fluids Article Large-Eddy Simulation of a Hydrocyclone with an Air Core Using Two-Fluid and Volume-of-Fluid Models Hassan Fayed 1,† , Mustafa Bukhari 2,† and Saad Ragab 2, * ,†   Citation: Fayed, H.; Bukhari, M.; Ragab, S. Large-Eddy Simulation of a Hydrocyclone with an Air Core Using Two-Fluid and Volume-of-Fluid Models. Fluids 2021, 6, 364. https:// doi.org/10.3390/fluids6100364 Academic Editor: Fatemeh Salehi Received: 26 August 2021 Accepted: 28 September 2021 Published: 14 October 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Narmer-EngSim LLC, Blacksburg, VA 24060, USA; hassan.fayed@narmer-engsim.com 2 Department of Biomedical Engineering and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA; mbukhari@vt.edu * Correspondence: ragab@vt.edu † These authors contributed equally to this work. Abstract: Large-eddy simulations have been conducted for two-phase flow (water and air) in a hydrocyclone using Two-Fluid (Euler–Euler) and Volume-of-Fluid (VOF) models. Subgrid stresses are modeled using a dynamic eddy–viscosity model, and results are compared to those using the Smagorinsky model. The effects of grid resolutions on the mean flow and turbulence statistics have been thoroughly investigated. Five block-structured grids of 0.72, 1.47, 2.4, 3.81, and 7.38 million elements have been used for the simulations of Hsieh’s 75 mm hydrocyclone Mean velocity profiles and normal Reynolds stresses have been compared with experimental data. Results of the two-fluid model are in good agreement with those of the VOF model. A fine mesh in the axial and radial directions is necessary for capturing the turbulent vortical structure. Turbulence structures in the hydrocyclone are dominated by helical vortices around the air core. Energy spectra are analyzed at different points in the hydrocyclone, and regions of low turbulent kinetic energy are identified and attributed to stabilizing effects of the swirling velocity component. Keywords: two-phase flow; hydrocyclone; large-eddy simulation; dynamic model; helical vortices; energy spectra 1. Introduction Hydrocyclones are used in many industries for separation of different phases. In the mineral-processing industry, classifying hydrocyclones are used to classify ores after grind- ing based on their particle sizes ([1–3]). A typical geometry of classifying hydrocyclone consists of a cylindrical section followed by a conical section with two outlets that are open to the atmosphere. The top outlet is called the overflow opening and the bottom one is called the underflow opening. Slurry of water and solid particles is forced tangentially into the hydrocyclone top, and it swirls as it goes downward. The swirling flow field generates a column vortex with pressure decreasing radially towards the center. The strength of the vortex depends on the rate of input angular momentum about hydrocyclone centerline. The radial pressure gradient affects the motion of particles based on their specific gravity and/or sizes. Because of the low pressure created by the swirling layer of slurry, air enters through the underflow opening and forms an air core around the hydrocyclone center- line. The structure and motion of the air core depends on the operating conditions of the hydrocyclone ([4]). Hararah et al. [5] found that the distribution of tangential and axial velocity of air inside the core depends on the pressure drop and geometry of hydrocyclone. Devulapalli [6] experiments show that the inlet flow rate has a direct effect on the air core diameter. Laboratory experiments and CFD techniques can be used for performance evaluation and improvements of hydrocyclones. Laboratory experiments are important to determine mean velocity profiles and turbulence statistics. However, such measurements are expen- sive and time consuming. The high cost of experiments limits their effectiveness to optimize Fluids 2021, 6, 364. https://doi.org/10.3390/fluids6100364 https://www.mdpi.com/journal/fluids