Jet-installation noise reduction with flow-permeable materials

This paper investigates the application of ﬂow-permeable materials as a solution for re- ducing jet-installation noise. Experiments are carried out with a ﬂat plate placed in the near ﬁeld of a single-stream subsonic jet. The ﬂat plate is modular and the solid surface near the trailing edge can be replaced with different ﬂow-permeable inserts, such as a metal foam and a perforated plate structure. The time-averaged jet ﬂow ﬁeld is character- ized through planar PIV measurements at three different velocities ( M a = 0 . 3 , M a = 0 . 5 and M a = 0 . 8 , where M a is the acoustic Mach number), whereas the acoustic far-ﬁeld is mea- sured with a microphone arc-array. Acoustic measurements conﬁrm that installation effects cause signiﬁcant noise increase, up to 17 dB for the lowest jet velocity, particularly at low and mid frequencies (i.e. St < 0 . 7 , with the Strouhal number based on the jet diameter and velocity), and mostly in the upstream direction of the jet. By replacing the solid trail- ing edge with the metal foam, noise abatement of up to 9 dB is achieved at the spectral peak for and the installed curves tend to collapse with the ones of the isolated jet, especially for the highest jet velocity. The results also show that the ﬂow-permeable materials are effective in reducing jet-installation noise in all assessed directions, particularly upstream. This indicates that the dipole sources on the plate are mitigated. In the downstream direction, for the metal foam case, the levels reach those of the isolated jet for θ > 120 ◦ and M a > 0 . 5 , indicating that there is no change in the turbulence-mixing noise component due to the presence of the plate. the metal foam, there is an increase in amplitude, but no signiﬁcant change to the spectral peak frequency, whereas for the perforated there is a low-frequency noise increase with a change in the spectral peak. It is believed that this difference is caused by the high permeability of the metal foam, which produces a new singularity and thus a new scattering region at the solid-permeable junction. These results show that a surface treatment with ﬂow-permeable materials is a potentially promising mitigation solution for jet-installation noise. However, the mechanisms that provide such reductions are still unclear. Further work is required to investigate the phenomena happening at the junction region and inside the ﬂow-permeable structure, particularly focusing on the change of impedance, pressure imbalance and the effect of permeability/resistivity of the ﬂow-permeable structures, since it is possible to achieve substantial noise reduction with a perforated structure, even with a low porosity.

(a) Sketch of the FAST facility layout with a nozzle mounted in the anechoic chamber and the air supply system at the basement below. Adapted from [17] . (b) Nozzle mounted with the flat plate inside the facility.

Facility and models
The experiments are performed in the Free jet AeroacouSTic facility (FAST) at the von Kármán Institute for Fluid Dynamics (VKI). This facility consists of a circular jet rig placed in a semi-anechoic room, as shown in Fig. 1 a, with a cut-off frequency of 350 Hz [17] . For the tests performed in this work, the air is supplied by a 7 bar pressure line located beneath the test chamber. The line is also bypassed to a seeding generator for PIV measurements. The seeded flow merges with the pressurized air in a buffer tank to ensure correct mixing. The jet blows vertically into an extractor equipped with a muffler [17] . In the anechoic chamber, a laser source and cameras are mounted for PIV measurements, whereas a microphone arcarray is present for the acoustic ones. The picture in Fig. 1 b shows the jet nozzle installed with the flat plate inside the facility.
