# Surrogate Based Optimization of Aerodynamic Noise for Streamlined Shape of High Speed Trains
## 2 Algorithms  
### Acoustic Algorithms and Validation  
Two kinds of approaches are adopted in the present work, NLAS [17] to solve the near field noise and FW-H sound propagation method to solve the far field noise, respectively. For the latter approach, an acoustic surface around the noise sources is built to record fluctuation data during NLAS calculation, which would be taken as the initial value for FW-H propagation equation. The overall solving process is shown in Figure 1:  
The NLAS is a numerical acoustics solver designed to model noise generation and propagation from an initial statistically-steady model of turbulent flow data, which can be provided by a simple Reynolds Averaged Navier-Stokes (RANS) turbulence model. Through the RANS calculation, the statistical steady mean flow could be obtained, from which the main generation zone of turbulence could be revealed. In the present paper, an anisotropic turbulence model, the cubic \(k\)-\(\varepsilon\) model, is utilized to preferably model the statistically steady flow field [18]. Non-linear terms are taken into consideration to account for normal-stress anisotropy, swirl and streamline curvature effects. Consequently, the local Reynolds-stress tensor could be provided precisely to synthesize the noise sources. The transient calculation of NLAS should be performed on the premise of the steady RANS calculation of the flow field. NLAS uses a reconstruction procedure to generate noise sources from the given set of statistics and allows the resulting propagation of the pressure disturbances to be simulated using a high-resolution pre-conditioned solver. The acoustic surface is used to record fluctuation data during the NLAS procedure. Once the data is obtained, Fowcs-Williams/Hawking equation can be solved based on these data. The FW-H equation approach [19; 20] can be used to predict noise at any observation point outside the acoustic surface, even if the observation point is outside the computational domain. The whole CAA analysis is performed by the commercial software CAA++ (Ver 10.1, Metacomp Technologies, Los Angeles, CA, USA, 2011). Numerical validation has already been performed in the literature by the author [4]. It took a backward step case as the test case. It comes from the experiment by [PERSON] and [PERSON] in a subsonic wind tunnel [21]. The flow conditions in the numerical simulation maintain the same with the experiment. In the experiment, the span wise width is 12.5 times of the height of the backward step to keep the central section two-dimensional. As a result, a two-dimensional simulation was conducted for the central section. The observation points are chosen just on the floor behind the step, as the experiment did. Fast Fourier Transformation (FFT) analysis is performed on the pressure fluctuating data. Meanwhile, numerical simulation with the Large Eddy Simulation (LES) approach  
Figure 1: The schematic drawing of solution procedure for Computational aero-acoustics (CAA) calculation. was also performed. The results from the NLAS approach, the LES approach and the experiment are listed together for comparison, which mainly focuses on the sound pressure level and corresponding dominant frequency (Tables 1 and 2). It can be seen that better dominant frequencies are achieved through the NLAS approach, except for the position \(x/H\) = 10. Meanwhile, the maximal sound pressure level predicted by NLAS agrees well with the experimental data. However, the maximal sound pressure level and dominant frequency obtained by LES under the same mesh and flow conditions show relative variation with experimental data. This can be related to that the synthetic reconstruction of sub-grid sources can be achieved in NLAS approach rather than LES approach, which makes the results from NLAS approach seems much more accurate.