Effect of boundary layer development on the dynamics of trains and train-like articulated systems travelling in confined fluid

Abstract

The effect of boundary layer development on the dynamics of trains of flexibly interconnected rigid cylinders subjected to fluid dynamic forces is investigated theoretically. Each cylinder in the model is flexibly coupled to the other cylinders and is supported by springs, such that it has both translational and rotational degrees of freedom. The kinetic, dissipation, and potential energies of the system and the generalized forces associated with the fluid dynamic forces acting on the system, such as inviscid fluid dynamic forces, viscous frictional forces, and form drag, are obtained first. Then the equations of motion are derived in a Lagrangian framework. The effect of the boundary layer development is taken into account by integrating variable viscous frictional coefficients into the equations of motion, instead of taking them to be constant. This is part of a broader study into the dynamics of high-speed trains running in a tunnel, or more generally of a train-like system travelling in a coaxial cylindrical tube and subjected to aerodynamic forces associated with lateral motions of the cylinders. The results of this study show that the system becomes less stable if the boundary layer is considered to be developing from the head toward the tail of the train. In addition, the average values of equivalent sand roughness kS⁎ for high-speed Japanese trains are estimated from the previous data obtained from running experiments.