# Jet Noise in Airframe Integration and Shielding
## 4 Numerical Simulation of the Shielding Effect
### Numerical Results
(2019) that has the same operating condition as that modelled in the current numerical results (NPR = 3.67, TR = 3.0). Figure 28 shows the pressure fluctuations of the flow and acoustic fields. The fluctuations shown in these figures are achieved after subtracting the time-averaged pressure from the instantaneous pressure (\(p^{\prime}=p-\overline{p}\)). The fluctuating pressure contours clearly exhibit the shielding effect of the flat plate. The flat plate prevents the waves generated by the jet to radiate in the shielded direction. On the other hand, the flow leaving the trailing edge of the flat plate behaves as an additional source of noise. This resembles the trailing edge noise in the airfoils. The strength of this source is much lower than the fluctuations in the shear layer and jet plume. For the spectral data presented here, 4 bins of 1024 samples are collected at a sampling frequency of 204.8 kHz. A Hanning window function, along with a 25% overlap for each segment, is used and fast Fourier transform (FFT) is applied to obtain the sound pressure level (SPL) (\(dB\) rel 20 uPa ) spectrum. The frequency is non-dimensionalized and represented as the Strouhal number, as explained in the earlier sections. The hydraulic diameter, \(D\), and the isentropic exhaust velocity, \(U_{j}\), of the jet are used as the length scale and velocity, respectively, for the calculation of the Strouhal number. Figure 29 compares the SPL spectra between the reflected side and the shielded for the free jet case, and Figure 30 shows the spectra for the same locations for the flat plate bounded case. Generally, the results shown in both figures show favorable agreement with the corresponding experimental data, both in terms of the predicted level of acoustics, as well as the trend of spectra. In fact, the agreement between the numerical results and the experiment is perfect up to the cut-off frequency (\(St=0.35\)) mentioned earlier calculated from the grid spacing requirements. Figure 28: Instantaneous fluctuating pressure, \(p^{\prime}\)\([Pa]\). (**a**) Baseline (BSL) case, (**b**) Shielded case. As expected, a drastic reduction in noise levels is observed for all plate configurations relative to the free jet. The observed reduction of noise levels is caused by the shielding effect of the plate on the noise sources from the jet plume. This is consistent with the reductions of waves observed in Figure 31. Such a drastic reduction in the SPL is due to the dimension of the flat plate used in the numerical simulations and the experiment, and as several experimental studies [27; 28; 29; 30; 31] have mentioned, the noise reduction in the shielded direction is highly influenced by the dimensions of shielding surface. Comparing the SPL spectra in Figures 29a and 30a, the shielded configuration increases noise levels across all frequencies, especially at the lower frequencies, about 10 dB more than the free jet. [PERSON] et al. [35] suggested that this low-frequency noise component is associated with the noise intensification generated by the jet-trailing edge interaction and the scrubbing noise mentioned by [PERSON] [29] and [PERSON] et al. [33]. The recent theoretical work by [PERSON] et al. [89] employs rapid distortion theory and exhibits the asymmetry of the shear layer when it exhausts over a flat plate. To elaborate the mechanism that causes an increase of SPL in the shielded direction due to the flat plate, the root mean square (RMS) of the fluctuation component of the pressure (\(p^{\prime}=p-\overline{p}\)) is illustrated at axial cutting plane locations of \(x/D=5,~{}18,\) and 30 in Figure 31. Comparing the evolution of pressure fluctuations along the jet axis for the free jet (a) with the shielded case (b), it can be observed that the flat plate maintains the energy of the jet much further from the jet exit. This was also shown earlier in TKE contours (Figure 28). The bounded nature of the shielding wall avoids the dissipation of the turbulence fluctuations in regions closer to the jet exit.