Analysis and Control of Flow-Acoustic Feedback-Loop Interactions in Transitional Airfoils

Transcription

1 Analysis and Control of Flow-Acoustic Feedback-Loo Interactions in Transitional Airfoils Vladimir GOLUBEV 1 ; La NGUYEN 2 Reda MANKBADI 3 ; Michel ROGER FCAAP Embry-Riddle Aeronautical University USA 4 LMFA Ecole Centrale de Lyon France ABSTRACT Our recent numerical and eerimental efforts are reviewed eamining flow-acoustic resonant interactions in transitional airfoil boundary layers and means of control of the resulting rominent tonal trailing-edge noise sources. Eerimentally recorded unsteady resonses of loaded transitional NACA0012 airfoil reveal oerational regimes characterized by the resence of the shifted ladder-tye tonal structures with dual velocity deendence observed in the surface ressure and the acoustic signals. High-fidelity numerical efforts emloy a 6 th -order Navier-Stokes solver imlementing a low-ass filtering of oorly resolved high-frequency solution content to retain numerical accuracy and stability over a range of transitional flow regimes. 2D and 3D ILES) numerical eeriments investigate the behavior of the boundary-layer statistical moments during the transitional flow regimes characterized by the resence of searation regions and the resulting formation of the highly-amlified instability waves scattered into noise at the airfoil trailing edge thus triggering and sustaining the acoustic feedback-loo rocess. The current aer articularly focuses on the sensitivity of the airfoil flow-acoustic interactions and the resulting acoustic signature) to the ustream flow conditions. Keywords: Flow-Acoustic Interactions Transitional Airfoil ILES I-INCE Classification of Subjects Number: INTRODUCTION The subject of flow-acoustic resonant interactions generally encomasses a number of interfering hysical henomena. Their intricate interlay renders this area of research a articularly challenging task with inherently multi-scale hysics sometimes oorly understood. The flow-acoustic interactions are usually characterized by the resence of self-sustained shear-layer flow instabilities couled with a resonant acoustic feedback mechanism. For high-seed flows the eamles of jet screech and cavity oscillations are well known and have been etensively studied in numerous works reviewed e.g. by Raman 1) and Colonius 2) both from the basic hysics and the flow control rosective. The current work on the other hand addresses related henomena for wall-bounded rather than free-shear) airfoil flows and at low seeds which have been treated less etensively in the ast and still remain the subject of some controversy as reviewed in reference 3). It is recognized that distinct acoustic signatures generated by small aircraft low-seed rotors and fans and wind-turbine blades are inherently linked to the isolated airfoil trailing-edge tones which are suddenly and in fact often intermittently) roduced during certain transitional flow regimes. The first comrehensive eerimental study by Paterson et al 4) focused on tonal noise emitted by symmetric NACA airfoils in a Reynolds number range corresonding to full-scale helicoter rotors. Their key finding illustrated in Fig. 1 shows an unusual ladder-tye structure staging) of tones wherein the eak frequencies are scaled ~U 1.5 U is the free-stream velocity) with sudden jums aearing between the rungs of the ladder scaled ~U 0.8. Tam 5) roosed a feedback-loo mechanism to elain the tonal staging with his original scenario of localized wake source corrected and further elaborated by Arbey & Bataille 6) based on a series of eeriments with NACA0012 airfoils. Their recorded acoustic sectra generally 1 golubd1b@erau.edu 2 nguye276@erau.edu 3 mankbadr@erau.edu 4 Michel.Roger@ec-lyon.fr Inter-noise 2014 Page 1 of 14

