Adaptive Control of Separated Flow

Transcription

1 44th AIAA Aerospae Sienes Meeting and Exhibit 9 - January 6, Reno, Nevada AIAA 6-4 Adaptive Control of Separated Flow Ye Tian * and Louis N. Cattafesta III Department of Mehanial and Aerospae Engineering University of Florida, Gainesville, FL, 36 Rajat Mittal Department of Mehanial and Aerospae Engineering, The George Washington University Washington DC, 5 Adaptive losed-loop ontrol is used to optimize the lift-to-drag ratio of post-stall separated flow over a NACA 5 airfoil using multiple amplitudemodulated (AM) or burst-modulated (BM), zero-net-mass-flux (ZNMF) atuators that over the entral 33% span of the airfoil. A simplex optimization approah uses the lift and drag measured by a strain-gauge balane for feedbak and searhes for the optimal AM or BM atuation parameters in a losed-loop fashion. An energy penalty funtion based on the eletrial power onsumption of the atuators is added to the ost funtion to study the tradeoff between the aerodynami performane and the power requirement. In the baseline post-stall separated flow over the airfoil, two dominant harateristi frequenies are identified via flow visualization and hot-wire anemometry: the onvetive instability of the separated shear layer and the global instability of the vortex shedding in the wake. Closedloop ontrol inreases the lift-to-drag ratio by a fator of -3 via smallamplitude AM and BM foring of nonlinear interations between these instabilities. I. Introdution low separation is the breakaway or detahment of flow from a solid surfae. It inurs a large F amount of energy/lift loss and limits the performane of many flow-related devies (e.g., airplanes, diffusers, et.). Researhers have sought to eliminate or at least mitigate flow separation for over a entury beause of its large potential payoff in many appliations. Reent efforts using periodi, as opposed to steady, exitation have demonstrated the ability to attah separated flow effiiently (e.g., Greenblatt and Wygnanski ). Leading-edge shear layer rollup and vortex shedding in the wake are two harateristi features of post-stall flow (Wu et al. 998). Huerre and Monkewitz (99) suggest that this type of shear flow (with a poket of absolute instability of suffiient size) may display intrinsi dynamis of the same nature as in a losed-flow system. Therefore, it is reasonable to postulate that separated flow over an airfoil ats as a nonlinear multi-frequeny losed-flow system (Mittal et al. 5). In suh a system, the shear layer instability (with harateristi frequeny f SL ) and * Graduate Researh Assistant, yetian@ufl.edu, Student Member AIAA. Assoiate Professor, attafes@ufl.edu, Assoiate Fellow AIAA. Assoiate Professor, mittalr@gmail.om, Assoiate Fellow AIAA. Copyright 6 by University of Florida. Published by the, In., with permission.

2 the global wake instability (with vortex shedding frequeny f wake ) may interat with eah other in a nonlinear fashion. The present study is foused on how this system responds to small amplitude-modulated (AM) (Wiltse and Glezer 993) or burst-modulated (BM) (Amitay and Glezer ), zero-net mass-flux (ZNMF) foring targeted at these instabilities. Although numerous studies are reported in the literature to determine the optimal foring frequenies for effetive separation ontrol, the observed values of optimal F + vary over a wide range. For example, Greenblatt and Wygnanski () onluded that the optimal range is < F + <4. Seifert and Pak (999) found that the exitation frequeny should be hosen suh that. 5 < F + <.5 over a wide range of high Reynolds numbers. Conversely, Amitay et al. () found that when the exitation frequeny F + >, the lift-to-pressure-drag ratio was larger than when the exitation frequeny F + < 4 for their unonventional airfoil. This study attempts to explore this ontroversy and determine optimal foring shemes by utilizing a quasi-stati, adaptive losed-loop ontrol approah. The approah implements a simplex optimization algorithm (Press et al. 99) and uses the measured lift and drag fores for feedbak and ZNMF atuators. An energy penalty funtion based on the eletrial power onsumption of the atuators is added to the ost funtion to onsider the tradeoff between aerodynami performane and power requirements. The outline of the paper is as follows. Setion II summarizes the experimental onfiguration and setup, while Setion III desribes the feedbak ontrol algorithm. Setion IV presents experimental results, and Setion V offers onlusions and disusses future work. U II. Figure : Experimental onfiguration. Experimental Configuration A NACA 5 airfoil with a 5.4 m hord and 3.48 m span serves as the test model in a low speed wind tunnel faility with a 3.48 m square test setion. The nominal Reynolds number based on hord length is 5 Re =. The angle of attak for this study is º. The BL is tripped at the leading edge using sand grit. As shown in Figure, the airfoil is fitted with four ZNMF atuators, all of whih are loated in the entral 33% spanwise region of the airfoil and have h =.5 mm wide slots. The first two (# and #) are loated near the leading edge of the airfoil at approximately 3% hord and are separated by.4 mm, while an idential seond pair (#3 and #4) is plaed near the point of maximum thikness at approximately 3% hord. Gallas et al. (3) desribe the design of the atuators. For this study, only the first atuator pair is used beause it is losest to the separation point for the hosen flow onditions. The slots of unused atuators are overed.

