A quasi-one-dimensional study on global characteristics of tube train flows

Abstract

The global characteristics of tube train flows under wide ranges of blockage ratios and train speeds are comprehensively investigated by quasi-one-dimensional numerical simulation and theoretical analysis. The established quasi-one-dimensional model for the tube train flow and the numerical method are both proven to be reliable and efficient. Investigation reveals the typical patterns of both inviscid and viscous flows. The transition limits for these flow patterns are determined. The flows tend to be unstarted when the train moves at a high subsonic speed or a low supersonic speed and tend to be started otherwise. The transition limits between started and unstarted modes do not vary much between inviscid and viscous flows, which allows the use of analytical inviscid criteria in approximate estimation of the start/unstart state of the viscous flow. Between the supersonic isentropic limit and the Kantrowitz limit lies a dual-solution area. Which solution the flow follows depends on how the attempted cruise speed of the train is reached; a large acceleration tends to induce a started flow. The unstarted inviscid tube train flow appears to be self-similar as the train suddenly moves at a constant speed. This flow involves a precursor shock wave in front of the train and a secondary shock wave on or behind the train at the same time. By contrast, the unstarted viscous flow eventually remains a steady laminar structure that moves with the train after a sufficiently long process of development. In the stabilized flow, the precursor shock wave only occurs in the supersonic case, and the secondary shock wave only occurs in the subsonic case. For both inviscid and viscous flows, the unstarted flow can be divided into two submodes according to whether the secondary shock wave detaches from the train. Aerodynamic drag on the train is strongly correlated with the flow modes. The drag in unstarted flow increases with train speed, while the drag coefficient peaks at the secondary shock attach–detach limit. The wall transport effects cause larger drag but do not change its overall features.