers.First, as α had more control authority than β on the pressure oscillations, it was justified to use it as controlinput for the pulsations. β was then used as control input for the NOx emissions. This led to the first DIDOcontroller, built of two independent single-input/single-output controllers (see Fig. 7(a)). As the controlof pulsation had priority over the control of NOx emissions, α oscillated with the frequency ωα which wasset two times higher than the oscillation frequency of β ωβ , i.e. ωα = 2ωβ . Thus the first priority of thecontroller was to minimize the pressure pulsations to their optimum p∗ by acting on α and the second prioritywas to minimize the NOx emissions to their optimum NOx

∗ by acting on β.

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3. SIDO Controller

For the second strategy, both signals were used to build a single function F which was sent to the single-input/single-output ESC presented in Fig. 7(b). The single cost function was first defined as follow:

F1 = wfOH· fOH (〈OH〉1) + wg · g (p) (3)

with fOH and g single cost functions of 〈OH〉1 and p respectively and wfOHand wg their corresponding

weighting factors. Because of the linearity found between 〈OH〉1 and NOx for the operating point B, Eq. 3was equivalent to

F = wf · f (NOx) + wg · g (p) (4)

Per definition, the maximal value of the cost function Fmax was set equal to one. With weighting factorsverifying the conditions w1 + w2 = 1, w1 ≥ 0, w2 ≥ 0, the maximal value of f and g were also equal to one.The objective of the controller was to minimize the value of F . As the pressure pulsation reduction hadpriority compared to the NOx emissions, a decrease in the pressure pulsation amplitude had to lead to astronger decrease of F than a reduction of the same order of 〈OH〉1. Simulations of the control algorithmwith different functionals were performed and the best and fastest results were obtained with the followingdefinition of the functions f and g:

f =

(1− 0.25)(

NOx−5NOx,max−5

)2

+ 0.25 if NOx > 5.77

0.0464 ·NOx if NOx ≤ 5.77(5)

g =(

p

pmax

)4

(6)

The weighting parameters were set equal to 0.5. Figure 8 shows a plot of the functions f and g, with theresulting stability map of the operating point B with symmetric injection (e.g. Fig. 9).

0 5 100

0.2

0.4

0.6

0.8

1

f

�

0 2 40

0.2

0.4

0.6

0.8

1

g

Figure 8. weighting functions f and g

α

β

� � �

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

� ��

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

α

β

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

Figure 9. F cost functional from Eq. 5 and Eq. 6

C. Improvements of the ESC

The ESC algorithm was implemented into a Simulink model running under Matlab. In order to achievereliable and faster control over the (α, β) injection field, following modifications were performed on thealgorithm:

• To allow for faster control of the mass flows through the valves, a combination of a PI controller witha feed forward compensator and an input compensator (to compensate the nonlinear static map of thevalve at low mass flow) was used.

• As α and β were bounded between 0 and 1, the controller had to be able to run even if the limits ofthe domain were reached. For this the integrator of the α and β ESC were limited when extremumvalues were reached, so that the α or β could not move out of the domain 0 ≤ α ≤ 1, 0 ≤ β ≤ 1.

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• The amplitude of oscillations of the controller output was scaled with the amplitude of the controllerinput. This implementation led for example to higher oscillations of α when the combustion wasinstable and to smaller oscillations when the system was stable. High oscillation amplitudes wereneeded in case of instable combustion in order to observe significant changes in pressure amplitudes,so that the controller could move faster towards the stable point.

• For fast systems, it is common to use the set point of the controller output to control the input. In thepresent configuration, a time lag between the oscillating set point αsp and the with the mass metersmeasured αis existed (due also to the low response time of the mass flow meter). To avoid a phaseshift between input- and output-perturbation being bigger than π/2 without decreasing the oscillationfrequency (or increasing the control time), the input-perturbation F was compared with the measuredoutput-perturbation αis. This change led to a non negligible gain in the maximal oscillation frequencyαsp which could be set.

IV. Open-loop control results

A. Stability maps of symmetric injection configurations

The three injection cases presented in Table 2 were investigated to select the one with the best controlauthority on combustion regarding pressure oscillations amplitude p over the (α, β) field for a given fuel/airratio φ. For these tests, operating point B was selected (φ = 0.64). The full premixed injection (α = 1)exhibited a strong and distinct instability at about 95 Hz.

As the first aim of the control system was to reduce pulsations, the stability of the different injectionconfigurations presented in Table 1 was investigated and is presented in Fig. 10. Because of the very highlevel of instability, only about 20 point per map were recorded to build up these maps and gave an overviewof the impact of the injection field on the pressure oscillations. The pressure amplitude presented weredivided by the reference amplitude at α = 1.

