Bay cavity noise for full-scale nose landing gear: A comparison between experimental and numerical results

Accepted Manuscript Bay Cavity Noise for Full-Scale Nose Landing Gear: A comparison between experimental and numerical results

Eleonora Neri, John Kennedy, Gareth J. Bennett

PII: DOI: Reference:

S1270-9638(17)31473-6 https://doi.org/10.1016/j.ast.2017.11.016 AESCTE 4291

To appear in:

Aerospace Science and Technology

Received date: Revised date: Accepted date:

11 August 2017 24 October 2017 9 November 2017

Please cite this article in press as: E. Neri et al., Bay Cavity Noise for Full-Scale Nose Landing Gear: A comparison between experimental and numerical results, Aerosp. Sci. Technol. (2017), https://doi.org/10.1016/j.ast.2017.11.016

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Bay Cavity Noise for Full-Scale Nose Landing Gear: a comparison between experimental and numerical results Eleonora Neria , John Kennedya , Gareth J. Bennetta,∗ a

Department of Mechanical and Manufacturing Engineering, Trinity College Dublin, University of Dublin, D02 PN40, Ireland

Abstract This paper presents results obtained from the wind tunnel testing of a highly detailed full-scale nose landing gear model of a regional aircraft. The full wheel bay, doors and a significant part of the fuselage are included in the model. The emphasis of this paper is on wheel bay cavity noise and its potential contribution to the far field at approach conditions and at M<0.2. A numerical analysis allows the pressure field in the wheel bay to be studied identifying the frequencies at which the Helmholtz resonance and the 3-D standing wave duct modes are excited by instabilities in the bay opening shear layer. Experimental results agree with those predicted, with the empty wheel bay radiating tones of up to 12dB at the Helmholtz resonance, at two duct modes as well as at interaction tones between them. The Rossiter equation is successfully used to explain fluid-resonant lock-on between the shear layer instability modes and the excited resonant modes as a function of tunnel velocity. However, when the full landing gear and doors are installed into the empty bay model, these bay tones no longer radiate to the far field. It is concluded that this is due to disruption of the shear layer by this particular nose landing gear configuration whose leg is centrally located and whose drag and side-stays occupy a large area of the wheel bay opening. Keywords: Landing gear noise reduction, Wheel Bay, Environmental Noise, Cavity resonance, Aeroacoustics

∗

[email protected]

Preprint submitted to Aerospace Science and Technology

November 13, 2017

1. Introduction

5

10

15

20

25

30

35

The reduction of aircraft noise and emissions is now critical to the continued competitiveness of the aerospace sector and a prerequisite for the development of new aircraft [1]. The successful reduction in aeroengine noise has resulted in airframe noise being identified as the next noise challenge to be met, with airframe noise contributing up to 60% of the total noise emission of aircraft on approach to landing and landing gear noise contributing up to 70% of airframe noise for large, long range aircraft. Landing gear is mechanically complex, primarily designed to support the load of a landing aircraft. In order to ease inspection and maintenance and constrained by safety requirements, the aerodynamic design is not refined. Whilst in principle, it should be an easy task to dramatically decrease landing gear noise by fully encasing it and the wheel bay in a solid aerodynamic fairing, the overriding requirements of weight and safety (including access for pre-flight inspections and free-fall and tire-burst criteria), and allowing for brake cooling, prevent this obvious solution from being adopted. The struts, wheels, braces and doors of the landing gear radiate noise directly due to the fluctuating lift and drag forces produced by vortex shedding from these bluff bodies [2]. The characteristics of the shedding may be affected by the mutual interaction between solid components and by the presence of the wheel bay cavity shear layer [2], which will be presented in Sec. 2.1. While at take off the engine noise is dominant, during approach the landing gear noise is more significant. It is therefore, necessary to address this issue if further noise reduction for communities living proximate to airports is to be achieved. Numerous experimental studies in open and closed jet wind tunnels, analyzing landing gear flow and associated sound fields have been reported. With some exceptions, the majority of experimental airframe noise research has been performed using small-scale models, with much of the work presented at 0.25 scale [3, 4]. This leads to great difficulty for full-scale noise predictions due to insufficient detail in the geometrical modeling. The signature of landing gear noise is both broadband and tonal in nature covering frequencies from approximately 90 Hz to 4000 Hz [5]. The large number of components in the gear assembly makes it difficult to predict landing gear noise. For this reason, it is important to include these small details in the gear assembly for wind tunnel tests in order to accurately measure or predict the noise [6, 7, 8, 9, 10]. To circumvent the difficulties associated with scaled models in open jet 2

40

45

50

55

60

65

70

wind tunnels, an alternative approach using phased arrays of microphones is sometimes used to obtain direct measures of aircraft noise sources [11, 12]. An important early step in landing gear fly-over measurements was performed by Heller and Dobrzynski [6] in 1977 with just seven microphones used and mounted at a height of 1.2m above the ground. In 1996 Michel et al. [13] studied the airframe and the engine noise of a Tornado combat aircraft in high speed low-level flight using a linear microphone array. In 1998 Michel et al [14] used for the first time a large planar array to obtain a two-dimentional mapping of the sound sources on landing gear commercial aircraft. Flyover noise measurements were conducted on an Airbus A319 in 2004 within a German national research project on the development of noise abatement procedures, in order to validate DLR’s airframe noise prediction schemes [15, 16]. Despite these and many other, even much more recent, wind tunnel and flyover tests that have been performed, a complete understanding of the flow physics and noise generation mechanisms of landing gear flows is still lacking. The presence of important parts related to the landing gear, such as the bay cavity, are often simplified or omitted in both numerical and experimental studies. Add-on technologies such as perforated fairings and meshes are currently being evaluated as potential low noise technologies [3, 4, 17] which will result in even more detail to be modelled, with the dynamics of such additions needing to be evaluated in order to prevent the potential of instabilities or “shimmy” [18] of the landing gear. For these reasons, further study into these flow mechanisms and associated noise generation is required on complete, and ideally, full-scale geometries. This study considers all the geometrical details of the full scale nose landing gear (NLG), with particular focus on the bay cavity. 1.1. Wheel Bay Cavity Noise Cavity resonance, depending on the design of the landing gear, can be one of the dominant noise sources related to landing gears in certain frequency ranges [6]. Wheel bays are susceptible to resonance based on feedback between the internal cavity pressure and the shear layer over the cavity opening as discussed by Bliss and Hayden [2]. The acoustic contribution of the landing gear wheel bay has gone largely unreported with the exception of a few studies. This is primarily due to either the cavity noise being masked by higher level noise sources in a similar frequency range or the limitations of

