Investigation of the unsteady flow and noise sources generation in a slat cove: hybrid zonal RANS/LES simulation and dedicated experiment

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1 20th AIAA Computational Fluid Dynamics Conference June 2011, Honolulu, Hawaii AIAA Investigation of the unsteady flow and noise sources generation in a slat cove: hybrid zonal RANS/LES simulation and dedicated experiment M. Terracol and E. Manoha ONERA, Châtillon, France. B. Lemoine LMFA, Ecole Centrale de Lyon, Ecully, France. This study presents numerical simulations of the unsteady flow and noise generation phenomena in the slat cove of a highlift wing profile by mean of a zonal hybrid RANS/LES approach. These computations are part of a joint numerical/experimental aeroacoustics collaborative program, dedicated to slat flow analysis. For that purpose, a dedicated twoelement wing profile (slat+main body) has been designed in order to isolate the slat noise sources from other possible spurious sources (flap for instance), while minimizing mean flow deflection effects in order to improve the reliability of open-jet wind tunnel measurements. The design of this two-element airfoil has been done numerically using an optimization process based on steady RANS calculations. This airfoil has been investigated experimentally in Ecole Centrale de Lyon open jet facility, therefore providing unsteady wall-pressure measurements in the slat cove area and farfield acoustic measurements. Unsteady zonal hybrid RANS/LES simulations have been performed to provide a comprehensive description of the unsteady flow inside the slat cove, with focus being made on the noise generation processes. A fine physical unsteady analysis of the flow inside the slat cove is presented, as well as a comparison of numerical results with available experimental ones. The pressure spectra associated to the slat cove flow appear to be characterized by several tonal peaks emerging from a global broadband content. The existence of such peaks is discussed and attributed to a feedback loop involving the main shear layer inside the slat cove. A theoretical law is proposed and assessed at the end of the paper to predict the associated tonal frequencies. I. Introduction The reduction of airframe noise is today a very important issue for aircraft manufacturers, due to the constant increase in air traffic and to more and more drastic constraints on the noise exposure levels. Due to the continued efforts in reducing engine noise, airframe noise becomes a significant contributor to the overall noise of the plane, especially in approach and landing configurations. Among the different noise sources, the highlift devices (slat and flap) which are deployed to increase the global lift of the plane at low speed have been identified as a major contributor to the overall noise. More specificaly, the cove region between the deployed slat and the main wing appears as a preponderant source of noise. For that reason, it becomes of outstanding importance to develop numerical and experimental approaches capable of not only predicting the noise generated by such devices but also of understanding the main involved physical phenomena responsible for noise generation, in order to propose active or passive noise control solutions. Numerous studies have been performed in that direction, both in the numerical and experimental domains. The growing capabilities of computational resources have led to an increase in the prediction capabilities Dr, ONERA, Department of CFD and Aeroacoustics, 29 avenue de la division Leclerc, F Châtillon, France. Ph.D. student, Centre Acoustique, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, Ecully cedex, France. 1 of 25 Copyright 2011 by ONERA. Published by the, Inc., with permission.

