ANALYSIS OF A SEMI-EMPIRICAL LEADING-EDGE SLAT NOISE PREDICTION
MODEL
Conference Paper · December 2020
CITATIONS
0
READS
76
5 authors, including:
Some of the authors of this publication are also working on these related projects: Fluid Mechanics of NatureView project
Multilevel/Multigrid Methods for Engineering and PhysicsView project Laura Botero Bolivar
University of Twente 10PUBLICATIONS 16CITATIONS SEE PROFILE Martinus Sanders University of Twente 9PUBLICATIONS 20CITATIONS SEE PROFILE C. H. Venner University of Twente 147PUBLICATIONS 3,265CITATIONS SEE PROFILE
ANALYSIS OF A SEMI-EMPIRICAL LEADING-EDGE SLAT NOISE
PREDICTION MODEL.
L. Botero-Bolivar
1M.P.J. Sanders
1L.D. De Santana
1C.H. Venner
1F.M. Catalano
21
Thermal Fluid Engineering, University of Twente, The Netherlands
2
Aeronautical engineering, S˜ao Carlos School of Engineering, Brasil
l.boterobolivar@utwente.nl, m.p.j.sanders@utwente.nl
ABSTRACT
In this paper semi-empirical formulas are presented that re-late macroscopic flow parameters observed in the slat cove and empirical constants proposed in Guo’s semi-analytical model. Fourteen slat configurations were sim-ulated using the Lattice Boltzmann Method (LBM)
imple-mented in PowerFLOW commercial software. These re-R
sults show an elementary relation between the four semi-empirical constants proposed in Guo’s slat model and im-portant flow parameters, e.g., the shear-layer path length
and the maximum shear velocity. Consequently, those
four semi-empirical constants were rewritten in terms of two empirical constants which values can be derived from RANS simulations. The proposed noise prediction model is consequently validated against wind tunnel aeroacous-tics tests performed with the 30P30N high-lift device model. Experiments performed in the UTwente
Aeroa-coustic Wind Tunnel at Rec = 1 · 106 and M = 0.15
showed good overall agreement between noise measure-ments and the proposed slat noise prediction model.
1. INTRODUCTION
Airframe noise is predominant when an aircraft flies in the approach flight to land e.g. over densely populated areas. The recent increase of the turbofan bypass ratio has contributed to the engine noise reduction turning the leading-edge slat and the landing gear the major airplane noise sources of an aircraft in landing configuration. Fast turnaround time and accurate noise prediction methods are essential in the preliminary design optimization permitting improved assessment of novel noise reduction solutions. However, the strong dependency of experimental parame-ters and lack of generality may jeopardize the applicabil-ity of state-of-the-art semi-empirical methods. This paper proposes to partially overcome these limitations by intro-duction of a relationship between flow parameters and the semi-empirical constants proposed in Guo’s model [1].
Recently, Guo [1] proposed a leading-edge slat noise prediction method based on the aerodynamic sound gener-ation theory and source flow physics. Guo’s approach re-lates the far-field noise spectrum to the sound source statis-tics, e.g., temporal and spatial coherence. Noise propaga-tion effects are considered in the Green’s funcpropaga-tion. Con-sequently, while simple, Guo’s model has a solid physical
foundation and is ideal for application in aircraft noise op-timization procedures.
The evaluation of the spectral shape function is key in Guo’s slat noise prediction model of the far-field power spectral density. Various studies have shown the applica-tion of Guo’s slat model [2–5], focusing on elaborating the fitting of the spectral shape function without relating it to specific features of the configuration. A general determi-nation of the spectral shape function by use of predominant flow features such as the shear layer path length or its max-imum shear layer velocity, an approach similar to Brooks et al. [6]), is not yet established.
Aiming at a more generic slat noise prediction model, LBM simulations of fourteen slat geometry configurations were performed. LBM simulations with PowerFLOW are preferred for the determination of local flow parameters and far-field radiated noise with affordable computational effort compared to other classical CFD solvers. The in-vestigated geometries represent parametric modifications with reference to the baseline generic slat. The slat gap and overlap are kept constant in all geometric configura-tions. Figure 1 shows the geometric parameters modified, i.e., 5 variations in the slat cusp length (κ), 5 changes of the slat trailing edge angle (α, w.r.t. the baseline) and 3 mod-ifications in the slat trailing edge length (ψ). Each config-uration produced a unique flow-field around the slat, shear layer path, reattachment point, and velocities through the shear layer [7].
