Acoustic Based Rapid Blowout Mitigation in a Swirl ... - Tim Lieuwen

Proceedings of GT2005 ASME Turbo Expo 2005: Power for Land, Sea and Air June 6-9, 2005, Reno-Tahoe, Nevada, USA

GT2005-68589 ACOUSTIC BASED RAPID BLOWOUT MITIGATION IN A SWIRL STABILIZED COMBUSTOR Shashvat Prakash Graduate Research Assistant School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 T. M. Muruganandam Graduate Research Assistant School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332

Suraj Nair Graduate Research Assistant School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332

Yedidia Neumeier Adjunct Professor School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332

Jerry M. Seitzman Associate Professor School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332 ABSTRACT This paper describes a method for efficiently detecting and preventing lean blow out (LBO) in a premixed, swirl stabilized combustor. The acoustic signal is processed to determine the real time LBO probability. This requires detection of localized extinction ‘events’ and rapid calculation of event frequency. As LBO probability increases, a proportional derivative controller actuates valves to redirect a fraction of the total fuel into a central, premixed pilot. The actuation increases the equivalence ratio in the stabilization region at a constant power setting and counters the flame lift associated with LBO. It is shown that the developed controller can prevent LBO even during rapid transients in equivalence ratio, φ. INTRODUCTION In an effort to meet strict emissions requirements, aircraft and land based gas turbine designs widely implement a lean, premixed mode of combustion. This permits combustion at lower temperatures and minimal NOx (nitrous oxides) emissions. However, the gas turbine combustor must operate near its lean blow out (LBO) limit. Equivalence ratio perturbations near LBO, which can occur during changes in

Tim Lieuwen Assistant Professor School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332

Ben T. Zinn Professor Schools of Aerospace and Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 operating conditions or arise from variations in fuel composition, may cause loss of combustion. In stationary gas turbines, such a blowout could cause expensive shut down and loss of power. In aircraft engines, a blowout could potentially lead to severe problems or engine loss, especially during military maneuvers and/or the approach and landing phases of the flight. To prevent LBO, current systems operate at equivalence ratios sufficiently removed from LBO and also over-conservatively schedule changes in load and/or operating conditions. This necessarily imposes emissions penalties and also restricts the rate at which engine power settings can be varied. Thus, there is a need for control approaches that would minimize emissions from future aircraft engines without compromising safety over the whole range of the engine’s operating conditions. An LBO control system must capably detect and mitigate impending blow out. This requires sensing the onset of LBO, real time determination of LBO probability, and effective actuation. A rapid control scheme is desired so the system may handle a wide range of disturbances and operating conditions. This paper presents a new approach for active control of lean premixed flames to mitigate LBO and increase the safety margin – i.e. the gap between the operating equivalence ratio

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and the LBO equivalence ratio for a given operating condition. In this study, the combustor acoustic signal is processed to determine LBO probability and a valve actuator redistributes the injected fuel between the main injectors and a premixed, central pilot injector that supplies fuel to the flame stabilization region. The objective of the controller is to allow for safe, lean operation of a flame in the presence of disturbances that are excited in the system as the LBO limit is approached. BACKGROUND Prior studies have shed light on the characteristics of the combustor flow and combustion processes as the lean blow out is approached. For example, Nicholson and Field1 noted large scale, low frequency flame pulsations as well as periodic detachment of the flame from its flame holder near the LBO limit. Chao et al.2 observed that the duration of these phenomena can range from a few short cycles up to several seconds. 10

Acoustic PSD [arb. units]