2 of unsteady turbulence-resolving numerical methods. Such approaches therefore provide a fine analysis tool for a better understanding of the physical mechanisms involved in the noise generation process. Since the pioneering works of Khorramiet al. 9 using a URANS strategy, several works have therefore been performed, using LES, 12,37 zonal hybrid RANS/LES methods 6,34,35 or global hybrid RANS/LES methods. 2,3,10,16,17,37 Several experimental works have also been performed to study slat noise. 5,7,8,11,25,31 These works are very useful to provide general trends and provide reliable databases to assess the simulations. However, the available experimental data are often limited to a statistical analysis of the flow and/or farfield noise measurements. For that reason it appears of crucial interest to combine the respective advantages of the two available approaches by developing joint experimental/numerical programs. The experimental study of slat noise is very difficult, because the test set-up must satisfy both aerodynamic and acoustic requirements that are generally contradictory. From the aerodynamic point of view, it is necessary to generate a mean flow around the slat that is as close as possible to the flow in infinite conditions, which generally requires testing a complete three-element configuration (slat, main wing and flap) in a closed section aerodynamic wind tunnel. However, such wind tunnels are generally not adapted to acoustic measurements because they are noisy and non-anechoic. On the other hand, from the acoustic point of view, it is much preferable to work in an open-jet, anechoic and silent wind tunnel. However, a conventional three-element wing generates a very high lift that is able to strongly deflect the open jet of the wind tunnel, with two consequences on both aerodynamic and acoustic point of views: i) Aerodynamic: the mean flow around the airfoil is distorted and no more representative of the flow in infinite conditions. In particular, it is always necessary to modify (increase) the airfoil global incidence in the wind tunnel to recover the pressure distribution that was predicted by CFD computations achieved in infinite conditions; ii) Acoustics: due to its deviation by the airfoil lift, the wind tunnel jet impinges the collector with a bad incidence, increasing the wind tunnel background noise and possibly damaging the structure. Moreover, the presence of the deployed trailing edge flap adds flow noise sources which complicate the study of slat noise. For these reasons, the first objective of this study was to design an airfoil with the following requirements: The flow (streamlines, velocity amplitudes, wall pressure distribution, turbulent kinetic energy distribution) in the slat cove should be representative of low speed (approach) flight conditions with a given classical three-element configuration at moderate global incidence. The overall wing lift and mean flow deflection by the airfoil should be minimized. The slat noise sources should be isolated from other possible flow noise sources. These requirements have led to the development of a slat-only airfoil configuration. The first objective of the present study is therefore to design a dedicated two-dimensional model adapted to a reliable experimental study of slat noise to be performed in the aeroacoustic open-jet wind tunnel of Ecole Centrale de Lyon. This database will be used in the FP7 European project VALIANT for further validation of the CFD/CAA codes to predict slat noise. For that purpose, the idea was to start from an existing three-element airfoil, to keep the upstream part of the airfoil (deployed slat and main wing leading edge) and to generate a new downstream shape for the airfoil with a given chord and a sharp trailing edge, without any deployed flap. This is practically done by using an optimization process in which the varying parameters are (i) the airfoil global incidence and (ii) the vertical position of the wing trailing edge. Using this optimization process, optimal values of these two parameter are derived, in order to satisfy as well as possible the above requirements. The optimization process, as well as the optimal retained configuration are first presented in section II. This configuration has been studied experimentally in Ecole Centrale de Lyon anechoic wind tunnel. The associated experimental set-up if briefly described in section III. The main contribution of the present study relies on several unsteady numerical simulations of this twoelement configuration. These simulations focus only on the slat cove area thanks to a zonal RANS/LES approach, the NLDE method, 13,29,33,35 which is briefly described and then applied to the retained configuration in section IV. A fine physical analysis of the flow and noise generation processes are carried out on the basis of the numerical results: the main physical features of the flow and a statistical analysis are reported in section IV.C. Then, an unsteady analysis of the flow is performed in section IV.D. It relies on a spectral analysis of the the main shear layer and of the wake of the upper trailing edge, as well as on the wall pressure spectra inside the slat cove. A first comparison between numerical and experimental results is also performed. The measured and computed pressure spectra appear to be characterized by tonal peaks emerging from the broadband frequency content. A possible interpretation based on a cavity feedback loop of these tonal 2 of 25

3 components is proposed in section V, as well as a theoretical prediction model for the associated discrete frequencies. II. Definition of the numerical/experimental setup: optimization approach II.A. Reference airfoil and configuration The reference airfoil is the FNG Airbus geometry that has been developed in the German R&T projects LuFo III and ProHMS between 2000 and 2003 and is released for all R&T related purposes. This airfoil has been widely used by DLR, 36 several models were built with various scales. The smaller one is called F16 and has been built for DLR AWB aeroacoustic wind tunnel. Its retracted chord is 300 mm and its span is 800 mm. The three-element reference configuration of this F16 geometry corresponds to the slat/flap deployed at / degrees. The 2D multi-block structured grid required for the calculation has been built using MESH3D 22 which is an in-house parametric grid generator developed at ONERA and is composed of approximately 180,000 cells. The flow conditions have been set to be: (i) as close as possible from realistic landing flow conditions; (ii) compatible with ECL wing tunnel facility; and (iii) still accessible for an unsteady turbulence-resolving numerical simulation. The retained flow conditions are: Flow Mach number M = 0.15 i.e. incoming flow velocity U= 51 m/s. Retracted chord of the airfoil c = 300 mm. Angle of attack α = 4. The associated chord-based Reynolds number of the problem is Re = 1,047,000. Figure 1 (left) shows the iso-mach contours and mean flow streamlines for this reference configuration obtained using a steady RANS calculation. It is worth noting that this airfoil introduces significant flow deflection effects, both in the upstream and downstream directions, therefore making it inappropriate for open-jet wind tunnel tests. II.B. Generation of low-lift slat-only configuration As stated in the introduction, the first step of this study was to design a dedicated airfoil configuration, focused on slat flow mechanisms and well suited for open-jet wind-tunnel tests. For that purpose, a twoelement airfoil composed of a deployed slat and a main wing body has been designed in such a way that: i) the flow in the slat cove area remains representative of a real highlift wing profile i.e. similar to the one of the reference three-element airfoil; ii) the airfoil minimizes mean flow deflection effects and generates only a low lift. II.B.1. Optimization process The global optimization process used for generating the two-element low-lift slat-only configuration can be recast as follows: The first step of this process consists in specifying two free input parameters (angle of attack α and position of the trailing edge). The vertical trailing edge position y TE being imposed, a new shape is generated for the main body: the upstream part (slat and main wing leading edge) is kept identical to the reference three-element airfoil, while the downstream part is reconstructed using the trailing edge position and splines. The second step then consists in generating a structured grid around this new shape using the parametric grid generator MESH3D. The RANS simulation is then run using this new mesh and the specified angle of attack. The results of the RANS simulation is then analyzed and compared to the targeted reference solution by calculating appropriate error norms. In the present study, two specific errors have been retained: E1 2 = (u u ref ) 2 + (v v ref ) 2 dω and E2 2 = Ω slat (v/u tan(α)) 2 dω, Ω wake where u and v denote respectively the streamwise and vertical components of the velocity vector; the subscript ref refers to the reference three-element solution; the two domains Ω slat and Ω wake denote respectively a domain located inside the slat cove and in the vicinity of the airfoil trailing-edge. Using 3 of 25