α

β

��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β

�

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β

��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β�

0.5 10

0.5

1

0

0.5

1

1.5

α

β

��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β

�

0 0.5 10

0.5

1

0

0.5

1

1.5

Figure 10. pressure pulsations p depending on (α, β) fuel repartition for the operating point A (φ = 0.65). Fromleft to right: case 1, case 2, case 3

One can clearly see that case 1 plotted in Fig. 10 was much more effective in reducing the pressureoscillations than the other cases. Decreasing α (or increasing the secondary injection) from one down toabout 0.6 led first to an increase of the pulsation amplitude for all the cases. The negative influence of thesecondary injectors in this range may be due to their low momentum which made them sensitive to pressureoscillations at the jet exit and fed the instability with more fuel/air oscillations. At α ≈ 0.5 and bellowa rapid change in the stability was observed with combustion stabilization for cases 1 and 3 while case 2remained unstable even if the pulsation amplitude decreased. The frequency of the instability increasedthen to 105 Hz. The stabilized case one showed a reduction of 25 dB of the pressure oscillations of the 97Hzinstability. For case one, the stability map was then taken at the operating point C (same φ but lower airmass flow). The measurements showed the same tendency: starting from one, a decrease of α was leadingfirst to higher pulsation amplitudes and then to a stabilization of the combustion. Thus, as case 1 showed awider stable (α, β) range than the two other configurations it was chosen for further investigations.

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B. Stability and emission maps of the injection case 1

In a further step, pressure and NOx emission maps of the operating points A and B were recorded. The resultsare plotted in Fig. 11. The same influence of α on the system stability could be found in both operatingpoints, but the optimum injection was located in a narrower α-band for the case B than for the case A.Looking at the emissions some (α, β) configurations had lower emissions than the baseline case (α = 1) butover a wide domain (α > 0.5), the emissions remained steady or even increased. These open loop maps showthat α had a stronger impact than β on the pulsations amplitudes, i.e. the premix/secondary repartitionwas much more susceptible to reduce pulsations than the repartition of the secondary fuel itself. In the caseof control of pulsation and emissions, it was then justified that pulsations p would be control by α and NOx

emissions by β, with a higher priority for the pulsation control than the emissions.

α

β

��

0 0.5 10

0.5

1

0

0.5

1

1.5

αβ

� ��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β

��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β� ��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β

��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β� ��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β

��

0 0.5 10

0.5

1

0

0.5

1

1.5

α

β

� ��

0 0.5 10

0.5

1

0

0.5

1

1.5

Figure 11. Stability maps for the two operating point A (top) and B (bottom), Case 1 and symmetric injection

V. Closed-loop control results

Different configurations were tested to validate the effectivity of the controller for different setups. Allthe configuration tested showed the high efficiency of the controller. For reason of clarity, only two of thetested cases will be presented to give an overview of system closed-loop control possibilities.

A. DIDO controller applied on asymmetric injection for operating point A

1. Stabilization of the system

The DIDO controller was implemented to suppress instabilities at the operating point A with asymmetricinjection. As the correlation between NOx and 〈OH〉 was not a good measure for fast emission prediction atthis operating point it was difficult to define a cost function and the DIDO controller was more appropriate.

The system started with a fuel repartition (α0 = 0.7, β0 = 0.5). Oscillations of α started at t = 0 ata frequency of 0.05Hz and a constant amplitude aα = 0.11. As the pressure oscillation amplitude p wasin phase with α, β oscillations were started at t = 1 min with a frequency of 0.025 Hz and an amplitudeaβ = 0.05. 40 sec later, the controller was switched on and the steady part of α started to decrease. After5 min, the system reached an optimum regarding the pressure amplitude p while NOx emissions increased.As the controller moved over the optimum α∗ towards zero, pressure oscillations increased (t ≈ 7− 8 min),so that the controller increased the steady part of α. (Between t = 5 min and t = 15 min, the effect of thebounding og α led to a decrease of the oscillation amplitude). After 20 min, the system reached the otherborder of the stable domain and pressure oscillations increased as α narrowed 0.5. α decreased then againto values around 0.25. In the mean time, β increased and allowed for a continuous decrease of the NOx

emissions, to values lower than the NOx emissions at the start of the controller. It must be noticed, that

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0

0.5

1�

0

5

10

15

�

0 5 10 15 200

0.5

1

time in min

p

NOx

βα

Figure 12. Evolution of the DIDO controller for the asymmteric injection and operating point A

even if the preliminary tests did not show a satisfying relationship between NOx and OH for the operatingpoint A, the controller stabilized the burner at the optimum (α∗, β∗) = (0.4, 0.6) repartition at t = 25 min.