3 A balane is used to measure the lift and drag fores of the airfoil. Several pairs of strain gauges are attahed to a antilevered, annular shaft that supports the isolated airfoil to measure the lift, drag, and pithing moment (not used in this study). The estimated unertainty of the fore balane is 7 mn, whih orresponds to an unertainty of ±.5 in lift and drag oeffiients at the urrent test onditions. As shown in Figure, dual-timing ontrol loops are onfigured to implement the optimization algorithms (desribed in Setion III). The first loop synhronously ontrols the atuators and measures the low-pass filtered and amplified balane signal, while the seond loop averages the balane output and performs optimization in an asynhronous fashion. The seond loop ats as a supervisory ontroller that updates the ontrol parameters in the first loop. The sampling rate of the first loop is 4 khz, while the seond loop runs on a host PC at O(Hz). The first-loop is implemented by a dspace (Model DS5) DSP system with 466MHz PowerPC CPU and 6- bit A/D and D/A boards. The optimization algorithm is programmed in Matlab and ommuniates diretly with the dspace system to adjust the atuator signal. The eletrial power onsumption of the atuator is defined as VrmsIrms, where Vrms and I rms are the root-mean-square values of the voltage and the urrent of the atuator, respetively. The urrent is measured by a Tektronix (Model TCP A3) urrent sensor. The eletrial power of the atuator is used by the optimization algorithm to impose a penalty funtion based on power onsumption. A Dante onstant-temperature, hot-wire anemometry system (CTA module 9C) is used to aquire instantaneous veloity data. Before the experiments, a alibration is performed by the alibration module and the flow unit (9H and 9H). A 5 µ m hot wire probe (55P) is mounted on a -dimensional Velmex traversing system with approximately.6 µ m/ step spatial resolution in both diretions. The veloity data were sampled at.4 khz by a 6-bit dynami signal aquisition system, and the alias-free frequeny span was set to 4 khz. Flow field visualization and quantitative veloity data over the surfae of the airfoil and in the wake are aquired using Partile Image Veloimetry (PIV). The PIV system onsists of two 5 Hz, 5 mj per pulse, Nd:YAG lasers with appropriate light sheet optis and a TSI model 6357 Powerview Plus MP (6 x pixels) -bit CCD amera. z III. Two different initial onditions y Figure : Simulation results of downhill simplex algorithm. Control Algorithm Various optimization strategies are disussed in the literature (Press et al. 99). After some experimentation with various 3 extremum-seeking algorithms (Artiyur and Krsti 3; Banaszuk et al. 3), the downhill simplex method was implemented to minimize the drag-to-lift ratio. The benefits of the algorithm are its simpliity and appliability to multi-parameter optimization. The key steps of the algorithm are summarized as follows: ) evaluate the ost funtion at hosen initial onditions, ) use the lowest value as referene and searh for a lower value of the ost funtion, 3) move only in the downhill diretion, and 4)

