CAUSALITY CORRELATION IN AEROACOUSTIC EXPERIMENTS BY MEANS OF SIMULTANEOUS PIV AND MICROPHONE-ARRAY MEASUREMENTS

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1 CAUSALITY CORRELATION IN AEROACOUSTIC EXPERIMENTS BY MEANS OF SIMULTANEOUS PIV AND MICROPHONE-ARRAY MEASUREMENTS Arne Henning Technicl University of Berlin, Institute for Aero- nd Astronutics (ILR), Berlin, Germny. Current ddress: Germn Aerospce Center (DLR), Göttingen, Germny Lrs Koop nd Klus Ehrenfried Germn Aerospce Center (DLR), Göttingen, Germny ABSTRACT In this pper we present pplictions of the cuslity correltion technique y mens of simultneous PIV mesurements in turulent flow nd microphone-rry mesurements in the erocoustic fr field. Both mesurements re conducted in synchronized mnner so s to enle the clcultion of the cross-correltion etween the coustic pressure nd flow quntities derived from the mesured velocity fluctutions. The min ide of the concept presented here is to use the therewith otined coefficient mtrix to identify regulrities in the flow tht re relted to the rdited sound field. Here we show comprtive study of the results for mesurements on different flow-configurtions with strong tonl components s well s with rodnd spectr in the coustic fr-field. INTRODUCTION Acoustic mirrors nd phsed microphone rrys re stndrd tools used to loclize nd quntify erocoustic sources. But mesurements in the fr field don t give ny direct informtion out the source processes occurring in the ner field, wheres mesurements in the ner field, lthough le to deliver informtion out the structures nd the dynmics of the involved flow, re nevertheless very difficult to nlyze in terms of n estimtion of the rdited fr-field sound. One wy round this is the simultneous mesurement of the coustic pressure in the fr-field together with some other ner-field quntity. In this mnner the fr-field pressure cn e correlted

2 with the ner-field quntity to identify erocoustic sources. The simultneous mesurement of coustic pressure fluctutions in the fr-field of turulent flow together with ner-field quntity hs een investigted y vrious uthors in the pst [, 6, ]. In this mnner the fr-field pressure cn e correlted with the ner-field quntity to identify flow structures which re relted to the erocoustic source mechnism. Rckl [8] introduced the nme cuslity correltion for this correltion pproch. Previous experiments [3, 4] hve shown tht synchronized PIV nd microphone mesurements cn e used to otin the cross-correltion function etween ner-field quntity nd the coustic pressure in the fr-field. These mesurements descried here hve een performed on different flow configurtions, nmely cylinder-wke nd rodirfoil configurtion. The dvntge of using Prticle Imge Velocimetry (PIV) for mesuring the ner field quntity is the non-intrusive determintion of the instntneous flow velocity in region instntneously.. Cuslity Correltion In the investigtions presented here, the correltion-coefficient R φ,p etween the ner-field quntity φ mesured vi PIV nd the coustic pressure p is clculted in the time domin y n ensemle verge over certin numer of PIV snpshots. The recording rte of the used PIV systems is in the order of Hz. Clerly, this rte is too slow to cpture the temporl development of n unstedy flow field in most prcticl pplictions in the field of erocoustics. But the low recording rte ssures tht the PIV mesurements re sttisticlly independent, which implies mximum suppression of uncorrelted prts of the mesured quntities per PIV snpshot during the clcultion of R φ,p. The normlized cross correltion R φ,p (x,y,τ) is defined s: R φ,p (x,y,τ) = S φ,p(x,y,τ) σ φ (x)σ p (y) = φ (x,t) p (y,t + τ) φ (x,t) p (y,t), () where φ(x,t) represents ner-field quntity mesured t position x nd time t. The vrile τ is the time shift etween the pressure signl p t the position y nd the point in time the quntity φ is otined. The cross correltion S φ,p (x,y,τ) is normlized y the root-men-squre (RMS) vlues of the fluctutions φ nd p which re denoted y σ φ (x) nd σ p (y). In the present experiments the flow field is recorded y the PIV system t discrete times t n nd the ner-field quntity is evluted from these recordings. The time etween the PIV mesurements is lrge enough so tht the individul imges cn e considered s sttisticlly independent. The frfield pressure is recorded t discrete times simultneously to the flow field mesurements, ut using much higher smpling rte thn with PIV. The system clock of the PIV system hs een synchronized with the dt-cquisition system used for the coustic pressure. Then the cross correltion etween the ner-field quntity nd the coustic pressure cn e clculted in discrete mnner using: S φ,p (x,y,τ) = N N [ φ (x,t n ) p (y,t n + τ) ]. () n= In the following τ k/ f p with k =,,3...K, where K is the totl numer of pressure smples recorded.