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φ = 0.81 φ = 0.75 φ = 0.748

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‘event’. This approach was unsuitable, however, for real time LBO detection. Control of lean flames has been previously pursued as a means for NOx reduction. Nakae et al.5 demonstrated low NOx operation in a lean, premixed, prevaporized (LPP) combustor where the equivalence ratio was varied based on CO emissions feedback. The controller varied the air distribution in the combustion chamber by modulating the air flow through an inlet downstream of the injection plane. General Electric LM6000 and similar engines have demonstrated blowout avoidance control using measured and calculated fuel flow values.6 When incipient blowouts were detected, the flame temperature was increased by manipulating fuel flow. LBO mitigation control has also been demonstrated using optical, OH-based, sensing and fuel split ratio actuation7. The optical sensing was comparatively faster than the emissions based method. Loss of combustion was prevented by use of “fuel split” actuation that redistributed the fuel flow between the pilot port and main fuel injection system. The rule based control system monitored LBO precursor events over a one second moving window and increased the fuel split if the number of events in the window exceeded a certain threshold value. The study described in this paper was undertaken to: i) improve on acoustic sensing by reducing response time and ii) present a scheme for acoustic based active control of LBO which allows for minimal NOx emissions over all operating conditions.

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Hot walls

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Figure 1. Fourier spectra of the acoustic signal from a premixed flame at varying equivalence ratios. Other characteristics of lean combustion were also studied. Muruganandam et al.3 observed that the frequency of local flame extinguishment ‘events’ increased as the flame became leaner. These events were characterized by ‘dips’ in the OH chemiluminescence signal. The study noted that the low frequency (10 Hz - 200 Hz) power content of both the acoustic (Figure 1) and optical OH spectra were higher in a lean flame. They postulated that this increase in low frequency power was due to a combination of localized extinction time scales (of the order of 10 ms) and the mean time between such events (of the order of 1s). It was further noted that as the flame became leaner, there was an increase in the frequency and duration of the localized flame extinguishment events. However, these studies employed acoustic based detection of events that used statistical methods that were slower than corresponding optical sensing. Previous studies have investigated various other acoustic approaches for detecting LBO precursor events. Nair and Lieuwen4 demonstrated that when LBO precursors are present, the acoustic signal exhibits a repeated pattern, which can be extracted with a wavelet whose shape resembles that of the

Dump region

Swirlers

Central preinjection pilot

Main mixture

Figure 2. A schematic of the utilized combustor. EXPERIMENTAL SETUP The experiments were performed in an atmospheric pressure, cylindrical quartz combustor with a 70 mm inner diameter and 190 mm in length (Figure 2). The investigated combustor design was expected to provide a simplified model

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ACOUSTIC SENSING Analysis of acoustic emissions provides means for detecting transient flame holding events because they are proportional to the temporal rate of change of heat release8. Fundamentally, combustion noise is generated by the unsteady expansion of reacting gases. It is known that the acoustic emissions of turbulent flames are dominated by unsteady heat release processes (as opposed to flow noise)9 that excite acoustic waves over a broad range of frequencies, typically between ~10 Hz – 25 kHz. Thus, acoustic measurements can be used to detect either global changes in heat release rate or fluctuations in heat release at certain time scales by measuring their acoustic emissions in corresponding frequency bands. Acoustic techniques are quite convenient since many landbased gas turbines are already instrumented with dynamic pressure transducers. Also, in contrast with optical sensors, acoustic sensors are not subjected to field of view limitations and can sense attributes of the entire flame. Finally, acoustic sensors are easier to install and shield in the harsh engine environment. Optic OH

1

Filt. Acoustic (Pa) Acoustic (Pa)

