Extremum-seeking optimisation of fluidic jet-noise control

Transcription

1 15th AIAA/CEAS Aeroacoustics Conference (th AIAA Aeroacoustics Conference) May 2009, Miami, Florida AIAA Extremum-seeking optimisation of fluidic jet-noise control R. Maury, M. Koenig, L. Cattafesta, P. Jordan, J. Delville, J.-P. Bonnet & Y. Gervais In this work we use an extremum-seeking algorithm to optimise a fluidic jet-noise controller. The device, which we call a fluidevron, has been shown to produce reductions in jet noise which are comparable with those achieved using conventional microjets, but the underlying flow-physics have been shown to be very different (see Laurendeau et al. 1 for details). A negative effect produced by the control comprises a high-frequency noise increase. The extremum-seeking algorithm is used to optimise the control either for maximum low-frequency noise-reduction, or for maximum overall noise-reduction. This is achieved through a specification of the frequency-range over which noise reduction is sought. The extremum-seeking is shown to perform well, producing flows with integrated low-frequency gains of the order of 2.5dB when tuned for maximum low-frequency benefit, and flows where the high frequency penalty is virtually eliminated when tuned for maximum spectral range. The extremum-seeking is then implemented using metrics computed from farfield microphones at different polar stations; the control effect is thus found to be omnidirectional. This shows that there is no directional bias in the response of the source mechanisms to the actuation. Finally, the relationship between noise reduction and flow-rate is studied and found to be non-linear: the source mechanisms are most receptive at low flow-rate, a saturation point being reached after which the actuation no longer has any control authority over the source dynamics. I. Introduction Jet noise reduction is severly hampered by two problems: we do not have a clear understanding of (1) the physics of aerodynamically-generated sound, or (2) the response of high Reynolds number jets to steady or unsteady actuation. Consequently, we cannot know, a-priori, what kind of perturbation to introduce to a turbulent jet in order to produce a desired change in either the structure of the turbulence or the sound it generates. The design of control strategies is, as a result, forced to function on a trial and error basis, and when effective strategies are achieved, there follows the difficulty of optimising the device in a parameter-space which is generally of un-manageable dimension. In this work we focus on a fluidic control device which we call a fluidevron. The device comprises pairs of microjets, azimuthally distributed over the nozzle lip, which both penetrate and converge (convergence angle corresponds to a yaw-angle) so as to produce an azimuthal distribution of fluidic chevrons. The flowphysics which underpin the control effect have been studied in detail by Laurendeau et al., 1 and shown to be very different from the non-converging microjet configuration. Furthermore, the control-mechanism which involves the ejection and turbulation of fluid from the main jet which is then re-assimilated by the mixinglayer downstream of the control-jets where it produces a local thickening of the mixing-layer, a subsequent calming of the velocity gradient and a 70% reduction in the turbulence production may be highly sensitive to parameters such as the penetration angle, convergence angle, and the relative velocity of the jets of a given pair. An undesirable side-effect of the controller comprises a high-frequency noise increase, similar to that produced by chevrons and non-converging microjets. The cross-over frequency (between noise-reduction and noise-increase) turns out to be a critical parameter when transposition to full-scale is considered: it lies Laboratoire d Etudes Aérodynamiques, CNRS UMR 69, Université de Poitiers, ENSMA, France. Professor, MAE Department, University of Florida, Gainesville, FL, USA, Associate Fellow AIAA. 1 of 10 Copyright 2009 by Peter Jordan. Published by the American American Institute of Institute Aeronautics ofand Aeronautics Astronautics, and Inc., Astronautics with permission.