A circular convergent nozzle with an exit diameter D j = 50 mm and contraction ratio of 36:1 is designed based on the geometry of the SMC0 0 0 nozzle, which has been used for several investigations of isolated and installed subsonic turbulent jets [2,18,19] . This nozzle, manufactured in aluminium, is attached to a straight pipe with 300 mm of diameter. A cut view of the nozzle is shown in Fig. 2 along with its main dimensions. The origin of the coordinates system used in the analyses is positioned at the center of the nozzle exit plane.  For the installed configuration, a stainless steel flat plate is mounted in the vicinity of the nozzle. The plate is realized with a modular structure, which allows for different surface lengths to be easily investigated. The length of each part is shown in Fig. 3 . The surface has a total dimension of 500 mm × 1140 mm × 10 mm. The large width is chosen to avoid side-edge scattering. The aft piece consists of a sharp trailing edge with a chamfer angle of 40 • . This modular design also allows for an easy replacement of the solid structure by the flow-permeable materials. Two pieces at the middle section (shown in blue in Fig. 3 ) can be replaced by the flow-permeable ones, allowing for the investigation of different porosity lengths ( L p = 1 D j and L p = 3 D j ).
Different geometric cases are tested by changing the length L and height h of the plate. As shown in Fig. 4 , the length is defined as the distance between the trailing edge and the nozzle exit plane, and the height as the radial position with respect to the jet centerline. A baseline installed case is defined with L = 6 D j and h = 1 . 5 D j . The leading edge of the plate is mounted upstream of the nozzle exit plane to avoid scattering at that region. A different plate length is also investigated ( L = 8 D j ) for a fixed h = 1 . 5 D j , as well as a different radial position ( h = 2 D j ) for a fixed L = 6 D j . Due to set-up constraints, it is not possible to mount the plate at a radial position h < 1 . 5 D j . Therefore, the effect of the plate height is addressed by moving it away from the jet. Moreover, with a length shorter than L = 6 D j at that position, it is possible that the relative noise increase due to installation effects would be much lower, particularly for mid and high jet Mach numbers, which could compromise the parametric analysis of the flow-permeable treatment.
The tests are performed at three jet flow velocities with different acoustic Mach numbers M a , where the jet velocity U j is divided by the ambient speed of sound c 0 . The flow characteristics such as the nozzle pressure ratio ( NPR ) and the static temperature ratio T R are reported in Table 1 , as well as the Reynolds number Re, based on the nozzle exit diameter. The measurements are conducted at static conditions, i.e. no flow external to jet, at average ambient conditions of p amb = 100 . 6 kPa and T amb = 294 K.

Flow-permeable materials
Two types of noise reduction solutions based on flow-permeable materials are investigated in this work. The first one is an open-cell NiCrAl foam manufactured by the company Alantum. The metal foam is manufactured through electrodeposition of pure Ni on a polyurethane foam, which is subsequently coated with high-alloyed powder [20] . This type of material consists of a homogeneous microstructure with a three-dimensional repetition of a dodecahedron-shaped cell [16] . Rubio-Carpio et al. [15] have investigated the application of this material with different cell diameters d c for airfoil TBL-TE noise reduction. A structure with nominal d c = 800 μm is chosen for this work since its porosity and permeability characteristics are available, and significant TBL-TE noise reduction was obtained with this structure [15] . Two inserts are manufactured for the plate, as shown in Fig. 5 a in order to assess the effect of porosity length on the noise reduction. The second type of flow-permeable material consists of a 3D-printed perforated insert with straight holes connecting the upper and lower side of the plate, as shown in Fig. 5 b. This insert is manufactured in R5, which is a liquid photopolymer that offers good surface finishing and strength properties [21] . The holes have a diameter d h = 800 μm and a spacing of l h = 2 mm.
The flow-permeable materials are characterized by properties such as porosity σ and permeability K. The porosity is defined as the ratio between the volumetric densities of the flow-permeable material ρ p and of the solid structure ρ s , as shown in Eq. (1) : The permeability is obtained through the Hazen-Dupuit-Darcy equation ( Eq. (2) ), which prescribes the static pressure loss p across a homogeneous sample with thickness t [22] : where μ is the flow dynamic viscosity, ρ is the flow density, v d is the Darcian velocity (defined as the ratio between the volumetric flow rate and the cross-section area of the sample [22] ), and K and C are the permeability and form coefficients, which account for pressure losses due to viscous and inertial effects, respectively. For the metal foam, the porosity and permeability parameters were obtained by Rubio-Carpio et al. [15] . The former was obtained by measuring the density of small samples, whereas the latter was obtained from characterization experiments performed with a permeability rig [15] . The results are reported in Table 2 . A similar procedure has been carried out for the 3D-printed perforated material. The resistivity R ( R = μ/K) is also included in the table for comparison.