4 terminate when some onvergene riteria are met. The performane of the downhill simplex algorithm is illustrated for -dimensional simulation ase (Figure ). The ost funtion is obtained in Matlab by the peaks ommand. The formula for the ost funtion is as follows: 3 5 x y ( x+ ) y Z = 3[( x) ( y+ ) ] ( x/ 5 x y ) e e / 3 This funtion has two loal minima and a global minimum. As shown in Figure, the optimization algorithm onverges to either a loal minima or the global minimum depending on the initial ondition. This is ditated by the inherent downhill nature of the algorithm. To inrease the probability of finding the global minimum, numerous initial onditions are used. () Rollup strutures in shear layer Airfoil Trailing edge Figure 3: Flow strutures in separated flow. Wake strutures PSD of wake veloity 3 f wake Rollup strutures in shear layer 5 5 Frequeny (H z ) PSD of shear layer veloity IV. Results Frequeny (H z ) Figure 4: Wake ( hord aft of TE) and shear layer (near separation) power spetral density at peak rms loation. - f SL -f wake fsl f SL +f wake Post-stall flow is haraterized by leadingedge shear layer rollup and vortex shedding in the wake as shown in Figure 3. The flow will likely be governed by nonlinear interations between these instabilities (Mittal et al. 5). Figure 4 shows a plot of the u rms power spetral density of the wake and the shear layer at the respetive peak RMS loations for the baseline, unontrolled flow obtained with a hot-wire probe. The wake spetral density is obtained hord 4

5 aft of the trailing edge, while the shear layer spetral density is obtained near the separation loation. The PSD was estimated using a 496 point FFT, a Hanning window with 75% overlap, and bloks. The plots zoom in on two interesting regions. The left plot learly shows the dominant wake frequeny f wake. The right plot provides evidene for the nonlinear oupling between the shear layer and wake instabilities via the presene of the shear layer frequeny f SL and the sum/differene frequenies f SL ± f wake. Note that f SL is muh higher than f wake in aordane with lassial saling arguments that fsl ~ U θsep and fwake ~ U Wwake. Based on the definition F = fxte U, f = fsl gives F ~ O(3) and f = f wake give F ~ O(). Thus, more than a single harateristi frequeny exists, perhaps explaining the wide range of effetive foring frequenies reported in. the literature. 3 Vpp 4 Vpp As suggested by Wiltse and 5 Vpp Glezer (993), amplitude. modulation is used as the exitation signal of the ZNMF.8 atuators to produe suffiient output at off-peak frequenies. In.6 this study, amplitude modulation takes the following form:.4 + sin( π fmt) et () = Asin( π ft ) u rms /Input (m/s)/v F (Hz) Figure 5: Frequeny response of ZNMF atuator. where A is the amplitude, f is the arrier frequeny (usually the resonant frequeny of the atuator) in Hz, and f m is the modulation frequeny (whih is also the targeted frequeny in the flow) in Hz. As an example, the frequeny response to sinusoidal exitation, i.e., rms veloity/voltage, of atuator # is plotted in Figure 5. The peak output ours at approximately Hz, and signifiant output is apparently limited to a bandwidth of 5-5 Hz, preluding the possibility of diretly foring the low-frequeny wake instabilities via sinusoidal exitation. Furthermore, the nonlinear nature of the atuators is revealed, sine the frequeny response funtion is not independent of the input voltage. It is this nonlinear behavior that is leveraged to enable foring at low and high frequenies, as explained below. 5

6 Veloity (m/s) t (se) Figure 6: Measured response (via hot-wire anemometry) to AM exitation of the ZNMF atuator. PSD f m f m Frequeny (Hz) f f ± f m Figure 7: Power spetral density of the AM hot-wire veloity signal shown in Figure 6. Modulation signal Carrier signal BM signal /f m /f duty yle/f m t (se) Figure 8: BM signal demonstration. Figure 6 shows the output of the ZNMF atuator measured by the hot-wire anemometry subjet to an AM exitation, where A = 5 V pp, f = 5 m Hz and f = 8 Hz. The wire was plae at a distane above the atuator slot so that there is no reverse flow and, hene, no signal retifiation is needed. The orresponding power spetrum of the AM signal shown in Figure 7 reveals the low frequeny output at 5 Hz is muh larger than an be obtained via sinusoidal exitation at 5 Hz. This shows that the atuator demodulates the AM signal due to the nonlinear nature of the system. Amplitude modulation thus allows an atuator operating at or near its resonant frequeny to generate signifiant disturbanes at harateristi frequenies of the flow that are far from the nominal bandwidth of the devie. Another type of atuation signal has been suggested by Amitay and Glezer (), and these authors all this pulse modulation. This waveform is generated by modulating a sine wave by a square wave with an adjustable duty yle. We term this type of the atuation signal burst modulation to be onsistent with standard funtion generator terminology. In this study, the duty yle is varied so that the signal ontains a single yle of the sine wave in eah pulse. The parameters to be optimized are again the amplitude, f and m f. Figure 8 demonstrates how the BM signal is generated. The arrier signal ( f = 4 Hz sine wave) is multiplied by the modulation signal ( fm = 4Hz square wave) to generate the periodi BM signal. Closed-loop ontrol experiments have been arried out using the downhill simplex algorithm. AM and BM exitation are used for the first pair of atuators. The goal is to searh for optimal A, f, and f to m minimize the drag-to-lift ratio using various initial onditions. Amplitude and frequeny 6