of a lean, premixed gas turbine combustor that includes a swirling premixer section. An annular opening supplied a swirling, combustible mixture of fuel (CH4) and air into the combustor and a secondary stream of combustible, richer air-fuel mixture was supplied through a pilot at the center of the injection plane (Figure 3). Under nominal operating conditions, (8E-4 kg/s fuel flow, .02 kg/s air flow, equivalence ratio .76) approximately 3% of the total mass air flow was directed toward the pilot, and the commanded fuel split ranged from 0% to 20%. The pilot equivalence ratio depended upon the fuel split. A split of 10% corresponded to a pilot equivalence ratio of approximately 3.5 and a 20% split corresponded to a pilot equivalence ratio of about 5. The overall combustor equivalence ratio remained constant regardless the percent fuel flow to the pilot. A valve manifold governed the proportions of total fuel that were directed to the main and pilot ports. The manifold consisted of ten Asco Scientific solenoid valves with a response time of 20 ms. The valves were driven from a control computer running QNX real time operating system with a Power DAQ I/O board running at 10 kHz. Generally, all the fuel and air were supplied to the combustor through the annular supply ring. The air supply rate was externally perturbed by the operator to simulate disturbances. When LBO precursors were detected, the valve manifold redirected a portion of the total fuel that depended upon the amount of actuation required into the center pilot port. MIC FLAME

CH4

AIR ACOUSTIC

PILOT

VALVE

Extinction 0.5 Reignition 0 0 20

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Figure 3. A schematic of the air, fuel, and signal flow. The air flow split was fixed while fuel split was governed by the valve. Acoustic oscillations were measured with a calibrated, Bruel and Kjaer type 4191 condenser microphone that has a flat frequency response up to 40 kHz. The microphone dynamic performance is similar to pressure transducers found in actual engines. The microphone was located ~61 cm from the combustor exit at ~90o from the flow axis. Since the flame noise exhibited little directivity, the results demonstrated weak dependence upon the microphone location. The principal exception to this occurred when the microphone was placed in the combustion chamber exhaust. In this case, hydrodynamic pressure fluctuations substantially increased background noise levels. For analysis, all sensing and control signals were fed into a 12 bit National Instruments A/D board connected to a computer running LabVIEW.

Figure 4. Anatomy of an extinction event, as captured by OH chemiluminescence (top), acoustic (middle), and bandpass filtered acoustic, 10.6 Hz to 95.5 Hz (bottom). It was previously determined that as a lean flame approaches its LBO limit, the frequency of localized extinction – reignition “events” increases and that such events typically last from 10-15 milliseconds. An optical sensor sensing such an event will detect an abrupt drop in OH chemiluminescence during the extinction phase followed by a sharp increase during reignition (Figure 4, top plot). On the other hand, the acoustic signal’s amplitude slightly increases during extinction, but with reduced amplitude fluctuation and the reignition phase is distinguished by a sudden “appearance” of a large amplitude oscillation as the flame deficient region is reignited with a noticeable ‘pop’ (Figure 4, middle plot). As the flame becomes leaner, the extinction regions may grow larger, and event durations may become longer. Prior studies of acoustic sensing of extinction events have investigated the statistical kurtosis and wavelet analysis approaches. It was noted that while these methods can capably detect extinction events, they require excessive computation

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cycles and would not be suitable for use in rapid response, real time control. 50 0

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-50 -100 -150 -200 5.30 Hz - 47.7 Hz 10.6 Hz - 95.5 Hz 21.2 Hz - 191 Hz

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Figure 5. Magnitude plot of the bandpass filters used to detect precursor events. 1 0.9

Alarms / AlarmsLBO

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SIGNAL PROCESSING Since the system’s LBO margin is determined by event frequency (i.e. number of events per second), an efficient method is required to calculate this parameter. In previous LBO feedback control studies by Muruganandam et al. the event frequency at a particular time was determined by summing dips in the optical chemilunimescence signal over the previous 1 second. The one second sum may be represented as a discrete transfer function:

