Theoretical and experimental demonstration of minimizing self-excited thermoacoustic oscillations by applying anti-sound technique

Applied Energy 181 (2016) 399–407

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Theoretical and experimental demonstration of minimizing self-excited thermoacoustic oscillations by applying anti-sound technique Shen Li a, Qiangtian Li a, Lin Tang b, Bin Yang c, Jianqin Fu d, C.A. Clarke e, Xiao Jin a, C.Z. Ji a,⇑, He Zhao a,⇑ a

School of Energy and Power Engineering, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang City, Jiangsu Province 212003, China Department of Mechanical Engineering, Guilin University of Aerospace Technology, Jinji Road 2, Guilin, Guangxi 541004, China c College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, Jiangsu Province, China d State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, Hunan, China e Department of Mechanical and Aerospace Engineering, University of Strathclyde, 16 Richmond Street, Glasgow G1 1XQ, UK b

h i g h l i g h t s
Minimizing self-sustained thermoacoustic oscillations is theoretically and experimentally studied.
LMS-based online identification algorithm is applied to achieve robust control.
Noise effect is theoretically studied by adding Gaussian noise to a van der Pol oscillator.
Off-design performance is experimentally evaluated by varying fuel flow rate.
45 dB sound pressure level reduction is experimentally achieved.

a r t i c l e

i n f o

Article history: Received 14 June 2016 Received in revised form 12 August 2016 Accepted 13 August 2016

Keywords: Thermoacoustic oscillation Combustion instability System identification Heat-to-sound conversion Feedback control

a b s t r a c t The coupling between unsteady heat release and acoustic perturbations can lead to self-sustained thermoacoustic oscillations, also known as combustion instability. When such combustion instability occurs, the pressure oscillations may become so intense that they can cause engine structural damage and costly mission failure. Thus there is a need to develop a real-time monitoring and control approach, which enables engine systems to be operated stably. In this work, an online monitoring and optimization algorithm is developed to stabilize unstable thermoacoustic systems, which are characterized by nonlinear limit cycle oscillations. It is based on least mean square method (LMS). The performance of the optimization algorithm is evaluated first on a Van der Pol oscillator. It can produce nonlinear limit cycle oscillations, which is similar to pressure oscillation as frequently observed in gas turbine engines. It is shown that implementing the control strategy leads to the oscillations quickly decayed. To further validate the control strategy, experimental study is conducted on a Rijke tube. It is found that approximately 45 dB sound pressure reduction is achieved by actuating a loudspeaker. In addition, the control approach is demonstrated to be able to track and prevent the onset of new limit cycle thermoacoustic oscillations resulting from the changes of fuel flow rate. The present work opens up a new applicable approach to stabilize engine system in terms of minimizing thermoacoustic oscillations. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Combustors play a critical role in determining the performance of aero-engines and gas turbines and other propulsion systems. However many combustion systems are susceptible to selfexcited thermoacoustic instabilities [1,2], especially under lean combustion condition [3,4]. They are characterized by large-

⇑ Corresponding authors. E-mail addresses: [email protected] (C.Z. Ji), [email protected] (H. Zhao). http://dx.doi.org/10.1016/j.apenergy.2016.08.069 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

amplitude pressure oscillations [5,6]. Such oscillations are wanted in thermoacoustic engines/prime movers [6,7] or cooling systems [8,9]. However, they are undesirable in aerospace and power generation industries. When thermoacoustic instabilities occur, premixed or diffusion flame may be blow out and the working life of practical engines may be seriously reduced due to structural vibrations and overheating [10]. Therefore it is important to understand the physics and to develop control approaches to mitigate these self-sustained thermoacoustic oscillations [11,12] in designing energy-efficient and stably operated combustors.