A description of the slat noise prediction model derived from the different slat geometry configurations is presented in Sec. 2 while Sec. 3 presents the application of the slat noise prediction to the 30P30N high-lift geometry. Sec-tions 3.1 and 3.2 discuss, respectively, the numerical and experimental setup of the 30P30N configuration. The val-idation and evaluation of the slat noise prediction model is examined in Sec. 4. Conclusions and prospects are dis-cussed in Sec. 5.
2. METHODOLOGY 2.1 Slat noise prediction model
Guo [1] modeled the slat noise power spectral density as:
Π = ρ20c20AGAFW (M ) F (f, M ) D(θ, φ)
csb
Figure 1: Slat geometry modifications.
where ρ0 is the air density, c0 the speed of sound, AG
the geometry dependent amplification factor, AFthe
flow-dependent amplification factor, W (M ) the Mach number dependent weighting function, F (f, M ) the spectral shape function, D(θ, φ) the directivity function in terms of polar
and azimuthal angles, csthe slat chord length, b the wing
span, and r the source to observer distance. Note the for-mulation in Eq. 1 neglects the contribution from the con-vective amplification (i.e. Doppler factor) and atmospheric absorption.
Equation 2 presents the spectral shape function
accord-ingly Guo’s formulation where Stcrepresents the Strouhal
number based on the slat chord. The spectral shape func-tion F (f, M ) primarily contains the dependency of the
Green’s functions and its gradients, e.g., term µ3. The
tem-poral coherence of the source distribution, e.g., included in
the term µ0, and the spatial coherence of the surface
pres-sure fluctuations of the source e.g., included in terms µ1
and µ2. The numerical constant µ3 is related to the
geo-metric characteristic length scale and speed of sound, µ0
to the slat chord length and mean flow, and µ1 and µ2 to
the characteristics length scales in the flow. As a result, the
constants µ0, µ1and µ2are close to unity.
The spectral shape function is intrinsically able to cap-ture the spectral shape since its asymptotic behavior re-sembles conventional wall pressure spectral models which
scale proportional to f2 in the low-frequency regime and
f−5as f → ∞. The temporal and spatial coherence length
scales mainly determine the spectral shape function, there-fore, it may be expected that strong variation of the spectral shape function will be driven mainly by sharp changes in mean flow straining induced by the local pressure gradi-ents linked to the anisotropic turbulence length scales. The spectral shape function is incorporated in the Mach num-ber weighting function W (M ) due the dependency of the spectral shape function on the Mach number and an in-creasing effect of acoustic (non-) compactness for increas-ing Mach number. For further details the reader is referred to Guo [1]. F (f, M ) =M 2c s c0 St2c (1 + µ2 0St2c)(1 + µ21(1 + M )2St2c) × 1 (1 + µ2 2M2St2c)(1 + µ3M Stc) (2)
2.1.1 Relevant parameters to the far-field leading-edge slat noise
Guo proposes a set of constants defining the spectral shape function and a set of parameters related to the amplitude
of the far-field radiated slat noise modeled in the AGand
AF, see Eq. 2. Geometry dependent factors (AG) relates
parameters such as the angle of attack, slat gap and over-lap and slat sweep angle. Whereas (local) flow-dependent
factors (AF) are related to parameters such as the shear
layer thickness, shear layer path length, shear layer reat-tachment point, vorticity in the shear layer, sectional lift coefficient of the slat or local pressure gradient near the slat trailing edge. Botero et. al. [7] identified geometric pa-rameters that strongly affect the local flow features thereby the far-field radiated noise. However, we assume changes in geometry will ultimately result in modifications of (lo-cal) flow quantities. Therefore, instead of modeling the noise based solely on geometric characteristics, we pro-pose using essential local flow parameter that are identi-fied as most important to the far-field radiated noise. These flow parameters can, for example, be extracted from rela-tively uncomplicated RANS simulations.
2.1.2 Dependency of far-field radiated noise on local flow parameters
A typical far-field slat noise spectrum is composed of three main components, i.e, mid-frequency tones, a high-frequency hump, and the main broadband component. The first component is attributed to a feedback loop mecha-nism between shear layer instabilities originated in the slat cusp and acoustic waves generated at the slat trailing edge. The behavior of these mid-frequency tones with Reynolds number is still not well understood, whereas the high-frequency hump is expected not to appear in flight condi-tions since it is related to the vortex shedding behind blunt slat trailing edges. The broadband component is character-istic of all slat models and is generated due to scattering of the turbulent boundary layers at the slat trailing edge.