3

75

80

85

90

95

100

105

110

beamforming arrays which need to very large to have sufficient spatial resolution at such low frequencies. The seminal paper by Heller and Dobrzynski [6] is one such exception whose work examined small scale, simplified nose and main landing gear models using an outdoor open-jet test facility as well as when mounted on a low noise, aerodynamic SB-10 glider, chosen to improve the signal to noise ratio. Helmholtz resonance and “lengthwise cavity resonance” peaks, which remained fixed in frequency despite velocity changes, were measured in both open-jet and fly-over tests. The wheel bay tones were typically lower than the peak of the hay-stack spectrum associated with the aerodynamic noise radiated from the landing gear itself. The main landing gear (MLG) cavity tones were lower than those from the NLG. It was noted that extremely high tone intensities could be measured when the cavity was empty but the “spoiling effect” of the gear components drastically reduced the levels. An examination by Langtry and Spalart [19] used computational methods to predict the unsteady pressure and subsequent noise generation by a landing gear wheel well of a commercial aircraft geometry. The research examined the specific stage when the landing gear has been retracted (or not yet deployed) and when the doors are open. The numerical analysis compared well with experimental studies with significant pressure and noise levels measured. Dedoussi et al. [20] performed fly-over measurements of a Boeing B747-400 which were used to determine the contribution of the landing gear to the overall noise emitted. Using beamforming methods, a tonal source from the nose landing gear was identified at 380 Hz with a harmonic at 760 Hz which, as the frequency was found to be independent of velocity, was concluded to be caused by flow over a cavity and in particular that of the landing gear wheel bay. The 760 Hz tone increased the overall airframe sound level by approximately 5 dB, and thus could prove to be a significant factor in the outcome of noise certification. In 2016, Neri et al. [21] in the precursor to the current work, examined the acoustic output of a nose landing gear wheel bay reporting the presence of higher order acoustic modes. This work was compared to fly-over measurements of similarly sized regional aircraft by Merino et al. [22] who measured cavity noise at approximately 2 kHz from a number of aircraft in the sample set. In their case, due to the relatively small size of the array, there was not sufficient resolution at low frequencies to allow for the identification of wheel bay resonance. In 2017, Saloua et al. [23] performed Zonal Detached Eddy Simulation (ZDES) simulations of the noise emission of a regional aircraft main landing gear bay. The aerodynamic analysis of Saloua et al. clearly shows the fundamental mechanisms such as three 4

115

120

125

130

135

140

145

dimensional vortices and a cavity turbulent shear layer associated with the Kelvin-Helmholtz instability mechanism. The results also show a cavity flow oscillating in a shear layer mode. The unsteady phenomena are influenced by the presence of the main landing gear, this element producing turbulent structures and modifying the ones generated by the bay leading edge. In this case, the numerical analysis is compared to experimental results from 1/2 scale main landing gear measurements with identical geometry performed within the EU Cleansky funded ALLEGRA project. In both sets of data, it was found that wheel bay cavity noise was radiated to the far field even in the presence of the landing gear itself although it is important to note that the MLG is located off-centre in the wheel bay opening and occupies less of the opening area compared to the NLG configuration. Partially covered cavity oscillations have been investigated over the years [24, 25, 26, 27, 28] but only few authors to date [29, 30, 31, 32, 33] have examined the excitation of higher order acoustic modes in cavities with typically only the lowest order mode/frequency being deemed important. With wheel bays increasing in size, thus lowering the cut-on frequency of the higher order modes, an awareness and understanding of the higher order acoustic modes is necessary if a comprehensive understanding of the acoustic behaviour of landing gear bay cavities is to be reached. This paper presents experimental and numerical results from the Clean Sky funded ALLEGRA (Advanced Low Noise Landing (Main and Nose) Gear for Regional Aircraft) project. This project was developed in order to assess low noise technologies applied to a full scale nose landing gear model and a half scale main landing gear model of a regional aircraft. One of the significant contributions of ALLEGRA is that a full representation of the landing gear detail and associated structures (e.g. wheel bay cavity, bay doors, belly fuselage and hydraulic dressings) have been included and addressed at a realistic scale. During the test campaign, a number of low noise treatments were applied to the NLG model such as wheel hub caps, a wheel axle wind shield, a ramp door spoiler and perforated fairings. Over 170 far field sensors were deployed in a number of microphone arrays and local internal pressure sensors were installed inside the wheel bay. Preliminary experimental results for the characterization of the same full scale nose landing gear with and without the application of low noise technologies were reported by Neri et. al [17, 34] for the nose landing gear and by Kennedy et al. [35] for the main landing gear. The numerical results for the same project, regarding the nose landing gear, are reported by Dahan et 5

150

155

160

al. [36, 37]. The fact that the model includes the bay cavity within the fuselage section, allows for an investigation of the contribution of the bay cavity modes to the overall noise emission of the model. Thus, in this paper, it is of interest to explore the contributions of both low and higher order cavity resonance, which can be calculated numerically, and compared with data from full scale testing of the nose landing gear bay cavity. For aircraft take-off and landing, where the flow speed varies, and where the geometry changes as doors open and close and as the gear is deployed and retracted, it is important to be able to predict these modes so that mitigation measures can be implemented. A comparison between the results obtained using far field sensors and local sensors mounted in the bay is presented, in order to characterize the bay cavity tones directivity and understand their influence on the far field noise. Numerical results were obtained using a Wave Expansion Method (WEM). 2. Methods

165

170

175

180

2.1. Cavity Oscillations Landing gear cavities may be either almost entirely open to the flow on one face or closed except for a small opening to the flow [2], as for the case presented in this paper. Cavity resonances are generated by a harmonic forcing function acting at the cavity opening. The occurrence of these oscillations depends on the cavity configuration, the flow speed and upstream boundary layer, and the presence of the struts, etc., which may disturb the flow. The cavity oscillation process seems to cause monopole radiation, at least at low speeds as proposed by Bliss and Hayden[2]. In the present case, this oscillation is produced by the vortex shedding in the shear layer. When the frequency corresponding to the vortex shedding coincides with a characteristic frequency of the cavity, resonance takes place. In addition, as the wheel bay opening of the aircraft under investigation in this study is small compared to the internal dimensions, Helmholtz resonance is also of interest as calculated by:  S c fHRtheoretical = (1) 2π V ls where S is the plan-view cross-sectional area of the bay opening, V is the volume of the wheel bay cavity, c is the speed of sound and ls is the length of the slug of air that oscillates in the opening, or neck of the cavity. Shear layer 6

185

190

cavity flows can also generate traveling acoustic waves in the cross-stream direction. These waves are reflected from the bottom of the cavity and can feed back to the shear layer. In 1964, Rossiter [38] presented his study on wind tunnel experiments of a high Mach number (M ≥ 0.5) flow over a series of rectangular shallow cavities. According to his work, the feedback mechanism is an upstream-traveling acoustic wave generated by turbulent structures impacting the downstream edge of the cavity. If this acoustic frequency excites the shear layer oscillation, a high amplitude feedback instability results [39]. The shear layer excitation frequency can be calculated using the empirical formula suggested by Rossiter [38]: fRossiter =

