A hybrid Eulerian-Eulerian/Eulerian-Lagrangian method for dense-to-dilute dispersed phase flows

Problems involving a transition between dense and dilute dispersed phase regimes often require hybridization of Eulerian-Eulerian (EE) and Eulerian-Lagrangian (EL) methods for accurate and efficient computational modeling. A hybrid EE-EL formulation is developed in this work from first principles, which asymptotes to well-established EE and EL methods in limiting conditions. A smooth and dynamic transition criterion and a corresponding algorithm for conversion between the two representations of the dispersed phase are developed. To use EE and EL in their respective regions of effectiveness, the transition criterion is designed as a function of local volume fraction and local kinetic energy of random uncorrelated motion of particles. Several one-dimensional numerical tests are conducted to analyze limits of the hybrid EE-EL method in dense (up to 65% volume loading) and dilute conditions, at first, without any conversion between EE and EL, and then the ability of the conversion algorithm to smoothly transition from EE to EL and vice versa is evaluated using prespecified and dynamically computed transition criteria for one- and two-dimensional tests. Particle evolution in two-dimensional frozen turbulence is simulated to evaluate the method's ability to dynamically transition from EE to EL and vice versa in regions of particle trajectory crossing. Finally, the hybrid method is used for simulating dispersion of an initially dense particle cloud in a three-dimensional spherical sector blast. (C) 2021 Elsevier Inc. All rights reserved.