2 Page 2 of 14 Inter-noise 2014 confirmed the tonal ladder structure of Paterson et al 1973) to roduce for a given velocity in the range of U=20 40 m/s Re c = ) a narrowband set of equidistant frequencies suerimosed on a broadband hum. In the interretation first suggested by Longhouse 7) such contribution was attributed to Tollmien-Schlichting T-S) instability waves develoing in the boundary layer and scattering as sound at the airfoil trailing edge. The acoustic feedback loo was resumed to be generated between selected trailing-edge frequency tones and the most amlified T-S wave based on the condition that both sound and convected waves are in hase at the oint of the instability aearance. In reference 2) we re-visited the roblem using comlementary eerimental and numerical studies investigating the resence of the flow-acoustic feedback interactions in NACA0012 airfoil in the transitional flow regimes. In articular arametric eerimental studies were conducted both with uniform and low-turbulence inflows with boundary-layer triing on one or both sides) and without triing at different angles of attack and for a range of flow seeds corresonding to M= Re c = ). Some results of these studies are reviewed in the current work. The numerical aroach emloyed high-accuracy 2D analysis based on the assumtion that the investigated flow regimes retain rimarily laminar boundary-layer structures. In other words although the local searation zones should induce inherently 3D structures the breakdown rocess was resumed to be at an early transitional stage so that the mechanism of the tonal noise generation cou ld still be well described using 2D analysis. More recently a comrehensive 3D Imlicit Large-Eddy Simulation ILES) study has been conducted to test such assumtion with the comarison against the 2D study discussed below. Particular emhasis is on the ability of both analyses to accurately resolve the laminar searation zones shown to lay a major role in the instability amlification saturation and reservation dominating the feedback-loo interaction rocess. The current numerical efforts include a study of the effect of ustream turbulence with different intensity levels on the flow-acoustic resonant interactions and the resulting unsteady aerodynamic and acoustic airfoil resonses. The results are further comared with linear stability analyses to eamine the amlification rates and the accumulated growth of the dominant frequency modes for different ustream flow conditions. Figure 1 Left: airfoil ladder-tye frequency structure from Paterson et al 4). Right: feedback loo in airfoil flow-acoustic interactions from Longhouse 7). 2. EXPERIMENTAL RESULTS Eeriments 2) conducted in anechoic low-seed wind tunnel facility at Ecole Centrale de Lyon ECL) Fig. 2) eamined the tonal signature of the low-seed NACA0012 airfoils for a range of transitional flow regimes characterized by variable flow velocity angle of attack and unsteady inflow conditions to carefully ma regions of tonal roduction including effects of ustream unsteadiness. Far-field acoustic measurements were erformed in the mid-san lane using a single microhone on a rotating arm to rovide an overview of frequency-angle characterization and sectral directivity of the sound. The wall-ressure fluctuations were measured using remote-microhone robes RMPs) flush-mounted along the airfoil surface at the locations shown in Fig. 3. Page 2 of 14 Inter-noise 2014

3 y mm ) Inter-noise 2014 Page 3 of 14 D C B A mm ) C' Figure 2 - Picture of ECL facility showing the nozzle flow and the horizontal end-lates. Figure 3 - Locations of RMPs on NACA-0012 mock-u red symbols) and reference oints for the analysis of wall-ressure fluctuations. Additional measurements included hot-wire traversing robe analysis of the near-wake velocity rofiles 2 mm downstream of the trailing edge) and flow visualizations that emloyed distemer fluid to eamine laminar turbulent and/or searated boundary layer regions and articularly identify the resence of laminar searation bubbles in the test case studies. Tests were conducted with rectangular airfoil sections of 8cm and 10cm chords and of 30 cm san asect ratio of nearly 3) both in clean flow and with controlled inflow disturbance with boundary-layer triing on one or both sides) and without triing at different angles of attack and for a range of flow seeds corresonding to M= Re c = ). Triing a transitional boundary layer forces transition to turbulence thus eliminating the onset of coherent instabilities. The one-side triing was suggested by results from the DNS study of Desquesnes et al 8) who roosed another view on the multi-tone acoustic resonse involving interaction of the main and the secondary feedback loos on both sides of the airfoil. However the resent results demonstrate that the ladder-tye acoustic tonal structure may reveal itself without such interaction. This is emhasized in Fig. 4 where the noise amlitude measured at 90 to the flow and at 2 m in the mid-san lane is lotted as a function of frequency and flow seed. The results were obtained for the one -side tried airfoil of 8 cm chord at geometrical angles of attack -5 0 and +5. Aart from the low-frequency contribution at the bottom right corner of each color ma the tonal signature is clearly observed in each case with different amlitudes and frequency ranges. The global oblique trace follows f s ~U 1.5 yellow atterns) though the trend is less ronounced for Configuration B. Suerimosed in red are the lines rungs) corresonding to tones with f~u Overall multile tones are observed at a given flow seed as shown in Fig. 4 and further in Fig. 5. The clearest ladder-tye structure is found at zero angle of attack Configuration A) and is close to observations by Arbey & Bataille 6). In Configuration B the triing is on the airfoil ressure side and the sound originates from instabilities amlifying along the suction side. The tones are less numerous and at much lower level but in contrast they can be detected at lower flow seeds. In Configuration C the triing is on the suction side and visualizations suggest that flow searates over a large art of the ressure-side boundary layer. Multile tones are also detected but with a less organized structure. Moreover their occurrence requires significantly higher flow seed. Based on the obtained eerimental data it may be concluded that two searate henomena are in fact at lay in the observed ladder-tye structures of acoustic tones. The rungs with f~u 0.8 are related to the amlified instability waves trailing-edge scattering while the effectively roduced vorte shedding corresonds to the dominant frequencies of each rung scaled with f s ~U 1.5. Inter-noise 2014 Page 3 of 14

