Discrete integration for measuring aerodynamic loads on trains in crosswinds − realizable strategies of discretization and discrete integration

Discrete integration occupies an important place in train aerodynamic tests in crosswinds. Improved delayed detached eddy simulations based on shear stress transport k-ω turbulence models were carried out to calculate the side force, lift, rolling moment around the lee rail, and surface pressure on bluff and streamlined vehicles. The changepoints and piecewise linearities of the pressure coefficients were evaluated, and the maximum coefficient of determination in the elements was 0.9973. A realizable strategy of the discretization based on the Lagrange rectangular elements was suggested, including the largest lengths and numbers of the elements. From this, a strategy of the discrete integration was presented to measure the aerodynamic loads, considering the real orientation of the elements. The maximum errors of the mean aerodynamic load coefficients of the bluff and streamlined vehicles were 4.1% and 2.2% (except the mean lift coefficient of the bluff vehicle), respectively. The errors were less than those in the previous studies, especially for the streamlined vehicle, which reduced by up to 8.7%. The unsteady aerodynamic loads with no delay obtained by the strategies were near to natural ones in the frequency range that people would be concerned about in crosswinds (at the Strouhal number of less than 0.4). Some suggestions were made for using the strategies in the full-scale tests and model tests, which provided a foundation for further studies of the running safety in natural crosswinds.