A 2D numerical benchmark of an air Ranque-Hilsch vortex tube based on a fractional factorial design

Abstract

This work presents a numerical benchmark for the modeling of air Ranque-Hilsch vortex tubes assessing the solver type (pressure- vs. density-based), two different turbulence models (Standard k − ε and k − ω SST), the near-wall region treatment (high-Reynolds vs. low-Reynolds number), different boundary conditions and the inclusion or not of source terms that model the pressure convection term ignored in most turbulent flow simulations. The significance of each parameter is obtained from an analysis of variance of a fractional factorial design.Using the density-based solver in combination with the k − ω SST turbulence model and the source term mentioned above yields the best prediction in terms of outlet cold mass fraction. The present simulations demonstrate also that the turbulent conductivity assumption is not appropriate to predict the cold outlet temperature. Predictions at high cold mass fractions are improved by adding a term modeling the pressure convection term. At low cold mass fractions, the model does not predict flow reversals. The Bödewadt boundary layer is appropriately reproduced.Turbulence models assuming isotropic turbulence fail to predict the velocity profiles through the tube. Some corrections to the k − ω SST model may provide adequate results for engineering applications.