Flow field measurements
A two-dimensional jet velocity field is obtained through PIV measurements on the xy -plane (normal to the nozzle exit).
This method allows for the measurements of time-averaged velocity components u and v (in the axial and radial directions, respectively), and the r.m.s. of their fluctuations u rms and v rms . The PIV measurements are performed only for the isolated jet configuration, since the investigated configurations (length and height) are chosen such to avoid grazing flow on the surface. It has been shown in a previous investigation that this does not affect the noise generated by turbulence mixing [6] . Seeding particles are produced by a PIVTEC Pivpart45 generator, comprised by 45 Laskin nozzles and using Shell Ondina 919 oil, with average size of 1 μm. These particles have a relaxation time of 1 μs [23] , which is suitable due to the flow acceleration in the nozzle. The illumination is provided by laser pulses generated with a double-cavity Quantel CFR200 Nd:YAG system. This equipment provides a laser wavelength of 532 nm, with a maximum energy of 200 mJ/pulse, and a pulse duration of 8 ns. Two LaVision Imager SX4M cameras (resolution: 2360 × 1776 pixel; frame rate: 31 Hz; pixel size: 5.5 × 5.5 μm; minimum time interval: 250 ns; digital output: 12 bit), positioned 0.5 m distant of the jet axis, are used for image recording. The cameras are equipped with two Nikkor f/1.8 lenses of 50 mm focal length. This configuration allows for measurements of two fields-of-view (FOV), in order to capture a larger portion of the jet development, as shown in Fig. 6 a. The FOVs of each camera are shown in Fig. 6 b with an overlap of 1 . 25 D j between them. The final FOV has a dimension of 12 D j × 4 D j (0.6 m × 0.2 m), and it is shown by the black lines. The resolution in the final FOV is approximately 6 pixel/mm.
With this set-up, 10 0 0 pairs of particle images are acquired with a sampling rate of 15 Hz. The illumination and image acquisition are triggered synchronously by the LaVision DaVis 8.4 software, which is also used for the post-processing of the images. The separation time between paired images is tuned with respect to the jet velocity in order to obtain a maximum of 25 pixels displacement at the jet core. This value is chosen to ensure a displacement of at least 3 pixels at regions of lower velocity. A multi-pass cross-correlation algorithm [24] with window deformation [25] is applied. The final interrogation window size is 24 × 24 pixel 2 with an overlap factor of 75%, which provides a final spatial resolution of 4 mm and a vector spacing of 1 mm. Spurious vectors, on the order of 1% of the total amount, are discarded by applying a universal outlier  detector and are replaced by interpolation based on adjacent data [26] . The main parameters of the PIV set-up are reported in Table 3 .
The estimation of the uncertainty in the PIV measurements is performed following the method proposed by Wieneke [27] . This method provides the uncertainty of a PIV displacement field by projecting the particles from one point to another with the obtained vectors and checking the resultant disparity [27] . The calculations result in a maximum uncertainty of 0.03 U j for the mean velocity, and 0.04 u rms inside the potential core region. At the lipline ( y = 0 . 5 D j ), due to the strong flow unsteadiness, maximum uncertainty values of 0.06 U j and 0.08 u rms are obtained.