2. Stability to transient

After the optimum fuel repartition was reached a transient from operating point A to B was started. Theresults of the system evolution are shown in Fig. 13.

Figure 13. Evolution of the DIDO controller for the asymmteric injection during transient from the operatingpoint A to the operating point B

For the presentation of the results, the parameters mall, mair, and Tpre were made dimensionless withtheir steady values at operating points A and B as follow

m′all (t) =

mall (t)− mall,B

mall,A − mall,B, m′

air (t) =mair (t)− mair,B

mair,A − mair,B, T ′

pre (t) =Tpre (t)− Tpre,B

Tpre,A − Tpre,B, (7)

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Thus values of these parameters would evolve from 1 to 0 during the transient. Successively fuel, air,fuel mass flows and temperature were modified from the stablized operating point A towards the operatingpoint B. During the whole time, the controller kept the combustion stable, reaching in the end the optimalfuel repartition of the point B. The characteristic points of the control are presented on the stability mapsof the two operating point in Fig. 14.

α

β

p/pα=1

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

NOx/NOx,α=1

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

p/pα=1

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

NOx/NOx,α=1

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

2 2

1 1

α

β

p/pα=1

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

NOx/NOx,α=1

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

p/pα=1

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

NOx/NOx,α=1

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

3 3

Figure 14. Evolution of the DIDO controller on the stability maps of operating points A and B with asymmetricinjection. 1: starting point of the controller, 2: stabilized operating point A, 3: system injection after transientfrom A to B

B. SIDO controller applied on symmetric injection for operating point B

1. Stabilization of the system

The SIDO controller was applied on the system for the operating point B with symmetric injection. Thetime evolution from the unstable fuel injection to the stabilized one is plotted in Fig. 15.

Figure 15. Evolution of the SIDO controller for the symmetric injection and operating point A

The combustor was first set at the unstable fuel injection configuration (α0 = 0.8, β0 = 0.3). After theNOx exhaust probe stabilized to its endvalue, oscillations of the fuel repartition α were started at t = 1min.The oscillation frequency was set to f = 0.034 Hz (period of 30 s) and the amplitude of oscillation scaledwith the amplitude of the cost function F so that the amplitude at this point was equal to aα = 0.1. Oneminute later, the oscillations of β (f = 0.0152 Hz) were started with aβ = 0.1. The cost function F clearly

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followed the oscillations of α with a phase lag smaller than π/2, necessary for the application of the ESC.The controller was thus started at t ≈ 3 min. After about two oscillations the mean value of α decreasedfollowed by F . After t ≈ 9 min α stabilized around its lowest limit α = 0.15 and the amplitude of oscillationdecreased to aα = 0.05. In the mean time, β stabilized also around β = 0.1. When looking at the pressureoscillations and NOx emissions over this (α, β) field, this corresponded to an absolute minimum. It mustbe noted, that during the whole control process, the overall fuel mass flow remained within ±5% of its setvalue.

The same test was performed with β0 = 0.7. The evolution of both output variables α and β is shownin Fig. 16, and evidence that the controller evolution is strongly dependent on the starting parameters ofthe algorithm. Like for many gradient based algorithms, it is thus possible to reach a local minimum of thestability map and not the absolute optimal value.α

β� � �

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

� ��

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

α

β

0 0.5 10

0.2

0.4

0.6

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1

0

0.2

0.4

0.6

0.8

1

α

β

0 0.5 10

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

Figure 16. Impact of starting conditions on the controller end values. Starting points: white circles. Endpoints: red circles

During the evolution of the controller, series of pictures of the OH-Chemiluminescence of the flame weretaken with an Intensified CCD Camera (IRO + Imager, LaVision) equipped with a 312 nm band pass filter.The pictures were taken with 20 short exposures of the camera sensor taken within 0.1 s. Figure 17 showsthe flame at the operating point B with the starting fuel repartition (α, β) = (0.8, 0.3) shown in Fig. 15, i.e.at unstable conditions. Figure 18 was taken after the flame stabilized at (α, β) = (0.22, 0.2). A significantchange in the flame shape between the two point is clearly visible. Both flame showed also almost the samemaximum intensity, but the unstable flame stabilized over the whole surface of the burner outlet while thestable flame was located on two distinct sides of the burner outlet. The position of the center of gravity ofthe stabilized flame moved also further downstream. Those pictures show the strong impact of the injectionprofile of the flame shape at the burner outlet.

