Design of a tunnel-entrance hood with multiple windows and variable cross-section

A theory is proposed for the design of a uniform tunnel-entrance hood whose cross-sectional area exceeds the tunnel area . A train entering the tunnel produces a low-frequency compression wave that can be subject to nonlinear steepening in a long tunnel. An optimized hood of length ℓ_h increases the initial thickness of the compression wave front from R/M to ℓ_h/M, where Rℓ_h is the nominal radius of the tunnel and M is the train Mach number. In addition, the pressure rise should be linear across the wave front to obtain an overall minimum value of the subjectively important pressure gradient. This is achieved in a uniform hood by distributing windows along the hood wall to vent away high-pressure air displaced by the train. We consider the problem of determining the distribution and sizes of these windows and the magnitude of the area ratio to ensure that the hood behaves optimally at low-train Mach numbers (M<0.2), when the hood can be regarded as being acoustically compact. At the projected higher Mach numbers of advanced high-speed trains (0.4, say) recent analysis for hoods of uniform cross-section by Howe in 2003 indicates that a hood optimized for low Mach number operations continues to produce an essentially linear pressure rise across a compression wave of thickness ℓ_h/M except for a low-amplitude oscillation at the very front of the wave.