Acoustic measurements
The acoustic measurements are carried out with 12 Bruel & Kjaer 4938 1/4" microphones (frequency range: 4 Hz to 70 kHz; pressure-field response: ±2 dB; max. output: 172 dB ref. 2 × 10 −5 Pa). The microphones are integrated to Bruel & Kjaer 2670 -1/4" microphone preamplifiers, and a Bruel & Kjaer NEXUS Type 2690-A conditioner is also used to amplify the recorded signals. The microphones are mounted on an arc-array dimensioned for measurements at 1 m radius ( 20 D j , centered at the origin of the coordinates system). The polar angle follows the convention of θ = 0 • in the upstream direction of the jet axis. Therefore, the microphone at θ = 90 • is aligned with the nozzle exit. The microphones are mounted from θ = 40 • to θ = 150 • , spaced of 10 • , as shown in Fig. 7 .
For the installed configuration, the arc-array is mounted on the reflected side of the plate (jet in between the plate and array), in order to assess the effect of the flow-permeable materials on the reflection of jet acoustic waves as well. The measurements are performed with a sampling frequency of 51.2 kHz for 20 s. For post-processing, the acoustic data are split into blocks of 2048 samples for each Fourier transform, and windowed with a Hanning weighting function with 50% overlap. These parameters result in a frequency resolution of 25 Hz. The spectra shown in the following sections have been also scaled to an observer at a distance of 100 D j from the origin, similarly as performed in the JIN benchmark studies at NASA Glenn [2] .

Jet flow field
In this section, the flow field of the isolated jet is discussed. The PIV measurements are performed for the 3 investigated acoustic Mach numbers and the results are displayed in terms of time-averaged axial velocity u and the r.m.s. of velocity fluctuations ( u rms ). The jet development for M a = 0 . 5 is shown in the contour plot in Fig. 8 . The region corresponding to the potential core and the downstream velocity decay can be detected, as well as the spreading of the jet and symmetry with respect to the centerline.
The velocity profiles are extracted at the jet centerline and plotted in Fig. 9 . The quantities are non-dimensionalized by the respective jet nominal velocity U j . The potential core length X c , defined as the distance between the point where u = 0 . 98 U j and the nozzle exit, is reported in Table 4 for all jet velocities. These values are compared with results obtained where ρ j and ρ ∞ are the jet and ambient densities, respectively. A good agreement is obtained between the experimental and predicted results. The centerline velocity decay downstream of the potential core is also shown to follow the trend defined by Witze with the equation [28] : where α is a constant equal to 1.43 [19] .
The increase in potential core length with the jet velocity is related to the change in the size of the structures in the mixing-layer with the jet Reynolds number [28] . For M a = 0 . 8 , the structures are likely to be smaller and thus, the merge of the shear layer at the centerline occurs further downstream. This is also confirmed by the r.m.s. of velocity fluctuations, plotted in Fig. 9 b, which are also lower for higher jet velocities.
Velocity profiles in the radial direction are also obtained at two axial stations, corresponding to the trailing-edge positions of the investigated installed jet configurations ( x = 6 D j and x = 8 D j ). The profiles are plotted in Fig. 10 , along with a line at y = 1 . 5 D j , which is the radial position where the plate is closest to the jet, for M a = 0 . 3 . Similar results have been obtained for the other jet velocities. It is shown that the axial velocity is zero at y = 1 . 5 D j for x = 6 D j and, therefore, a plate with a trailing edge at this position is located outside of the plume. Conversely, for x = 8 D j , at y = 1 . 5 D j , the local axial velocity is non-zero and equal to 0 . 05 U j . However, due to the relatively low velocity at this point, it is not likely that the surface significantly changes the characteristics of the turbulent structures in the mixing-layer, i.e. no changes in the noise due to turbulence mixing are expected even for the longest surface. These results also allow for the calculation of the jet spreading angle δ. Values of δ = 9 • ( M a = 0 . 3 ); δ = 8 . 9 ( M a = 0 . 5 ) and δ = 8 . 6 ( M a = 0 . 8 ) are obtained. These results are consistent with those from the NASA Glenn tests [19] , and they confirm that the jet is fully turbulent.