4 Page 4 of 14 Inter-noise 2014 Figure 4 - Frequency versus flow-seed charts of airfoil tonal noise. One-side tried NACA cm chord length triing stri on the ressure side +5 ) and on the suction side -5 ). Figure 5 - Tyical sound sectra measured at 5 angle of attack at various flow seeds. B: triing on ressure side C: triing on suction side BC: no triing. To show the effect of a non-uniform inflow on flow-acoustic resonant interactions eeriments were also conducted with a weak grid-generated ustream turbulence. The grid mesh installed in the nozzle duct was of 1 cm width and the diameter of the mesh wires was 1.5 mm. The turbulence sectrum measured in the resence of the grid fitted well with the homogeneous isotroic von Kármán model accounting for an additional Gaussian attenuation to reroduce the dro towards the Kolmogorov scale with cut-off frequency around 9500 Hz). The corresonding integral length scale was 3.5 mm and the rms velocity was 0.2 m/s 0.8 % turbulence rate). The results in Fig. 6 comare with Fig. 4) show that the eternal boundary-layer ecitation suresses all tones associated with the Page 4 of 14 Inter-noise 2014

5 Inter-noise 2014 Page 5 of 14 Inter-noise 2014 Page 5 of 14 acoustic feedback i.e. 0.8-ower deendence in the ladder-tye tonal structure) while the 1.5-ower deendence is still reserved for the low turbulence intensity. Further details of this eerimental study may be found in reference 2) but the effects of the ustream turbulence are further discussed below based on the results of numerical simulations. Figure 6 - Frequency versus flow-seed charts for a symmetrical NACA-0012 airfoil of 8 cm chord length set at 0 left) and 5 right) angles of attack in low-intensity ustream turbulence. 3. NUMERICAL FORMULATION The emloyed numerical formulation 9) solves a set of the comressible Navier-Stokes equations reresented in strong conservative time-deendent form in the generalized curvilinear comutational coordinates ξηζτ) transformed from the hysical coordinates yzt): The solution vector is defined in terms of the flow density ρ Cartesian flow velocity comonents u v w) and flow secific energy with assumed erfect gas relationshi connecting the flow ressure temerature T and the freestream Mach number M γ is the secific heat ratio). The other variables in Eq. 1) include the inviscid flu vectors defined by the transformation Jacobian the metric quantities defined e.g. as etc. and the transformed flow velocity comonents S H G F H G F J Q v v v i i i ] [ Re 1 ) ) e w v u Q ) 2 1 1) w v u M T e 2 / M T u e wu vu uu u F t z y i ) v e wv vv uv v G t z y i ) w e ww vw uw w H t z y i ) ) )/ t z y J J / ) 1 1) 2) 3)