Previous studies demonstrated a strong relationship be-tween local flow-field conditions and the sound genera-tion process [7, 8]. The amplitude of the mid-frequency tones has been related to the distance between shear layer reattachment point and trailing edge. A shorter distance resulted in an increase of the mid-frequency tones. Fur-thermore, Terracol et. al. [8] related the frequency of the tones to the ratio between the shear-layer path and acous-tic path. On the other hand, the broadband component has been related to the local vorticity thickness in the slat
mix-ing layer, defined as δw = |U1− U2|/max(dU/d~n) [8],
where U1is the velocity inside the slat shear-layer, U2 is
the velocity outside the shear-layer and ~n is a normal-shear
vector. Figure 2 shows the definition of U1, U2, ~n and the
shear-layer path. The vorticity thickness increases along the shear-layer path from the cusp [8]. Furthermore, Stud-ies conducted by Botero et. al. [7] demonstrated the am-plitude of slat broadband noise is inversely proportional to the slat shear-layer path length and directly proportional to the shear velocity along it. In this way, slat broadband
noise level (AGAF) and spectrum shape (µ0,1,2,3) could be
0.06 0.04 0.02 0 TKE 2 D [-] ~ n U1 U2
Figure 2: Schematic of the shear layer flow in the 30P30N
slat cove region. TKE2D(=12(hu02i + hv02i)/U02)
distribu-tion is from 30P30N LBM simuladistribu-tions with αg= 6.5◦and
Rec= 1 · 106(see section 3.1).
.
2.1.3 Proposed slat noise prediction model
The far-field and local flow-field results of the 14 differ-ent slat configurations from LBM simulations were ana-lyzed to find functional dependencies. The numerical
con-stants (µ0,1,2,3) and AGAF term were determined for each
configuration from the computed far-field noise by nonlin-ear least-square fitting using bisquare weights. Figure 3
shows the resulting variation of AGAF in function of the
dimensionless shear-layer length (SL/cs) and the
differ-ence of the squared dimensionless velocities. Parameter
δE = (U1
U∞)
2− (U2
U∞)
2 aims to relate the kinetic energy
outside and inside the slat cove (0.5ρU2). The velocity
component was taken at 10% of shear layer path from the slat cusp where the shear velocity is generally the largest.
The parameter AGAF varies almost linearly in function of
each parameter with the same relation observed in the pre-vious results (the noise level increases as the shear-layer path length decreases and ∆U increases) [7]. Figure 4
and 5 show the variation of µ0,1,2,3constants with the same
parameters. The value of each constant does not vary sig-nificantly among all configurations, and no clear tendency can be noted. In section 2.1 we have discussed why this may be the case.
Finally, a surface for each numerical constant and
AGAF factor can be created in function of SL and δE,
see Fig. 6 for AGAF case. The equations that modeled
each surface are presented in Eq. 3 (a,b,c, and d) with an R-squared indication, i.e., variance, of the fit. Using a surface to relate each constant with both flow parameters reduces
the value of the statistical parameter R2. However, it
in-creases the range of different slat configurations for which
the equations are valid. The noise level factor (AGAF)
is approximated presenting low variance (R2 = 0.96)
since, as previously demonstrated, those local flow features strongly affect the turbulence related to the noise
genera-tion process at the slat trailing edge. However, µ3presents
the lowest value of R2 since it is related to the Green’s
function and likely unrelated with flow features. Note-worthy is that the equations are made dimensionless, i.e.,
the shear-layer length non-dimensionalized using the slat chord and the velocity normalized by the free-stream flow velocity. 0.55 0.6 0.65 0.7 0.75 0.8 0.85 SL/cs 0.01 0.02 0.03 AG AF 1.2 1.4 1.6 1.8 2 2.2 2.4 (U1/U∞)2-(U2/U∞)2 0.01 0.02 0.03 AG AF
Figure 3: Variation of AGAF factor with the shear-layer
path length and δ E.