3 where N is the numer of PIV mesurements. The RMS-vlue of the ner-field quntity, which is required for normliztion, cn e clculted from the mesured dt y: N σ φ (x) = N φ (x,t n ) und σ p (y) = p (y). (3) n= The verging for the stndrd devition σ p (y) is crried out over ll recorded pressure smples. The numer of these smples is typiclly severl orders of mgnitude higher thn N. It should e noted here tht the criticl prmeter is the numer of PIV recordings N. If N is too low, uncorrelted prts of the mesured quntities cnnot e sufficiently suppressed. This results in high noise level in the resulting cross-correltion S φ,p. The definition of sufficient numer of recordings my of course depend strongly on the prticulr cse under considertion. In cse of simultneous microphone mesurements t different loctions y m in the fr field (e.g. using microphone-rry), the correltion of φ with the delyed nd summed up pressure signls p f reds: S φ,p f (x,x q,τ) = N = N N n= N n= [ φ (x,t n ) p f (x q,t n + τ) ], [ φ (x,t n ) ] M w m p(y m,t n τ mq + τ). m= Here w m is n pproprite weighting fctor for ech microphone signl, x q is chosen point in the flow field nd τ mq = y m x q /c is the trvel time from x q to y m with the speed of sound c. After rerrnging one otins: S φ,p f (x,x q,τ) = [ ] M N m= N φ (x,t n )w m p(y m,t n τ mq + τ), n= = M [ wm S φ,p (x,y m,τ τ mq ) ]. (4) m= Thus, the summtion of the time-shifted nd weighted correltion functions is equivlent to direct clcultion of the correltion function etween the delyed nd summed up pressure signls with the ner-field quntity φ. The dvntge of using Eq. (4) is tht the computtion time for the summtions over m is comprtively smll, once the correltion functions for ll microphones re clculted. Note tht in the investigtion presented here, the cross-correltion coefficient is the mjor ojective. Therefore S φ,p f (x,x q,τ) needs to e normlized y σ φ nd σ p f. But ssuming ergodicity, σ p f cn e clculted from reduced numer of pressure smples, resulting in negligile computtion time. The numer of microphones M is usully smll compred to the numer of recorded PIV smples N. 3

4 EXPERIMENTS in first step, the flow configurtion of cylinder wke hs een investigted in closed testsection. Figure shows schemtic setup nd picture of the configurtion. The experiments y/d 3,4 y U 7 θ 8,7 d = 5mm r x/d 9 Mirror Cmer Microphone 3,4 Cylinder Figure : PIV nd microphone mesurement of cylinder wke flow. : Schemtic setup of the experiment. The dshed squre indictes the PIV field of view. : Picture of the experimentl setup. The PIV cmer is mounted on the wind tunnel ceiling nd records prticle imges vi n mirror locted upstrem. re conducted in the..4m Göttingen type wind tunnel with closed test section nd reverernt side wlls. The Reynolds-numer is Re = 9 sed on cylinder dimeter of d = 5mm nd free strem velocity U =.55 m/s. The microphone is lterlly shifted t n ngle of θ = 5 t distnce r/d = 4.7 to the cylinder. The smpling rte for the pressure signl is f p =.4kHz. Velocity dt re cquired with D-C PIV system t f s =.5Hz. In next step the correltion technique hs een pplied to rod-irfoil flow configurtion y mens of simultneous microphone-rry nd PIV mesurements [4]. In such configurtion the irfoil undergoes rodnd perturtion dominted y the turulent periodic shedding frequency of the vortex seprting from the rod. Compred to the flow field generted y single cylinder, the rdited noise is spred over wider rnge of frequencies. The outline of the experimentl setup is depicted in Fig.. Experiments were conducted in n erocoustic open-jet, closed-circuit wind tunnel t Re c = 5 sed on chord-length of c = 5mm nd free strem velocity U = 5 m/s. The spn of the configurtion is s = 8mm. For ll mesurements presented here the cylinder is shifted to y rod /c = 6.5mm, in order to include n lmost turulence free section in lower region of interest. A numer of 87 microphones re rrnged in the plne y/c = 8 t positions depicted in Fig. c ( f p = 5kHz). A coplnr multiplne PIV system hs een used ( f s =.7Hz), providing sttisticlly independent smples of the temporl derivtive of the velocity vector-field. In more recent investigtion the correltion technique is tested on rodnd erocoustic 4

