Journal of Non-Newtonian Fluid Mechanics 266 (2019) 80–94 Contents lists available at ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: www.elsevier.com/locate/jnnfm Fully-resolved simulations of particle-laden viscoelastic fluids using an immersed boundary method C. Fernandes a,∗ , S.A. Faroughi b , O.S. Carneiro a , J. Miguel Nóbrega a , G.H. McKinley b a Institute for Polymers and Composites/i3N, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal b Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, US a r t i c l e i n f o Keywords: Particle-laden flow Viscoelastic fluid Finite volume method Immersed boundary method Fully resolved simulations a b s t r a c t This study reports the development of a direct simulation code for solid spheres moving through viscoelastic fluids with a range of different rheological behaviors. The numerical algorithm was implemented on an open- source finite-volume solver coupled with an immersed boundary method, and is able to perform fully-resolved simulations, wherein all flow scales associated with the particle motion are resolved. The formulation employed exploits the log-conformation tensor to avoid high Weissenberg number issues when calculating the polymeric extra stress. A number of benchmark flows were simulated using this method, to assess the accuracy of the newly- developed solver. First, the sedimentation of a sphere in a bounded domain surrounded by either Newtonian or viscoelastic fluid was computed, and the numerical results were verified by comparison with experimental and computational data from the literature. Additionally, the spatial and temporal accuracies of the algorithm were evaluated, and different transient and advection discretization schemes were investigated. Second, the rotation of a sphere in a homogeneous shear flow was studied, and again the numerical results obtained were compared to those from the literature. Good agreement is obtained for the variation in the particle rotation rate as a function of Weissenberg number, using both the newly implemented algorithm and an alternative fixed-mesh approach. Finally, the cross-stream migration of a neutrally buoyant sphere in a steady Poiseuille flow, consisting of either a Newtonian or viscoelastic suspending fluid was investigated. For the Newtonian fluid good agreement was obtained for the particle equilibrium position when compared to the well known Segré–Silberberg effect, and for the viscoelastic fluid the effect of the retardation ratio on the final particle equilibrium position was studied. Additionally, the newly-developed solver capabilities were tested to study the shear-induced particle alignment in wall-bounded Newtonian and viscoelastic fluids. The role of the fluid rheology and finite gap size on both the rate and approach pathways of the solid particles is illustrated. 1. Introduction Fluid-particle transport problems occur in many different forms, and with significant practical relevance, in several engineering applications, such as oil sands mining, fluidized beds, coal-based combustion cham- bers and biomass gasifiers [1–4]. In many applications it is essential to consider that the fluid, in which the particles are dispersed, has under- lying viscoelastic characteristics. The use of numerical simulations to understand the behavior of multiphase flows, including those with viscoelastic matrix fluids, pro- vides a very important source of insight into the physical transport pro- cesses that occur between freely-moving particles and nonlinear flu- ids. Amongst others, one commonly method employed to solve such simulations is the Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) [5], which in turn can be categorized as following a ∗ Corresponding author. E-mail addresses: cbpf@dep.uminho.pt (C. Fernandes), faroughi@mit.edu (S.A. Faroughi), olgasc@dep.uminho.pt (O.S. Carneiro), mnobrega@dep.uminho.pt (J.M. Nóbrega), gareth@mit.edu (G.H. McKinley). resolved or unresolved approach, depending on the size of the particles relative to the smallest computational mesh cell size. In resolved CFD- DEM [6,7] the particles are substantially larger than the individual com- putational cells, i.e., when represented within the mesh a particle cov- ers multiple cells. Due to limitations on computational capabilities this method can only be used for cases where relatively small number of par- ticles, say a few hundreds or O(1000) particles, need to be considered. The fluid field around each particle is resolved with a detailed mesh, and the force balance on each particle is calculated individually, which provides a comprehensive understanding of the underlying physics [8– 12]. This approach belongs to the class of Direct Numerical Simulations (DNS) [13,14]. In contrast, unresolved CFD-DEM [15] is designed for handling very large numbers of particles, which should be significantly smaller than the computational mesh cells. Consequently, each cell can contain several particles. For such simulations it is essential to know https://doi.org/10.1016/j.jnnfm.2019.02.007 Received 11 August 2018; Received in revised form 16 February 2019; Accepted 16 February 2019 Available online 18 February 2019 0377-0257/© 2019 Elsevier B.V. All rights reserved.