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Nomenclature ak, At D(n) e(n) fx(n) b HðnÞ H(n) L M n p t t⁄ x x(n) y(n) yˆ(n) ~ y Ys(n)

FIR filter coefficients external noise entering the system error output estimate from secondary propagation path adaptive LMS filter ordinary LMS filter total length of the tube (m) Length of the samples used in the LMS method Sample number at current time step Pressure oscillation time (s) normalized time Van der Pol parameter Input signal Real output signal Estimate output signal FIR filter output signal signal from secondary propagation path

Greek letters Coefficient involved in Van der Pol oscillator

x

Frequency of pressure oscillations

Subscripts n sampling time k k = 0 to M, where M = L  1 and L is filter length Superscripts 0 first order derivative 00 second order derivative ⁄ normalized term b estimation  FIR filter estimation Abbreviations LMS least mean square FIR Finite Impulse Response IIR Infinite Impulse Response ANC active noise control, active noise cancellation SPL sound pressure level

l

The main cause of self-sustained thermoacoustic oscillations [13,14] are due to the energy transferred from unsteady heat source to acoustic waves [15,16]. Unsteady heat release from a heat source is an efficient sound source [17,18], which produces acoustic disturbances. These acoustic disturbances propagate along the combustor and are reflected back due to the change of the boundary condition. Under certain conditions, the acoustic disturbances can further perturb the heat release rate and result in a ‘constructive’ feedback loop between heat release and acoustic waves [19,20]. This will lead to small-amplitude flow disturbances growing quickly into limit cycle oscillations [21,22]. Rayleigh’s criterion is widely used to characterize the generation mechanism of thermoacoustic instability [23]. It states that if unsteady heat release and pressure disturbances are in-phase, thermoacoustic instability occurs and combustion system will be unstable [24]. However, if the heat-release rate and pressure disturbances are out of phase, flow disturbances decay. And the combustion system is stable. In order to mitigate such thermoacoustic instabilities, the coupling between unsteady heat release and the acoustic perturbations must somehow be broken. Active [25,26] or passive [27,28] control techniques can be applied to achieve this. Passive control approaches [29,30] involves modifying the fuel injection system [29], changing the geometry of the combustion system or attaching acoustic dampers [31,32]. The main advantages of passive control approaches include that (1) the lack of moving component [33], (2) low maintenance cost [34] and (3) high durability [35]. Generally, implementing passive control approaches does not involve any risk to destabilize a stable combustor. However, modifying the combustion system can be costly and time consuming, while acoustic dampers cannot respond to changes in operating conditions due to the absence of a dynamic control system. These drawbacks limit the usage of passive control approaches to engine systems. Conventional passive control approaches are aimed to dissipate acoustical energy without utilizing it. Recently attempts [36,37] are made to apply some energy conversion devices to combustors susceptible to self-sustained thermoacoustic oscillations [38,39]. In

this way, the acoustical energy is converted into electricity for energy harvesting purpose. The study on heat-to-sound energy conversion recently became more and more popular. Various energy conversion techniques are developed and tested, for example, piezoelectric [36,37] and thermoelectric [38] power generators applied on a Rijke-Zhao system [39] with a premixed laminar flame confined. Promising results are obtained. And these energy conversion techniques may have great potential to be apply to a combustion system with a diffusion flame [40,41]. Active control approaches are generally applied in closed-loop configuration [20,21] by using a dynamic actuator such as a loudspeaker. Such configuration is also known as feedback control. In feedback control configuration, the controller drives the actuator in response to a sensor’s measurement [23,42]. Annaswamy et al. developed and tested a self-tuning controller to stabilize an unstable combustor. Comparison is then made between a fixed phase-lead controller and the self-tuning one. Neumeier et al. [23] developed an FFT-like online algorithm to stabilize an unstable premixed turbulent combustor. The algorithm can determine the amplitude, frequency and phase of the pressure oscillations in real time. Yi and Gutmark [42] developed a similar observerbased adaptive control algorithm. And it’s performance is evaluated in a modelled Cambridge combustor by stabilizing two unstable modes. One of the typical feedback control strategy is based on an infinite impulse response filter [20], whose coefficient is optimized by using least mean square algorithm (LMS). Numerical implementation of X-filtered LMS algorithm on a modelled combustor can reduce the pressure oscillations by about 15% [21]. In practice, the condition of the combustion system needs to be monitored in real-time. If there are small-amplitude oscillations or no limit cycle, then it is not necessary to activate the controller and actuator. Thus real-time monitoring and control of a combustion system is necessary for achieving safe operations. This partially motivated the present work. In addition previous studies did not experimentally validate the LMS control algorithm. Lack of such investigations partially motivated the present work. In this work, real-time monitoring and minimizing thermoacoustic instabilities are theoretically and experimentally studied.