195

200

205

210

215

U n−α L M + 1/k

(2)

where α is the phase delay, k is the convection velocity of the shear layer normalized by the free stream velocity, n = 1, 2, 3, ... is the order of the shear layer mode, U is the flow velocity and L is the cavity length. As the Mach number, M, considered in this paper is always below 0.18, this upstream propagating acoustic feedback mechanism usually associated with Rossiter is not expected to occur. However, the empirical relation suggested by Rossiter can be used to estimate the shear layer excitation frequency. In fact, this equation has been used by many authors to accurately model other fluidresonant feedback mechanisms [28, 32, 33], where the terms fluid-resonant and fluid-dynamic in this paper correspond to those as defined by Rockwell and Naudascher [40]. 2.2. The Wave Expansion Method The Wave Expansion Method, commonly known as WEM, is a highly efficient finite difference method, originally introduced by Caruthers et al. [41], that uses wave functions which are exact solutions of the governing differential equation and models the propagation of sound from point sources in a duct or a cavity. The WEM code used was further developed by Ruiz and Rice [42], Rolla and Rice [43] and Bennett et al. [39] to investigate sound propagation in quiescent media and has been examined by Bennett et al. [44] and by Stephens et al. [45] for its applicability in ducts. In order to simulate an oscillation in the shear layer, a numerical monopole volume source was located at the orifice opening in accordance with the work of Bliss and Hayden[2]. The complex pressure was solved for in the meshed 7

220

domain as a function of frequency and the amplitude plotted over the mesh in order to obtain the pressure field. We refer to the papers from Bennett et al. [44, 33] for the theory behind the mode propagation in ducts and the wave expansion method. 3. Experimental Set-Up

225

230

235

3.1. Wind Tunnel, Instrumentation and Landing Gear Model Tests were performed in the Pininfarina open jet semi-cylindrical aeroacoustic wind tunnel facility in Turin, Italy, which has a test section of 8m x 9.60m x 4.20m. The facility contains a main fan of 29 blades and an additional low noise, high speed fan-drive system of 13 fans which increases the flow speed up to 72 m/s and reduces the background noise level to 78 dBA at 38 m/s. The velocity produced by the wind tunnel is very uniform, since it varies by only 0.5% over the area. The turbulence level can be adjusted to be between 0.3% and 8%. Regarding the coordinate system employed, the the xz plane is the symmetry plane of the test model, the yz plane corresponds to the plane parallel to the wind tunnel nozzle exit with the origin situated on the floor of the testing platform, along the center of the nozzle. The coordinate system can be seen in Figs 1 and 2.

Figure 1: Front view of the relative position of the model and the microphone arrays within the wind tunnel.

8

Figure 2: Plan view schematic of linear far field array angles, where the first and the last microphones are highlighted, as well as the one at approximately 90◦ (mic 6).

240

Four microphone arrays were installed inside the wind tunnel but it is primarily the measurements from the far field linear array of 13 microphones aligned parallel to the model axis and at a distance of 4.22m from the axis centerline that are examined in this study. In addition, three local internal pressure sensors were installed inside the bay cavity. The positions and the names that will be used to refer to them are shown in Fig. 3.

Figure 3: Surface mounted pressure sensors located within wheel bay.

245

Figure 1 presents the relative position of the model to the microphone arrays and the collector within the wind tunnel as viewed from upstream of the nozzle. Results presented in this paper focus on those obtained using the 13 microphones of the linear far field array: indicated with a square in the 9

250

255

top right of the figure. The coordinates of the centre of this sideline array are x = 3.075m, y = −4.22m, z = 2.75m. The layout of this array was chosen to cover the maximum emission angle possible. Figure 2 presents a top-down/plan view of the relative position between the wheels and the linear far field array on the side and provides more detail on the layout of this array which spanned angles from approximately 41◦ to 142◦ from the nose landing gear wheel axle. Data were acquired for 10 seconds at a sampling rate of 32,768 Hz. The full scale nose landing gear model complete with the belly fuselage and bay cavity was positioned in the wind tunnel such that the distance between the wind tunnel nozzle and the landing gear wheel axis was 2.8 m. The wheel axle coordinates were: X = 2.8 m Y = 0 m Z = 2.175 m

260

Figure 4 shows the dimensions of the wind tunnel test model while Fig. 5 shows a photograph of the NLG model inside the wind tunnel.

Figure 4: Dimensions of wind tunnel test model in mm.

265

3.2. Test Configurations In order to assess the contribution to the total noise of the wheel bay cavity tones, a number of different configurations were tested. NLG, as presented in Fig. 5, is considered to be the baseline test. The fuselage-only configuration was tested with the bay closed (configuration NF) and with the bay open (configuration NB) where there landing gear and doors were removed.. Figure 6 presents an isometric view of the fuselageonly configuration, which highlights the geometry of the cavity/wheel bay being analyzed.

10

Figure 5: NLG model inside the wind tunnel.

Figure 6: View of the fuselage-only configuration, which includes the original geometry of the cavity being analyzed.

270

Considering the angle of attack as the angle between the oncoming air and a reference line on the aircraft, all the wind tunnel models had a fixed, built in, angle of attack setting of 4◦ in order to simulate approach conditions. In the full ALLEGRA test campaign, each model configuration was tested at a variety of flow speeds and yaw settings. The yaw settings allowed the 11

275

performance of the technology to be evaluated under conditions equivalent to landing with a cross wind. No yaw angle variation is considered in the current paper. 4. Results

280

285

290

295

300

305

This section describes the different techniques used to quantify the noise emitted from the nose landing gear and to study the noise associated with the bay cavity. The noise has been assessed as a function of frequency. Results are presented primarily for the 50 m/s velocity and 0◦ yaw angle test point although velocities of 40 m/s and 60 m/s are also examined here. 4.1. Fuselage Noise and Dressed Nose Landing Gear Noise Preliminary tests were conducted in order to characterize the background noise. No acoustic measurements were recorded of the empty wind tunnel, therefore the spectra of the NF configuration characterises both the NF and wind tunnel acoustic output. The NF configuration therefore is considered to be the baseline background noise case, above which we can identify the contributions from individual components and assemblies such as the wheel bay and landing gear etc. One of the additional benefits of manufacturing this accurate fuselage in the test campaign, as well as to house the wheel bay, was to provide the correct boundary layer and aerodynamic flow field, resulting from the associated curvatures of the fuselage, to impinge upon the gear. Narrow band A-weighted spectra were obtained for all the microphones in the linear far field array. Figure 7 presents the results for NLG and NF, for microphones 3, 6 and 11, corresponding to 62◦ , 87◦ , 124◦ for 50 m/s. Spectra are confined to the region between 10Hz and 10kHz within which the main noise sources are found. As stated above, the spectra presented here are for the fuselage-only case: NF, and the baseline nose landing gear case: NLG. In this way, it is possible to identify the contribution of the summation of the landing gear, bay and doors above the background noise. From observation of Fig. 7, the landing gear increases the noise by approximately 10dB above the background noise level across a very wide frequency range, especially in the region of 200 Hz, and at all emission angles. Increases of up to 15dB can be seen at different emission angles.

12

(a) 62◦ (mic 3)

(b) 87◦ (mic 6)

(c) 124◦ (mic 11) Figure 7: Narrow Band Experimental A-weighted Spectra for NLG and NF for 50 m/s flow speed at different emission angles.

