Estimation of the Flow Characteristics Between the Train Underbody and the Ballast Track

Abstract

The purpose of this work is to estimate the equivalent roughness of the ground below the train, which consists of both ballast and sleepers. The motivation is that, in order to study the flow between the train and the ground utilizing a Reynolds Averaged Stress model, and to make a stationary analysis, the sleepers can not be treated individually and have to be considered as a part of the roughness of the ground. The flow under a train can be simplified in order to study the effect of the wall made up by sleepers and ballast. The easiest configuration to carry out this work is that corresponding to two-dimensional fully developed flow, in which periodic boundary conditions can be imposed at the entrance and exit. The Couette flow has been chosen, because it is the easiest one, and besides represents better the physics of the flow below the train. A k-coclosure model to simulate turbulence was used, and calculations were carried out with Fluent. The average velocity profile is estimated and this is fitted to a logarithmic profile, from which the average roughness is obtained. The influence of the configuration on the obtained values of the equivalent surface roughness is analyzed. The following parameters have been changed: height of the gap, Reynolds number, roughness of the upper wall. The equivalent roughness seemed to be insensitive, to variations of these parameters. The influence of the turbulence closure procedure on the results has been examined and different equivalent rough nesses are obtained, depending on whether the k-coor k-eclosure procedure is used. In order to estímate the validity of the whole profile across the gap, an analytic solution of the turbulent Couette flow (using the equivalent roughness for the lower wall) has been calculated. This analytic solution is obtained using either the k-coor k-e closure model; and it turns out to be the same, independently of which of the two models is used. The comparison between the analytic solution andthe average velocity profiles is good. This analytical solution can also be of interest to estimate the shear stress in the ground that is related to the raise of the ballast. Comparisons between the analytical results for smooth walls with experiments and classical models for turbulent Couette flows have been also included.