# Surrogate Based Optimization of Aerodynamic Noise for Streamlined Shape of High Speed Trains
## 5 Computational Models, Mesh and Conditions  
A three-grouping high-speed train model has been adopted in the present paper, which is named as EMU1. The total length of the train is about 78 m and the height of the train is about 4.05 m. The whole train is shown in Figure 6.  
Figure 5: Schematic drawing of surrogated based optimization.  
In order to reduce the computational cost, some additional components are eliminated, such as the pantograph. When performing the CFD calculation, components such as the windshields and bogies are reserved. However, since the computational cost of CAA analysis is extremely larger than that of CFD, the windshields and bogies are both neglected to reduce the calculation time, yet the influence of the streamlined shape on acoustic characteristics could still be considered.  
Take the height of the train as the characteristic length H, the computational domain extends 30 H ahead of the train nose and 60 H from the train tail to the exit of the computational domain. The top of the computational domain is at a distance 30 H from the bottom of the rail and the sides are at a distance of 30 H from the center axis of the train, the outline of computational domain and the model are shown in Figure 7.  
The hybrid Cartesian/prism grids is adopted and six layers of prism grids are generated with an increasing ratio of 1.2 and a total length of 30 mm, which keeps the value of \(y+\) of the first layer near the train surface in a range of 30\(\sim\)100. The total number of the cells is about 32 million. Figure 8 shows the grids on the longitudinal section and on the surface of leading streamline, while Figure 9 shows the grids on the longitudinal section of wake region.  
Figure 8: The grids on the longitudinal section and on the surface of leading streamline: (**a**) mesh distribution on the longitudinal section; and (**b**) surface grids of the leading streamline.  
Figure 6: The whole train model.  
Figure 7: Computational domain.  
The flow velocity is 300 km/h; the far-field pressure is 1 atm; the temperature is 288 K; and the reference area is the maximum cross-sectional area of the train. As a result of the compressibility calculation model, one-dimensional inviscid flow of the Riemann invariants is introduced as the far-field boundary conditions, which are also known as non-reflective boundary conditions. Inflow, outflow and the top boundaries are all set as far-field boundary conditions and the train body is non-slip solid wall boundary condition. The ground is treated as the moving wall to simulate the ground effect, and the moving speed is equal to the train speed.  
When the NLAS procedure is conducted, three absorbing layers are imposed to the inlet boundary, the outlet boundary and the far field boundary respectively to prevent wave reflections from these boundaries. Two hundred Fourier modes are set to perform synthetic reconstruction for the turbulent fluctuating quantities to capture the sub-grid sources correctly. The time step in NLAS simulation is set to 2 \(\times\) e\({}^{-5}\) s, and the simulated physical time is 0.3 s, which insures that the noise whose frequencies locate between 10-10,000 Hz could be precisely predicted.  
After solving the acoustic field in the near field, the far field noise could be obtained with the use of FW-H equation. The observation probes are set according to the ISO-2005-3095 standard, which requires the probes to be 25 m far from the train body and 3.5 m height from the ground. Thirteen probes are placed along the train body with an equal distance of 10 m, which range from the leading head to the trailing streamline, as shown in Figure 10.