0.55 0.6 0.65 0.7 0.75 0.8 0.85 SL/cs 0.3 0.35 0.4 µ0 0.55 0.6 0.65 0.7 0.75 0.8 0.85 SL/cs 0.3 0.35 0.4 µ1 0.55 0.6 0.65 0.7 0.75 0.8 0.85 SL/cs 2 2.5 3 µ2 0.55 0.6 0.65 0.7 0.75 0.8 0.85 SL/cs 6 7 8 µ3
Figure 4: Variation of µ0,1,2,3 constants with the
1.2 1.4 1.6 1.8 2 2.2 2.4 (U1/U∞)2-(U2/U∞)2 0.3 0.35 0.4 µ0 1.2 1.4 1.6 1.8 2 2.2 2.4 (U1/U∞)2-(U2/U∞)2 0.3 0.35 0.4 µ1 1.2 1.4 1.6 1.8 2 2.2 2.4
(U1/U∞)2-(U2/U∞)2
2 2.5 3 µ2
1.2 1.4 1.6 1.8 2 2.2 2.4
(U1/U∞)2-(U2/U∞)2
6 7 8 µ3
Figure 5: Variation of µ0,1,2,3constants with δE
AGAF = − 0.0113 − 0.0166(SL) + 0.0264(δE) R2= 0.96 µ0=0.7012 − 0.1739(SL) − 0.1278(δE) R2= 0.55 µ1=0.5537 − 0.05961(SL) − 0.1044(δE) R2= 0.56 µ2=4.854 − 1.283(SL) − 0.9655(δE) R2= 0.57 µ3=21.25 − 11.05(SL) − 4.081(δE) R2= 0.15 (3)
Figure 7 shows a comparison of the far-field spectra of a generic slat obtained with different methodologies. The continuous gray line is obtained from LBM simulations, the dash orange line is obtained fitting the Guo’s model to the numerical results, the dotted black line is obtained using Guo’s model but calculating the constants and the level with eq. 3, and the continuous blue line is obtained
from the original Guo’s model (µ0,1,2,3= 1). It is worth to
note the new model changes significantly the slope of the
curve up Stc= 25 and shifts the location of the maximum
level from Stc = 1 (original Guo’s model) to 1.7, closer
to the actual maximum (Stc = 2.6). The new model
com-pletes Guo’s noise prediction model, which is generic for
Figure 6: Surface for fitting the data with flow parameters
all slat, calculating specific constants for each slat using simple parameters that could be obtained from stationary 2D simulations. 100 101 St [-] -70 -60 -50 -40 -30 PSD [dB] Numerical results Fit curve
Enhanced Guo’s model Guo’s prediction model
Figure 7: Far-field spectra with different prediction model
3. APPLICATION OF THE SLAT NOISE PREDICTION MODEL TO THE 30P30N
GEOMETRY.
The slat noise prediction model described in the previous section is applied to the 30P30N high-lift airfoil geome-try, and results were compare with wind tunnel measure-ments and LBM simulations. Inputs needed in the
pre-diction model (shear-layer length, U1 and U2) were taken
from LBM simulations. We will first describe the setup of the numerical configuration followed by a description of the wind tunnel measurements. A comparison of the numerical and experimental results with the slat noise pre-diction model will finally be shown in Sec. 4.
3.1 Numerical set-up
Numerical simulations were carried out on the
commer-cial software PowerFLOW 5.3 which uses the LatticeR
Boltzmann Method (LBM) as fluid solver and Very Large Eddy Simulations (VLES) based on the κ − RNG model
as turbulence model. The effects of the unresolved (sub-grid) scale-flow properties on the resolved large scale are exerted via eddy viscosity and turbulent Prandtl numbers. The elements closest to the surface are resolved with the universal law-of-the-wall velocity profile coupled with a wall model pressure gradient extension to determine the local skin friction. For the far-field analysis, PowerFLOW uses the Ffowcs William-Hawking (FW-H) acoustic anal-ogy; in all cases a solid FW-H was used.
The computational domain has dimensions 3.7 × 0.7
× 0.9 m3; x and y located in the streamwise and
span-wise directions, respectively and is delimited by hard walls modeled as ideal walls. The velocity inlet was set at 50 m/s with 0.3 % turbulence intensity, and 1 mm turbu-lence length. These conditions are setup to replicate the wind tunnel conditions at the University of Twente [9] de-scribed in Sec 3.2. The outlet condition is imposed with no pressure gradient and the outermost fluid region was mod-eled as a high viscosity fluid for the absorption of acous-tic waves. The minimum element size was 0.225 mm, which demanded a spatial discretization of 200 millions of element and temporal discretization of 845214 timesteps (equivalent to 0.32 sec in real-time). The surface pressure measurements for the FW-H calculation were taken from the slat and main element leading edge along 0.3 m span, according to the ROI dimensions used in the beamform-ing methodology (Fig. 10). The noise was then propagated to the center array microphone located at the wind tunnel wall in the identical configuration to the CTS wind tunnel experiment. The sampling frequency of FW-H measure-ments was 80 kHz, and the initial 0.064 s were neglected to avoid initial transient effects. Simulations took 27,000 CPU-hours.
