CONJUGATE MATHEMATICAL MODELING OF UNSTEADY FLOWS IN HYDROPNEUMATIC SPRINGS OF ROLLING STOCK

A computational technique is developed for predicting the dynamic characteristics of hydropneumatic springs of railway transport based on the conjugate solution of equations of hydrodynamics and thermodynamics. Unlike traditional zero-dimensional hydraulic models, the proposed approach takes into account the viscosity, inertia and compressibility of the working fluid, which eliminates the overestimation of the attenuation time of transient processes and peak pressures characteristic of simplified methods. The mathematical model includes two-dimensional axisymmetric non-stationary Navier–Stokes equations for a viscous incompressible fluid, the equation of piston motion under the interaction of external load and back pressure in the working chamber, as well as a zero-dimensional thermodynamic model of a gas cavity (considering a polytropic process), which is an elastic suspension element. The numerical implementation was performed by the finite volume method using PISO algorithm and dynamic grid reconstruction to account for the movable piston boundary. The scientific novelty of the work consists in the fact that for the first time, for the problems of the dynamics of railway rolling stock hydropneumatic springs a complete coupling of a two-dimensional viscous fluid model and a thermodynamic gas model with feedback through the flow rate of the working fluid in the throttle was realized. It is quantitatively confirmed that neglecting viscosity and compressibility in zero-dimensional models leads to a significant increase in the vibration attenuation time (up to a number of magnitudes) and distortion of amplitude loads. The developed approach can be used as a virtual test bench in the design of promising hydraulic springs for passenger cars and locomotives, as well as to refine resource testing and create digital doubles of spring suspension units.