# Jet Noise in Airframe Integration and Shielding
## 3 Options for Computation of Jet Noise
### Faster Simulations Using Linearized Euler Equations  
Linearized Euler equations (LEEs) have been proposed both as an extension technique, as well as for directly predicting the unsteady noise sources in the flow field along with its radiated noise. Regarding the use of LEE only as an extension technique, [PERSON] et al. [60] developed a less expensive approach in which LES is used to solve the noise generation region, but LEE is used outside of this region wherein the process is linear and inviscid. The results were practically the same as the corresponding full LES but with less computational power requirements.  
LEE is expected to perform well in capturing noise propagation but is usually not thought of for capturing the nonlinear noise generation process. However, [PERSON] et al. [61] showed that for supersonic jets free from shocks, LEE can successfully capture the noise generation process for a given mean flow. Thus, LEE can be used for the prediction of noise generation as well. The results  
Figure 14: Full 3D large eddy simulation of a supersonic jet at M = 2.1 excited at the first helical mode showing the pressure near field (Ref. [58]).  
Figure 12: Lighthill stress tensor, indicating noise source at \(St=0.5\) (Ref. [55; 58]).  
Figure 13: (**a**) Directivity of the predicted noise level in dB from the large-scale simulations of supersonic jet noise (Ref. [57]). Compared with (**b**) the corresponding experimental data (Ref. [59]).  
of [PERSON] et al. [61], though linear, agreed quite well with the experimental results of [PERSON] and [PERSON] [59]. This is because in this case, the dominant noise source is the Mach waves, which is produced by the large-scale wave-like structure. One caveat to note is that because LEE is linear, spurious modes may be easily amplified and, therefore, extra attention is needed when implementing boundary conditions for LEE calculations. The successful boundary treatments are shown in Figure 15a for a supersonic jet with \(M=2.1\). A snapshot of the unsteady jet flow as well as the radiated sound is shown Figure 15b along with contours of the computed noise level in Figure 15c.  
Figure 15: Prediction of the unsteady flow and acoustics of a supersonic jet using Linearized Euler Equations (Ref. [58; 61]). (**a**) Boundary treatments, (**b**) Snapshot of the oscillating pressure field, and (**c**) root mean square of the acoustic pressure distribution.  
The acoustic pressure fluctuations shown in Figure 15 were used to calculate (Sound Pressure Level) SPL at the distance \(R/d=24\). The SPL levels and directivity were found to be in excellent agreement with the corresponding experiment of [PERSON] and [PERSON] (2016) for a supersonic jet as shown in Figure 16. Figure 16a shows the predicted SPL in which the initial disturbances were axisymmetric but was taken either to be at \(St=0.2\) or computer-generated random disturbances. Figure 16b shows the predicted directivity at the distance \(R/d=24\) in which the initial input disturbance to the jet was taken to be either an axisymmetric or the first helical mode.