0.6 0.5 0.4 0.3 0.2

5.305 - 47.75 Hz 10.61 - 95.49 Hz 21.22 - 191 Hz

0.1 0 0.7

0.71

0.72

0.73 0.74 Equiv. Ratio Φ

standard deviation of the absolute value of the acoustic signal from a flame with equivalence ratio 0.75. The threshold was chosen empirically to balance detection and noise mitigation across the range of operating conditions. With this criterion, the dependence of the (normalized) average number of threshold crossings (or “alarms”) per second, upon the equivalence ratio was determined (Figure 6). Figure 6 shows that while the low frequency filter exhibited the greatest overall increase in alarm ratio, the rate of increase did not become significant until the equivalence ratio was below 0.72. Furthermore, the number of detected events for the low filter was markedly fewer than the other filters, reducing the likelihood of event detection until the system was uncomfortably close to the LBO limit. The higher frequency filter (21.22 – 191 Hz) was a good candidate for sensing because of the high event count throughout the monitored operating range (number of alarms per second at LBO was 153). However, the rate of increase was not as impressive as the other filters. The middle frequency range filter (10.6 – 95.5 Hz) was ultimately chosen both for its range and its linearity. The bottom plot of Figure 4 shows how an acoustic signal passed through this filter (10.6-95.5 Hz) behaves during an event cycle. The extinction and reignition phases combined last approximately 15 ms, corresponding to a 66.67 Hz event ‘cycle’. Since this frequency lies within the range amplified by the employed bandpass filter, a threshold crossing occurs in the filtered signal.

0.75

0.76

H sum ( z ) =

0.77

Figure 6. Dependence of the number of threshold crossings (alarms) per second normalized with the number of alarms at LBO upon the filter frequency range and equivalence ratio. Maximum alarms per second were 154, 73, and 15 for the high, medium, and low frequency filters respectively. At the onset of this study it was argued that if the extinguishment and reignition events occur at a specific frequency or range of frequencies, filtering the measured acoustic signal could separate acoustic spectra of the events from the combustion and flow processes. To further examine this possibility, the measured acoustic data were analyzed by three different bandpass filters. The filters were Butterworth 8th order (4th order high pass and 4th order low pass) with center frequencies of 15.9, 31.8 and 63.7 Hz and a bandpass ratio of 3 (Figure 5). These filters spanned 5.30-47.7, 10.6-95.5 and 21.2–191 Hz. frequency ranges, respectively. To be considered as an event, the magnitude of the filtered data had to exceed a threshold amplitude of 4σ, where σ is the

z N+1 − 1 . z N+1 − z N

(1)

Equation (1) is the z-domain representation of a one second moving window summation. The transfer function relates output (threshold crossings over previous 1 second) to the input (threshold crossing flag). N is the sampling frequency in Hz. This calculation imposed a calculation response time on the order of 0.5 seconds and frequency response characteristics similar to a zero order hold (Figure 7). The zero order hold (ZOH) is an operation that samples the input signal and holds the value for a prescribed time until the next sample is obtained. Used for digital to analog conversion, the periodic frequency response imposed by the ZOH is normally corrected with a low pass filter. In the s-domain the zero order hold has the following representation:

Gh0 ( s ) =

1 - e -Ts . s

(2)

Figure 7 compares the frequency response of a 1 second moving window summation at 40 Hz and 400 Hz sampling frequencies and a 1 second zero order sample and hold. Sampled signals have a periodic frequency response, with a “folding frequency” at the Nyquist frequency (half the sample

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⎛1⎞ ⎛α ⎞ y ( k ) = ⎜ ⎟u ( k ) + ⎜ ⎟ y ( k − 1) ⎝T ⎠ ⎝T ⎠

-100 1sec sum, fs = 40 Hz 1 1sec sum,2fs = 400 Hz3 ZOH 1 sec

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100 0 -100 -200 0

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Figure 7. Frequency response of one second summing windows at 40 and 400 Hz sampling frequencies, compared with a 1 second zero order sample and hold (ZOH).