6 Page 6 of 14 Inter-noise 2014 u u v w t v u v w t w u v w t y y y z z z 4) The viscous flu vectors in equation 1) are defined e.g. in reference 10) while S reresents the source term which in the current work generates an incomressible ustream turbulence ustream of the wing section. All flow variables are normalized by their resective reference freestream values 2 ecet for ressure which is nondimensionalized by u. Note that the governing equations are reresented in the original unfiltered form used unchanged in laminar transitional or fully turbulent regions of the flow with reference 11) roviding further details on the code s emloyed ILES rocedure in which a high-order low-ass filter oerator is alied to the deendent variables during the solution rocess in contrast to the standard LES addition of sub-grid stress SGS) and heat flu terms. The resulting filter selectively dams the evolving oorly resolved high-frequency content of the solution. The code emloys a finite-difference aroach to discretize the governing equations with all the satial derivatives obtained using the high-order comact-differencing schemes from reference 12). For the wing section comutations of the current aer a sith-order scheme is used. At boundary oints higher-order one-sided formulas are utilized which retain the tridiagonal form of the scheme. In order to ensure that the Geometric Conservation Law GCL) is satisfied the time metric terms are evaluated emloying the rocedures described in detail in reference 11). Finally the time marching is accomlished by incororating a second-order iterative imlicit aroimately-factored rocedure as described e.g. in reference 9). 4. NUMERICAL RESULTS The original 2D numerical study of reference 2) emloyed a O-mesh generated about NACA0012 airfoil and efficiently artitioned into sets of overlaed blocks assigned to different rocessors during arallel imlementations. The mesh was carefully clustered near the airfoil surface to achieve the wall-normal and wall-tangent mesh sizes of Δy/c= and Δ/c=10-3. In terms of the wall units y w + /c= estimated for the characteristic flow condition with M=0.1 and Re c = such grid refinement corresonds to the non-dimensional values of Δy + 1 and Δ + =20 with 12 grid oints clustered in the region 0< y + <10. For 3D simulations such grid arameters corresond to a high-resolution LES according to estimates in Wagner et al 13).209). The grid is also finer comared to the mesh emloyed in a similar DNS study by Desquesnes et al 8) conducted using the mesh with Δy/c= and Δ/c= Table 1 - Grids emloyed in 2D and 3D studies. Cases Dimension Δy/c Δ/c 2D BASE D FINE D FINEST D BASE D FINE The 2D aroach may be justified based on the assumtion that though inherently unsteady the investigated flow regimes remain rimarily laminar with ossible searation zones) and may just start to ehibit transitional features without an etended turbulent region. To test this assumtion 3D ILES study of reference 14) emloyed a wing section with sanwise etension of 0.2c with eriodic conditions alied at the san ti lanes. The comarative analysis emloyed a matri of 2D and 3D case studies using the grid configurations shown in Table 1. Page 6 of 14 Inter-noise 2014

7 Inter-noise 2014 Page 7 of 14 All comutations discussed in the current work emloy a hysical time ste of sec corresonding to the code non-dimensionalized time ste of In the simulations the steady-state flow conditions are first reached after marching for stes. The ressure signals are then recorded for over stes hence collecting the data samle for 0.26 sec with the samling rate of 62.7 khz achieving the frequency resolution of f=3.83hz. 4.1 Uniform Ustream Flow The comarison of 2D and 3D ILES redictions was conducted in reference 14) for a test case selected from the measurements 2) erformed for NACA0012 airfoil with the chord c=0.1m installed at the geometric angle of attack α=5 0. In the numerical analysis the calculations were erformed for α=2 0 to account for wind-tunnel corrections according to reference 15). The selected benchmark case corresonds to the mean flow velocity of 25 m/sec M=0.072) with clean ustream flow. The analysis was conducted for Re c = closely reresenting the eerimental conditions. The reliminary 2D study of reference 2) emloyed the baseline grid configuration with the obtained results successfully validated against DNS analysis by Desquesnes et al 8). Furthermore an ecellent match of the redicted sectral eak frequencies against the feedback-loo formula was achieved. 2D and 3D ILES studies of reference 14) etended the 2D analysis of reference 2) with focus on investigating effects of various numerical arameters on the boundary-layer statistics and gaining further insight in the flow-acoustic interaction rocess. Results of the sectral analyses were eamined in comarison with the eerimental data 2) at the monitor oints indicated by letters A B C suction side) and C ressure side) in Fig. 3. Deviations were observed between the baseline and the fine grid configurations articularly on the uer surface towards the trailing edge but the comarison of the results obtained using the fine and the finest meshes as secified in Table 1) showed minor differences. Hence the fine mesh was emloyed in the subsequent numerical studies. Fig. 7 comares the sectra of the surface ressure time histories at the selected monitor oints obtained using the fine meshes in 2D and 3D analyses. 3D results show a dro in the broadband levels accomanied by an overall better agreement with eerimental data. This is articularly notable for some of the rominent tones although the overall comarison of tonal resonse redictions in 2D and 3D analyses may be considered satisfactory. Hence this to a certain etent may justify the 2D assumtion. At the same time the results still ehibit significant differences with eeriment in the broadband levels which may be related to the eerimental installation effects as indicated in reference 16). Figure 7 - Comarison of 2D magenta) and 3D blue) redicted using fine meshes) vs. measured green) airfoil surface ressure sectra at selected monitor oints on suction and ressure sides. For the baseline grid configuration the mean ressure distributions have been reviously validated against eerimental data in reference 2). In Fig. 8a) the RMS ressure distributions obtained from 2D simulations with baseline and fine meshes corresond well with one another and sustain the levels nearly to the trailing edge. In contrast 3D results indicate a raid decrease of RMS ressure amlitudes after reaching the eak levels which aears to be related to the sanwise energy redistribution as illustrated further below. The eak RMS levels obtained using the fine mesh are similar in 2D and 3D comutations but the grid differences are more ronounced in 3D results. Inter-noise 2014 Page 7 of 14

