Stepwise approximation of an optimally flared tunnel portal

An optimally flared tunnel portal causes the pressure to rise linearly across the front of the compression wave generated by an entering high-speed train. The wave front thickness ∼ ℓ / M when the flared section has length ℓ and the train Mach number is M. The flared portal would likely be constructed in practice using a set of coaxial cylindrical sections that together approximate the ideal flared geometry. A numerical study is described in this paper to determine how these discrete sections modify the generation of the compression wave. The interaction of train nose `sourcesʹ with successive changes in portal diameter produces a `ripplingʹ of the pressure wave profile. Our results show how the amplitude of these fluctuations depends on the length of the train nose and on the number of cylindrical sections, and suggest that an ideally flared portal is well approximated by a stepped-portal fabricated from three or four sections. The results are applicable for train Mach numbers up to about 0.25 ( ∼ 300 kph ) .