80 70 60

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Events /s

50 0

-45

(3b)

where y(k) is the calculated event frequency at the kth time sample and u(k) is the input threshold crossing flag at the kth time sample; it can take on a value of 0 (no threshold crossing) or 1 (threshold crossing detected at the kth sample). The overall filter gain is 1/T and the forgetting parameter, α/T, is set to some value between 0 and 1. This filter scales the current input by 1, the input at the previous sampling instant by (α/T), and the input two samples ago by (α/T)2 and so on. The weighted values are theoretically summed over an infinite history of weighted inputs and multiplied by an overall gain (1/T). In practice, the filter is implemented recursively as in equation 3b. The forgetting filter “exponentially forgets” old values and gives recently measured samples maximum weighting.

Filt. Acoustic (Pa)

90 Magnitude (dB)

(3a)

or

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1 ∞ ⎛α ⎞ ∑ ⎜ ⎟ u ( k − n) T n =0 ⎝ T ⎠ n

y(k ) =

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forgetting filter used to calculate event frequency in this study is given by:

Equiv. Ratio Φ

Magnitude (dB)

frequency). However, in this case, the Nyquist frequency of the summation signals (20 and 200 Hz for the two cases) were well above the frequency where the periodicity first occurred (1 Hz).

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Figure 8. Frequency response of the ‘Forgetting Filter’ transfer function used to determine event frequency, for α/T=0.9995. As sampling frequency was increased, the frequency response of the moving window summation appeared more identical to the 1 second zero order hold, differing only by a DC offset. The periodic frequency response produces undesirable amplification of higher frequencies. The response time remains of the order of 0.5 seconds, irrespective of the sampling frequency. To improve the response time, the window can be truncated to a 0.5 or 0.25 second moving window summation. However, the effects of digitization will persist: the frequency response will remain periodic, and high frequencies will be not be properly attenuated. The calculated time response and frequency characteristics of the event frequency may be improved by choosing an appropriate ‘forgetting’ filter. Such a filter “accentuates” recently measured data over previously measured data. The

Figure 9. Characteristics of an unpiloted flame undergoing equivalence ratio variations over time. The equivalence ratio is shown in the top plot and the bandpass filtered acoustic signal (10.61 to 95.49 Hz) is shown in the middle plot. The bottom plot compares the 1 second moving window event summation with the result produced by the forgetting filter. The filter may also be represented as the following discrete transfer function: Y ( z) z , (4) = H ff ( z ) = U ( z ) Tz − α where T and α are the parameters used in Eqs. 3a,b above. For stability, the parameters must be chosen so that the transfer function in Eq. (4) has singular values (poles) within the unit circle. Hence, the ratio α/T must be between -1 and 1 for stability. Since the filter is intended to handle the input over time in an accumulative manner, all the weighting values (α/T)n must be positive for all integers n, and therefore α/T must be positive. If the ratio is set to 1, the filter becomes an accumulator; i.e., the input is continually summed and there is

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ACTUATION Effective actuation requires countering the flame lift and detachment mechanism associated with LBO. Muruganandam et a1. have shown that redistributing part of the fuel in a premixed swirl stabilized combustor to a central premixed pilot can effectively shift the LBO limit to lower equivalence ratios. As the lean flame lifts from the flame holding device, an increase of the equivalence ratio at the central flame stabilization region a richer reattaches the flame. When the pilot is activated, the total fuel flow supplied to the combustor remains constant. The LBO control experiments of this study were conducted on the same apparatus as the referenced studies3,4,7. The objective of this study was to determine whether acoustic sensing in combination with the developed data analysis can be effectively used to control LBO. Figure 10 presents some of the results of this study. It shows that increasing pilot fraction shifts the LBO limit to a lower equivalence ratio and also decreases the number of alarms detected, indicating that the flame has become more stable. Although piloting alone increases NOx (nitrous oxides) emissions, for a given safety margin (i.e. the difference between operating and LBO equivalence ratios), Muruganandam et al. have shown that the pilot-stabilized combustor produces less NOx than the unpiloted combustor. Thus, an efficient control algorithm that will provide piloting based on real time safety margin requirements – i.e., actuate according to probability of LBO, will allow operation at lower equivalence ratios and, thus, reduce emissions.

