Open-source one-dimensional modelling of piston-effect pressure waves in high-speed railway tunnels: verification, benchmarking against 3D CFD and single-train design-load screening

Abstract

The piston effect of a high-speed train passing through a tunnel produces pressure transients that drive tunnel cross-section design and impose loads on rolling stock and equipment. This paper verifies an open-source one-dimensional solver for these transients and defines the limits of its predictive capability. The train is represented as a moving cross-sectional-area blockage in the quasi-one-dimensional compressible Euler equations, discretised with a second-order MacCormack scheme. The solver is verified against the analytical entry-wave solution, validated against a published full-scale measurement of the piston-wind field, benchmarked against published three-dimensional computational fluid dynamics (CFD), subjected to a five-level grid-refinement study with dissipation and nose-ramp sensitivity tests and applied to a single-train design case. The compression-wave amplitude agrees closely with both the analytical solution and the published three-dimensional CFD results. The principal result concerns the localised suction peak beneath the train nose, commonly assumed to lie beyond the reach of area-averaged one-dimensional models: once the cell size resolves the nose ramp, it is grid-convergent, with a Richardson value within a few per cent of the three-dimensional CFD result. What had appeared to be non-convergence was due to under-resolution. Coupling to a cabin-sealing model shows that a narrower tunnel is viable only if the rolling stock carries a more demanding sealing specification. The solver is, to the author's knowledge, the first permissively licensed one-dimensional tool for high-speed compression-wave transients released with a reproducible verification-and-validation suite, providing a common baseline for benchmarking new closures. The grid study also corrects a limitation commonly attributed to this class of model.