Unique aspects

The unique aspect of this work is the simultaneous measurement of the far-field pressure, enabling analysis of the causal link between the near-field wavepackets and the emitted sound. The measured data are used to establish a relationship between the near-field fluctuations and the far-field pressure by means of correlation analysis and to characterize the wavepacket behaviour in the near field in terms of wavepacket parameters. A Green’s function tailored to the geometry of the conical microphone array is used to propagate the recorded near-field wavepacket signatures to the far field using both statistical and time-domain analysis. This method follows the approach

ofRebaet al.(2010), and the statistical calculations used the code already developed

and validated byLéon(2012) andLéon & Brazier(2013) for far-field sound estimates from PSE predictions. The time-domain Green’s function predictions were obtained by modifyingLéon’s (2012) code to retain the pertinent information.

4.3

Experimental setup

The experiments were carried out in an anechoic free jet facility with a cut-off frequency of 200 Hz at theCentre d’études aérodynamiques et thermiques(CEAT), Institut Pprime, Poitiers, France. Two experimental campaigns obtained measurements in the pressure field generated by a jet with nozzle diameterD=50 mm and Mach numbers in the range 0.4≤ M ≤ 0.6. The corresponding Reynolds number range was 4.2×105 to 5.7×105. A carborundum trip placed 2.7Dupstream of the nozzle lip ensured the boundary layer was turbulent at the jet exit. Both the acoustic far field (Cavalieriet al., 2012a) and the velocity field (Cavalieriet al.,2012b) of this jet have been previously examined, and more details are available in the cited papers. The potential core length of the jet ranged between 5≤x/D≤5.5.

4.3. EXPERIMENTAL SETUP x y z 8º +Á 20º jx_oj Far-field Mics Near-field Mics Jet ±Á

(a) Overview (b) Installed rig

Figure 4.5: Overview of 4-ring setup

Table 4.1: Experiment conditions for both experimental campaigns

Campaign X/D Xmax/D rA/D ∆X/D M 1.25 5.75 0.8

7 Ring 2 6.5 0.7 0.75 0.4, 0.45, . . . , 0.6 2.75 7.25 0.6

4 Ring 0.5 8.9 0.8 0.4 0.6

an azimuthal ring array of three equispaced 1/4” GRAS 40BP microphones atθ =20◦

and|xo|/D=47.1. The far-field array was limited to three microphones because the sound field of this jet atθ=20◦ has been shown to be dominated by fluctuations in

the axisymmetric mode (m= 0,Cavalieriet al.,2012a), making resolution of higher azimuthal modes unnecessary for the Strouhal number range investigated here. The near-field array was made up of a number of azimuthal ring arrays. Azimuthal arrays were used to enable decomposition of the pressure signals into azimuthal Fourier modes, enabling azimuthal mode-by-mode analysis consistent with the azimuthal mode-by-mode calculation of the linear PSE solutions. An overview of the test setup is illustrated infigure 4.5for one of the campaigns, and the experimental conditions for both campaigns are tabulated intable 4.1.

The focus of the first campaign was a simultaneous measurement of as much of the near field as possible to enable a time-domain comparison to the near-field fluctuations and the far-field sound. To that end the near-field array comprised seven azimuthal rings, each with six microphones distributed azimuthally. A schematic of the setup is given infigure 4.6. There were a total of 42 microphones in the near-field cone. Two types of microphones were used in the near-field array because there was a limited number of high-quality precision microphones available. The first three

6-mic5near-field5azimuthal5arrays 3-mic5far-field5azimuthal5array X 8º U jx_oj=D 5=547.15 µ 5=520º r x Xll 14-mic5lip5azimuthal5array ¢x/D5=50.75 rA

Figure 4.6: 7-ring near-field azimuthal array setup (7pt correlation)

rings used inexpensive 1/4” electret microphones, while the last four rings used 1/4” GRAS 40BP precision microphones. The frequency response of the electrets was found to closely match the GRAS microphones up to about 9 kHz (St ≈2.2 for M = 0.6). The half-angle of the cone, α = 8◦, matched the expansion of the jet so that each

microphone measured pressure amplitudes of the same order of magnitude. The conical surface intersected the jet nozzle plane at radial distance labeledrA, which was set between 0.6 and 0.8Ddepending on the test configuration. The entire array was mounted on a traverse, which allowed the rings to span different portions of the jet near field ranging fromXtoXmax. In this campaign, the radii of the rings were not adjusted whenXwas changed, meaning that eachXcorresponded to a differentrAas well as different axial coverage of the jet. Since the axial spacing was 0.75D, shiftingX in multiples of this amount gave measurements at the same axial locations on different conical surfaces, allowing a partial evaluation of the radial decay of the near-field fluctuations. At each axial position, measurements were obtained in the velocity range 0.4 ≤ M ≤ 0.6 in increments of 0.05. An additional ring of 14 microphones was included close to the nozzle lip in order to investigate the relationship between nozzle fluctuations and downstream activity. These data have not been examined here.

The second campaign, illustrated in figure 4.7, was designed to provide finer- resolution measurement of the statistics of the near-field fluctuations. This array consisted of four rings of six 1/4” GRAS 40BP microphones that could be moved independently in the axial direction. This setup does not allow the monitoring of the space–time structure of the near-field pressure, but it does allow the statistical shape and energy of the modes to be determined via two-point correlations, allowing the construction of the Cross-Spectral Matrix (CSM) describing the jet statistics. To ensure that all the measurements fell on the same conical surface (rA/D=0.8), the