Far-field acoustic results
In this section, the results of the acoustic measurements for the installed jet with flow-permeable materials are reported and compared with the isolated and installed (solid trailing edge) jets, initially for the baseline plate configuration ( L = 6 D j and h = 1 . 5 D j ). Two types of flow-permeable materials are investigated: a metal foam and a perforated plate with straight holes; both inserts have a length L p = 3 D j . The results are displayed in Fig. 11    Firstly, comparing the spectra for isolated and installed jets (solid plate), it is shown that installation effects are responsible for a strong noise increase at low and mid frequencies; for M a = 0 . 3 and θ = 40 • , there is a 17 dB increase in SPL with respect to the isolated case at the installed spectral peak ( St = 0 . 37 ). This strong noise amplification occurs up to St = 0 . 7 for this condition, and at higher frequencies there is a constant shift of approximately 3 dB from the isolated curve, which characterizes reflection of acoustic waves on the surface. In the sideline direction ( θ = 90 • ), the SPL increases for St < 0 . 3 , whereas for 0 . 3 < St < 0 . 6 there is a reduction with respect to the upstream direction. Therefore, for θ = 90 • , the spectral peak shifts to a lower frequency, possibly lower than the range where the measured data are reliable; this implies that the effect of the flow-permeable materials at the spectral peak might be not significant for a full-scale application, where the peak is likely located below the hearing range. Nonetheless, for a frequency of St = 0 . 25 , there is also a 17 dB increase with respect to the isolated case. In the downstream direction of the jet ( θ = 150 • ), there is a maximum amplification of 7 dB at St = 0 . 25 due to the dipolar directivity of the noise generated by the plate, as well as increased noise from turbulence mixing by the jet. For higher jet velocities, similar trends are obtained, but the relative amplification with respect to the isolated noise levels is lower due to increased significance of turbulence-mixing noise.
For the plates with flow-permeable treatments, the spectra show considerable noise reduction with respect to the solid Comparing the two different treatments, the metal foam provides more benefits than the perforated inserts for all tested cases. Since the former has a higher permeability, it is likely that the differences in noise levels between the two cases can be attributed to a better pressure balance between the upper and lower sides of the plate for the metal foam case, thus reducing the surface pressure fluctuations near the trailing edge and, consequently, the noise due to scattering. The differences between the two flow-permeable configurations is more noticeable at low frequencies ( St < 0 . 4 ). This occurs because, for θ = 40 • , while the noise reduction with the perforated trailing edge is approximately constant for St < 0 . 5 , for the metal foam there is a change in the spectral shape, with a new distinct peak at St = 0 . 45 , in that direction. This is an indication that there is an additional noise source other than the trailing edge.
Similar trends are obtained for higher jet velocities. For M a = 0 . 5 , there is a similar absolute noise abatement at the spectral peak as the previous case (10 dB reduction with the metal foam and 6 dB with the perforated). For this velocity, the   noise increase due to installation effects is relatively lower when compared to the M a = 0 . 3 jet. Therefore, with the same absolute noise reduction provided by the flow-permeable materials, the spectra approach more the levels of the isolated configuration. This effects becomes more visible for the M a = 0 . 8 jet, where the curves of both treated surfaces practically collapse with the isolated one for θ > 90 • , indicating that the trailing-edge source has been completely mitigated in these cases. The Overall Sound Pressure Level (OASPL) for each case is calculated at all polar angles by integrating the SPL spectra in the range of 350 Hz < f < 20 kHz and the results are shown in the polar plots in Fig. 12 , for three jet velocities.
The directivity plots show that the highest differences between isolated and installed (solid plate) cases are found in the upstream direction, which is consistent with noise from scattering at the plate trailing edge [4] . In the downstream direction, this difference is smaller and the installed curves tend to collapse with the ones of the isolated jet, especially for the highest jet velocity. The results also show that the flow-permeable materials are effective in reducing jet-installation noise in all assessed directions, particularly upstream. This indicates that the dipole sources on the plate are mitigated. In the downstream direction, for the metal foam case, the levels reach those of the isolated jet for θ > 120 • and M a > 0 . 5 , indicating that there is no change in the turbulence-mixing noise component due to the presence of the plate.