310

315

320

325

Preliminary results of the background noise (NF) reveal peaks that on occasion appear in subsequent results and that are related to the closed fuselage/wind tunnel noise as opposed to the landing gear noise. For this reason, it is of importance to underline the contribution of this background noise: NF to the overall noise, highlighting the broadband noise and the peaks generated by the presence of the fuselage in the wind tunnel. The result presented in Fig. 8 is for 50 m/s for microphone 11 of the linear far field array. Peaks are to be found at 125 Hz, 249 Hz and 372 Hz, which are identified as WT1, WT2 and WT3 in Fig. 8. No rpm of the main fan was recorded in these tests but it is assumed that these strong, narrowband wind tunnel tones are related to the single main fan of 29 blades. Peaks at the same frequencies are visible using alternative sensors from the linear and top array. Presumably, 125Hz is a fundamental frequency with the higher tones being harmonics. These frequencies were examined and found to be proportional to the wind tunnel velocity. In addition, for a fixed nominal wind tunnel velocity setting, the frequencies of these peaks were found to decrease for both the NLG or NB configuration compared to the NF test case. This effect can be seen clearly in Fig. 20 and Fig. 21 for example. It is assumed that this was due to the changes in loading on the main fan resulting from the different configurations. These tones appear in subsequent

13

330

plots but, for the reasons outlined above, are to be disregarded, not being related to the landing gear, doors or wheel bay.

Figure 8: Background noise tones:125 Hz (WT1), 249 Hz (WT2) and 372 Hz (WT3) (tunnel blade passing frequencies), resulting from the closed fuselage (NF) and wind tunnel noise. Narrow Band Experimental A-weighted Spectra for NF for 50 m/s flow speed for mic 11 of the linear far field array.

335

340

345

Spectrograms as a function of frequency and emission angle were generated using the data of the linear far field array for the 50 m/s velocity. In this way the directivity of the landing gear sources alone can be emphasised through subtraction. If the spectrogram for the fuselage-only: NF, is subtracted from the spectrogram for the NLG baseline configuration, the result, shown in Fig. 9, is therefore the noise coming from the full nose landing gear itself, in addition to that from the doors and wheel bay. The large scale objective is to characterise and reduce this noise. Blue colours indicate a noise reduction while red colours indicate a noise increase. As shown in Fig. 9, the greatest contribution from the nose landing gear, up to 10 dB, can be found in the frequency range between 160 Hz and 1000 Hz, in particular concentrated between 180-216 Hz and 320-348 Hz. The decomposition of the acoustic output of the NLG into contributions related to its constituent parts, e.g. wheels, doors, torque link, steering pinion etc. will be published in a subsequent article as will the beneficial effect of the low-noise technologies. The emphasis of the current work is on the contribution of the wheel bay itself and how its acoustic output is effected by the presence of the landing 14

gear.

Figure 9: (NLG)-(NF) ΔSPL. Acoustic signature from dressed nose landing gear, complete with wheel bay and doors once the fuselage and wind tunnel noise have been subtracted. Spectrogram as a function of frequency and radiation angle: 50 m/s. Dominant frequency range is between 160 Hz - 1000 Hz.

350

355

360

4.2. Study of wheel bay cavity noise As stated above, a principal focus of this paper is to assess the contributions of low and higher order cavity resonance, which can be calculated numerically, and compared with the experimental results from the full scale testing of the bay cavity, both from far field sensors and the local internal pressure sensors, which are shown in Figures 3 and 2. 4.2.1. Numerical Results In order to better understand the formation of standing waves inside the bay and the potential importance of the bay cavity tones to the overall far field noise, an equivalent domain to the landing gear cavity presented in Fig. 6 was meshed and tested using a series of numerical simulations. The method used is the wave expansion method (WEM) (see Sec. 2.2). In order to simulate an oscillation in the shear layer, in accordance with observations by Bliss and Hayden [2], a numerical monopole volume source was located in the bay cavity opening. The complex pressure was solved for in the meshed

15

365

370

375

domain as a function of frequency and the amplitude was plotted over the mesh in order to examine the pressure field in the cavity. A mesh resolution analysis was conducted to determine the optimum grid mesh density to achieve a sufficiently accurate solution while minimizing computational cost. Thus, using this optimum mesh, the accuracy of the results are good enough to capture all the necessary pressure features. Figure 10 shows the geometry of the bay, as it was recreated using Creo Parametric 3.0, and the meshed domain. The three-dimensional unstructured mesh encompassing the bay cavity and the domain external to it was generated with Ansys R17.0, resulting in 466,586 tetrahedral elements and 90,575 nodes. The response of the system as a function of frequency was determined by running the WEM code in a loop over 381 frequencies in the range 20 Hz 400 Hz.

(a)

(b) Figure 10: (a) Geometry of the landing gear bay cavity and (b) meshed domain.

Figure 11 indicates the positions in the cavity, corresponding to the loca16

380

385

390

tions of the three sensors physically installed inside the wheel bay (as in Fig. 3). At each of these three positions, the pressure solution from the WEM analysis was recorded as a function of frequency and the spectra calculated. Figure 12 represents the numerical spectrum for the node inside the meshed bay domain corresponding to pressure sensor B5 in Fig. 3. Similar results were found using the other two local internal pressure sensors, B3 and B4. In the interests of rigor, figure 13 plots an overall spectrum calculated considering all nodes in the meshed cavity and identifying the maximum pressure in the bay for each frequency. In this way, it is possible to have a clearer idea of the maximum sound pressure inside the bay, independent of the node considered. This avoids the situation where a chosen position might coincide with an acoustic node of a particular acoustic mode shape. In this case, the peak would be absent from the spectrum and information of that mode would be lost. As anticipated, it is possible to note how some of the peaks that appear in the spectrum calculated considering all nodes, Fig. 13, do not appear in the spectrum for pressure sensor B5, Fig. 12, or else they appear with a different relative amplitude.

Figure 11: Position of the nodes inside the cavity in black. The four different shapes highlight the nodes corresponding to the position of the three local internal pressure sensors physically located inside the bay and the numerical monopole source located at the shear layer opening. 395

From analysis of the spectrum in Fig. 13, it should be possible to identify the cavity modes corresponding to the peaks. The design of this nose landing gear wheel bay, seen in figure 6, is a large, partially closed volume, and thus, a tone should correspond to the Helmholtz resonance frequency. This frequency can be calculated analytically, for the same shape of the bay, using 17

Figure 12: Narrow Band numerical spectrum calculated from WEM solution as a function of frequency for a position in the meshed numerical domain corresponding to the position of a local internal pressure sensor inside the bay of the full scale experimental model (mic B5).

Figure 13: Narrow Band numerical spectrum computed from WEM solution as a function of frequency, calculated considering all nodes and taking the maximum pressure in the bay for each frequency.

400

the modification of the Helmholtz formula, see Eqtn. 1, developed by Ma et

18

405

410

415

420

al. [28]. In this case, the neck length of the bay cavity is effectively zero, so, according to Ma et al., an equivalent neck length, ls , equal to the opening length can be used in order to account for the radiation impedance. The result obtained: fHRtheoretical = 36.95Hz, agrees well with the first peak to be seen in the WEM plots. Considering the arbitrary wheel bay coordinate system defined in Fig. 14 and from examining all the figures that represent the pressure field inside the cavity at each peak, e.g. Fig. 15, it was possible to approximate each peak and its frequency with a corresponding mode. Table 1 reports the approximate modes corresponding to these frequencies, while examples of some corresponding pressure fields inside the bay are provided in Figs. 15 and 16, respectively, for modes (1,0,0), (2,0,0) and (2,2,0). It is important to note, that as the bay cavity is not a pure cuboid due to the fact that the depth of the wheel bay decreases towards the nose, this results in modes being cut-off towards the nose that exist at the bay opening end of the bay. The modes defined here, as seen in Table 13, are therefore not accurate at both ends of the wheel bay but are just compromise approximations. An example can be seen in Fig. 16, in which the mode on the right is described as mode (2,2,0) as there are two nodal lines along the z-direction at the opening. However, towards the nose of the bay cavity where the height is lower there is only one nodal line and at this point the mode could instead be described as (2,1,0).

