On the role of separation in compression wave generation by a train entering a tunnel hood with a window

Abstract

An approximate analytical theory is proposed for calculating the compression wave generated when a train enters a tunnel fitted with an entrance hood with an open window. The pressure rise ahead of the entering train causes air to exhaust from the window in the form of a high-speed jet. The profile of the compression wave transmitted into the tunnel is modified by the interaction of the train nose with the window, by multiple reflections of wave energy between the window and the hood portal prior to transmission into the tunnel, and in addition by the production of a pressure pulse by the jet. The wave generation problem can be formulated in a quasi-one-dimensional manner, whereby the pressure field generated in front of and to the sides of the train in the absence of the window is assumed to be scattered by the window. A self-consistent solution is obtained by evaluating the jet flow from the window using a nonlinear empirical equation proposed and validated by Cummings (1984, Amer. Inst. Aeron. Astron. J., 22, 786-792; 1986, J. Acoust. Soc. Amer., 79, 942-951) for the velocity in the window-exit plane. Predictions are found to be in excellent agreement with measurements of compression wave profiles obtained in model scale experiments reported by Howe et al. (2003, J. Fluid Mech., 487, 211-243) at train speeds ∼ 350 km h -1 .