4 these two definition, E 1 represents a measure of the mean flow difference in the slat cove between the two-element airfoil and the reference three-element airfoil while E 2 is a measure of the mean flow deflection by the two-element airfoil. New input parameters (α and y TE ) are decided, in order to minimize the error(s) between the new solution and the targeted solution. The process is started again using this new set of input parameters until the errors reach an acceptable lower threshold. II.B.2. Numerical method All the computations presented in this study have been performed using the in-house CFD/CAA code FUNk (Onera code derived from sabrina 35 ) on structured multi-block grids. This compressible solver handles several sets of equations: Euler, Navier-Stokes, Filtered Navier-Stokes (LES) and Reynolds-Averaged Navier-Stokes (RANS). These equations can be solved considering either a full variables or a perturbation formulation. The solver also incorporates zonal RANS/LES capabilities. Several subgrid models are available for LES: Smagorinsky model, Selective Mixed-Scale Model, Approximate Deconvolution Model, Mixed and multiscale deconvolution models. RANS equations are solved using the Spalart-Allmaras turbulence model. The solver allows several numerical schemes to be used: high-order (sixth-order) finite difference schemes as well as finite volume schemes (modified second order AUSM+(P) scheme with wiggle detector, Roe scheme) are available. Time integration can be performed using a second-order implicit backward-euler scheme (using a Newton sub-iteration process) or an explicit third-order accurate compact Runge-Kutta scheme. Great care has been taken to ensure a very good efficiency of the solver on both massively parallel or vectorial supercomputers. The optimization process used for this part of the study relies on steady RANS simulations for which the Spalart-Allmaras turbulence model has been retained. For these steady flow simulations, Roe scheme has been used for spatial discretization while time integration has been performed using an implicit local timestepping approach. The optimization process itself is based on an external optimization software DAKOTA which is developed at Sandia National Laboratories 30 that makes it possible to select automatically a new set of optimization parameters (α;y TE ) from the evolution of E 1 and E 2. However, first simulations have shown that using a too wide parameters space for (α;y TE ) leads the optimization algorithm to an unacceptable local minimum for the error norms. For that reason, it has been chosen to first perform a coarse exploration of the parameter space and to identify manually a reduced parameter space where the automatic optimization could be restarted. For that purpose, 114 RANS computations have been performed, where the angle of attack α has been varied from 4 to 22 degrees - with a step of 1 degree and the vertical position of the trailing edge y TE has been varied from 0 to 0.125c, with a step of 0.025c. Based on the obtained error maps, a reduced parameter space has been defined and the automatic optimization process using DAKOTA has been re-started in this region. Convergence of the algorithm was then obtained after only 24 additional simulations. II.B.3. Results: optimized two-element airfoil After a total of 138 RANS calculations, an unconventional optimal configuration has been determined. It corresponds to the following set of parameters: α = 18 and y TE /c = Figure 1 presents a comparison between the three-element reference configuration and the optimized slat-only airfoil. It is to be noted that the angle of attack used for the optimized configuration is considerably higher than for the reference configuration. Despite this, it can be observed that the optimized configuration leads to a significant reduction of the mean flow deflection effects, both in the downstream and upstream parts of the flow, thanks to the unconventional shape of the airfoil near the trailing edge. This point reveals a good performance of the optimized airfoil in minimizing deflection effects, which is a very good point for wind tunnel tests. As a consequence, the global lift of the airfoil is also significantly decreased: the global lift forces have been computed for the two airfoils (for the planned experimental span of 300 mm) and are respectively of 318N for the three-element airfoil and 127N for the two-element airfoil. Figure 2 presents mean flow visualizations in the slat cove area of the reference and optimized airfoils, respectively. It can be seen that the two flows look very similar in this region. This is also confirmed by looking at the pressure coefficient distribution. Therefore, the flow in the slat of the optimized two-element airfoil appears representative of a realistic highlift airfoil, 4 of 25

5 Figure 1. Iso-Mach contours and mean flow streamlines in the slat cove area. Left: reference three-element profile; Right: optimized two-element airfoil. while the global flow deflection and lift force are significantly decreased with comparison to a conventional three-element airfoil, which makes it significantly more suitable for wind tunnel tests. Figure 2. Iso-Mach contours and mean flow streamlines in the slat cove area. Left: reference three-element profile; Right: optimized two-element airfoil. III. Experimental setup and measurements The experimental investigations were conducted at the Centre Acoustique of ECL, in the open-jet anechoic wind-tunnel. The anechoic chamber dimensions are 10 m by 8 m, with a height of 8 m and a typical overall background noise level of 21 db. The wind-tunnel exit duct has a square cross-section of 0.56 m side. For the experiments a convergent nozzle has been added, leading to a rectangular cross section of 0.4 m width by 0.3 m height. Finally, two horizontal end-plates fixed on the nozzle lips hold the investigated mock-ups mounted vertically. The sketch of the set-up is shown in figure 3, together with two pictures of the airfoil. Brushes have also been installed along the downstream edges of the end-plates in order to minimize spurious noise sources contaminating the low-frequency range. Due to expected flow deflection effects, the angle of attack of the airfoil had to be tuned to match as well as possible the reference C p distribution provided by freestream RANS calculations at α = 18. The optimal and retained value of the angle of attack for the measurements is finally of 25