Figure 14: Coordinate System on the bay.

425

4.2.2. Comparison Between Experimental Results and Numerical Results This section presents the comparison between experimental and numerical results. The experimental results match the numerical results quite well, with 19

Table 1: Frequency at each peak of the WEM spectrum (as in Fig. 13) and corresponding modes

Frequency 35 Hz 92 Hz 161 Hz 180 Hz 206 Hz 241 Hz 285 Hz 304 Hz 316 Hz 336 Hz 357 Hz 378 Hz 395 Hz

430

435

440

Mode (x,z,y) Helmholtz resonance (1,0,0) (2,0,0) (0,1,0) (1,1,0) (3,1,0) (2,0,1) (3,1,0) (4,2,0) (3,1,1) (2,2,0) (2,2,0) (5,0,0)

many peaks previously identified in the numerical spectra, being measured in the experimental spectra also. The surface mounted internal bay cavity sensors are examined initially. Figure 17 plots a narrow band experimental A-weighted spectra of B5, for the NB configuration. For this sensor location, we see that the Helmholtz and first longitudinal mode (1,0,0), see Fig. 15, dominate at such a high amplitude, that the remaining peaks are identified as either sum and difference frequencies between the two or else harmonics of each. For this first longitudinal mode frequency, there is a 16 Hz difference between the WEM and experimental result. The WEM solution does not model the air flow and based on previous work in the Flow-Induced Vibration (FIV) and Fluid-Structure Interaction (FSI) domains [46, 39], it is thought here that the longitudinal mode is “locked-on” to the second harmonic of the Helmholtz frequency resulting in a high amplitude response at the slightly higher frequency. Some of the other duct modes predicted by the WEM are discernible but only at a relatively low magnitude. It it important to remember that this sensor is subject to high levels of hydrodynamic noise due to flow entrainment and recirculation within the bay. Similar results were found through observation of the spectra from sensors B3 and B4. 20

Figure 15: Numerical (WEM) pressure field plotted in the cavity for mode (1,0,0) at 92 Hz. 445

450

455

460

In order to gain more insight, the response at this sensor location was examined at additional tunnel velocities. Figure 18 shows the spectra for the same sensor, B5, but here for three different wind tunnel velocities: 40m/s, 50m/s and 60m/s and in a plan view. Superimposed on this plot are the first two shear layer modes, SL1 and SL2, as calculated from Eq. 2. The values chosen for α and k are 0.25 and 0.75 respectively. Here we observe that for 40m/s both the WEM predicted (1,0,0) mode at 92 Hz and the 104 Hz tone are excited but at relatively low amplitudes. However, at 60m/s a very large tone at precisely 94Hz is evident. This agrees very well with the WEM predicted frequency of 92Hz. In addition, we see that the Helmholtz frequency is strongly excited at 50m/s and still so at 60m/s but at a lower amplitude. From observation of this plot we see therefore that resonance is controlled by the wind tunnel velocity. Similar observations can be seen in the basic cylindrical cavity studies of Bennett et al. [39, 31, 45] but demonstrated here for a full scale, irregularly shaped aircraft wheel bay. The physics of this plot are that the shear layer modes provide input energy via shear layer oscillations. These relate to vortex shedding from the

21

(a) Mode (2,0,0) at 161 Hz (b) Mode (2,2,0) at 357 Hz Figure 16: Numerical (WEM) pressure field plotted in the cavity for modes (2,0,0) and (2,2,0).

Figure 17: Experimental Narrow Band A-weighted Spectra for NB for 50 m/s flow speed for a sensor inside the bay (mic B5).

22

465

470

leading edge of the wheel bay opening. The vortex shedding and therefore the oscillation frequency increase with main flow velocity. When these oscillation frequencies coincide with a wheel bay characteristic frequency, resonance results, leading to high amplitude acoustic output. In Fig. 18 we see that SL1 coincides with the Helmholtz frequency at 50m/s and that SL2 coincides with the first longitudinal mode at 60m/s which explains why these modes are excited at these tunnel speeds at such high amplitudes compared to the others. At 40m/s and at 50m/s we also see the first harmonic of the Helmholtz frequency and the main anomoly in this figure is that the Helmholtz frequency appears to resonate at a lower frequency at 40m/s. This has also been observed by Bennett et al. also [39] but no verified explanation has yet been provided other than to guess that the frequency changes as a result of the boundary layer modifying the effective neck length.

Figure 18: Frequency response of the B5 pressure sensor for three different wind tunnel velocities. The first two shear layer mode from equation 2 are superimposed on the plot. α = 0.25 and k = 0.75. 475

480

Equipped with some understanding of the noise generating mechanisms of the wheel bay, attention is now directed to the modes radiating to the far field. The numerical results presented in Fig. 13 are compared with the experimental results measured with the far field microphones, both for the NB and the NLG configurations. Several array microphones were used for this analysis, both from the linear far field array and the top array. In this way it was possible to assess the propagation of the bay cavity modes to the 23

485

490

495

far field and their directivity. Figure 19 provides an example of a far field noise measurement, demonstrating how three modes predicated by the numerical analysis, namely the Helmholtz resonance and modes (1,0,0) and (2,0,0) propagate to the far field at this emission angle. Results obtained with different sensors from the top and linear arrays show how, as expected, these modes radiate with different amplitudes in different directions. These two standing wave modes that radiate to the far field, (1,0,0) and (2,0,0) are those plotted in Figs 15 and 16. The Helmholtz resonance mode is not plotted as a pressure field as it simply appears as a single colour in the WEM calculated pressure field, being not the result of a standing wave, but rather a full volume compressibility effect. In Fig. 19, also measured and indicated, are the background noise wind tunnel tones WT1, WT2 and WT3 as well as sum and difference tones between the Helmholtz Frequency and the (1,0,0) duct resonant mode.

Figure 19: Narrow Band Experimental A-weighted Spectra for NB for 50 m/s flow speed for mic 6 of the linear far field array.

500

505

Figure 20 plots the spectrogram for the open wheel bay configuration: NB-NF. In this case, the background noise is subtracted from the open bay: NB configuration with no landing gear or doors installed. It is possible again here to see the three resonant peaks of Fig. 19 at 32 Hz, 104 Hz and approximately 160 Hz for this 50 m/s wind tunnel velocity setting, (ref. Table 1) and it is important to note that their relative magnitudes vary with radiation angle. The noise generated at many angles is up to 10 dB above the noise level generated by the fuselage-only. Quite striking in this spectogram are the clear red and blue lines at approximately the WT1, WT2 24

510

and WT3 frequencies. Figure 21 helps to explain this. As mentioned, the wind tunnel background tones were found to decrease in frequency upon the addition of the NLG, possible due to extra loading on the wind tunnel fans. The consequence of this, is that upon subtraction of the two configurations to form the spectrogram, a peak and a dip at these frequencies are created.

