# Acoustic Pressure Amplification through In-Duct Sonic Black Holes
## 4 Experimental Study  
The performance of the MPP-SBH predicted by the TMM and FEM for enhancing acoustic pressure signals has been experimentally assessed in an aero-acoustic waveguide. The characterization test bench consists of a low-speed wind tunnel with a square cross-sectional area of \(0.15\,\mathrm{m}\times 0.15\,\mathrm{m}\), sketched in Figure 12a. A square MPP-SBH (S-MPP-SBH) was inserted between the 1 m long upstream and downstream square sections of the low-speed wind tunnel, as shown in Figure 12b. The first section was equipped with a compression driver flush-mounted on the upstream section, as indicated in the sketch of Figure 12a, itself connected to the wind-tunnel fan section. The S-MPP-SBH was first excited in the no-flow case by an acoustic plane wave consisting of a white random noise with a flat spectrum between 50 Hz and 5 kHz generated by the compression driver. The sensor's performance was also tested under a low-speed grazing flow with a mean axial velocity equal to \(30\,\mathrm{m.s}^{-1}\). The flow was generated by a centrifugal fan located upstream of the test section, coupled to a silencing system, laminarized through honeycomb filters, and then accelerated through a convergent connected to the upstream square duct. The characterization of the S-MPP-SBH pressure amplification was thus achieved either under pure acoustic or aero-acoustic excitations. For that, a probe microphone (GRAS 40 SC, Holte, Denmark) with variable tip lengths was used to sequentially measure the pressure fluctuations at the back of the S-MPP-SBH cavities, as sketched in Figure 12a. As shown by the in-duct photography of the S-MPP-SBH in Figure 12b, the probe tip of diameter 1.25 mm could be inserted into the MPP holes of diameter 2.6 mm to measure \(p_{\mathrm{cav-back},n}\). It weakly perturbs the MPP effect, which has 24 holes at a given axial position The probe provides a pressure build-up lower than 0.2 dB (according to the manufacturer specifications) at the duct cut-on frequency (1140 Hz). Hence, probe diffraction effects are negligible in the plane wave regime. The most important effects are the viscous losses induced inside the probe tip, especially when probing the deepest cavities. These have been corrected by frequency response calibration performed at 250 Hz for each tip length, cross-checked against the calibration data provided by the manufacturer up to a tip length of 160 mm. \(p_{\mathrm{rigid},n}\) was measured in the main duct at the same axial locations, but with the holes of the perforated panel closed by an aluminum tape. The measurement was monitored by the OROS acquisition system (type OR38) operating on one input and one output signal with a bandwidth between 50 Hz and 5 kHz and a spectral resolution of 1.56 Hz. Figure 13 shows the spectral and axial variations of the pressure gain measured in the no-flow and low-speed flow cases. One observes that the measured PG spectrogram in the no-flow case [Figure 13a] reasonably correlates against the spectrogram predicted by the TMM [Figure 7b]. Because of the larger diameter of the holes (2.6 mm instead of 1.5 mm) and the larger perforation ratio (2.8% instead of 2%), the inertial effects brought by the MPP are lower with respect to those obtained in Figure 7b. It still provides a shift of the PG peak frequencies down to 800 Hz (instead of 500 Hz) and a similar quadratic increase of the peak frequencies when moving the probe axial locations from the deepest to the shallowest cavity depths. A larger diameter of the holes and a higher perforation ratio also produce lower resistances and losses through the MPP. It results in a higher PG reaching a maximum value of 15 instead of 12, as obtained in Section 3.2. This translates into a SNR of 11.8 dB related to the maximum PG measured in the no-flow case, which is slightly above the SNR of 11 dB calculated in Section 3.2 with a less resistive MPP. One notes that, for each cavity location, extra peaks appear that contribute to the pressure gain below the cavity resonance frequencies.