7 range limits are employed to protet the atuator as well as to onentrate on interesting regions. First, simple one-dimensional optimization (i.e., optimize only one parameter while others are fixed) is arried out using the AM signal. The results are obtained by starting from several different initial onditions. The results reveal that A always onverges to the maximum limit for both of the atuators. When atuator # is operated alone, the modulation frequeny f onverges to ~ ( to4) f wake, while f is fixed at the peak response frequeny of the atuator shown in Figure 5. Table summarizes the optimization results. Alternatively, the arrier frequeny f onverges to the viinity of f SL, orresponding to sub-harmoni foring of the shear layer, when f m is fixed at 8 Hz ( f wake ). Table summarizes the optimization results. Note that, in both ases, the lift-to-drag ratio, using only 33% span foring, is inreased by approximately a fator of. m Optimized f m (Hz) Optimized L D (Baseline =.7) Table : f m # with optimization results for the atuator A = 5V and f = 8 Hz. Optimized f (Hz) Optimized L D 4.65 Table : f # with optimization results for the atuator A = 5V and f = 8 Hz. m When atuator # is operated alone, the modulation frequeny f m onverges to the same range as atuator # ( fwake ~ 4 f wake ). However, the arrier frequeny f onverges to the viinity of the shear layer f SL (7 Hz ~ 5 Hz). An interesting fat is that this range is far from the maximum response of the atuator (see Figure 5). Figure 9, Figure, and Figure show instantaneous smoke-flow visualizations of baseline and ontrolled ases by atuator # and #, respetively. Interestingly, both atuators only partially reattah the separated flow. Further investigation is required to determine if this is an optimal result when seeking to maximize LD or merely due to a limitation of the atuators. The ase in whih two atuators are run simultaneously has also been studied. Sine the optimal f of atuator # is ~/ of the optimal f of atuator #, f is onstrained to be f. When f onverges to 3 Hz, LD onverges to.74, whih is an improvement ompared to the single atuator ases at the expense of inreased input power. 7

8 Figure 9: Flow visualization: baseline. Figure : Flow visualization: atuator # operating at optimal onditions. Figure : Flow visualization: atuator # operating at optimal onditions. Next, three-dimensional optimization (i.e., A, f and m f ) is attempted using both AM and BM signals but only atuator #. In addition, an energy penalty is also implemented. The overall dimensionless ost funtion onsists of the sum of the drag-to-lift ratio and a normalized D VrmsIrms power: f = W L + DU, where W is a weighting fator to balane the DL and the energy penalty. Table 3 summarizes the optimization results. Cases and 3 are the results for AM and BM signals without power penalty, respetively. Then, after the optimization algorithm is onverged, the power penalty is turned on (i.e., W=), and the results are summarized as ases and 4. µ = urmsh.5u for eah ase is also estimated using the hot wire anemometer and is The ( ) summarized in Table 3. The onstraint on the amplitude of the exitation signal was 3 V pp. One an see that f m and f onverge to similar values as shown in Table and Table. The optimization using an AM signal without energy penalty gives the best performane in terms of LD. On the other hand, the optimization using a BM signal only slightly degrades LD while requiring only about % of the power required by amplitude modulation. Another interesting point is that after the energy penalty is turned on, the algorithm is able to signifiantly redue the power with only slight performane degradations. Figure 3 to Figure 6 show the time-averaged veloity fields obtained using 3 PIV image pairs for the baseline ase and the four ases in Table 3. The blak line in the figures indiates the zero veloity ontour and reveals the separation loation. The separation is delayed by 43%, 33%, 33% and 3% hord length for ases,, 3 and 4, respetively. These results onfirm the performane shown in Table 3. 8

