Modal Spectral Element Solutions to Incompressible Flows over Particles of Complex Shape

Abstract

This paper develops the virtual identity particles (VIP) model to simulate two-phase flows involving complex-shaped particles. VIP assimilates the high efficiency of the Eulerian method and the convenience of the Lagrangian approach in tracking particles. It uses one fixed Eulerian mesh to compute the fluid field and the Lagrangian description to handle constitutive properties of particles. The interaction between the fluid and complex particles is characterized with source terms in the fluid momentum equations, while the same source terms are computed iteratively from the particulate Lagrangian equations. The advantage of VIP is its economy in modeling a two-phase flow problem almost at the cost of solving only the fluid phase with added source terms. This high efficiency in computational cost makes VIP viable for simulating particulate flows with numerous particles. Owing to the spectral convergence and high resolvability of the modal spectral element method, VIP provides acceptable resolution comparable to DNS but at much reduced computational cost. Simulation results indicate that VIP is promising for investigating flows with complex-shaped particles, especially abundant complex particles.

Smoothed‐profile method for momentum and heat transfer in particulate flows

“…Therefore, these methods suffer a dramatic loss of accuracy in a layer around the particle's surface with depth of approximately 25 % of the particle's radius . If the Eulerian multiphase approach is coupled with an h / p method, spectral convergence can be achieved for both latter cases , as well as for the virtual‐identity‐particles method (VIP, ).…”

“…Therefore, these methods suffer a dramatic loss of accuracy in a layer around the particle's surface with depth of approximately 25% of the particle's radius [20]. If the Eulerian multiphase approach is coupled with an h=p method, spectral convergence can be achieved for both latter cases [21-23], as well as for the virtual-identity-particles method (VIP,[24]). Aside from a representation of the particulate phase by a fictitious-domain method (e.g., DLM) or by distributed body forces (e.g., FCM), other approaches can be employed.…”