5 3rd Berlin Bemforming Conference Henning, Koop nd Ehrenfried Cylinder y = 6.5 mm. y/c -. NACA Airfoil c = 5 mm U x/c 3 z/c c x/c Figure : PIV nd microphone-rry mesurement of rod-irfoil configurtion. : Schemtic setup of the experiment. The dshed squres indicte the PIV fields of view. : Picture of the used microphone-rry. 87 microphones re rrnged in the plne y/c = 8 t positions depicted in c. source. The flow inside jet ws chosen ecuse vriety of experimentl results re ville for comprison [7,, ]. Mesurements hve een performed on cold jet in the region of the potentil core t three different Mch numers M =.5, M =.7 nd M =.9. The cold jet ws generted y 5 mm dimeter (D) nozzle mounted on settling chmer of mm in dimeter nd pproximtely.5 m in length. A numer of microphones ( f p = 5 khz) re rrnged t different distnces r to the nozzle exit nd different ngles θ etween the jet xis nd the direction of oservtion (see Tle ). In order to otin ll three velocity components in plne, D-3C Stereo-PIV system is used in two different fields of view s shown in Fig. 3. The setup in this experiment ws chosen to llow proof of concept of the presented correltion technique nd is not optimized for the erocoustic investigtion of the jet-flow field itself. For exmple the test-fcility is not nechoic. Acoustic sorent mteril ws plced round the vicinity of the nozzle only nd not t the ceiling nd wlls of the room. 5

6 y/d y m z/d r m Nozzle θ m x/d Figure 3: Schemtic setup of the experiment on cold jet in the region of the potentil core. The dshed squres indicte the PIV fields of view. Tle : Microphone Positions t different distnces r to the nozzle exit nd different ngles θ etween the jet xis nd the direction of oservtion. All microphones re locted t the hlf-spce y >. m θ r/d z/d RESULTS AND DISCUSSION 3. Cylinder-Wke All quntities nd xes re mde dimensionless using the cylinder dimeter d nd the free strem velocity U =.55m/s. x nd y re locl coordintes in the mesurement plne, where the x- xis points in the men flow direction. The sptil resolution of the PIV mesurement is.6mm in the x- nd y direction resulting from interrogtion windows with size of 3. 3.mm (3px 3px, 5% overlp). The thickness of the light-sheet is pprox..5mm. A numer of 5 PIV snpshots re considered for the clcultion of the cross-correltion. The temporl evolution of the cross correltion coefficient R v,p t [x/d;y/d] = [.6;.55] is plotted in Fig. 4. The correltion ecomes significnt t τ.4s nd fluctutes over time in sine type oscilltion with mximum vlues of out R v,p =. t τ =.5s. Hence forwrd the mplitude of R v,p decreses with τ. Both R u,p nd R v,p show this periodic ehvior with phse shift of π/ with respect to ech other. This is illustrted in Fig. 4 which shows the instntneous distriution of the normlized cross correltion (R u,p R v,p ) depicted s vector plot for τ = ms. 6