3.2 Experimental Set-up
3.2.1 Aeroacoustic Wind Tunnel Facility
Wind tunnel measurements were conducted in the closed-circuit Aeroacoustic Wind Tunnel facility at the Univer-sity of Twente [9]. The testing section measures 0.7 m in height and 0.9 m width. The flow velocity of the wind tun-nel measurements presented in this paper is 50 m/s with a measured free stream turbulence intensity below 0.4%.
An anechoic chamber with dimensions 6 × 6 × 4 m3
en-closes the testing section which has a cut-off frequency of 160 Hz.
Aeroacoustic measurements of the 30P30N model are conducted in both a hard-wall and open-jet test section
configuration (Fig. 9). The hard-wall configuration is
equipped with a acoustic transparent window based on
a design proposed by Bokhorst and Tuinstra [10]. A
1.5 mm stainless steel perforated plate (R3T5 and 33% open area ratio) is covered with a 5 mm polyether foam
plate (35 kg/m3density rating). The foam layer is added
to suppress the turbulent boundary layer noise [11] on the wind tunnel wall. Furthermore, the microphones are re-cessed by 0.15 m in order to minimize the effect of bound-ary layer noise. Recent measurements at the University of Twente have shown that this type of acoustic panel has similar acoustic performance as a stretched Kevlar panel (widely used in recent aeroacoustic studies).
3.2.2 30P30N Wind Tunnel Model
A 30P30N high-lift model with 300 mm retracted chord and 1036 mm total span is mounted in the wind tunnel testing sections. The model is equipped with a total of 84 pressure ports having a diameter of 0.3 mm. The chord-wise oriented pressure ports have an inclination angle of
15◦with respect to the leading edge and are located around
the center-line of the wing model. Pressure sampling is performed by a total of 9 pneumatic pressure scanners (model’s 9116 and 9216 by NetScanner) having a system accuracy of ±0.05%. Static pressure is sampled at 100 Hz for 10 seconds. Noise treatment is applied to the wind tun-nel model in order to reduce extraneous noise sources orig-inating from the slat brackets and wall junction near the slat cove. No tripping devices were used for the results shown in this paper.
Figure 8: Schematic of the 30P30N wing model and
pres-sure orifice locations (•).
3.2.3 Microphone Phased Arrays
Acoustic beamforming measurements are performed us-ing 64 GRAS 40PH (free-field) microphones. The micro-phones are arranged according to a Vogel spiral design [12] as illustrated in Fig. 10. The hard-wall microphone array is a scaled-down version of the open-jet array in order to ob-tain a similar geometric opening angle. Microphone pres-sure is sampled using 4 National Instruments PXIe-4499 Sound and Vibration modules installed on a NI PXIe-1073 chassis. Samples were acquired for 45 seconds at a sam-pling frequency of 102.4 kHz. The microphone’s sensitiv-ity was calibrated using a GRAS 40 AG Sound Calibra-tion. Wind caps (GRAS type AM03464) were used in the open-jet measurements due to the strong recirculation ex-perienced during these tests.
3.2.4 Beamforming Methodology
In-house beamforming algorithms developed at the Uni-versity of Twente (BEAMUT) are used to process the mi-crophone data. These algorithms were benchmarked with the Arraybenchmark database hosted by the Brandenbur-gische Technische Universit¨at [13, 14]. The spectral analy-sis is performed following the Welch, i.e., WOSA, method by taking a constant number of FFT blocks of 8192 sam-ples for each frequency. A Hanning window is used with an overlap of 50%. Diagonal removal of the cross spec-tral matrix (CSM) is applied. No weighting functions are applied to the microphone signals.
The applied search grid is set to have a spacing dx and dy of 0.01 m in both directions. The focal distance of the
0.6
m
hard-wall microphone array x z y shear layer Acoustic window 0.9 m
(a) Hard-wall test section.
