On forced flow through a baffled wall aperture, with application to compression wave generation in a tunnel

An analysis is made of the sound produced by vorticity generated as high pressure fluid is forced through an aperture in the wall of a duct in the presence of an exterior baffle plate. The aperture typically behaves as a ‘pressure release’ opening when the flow is ideal and irrotational, corresponding to the traditional interpretation of the action of a finger hole of a woodwind instrument, although theoretical predictions that neglect vorticity are irrelevant in practice except at very high frequencies. The theory of vortex sound is applied to derive an approximate nonlinear equation for the volume flux through the baffled aperture that generalises Cummingsʹs empirical equation for a jet exhausting through a fully open orifice in a large wall. The equation takes account of the impingement of the jet on the baffle and of the nonlinear ‘inertial blocking’ of the aperture flow. Application is made to the problem of compression wave generation by a high-speed train entering a tunnel fitted with an entrance hood whose windows are partially ‘closed’ by the presence of a side-wall of a railway cutting or embankment. Theoretical predictions are found to be in good agreement with measurements made at model scale at train speeds ∼ 300 – 400 km / h .