7 Rv,p y/d τ [ms] x/d Figure 4: : The temporl evolution R v,p t [x/d;y/d] = [.6;.55]. : Instntneous distriution of (R u,p R v,p ) depicted s vector plot for τ = ms. The oserved results re very different from those we present in section 3. for the correltion function etween the coustic pressure nd the velocity fluctution in jet. In the cse of jet, typiclly the correltion function shows only reltively short event which consists minly of single positive nd negtive deflection. The regulr oscilltions of R v,p in the present result cn e explined y the strong coherence of the periodic structures in the flow field, illustrted y the cross-correltion R v,v t [x/d; y/d] = [; ] depicted in Fig. 5. The structures generte sound field with the sme periodicity, which is perceived s tone. Hence, the correltion etween the velocity fluctutions nd the coustic pressure shows the sme oscilltions s the input signls. The lrger temporl coherence of oth signls leds lso to significnt correltion t negtive τ vlues. This is lso oserved y [] for the correltion etween the velocity t two different positions in the cylinder wke. The specific shpe of the envelope of the plot R v,p s function of τ cn e explined y reflections t the side wlls of the test section, which hve strong influence on the microphone signl s cn e seen from the envelope of the utocorreltion-function R p,p depicted in Fig. 5. Without reflections one would expect the mximum mplitude of the correltion function t vlue τ = r/c which mtches with the trvel time directly from the cylinder to the microphone. But in the present experiment multiple reflected signls re lso received y the microphone nd contriute to the correltion function t lrger positive dely times τ, which correspond to trvel distnces of severl times the chnnel width. A complicted interference of the directly emitted nd the reflected wves tkes plce in the test section, nd the superimposed wves interct constructively nd destructively. Depending on the coherence length in the flow nd the position of the microphone, the mximum mplitude of the correltion function cn e shifted towrds lrger τ vlues, s is oserved here. The dely time of τ =.5s is equivlent to trvel distnce of out 8m. This shift cnnot e ttriuted to the lrger sound trvel time from the cylinder to the microphones, since this difference would e of the order of 5 s Thus, in the present cse the correltion function is clerly dominted y reflected wves. The widespred distriution of R v,p is depicted in Fig. 6 for τ = ms. Figure 6 shows the temporl evolution of the normlized correltions R v,p long the xis y/d =.85. The solid 7

8 line represents the propgtion time τ p of the flow structures with the time verged velocity U(x) = u(x) long the xis with τ p (x) = ( x)/u(x) + r/c. It cn e seen, tht for x/d > the phse shift of R v,p corresponds to the group velocity U(x) of the flow structures trveling the downstrem distnce x from the rod, nd cnnot e ttriuted to the lrger sound trvel time from the loctions x to the microphone. Rp,p τ [ms] y/d x/d Figure 5: : Autocorreltion-function R p,p of the pressure fluctutions p. : Sptil distriution R v,v t [x/d; y/d] = [; ]. y/d x/d x/d τ [ms] Figure 6: : Sptil distriution of R v,p for τ = ms. Temporl evolution of R v,p long the xis y/d =.85. : The solid line depicts τ p (x) = ( x)/u(x) + r/c. 3. Rod-Airfoil Unless otherwise specified, the following results hve een otined from the configurtion with U = 5m/s. The xes in the figures re scled to the chord-length c. x nd y re locl coordintes in the mesurement plne with the origin t the cylinder xis for y rod /c =. The 8