2 in a frequency range over which the human ear is most sensitive. When laboratory-scale results are thus transposed, what was a global noise reduction at lab-scale can even turn out to be a global noise increase at A-weighted full-scale. In view of this we use an extremum-seeking algorithm to optimise the noise-reduction capabilities of this control device in different ways. In a first test we tune the algorithm to optimise the device in terms of maximal peak reduction this can be of interest for understanding the physics associated with reducing the peak farfield levels (often associated with coherent structures). In a second test we focus on the broadband levels, with the idea of minimising the high-frequency noise increase. Alternative optimisations include: (1) maximising the cross-over frequency (between noise reduction and increase), (2) selecting frequency-bands which can be of interest in view of the transition to full-scale, (3) optimising for specific emission directions (such an approach may be useful for tailoring the jet-noise directivity in view of the certification test setup - relative position of the certification microphones and the jet). Another utility of such tuned optimisation is of course that the physics which underpin the various reductions may be different, and so the generation of a set of noise-controlled flows constitutes a valuable departure point for understanding the different mechanisms which are at work in producing sound in the different flows. Results presented in this paper demonstrate the effectiveness of the extremum-seeking algorithm in achieving such tuned control where the injection velocity is the control parameter: for targets of maximal peak gain and maximal broadband gain the algorithm is successful. II. Experimental setup The main jet and the control device are shown in figure 1(a), and schematically in figure 1(b). Figure 1. Photo and front-view schematic of jet and control device. The experiments were carried out in the LEA anechoic wind tunnel facility Bruit et Vent ( Noise and Wind in english) at the CEAT (Centre d Etudes Arodynamiques et Thermiques), Poitiers. The wind tunnel test facility is regulated in speed (main jet velocity of 128 m/s; M= 0.37) and temperature (ambient). The jet has a Reynolds number of approximately 7x10 5. The cutoff frequency of the anechoic chamber is 200 Hz. The inner diameters are 80 mm for the main jet and 2.1 mm for the control jets. For these experiments, four 1/4 inch G.R.A.S. microphones calibrated at 94 db, positioned on an arc at r/d=31 and,, and 90 degrees as shown in figure 2 (with respect to the downstream jet axis) were used to measure the control effect on the radiated sound field. The microphone signals were band-pass filtered from 200 Hz to khz and sampled at 120 khz. The band-pass filter is composed of a third order high-pass Butterworth filter (to 2 of 10

3 take account of the cutoff frequency of the anechoic chamber) and a second order low-pass filter. Power spectral densities were estimated using blocks of 8192 points with exponential averaging on RMS values and integrated from 200 Hz to a user-adjusted cutoff or cross-over frequency, f ctheo, to obtain a running average of the integrated far-field noise over sec. This averaging time was large enough to reduce random errors in the noise spectra to acceptable levels but was still small compared to the period (1 sec) of the perturbations, as explained in section III. Figure 2. Schematic representation of the microphones array. The mass flow rate of the sixteen microjets was controlled and measured using an integrated mass flow controller and meter (Brooks Smart Series TMF Model 5853S). This device allows a variation of input voltage from 2.5 V to 8.1 V. This range of voltage corresponds to a variation of flow rate from 0% to 2% relative to the flow rate of the main jet. The acquisition of the input data is performed by a National Instruments PXI III. Extremum-seeking Extremum-seeking is a control technique which allows a local extremum (maximum or minimum) of an objective function to be found. It has proved useful in numerous applications, such as: combustion instabilitiy control, 2 noise control in turbomachinery, 3 flow control, 4 thermoacoustic control, 5 cavity noise control. 6 Its fundamentals are outlined in reference. 10 The original idea of extremum-seeking was developed by Morosanov 8 in It involves a relatively simple self-adjusting closed-loop system based on an adaptive gradient, and stability is gauranteed if the system is designed properly (see Krstic et al. 9 ). The most straightforward scheme involves a single input (control variable) and a single output (variable to be controlled), or SISO. Other, more sophisticated schemes, can be implemented in order to improve the overall performance; for example, multiple-input,multiple-output (MIMO) schemes can be implemented in order to control complex systems with many parameters (see King et al. 10 and Henning et al 11 ). Another variation of the extremum seeking involves slope-seeking (see Ariyur et al. 12 ). This allows a plateau to be found by means of the calculation of a slope. It can be useful in flow control scenarios where distinct extrema do not exist. Other improvements are possible in order to speed up the algorithm: for example, using an extended Kalman filter algorithm for fast real-time estimation of the local gradient of the steady-state map (see King 7 ). A. Extremum-seeking algorithm Extremum seeking control is well documented in the literature and is only briefly described here (see Becker et al. 13 for more details about extremum-seeking). The goal is to reach an extremum (i.e., a maximum or minimum). As shown in Figure 3, u o is a nominal actuator input parameter (e.g., the mass 3 of 10