Figure 17. Flame at unstable combustion(α, β) = (0.8, 0.3)

Figure 18. Flame at stable combustion (α, β) =(0.22, 0.2)

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VI. Conclusions and Outlook

To control combustion instabilities and NOx emissions in a premixed swirl combustor, secondary gasinjections were used to change the overall fuel repartition upstream of the flame. Open loop tests showed,that one of the injection combination (Case 1) was able to suppress combustion instabilities over a wide rangeof the fuel repartition. Furthermore, the secondary injection could also reduce the NOx emissions comparedto the baseline case. To allow for fast control, a fast NOx sensor based on OH-chemiluminescence wasapplied. Mesurements showed a good correlation between the chemiluminescence signal and the measuredNOx emissions of the different fuel repartitions of the leanest operating point (φ = 0.56). This relationshipcould not be found at the operating point with higher fuel air ratio (φ = 0.64), thus limitating a good useof this sensor to leaner mixtures. Nevertheless, the sensor allowed for a fast estimation of the emissionscompared to standard gas analyzers (2 s against t≈80 s).

Closed loop control based on the extremum seeking algorithm was applied on the fuel repartition field(α, β). The extremum seeking algorithm was modified in a way that the amplitude of the oscillating param-eter were depending on the amplitude of the controller inputs. DIDO and SIDO controllers were successfullyapplied for two operating points A and B and symmetric and asymmetric fuel injections. The controllerswere able to bring the combustion system within less than 10 min to an optimum fuel repartition where thecombustion was stable and NOx emissions maintained low. It was also possible to keep the system stable ontransients from one operating point to another.

The closed loop controller may also be applied on other functionals depending on the aims of the inves-tigations. Further work will focus on the implementation of a physical model to increase the speed of thecontroller. The main limitation of the speed of the control algorithm was mainly due to the response time ofthe mass flow meters to changes in the flow. Thus a significant increase in the speed of the controller wouldbe expect when using faster flow sensors.

References

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2Lieuwen, T. and Wu, L., “Coherent Acoustic Wave Amplification/Damping by Wrinkled Flames,” paper AIAA-2003-0114, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2003.

3Lieuwen, T. and Zinn, B. T., “A Mechanism for Combustion Instabilities in Premixed Gas Turbine Engines,” Journal ofEngineering for Gas Turbines and Power , Vol. 242, No. 5, 2001, pp. 893–905.

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8Kokanovic, S., Guidati, G., Torchalla, S., and Schuermans, B., “Active Combustion Control System for Reduction ofNOx and Pulsation Levels in Gas Turbines,” Proceedings of the ASME Turbo Expo, Spain, May 8-11, 2006 , No. ASME Paper2006-GT-90895, 2006.

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10Paschereit, C. O., Schuermans, B., and Buchey, D., “Combustion Process Optimization using Evolutionary Algorithm,”Proceedings of ASME Turbo Expo 2003 June 1619, 2003, Atlanta, USA, 2003.

11Samuelson, J. and Miyasoto, M., “Active Control for Reducing the Formation of Nitrogen Oxides in Industrial GasBurners and Stationary Gas Turbines,” Tech. rep., California Energy Commission, 2000.

12Sattelmayer, T., Felchlin, M. P., Haumann, J., Hellat, J., and Styner, D., “Second Generation Low-Emissions ABBCombustors for Gas Turbines: Burner Development an Tests at Atmospheric Pressure,” No. ASME Paper, 1990-GT-192, 1990.

13Albrecht, P., Bauermeister, F., Bothien, M. R., Lacarelle, A., Moeck, J. P., Paschereit, C. O., and Gutmark, E., “Char-acterization and Control of Lean Blowout Using Periodically Generated Flame Balls,” 2006, ASME Paper GT2006-90340.

14Haber, L. C., Vandsburger, U., Saunders, W. R., and Khanna, V. K., “An examination of the relationship betweenchemiluminescence light emissions and heat release under non-adiabatique conditions,” Proceedings of IGTI: International GasTurbine Institute, May 8-11, 2000 Munich, Germany, 2000.

15Moeck, J., Bothien, M., Paschereit, C., Gelbert, G., and King, R., “Two-Parameter Extremum Seeking for Control ofThermoacoustic Instabilities and Characterization of Linear Growth,” 45th AIAA Aerospace Sciences Meeting and Exhibit,8-11 Jan, Reno, Nevada, 2007.

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16Krstic, M. and Wang, H.-H., “Stability of extremum seeking feedback for general nonlinear dynamic systems,” Automat-ica, Vol. 36, 2000, pp. 595–601.

17Ariyur, K. and Krstic, M., Real-Time Optimization by Extremum-Seeking Control , John Wiley & Sons, Hoboken, 2003.18Wang, H.-H. and Krstic, M., “Extremum Seeking for Limit Cycle Minimization,” IEEE Transactions on Automatic

Control , Vol. 45, No. 12, 2000, pp. 2432–2437.19Becker, R., King, R., Petz, R., and Nitsche, W., “Adaptive Closed-Loop Separation Control on a High-Lift Configuration

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