Investigation of сomputational meshes for modeling the air dynamics in a vortex tube channel by OpenFOAM software

Abstract

A vortex tube is a simple device with no moving parts that separates a swirling gas stream into two vortexes that differ in temperature, usually above and below the temperature of the inlet gas. This paper presents a mathematical model of a vortex tube which is based on gas dynamics laws and is supplemented by a k-ω turbulence model. A description of the technique for constructing a finite volume mesh with definition of the near-wall region based on the blockMesh utility is given when the conditions for the uniformity of the mesh elements are met while maintaining their orthogonalization. The numerical solution is carried out on a computational cluster using the sonicFoam solver of the OpenFOAM free software. Three series of numerical simulation experiments were carried out to determine the temperature distribution in the channel of a cold air diaphragm depending on the diaphragm diameter. One of the three computational mesh scales considered in this work is used. It is shown that mesh size reduction leads to convergence of simulation results. It is also demonstrated the qualitatively correct results can be obtained by generating a mesh in which the average linear size of a finite volume does not exceed 0.4 mm (0.025 in dimensionless representation). To improve the accuracy of quantitative data, an even greater computational mesh size reduction is required; in particular, a fine mesh with an average linear size of the finite volume less than 0.02 is considered in this work. The results obtained on a fine mesh are in a qualitative agreement with the results determined using a coarser mesh. However, the numerical values can differ significantly, which is shown by the calculations for the cold air diaphragm of large diameter. Thus, the computational time increases with decreasing mesh size, which implies that the construction of a computational mesh for vortex tube modeling requires finding a balance between the quality of results and the simulation time.