A New Simple Equation Governing Distortion of Compression Wave Propagating Through Shinkansen Tunnel with Slab Tracks

Abstract

A high-speed train entering a tunnel generates a compression wave that propagates through the tunnel toward its exit. When the compression wave reaches the tunnel exit, a pressure pulse causing environmental problems (the micro-pressure wave) is radiated from the exit portal. The micro-pressure wave magnitude is approximately proportional to the maximum pressure gradient of the tunnel compression wave arriving at the exit portal. In a long Shinkansen tunnel with concrete slab tracks, the compression wavefront steepens due to the nonlinear effect during its propagation because all surfaces of the tunnel wall are smooth. Therefore, it is necessary to investigate the compression wave distortion in a tunnel and to clarify the characteristics of the compression wave propagation for estimating and reducing the magnitude of the micro-pressure wave. In this paper, we introduce a new simple equation governing distortion of the tunnel compression wave propagating through a Shinkansen tunnel with concrete slab-tracks. We propose a new simple scheme for numerical calculations. A space evolution type equation with one variable is derived from the three conservation equations (mass, momentum, and energy including the wall friction and heat transfer terms) of the 1D CFD by assuming small disturbances excited by the compression wave. The numerical calculation scheme based on the simple equation reduces the computing time remarkably because its CFL condition is relaxed. The calculation results obtained using the proposed scheme agree well with those by a conventional scheme based on the 1D CFD. The accuracy of the simple equation is verified.

Propagation characteristics of tunnel compression waves with multiple peaks in the waveform of the pressure gradient: Part 1: Field measurements and mathematical model

“…2,11 The distortion at the junction between the main tunnel and a large shaft (Figures 1 and 2) was calculated using the acoustic analysis described in Appendix 2. The Courant number (γ+1)uΔx/2Δt determined for this calculation 16 was approximately equal to 0.5. In addition, the friction parameters ɛs and ɛus were determined by preliminary calculations from P3 to P4 for both friction models, i.e.…”

“…Miyachi et al. 16 derived the following mathematical model from the basic equations for one-dimensional compressible flows (such as in Fukuda et al. 11 ), i.e.…”

Propagation characteristics of tunnel compression waves with multiple peaks in the waveform of the pressure gradient: Part 2: Theoretical and numerical analyses

“…We obtained equation (1) by applying the friction model proposed in the first paper 3 to a one-dimensional equation derived from the three conservation laws. 6…”

“…The first-order method was used for the space integral in equation (1). The Courant number (γ+1)uΔx/2Δt for this calculation 6 was taken to be approximately 0.5. The unsteady friction was calculated with first-order accuracy and the singular point around φ=0 was eliminated by locally fitting a quadratic function to the pressure, if you need p .…”

Substantiation of Parameters of the Network Model of the Air Distribution Due the Piston Effect in the Extra-Long Tunnels

“…The research on the piston effect of moving trains and vehicles in tunnels [4][5][6][7][8][9][10][11][12] was mostly studied in tunnels up to 1000 m long with vehicles and trains not exceeding 150-200 m in length. Throughout this article, we discuss freight trains that are 1200-1500 m long.…”