S. Li et al. / Applied Energy 181 (2016) 399–407

For this, a Van der Pol oscillator [43] is used as a platform to produce limit cycle oscillations and to evaluate the performance of a control strategy to minimize such oscillations. The Van der Pol oscillator is an analog to a practical engine system [44,45], which generates limit cycle thermoacoustic oscillations. This is described in Section 2. To minimize the self-sustained oscillations, an online optimization algorithm based on least mean square method is developed and implemented. This is described in Section 3. The performance of the optimization algorithm is evaluated in Section 4. To further validate the optimization algorithm, experimental studies are performed on a Rijke tube with a loudspeaker implemented. The experimental setup and preliminary limit cycle measurements are described first. The effectiveness of the monitoring and control scheme is then evaluated. In addition, the performance of the control strategy at off-design condition is examined to check if it is able to track and prevent the onset of new limit cycle, even when the fuel flow rate is varied.

2. Theoretical modelling of nonlinear thermoacoustic oscillations To produce limit cycle oscillations as frequently observed in thermoacoustic systems [46,47], Van der Pol oscillator is chosen as a platform. It is an analog to an unstable dynamic combustion system such as a Rijke tube [48,49] as discussed later and used to evaluate the performance of control strategy. The Van der Pol oscillator is a nonlinear, 2nd order ordinary differential equation as

x þ lðx  1Þx þ x ¼ 0 00

2

0

ð1Þ

The Van der Pol oscillator model produces limit cycle oscillations which are similar to that observed in an unstable combustor as shown in Fig. 1. In general, the Van der Pol oscillator itself may not accurately model the physics of a particular unstable combustion system [50,51]. However, it does provide a nonlinear dynamic system/platform to evaluate the performance of feedback control approaches. Such platform is an analog to a combustor, which has a nonlinear feedback mechanism that results in limit cycle oscillations [52,53].

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3. Online optimization algorithm In this work, the least mean square (LMS) algorithm is chosen as an online optimization algorithm to minimize thermoacoustic oscillations. For this particular problem, we use the standard LMS and normalized (X-filtered) LMS. The standard LMS algorithm deploys an adaptive filter whose coefficients are chosen to minimize the error that a key variable has from its desired value. In the case, the algorithm takes the output signal, yˆ, from the filter and compares it with the real (desired) output, y. The error is found as

b ðnÞ EðnÞ ¼ YðnÞ  Y

ð2Þ

where ‘n’ denotes the sample number at that current time step. The algorithm then acts to reduce this error with each sample batch. The controller works by using a sensor to measure the happenings inside the thermoacoustic combustor [54,55] and hence gaining the input for the algorithm, x(n). In this case, the input to the controller is the limit cycle caused by the Van der Pol equation. The algorithm then calculates an estimate of the signal. Although in this case the input is known, in a real life system it is not and hence an accurate estimation of the input value is required. Fig. 2 shows the schematics of the LMS adaptive filter. The box on the left is the adaptive filter which produces the estimate result b ðnÞ. The box on the right is an ordinary filter which the input data Y is sent through to produce Y which is the value compared with b ðnÞ to produce the error output e(n). At each iteration the input Y is sent through both filters and compared. The result is then fed back into the adaptive filter in order to produce a closer estimate than the previous iteration. This is continued even after convergence is reached to ensure future input activity is accurately predicted. The input to the algorithm of the 4th order Runge-Kutta is the samples obtained earlier. This convergence method is based on the use of a Finite Impulse Response (FIR) filter. A FIR filter is a digital filter with a finite impulse response. It is also sometimes known as non-recursive filters as they do not involve any feedback, unlike the Infinite Impulse Response (IIR) filter which does adopt the use of feedback. When designing a FIR filter the ideal characteristics are sought but never achieved, as close as this to possible is desirable though of course. As the filter order increases so does the models likeness to that of an ideal filter. But as well as this the complexity and processing time of the filter is also increased. For a FIR filter, the output is related to the input as follows;