4 flow rate of the microjets), and û is a perturbation. The total input to the plant is u = u o +û+a sin(ωt), and the output (e.g., the integrated far-field jet noise) consists of the sum of a mean value and a perturbation y(t) = y s + af sin(ωt), where f is the local slope of the function. If the frequency, ω, of the perturbation is much less than the characteristic frequency(ies) of the system, then the output tracks the input in phase. The output is then high-pass filtered to remove the dc offset, y s, to produce y HP (t) G HP af sin(ωt+ φ HP ), where φ HP = 0 and G HP (jω) is the magnitude of the HP filter transfer function. This output is multiplied by sin(ωt) to yield y P (t) = G HP (jω) af sin 2 (ωt). Then a low-pass filter is applied to remove the oscillations, and the result is integrated over a cycle and multiplied by a constant gain K > 0 to obtain a positive û for a positive slope f, which moves the system toward the maximum. When f < 0, for example when approaching the maximum from the right, the change in the sign of the slope produces a negative û. Figure 3. Basic operating principle of extremum seeking controller (from 13 ). The extremum seeking algorithm can be implemented in real-time using analog circuitry: LP and HP filters, an integrator, an amplifier (for the gain), and an adder circuit. Alternatively, it can be implement in real-time using an A/D, D/A, and a digital signal processor. Neither of these options was available for the current experiment. As a result, the algorithm was implemented using standard (i.e., not real-time) LabVIEW code to implement the algorithm steps. B. Optimisation of perturbation parameters The previous paragraph introduces two main perturbation parameters in the term a sin(ωt), namely the amplitude and frequency of the perturbation. As a consequence, it is necessary to find the best parameters by studying the behaviour of the mass flow controller. Thus, we apply a sinusodal perturbation around a fixed flow rate value. In one case, we fix the frequency of the perturbation and we modulate its amplitude. In the second case, we fix the amplitude of the perturbation and we modulate its frequency. By means of these experiments, we obtain the optimal values of the perturbation parameters for the mass flow controller, such that the output noise perturbation is in phase with the input mass flow rate perturbation. A hysteresis in the measured-versus-commanded mass-flow control rate was observed during the experiments as the perturbation amplitude and/or frequency were increased. Figure 4(a) shows the hysteresis as the amplitude increases for a fixed frequency of Hz around a commanded flow rate of 0.%. This effect can be attributed to a phase-lag in the response of the valve. As the commanded flow rate is increased, the flow rate increases linearly. However, at large amplitude perturbations, the hysteresis is more visible. In light of this, the amplitude chosen is 0.1 V, corresponding to a perturbation of approximately 0.%. Indeed, the 0.05 V amplitude is more precise but the flow rate perturbation is too small to produce a measurable change in the output noise. Figure 4(b) shows the response of the valve as the frequency is increased from Hz to Hz for a fixed perturbation amplitude of 0.1% around a flow rate of commanded 0.4%. Here, an increasing phase lag is evident as the frequency is increased. Thus, a frequency of Hz (with a period of 1 sec) is chosen, as this results in acceptable phase lag. 4 of 10

5 Measured flow rate [%] Measured flow rate [%] Command flow rate [%] (a) Command flow rate [%] (b) Figure 4. (a) Mass flow hysteresis for various amplitude perturbations about a commanded flow rate of 0.% of the main jet for a fixed frequency of Hz.; (b) Mass flow hysteresis for various frequency perturbations about a commanded flow rate of 0.4% of the main jet for a fixed perturbation amplitude of 0.1%. IV. Results We first perform an experiment with the microjets at maximum flow rate (1.%) without using the extremum-seeking algorithm. A comparison between the controlled and uncontrolled jet-noise spectrum is shown in figure 5 for a farfield microphone located at degrees. As can be seen, the microjets reduce the low frequency noise (peak reductions of between 3 and 4 db) below about 5 khz (St = 3; St = fd/u j, where f is frequency, D the main jet diameter and U j the main jet exit velocity) and increase the noise above this frequency. Figure 5. Measured time-averaged sound pressure level (0 linear averages) for the cases with the microjets off and on at maximum flow rate. 5 of 10