Figure 20: (NB)-(NF) ΔSPL. Acoustic signature from wheel bay-only once the fuselage and wind tunnel noise have been subtracted. Spectrogram as a function of frequency and radiation angle: 50 m/s. Resonant tones to be seen at 32 Hz, 104 Hz and 160Hz.

515

520

Reviewing the results in this section so far and with reference to Figs. 19 and 20, observations on the radiation of the empty wheel bay resonant tones conclude that the Helmholtz resonance and the next two cavity tones are excited at significantly high amplitudes and over a wide range of angles. Even higher order modes, as predicted by the numerical analysis, would be excited either at higher tunnel speeds (aircraft landing velocity) or by increasing the internal dimensions of the bay. It is important to note that the main landing gear wheel bays of large aircraft would have significantly more voluminous wheel bays than this nose landing gear wheel bay of a regional aircraft. However, for this NLG model, it is significant that is has been demonstrated that these first three modes are excitable within the velocity range of a landing aircraft up to M=0.18. 25

Figure 21: Narrow Band Experimental A-weighted Spectra for NB and NF for 50 m/s flow speed for mic 5 of the linear far field array.

525

530

535

540

The next analysis concerns the addition of the Nose Landing Gear into the empty wheel bay. Regarding the baseline NLG configuration, results are presented in Fig. 22 for microphone 5 of the linear far field array. We see now that not only do these three modes no longer radiate to the far field but neither do any other. The peaks in Fig. 22 correspond to background wind tunnel tones. The noise levels measured now are as a result of the presence of the landing gear and of the background noise. Results obtained with different sensors from the top and linear arrays confirm these results. To try and understand why the modes no longer radiate to the far field for the NLG configuration, i.e. with the addition of the landing gear and doors, components were added piecemeal to the open-bay: NB configuration, to see at which stage the tones disappear. Initially, the basic leg structure was added to the empty bay. In order to do so, it is necessary to introduce a configuration that was tested during the test campaign and that consists of the nose landing gear with dressings (Dress), wheels (W), torque link (T), steering pinion (S) and doors (D) removed. In other words, this configuration presents only the fuselage with the open bay and the undressed basic leg structure. Figure 23 shows this configuration, which is called NLGDressWTSD. Subtracting from the spectrogram for this configuration the 26

Figure 22: Narrow Band Experimental A-weighted Spectra for NLG for 50 m/s flow speed for mic 5 of the linear far field array.

545

one for the fuselage: NF, the contribution of the bay and leg structure only can be assessed. Thus, when this basic leg structure is added to the NB bay-only configuration (spectrogram reported in Fig. 20) a new spectrogram can be generated, as shown in Fig. 24.

Figure 23: NLG-DressWTSD configuration, consisting of the nose landing gear with dressings, wheels, torque link, steering pinion and doors removed.

In this spectrogram it is possible to identify the contribution of the leg 27

550

555

structure, mainly between 124 and 250 Hz, and the same peaks from the bay as in Fig. 20, at 32 Hz and 104 Hz. However, while the second cavity peak remains at a similar level, albeit for reduced radiation angles, the first one significantly decreases by 4 dB at some angles. It is still, however, present to some degree, especially as measured by microphones 3, 9 and 10. The reduction in level is thought to be due to the presence of the leg as well as the drag and side-stays disrupting the shear layer and therefore reducing both the Helmholtz resonance and the excitation of the first longitudinal mode. Regarding the tone corresponding to the (2,0,0) mode at approximately 160 Hz, it is difficult to determine how this has been effected as there is a significant noise level increase in this frequency range due to the addition of the basic leg structure.

Figure 24: (NLG-DressWTSD)-(NF) ΔSPL. Spectrogram as a function of frequency and radiation angle for 50 m/s flow speed. Contributions from bay and leg structure only are shown (dominant frequency range is between 124-250 Hz (leg) + two peaks at 32 Hz and 104 Hz (bay)).

560

In a similar manner, the consequence of the addition of the doors can be evaluated, as reported in the spectrogram in Fig. 25. Also in this case, in order to do so, it is necessary to introduce another configuration that was tested during the test campaign and that consists of the nose landing gear with dressings, wheels, torque link and steering pinion removed. In other words, this configuration presents only the fuselage with the open bay, the 28

565

570

575

undressed leg structure and the doors. Figure 26 shows this configuration, which is called NLG-DressWTS. Subtracting from the spectrogram for this configuration the one for the fuselage NF, the contribution of the bay, leg structure and doors only can be assessed. Thus, in the spectrogram again it is possible to highlight the contribution of the leg structure, as in Fig. 24, mainly between 124 Hz and 250 Hz. The contribution of the doors is present at slightly higher frequencies, between 130 Hz and over 400 Hz. The bay peaks that were clearly seen in Fig. 20 and slightly disrupted in Fig. 24, are instead here completely eliminated with the addition of the doors. This, as discussed above, agrees with the results previously found in the spectra. Certainly, the presence of the doors blocks radiation to the sideline microphones but the fact that the tones are no longer measured by microphones in the top array either verifies that the modes are no longer excited as opposed to just being shielded.

Figure 25: (NLG-DressWTS)-(NF) ΔSPL. Spectrogram as a function of frequency and radiation angle for 50 m/s flow speed. Contributions from bay, leg structure and doors only are shown (dominant frequency range is between 124-250 Hz (leg) + 130-400 Hz (doors)).

29

Figure 26: NLG-DressWTS configuration, consisting in the nose landing gear with dressings, wheels, torque link and steering pinion removed.

5. Conclusions 580

585

590

595

600

This work reports on the wind tunnel testing of a highly detailed nose landing gear model. The model was built at full scale and is one of the first to simultaneously include the leg structure, a realistic fuselage, full bay cavity with doors and to use a completely realistic geometry including the application of hydraulic dressings. The experimental results of narrow band spectra and spectrograms were compared with a numerical analysis. The evaluations presented here are primarily for a wind tunnel velocity of 50m/s, a 0◦ yaw angle and a 4◦ angle of attack. Results show that the techniques used, successfully quantified the landing gear noise in different frequency ranges. The landing gear noise was found to be dominant in the frequency range between 160 Hz and 1000 Hz, with particular contribution at 180-216 Hz and 320-348 Hz. The noise increment obtained by the installation of the dressed landing gear complete with wheel bay and doors reached 15 dB. The contribution of the wheel bay cavity noise to the overall noise has been assessed through both experimental and numerical methods, in order to calculate the contribution of the bay noise to the total noise emission. The frequencies of the bay cavity modes were identified numerically and the corresponding pressure fields were plotted over the meshed domain of the wheel bay for each mode. These frequencies matched well with the experimental ones measured by far field microphones as well as with measurements from local internal pressure sensors mounted inside the bay cavity. The success30

