Abstract
Various modifications to tunnel portals may be employed to reduce the sudden pressure jump which occurs as a train passes through the entrance or exit. Tunnel entrance gives rise to pressure waves which may travel down the length of the tunnel and reflect back to cause ear discomfort to the passengers. Various distortions are introduced to the shape of these waves if they reflect off a modified tunnel portal. A linearized analysis of a pressure impulse and a pressure step reflecting off a portal consisting of a long slotted section is presented. A closed-form solution is obtained. It is shown in both cases that the infinitely steep rise of the incident wave is reflected as a pressure rise of finite slope, and the pressure amplitude may exceed that of the input for some points in time. The apparent mass of flow through a narrow slot is calculated. It is shown that the magnitude of pressure waves produced by tunnel entry may be sufficiently large that significant non-linear acoustic effects may be present.
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