Theoretical and experimental investigation of the compression wave generated by a train entering a tunnel with a flared portal

The compression wave generated by a high-speed train entering a tunnel is s tudied theoretically and experimentally. It is shown that the pressure rise across the wavefront is given approximately by rho oU2/1-M2 ,A(o)/A(1+A(o)/A), where rho (o), U, M, A(o) and A respectively denote the mean air density, t rain speed, train Mach number, and the cross-sectional areas of the train a nd the uniform section of the tunnel. A monopole source representing the di splacement of air by the train is responsible for the main pressure rise ac ross the wave, but second-order dipole sources must also be invoked to rend er 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 pr actice, 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 S(x)/A =1/[A/A(E) -x/l (1- A/A(E))] , -l < x < 0 where x is distance increasing negatively into the tunnel, l is the prescri bed length of the flared section, and A(E) is the tunnel entrance cross-sec tional area, given by A(E)/A = (l/2R)(2/3) [(1 + root1-(2R/3 root 3l)(2))(1/3)](2), R = rootA/pi. This portal is predicted theoretically to cause the pressure to increase li nearly with distance across a compression wavefront of thickness similar to l/M, which is very much larger than in the absence of Raring. The increase d wave thickness and linear pressure variation counteract the effect of non linear steepening of the wave in a long tunnel, and tend to suppress the en vironmentally harmful 'micro-pressure wave' radiated from the far end of th e tunnel when the compression wave arrives. Our experiments are conducted a t model scale using axisymmetric 'trains' projected at U similar to 300 k.p .h. (M approximate to 0.25) along the axis of a cylindrical tunnel fitted w ith a flared portal. The blockage A(o)/A = 0.2, which is comparable to the larger values encountered in high-speed rail operations.