Improving the procedure for modeling low-frequency oscillations of the free surface liquid in a tractor tank

Abstract

This paper considers the influence of hydrodynamic processes in the movement of the free surface of liquid in partially filled tractor tanks. Splashing liquid in partially filled containers is a significant problem in the study of functional stability of movement in the marine, aerospace, rail, and automotive industries. After all, it affects productivity and traffic safety. The same effect was observed when performing transportation work while delivering liquid cargoes in the agricultural sector. That was due to increasing the transportation speeds of wheeled tractors. In the procedure, using the Rayleigh theory of surface waves, a linearized problem of motion of the free surface of a liquid is obtained. Based on Helmholtz's theorem, the components of scalar and Laplace field vector potentials of fluid velocity vector are separated. The potential problem for translational motion of fluid, in which vortex component of the field is absent, is considered. Instead of the fluid velocity potential, a scalar fluid displacement potential in Rayleigh surface waves was introduced. Comparing the results of calculating fluid splashing with the work of other scientists, a high convergence of natural frequencies of partial oscillators in 3D space was found. This is noticeable in the last quarter of the filling of the tank, in which significant displacements of the deep liquid occur. A feature of the results is the introduction, instead of the real shape of the container, an equivalent form of a parallelepiped, the final shape of which depends on the level of fullness. The frequency properties of movement of the free surface of liquid based on the standard size of tanks used in agriculture are separated. The proposed improved methodology could be used to increase stability, controllability, and smoothness when operating tanks with a wheeled tractor.