6 A. Variation of the frequency bandwidth and optimisation of the cross-over frequency To begin we only consider the microphone at degrees (with respect to the downstream jet axis). We examine the case of maximum low-frequency noise reduction by choosing a target cross over frequency f ctarget =5 khz. Figure 6(b) shows that the controller achieves an integrated noise reduction of approximately 2.5 db (integration is between 200 Hz and the cross-over frequency); the corresponding SPL spectrum is given in (a). The scatter in 6(b) is indicative of both the perturbations in the mass flow rate, starting from an initially closed valve, and the random uncertainty in the noise metric. We see that the spectrum is reduced below approximatively 5 khz, as for the maximum flow rate case without extremum-seeking; the extremum seeking is thus seen to successfully reproduce the maximum flow-rate case Integrated Noise [db] (a) Flow Rate [%] (b) Figure 6. Result of extremum seeking control with f ctarget = 5 khz. (a) SPL; (b) integrated noise metric vs. flow rate. The duration of the experiment is approximatively 10 minutes, this time being determined by the dynamics of the mass flow meter. The algorithm is stopped when the value u 0 + û converges. An example of convergence is given in figure Nominal Mass Flow Rate [%] iteration number Figure 7. Convergence of the algorithm for a cutoff frequency of 5 khz and a microphone at degrees. Figures 8 and 9 show results for target cross-over frequencies of 15 khz and khz. These figures, in addition to Figure 6, show that a tradeoff exists between mass flow rate and the corresponding noise reduction bandwidth. As one increases, the other decreases. We see that target cross-over frequency, f ctarget, is generally not achieved. However, it is increased when higher target frequencies (i.e. integration bandwidths) are specified. We obtain f cexp =7 khz (St = 5) 6 of 10

7 when f ctarget =15 khz is specified, and f cexp =10 khz (St=8) when f ctarget = khz is specified. The high frequency noise increase is also reduced for f ctarget =15 khz, and indeed it is virtually eliminated for f ctarget = khz. The overall integrated noise reduction in this case is about 0.7 db, and the flow rate is 0.5%. Integrated Noise [db] (a) Flow Rate [%] (b) Figure 8. Result of extremum seeking control with f ctheo = 15 khz. (a) SPL; (b) integrated noise metric vs. flow rate Integrated Noise [db] (a) Flow Rate [%] (b) Figure 9. Result of extremum seeking control with f ctheo = khz. (a) SPL; (b) integrated noise metric vs. flow rate. B. Variation of the angular position of the microphone In this section, we study the influence of the angular position of the microphone on the behaviour of the extremum-seeking algorithm, and in particular we look at the relationship between flow rate and noise reduction/increase. We first consider microphones at and 90 degrees, and we specify a target cross-over frequency of 10kHz. The spectra, shown in Figure 10, demonstrate how the noise reduction is similar at both low and high emission angles, while for the high-frequency noise increase there is a difference of the order of 5 db. This is due to the directivity of the control jets: like any round jet they radiate more energy at low emission angles; in fact it can be seen how the same 5dB difference is manifest between the peaks of the and 90 spectra of the main jet (SPL curves of the main jet in dashed lines at St 0.3). 7 of 10

8 65 65 (a) (b) Figure 10. SPL result of extremum seeking control with f c = 10 khz. (a) microphone at degrees ; (b)microphone at 90 degrees. The variation of the low-frequency noise-reduction as a function of flow-rate is shown in figure 11. This figure provides two pieces of information. First of all it shows that the noise reduction achieved is approximately omnidirectional. In terms of source mechanisms, if we consider that there are different mechanisms implicated in radiation to different farfield stations, this implies that they all respond in the same way to the control; if, on the other hand, we consider that one and the same mechanism underpins radiation to all angles, then the impact of the control on this mechanism comprises a global reduction in its radiation efficiency. The second piece of information which is provided is that the relationship between noise reduction and flow-rate is non-linear the actuation has greatest control authority at low flow-rate. In terms of the control dynamics, it is at these low flow-rates that the controllability of the source mechanism(s) is greatest the actuation is here pertinent; at higher flow rates the source mechanism(s) is(are) no longer receptive to the actuation a different kind of actuation dynamic is now necessary to elicit a response from the source mechanism(s) degrees degrees 90 degrees Integrated Noise [db] Flow Rate [%] Figure 11. Integrated noise metric vs. flow rate result of extremum seeking control with f ctarget = 5 khz. Globally similar trends are observed as the target frequency is increased: omnidirectional noise reduction; noise increase with a characteristic jet-noise directivity pattern; non-linear relationship between noise reduction and flow-rate. 8 of 10