The differences between the OASPL for flow-permeable and solid surfaces are reported in Table 5 , for a polar angle θ = 40 • . The overall increase due to installation effects with respect to the isolated jet is also included for reference. It can be seen that the metal foam provides higher noise reduction than the perforated structure, particularly for M a = 0 . 3 . From the 11.5 dB overall increase due to installation effects, it is possible to reduce 7.7 dB by applying the metal foam at the plate trailing edge. For higher jet velocities, the installation noise is practically eliminated with this porous material. Despite having a lower permeability, the perforated trailing edge still provides significant noise reduction, of approximately 4 dB for M a = 0 . 3 and M a = 0 . 5 . The dependence of the OASPL with the jet velocity for an angle θ = 40 • is also calculated and plotted in Fig. 13 for each case. Reference curves are also added for OASPL ∝ U 8 j , which is consistent for turbulence-mixing noise [29] , and OASPL ∝ U 5 j , consistent with scattering at the surface trailing edge [3] . By applying the permeable treatment, the exponent of noise levels with the jet velocity increases from n = 5 . 8 to n = 6 . 4 , for the perforated plate, and to n = 7 . 2 for the metal foam. The isolated jet has n = 7 . 9 . These results are in qualitative agreement with those from Geyer and Sarradj [13] . This confirms that, when flow-permeable treatments are applied to the surface, the scattering becomes less dominant with respect to other sources such as turbulence-mixing.
The effect of the configuration geometry on the noise reduction that can be achieved using flow-permeable materials is investigated in the following. Firstly, the effect of the plate radial position is addressed by moving the plate in this direction.
The spectra shown in Fig. 14  Since lower absolute levels are obtained in the spectra for the treated plate farther from the jet, it is interesting to plot the results in terms of noise reductions with respect to each solid case. The curves in Fig. 15 are given in terms of SPL for the respective plate height, and for each permeable configuration, for M a = 0 . 3 . Higher jet velocities are not shown since the turbulence-mixing noise becomes significant and it is not possible to properly assess the effect of the permeable materials. It can be seen that the curves are similar, with minor local deviations, indicating that the absolute noise reductions provided by the permeable materials are independent on the plate radial position, i.e. independent on the amplitude of impinging pressure waves. It is likely that this property is also the reason why the SPL for the installed jets with flow-permeable trailing-edges approach more the isolated jet levels for higher jet velocities.
The effect of the plate length is investigated for a surface with L = 8 D j and h = 1 . 5 D j , as shown in Fig. 16 for θ = 40 • .
The results show that, for this geometry, there is a significant noise increase at low frequencies ( St < 0 . 35 , for M a = 0 . 3 ). Moreover, the benefits provided by the flow-permeable materials are lower than in the previous cases (6 dB decrease at St = 0 . 35 , for M a = 0 . 3 and both types of inserts). At mid frequencies ( 0 . 35 < St < 0 . 7 , for M a = 0 . 3 ), the metal foam and perforated inserts provide similar noise reduction for this configuration. The main differences between the two of them  occur in the range of noise increase due to the increment in the plate length. This is likely the result of the different permeability of the surfaces at the trailing edge, where large-scale pressure waves impinge on the plate; the metal foam provides a better pressure balance between the upper and lower sides of the plate, thus better reducing the surface pressure fluctuations at low frequencies. On the other hand, it is likely that the noise at 0 . 35 < St < 0 . 7 is generated by surface fluctuations upstream of the flow-permeable region, which is the same for both cases. Similar trends occur for the other jet velocities.