6 Figure 3. Experimental set-up. Inflow speeds ranging from 30 to 70 m/s have been tested, with a focus on the reference speed of 50 m/s. Several unsteady pressure probes have been placed on the interior slat surface and in the leading edge region of the main wing element to allow unsteady wall pressure measurements to be done. These pressure probes consist of small-diameter (0.5 mm) holes drilled at the airfoil surface which are connected to remote microphones using tubular ducts. Such a set-up makes it possible to minimize significantly the size of the measurement devices at the wall. However, empirical probe-dependent frequency correction functions have to be applied to the measured pressure signals in order to account for viscosity attenuation and wave reflection in the ducts. Figure 4. Measured farfield pressure spectra at α = 25 for different values of the inflow velocity. Figure 5. Measured farfield pressure spectra at U = 50 m/s for different values of the angle of attack. Additional farfield pressure measurements have also been performed thanks to an acoustic antenna composed of 109 B&K 1/2-inch microphones mounted in diametrically opposite positions on a rotating system. The support of each microphone has a length of 2 m and the measurement plane fits with the set-up midspan plane. This device also made it possible to perform source localizations that confirmed that the main acoustic source is located in the slat cove region. Figure 4 displays the farfield pressure spectra measured by one microphone of the acoustic antenna, for different inflow speeds ranging from 30 m/s to 70 m/s. It is worth noting that these spectra are characterized by the presence of several tonal peaks emerging from the broadband content. This point is discussed in section V, where a possible physical interpretation for the presence of these discrete peaks is proposed, together with an analytical prediction model of the discrete frequencies. As it can be observed on figure 5, the sensitivity of the amplitude of these tonal components to 6 of 25

7 the airfoil angle of attack is rather high: for an inflow speed U =50 m/s, an increase of the incidence of the airfoil from 25 to 27 results in an attenuation of about 6 db of the amplitude of the main tonal peak in the acoustic field. IV. Hybrid RANS/LES simulation of the slat cove area IV.A. Methodology In the slat cove region, the resolution is performed thanks to a zonal RANS/LES approach, the NLDE 13,29,33,35 (Non-Linear Disturbance Equations) method which relies on a decomposition of the flow between a mean field (computed by RANS) and turbulent fluctuations (computed by LES in a reduced domain). For that purpose, the original grid has been divided in two distinct regions, resolved either in pure RANS or in pure LES mode. This domain decomposition in the present case is detailed in figure 6. Figure 6. Domain decomposition between the 3D LES region and the 2D RANS region Figure 7. Close-up view of the grid in the slat cove area The principle of the method is to decompose the conservative variables vector U as a mean and a fluctuating part. The mean part U can be computed using a classical RANS parametrization on the whole configuration, while the calculation of the fluctuating part U is performed locally only thanks to a LES-like formulation. This decomposition therefore represents a triple decomposition of the full unsteady field U as: U = U + U + U SGS = U + U SGS (1) where the notation (.) stands for the application of a LES filtering operator, and U SGS refers to the usual (unresolved) subgrid scales in the LES terminology. In the following, it will then be chosen to work with the perturbation variables U in order to compute turbulent fluctuations around the mean field U computed using the RANS approach, with a similar degree of accuracy than the one obtained in classical LES. As a starting point for the derivation of a set of evolution equations for the fluctuating field U, let us first consider the following compact notations for the system of the Navier-Stokes equations: where N denotes the Navier-Stokes operator: N(U) = U t + N (U) = 0 (2) (ρu) (ρu u) + p σ ((ρe + p)u) (σ u) + Q, (3) where p denotes pressure, ρ density, u the velocity vector, ρe the total energy, σ the viscous stress tensor and Q the viscous heat flux vector. By subtracting the associated averaged and filtered NS equations and 7 of 25

