Investigation of the influence of boundary conditions in the numerical solution of a vortex tube model

Abstract

The applicability of various boundary conditions in the computational simulation of a Ranque–Hilsch vortex tube is investigated. A review of existing works on the effect of geometry and various thermodynamic parameters on the efficiency of the pipe is made. The substantiation of the possibility of introducing additional computational domains when moving the boundaries to study the influence of boundary conditions when modeling gas dynamics problems is given. To simulate the dynamics of a gas in a vortex tube, a mathematical model is written that includes the Navier–Stokes system of equations describing a compressible viscous fluid, which is closed by the equation of state of an ideal gas. Existing methods for calculating turbulent flows are considered. The applicability of various semi-empirical models of turbulence for modeling a vortex tube is described. The possibility of using the selected k−ε model and its description is argued. The boundary conditions characteristic of the vortex tube model are described, and the boundary conditions most combined in the simulation of gas dynamics problems are also shown. Presents a grid that takes into account the area formed by the removal of boundaries. The solution is based on the sonicFoam algorithm in the OpenFOAM package. Utilities of the postprocessor are used when preparing the model for calculations on a high-performance cluster and utilities for averaging the obtained physical quantities. The simulation results for different combinations of boundary conditions and models with remote boundaries are given. Comparison of the results obtained. It is shown that the geometrical dimensions have a strong influence on the operation of the pipe; the correct choice of boundary conditions makes it possible to obtain the values of physical quantities that are closest to the known experimental ones. Moving the boundaries away from direct exits provides an opportunity to more accurately estimate the effects that arise near the real boundaries of the vortex tube, especially affecting the magnitude of the Ranque–Hilsch effect.