8 Page 8 of 14 Inter-noise 2014 a) b) c) Figure 8 a) Airfoil surface RMS ressure distributions; Suction-side: b) Skin friction coefficient c) MaV t_rms ). Locations of the searated regions can be deduced from the surface distribution of the skin friction coefficient shown in Fig. 8b) for the suction side. The searated regions aear to form at =0.45c with a very thin searated layer followed by a reattachment oint at =0.67. Fig. 8c) quantifies the growth of the boundary-layer velocity fluctuations indicative of instability growth) on the suction side by showing the redicted evolution of the RMS maima for the tangential velocity comonents V t. The maimum instability growth and saturation are clearly associated with the laminar searation zones. Note that the results correlate well with RMS ressure distributions shown in Fig. 8a) ehibiting a ronounced decrease both in the ressure and velocity fluctuation levels in 3D analysis in contrast to 2D results. Along the ressure side the results not shown) indicate much less noticeable boundary-layer dynamics ecet very close to the trailing edge where the formed searated region is accomanied by raid growth of mav t_rms ) and RMS ressure in Fig. 8a)). Overall the results indicate that both suction and ressure sides may contribute to the flow-acoustic resonant interactions in this flow regime. a) b) Figure 9 - Samle-averaged vorticity and ressure contours in a) 2D study; b) 3D study including Q-criterion on the right) The boundary-layer dynamics is further illustrated in Fig. 9 showing the samle-averaged vorticity lus Q-criterion) and ressure contours obtained from 2D and 3D fine-mesh simulations. The aearance of the fine-scale vortical structures with strong sanwise redistribution towards the trailing edge in 3D studies Fig. 9b)) contributes to the corresonding reduction of RMS ressure and velocity levels observed in Figs. 8a) and 8c). The boundary-layer dynamics is also noticeable on the ressure side but very close to the trailing edge. Reference 17) initiated numerical studies investigating effect of the ustream flow velocity in the range of 25 to 45 m/s on the feedback-loo rocess and the corresonding sectral resonse. Fig. 10 comares the latter results obtained in 2D study for the ustream velocity of 25 m/s against those obtained for 45 m/s with the corresonding shift in the Re c number between and in contrast to reference 17) where it was ket constant). The rimary tones in the surface ressure sectra are also shifted and the tonal eak levels increase for 45 m/s in accordance to the attern roosed by Lowson et al 18). The observed tonal shifts rimarily scale with 0.8-ower velocity deendence tyical of instability-roduced acoustic signature). The shedding-dominated 1.5-ower deendence associated with sudden jums in the ladder-tye frequency structure of rimary tones Fig. 1) does not easily reveal itself in fact not at all in Nash et al 19)) and this asect will be re-visited in Page 8 of 14 Inter-noise 2014

9 Inter-noise 2014 Page 9 of 14 the net section. Figure 10 - Comarison of 25m/s magenta) and 45m/s blue) 2D-redicted airfoil surface ressure sectra at selected monitor oints measured results for 25 m/s are shown in green for reference). 4.2 Turbulent Ustream Flow A novel method to introduce a turbulent flowfield in numerical simulations using a momentum source located in a region ustream of the airfoil 20 21) and based on the random flow generation technique 22) was emloyed in reference 23) to study the effect of ustream flow non -uniformities on the flow-acoustic resonant interactions in NACA0012 airfoil. In the numerical eeriments the ustream turbulence rescribed with non-dimensional integral length scale L=0.035 and intensities I=0.008 and 0.07 was continuously generated in order to collect sufficient statistical data for the sectral analyses. Figure 11 - Comarison of ressure sectra at selected monitor oints for uniform and turbulent inflows. Results in Fig. 11 comare the ressure sectra for the turbulent and uniform flow cases obtained at oints A and A symmetrically located near the trailing edge on the suction and ressure sides corresondingly and in the near field 2 chords above the trailing edge. Shifts in the dominant frequencies are notable and it is also evident that the resonant interactions are not eliminated as a result of the iminging low-intensity turbulence with I= On the contrary more rominent tones are observed for this case on the suction side comared to the case with the uniform ustream flow with the frequency shift in the rimary tones. For the higher turbulence intensity I=0.07) the results indicate a comlete suression of rominent tones and thus the acoustic feedback loo) in the suction-surface sectra due to the turbulent transition. Nonetheless the tonal eaks are still resent at oint A which indicates that the feedback loo remains sustained on the ressure side contributing to the same frequency tones observed in the near field in Fig. 11. Both in the low-turbulence and uniform-flow cases the sectral tonal contents aear rather close in oints A and A and the near field indicating that both sides develo similar acoustic feedback-loo characteristics. Additional information may be derived from the instantaneous vorticity contours shown in Fig. 12. In the low-turbulence and uniform flow cases the instability dynamics on the uer airfoil surface is hase-locked with acoustic modes in the feedback-loo mechanism that cuts on the distinct tones observed in Fig. 11. In contrast in the high-turbulence case the boundary-layer vorticity dynamics on the suction side observed in Fig. 12 is induced by the iminging uncorrelated turbulence modes through the hase-locking mechanism and thus may only roduce a broadband sectrum at oint A. Inter-noise 2014 Page 9 of 14