8 considering that the mean field U is steady, one obtain (see 13,29,33,35 for details) the following set of the so-called Non Linear Disturbance Equations (NLDE) for the perturbation variable U : U t + N (U + U ) = T L, (4) where T L denotes the usual subgrid terms that can be acocunted for thanks to any classical subgrid model. In the present study, the selective mixed-scale model (MSM) has been retained as subgrid closure. This model was fully assessed in the works by Lenormand et al. 14,15 and is described in details in the monograph by Sagaut. 28 At the boundaries of the LES region, the RANS solution is imposed as mean field, while a non-reflecting characteristic approach is used for the turbulent fluctuations. Since the flow remains laminar on the suction side of the slat, it has not been necessary to introduce any turbulent fluctuations in the boundary layers at the inflow of the LES region. Finally, classical adiabatic non-slip boundary conditions are used at the walls, while a periodicity condition is used in the spanwise direction. IV.B. Simulation parameters and numerical method Starting from the RANS grid topology used for the optimization step, a finer grid has been generated to perform the unsteady simulation. This grid is highly refined in the slat cove region since it aims at resolving this area in LES mode, as it can be observed in figure 7. The grid cell size used near the walls is non-dimensional units in the wall normal direction, i.e m, which ensures that the wall-normal grid resolution remains lower than one wall unit all along the airfoil. This fine grid consists of 585,000 cells in the 2D x-y plane, to be compared to the original grid of 126,000 cells. The grid in the slat cove area (red part in Figure 14) has been duplicated in the spanwise direction using N z discretization points. Different spanwise extents have been considered: L z = c s /4, L z = c s /2 and L z = c s, where c s 0.13c 39 mm is the chord of the slat. As detailed in table 1, two different spanwise resolutions have also been investigated for the case L z = c s /2. The finest resulting three-dimensional grid in the slat cove area is composed of roughly 30 millions of points. It has to be mentioned that due to the very fine grid resolution, the mean ratio between the subgrid and the fluid viscosities barely reaches 0.9 in the most turbulent regions of the flow for all these simulations, i.e. turbulence is finely resolved. The numerical scheme used to perform these unsteady computations is the modified AUSM+(P) scheme 21 Simulation Spanwise extent L z N z z N xyz A c s / m 7,586,000 B1 c s / m 15,172,000 B2 c s / m 30,345,000 C c s m 30,345,000 Table 1. Main characteristics of the LES domain used for the different RANS/LES simulations, where c s = 39 mm is the slat chord length that makes it possible to minimize the numerical dissipation by introducing a wiggle detector. Time integration uses a second-order implicit backward-euler scheme. The resolution has been performed using Onera in-house research code FUNk using 45 (case A) and 90 (cases B1, B2 and C) Intel Nehalem processors (2.8 GHz). Unsteady flow calculations have been conducted with a time step of s. At each time step, the resolution involves a Newton resolution process for which 8 inner sub-iterations are used. As it will be detailed later, only simulation C was considered for the unsteady analysis and therefore required a consequent physical integration time: starting from the steady RANS solution, this computation has been performed during a transient physical integration time of 54ms (representing about 60 characteristic times of the main recirculation bubble in the slat cove). After this, statistics and unsteady data have been collected during a physical time of 60 ms. The total cost of this simulation is approximately 26,000 CPU hours, for a total physical time of 114 ms. 8 of 25

9 IV.C. Main flow features and statistical analysis IV.C.1. Main flow features Figure 8 presents instantaneous iso-surfaces of the Q criterion, colored by the local velocity magnitude for the four different simulations. It is to be noted that the level of resolved turbulence inside the slat cove is very high since a significant value of Qc 2 /U 2 =10,000 has to be considered to isolate coherent structures in a visible manner. The general aspect of the flow appears to be similar for the four cases, although simulation B2 seems to exhibit finer turbulent structures due to the enhanced spanwise grid resolution. It can also be noted that large packets of vortices organizing themselves as streamwise-oriented vortices are observed at the upper trailing edge of the slat. For simulation A, one of these packets covers a spanwise extent which appears to be at least one half of the total computed spanwise extent; therefore in this case, it can be expected that the flow may be affected by the spanwise periodicity condition. Figure 8. Instantaneous iso-q surfaces in the slat cove region (Qc 2 /U 2 =10,000), colored by the velocity magnitude. Top: sim. A (left); sim. B1 (right). Bottom: sim. B2 (left); sim. C (right). The main wing element has been removed in order to facilitate the visualization. As detailed in figures 9 and 10, several physical phenomena are observed: A large recirculation bubble occurs in the slat and is surrounded by a large shear layer originating from the lower trailing edge. A fast 2D/3D transition occurs in this shear layer which finally impinges the upper wall. At the impingement location, large contra-rotative streamwise-oriented vortices and hairpin vortical structures are visible. 9 of 25

10 Some of these structures are re-injected in the main recirculation bubble, while the others are strongly accelerated, convected downstream and interact with the upper trailing edge. An additional mixing layer is also visible at the upper trailing edge, due to the vortex shedding at the upper (blunt) trailing edge. Complex interactions between these different phenomena are also observed. As it will be detailed later in the paper, the impingement of the main shear layer on the upper surface of the slat is one of the most important phenomena occurring in the slat cove that leads to noise generation. Figure 9. Global sketch of the main physical mechanisms inside the slat cove. The main wing element has been removed in order to facilitate the visualization. Figure 10. Instantaneous Schlieren-like view (distribution of (ρ) in a plane) in the slat cove region. IV.C.2. Statistical analysis Figure 11 displays the mean spanwise vorticity component distribution and the mean flow streamlines in the slat cove area for the different unsteady simulations, compared to the original RANS result. It is striking that all the simulations lead to a modification of the main recirculation bubble aspect compared to the RANS simulation which seems unable to predict correctly the development of the main shear layer. The spanwise vorticity magnitude in the main shear layer is considerably increased in the unsteady simulations compared to the steady RANS result, with similar levels in all the four zonal simulations that compare quite well with Jenkins et al. 8 PIV measurements in quite similar flow conditions and to existing numerical results. 2,6,16,17 It must be noted that the point where the main shear layer impinges the upper wall of the slat is shifted downstream in all the turbulence resolving simulations, to x/c , compared to x/c for the RANS-SA computation. A similar trend can be observed in the numerical study by Deck 3 where steady RANS-SA computations seem to slightly underestimate the size of the separated region. It can be appreciated that the two simulations B1 and B2, corresponding to the same spanwise extent but with different spanwise grid resolutions lead to a similar aspect of the mean flow. Simulation C, using the largest spanwise extent, also provides a very similar result. This is however not the case for the short-span simulation A in which the vorticity seems to be enhanced at the center of the main recirculation bubble. This is a classical 2D effect that indicates that the spanwise extent of the computational domain may be too short in this simulation. The mean resolved turbulent kinetic energy (TKE) distribution obtained in each zonal computation are displayed in figure 12. All the simulations lead to consequent levels of TKE along the main shear layer and to a region of high TKE levels where this shear layer impinges the upper slat surface and interacts with the upper trailing edge. This region appears to be distributed over a quite wide area due to the large amount of flow unsteadiness and shear layer flapping around this location. Such a distribution is in good qualitative agreement with the with experimental PIV 8 or LDA 31 visualizations and with the numerical 10 of 25

