SOME ISSUES OF MATHEMATICAL MODELING OF TURBULENT FLOWS AROUND TRANSPORT VEHICLES AND THEIR ELEMENTS - Sokhatskyi, A. V. (Systems and Technologies, 2025)
The flow of vehicles in a turbulent flow is a complex nonlinear dynamic system. To study these complex nonlinear systems, certain methodological approaches are implemented. These approaches should be based on objective physical laws that describe the behavior of a dynamic system. As a result of the analysis of the processes under study, it is necessary to identify their regularities and develop their description.Mathematical modeling of such nonlinear dynamical systems is an interdisciplinary tool for studying various physical processes. The problems of modeling advanced turbulence remain open. A single mechanism of transition to turbulent chaos in different types of hydrodynamic flows has not yet been found. In a developed turbulent flow, there are pulsations with scales ranging from the largest to very small. To date, four mechanisms are known for the transition of laminar flow to turbulent flow when the Reynolds number reaches a critical value. It is believed that the phenomenon of turbulence is to some extent related to chaos.Today, there is no comprehensive theory of turbulence in various aerodynamic flows. To date, a number of scenarios for the development of turbulent flows based on the processes of motion chaos have been proposed. These are the following scenarios: based on the idea of the hierarchy of quasi-periodic motions; the process of chaoticization of fluid motion by Ruel- Tuckens; transition to turbulent chaos through a sequence of doubling period bifurcations; transition to turbulence through intermittency. These approaches originated as a result of studies of model systems of turbulent flows and their analysis using differential equations. Their mathematical description is extremely complex and requires further development. To numerically solve the problem of calculating the characteristics of turbulent flow around a ground vehicle, a model of viscous compressible gas flow described by the Reynolds-averaged Navier-Stokes equations was chosen. The computational domain around the vehicle is complex, so it is advisable to use a multi-block approach and a curved coordinate system. The methodology was developed, the algorithm was constructed, and the codes of the software package were written in Fortran-95.By numerically solving the Reynolds-averaged Navier-Stokes equations closed by the Spalart-Allmaras turbulence model in the realization of separated vortices, the plane-parallel flow of a circular cylinder is calculated. The obtained results are compared with experimental data.