This effect can be verified by analysing the influence of the flow-permeable insert length on the noise reduction, for a fixed plate length L = 6 D j and height h = 1 . 5 D j . Measurements are taken for inserts with length L p = 1 D j , and compared to the ones previously shown ( L p = 3 D j ). Spectra are plotted in Fig. 17 , for a polar angle θ = 40 • and three M a . The results show that, for the metal foam, the smaller insert still provides significant noise abatement, particularly for M a = 0 . 3 (6 dB reduction at the peak). For M a = 0 . 5 , similar absolute noise reductions are obtained and, for M a = 0 . 8 , the curves are more similar since turbulence-mixing noise is significant. Therefore, longer flow-permeable sections provide higher benefits since there is a shorter solid section of the plate subjected to strong surface pressure fluctuations. For the perforated structure, the small insert ( L p = 1 D j ) provides less noise reduction, of approximately 4 dB at St = 0 . 37 , for M a = 0 . 3 . The difference in amplitudes between the curves for the two insert lengths is also more significant at low frequencies ( indicating that the additional solid length, for the cases with a shorter insert, generates noise in this frequency range. This is a similar behaviour to that of increasing the overall plate length, as shown in Fig. 16 . Nonetheless, it can be concluded that even small sections of permeable treatment are sufficient for achieving noise reduction. This is important since those types of structures usually lead to performance degradation (loss of lift and drag increase) [12,16] .
It is shown that the solid extension of the plate affects the final spectral shape and amplitude, also shifting the frequency of peak SPL. Therefore, it is also important to analyze the effect of changing the length of the porous insert, but keeping the size of the solid section of the plate constant. For that purpose, spectra of two cases are compared: L = 6 D j with L p = 1 D j and L = 8 D j with L p = 3 D j . Therefore, both cases have a solid section of 5 D j between the nozzle exit and the flow-permeable section. Results are shown in Fig. 18 , for the two types of permeable materials and three M a . The results are similar to those shown in Fig. 17 . The case with an overall longer plate has more noise generated at lower frequencies ( St < 0 . 3 for M a = 0 . 3 ), for both metal foam and perforated inserts; at St = 0 . 27 , there is a 5 dB difference between the metal foam curves and 4.4 dB for the perforated ones. Therefore, this is likely attributed to the difference in total plate length so that the noise is generated due to the impingement of high-amplitude and low-frequency pressure waves on the flow-permeable region of the plate. On the other hand, the noise at mid frequencies does not show significant change when comparing the two cases. Therefore, it is probable that the dominant source in this range is the same for both of them, and it is likely that the source is now located at the solid-permeable junction in the plate. It is speculated that the junction between solid and flow-permeable surfaces has become the dominant source location for the metal foam case. The effect of the junction has been described in the literature as an additional geometric singularity, and thus, as a new scattering region, as shown by Kisil and Ayton [30] . Scattering at the junction is then responsible for noise increase at mid and high frequencies, also changing the directivity pattern of the overall configuration [30] . Moreover, beamforming results from Rubio-Carpio et al. [16] showed that, for frequencies where TBL-TE noise reduction is achieved with flow-permeable materials, the dominant source is placed at the solid-flow-permeable junction [16] . Therefore, it is possible that there is an additional contribution from that region, particularly for the cases with the metal foam due to its high permeability. The junction effect would thus be the cause of the different spectral shape, as well as of the SPL peak at a higher frequency, relative to the fully solid and perforated cases. The results previously shown for the metal foam case are in agreement with this hypothesis; for the reduced insert length, the junction is placed at x = 5 D j (as opposed to x = 3 D j in the baseline case), and the spectral peak shifts towards a lower frequency ( Fig. 17 ). On the other hand, when the junction is placed at the same position and the porous extent is changed, there is simply an increase in amplitude, but the spectral peak frequency remains unchanged ( Fig. 18 ). This effect is likely not obtained with the perforated configuration, since the low permeability does not result in a strong impedance jump at the junction, and, consequently, scattering at that region. Further work is necessary to confirm these hypotheses.

Conclusions
An experimental study on the effect of flow-permeable materials on the noise produced by an installed jet is performed. The configuration is comprised by a single-stream subsonic jet and a nearby flat plate, placed in the jet near-field. Two types of flow-permeable structures are investigated: a metal foam and a perforated insert with straight holes normal to the axis. The metal foam has a higher porosity and permeability than the perforated structure and its channels are also interconnected.
