# Jet Noise in Airframe Integration and Shielding
## 4 Numerical Simulation of the Shielding Effect
### Numerical Results  
Some results of this simulations are presented here. In Figure 24, the time-averaged axial velocity component is compared with two sets of data available in the literature. The red line represents the results presented by [PERSON] et al. [84] for a nozzle NPR of 3.67 and TR 3.0, which is the exact same operating condition as the current work. It can be observed that the current numerical results definitively agree with the results reported by [PERSON] et al. [84]. The numerical shadowgraph is calculated in Figure 25 and compared with the Schillerian imaging results of the experiment reported by [PERSON] et al. [35]. Looking at the results for the nozzle without the plate, the Mach waves propagating downstream of the jet seem to be the main sources of noise in the far field. [PERSON] et al. [35] noticed the existence of crackle noise, specifically for heated jets, which was pointed out earlier by [PERSON] et al. [85] as a possible component of supersonic jet noise. Crackle noise is characterized by intermittent positive pressure fluctuations radiating downstream at an angle associated with the peak jet noise. Such waves are somewhat different from Mach waves, which are long, straight, and have about equal angles [86]. The crackle waves are mainly due to the high kinematics of the heated jet and can be observed in the numerical results shown in Figure 25, much like the ones observed in the experimental imaging. Figure 24: Time-averaged center line velocity (no plate). Next, the time-averaged velocity is illustrated in Figure 26 for the shielded case with the plate located at \((h/D=0)\) and compared with experimental data of the ideally expanded heated jet (\(NPR=3.67\), \(TR=2.4\)) reported by [PERSON] et al. [87, 88]. The nozzle operating conditions of the experimental data are much closer to those of the current numerical results. The extension of the core of the jet predicted by the numerical simulation is in close agreement with the experiment. The core of the jet can be identified as the red region, where \(U/U_{j}=1\), the numerical results predict the same extent for the plume as the experiment, which is located at \(x/D=12\). The turbulent kinetic energy (TKE) is illustrated in Figure 27. TKE is normalized with respect to the jet velocity squared (\(TKE/U_{j}^{2}\)), and is compared with the experimental results for the ideally expanded heated jet reported by [PERSON] et al. [87, 88] (\(TR=2.0\), and \(TR=2.4\) for the baseline and the shielded case, respectively). These experimental results are chosen for comparison, since these results have the closest operating conditions to the current numerical simulations among all experimental results available in the literature for this nozzle geometry, at this time. Figure 27: Turbulent kinetic energy normalized by jet velocity squared. (**a**) Baseline, Numerical (NPR = 3.67, TR = 3.0), (**b**) Baseline, Experiment (NPR = 3.67, TR = 2.0) (Ref. [88]). (**c**) With Plate, Numerical (NPR = 3.67, TR = 3.0), (**d**) With Plate, Experiment (NPR = 3.67, TR = 2.4) (Ref. [87]). Figure 25: (**a**) Instantaneous numerical shadowgraph, (**b**) Instantaneous Schillerian from experimental measurements (Ref. [35]). The maximum TKE for the shielded case is provided and compared with the experimental data for an ideally expanded heated jet from [PERSON] et al. (2018, 2019). The numerical results exhibit the same structure of turbulence, especially in the near-wall region. Furthermore, the location of the separation of the boundary layer on the flat plate can be observed in Figure 27c, which is located at \(x=6D\) and agrees with the experiment (Figure 27d). The jet is held by the flat plate from one side, which prevents the dissipation of the jet from that side and causes the asymmetric structure of the kinetic energy dissipation. Next, the acoustic field of the supersonic jet and the effect of the flat plate on the noise generation and radiation is illustrated and compared with the acoustic spectra from [PERSON] et al.