COMPARATIVE ANALYSIS OF TWO MULTIPHASE MODELLING APPROACHES FOR BLOOD FLOW Mohit P. TANDON 1∗ , Jebin ELIAS 1 , Simon LO 2 1 CD-Adapco India, 4th Floor, Parakh House, 1, Boat Club Road, Pune - 411 001, India 2 Trident House, Trident Park, Basil Hill Road, Didcot, OX11 7HJ, United Kingdom ∗ Corresponding author, E-mail : mohit.tandon@cd-adapco.com ABSTRACT The Euler-Euler methodology implemented in STAR- CCM+ is used for modelling blood flow in narrow tubes. Two particulate flow modelling approaches, one: kinetic theory based granular flow (KTGF), and second: two-fluid theory based suspension rheology, are used to understand the phenomenon behind the migration of red blood cells (RBCs) from the walls to the core in narrow flow channels. It is demonstrated that the stress induced diffusion is responsible for the motion of the RBCs towards the center, and this par- ticle migration phenomenon explains the Fåhræus-Lindqvist effect. The computed haematocrit distribution from the numerical simulations performed agrees with experimental measurements, and both KTGF model and suspension model are able to predict the flow characteristics analogously. But, it is highlighted that by accounting for the inelasticity of the walls, KTGF approach significantly influences and improves the near wall prediction of the haematocrit concentrations. Keywords : Blood Flow, Two Fluid Model, Kinetic Theory of Granular Flows, Suspensions, Stress induced diffusion. Nomenclature Greek Letters λ Anisotropy parameter γ s Collisional dissipation rate [kg/(m.s 3 )] ρ Density [kg/m 3 ] η Dimensionless Viscosity θ Granular temperature [m 2 /s 2 ] ϕ Specularity coefficient ε Strain rate τ Stress Tensor [kg/(m.s 2 )] μ Viscosity [kg/(m.s)] α Volume Fraction Latin Symbols A Interphase momentum coefficient [kg/ (m 3 .s)] F Force [N] Q Normal stress anisotropy tensor Re Reynolds Number c Fluctuating velocity [m/s] d Particle diameter [m] e Coefficient of restitution g Gravity [m/s 2 ] g 0 Radial Distribution Function k Granular conductivity [kg/(m.s)] n Normal [m] p Pressure [Pa] u Velocity [m/s] Sub/superscripts NS normal stress S shear stress b bulk i,k i,k-th phase int interaction l liquid phase max maximum packing limit p particle contribution s solid phase slip slip between phases w wall INTRODUCTION Blood is a rich suspension of red blood cells (RBCs) in Newtonian fluid, plasma. Biophysics of blood flow in micro-vessels has been studied for many years, and it has been known for long now that RBCs in narrow blood ves- sels migrate away from the wall which leads to a cell-free layer near the wall. This causes the blood viscosity to reduce and causes apparent viscosity of blood to depend on the tube diameter. This phenomena is referred as Fåhræus-Lindqvist effect (1931). Migration of RBCs from the wall to the core of the blood vessels has been widely studied in the literature. Nu- merous studies on this effect have been based on multiphase nature of the blood. Nair et al. (1989) used a two fluid model for blood in modelling transport of oxygen in arterioles but the study did not account for the dependence of thickness of cell-free layer on the haematocrit concentration. Sharan and Popel (2001) put forward a model with central core of suspended erythrocytes and a cell-free layer surrounding the core. In their study roughness at the interface between the plasma rich annulus and the core is accounted by modelling an increased effective plasma viscosity in the cell-free layer. Jung et al. (2006) suggested to model blood flow as a mix- Copyright c  2015 CSIRO Australia 1 Eleventh International Conference on CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia 7-9 December 2015