605

610

615

620

625

ful validation of the WEM by the experimental results conclude that such numerical methods should be used at the preliminary design stage of wheel bays so that noise mitigation measures can be taken. Observations on the radiation of the empty wheel bay resonant tones conclude, that for this nose landing gear bay of a regional aircraft, the Helmholtz resonance and the next two cavity tones are excited at significantly high amplitudes and over a wide range of angles. This noise was found to contribute up to 12 dB, with dominant peaks at 32 Hz (corresponding to the Helmholtz resonance) and two other empty wheel bay resonant modes (1,0,0) and (2,0,0) at 94Hz/108Hz, 156Hz respectively. Even higher order modes, as predicted by the numerical analysis, would be excited either at higher tunnel speeds (aircraft landing velocity) or by increasing the internal dimensions of the bay. However, for this NLG model, it is significant that is has been demonstrated that these first three modes are excitable within the velocity range of a landing aircraft. Final results show that, for this symmetrical configuration, once the NLG is installed, none of the wheel bay cavity modes are excited and thus do not radiate to the far field. In fact, the installation of the basic leg and the doors were found to be sufficient to suppress the tones. It is believed that, unlike for other cases to be found in the literature, such as the MLG study of Saloua et al. [23], where wheel bay tones do radiate to the far field even in the presence of the gear, the nose landing gear leg design here is located in the centre of the wheel bay opening and together with the drag and side stays-struts are sufficient to significantly disrupt the shear layer preventing the excitation of the bay cavity tones. Acknowledgments

630

635

The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) for the Clean Sky Joint Technology Initiative under grant agreements n◦ [308225] (ALLEGRA) and n◦ [620188] (ARTIC). Authors acknowledge all the partners that took part in the ALLEGRA and ARTIC projects: KTH Sweden, Pininfarina SPA, Eurotech, Teknosud, Magnaghi Aeronautica. The authors would like to acknowledge the work of Dr. Francesco Amoroso of Eurotech who led the manufacture of the model and Mr. Marco Esposito of Teknosud who led the wind tunnel model design.

31

References

640

[1] R. J. Astley, A. Agarwal, P. F. Joseph, R. H. Self, M. G. Smith, R. Sugimoto, B. J. Tester, Predicting and reducing aircraft noise, 14th International Congress on Sound Vibration. URL http://eprints.soton.ac.uk/50463/ [2] D. B. Bliss, R. E. Hayden, Landing gear and cavity noise prediction, in: NASA Technical Report, 1976. URL https://ntrs.nasa.gov/search.jsp?R=19760021873

645

650

[3] K. Boorsma, X. Zhang, N. Molin, Landing gear noise control using perforated fairings, Acta Mechanica Sinica 26 (2) (2009) 159–174. doi:10.1007/s10409-009-0304-0. URL http://link.springer.com/article/10.1007/s10409-009-0304-0 [4] M. G. Smith, L. Chow, N. Molin, Control of landing gear noise using meshes, in: AIAA-2010-3974, 2010. URL http://arc.aiaa.org/doi/abs/10.2514/6.2008-2816 [5] J.-F. Piet, N. Molin, C. Sandu, Aircraft landing gear provided with at least one noise reducing means, in: Patent number 8256702, 2012.

655

[6] H. H. Heller, W. M. Dobrzynski, Sound Radiation from Aircraft WheelWell/Landing-Gear Configurations, Journal of Aircraft 14 (8) (1977) 768–774. doi:10.2514/3.58851. URL http://arc.aiaa.org/doi/10.2514/3.58851 [7] W. Dobrzynski, H. Buchholz, Full-scale noise testing on airbus landing gears in the German Dutch wind tunnel., AIAA-97-1597.

660

665

[8] S. Jaeger, N. Burnside, P. Soderman, W. Horne, K. James, Microphone array assessment of an isolated, 26%-scale, high-fidelity landing gear, in: AIAA-2002-2410, 2002. URL http://arc.aiaa.org/doi/abs/10.2514/6.2002-2410 [9] W. Dobrzynski, L. Chow, P. Guion, D. Shiells, Research into landing gear airframe noise reduction, in: AIAA-2002-2409, 2002. URL http://arc.aiaa.org/doi/abs/10.2514/6.2002-2409

32

[10] L. V. Lopes, K. S. Brentner, P. J. Morris, D. P. Lockard, Increased fidelity in prediction methods for landing gear noise, in: AIAA-20062624, 2006. 670

[11] G. P. Howell, A. J. Bradley, M. A. McCormick, J. D. Brown, De-dopplerization and acoustic imaging of aircraft flyover noise measurements, Journal of Sound and Vibration 105 (1) (1986) 151–167. doi:10.1016/0022-460X(86)90227-0. URL http://www.sciencedirect.com/science/article/pii/0022460X86902270

675

[12] U. Michel, W. Qiao, Directivity of landing gear noise based on flyover measurements, in: AIAA-99-1956, 1999. doi:10.2514/6.1999-1956.

680

[13] U. Michel, P. B¨ohning, Investigation of aircraft wake vortices with phased microphone arrays, in: AIAA-2002-2501, American Institute of Aeronautics and Astronautics, 2002. URL http://arc.aiaa.org/doi/abs/10.2514/6.2002-2501

685

[14] U. Michel, J. Helbig, B. Barsikow, M. Hellmig, M. Schuettpelz, Flyover noise measurements on landing aircraft with a microphone array, in: AIAA-1998-2336, American Institute of Aeronautics and Astronautics, 1998. URL http://arc.aiaa.org/doi/abs/10.2514/6.1998-2336

690

[15] S. Guerin, U. Michel, H. Siller, U. Finke, G. Saueressig, Airbus A319 database from dedicated flyover measurements to investigate noise abatement procedures, in: AIAA-2005-2981, American Institute of Aeronautics and Astronautics, 2005. URL http://arc.aiaa.org/doi/abs/10.2514/6.2005-2981

695

[16] M. Pott-Pollenske, W. Dobrzynski, H. Buchholz, S. Gu´erin, G. Saueressig, U. Finke, Airframe noise characteristics from flyover measurements and prediction, in: AIAA-2006-2567, American Institute of Aeronautics and Astronautics, 2006. URL http://arc.aiaa.org/doi/abs/10.2514/6.2006-2567

700

[17] E. Neri, J. Kennedy, G. J. Bennett, Characterization of low noise technologies applied to a full scale fuselage mounted nose landing gear, in: ASME 2015 Noise Control and Acoustics Division Conference at InterNoise 2015, San Francisco, California, USA, 2015. URL http://arc.aiaa.org/doi/abs/10.2514/6.2008-2816 33

705

[18] Petr Eret, John Kennedy, Gareth J. Bennett, Effect of noise reducing components on nose landing gear stability for a mid-size aircraft coupled with vortex shedding and freeplay, Journal of Sound and Vibration 354 (2015) 91–103. doi:10.1016/j.jsv.2015.06.022. URL http://linkinghub.elsevier.com/retrieve/pii/S0022460X15005040 [19] R. B. Langtry, P. R. Spalart, DES investigation of a baffle device for reducing landing-gear cavity noise, AIAA-2008-13.