11 Figure 11. Mean spanwise vorticity component distribution and mean flow streamlines in the slat cove. Top: sim. A (left); sim. B1 (right). Center: sim. B2 (left); sim. C (right); Bottom: RANS. results of Choudhari and Khorrami, 2 Lockard and Choudhari 16,17 and Imamura et al. 6 who also observed similar TKE levels. It is to be noted that the corresponding 2D TKE levels (computed only from the x and y components of the velocity fluctuations) in the main shear layer are of the order of 0.02U 2 which is in a close agreement with the PIV measurements by Jenkins et al. 8 in similar flow conditions. Again, it can be appreciated that simulations B1 and B2 lead to quite similar distributions. It can also be observed that the large-span simulation C leads to higher TKE levels inside the main recirculation bubble, which may be due to a better representation of large-scale spanwise oscillations of the main vortex core. Figure 13 presents the RMS wall pressure coefficient distribution inside the slat cove obtained in the zonal simulations. These distributions are in a good qualitative agreement with available numerical studies: 2,16,17 all the simulations exhibit a strong peak of C p at x/c 0.04 that is clearly associated to the impingement of the main shear layer on the upper surface of the slat, as it can be seen on figure 14. This phenomenon 11 of 25

12 Figure 12. Mean resolved turbulent kinetic energy distribution in the slat cove. Top: sim. A (left); sim. B1 (right). Bottom: sim. B2 (left); sim. C (right). is therefore expected to be one of the main sources of sound in the slat cove area. It can be noted that simulations B1 and B2 lead again to similar results, while simulation C leads to a higher peak level of C p. In order to investigate more in detail the effect of the spanwise extent of the computational domain, the Figure 13. RMS wall pressure coefficient distribution inside the slat cove. Figure 14. RMS pressure distribution in the slat cove region (sim. C). two-point spanwise correlation coefficient has been investigated. Figure 15 presents the two-point spanwise 12 of 25

13 correlation coefficient of the shear-normal component of velocity (similar trends are obtained for other flow quantities) computed in each simulation at several discrete points located along the main shear layer (points M 2, M 7, M 12 and M 17 see figure 16 for details). From these curves, several comments can be done: simulation A is clearly not able to get a proper decorrelation along the span due to a too short spanwise extent; simulations B1 and B2 lead to similar results, therefore indicating that the spanwise grid resolution corresponding to simulations A, B1 and C should be sufficient; in these two simulations it however appears that the spanwise extent of c s /2 is a bit too short, or just what needed, to allow a full spanwise decorrelation. Simulation C with L z = c s seems more suitable to represent properly the spanwise integral lengths. This observation is in good agreement with the conclusions of Lockard and Choudhari 16 who concluded that a spanwise extent of about 0.8c s is necessary to get a proper spanwise decorrelation of the flow. Figure 15. Two-point spanwise correlation coefficient of the shear-normal component of velocity at several points of the main shear layer. Top: probe M 2 (left); probe M 7 (right). Bottom: probe M 12 (left); probe M 17 (right). IV.D. Unsteady flow analysis The following unsteady analysis has been performed for simulation C only, according to the conclusions of the previous part. For that purpose, several numerical probes have been introduced in the computational domain as depicted in figure 16. Each of this probe consists in practice of a rake of 128 points in the spanwise direction that allow a spanwise averaging of the spectra to be performed. At each of these points, the unsteady field has been stored in time, with a sampling frequency of 1 MHz i.e. one time step over five in order to avoid aliasing of the data. As mentioned previously, unsteady data have been collected after a transient time of 54 ms, during a physical time of 60 ms. These data have been used to compute velocity 13 of 25