~n ¼ y

M X ak  xnk

ð3Þ

k¼0

~n denotes the output. The where xn denotes the sample inputs and y sampling time is denoted by ‘n’ and ak represents filter coefficients

Fig. 1. (a) Limit cycle oscillations in an unstable combustor and (b) a Van der Pol oscillator simulation with l = 0.2.

b ðnÞ is the Fig. 2. Schematic of a least mean square adaptive filter. Here, Y b ðnÞ approximation of Y(n). e(n) is the error/difference between the estimation of Y and Y(n).

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from k = 0 until k = M, where M = L  1, and L is the filter length. Eq. (3) is sometimes expressed in matrix form for ease of implementation, this is shown below:

~ n ¼ At  X n y

ð4Þ

where At = (a0, a1, . . ., aM) the filter coefficients and Xn = (xn, xn1, . . ., xnM)t the inputs. This is what we used in MATLAB code to successfully implement the algorithm. Once it is known that the prediction is accurate enough the next step is to attenuate the instabilities by sending the relative information to the actuator so it can produce the required deconstructive signal. A basic diagram of the feedback control of a combustor is shown and described below. Fig. 3 shows a typical scheme of an active feedback control system [56,57], which contains a ‘black box’ controller. A sensor is used to provide an input measured from the combustion chamber to the controller, and then it determines an output of ‘destructive oscillations’ to the actuator to mitigate the combustion-driven oscillations [58,59]. The destructive oscillations will be the same amplitude of the estimate obtained from the algorithm but sent in 180° out of phase. This is similar to ‘anti-sound’ approach as discussed later. 3.1. X-filtered LMS algorithm When X-filtered LMS algorithm is considered, it differs slightly from the standard LMS. It involves the secondary propagation path identification. This describes the path taken from the actuator device back into the system. If the device has a delay or an offset this will have an effect on the results and so any discrepancies must be considered. To do this the actuator is usually tested with the system off and the resultant wave analyzed for any errors, however slight. These are then incorporated into the algorithm to make them void. The algorithm still works in the same way as described previously for the standard method in that it acts to reduce the error. A diagram of an adaptive filter using the xfiltered algorithm is shown in Fig. 4. x(n) & y(n) denote the input and output respectively. Ys(n) is the signal from the secondary propagation path and fx(n) is the estimate. d(n) denotes external noise entering the system. E(n) is as described earlier, the resultant signal of the various inputs. Active control of combustion instability [60,61] is quite similar to active noise control (ANC) problems in many ways. They are both problems caused by unstable oscillations within their relative systems which can cause harm and/or damage to machinery. Both are desired to be avoided at all costs and are commonly solved using identification algorithms. The X-filtered LMS algorithm is a very popular algorithm choice for solving ANC problems because of its robustness and consideration of the secondary propagation path. That is why it is chosen to be applied to solve combustion instability problem. Active noise control is the method of reducing noise in a system by introducing ‘anti-noise’, whereby the ‘anti-noise’ is simply another sound source acting in such a way that it cancels out the unwanted noise. Fig. 5 shows an illustration of ANC. In theory, the resultant wave produced from this ANC system should be zero.

Fig. 3. A typical scheme of an active feedback control system.

