2021/12/20 by Célio Fernandes, Salah Faroughi, Fernandes, Célio +7
Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2112.10834
arxiv created 2021/12/20 · arxiv updated 2021/12/22
Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid-particle force ⟨ F ⟩ on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix. Here we use direct numerical simulations (DNS) to study the creeping flow (Re≪ 1) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier-Stokes/Cauchy momentum solver. The numerical study consists of N=150 different systems, in which the normalized average fluid-particle force ⟨ F ⟩ is obtained as a function of the volume fraction ϕ (0 < ϕ≤ 0.2) of the dispersed solid phase and the Weissenberg number Wi (0 ≤ Wi ≤ 4). From these predictions a closure law ⟨ F ⟩(Wi,ϕ) for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model which is, on average, within 5.7% of the DNS results. Additionally, a flow solver able to couple Eulerian and Lagrangian phases is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, in order to assess the accuracy and robustness of the newly-developed approach for handling particle-laden viscoelastic flow configurations with O(105-106) rigid spheres that are representative of hydraulic fracture operations.