9 x-xis points in the men flow direction. Some fields of view include res of missing vectors corresponding to shdow zones of the lser light-sheet. The sptil resolution of the PIV mesurement is.94mm in the x- nd y direction (interrogtion-window size: 48px 48px; 5% overlp). The thickness of the lightsheed is pprox. mm. A numer of 5 PIV snpshots re considered for the clcultion of the cross-correltion. The cross-correltion coefficient is clculted using Eq. (4) using the signls of ll 87 microphones. The temporl evolution of the cross-correltion coefficient R v,p t position [x/c;y/c] = [.98;] is plotted in Fig. 7. The coefficient fluctutes over time in sine-type oscilltion with mxi-.. Rv,p y/c τ [ms] x/c Figure 7: : The temporl evolution of the cross-correltion coefficient R v,p t position [x/c;y/c] = [.98;]. : The instntneous distriution of the cross-correltion coefficient [R u,p, R v,p ] for τ = ms depicted s vector plot. mum vlues of out R v,p =.3. The envelope of R v,p s function of τ shows no skewness nd the distriution is symmetric round mximum, locted t τ = ms. This results differ significntly from findings in section 3., where the rod is instlled in closed test section with reverernt side wlls. Therein, shift of the correltion coefficient towrds lrger τ vlues is oserved, not mtching the sound trvel time directly from the cylinder to the instlled in-flow microphone. This difference in shpe s well s the lrger kurtosis of the envelope hs een ssigned to the dominnce of the reflected wves from the side wlls. This is not the cse in the present investigtion where strong reflections re dmped y the nechoic chmer. The fundmentl difference of the sound field cn e seen y compring the utocorreltion functions of p depicted in Fig. 7 nd 5 (section 3.). Both figures re lso illustrting the strong coherence of the pressure fluctutions nd therewith the need for low smpling frequency in order to otin sttisticlly independent PIV snpshots. Fig. 7 shows the instntneous distriution of the cross-correltion coefficient [R u,p, R v,p ] for τ = ms depicted s vector plot. Vorticl structures split t the leding edge nd stretch long the irfoil. The resulting pttern hs strong similrity to the first POD modes, stisfctorily descriing the vortex-irfoil interction (see Jco et l. [5] nd references therein). The results in section 3. hve lredy indicted tht the correltion technique functions s extrction of the most energetic structures in the flow, which re responsile for the sound generting process. Figure 9 shows the sptil distriution of R v,p in the region etween the rod nd the irfoil for τ =. The sign of R v,p lterntes etween positive nd negtive vlues downstrem of the 9

10 Rp,p τ [ms] y/c x/c Figure 8: : The utocorreltion-function R p,p where p is the pressure fluctution from single microphone t y m = [x/c;y/c;z/c] = [5.7; 8;.9]. : The cross-correltion R v,v t [x/d; y/d] = [; ] y/c x/c Figure 9: Sptil distriution of R v,p in the region etween the rod nd the irfoil for τ =. cylinder nd the vlues re mximl in the ner-wke of the cylinder nd not t the irfoil LE. This is remrkle, since the leding edge is suspected to e the min erocoustic source region. But the flow structures ecome less periodic with incresing downstrem distnce from the rod nd most likely more three dimensionl. Therefore nd ecuse of the resulting higher noise level of v nd u in the LE region, lower correltion coefficient is oserved in this re. It will e shown in the following tht the temporl evolution of R v,p with τ supports this explntion; nd tht the min source region cn indeed e ttriuted to the leding edge of the irfoil y mens of the correltion technique presented here. Figure shows the temporl evolution of the normlized correltions R v,p long the xis y/c =. The solid line represents the propgtion time τ p of the flow structures with the time verged velocity U(x) = u(x) long the xis with τ p (x) = (x LE x)/u(x) + r/c, where x LE is the coordinte of the irfoil leding-edge, nd the dshed line depicts r/c only. The position of the mximum vlues of

11 R v,p long x re mrked y red dots. For x/c >.3 the phse shift of the R v,p corresponds to the group velocity U(x) of the flow structures trveling the downstrem distnce x from the rod nd cnnot e ttriuted to the lrger sound trvel time from the loctions x to the microphone. x/d τ [ms] -.4 Figure : Temporl evolution of the normlized correltions R v,p long the xis y/c =. Solid line: τ p (x) = (x LE x)/u(x) + r/c ; dshed line: r/c ; dots: mx(r v,p )(x). 3.3 Jet The following results hve een otined from the M =.5 configurtion. The xes in the figures re scled to the nozzle dimeter D. In the following p re the pressure fluctutions from microphone No. 4 locted t r/d = 74 nd θ = 35 (see Tle ). Two fields of view with size of 3.89D.5D hve een investigted. The loctions of their lower left corner re [x/d; y/d] = [.73;.87] nd [x/d; y/d] = [6.6;.87] respectively. x, y nd z re lefthnded crtesin coordintes with the origin t the center of the nozzle exit. The x-xis points in the men flow direction. A numer of 8 PIV snpshots re considered for the clcultion of the cross-correltion. In Fig. [R u,p, R v,p ] is depicted s vector field for τ =.57ms. Here the retrded time τ = τ r/c is used with r = y x where y denotes the microphone position, x = [x/d; y/d] = [;] nd c is the mient sound speed. A regulr pttern of vorticl structures cn e identified nd mximum vlues cn e oserved t the core region of the jet s well s in regions outside the jet where the medium is t rest on verge. It is ssumed tht in the outer region the coustic prticle velocity in the ner-field correltes with p. The temporl evolution of R vm,p is plotted in Fig. for the position [x/d; y/d] = [3.;] in the core-region of the jet () nd t [x/d; y/d] = [.87;.7] outside the jet (). Here, v m is the velocity component in the direction of the microphone. Note tht R vm,p in Fig. outside the jet hs mximum first with respect to the time dely τ fter ecoming minimum, in contrst to the temporl evolution of the correltion function in the core region depicted in Fig.. The shift towrds negtive τ -vlues cnnot e ttriuted to the difference in sound trvel time from the jet-core region to the microphones.

