The compression wave generated by a high-speed train entering a tunnel is studied
theoretically and experimentally. It is shown that the pressure rise across the wavefront
is given approximately by
formula here
where ρo, U, M, [Ascr ]o and [Ascr ]
respectively denote the mean air density, train speed,
train Mach number, and the cross-sectional areas of the train and the uniform section
of the tunnel. A monopole source representing the displacement of air by the train is
responsible for the main pressure rise across the wave, but second-order dipole sources
must also be invoked to render theoretical predictions compatible with experiment.
The principal dipole is produced by the compression wave drag acting on the nose
of the train. A second dipole of comparable strength, but probably less significant in
practice, is attributed to ‘vortex sound’ sources in the shear layers of the back-flow
out of the tunnel of the air displaced by the train.
Experiments are performed that confirm the efficacy of an ‘optimally flared’ portal
whose cross-sectional area S(x) varies according to the formula
formula here
where x is distance increasing negatively into the tunnel, [lscr ] is the prescribed length of
the flared section, and [Ascr ]E is the tunnel entrance cross-sectional area, given by
formula here
This portal is predicted theoretically to cause the pressure to increase linearly with
distance across a compression wavefront of thickness ∼ [lscr ]/M, which is very much
larger than in the absence of flaring. The increased wave thickness and linear pressure
variation counteract the effect of nonlinear steepening of the wave in a long tunnel,
and tend to suppress the environmentally harmful ‘micro-pressure wave’ radiated
from the far end of the tunnel when the compression wave arrives. Our experiments
are conducted at model scale using axisymmetric ‘trains’ projected at
U ∼ 300 k.p.h. (M ≈ 0.25) along the axis of a cylindrical tunnel fitted with a flared portal. The
blockage [Ascr ]o/[Ascr ] = 0.2, which is comparable to the larger values encountered in
high-speed rail operations.