710

715

720

725

[20] I. C. Dedoussi, T. P. Hynes, H. A. Siller, Investigating landing gear noise using fly-over data: the case of a Boeing 747-400 (AIAA 20132115), American Institute of Aeronautics and Astronautics, 2013. doi:10.2514/6.2013-2115. URL http://arc.aiaa.org/doi/10.2514/6.2013-2115 [21] Eleonora Neri, John Kennedy, Gareth J. Bennett, Noise characterization and noise treatment of a detailed full scale nose landing gear, in: in Greener Aviation Conference: Achievements and Perspectives in Clean Sky and Worldwide, Brussels, Belgium, 2016. [22] R. Merino Martinez, E. Neri, M. Snellen, J. Kennedy, D. Simons, G. J. Bennett, Comparing flyover noise measurements to full-scale nose landing gear wind tunnel experiments for regional aircraft (AIAA 2017-3006), American Institute of Aeronautics and Astronautics, 2017. doi:10.2514/6.2017-3006. URL https://arc.aiaa.org/doi/10.2514/6.2017-3006 [23] B. K. Saloua, P. Bardoux, J.-L. Godard, T. Le Garrec, J. Kennedy, G. J. Bennett, Investigation of the noise emission of a regional aircraft main landing gear bay, in: AIAA-2017-3012, 2017. [24] H. v. Helmholtz, A. A. Wangerin, Theorie der Luftschwingungen in R¨ohren mit offenen Enden, Leipzig, W. Engelmann, 1896. URL http://archive.org/details/theoriederlufts00wanggoog

730

[25] R. L. Panton, J. M. Miller, Resonant frequencies of cylindrical helmholtz resonators, The Journal of the Acoustical Society of America 57 (6) (1975) 1533–1535. doi:10.1121/1.380596. URL http://scitation.aip.org/content/asa/journal/jasa/57/6/10.1121/1.380596

34

735

[26] F. C. Demetz, T. M. Farabee, Laminar and turbulent shear flow induced cavity resonances, in: AIAA-77-1293, 1977. URL http://adsabs.harvard.edu/abs/1977aiaa.confQ....D [27] S. A. Elder, Self-excited depth-mode resonance for a wall-mounted cavity in turbulent flow, The Journal of the Acoustical Society of America 64 (3) (1978) 877–890. doi:10.1121/1.382047. URL http://asa.scitation.org/doi/abs/10.1121/1.382047

740

745

750

755

760

[28] R. Ma, P. E. Slaboch, S. C. Morris, Fluid mechanics of the flow-excited helmholtz resonator, in: Journal of Fluid Mechanics, Vol. 623, 2009, pp. 1–26. URL http://arc.aiaa.org/doi/abs/10.2514/6.2008-2816 [29] Gareth J. Bennett, J. Kennedy, C. Meskell, M. Carley, P. Jordan, H. Rice, Aeroacoustics research in Europe: The CEAS-ASC report on 2013 highlights, Journal of Sound and Vibration 340 (2015) 39–60. doi:10.1016/j.jsv.2014.12.005. URL http://linkinghub.elsevier.com/retrieve/pii/S0022460X14009663 [30] Francisco Rodriguez Verdugo, Roberto Camussi, Gareth J. Bennett, Aeroacoustic source characterization technique applied to a cylindrical Helmholtz resonator, in: 18th International Congress on Sound and Vibration (ICSV18), Paper No. 2062, Rio de Janeiro, Brazil, 2011, paper No. 2062. URL http://people.tcd.ie/bennettg [31] Gareth J. Bennett, Francisco Rodriguez Verdugo, David B. Stephens, Shear Layer Dynamics of a Cylindrical Cavity for Different Acoustic Resonance Modes, in: 15th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2010. [32] F. R. Verdugo, A. Guitton, R. Camussi, M. Grottadaurea, Experimental investigation of a cylindrical cavity, in: AIAA-2009-3207, 2009. URL http://arc.aiaa.org/doi/abs/10.2514/6.2009-3207 [33] G. J. Bennett, D. B. Stephens, F. Rodriguez Verdugo, Resonant mode characterisation of a cylindrical helmholtz cavity excited by a shear layer, in: The Journal of the Acoustical Society of America, Vol. 141,

35

765

770

2017, pp. 7–18. doi:10.1121/1.4973212. URL http://asa.scitation.org/doi/abs/10.1121/1.4973212 [34] E. Neri, J. Kennedy, G. J. Bennett, Aeroacoustic source separation on a full scale nose landing gear featuring combinations of low noise technologies, in: ASME 2015 Noise Control and Acoustics Division Conference at InterNoise 2015, San Francisco, California, USA, 2015. URL http://arc.aiaa.org/doi/abs/10.2514/6.2008-2816 [35] J. Kennedy, E. Neri, G. J. Bennett, The reduction of main landing gear noise, in: AIAA-2008-2816, 2016. URL http://arc.aiaa.org/doi/abs/10.2514/6.2008-2816

775

780

[36] J. Dahan, R. Futrzynski, C. O’Reilly, G. Efraimsson, Aero-acoustic source analysis of landing gear noise via dynamic mode decomposition, in: 21st International Congress on Sound and Vibration, Beijing, China, 2014. [37] J. Dahan, C. O’Reilly, G. Efraimsson, Numerical investigation of a realistic nose landing gear, in: AIAA-2014-2077, 2015. URL http://arc.aiaa.org/doi/abs/10.2514/6.2014-2077 [38] J. E. Rossiter, Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds, RAE Technical Report No. 64037.

785

[39] G. J. Bennett, K. Zhao, J. Philo, Y. Guan, S. C. Morris, Cavity Noise Suppression Using Fluidic Spoilers (AIAA2016-2756), AIAA-2016-2756, 2016. [40] D. Rockwell, E. Naudascher, Review - self-sustaining oscillations of flow past cavities, Journal of Fluids Engineering 100 (1978) 152–165.

790

[41] J. E. Caruthers, R. C. Engels, G. K. Ravinprakash, A wave expansion computational method for discrete frequency acoustics within inhomogeneous flows, in: AIAA-1996-1684, 1996. [42] G. Ruiz, H. J. Rice, An implementation of a wave based finite difference scheme for a 3-D acoustic problem 256 (2) (2002) 373–381.

36

795

[43] L. B. Rolla, H. J. Rice, A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems, in: Journal of Sound and Vibration, Vol. 296, 2006, pp. 406–415. doi:10.1016/j.jsv.2006.02.023. URL //www.sciencedirect.com/science/article/pii/S0022460X06001970

800

[44] G. J. Bennett, C. J. O’Reilly, H. Liu, Modelling multi-modal sound transmission from point soucres in ducts with flow using a wave-based method, 16th Congress on Sound and Vibration.

805

810

[45] D. B. Stephens, F. R. Verdugo, G. J. Bennett, Shear layer driven acoustic modes in a cylindrical cavity, in: Journal of Pressure Vessel Technology, Vol. 136(5), 2014. URL http://arc.aiaa.org/doi/abs/10.2514/6.2008-2816 [46] S. L. Finnegan, C. Meskell, S. Ziada, The Effect of Sound Pressure on the Aeroacoustic Sources Around Two Ducted Tandem Cylinders, ASME, 2010, pp. 723–733. doi:10.1115/FEDSM-ICNMM2010-30271. URL http://proceedings.asmedigitalcollection.asme.org/proceeding. aspx?articleid=1621718

37