One-dimensional analysis of pressure variations induced by trains passing each other in a tunnel.

In this study, the asymptotic solutions of the pressure variations induced by two trains passing each other in a tunnel are theoretically investigated. The one-dimensional inviscid compressible airflow is analysed, and two methods to obtain numerically exact solutions and MH expansion formulas for approximate equations are presented, where MH is the Mach number of the high-speed train. The pressure coefficient, corresponding to the maximum value of the magnitude of the pressure, is expressed as |cp|max = |cp,min| = [(R/(1 - R))(1 + a)2 + (R(1 - R)/(1 - 2R)2)(1 - a)2] + O[MH], where cp,min < 0, a = UL/UH and UL and UH denote the speeds of the low- and high-speed trains, respectively, and R is the cross-sectional area ratio of the train to the tunnel. The theoretical results indicate the dependence of the speeds of the two trains on the pressure distribution and that the maximum magnitude of the asymptotic pressure for a fixed value of MH is obtained for a = 1 and a = 0 when R < Rc and R > Rc, respectively, where Rc denotes the critical blockage ratio. Because the airflow along the side of the low-speed train, induced by the low-speed train, is along the running direction of the high-speed train and reduces the relative velocity of the high-speed train as the two trains pass each other, |cp|max for a = 0 is larger than |cp|max for a = 1 when R > Rc. It is theoretically demonstrated that, as conventional high-speed railway systems satisfy R < Rc, a conservative pressure estimation can be established assuming a = 1. [ABSTRACT FROM AUTHOR]