1. θ0/D Δx/D Δx/θ0Δr/D Δr/θ0rΔθ/D rΔθ/θ0Brès etal. [36] 0.007~0.03 0.9~3.8 0.004~0.05 0.5~6.0 0.0003-0.01 0.04-1.25 0.008
2. Lorteau [8] 0.0006 ~0.02 0.08 ~2.5 0.0006~0.02 0.08 ~2.5 0.015-0.007 1.9-0.9 0.008 Bogeyet al. [5] 50M 0.007~0.03 0.4~1.7 0.004~0.02 0.2~1.1 0.012 0.67 0.018 Bogeyet al. [5] 256M 0.004~0.04 0.2~2.1 0.002~0.02 0.1~1.1 0.003 0.17 0.018
3. Following usual practices and fundamental studies of Daude et al. [38], the time step was set at 1 µs to reach a maximum CFL number based on the maximum acoustic velocityof 15-20 in the LES parts of the ZDES simulations (see Fig. 9). After an initial transient of 200 D/Uj(0.03 s) corresponding to the establishment of a pseudo-steady flow, the total simulation time used for data analysis and statistics collection is 300 D/Ujforbothsimulations,which isacceptable regardingthe objective ofthe present studyaccordingto [22]. (a) ZDES mode 2 (b) ZDES mode 3+2
4. Downstream of the nozzle exit along the jet centerline, the ZDES mode 2 and mode 3+2 results are almost identical. The frequency peaks attributed to trapped acoustic waves inside the jet potential core identified in Fig. 23 are observed up to x/D=2. Some accumulation of energy and a frequency bump are observed around StD~4-10 at x/D=2. In general, these features are attributed to an insufficient subgrid scale dissipation near the grid cut-off frequency and/or to the spatial scheme, but no firm conclusion can be drawn based on the present data. Note that the WMLES of Brès et al. [6] seems to present the same feature, as can be seen on the near field pressure spectra presented inFig. 35 (no pressure spectra alongthe jet centreline are available for Brès'WMLES).