14 end pressure spectra at each of the extraction points, with a frequency resolution of 100 Hz. Figure 16. Unsteady numerical probes locations in the slat cove, superimposed on mean flow streamlines. Figure 17. Tangential velocity profile and associated shear-normal derivative used for the estimation of the vorticity thickness at the beginning of the main shear layer. IV.D.1. Main physical features identification Figure 18 makes it possible to investigate the evolution of the spectral content of the flow along the mean shear layer trajectory. It is interesting to note that a broadband hump around 25 khz is present in all the spectra at the beginning of the shear layer. This frequency has been identified as the main amplified frequency in the mixing layer occurring at the lower trailing edge of the slat i.e. it is linked to the development of initial Kelvin-Helmholtz instabilities as observed in figure 9. Indeed, in the general case of a mixing layer between two parallel flows with respective velocities U 1 and U 2, this frequency can be estimated as f 0 = 1 2 (U 1 + U 2 ) /(7δ 0 ), where δ 0 = U 1 U 2 /max du dn is the initial vorticity thickness (n denotes the shear-normal direction). The initial velocity profile and its associated normal derivative in the present case are shown in figure 17, leading to δ m and f khz that corresponds to the observed frequency. This broadband hump then shifts gradually towards lower frequencies when advancing along the shear layer, which is the signature of vortex merging. Finally, at the end of the shear layer, an inertial range is visible in the spectra for the three components of velocity as in fully-developed turbulent mixing layers. Figure 19 shows the streamwise evolution of the spectral content of the flow in the wake downstream of the upper trailing-edge. All the spectra are characterized by a broadband hump around 40 khz, which is due to the vortex shedding from the blunt trailing-edge interacting with the upstream turbulence coming from the cove. Similar spectra have been observed by Khorrami et al. 9 By focusing on the velocity spectra, it is striking that the turbulence downstream from the cove is far from being isotropic, as it can also be observed on instantaneous visualizations (see figure 9) where large streamwise-oriented and hairpin vortices are visible. Figure 20 presents the wall spectral densities of pressure computed on the interior slat surface, at points S 1 S 6 (see figure 16). At point S 1 which is the closest one from the impingement location of the main shear layer, strong levels of wall-pressure fluctuations are observed, over a wide range of frequencies due to the high turbulence intensity of the flow in that area. As far as the global turbulence level decreases by moving away from the impingement point, the global level of the pressure spectra also decreases significantly. It can be seen that several peaks appear at some discrete frequencies ( 1800 Hz, 2500 Hz, 3500 Hz, 4350 Hz, 5200 Hz with an accuracy of ±50 Hz) that are a priori not linked to any of the aerodynamic physical events listed previously. As it can be seen in figure 4, strong peaks at these frequencies also emerge from the broadband content as tonal components in the farfield acoustic spectra. Section V will be devoted to a possible physical interpretation of these tones. By approaching the lower trailing edge of the slat (points S 4, S 5 and S 6 ), the broadband hump around 25 khz is recovered in the pressure spectra. As mentioned previously, this hump in the spectra appears to be linked to Kelvin-Helmholtz instabilities developing in the main shear layer. 14 of 25

15 Figure 18. Velocity and pressure spectra along the main shear layer. Top: spectra of the shear-layer-tangential component of velocity (left) and of the shear-layer-normal component of velocity (right). Bottom: spectra of the spanwise component of velocity (left) and pressure spectra (right). See figure 16 for detailed probes locations. Figure 20 presents the wall spectral densities of pressure computed at the surface of the main wing element, in the leading edge region i.e. at points W 1 W 7 (see figure 16). It can be observed that probes W 1 and W 2 which are located downstream of the gap present broadband spectra where no specific peaks are observed. This is certainly due to the presence of the highly turbulent flow coming from the slat cove. At the other points, several peaks are visible at the same discrete frequencies as those observed at the slat surface and in the acoustic field. These peaks are mostly visible for points W 6 and W 7 which are located in a flow region where the pressure field is not contaminated by turbulent structures. The broadband hump around 25 khz is still visible there, indicating that the shear layer itself contributes to the overall noise. Regularly-spaced smaller peaks are also visible at high frequencies, which may be the signature of a temporal modulation of the signal with an associated modulation frequency of the order of 9 khz. Although such a modulation may be attributed to wave reflections inside the slat cove, this phenomenon remains quite unclear up to now. Finally, it is worth noting that the pressure spectra exhibit a general f 3 dependency (except in fully turbulent regions), consistently with previous works. 7,11 IV.D.2. Comparison with experimental results The computed wall pressure spectra have been compared to early experimental results. As stated in section III, unsteady wall pressure measurements have been performed using a specific arrangement consisting of small-diameter (0.5 mm) holes at the airfoil surface connected to remote microphones with tubular ducts. 15 of 25