80 0% Pilot 10% Pilot 15% Pilot 20% Pilot

70 60 Alarms per Second

no exponential decay of previously measured data. A value less than but close to 1 can provide the desired summing characteristic. In this study, optimal values for T and α/T were empirically determined to be T=0.2 and α/T=0.9995, respectively; the frequency response of the resulting forgetting filter is given in Figure 8. Unlike the moving window summation, the frequency response is not periodic below the Nyquist frequency and higher frequencies are more completely truncated. Furthermore, the 1 second summing window imposed a 0.5 second response time, and a bandwidth of 0.44 Hz. In contrast, the ‘forgetting filter’ has a bandwidth of 0.8 Hz. A comparison of the performance of the 1 second moving window and the forgetting filter is presented in Figure 9. In this case, the air flow rate was varied manually at about 1 Hz. The 1 second moving window was unable to capture the variation while the forgetting filter was able to replicate it.

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Figure 10. Effect of pilot fraction on the LBO limit, as determined by acoustic based sensing. Increasing the fraction of fuel directed to the pilot effectively shifts the LBO limit to leaner equivalence ratios. CONTROL Mitigation of lean blow out requires rapid, effective actuation based on real time LBO probability. Lean flames are by nature unstable and chaotic. Small perturbations caused by, e.g., flow fluctuations, may lead to LBO. Thus, control action to avoid such a scenario must be timely and effective. While piloting can improve safety margin in a leaning flame, excessive margin at a point sufficiently removed from LBO will carry an emissions penalty. Therefore, control must also be brief, providing pilot split only as necessary. The control system must, therefore, be fast enough to handle disturbances over a wide frequency range to qualify as a viable LBO mitigation method. The above described signal processing schemes to detect LBO precursors have slightly simplified the control problem. The bandpass filter, coupled with thresholds, provides a linear correlation between event frequency and equivalence ratio for a fixed pilot (Figure 6). Since LBO – regardless of pilot – occurs at approximately the same event frequency (Figure 10), this parameter may be considered a gauge of the overall LBO probability. The event frequency has also taken on greater significance since the described ‘forgetting filter’ has sped up its calculation. Whereas previous work on control of combustion instabilities has accounted for both model uncertainty and nonlinearities10, a simpler approach should be initially used as a proof of concept platform to understand the behavior of a lean flame and validate the proposed actuation and sensing approaches. The developed sensing methods have made the system both (fairly) linear (with bandpass filtering) and dynamically well behaved (with the forgetting filter). To further improve the controller performance, the pilot fraction actuation was required to be proportional to both the events per second ( f e ) and its derivative; i.e.

~ d ~ %Pilot = K p ∗ ( f e ) + K d * ( f e ) Filtered dt

6

(5)

Copyright © 2004 by ASME

where the relative event frequency is computed as a difference from a fixed set point: ~ (6) f e = f e − f e, set In order to compute a meaningful derivative, this signal must be filtered of high frequency noise via a low pass filter. For this purpose, a 2nd order Butterworth filter was used. It was designed to balance time response and noise attenuation characteristics. The computation of the derivative term may be characterized as a convolution of derivative and filtering operations; i.e., ~ d ~ (7) e Filtered

Magnitude (dB)

where D(z) is the derivative transfer function and F(z) is the 2nd order low pass Butterworth filter. The control law can now be reformulated as the following transfer function relating controller output to input:

Figure 11 displays a block diagram showing the system’s comprehensive signal and fluid flow. MIC FLAME

AIR

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Figure 11. Processing and control diagram showing signal and fluid flow. Control parameters were chosen to optimize performance while minimizing noise sensitivity. In the frequency domain, proportional derivative control is a high pass filter, and in combination with a 2nd order lowpass, the controller appears as a ‘peak’ in frequency (Figure 12). As seen in the figure, the ratio Kp/Kd determines the first corner frequency, where the magnitude rises at a fixed rate of 20 dB per decade frequency. The location (and height) of the peak is determined by the low pass cutoff frequency. The phase lead provided by the derivative term exists up to the low pass cutoff frequency.