As shown in Fig. 5, the noise signal A from speaker 1 and the noise signal B from speaker 2 are out of phase by 180°, so the waveforms peak at the exact opposite times causing the overall result to be equal to zero. This is very similar to what happens in active control of unstable combustion systems. This method is very useful when operating loud machinery that can be damaging to the ears or even the equipment and the unwanted noise is required to be lessened or removed. The resultant output from this cancellation is zero, where the dash lines in Fig. 5 indicate the noise and anti-noise waves are still there but can no longer be heard as they cancel out each other. Implementing the X-filtered algorithm to attenuate nonlinear limit cycle oscillations involves the following 3 main steps:
Step 1: the X-Filtered LMS algorithm is used to generate a synthetic secondary propagation path. When the system is on the secondary propagation path is not known until it is occurring so if there is a time delay or other offset error it has to be taken into consideration before the system is in operation. A signal must be generated from the actuator before the system is in use to discover these discrepancies.
Step 2: the secondary propagation path is estimated and adapted. As this signal is not known until it is happening an accurate estimate must be made. This step will ‘observe’ the synthetic signal created in step 1 and produce an estimate of its output. The estimate must be as accurate as possible to the real value of the wave so that when the system is in action it is known how the secondary propagation path will perform. Using this information the actuators signal is now altered to account for any results found. For example, an appropriate filter length needs to be chosen to accommodate for any time delay present. If the filter length is too long or short the delay could throw the results off initially causing some problems.
Step 3: the primary propagation path is introduced, which is simply the Van der Pol limit cycle described earlier. Following this, the final step is to activate the control algorithm and run the program. It should be noted that the level of detail into this algorithm will be much less than that of the standard LMS. This algorithm is mainly used to compare the results of extra noise being added on top of the input signal. As it is popular in ANC applications it suggests it will deal with the additional noise better.

4. Theoretical results and discussion With the control algorithms implemented to the Van der Pol oscillator, the system response and the following results are produced. Firstly, the standard LMS algorithm will be analyzed with the results from this section shown before the results achieved from the X-filtered algorithm are shown. Fig. 6 shows the estimation accuracy of the standard LMS algorithm. It can be seen that the algorithm converges very quickly on the input waveform and matches it more or less exactly by around normalized time t⁄ = 0.1. Fig. 6(a) shows the limit cycle as the output ˆ ) in red and the from the FIR filter (Y) in blue1, the Estimate (Y difference between the two, the error (E) in black. It can be seen that while the algorithm converges at the start of the graph the error begins to increase before falling when the values are estimated accurately. Fig. 6(b) shows the estimation of the secondary path. It can be seen that the estimates are very close to the real values and only differ by a maximum of around normalized time t⁄ = 0.1. This estimation will increase as the time goes on and the error is reduced. 1 For interpretation of color in Fig. 6, the reader is referred to the web version of this article.

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Fig. 4. X-filtered LMS adaptive filter.

Fig. 5. Illustration of active noise cancellation (ANC) concept with anti-sound technique applied.

Fig. 7. Phase diagram of the output, estimation and error signal, as l = 0.2, t⁄ = 0.5. The arrow denotes the time being increased.

Fig. 6. Performance of the standard LMS algorithm with online secondary path identification applied (a) time evolution of the signal and (b) online secondary path identification.

Fig. 7 shows the performance of the controller activated at t⁄ = 0.5 in terms of phase diagram. This is to show that the limit cycle reaches its full potential if left undeterred, as shown in the circle-shaped phase diagram. However, as the controller is actuated, the limit cycle is quickly dampened, as illustrated by the output converging to the point of (0, 0). As it can be seen, the controller estimates the values very quickly. This is because once the limit cycle is in full form it is very repetitive and the algorithm can notice this and estimate it accurately within short time. The attenuation takes roughly t⁄ = 0.1 to get completely to zero. However, safe levels are reached long before this, probably nearer to t⁄ = 0.01 after controller being actuated.

