When a high-speed train enters a tunnel it pushes the air ahead of it and generates a compression wave. That wave travels along the tunnel at close to the speed of sound, reflects from the far end and runs back and forth inside.
It causes two distinct problems.
1. Tunnel boom
When the compression wave reaches the far end of the tunnel it produces a sudden pressure release, and a bang-like noise is heard outside. For tunnels near residential areas this is a project-limiting factor.
How much the wave front steepens is decisive: in long tunnels non-linear effects sharpen the front and the noise increases. The countermeasure is a portal hood at the tunnel entrance providing a gradual change of section — it lengthens the rise time of the wave and lowers the peak amplitude.
2. Passenger comfort
The waves travelling back and forth inside the tunnel create pressure fluctuations in the vehicle. Ear discomfort thresholds are defined in terms of the rate of pressure change — not the absolute value but the change per second. The body's sealing determines how much of the fluctuation gets inside.
If two trains pass inside the tunnel the waves superpose and the worst case arises.
Modelling
Compressible and transient. The phenomenon is by definition an acoustic wave propagation; an incompressible model cannot produce it at all. See the compressible flow note.
A moving train. Either the train is moved (overset mesh) or the reference frame is attached to it. See the moving boundaries note.
Mesh resolution along the tunnel. Enough cells along the axis are needed to capture the steepening of the wave front; a coarse mesh smooths the wave numerically and underpredicts the noise. See the discretisation scheme note.
Tunnel length and blockage ratio are the governing parameters; the wave amplitude rises rapidly as the train-to-tunnel area ratio increases.
References
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6
- Fay, J. A. & Riddell, F. R. (1958). Theory of stagnation point heat transfer in dissociated air. Journal of the Aerospace Sciences, 25(2), 73–85. DOI: 10.2514/8.7517