-30

The location, size, and shape of the frequency response should honor two requirements: performance and noise attenuation. For the reported experiments, Kp was 0.55 and Kd was set to 5.5, giving a ratio of 10, and a first corner frequency of 1.56 Hz. The cutoff frequency was set at 5 Hz. The set point for event frequency ( f e , set ) was 15, and the pilot split was restricted to values between 0% and 20%. The gains could thus set high enough for rapid response, as noise attenuation was provided by the low pass characteristics of the forgetting filter.

MAIN

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Figure 12. Bode diagram of the proportional derivative controller frequency response.

VALVE

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(8)

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= D( z ) * F ( z ) * ( f e )

%Pilot( z ) = K p + K d * D( z ) * F ( z ) ~ fe ( z)

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Figure 13. Bode diagram of the combined forgetting filter and PD control system with a one sample delay. The magnitudes have been normalized with respect to the DC gain. Figure 13 illustrates the combined effect of the forgetting filter and the PD controller in the frequency domain. A one sample delay has been included in the combined system. The controller’s main advantage is its speed, i.e. it boosts bandwidth. Whereas the forgetting filter alone has a bandwidth of .8 Hz, with the controller the bandwidth has been increased to 2.5 Hz. Noise suppression is provided by the low pass part of

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the controller and the low pass characteristics of the forgetting filter.

65 60 55 50 Events /s

RESULTS A viable control scheme will allow continuous operation below the original LBO limit and rapidly respond to equivalence ratio variations. To investigate the controller’s performance, the combustor was subject to air flow variations that dynamically altered the equivalence ratio, and the system was monitored for time response. For the reported experiments, a steep drop in the equivalence ratio caused a brief overshoot, providing a quick ‘blast’ of maximum pilot and stabilizing a potentially unsteady condition. Subsequently, the proportional term allowed the pilot to track the event frequency, which was proportional to real time LBO probability.

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Figure 14. System response to rapid change of operating conditions. The three plots show the equivalence ratio, the event frequency, as calculated by the forgetting filter, and the pilot actuation commanded by the PD controller. Figure 14 shows the results of the system response to a series of sharp dips in equivalence ratio caused by rapidly increasing air flow rate. After each sharp dip a corresponding reaction by the controller is evident. The proportional derivative controller anticipates each dip and commands the pilot to saturation. A 0.05 drop in equivalence ratio over 0.1 seconds to an equivalence ratio below the LBO limit would normally have blown out the flame but the controller prevented this outcome with rapid actuation. The event frequency for the time traces shown remained between 40 to 60 events per second. Figure 15 illustrates how the system responds during the steep equivalence ratio dips in terms of events per second. The three traces correspond to the three equivalence ratio drops depicted in Figure 14. Initially, there is a linear rise, but below an equivalence ratio of about 0.72, the event frequency saturates as the actuation takes effect.

0.8 s - 1 s 3.25 s - 3.55 s 6.4 s - 6.6 s

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Figure 15. System response to rapid drops in equivalence ratio, as depicted in the time traces in Figure 14. The event frequency rises, then saturates as the actuation takes effect. SUMMARY AND CONCLUSIONS Lean blow out is a rapid, potentially devastating phenomenon. Sensing and actuation schemes involved with mitigating LBO must be fast and effective. This study has shown how acoustic sensing can be improved to detect the frequency of lean instabilities (events) faster and how a proportional derivative controller can be used for rapid actuation. With improved control techniques, the flame can be operated in a leaner region. Acoustic sensing was based on two fundamental properties; i.e., the dependence of the acoustic signal on the derivative of combustion process heat release, and the fact that leaner flames emit more acoustic power at low frequencies (