1.45
m
open-jet microphone array windtunnel nozzle x z y shear layer 0.9 m
(b) Open-jet test section. Figure 9: Schematic of the wind tunnel test section configurations.
-0.5 0 0.5 x [m] -0.5 0 0.5 y [m] OTS array CTS Array CBF ROI FWH
Figure 10: Microphone phased arrays with region of in-terest (ROI) of the source power integration technique and the Ffowcs-Williams Hawkings integration area.
search grid is set to the centerline of the wind tunnel. The effect of rotating the search grid plane along with the an-gle of attack of the wing model was found to have a neg-ligible effect on the beamforming results. Corrections for the mean flow convection and shear layer are applied fol-lowing the Amiet shear layer correction [15]. We assume that the speed of sound in the wind tunnel flow and station-ary surrounding air is approximately the same. Corrections for the transmission loss of acoustic panel (Fig. 9) are ap-plied according to the model developed by Phong and Pa-pamoschou [16].
Integrated spectral levels are obtained using the source power integration technique [17] in combination with con-ventional frequency domain beamforming (CBF). The re-gion of interest (ROI) is located on the center span and extends a total of 0.3 m along the spanwise direction
(Fig. 10). This avoids the inclusion of sidelobes from
the slat bracket and wind tunnel side wall junction. The
streamwise (e.g. x-direction) extend of the ROI is set suf-ficiently to capture the main-lobe at lower frequencies of interest.
4. RESULTS
This section discusses the comparison of the far-field noise calculated from the numerical (LBM) simulations and ex-perimental measurements of the 30P30N high-lift geome-try. The enhanced slat noise prediction model described in Sec. 2 is then evaluated using this dataset.
4.1 Aerodynamic results 4.1.1 Static Pressure Coefficients
A comparison of the chordwise pressure coefficient distri-bution is shown in Fig. 11. We will consider only a single
angle of attack corresponding to an angle of attack of αe=
4.5◦computed from a free-flight CFD simulation (obtained
from the BANC workshop database [18]). This free-flight angle of attack corresponds to a geometric angle of attack
of 6.5◦ in the LBM simulation. This is due to the wind
tunnel effect, mainly caused by blockage and low aspect ratio effects. The corresponding geometric angle of attack
in the CTS wind tunnel experiment is 8.5◦. This is due to
an effect of the flow permeability of the acoustic window (Fig. 10) which lowers the effective angle of attack. Flow deflection in the OTS wind tunnel experiment due to heavy loading significantly affect the effective perceived angle of
attack as the geometric angle required was 18◦.
Further-more, we can observe that the pressure recovery over the main wing element is also reduced in the OTS experiment due to a change in effective chamber line shape from
curv-ing streamlines [19]. Nonetheless, we can argue that the Cp
distribution around the slat region is identical and therefore the noise signature will be identical [20].
4.2 Aeroacoustic results
The normalized far-field noise results from the LBM sim-ulation and wind tunnel tests are compared in Fig. 12.
-0.2 0 0.2 0.4 0.6 0.8 1 x/c [-] -6 -4 -2 0 2 Cp CFD free-flight αg= 4.5◦ POWERFLOW αg= 6.5◦ UT CTS Exp. αg = 8◦ UT OTS Exp. αg= 18◦
Figure 11: Chordwise pressure distribution coefficient.
Good overall agreement is observed in the broadband noise components as well as the discrete slat tones. The high-frequency hump (associated with vortex shedding in the slat cove) is clearly visible in the experimental slat noise spectrum. It is strongly related to the boundary layer state on the upper side of the leading-edge slat. Application of a tripping device to the upper side of the leading-edge slat resulted in a significant reduction of this hump.
The low-frequency deviation between the numerical and experiment can be attributed to a reduction of the
beamforming performance. For Stc < 1, i.e., f < 1000
Hz, the beamforming methodology inherently exhibits a
physical limitation. Towards the high-frequency range
St > 25, i.e., f > 30, 000 Hz, we note that shear-layer coherence loss effects can no longer be neglected and need to be corrected for.
Acoustic source maps obtained from the CTS wind tun-nel experiment are presented in Fig. 13. These maps show a good distinction of the ’clean’ leading-edge slat noise compared to other extraneous noise sources such as the side-wall junction and slat bracket interfaces. The increase in main-lobe beamwidth for low frequencies can be clearly observed. In combination with a significant contamination of noise originating from the wall junction this results in an overestimation of the low-frequency range in the source power integration method.