9 The results are summarised in table 1. We see how the high-frequency penalty leads to a more modest OASPL reduction when compared with the low frequency gain. In a companion paper 15 we see that when results such as these are transposed to full-scale, and the integrated effect (inclusion of other noise sources on the aircraft) of the change in the jet noise is considered, the critical parameter tends to be the crossover frequency results at lab-scale which show small overall noise reduction often correspond to a more favourable EPNL decrease at full-scale; and, similarly, results with good low-frequency noise reduction can correspond to an unfavourable change in EPNL at full scale. This point emphasises the delicate nature of jet-noise control optimisation using laboratory-scale experiments, and again it makes clear the interest of approaches such as extremum-seeking, which allow the optimisation process to be both tuned and automated as a function of the requirements at full-scale. For optimisation which is to be pertinent at full scale, the industrial filter must be integrated into the laboratory-scale optimisation. Microphone angle f ctarget [khz] f cexp [khz] LF gain [db] HF loss [db] Overall OA Microphone angle f ctarget [khz] f cexp [khz] LF gain [db] HF loss [db] Overall OA Table 1. Résumé of extremum-seeking results. V. Future work Future work will include the investigation of other control parameters (Multiple Input-Output extremumseeking algorithm), such as the velocity difference between two jets of each fluidevron; the frequency of unsteady, pulsating microjets; the azimuthal, modal structure of such pulsations. And, for promising looking controlled flows (both at lab-scale and full-scale), the underlying flow physics will be probed in a manner similar to the experiments of Laurendeau et al. 1 Furthermore, future experiments will be performed on co-axial flows issuing from complex nozzle, such as used by Basara et al. 15 VI. Acknowledgements The authors gratefully acknowledge the helpful input of R. King and B.R. Noack from Technische Universität Berlin and wish to thank J.-M. Mougenot for its contributions to the experiments. References 1 Laurendeau E., Jordan P., Bonnet J.-P., Delville J., Parnaudeau P., Lamballais E. (2008) Subsonic jet-noise reduction by fluidic control: the interaction region and the global effect. Physics of Fluids, Vol. 20, Banaszuk A. (1951) Extremum-seeking control of combustion instabilities Workshop on real-time optimization by 9 of 10

10 extremum-seeking control, ACC Garwon M., Schulz J., Satriadarma B., King R., Mser M. Neise W. (2004) Adaptive and robust control for the reduction of tonal noise components of axial turbomachinery with flow control CFA-DAGA, Strasbourg. 4 Garwon M., Urzynicok F., Darmadi L.H., Brwolff G., King R. (2003) Adaptive control of separated flows In Proc. of the ECC Cambridge. 5 Gelbert G., Moeck J.P., Bothien M., King R., Paschereit C. (2008) Model predictive control of thermoacoustic instabilities in a swirl stabilized combustor In Proc. of the 46 th AIAA Aerospace Sciences and Meeting Exhibit. 6 Kim K., Kasnakolu C., Serrani A., Samimy M. (2009) Extremum-seeking control of subsonic cavity flow AIAA Journal, Vol. 47, No. 1, King R. (2009) Closed-loop flow control part 2 : adaptive and model predictive control VKI Lecture Series , Flow control : fundamentals, advances and applications. 8 Morosanov I.S. (1957) Method of extremum control Automation Remote Control, Vol. 18., Krstic M., Wang H.H. (2000) Stability of extremum-seeking feedback for general nonlinear dynamic systems Automatica, Vol. 36, King R., Becker R., Feuerbach G., Henning L., Petz R., Nitsche W., Lemke O., Neise W. (2006) Adaptive flow control using slope-seeking 14 th IEEE Mediterranean Conference on Control Automation, Ancona. 11 Henning L., Feuerbach G., Muminovic R., Brunn A., Nitsche W., King R. (2008) Extensions of adaptive slope-seeking for active flow control Proc. Imech, Part I : J. Systems and Control Engineering, Ariyur K., Krstic M. (2003) Real-time optimization by extremum-seeking control Hoboken. 13 Becker R., King R., Petz R., Nitsche W. (2007) Adaptive closed-loop separation control on a high-lift configuration using extremum seeking AIAA Journal, Vol., No. 6, Barre S., Fleury V., Bogey C., Bailly C., Juve D. (2006) Experimental study of the properties of near-field and far-field jet noise 12th AIAA/CEAS Aeroacoustics Conference 8-10 May 2006, Cambridge, Massachusetts AIAA paper Basara L., Bonnet J.-P., Delville J., Fourment C., Hubert J., Jordan P. (2009) A parametric study of jet noise reduction by fluidic injection on co-axial jets AIAA of 10