Influence of Shear-Thinning Blood Rheology on the Laminar-Turbulent Transition over a Backward Facing Step

Abstract

Cardiovascular diseases are the leading cause of death globally and there is an unmet need for effective, safer blood-contacting devices, including valves, stents and artificial hearts. In these, recirculation regions promote thrombosis, triggering mechanical failure, neurological dysfunction and infarctions. Transitional flow over a backward facing step is an idealised model of these flow conditions; the aim was to understand the impact of non-Newtonian blood rheology on modelling this flow. Flow simulations of shear-thinning and Newtonian fluids were compared for Reynolds numbers ( R e ) covering the comprehensive range of laminar, transitional and turbulent flow for the first time. Both unsteady Reynolds Averaged Navier–Stokes ( k − ω SST) and Smagorinsky Large Eddy Simulations (LES) were assessed; only LES correctly predicted trends in the recirculation zone length for all R e . Turbulent-transition was assessed by several criteria, revealing a complex picture. Instantaneous turbulent parameters, such as velocity, indicated delayed transition: R e = 1600 versus R e = 2000, for Newtonian and shear-thinning transitions, respectively. Conversely, when using a Re defined on spatially averaged viscosity, the shear-thinning model transitioned below the Newtonian. However, recirculation zone length, a mean flow parameter, did not indicate any difference in the transitional Re between the two. This work shows a shear-thinning rheology can explain the delayed transition for whole blood seen in published experimental data, but this delay is not the full story. The results show that, to accurately model transitional blood flow, and so enable the design of advanced cardiovascular devices, it is essential to incorporate the shear-thinning rheology, and to explicitly model the turbulent eddies.

Keywords

• blood
• rheology
• transition
• Newtonian
• shear-thinning
• non-Newtonian