4.3 Evaluation of the Prediction model
The leading-edge slat prediction model described in Sec. 2 and given in Eq. 3 are applied to the generated dataset of the 30P30N high-lift geometry, which results in the black curve in Fig. 12. A good agreement of the applied Guo’s model is found even though the 30P30N slat geometry is different from the geometries used to determine the param-eters of the model (in Eq. 3). The Strouhal peak value is sufficiently modeled as well as the spectral decay. To-wards the high frequency range, a larger deviation > 5dB between prediction model and numerical and experimen-tal data may be observed. Further analysis of the wind tunnel data can improve the agreement in this region. Fur-thermore, the spectral decay in the high frequency range is expected to be influenced by the local pressure gradient in the slat trailing edge region [21]. This effect is not yet included in the current prediction model.
0.5 1 5 10 25 50 Stc 0 10 20 30 40 50 60 70 Normalized SPL [dB/Hz] Guo Model POWERFLOW αg= 6.5◦ UT CTS Exp. αg= 8◦ UT OTS Exp. αg= 15◦
Figure 12: Far-field slat noise power spectrum obtained from the regions defined in Fig. 13. The levels are scaled to an observer distance r and wing span b of 1 m. The
strouhal number is defined as Stc = f cs/U . The 30P30N
configuration is at Rec = 1 · 106with M= 0.15. -0.25 0.25 -0.4 0 0.4 y [m] SPL [dB] SPL [dB] Stc= 1.8 70 80 -0.25 0.25 Stc= 3.6 62 72 -0.25 0.25 x [m] -0.4 0 0.4 y [m] Stc= 7.2 54 64 -0.25 0.25 x [m] Stc= 14.4 52 62
Figure 13: Acoustic source maps in 1/3 octave band
rep-resentation of the CTS wind tunnel experiment (αg = 8◦
and Rec= 1 · 106). The Strouhal numbers correspond to a
frequency of 2, 4, 8 and 16 kHz.
5. CONCLUSIONS
This study has investigated the further development of leading-edge slat noise prediction based on the model of Guo. LBM simulations of 14 different slat geometries have been used to derive a prediction model based on rel-evant slat cove flow parameters. These parameters are the shear layer path length and a measure for the maximum shear velocity along the shear layer path. This model is a first step in the further development of slat noise predic-tion. Further investigations will investigate the importance
of including other parameters such as the shear layer reat-tachment point, local pressure gradient at the slat trailing edge or the overall slat lift coefficient. The slat noise pre-diction model has been applied to LBM simulations and small-scale wind tunnel measurements of the 30P30N con-figuration. The LBM simulations were carefully setup to resemble the wind tunnel measurements. Far-field noise measurements were compared to numerically obtained re-sults by FW-H calculations. Good overall agreement was found between the numerical far-field noise spectrum and those measured in the wind tunnel experiment. Application of the slat noise prediction model to this dataset showed satisfactory results.
6. ACKNOWLEDGMENTS
The authors would like to acknowledge the ’FINEP IN-OVA AERODEFESA 0/2013: Advanced configuration for noise reduction’ project for enabling the use of the Pow-erFLOW software. We also acknowledge the ’TKI-Silent
Approach’ project for financial support. The lab
tech-nicians Elise, Walter, Steven and Herman are especially thanked for their assistance with the experimental setup.
7. REFERENCES
[1] Y. Guo, “Slat noise modeling and prediction,” Journal of sound and vibration, vol. 331, no. 15, pp. 3567– 3586, 2012.
[2] R. Ewert, J. Dierke, J. Siebert, A. Neifeld, C. Appel, M. Siefert, and O. Kornow, “Caa broadband noise pre-diction for aeroacoustic design,” Journal of Sound and Vibration, vol. 330, no. 17, pp. 4139–4160, 2011. [3] J. Dierke, C. Appel, J. siebert, M. Bauer, M. Siefert,
and R. Ewert, “3d computation of broadband slat noise from swept and unswept high-lift wing sections,” in
17thAIAA/CEAS Aeroacoustics Conference, no. AIAA
2011-2905, 2011.
[4] B. Bai, X. Li, Y. Guo, and F. Thiele, “Prediction of
slat broacband noise with rans results,” in 21st AIAA
Aviation Forum, no. AIAA 2015-2671, 2015.