10 Page 10 of 14 Inter-noise 2014 Figure 12 - Instantaneous vorticity contours for left to right) uniform low-turbulence and high-turbulence flow regimes. Figure 13 - Comarison of ressure sectra at oint A for 25m/s and 45m/s redicted for uniform and low-turbulence I=0.001) cases measured results for 25 m/s are shown in green for reference). Figure 14 Velocity deendence of eak frequencies at oint A for uniform left) and low-turbulence I=0.001) right) cases rimary tones are shown in closed circles). To re-address the ladder-tye velocity-deendence structure of the dominant tones Fig. 1) and their sensitivity to the ustream flow conditions Fig. 13 indicates that just a slight increase in the ustream turbulence level with intensity I=0.001) may roduce a notable rearrangement in the content of the tonal frequencies. The latter aears significant enough to reveal a jum in the velocity deendence of the rimary tone to align with 1.5-ower law at 45 m/s. Note that the shedding-frequency hum is observed even in the uniform-flow case but becomes more ronounced with a distinct tonal signature once a small turbulent ecitation is introduced. Interestingly this observation corresonds to that of Page 10 of 14 Inter-noise 2014

11 Inter-noise 2014 Page 11 of 14 Nash et al 19) who attributed the ersistently observed 0.8-ower velocity deendence of the rimary tonal frequency to their articularly clean eerimental conditions. Different number of ladders in the tonal structures observed in different eeriments may also be related to such sensitivity to the test environment. To comare the growth of the boundary-layer velocity fluctuations in absence and resence of the ustream flow non-uniformities Fig. 15 shows the redicted evolutions of the maima of the RMS of the tangential velocity comonents V t evaluated across the boundary layers on both airfoil sides. a) b) Figure 15 - Evolution of MaV t_rms ) along suction a) and ressure b) sides for turbulent vs. uniform ustream flow conditions. As indicated above the raid growth of the RMS velocity amlitudes is closely correlated with the formation of thin laminar searation zones on both sides of the airfoil. The saturation of such growth aears to be linked to the flow reattachment. For the high-intensity turbulence case with I=0.07 much higher RMS levels are associated with fully turbulent flow conditions on the suction side where the laminar instabilities and the feedback-loo rocess are suressed. In all the considered cases the ressure side aears to sustain the flow-acoustic resonant interactions associated with the raid instability growth through the searation regions forming close to the trailing edge. Such findings are further substantiated by emloying a linear stability analysis imlemented in LASTRAC code 24) solving the linearized Navier-Stokes equations with the assumtion of a quasi-arallel flow. The results based on the comuted time-averaged boundary-layer tangential velocity rofiles sulied by the high-fidelity simulations) include the nondimensional growth rate of an instability mode and N-factor describing the normalized accumulated growth rate of the modal amlitudes integrated over a secified streamwise distance along the boundary layer. One may establish an analytical connection between the RMS and N-factor curves which is easily traced through comarison of Figs. 15a) and 15b) with resectively Figs. 16 and 17 describing the obtained N-factor curves for the cases of uniform and low-turbulence inflows. The latter show results of the linear stability analysis for corresondingly the suction and ressure side N-factors calculated for the instability modes with the highest sectral amlitudes at the trailing-edge locations and in the near field. For the suction side the results indicate that the highest modal amlification rates are reached soon after the searation oint and dro to near zero values close to the reattachment oint hence forcing the modal N-factors in Fig. 16 and corresondingly the RMS curve in Fig. 15a)) to lateau. Interestingly the stability analysis describes a continuous growth of the N-factors from the oint of instability incetion in contrast to the seemingly elosive growth of the RMS values in the searation region Fig. 15a)). At the same time such analysis succeeds in redicting the dominant contribution s of the rimary frequency modes observed in the near-field tonal sectra in Figs. 7 and 11 both for the uniform and low-turbulence inflows. Note that the continued slight growth of the N-factors in Fig. 16 is due to the quasi-arallel flow assumtion. A searate analysis conducted using LASTRAC code s more comutationally-intensive non-arallel flow otion generally comares well with the current results but reveals a saturation with a slight reduction of the N-factor levels in the ost-reattachment Inter-noise 2014 Page 11 of 14