Planar PIV measurements are carried out to characterize the jet velocity field. Based on the potential core length and spreading angle, it is concluded that the jet has a turbulent behaviour for all tested velocities. Moreover, it is confirmed that there is no direct grazing of the jet on the plate, except for the longest surface tested. However, for this case, the surface is in a region of very low velocities compared to the potential core, and it is likely not affecting the noise generated by turbulence mixing. Acoustic measurements show that the installation effects are responsible for strong low-frequency noise increase with respect to isolated levels. This amplification is more significant at a low jet velocity, where the dipole sources on the surface are more acoustically efficient than the quadrupole sources from turbulent mixing. The spectral shape and amplitude are shown to be dependent on the geometry of the configuration; longer surfaces produce more noise at low frequencies, whereas moving the plate towards the jet in the radial direction results in noise increase, especially at mid frequencies.
Significant noise reduction is achieved when the solid plate trailing edge is replaced by flow-permeable inserts, particularly in the low/mid frequency range, where the scattering is the dominant mechanism. Comparing the two types of structures, the metal foam is more effective in reducing JIN, likely due to a higher permeability, which can mitigate the pressure imbalance between the upper and lower sides of the plate, and thus reduce the noise generated by surface pressure fluctuations. For low jet velocities, a noise decrease of up to 10 dB is obtained at the spectral peak with the metal foam, but the installation noise is still visible. When the jet velocity is increased, the attenuation provided by the flow-permeable treatment brings the noise levels closer to the isolated case, and the trailing-edge source is no longer dominant with respect to the jet quadrupoles. It is worth mentioning that the highest noise levels for the investigated installed configurations occur at low frequencies ( St < 0 . 3 for M a = 0 . 3 ), particularly at the sideline direction ( θ = 90 • ). For a full-scale aircraft, these frequencies may not be of particular significance. However, the flow-permeable trailing edges assessed in this work also provide noise reductions at mid and high frequencies, including reflection effects on the surface, which would be significant in a full-scale configuration.
The effect of surface treatment is also assessed for different configuration geometries. By moving the plate away from the jet, flow-permeable materials provide similar absolute noise reduction as the baseline case. Conversely, by increasing the plate length, lower noise abatement is obtained with the flow-permeable treatments, particularly at low frequencies ( St < 0 . 35 for M a = 0 . 3 ), with the metal foam still providing higher benefits. On the other hand, the noise at mid frequencies ( 0 . 35 < St < 0 . 7 for M a = 0 . 3 ) is similar for the two types of insert, indicating that it is generated by the impingement of pressure waves in the solid region of the plate, upstream of the flow-permeable treatments.
For a fixed plate length, a shorter flow-permeable insert is shown to provide noise reductions with respect to the solid case, but in a lower degree compared to the larger insert. The main differences occur at low frequencies, which indicates that the increased noise is due to the additional solid length, compared to the case with the longer insert. The frequency of highest SPL also shifts towards low frequencies. On the other hand, when the plate length is changed, but the solidpermeable junction is kept at the same axial position, the flow-permeable materials behave differently. For the metal foam, there is an increase in amplitude, but no significant change to the spectral peak frequency, whereas for the perforated there is a low-frequency noise increase with a change in the spectral peak. It is believed that this difference is caused by the high permeability of the metal foam, which produces a new singularity and thus a new scattering region at the solid-permeable junction.
These results show that a surface treatment with flow-permeable materials is a potentially promising mitigation solution for jet-installation noise. However, the mechanisms that provide such reductions are still unclear. Further work is required to investigate the phenomena happening at the junction region and inside the flow-permeable structure, particularly focusing on the change of impedance, pressure imbalance and the effect of permeability/resistivity of the flow-permeable structures, since it is possible to achieve substantial noise reduction with a perforated structure, even with a low porosity.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.