Unsteady Potential Flow Analysis of Tunnel Compression Wave (Comparison with Computational Results by the Lattice Boltzmann Method)

Abstract

The generation of compression wave produced when a high-speed train enters a tunnel is studied by solving the two dimensional incompressible irrotational flow over the train nose. The Schwarz-Christoffel conformal mapping is applied to model the train and tunnel portal configuration. The complex velocity potential of the flow field is defined by a distribution of sources on the nose. The contribution from the exit-flow shear layer vortex is estimated by modeling a pair of point vortices placed at short distances from the corner of the tunnel portal and imposing the Kutta condition that the velocity should be finite at the corner. The unsteady potential equation is solved to obtain the pressure field at each step of train translation. The results are compared with numerical calculations of the pressure rise obtained by the finite difference lattice Boltzmann method (FDLBM), which recovers the compressible Navier-Stokes equation of fluids. It is shown that the contribution from the exit-flow vortex increases up to approximately 7 % during the time in which the train nose enters the tunnel. The prediction with point vortices shows close agreement with the FDLBM.