12 Page 12 of 14 Inter-noise 2014 region thus more closely reroducing the RMS curve behavior in Fig. 15a). a) b) Figure 16 - Suction-side N-factors for selected frequency modes with the highest sectral amlitudes at oint A and the near field for uniform a) and low-turbulence I=0.008) b) ustream inflows. a) b) Figure 17 - Pressure-side N-factors for selected frequency modes with the highest sectral amlitudes at oint A and the near field for uniform a) and low-turbulence I=0.008) b) ustream inflows. Figs. 17 illustrates the corresonding results of the linear stability analysis obtained for the airfoil ressure side. Note that the redictions of the N-factors comare well with the RMS curves in Fig. 15b) and are similar for both uniform and low-turbulence cases indicating a raid growth of the amlification rates and thus the instability amlitudes in the searated regions close to the trailing edge. The frequency distribution of the N-factors accumulated at the oints close to the trailing edge on the suction and ressure sides are shown in Fig. 18. The eak frequency of the airfoil near-field tonal resonse in Fig. 11) is well-redicted by the stability analysis for the case of the uniform flow. However the discreancy aears to be larger for the low-turbulence case. Finally note that the accumulated modal growth rates aear lower in the turbulent inflow case on both airfoil sides in Figs 16 and 17 and thus the resulting tonal scattered acoustic levels are eected to be lower as well in accordance to the reliminary results of the far-field acoustic studies. Page 12 of 14 Inter-noise 2014

13 Inter-noise 2014 Page 13 of 14 Figure 18 - N-factor frequency distribution on suction and ressure sides near the trailing edge for left to right) uniform and low-turbulence flow regimes vertical lines mark the eak frequencies in the near-field sectra in Fig. 11). 5. CONCLUSIONS Eerimental and numerical studies of flow-acoustic resonant interactions in transitional NACA0012 airfoil installed at α=5 0 were resented. With uniform ustream flow conditions the eeriments revealed a ladder-tye structure of acoustic tones with dual velocity deendence corresonding to the rungs with frequency f~u related to the amlified instability-wave trailing-edge scattering and the effectively roduced vorte shedding corresonding to the dominant frequencies of each rung scaled with f s ~U 1.5. Introduction of a weak grid-generated ustream turbulence suresses all tones associated with the acoustic feedback 0.8-ower velocity deendence in the ladder-tye tonal structure) while reserving the 1.5-ower velocity deendence of the rimary sectral hum. High-accuracy numerical study comared the unsteady resonse redictions in the tones-generating transitional flow regime based on 2D and 3D ILES analyses. Effects of various numerical and hysical arameters were investigated. In 3D ILES simulations a significant dro in the broadband levels of the surface ressure resonse was observed along with an overall better agreement with eerimental data articularly notable for the rominent tones. The remaining discreancy with eeriment may indicate the necessity to more closely reresent the eerimental set-u in the numerical studies. Boundary-layer statistical moments showed an overall similarity between 2D and 3D analyses but 3D results indicated a raid decrease of RMS ressure amlitudes after reaching the eak levels with similar trend for the velocity fluctuations) which aeared to be related to the sanwise energy redistribution and aearance of fine-scale vortical structure observed in 3D analysis towards the trailing edge. Studies of the effect of turbulent inflow with different intensity levels revealed notable shifts in the dominant frequencies of the unsteady airfoil resonse in the low-turbulence case and the suction-side suression of the tones-roducing acoustic feedback loo in the high-turbulence case. Analysis of the boundary-layer statistical moments indicated that both for the uniform and low-turbulence ustream flow conditions the maima of the velocity RMS amlitudes on the suction side were reached in the laminar searation zones. The growth saturation was linked to the flow reattachment occurring without subsequent turbulence transition thus enabling reservation of the coherent instability modes and the acoustic feedback mechanism. The results were substantiated by the linear stability analysis erformed based on the samle-averaged boundary layer velocities on both sides of the airfoil. Such analysis confirmed the growth and saturation of the instability modes thro ugh the searated regions on either airfoil side and was successful in matching the eak frequency of the airfoil near-field sectral resonse with the most amlified instability mode in the case of the uniform ustream flow. The accumulated modal growth rates aeared lower in the turbulent inflow case on both airfoil sides which may result in the reduced scattered tonal acoustic levels. Inter-noise 2014 Page 13 of 14