Fig. 8. Time evolution of the predicted signal in the presence of background noise, as the standard LMS algorithm actuated at t⁄ = 0.5 and l = 0.2.

Once the properties of the limit cycle have been adapted and the results of the controllers reactions analyzed an additional noise source is added to the input signal to act as an external disturbance. This will test the controller’s ability to estimate and attenuate a noisy limit cycle input. Fig. 8 shows time evolution of the

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5. Experimental demonstration

Fig. 9. Time evolution of the normalized signal in the presence of background noise, as X-filtered LMS algorithm is actuated at t⁄ = 0.05 and l = 0.2.

performance of the X-filter algorithm. The additional noise was added by using MATLAB code ‘KK = 0.5 ⁄ randn(size(X))’ which produced a matrix KK of random values of size ‘X’. This matrix was then added to the original input ‘X’ to produce a limit cycle with Gaussian noise added. The results obtained by implementing the X-filtered LMS algorithm will now be shown and discussed with comparison to those achieved using the standard LMS method. As mentioned previously, this algorithm is used as it is a popular algorithm choice for ANC applications and it is similar to the standard LMS algorithm already implemented. This algorithm will not be looked at it in as much detail as the previous one. The algorithm will be tested with the addition of external noise and compared to the result obtained from the standard LMS algorithm with the addition of external noise. Fig. 9 shown above displays the results of the X-filtered controller being activated from t⁄ = 0 with additional noise present in the system. It can be seen that as though the controller has complete control over the noise apart from the initial spurt of peak oscillations.

The experimental setup of Rijke tube [62,63] is shown in Fig. 10(a). A loudspeaker with a power of 100 W and a resistance of 8 X is attached to the bottom open end of the Rijke tube. Since combustion noise at low frequency (<1000 Hz) is of interest, the loudspeaker gives a flat response in this frequency range. The total length of the tube, L was 0.75 m. A propane-fueled Bunsen burner is used to provide a premixed laminar flame, with the flame 8.0 cm from the bottom tube end. With heating in place, the combustionexcited oscillations are generated. The pressure at 35 cm from the bottom open end is fed into the identification algorithm and LMS-based filter. A B&K microphone (Type 4957) is used to measure pressure perturbation. Before the microphone is used, calibration is conducted by using a ¼ inch. Piston-phone that produces a standard waveform of 1000 Hz at a sound pressure level of 94 dB. The frequency measurement error is found to be ±1 Hz. And the amplitude measurement error is less than 0.1 dB. The microphone was attached to side arm along the tube, with the semi-infinite line technique used to obtain thermal insulation without distortion from acoustic reflections. The mean flow speed is neglected, since it is much smaller than the speed of sound. The control algorithms are implemented in LabVIEW, with the data acquisition system consisting of a NI PXIe-1062Q chassis with a PXIe-7961R card. With the loudspeaker unactuated, the temperature contour and combustion-excited oscillations [64,65] are measured as shown in Figs. 10(b) and 11 respectively. The temperature contour is obtained by using an infrared thermal imaging camera. Before the infrared camera is used, calibration is conducted by comparing its measurement with a K-type thermocouple couple. The difference between the infrared camera and the thermocouple measurements is approximately ±1 K. It can be seen from Fig. 11(a) that the limit cycle thermoacoustic oscillations are produced from the Rijke tube. These limit cycle oscillations are quite similar to those produced from the Van der Pol oscillator. This confirms that the Van der Pol oscillator is a good platform to study nonlinear thermoacoustic oscillations and to evaluate the performance of the control strategy developed in this work to minimize limit cycle oscillations. Further analysis of the measured signal as shown in Fig. 11(b) reveals that the sound pressure level can reach about

Fig. 10. (a) Schematic of a Rijke tube with a loudspeaker acted as an auctor and a microphone as a real-time sensor and (b) measured temperature contour.

