差分格子ボルツマン法によるトンネル圧縮波の発生と伝播計算(流体工学,流体機械)

Abstract

Direct numerical simulation of compression wave produced when a high-speed train enters a tunnel, distortion of the compression wave front as it travels in the tunnel, radiation of micropressure wave from the tunnel exit are performed using the finite difference lattice Boltzmann method. The discrete Boltzmann equation for the 3D39Q thermal BGK model is solved in three-dimensional space using a second-order Runge-Kutta scheme in time and a third-order-upwind finite difference scheme in space. The arbitrary Lagrangian-Eulerian formulation (ALE) is applied to model the interaction of the moving train nose and the tunnel portal. Detailed numerical calculations were carried out for axisymmetric trains with the blockage of 0.2 and various nose profiles entering a long circular cylindrical tunnel with straight and stepwise flared portals. The predicted compression wave profiles are found to be in good agreement with linear theory predictions obtained from the analytic expression derived by Howe. It is shown that the distortion of the compression wave front is consistent with the time-domain computation of one-dimensional Burgers equation. Longer nose profiles and tunnel entrance with flared portals are confirmed not only to decrease the initial steepness of the compression wave front but also to counteract the effect of nonlinear steepening.