[5] M. Herr, M. Pott-Pollenske, R. Ewert, D. Boenske, J. Siebert, J. Delfs, A. Rudenko, A. Buescher, H. Friedel, and I. Mariotti, “Large-scale studies on
slat noise reduction,” in 21st AIAA/CEAS
Aeroacous-tics Conference, no. AIAA 2015-3140, 2015.
[6] T. Brooks, D. Pope, and M. Marcolini, “Airfoil self-noise and prediction,” NASA Reference Publication 1218, 1989.
[7] L. Botero, L. T. Lima Pereira, D. Acevedo, F. Catalano, D. C. Reis, and E. L. Coelho, “Parametric analysis of the influence of slat geometry on acoustic noise,” in 2018 AIAA/CEAS Aeroacoustics Conference, p. 3593, 2018.
[8] M. Terracol, E. Manoha, and B. Lemoine, “Investiga-tion of the unsteady flow and noise genera“Investiga-tion in a slat cove,” AIAA Journal, vol. 54, no. 2, pp. 469–489, 2016.
[9] L. D. de Santana, M. P. Sanders, C. H. Venner, and H. W. Hoeijmakers, “The utwente aeroacoustic wind tunnel upgrade,” in 2018 AIAA/CEAS Aeroacoustics Conference.
[10] E. van Bokhorst and M. Tuinstra, “Design and per-formance of an acoustic transparent window,” in 25th AIAA/CEAS Aeroacoustics Conference, 2019.
[11] P. Sijtsma and H. Holthusen, “Source location by phased array measurements in closed wind tunnel test
sections,” in 5th AIAA/CEAS Aeroacoustics
Confer-ence and Exhibit, no. AIAA-99-1814, 1999.
[12] E. Sarradj, “Optimal planar microphone array ar-rangements,” in Fortschritte der Akustik, DAGA 2015, N¨urnberg, 41. Jahrestagung f¨ur Akustik, 16. - 19. M¨arz 2015, 2015.
[13] E. Sarradj, G. Herold, P. Sijtsma, R. Merino-Martinez, A. Malgoezar, M. Snellen, T. Geyer, C. Bahr, R. Porte-ous, D. Moreau, and C. Doolan, “A microphone array method benchmarking exercise using synthesized
in-put data,” in AIAA Aviation Forum, 23rdAIAA/CEAS
Aeroacoustics Conference, 2017.
[14] C. Bahr, W. Humphreys, D. Ernst, T. Ahlefeldt, C. Spehr, A. Pereira, Q. Leclere, C. Picard, R. Porte-ous, D. Moreau, J. Fischer, and C. Doolan, “A compar-ison of microphone phased array methods applied to the study of airframe noise in wind tunnel testing,” in
AIAA Aviation Forum, 23rdAIAA/CEAS
Aeroacous-tics Conference, 2017.
[15] R. Amiet, “Refraction of sound by a shear layer,” Jour-nal of Sound and Vibration, vol. 58, no. 4, pp. 467–482, 1978.
[16] V. Phong and D. Papamoschou, “High frequency acoustic transmission loss of perforated plates at nor-mal incidence,” The Journal of the Acoustical Society of America, vol. 134, no. 2, pp. 1090–1101, 2013. [17] T. Brooks and W. Humphreys, “Effect of directional
ar-ray size on the measurement of airframe noise compo-nents,” in 5th AIAA Aeroacoustics Conference, 1999. [18] M. Choudhari and D. Lockard, “Assessment of slat
noise predictions for 30p30n high-lift configuration
from banc-iii workshop,” in 21st AIAA/CEAS
Aeroa-coustics Conference, no. AIAA 2015-2844, 2015. [19] T. Brooks, M. Marcolini, and D. Pope, “Airfoil
trail-ing edge flow measurements and comparison with the-ory incorporating open wind tunnel corrections,” in AIAA/NASA 9th Aeroacoustics Conference, 1984. [20] S. Kr¨ober and L. Koop, “Comparison of
micro-phone array measurement of an airfoil with high-lift devices in open and closed wind tunnels,” in
17thAIAA/CEAS Aeroacoustics Conference, no. AIAA
2011-2721, 2011.
[21] Y. Rozenberg, G. Robert, and S. Moreau, “Wall-pressure spectral model including the adverse “Wall-pressure gradient effects,” AIAA Journal, vol. 50, pp. 2168– 2179, 10 2012.