12 An explntion could e to consider the so clled lip-noise (see [9]) s the min source of noise t the Mch-numer presented here, since extrpolting the time shift from the τ -vlues one would end t the nozzle position for τ =..5 y/d x/d Figure : [R u,p, R v,p ] depicted s vector field for τ =.57ms. τ = τ r/c with r = y x..3. R pv m τ [ms] R pv m τ [ms] Figure : Temporl evolution of the cross-correltion coefficients (R vm,p) with τ [x/d; y/d] = [3.; ], right: [x/d; y/d] = [.87;.7]. left: 4 CONCLUSION The presented tests show tht the PIV method cn e used to otin correltion function etween ner-field quntities nd the generted coustic pressure. The correltion technique presented here hs een successfully pplied to cylinder-wke, rod-irfoil configurtion nd

13 cold jet. The otined coefficient mtrix provides time nd spce resolved informtion out the sttisticl dependency etween flow structures nd the coustic pressure, even under nonnechoic conditions. References [] L. Chtellier nd J. Fitzptrick. Sptio-temporl correltion nlysis of turulent flows using glol nd single-point mesurements. Experiments in Fluids, 38, , 5. [] P. J. F. Clrk nd H. S. Riner. Direct correltion of fluctuting lift with rdited sound for n irfoil in turulent flows. J. Acoust. Soc. Am., 46(3), 8 85, 969. [3] A. Henning nd K. Ehrenfried. On the ccurcy of one-point nd two-point sttistics mesured vi high-speed piv. In 4th Int. Symp. on Appl. of Lser Techn. to Fluid Mechnics. Lison, Portugl. 8. [4] A. Henning, L. Koop, K. Ehrenfried, A. Luterch, nd S. Kroeer. Simultneous multiplne piv nd microphone rry mesurements on rod-irfoil configurtion. 5th AIAA/CEAS Aerocoustics Conference, Mimi, USA, AIAA-9-384, 9. [5] M. C. Jco, J. Boudet, D. Cslino, nd M. Michrd. A rod-irfoil experiment s enchmrk for rodnd noise modeling. Theoret. Comput. Fluid Dynmics, 9, 7 96, 5. doi:.7/s [6] H. K. Lee nd H. S. Riner. Direct correltion of noise nd flow of jet. J. Acoust. Soc. Am., 5(5), 8 9, 97. [7] J. Pnd, R. G. Sesholtz, nd K. A. Elm. Investigtion of noise sources in high-speed jets vi correltion mesurements. J. Fluid Mech., 537, , 5. [8] R. Rckl nd T. E. Siddon. Cuslity correltion nlysis of flow noise with fluid dilttion s source fluctution. J. Acoust. Soc. Am., 65(5), 47 55, 979. [9] D. R. Regn nd W. C. Meechm. Determintion of lip noise y correltion mesurements. The Journl of the Acousticl Society of Americ, 55(S), S73 S73, 974. doi:./ [] H. S. Riner. Qudrupole correltions governing the pttern of jet noise. J. Fluid Mech., 38(), 4, 969. [] M. Schffr. Direct mesurement of the correltion etween xil in-jet velocity fluctutions nd fr field noise ner the xis of cold jet. J. Sound Vi., 64(), 73 83, 979. [] T. E. Siddon. Surfce dipol strength y cross-correltion method. J. Acoust. Soc. Am., 53(), ,