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Fig. 11. (a) Measured limit cycle thermoacoustic oscillations and (b) frequency spectrum of the measured pressure signal.

137 dB. The dominant mode in Rijke tube is at around 248 Hz and it has several harmonics. In our experiment, the output of the revised IIR filter does not interfere immediately or directly with the flame. The interference occurs after a ‘secondary’ path, which involves the loudspeaker actuation and the process of the pressure wave generation and propagation through the Rijke tube. Since the ‘secondary’ path is associated with a phase delay, its information must be taken into account by the controller. Neglecting the phase delay might results in control failure. The secondary path information is obtained with the path ‘identification’ procedure as described above. The damping effect of the active control approach is shown in Fig. 12. It can be seen from Fig. 12(c) that as the loudspeaker is actuated, approximate 45 dB sound pressure level reduction is achieved for the dominant mode. The harmonic peaks are also eliminated. In

addition, time evolution of the measured pressure and actuation signals are illustrated in Fig. 12(a) and (b) respectively. It can be seen that the pressure oscillations are quickly dampened to zero. This indicates the potential of applying the control approach in mitigating combustion-excited acoustic oscillations. One of the main features of the feedback control scheme is that it can track the operating conditions change and is able to achieve control at some off-design conditions. Such feature is not available in conventional passive control [66–71]. In order to evaluate the off-design performance of the control scheme, the LPG gas flow rate is suddenly changed at t = 5.5 s. This modification can cause the frequency of the unstable modes to vary. The time domain response of the pressure measurement [72,73] is recorded to illustrate the performance of the control strategy as shown in Fig. 13(a). The corresponding controller output is shown in Fig. 13(b). It can

Fig. 12. Time evolution of (a) measured pressure signal, (b) actuation signal and (c) comparison of frequency spectra of the measured pressure measurements before and after control.

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minimize limit cycle oscillations in real-time. It may have great potential to be applied in industry. Acknowledgment The work has been financially supported by the National Natural Science Foundation of China under Grant Nos. 51506079 and 51506050, and Jiangsu province specially-appointed Professorship. Prof. Bin Yang would like to acknowledge the financial support by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161522). References

Fig. 13. When fuel flow rate is varied from 240 ml/s to 220 ml/s, the response of the pressure measurement (a) and the controller output (b).

be seen that the control strategy is able to prevent the onset of new limit cycle, even when the operation conditions are slightly changed. 6. Conclusions Self-excited thermoacoustic oscillations usually occur in many practical engine systems such as gas turbines, aeroengines, boilers and rocket motors. Such oscillations can cause over-heating and structural vibration. To enable these engines to be operated stably, effective control approaches are needed. In this work, theoretical and experimental demonstration of minimizing self-excited thermoacoustic oscillations is conducted. For this, an online identification and optimization algorithm based on least mean square (LMS) method is developed to mitigate thermoacoustic oscillations in real-time. The working principle of the control strategy is similar to anti-sound technique, which produces an actuation signal with a phase difference of 180°. The control algorithms are evaluated on a Van der Pol oscillator first. It produces nonlinear limit cycle oscillations, as frequently observed in practical engine systems with lean combustion involved. The Van der Pol oscillator is an analog to an unstable engine system. And it is used as a platform to simulate the nonlinear dynamic heat-to-sound coupling and to evaluate the control strategy performance. It is shown that the limit cycle oscillation can be successfully minimized, even in the presence of a strong background noise. To further validate the control algorithms, experimental study is then performed to minimize thermoacoustic limit cycle oscillations produced from a Rijke tube with a loudspeaker implemented. The control strategy consists of a X-filtered LMS algorithm with a nonlinear secondary path identification. With the implementation of the identification and optimization algorithms, sound pressure level in the Rijke tube is found to be reduced by approximately 45 dB. In addition, the control strategy is shown to be able to prevent onset of new limit cycle oscillations, even when the operating condition is changed slightly. The present work opens up an alternative applicable approach to

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