9 Table 3: Optimization results for both AM and BM signals with and without energy penalty. Case : AM Case : AM Case 3: BM Case 4: BM Converged Values (W=) (W=) (W=) (W=) f (Hz) m f (Hz) V pp overall ost funtion L D normalized power µ Figure : Flow veloity field for the baseline ase (no ontrol). Figure 3: Flow veloity field for ase. Figure 4: Flow veloity field for ase 3. Figure 5: Flow veloity field for ase. Figure 6: Flow veloity field for ase 4. 9

10 V. Conlusions and Future Researh The flow over a NACA 5 airfoil, at angle of attak and Re =,, is separated at the leading edge. In the post-stall separated flow, there are two harateristi instabilities: the shear layer and wake instabilities. Experimental evidene has suggested that they are nonlinearly oupled. Both instabilities are important to ontrol the separated flow via unsteady exitations. A quasi-stati, adaptive, nonlinear losed-loop ontrol sheme for the separated flow has been developed to searh for the optimal AM or BM atuation parameters using ZNMF devies. The downhill simplex algorithm is used as the optimization algorithm. The results seeking to maximize LD with and without an energy penalty are promising and reveal the importane of foring nonlinear interations between the shear layer and wake instabilities. Furthermore, the importane of atuator dynamis is revealed. ZNMF atuators are nonlinear systems themselves. Their nonlinear harateristis add omplexity but also enable foring of instabilities with harateristi frequenies that are widely separated. The BM atuation signal gives omparable performanes while requiring less energy ompared with the AM atuation signal. An energy penalty funtion based on the eletrial power of the atuator is added to the ost funtion to onsider the trade off between the aerodynami performane and power requirements. The implementation of the energy penalty funtion is able to redue the required power with only modest performane redutions for both AM and BM atuation signals. On the other hand, preliminary tests have shown that, when starting with a separated flow with the energy penalty funtion turned on, results in poorer aerodynami performane. This highlights the differenes between attahing a separated flow and keeping an attahed flow from separating. Future researh inludes detailed flow measurements using the hot-wire anemometry and PIV to understand what the effet of the ontrol is on the flow. Furthermore, we plan to investigate other ost funtions, besides DL, that seek, for example, to maximize lift or minimize drag. Aknowledgments This work was supported by the Air Fore Offie of Sientifi Researh Grants FA and FA , monitored by Dr. Rhett Jefferies. Referenes Amitay, M, and Glezer, A., Controlled transients of flow reattahment over stalled airfoils, International Journal of Heat and Fluid Flow, Vol. 3, pp ,. Amitay, M., Smith, D., Kibens, V., Rarekh, D. and Glezer A., Aerodynami Flow Control over an Unonventional Airfoil Using Syntheti Jet Atuators, AIAA Journal, Vol. 39 No.3, Marh, pp Artiyur, K. B. and Krsti, M., Real-Time Optimization by Extremum-Seeking Control, Wiley-Intersiene, 3. Banaszuk, A., Narayanan S. and Zhang Y., Adaptive Control of Flow Separation in a Planar Diffuser, AIAA paper 3-67, 3. Greenblatt, D and Wygnanski, I, The ontrol of flow separation by periodi exitation, Progress in Aerospae Sienes, 36: ,. Griffin, B., Senior Thesis, University of Florida, 3. Hajj, M. R., Miksad, R. W. and Powers, E.J., Perspetive: Measurements and Analyses of Nonlinear Wave Interations with Higher-Order Spetral Moments, Journal of Fluids Engineering, Vol. 9, Mar. 997, pp Holman, R., Quentin, G., Carroll, B. and Cattafesta, L., Interation of Adjaent Syntheti Jets in an Airfoil Separation Control Appliation, AIAA paper 3-379, June 3, Orlando, FL. Huerre, P. and Monkewitz, P., Loal and Global Instabilities in Spatially Developing Flows, Annual Review Fluid Mehanis, 99. : pp Kegerise, M. A., Spina, E. F., Garg, S. and Cattafesta, L., Mode-Swithing and Nonlinear Effets in Compressible Flow over a Cavity, Physis of Fluids, Vol. 6, No. 3, Mar. 4, pp Mittal, R., Kotapati, B. and Cattafesta, L., Numerial Study of Resonant Interations and Flow Control in a Canonial Separated Flow, AIAA paper 5-6, Reno, Nevada, Jan. 5.

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