14 Page 14 of 14 Inter-noise 2014 ACKNOWLEDGEMENTS Suort for this work through Air Force Office of Scientific Research Award Number FA Program Manager Dr. D. Smith) and Florida Center for Advanced Aero Proulsion is acknowledged. REFERENCES 1. Raman G. Suersonic Jet Screech: Half-Century from Powell to the Present. Journal of Sound and Vibration 1999; 225: Colonius T. An Overview of Simulation Modeling and Active Control of Flow/Acoustic Resonance in Oen Cavities. AIAA Paer Golubev VV Nguyen L Mankbadi RR Roger M Visbal MR. On Flow-Acoustic Resonant Interactions in Transitional Airfoils. Int. J Aeroacoustics 2014; 131): Paterson R Vogt P Fink M Munch C Vorte Noise of Isolated Airfoils. J. Aircraft. 1973; 10: Tam CKW Descrete Tones of Isolated Airfoils J Acoust Soc Am. 1974; 55: Arbey H Bataille J Noise Generated by Airfoil Profiles Placed in a Uniform Laminar Flow. J. Fluid Mechanics : Longhouse RE Vorte Shedding Noise of Low Ti Seed Aial Flow Fans. J Sound and Vibration 1977; 53: Desquesnes M Terracol M Sagaut P Numerical Investigation of the Tone Noise Mechanism over Laminar Airfoils J. Fluid Mechanics. 2007; 591: Visbal MR. Gaitonde DV On the Use of High-Order Finite-Difference Schemes on Curvilinear and Deforming Meshes. J. Comutational Physics 2002; 181: Anderson DA Tannehill JC Pletcher RH Comutational Fluid Mechanics and Heat Transfer. McGraw-Hill Book Comany Visbal MR. Morgan PE Rizzetta DP An Imlicit LES Aroach Based on High-Order Comact Differencing and Filtering Schemes. AIAA Paer Lele SK Comact Finite Difference Schemes with Sectral-like Resolution. J. Comutational Physics 1992; 103: Wagner C Huttl T Sagaut P Large-Eddy Simulation for Acoustics. Cambridge University Press Golubev VV Nguyen L Mankbadi RR Roger M Visbal MR Acoustic Feedback-Loo Interactions in Transitional Airfoils. AIAA Paer Brooks TF Poe DS Marcolini MA Airfoil Self-Noise and Prediction. NASA RP ; Moreau S Henner M Iaccarino G Wang M Roger M Analysis of Flow Conditions in Freejet Eeriments for Studying Airfoil Self-Noise. AIAA Journal. 2003; 41: Golubev VV Nguyen L Mankbadi RR Roger M Dudley J Visbal MR. On Self-Sustained Flow-Acoustic Resonant Interactions in Airfoil Transitional Boundary Layers. AIAA Paer Lowson MV Fiddes SP Nash EC Laminar boundary layer aeroacoustic instabilities. AIAA Paer Nash EC Lowson MV McAline A. Boundary Layer Instability Noise of Airfoils J. Fluid Mechanics 1999; 382: Golubev VV Brodnick J Nguyen L Visbal MR New Aroach to Modeling Airfoil Interaction with Ustream Turbulence. AIAA Paer Golubev VV Brodnick J Nguyen L Visbal MR High-Fidlity Simulations of Airfoil Interaction with Ustream Turbulence. AIAA Paer Smirnov R. Shi S Celik I Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling. Journal of Fluids Engineering 2001; 123: Golubev VV Nguyen L Mankbadi RR Roger M Pasiliao C Visbal MR. Effect of Ustream Turbulence on Flow-Acoustic Resonant Interactions in Transitional Airfoils. AIAA Paer Chang C Langley Stability and Transition Analysis Code LASTRAC) Version 1.2 User Manual. NASA/TM Page 14 of 14 Inter-noise 2014