16 Figure 19. Velocity and pressure spectra along the wake of the upper TE. Top: spectra of the streamwise component of velocity (left) and of the vertical component of velocity (right). Bottom: spectra of the spanwise component of velocity (left) and pressure spectra (right). See figure 16 for detailed probes locations. The exploitation of the pressure signals therefore requires an additional frequency-dependent correction that accounts for wave attenuation by viscosity effects and wave reflections in the ducts. The following experimental spectra have been obtained using a theoretical expression 24 of the frequency response function for each probe although a more rigorous treatment should involve an experimental characterization of this function for each probe. A first comparison of the computed wall pressure spectral densities on the slat interior surface against experimental results is presented in figure 22. It can be seen that the global magnitude of the spectra obtained in the simulation is significantly higher than in the experiment, which may highlight a higher level of turbulence. This is particularly true at points S 1 and S 2. For the other considered points, the global broadband trend of the spectra is well recovered with again a general overestimation of the global level. It is to be noted that the broadband frequency hump around 25 khz is also present in the experimental measurements. For all the considered points, the tonal peaks present in the experimental measurements are also present in the simulation, but with a significantly less pronounced magnitude: the spectra obtained in the simulation exhibit a more broadband content, especially close to the impingement point. Similar trends in the pressure spectra are observed in the experimental results of Imamura et al. 7 The exact reason for that difference between experimental and computational results remains unclear up to now. Figure 23 presents the same comparison at the leading edge of the main wing element. Unfortunately, several experimental probes appeared to be deficient in this area due to manufacturing issues. As a consequence, a comparison is performed here for probes W 2 and W 6 only. It can be seen that the agreement 16 of 25

17 Figure 20. Computed wall pressure spectra at several points along the slat interior surface. See figure 16 for detailed points locations. Figure 21. Computed wall pressure spectra at several points located in the leading-edge region of the main wing element. See figure 16 for detailed points locations. between the simulation and the experiment is globally satisfactory, although the tonal peaks are still less pronounced in the simulation. One possible explanation may be due to a possible difference of the effective angle of attack of the airfoil between the simulation (performed at α = 18 in free stream) and the open-jet experiment (α = 25 ). Indeed, as shown in section III, the magnitude of the tonal peaks appears to be extremely sensitive to the angle of attack. This point will be investigated in more detail in future studies. Figure 22. Comparison between computed wall pressure spectra and available experimental measurements along the slat interior surface. Plain line: simulation C; symbols + dashed line: experiment. Top, from left to right: points S 1, S 2 and S 3; bottom, from left to right: points S 4, S 5 and S 6 (see figure 16 for detailed points locations). 17 of 25

18 Figure 23. Comparison between computed wall pressure spectra and available experimental measurements in the vicinity of the leading-edge of the main wing element. Plain line: simulation C; symbols + dashed line: experiment. Left: points W 2; right: point W 6 (see figure 16 for detailed points locations). V. Physical interpretation of discrete tones As detailed in the previous sections, both the acoustic and aerodynamic fields are characterized by the presence of discrete tonal components in the pressure spectra. Such tones are observed both in the experimental and numerical results, at mid-range frequencies that could not be related directly to any specific flow features. It is to be noted that the presence of tonal components in slat noise measurements is not a new observation and that several experimental works reported in literature exhibit the presence of such a feature in the acoustic spectra. However, the exact reason for their existence remains quite unclear up to now although two possible explanations are generally considered. The first one supposes these tones as being due to laminar effects i.e. to a feedback loop between acoustic waves and Tollmien-Schlichting waves generated in the slat boundary layers. Such a coupling has mainly been investigated both experimentally and numerically for simple airfoils 1,4,18,19,23,32 and remains an open topic. Under this assumption, the tonal components are therefore considered has being a direct consequence of low Reynolds number effects and are therefore expected to disappear at full scale, i.e. when the boundary layers at the slat surface become naturally turbulent. The possible occurrence of a coupling between acoustic waves and boundary layer instability waves on the suction surface of a slat was only studied recently by Makiya et al. 20 who observed such a coupling in low Reynolds number experiments (chord-based Reynolds numbers only up to ) of the flow past a two-element airfoil. In the present work, additional experimental tests have been performed by including a transition strip at the upper surface of the slat in order to trigger artificially the transition of the boundary layer. It was observed that in this case, tonal noise components were still present in the acoustic spectra. Such an observation was also done by Pott-Polenske et al. 25 and Kolb et al. 11 who did not get any significant effect of tripping devices on tonal frequencies removal, therefore arguing for a quite stable underlying physical mechanism. In practice, tone removal seems to be only obtained when using quite thick serration strips (with a width of the order of the boundary layer thickness itself) that may also affect the mean flow. In their experimental tests, Imamura et al. 7 also observed the occurrence of multiple tonal peaks in the acoustic spectra. The authors also indicate that using tripping devices on the lower slat surface did not work sufficiently to remove the tonal components. Therefore it seems that forcing turbulent transition of the boundary layers is not sufficient to remove tonal components and that an additional quite stable physical mechanism is involved in the generation of multiple tonal peaks. Finally, it is also to be noted that the reduced computational domain retained for our RANS/LES computations does clearly not make it possible to resolve any receptivity mechanism of the slat boundary layers which are almost not included in the region computed by LES. Since our unsteady computations also exhibit the presence of discrete tonal peaks in the pressure spectra, it therefore seems that such a receptivity mechanism can be reasonably discarded. One of the other possible scenarios relies on the existence of a feedback loop between sound waves generated by the impingement of the main shear layer on the slat upper surface and the mixing layer originating from the lower trailing edge as it is the case for cavity flows. Such a scenario has been proposed by Roger and Pérrenès 26 who observed experimentally that the slat cove and the flap cove of a 2D highlift 18 of 25