Abstract
Introduction
Blood is a multiphase, non-Newtonian fluid which exhibits shear-thinning behaviour at low shear rates. It is often simplified as Newtonian, but this results in incorrect predictions of behaviour in blood contacting medical devices, and in diseased arteries, where flow becomes turbulent and eddies orders of magnitude larger than red blood cells (RBCs) are present [1]. The purpose of this project is to consider the multiphase nature of blood and create a numerical model for the design and analysis of medical devices. The aim of this work was to calculate the velocity fields over a backward facing step with Newtonian and shear-thinning blood analogs, finding the transition in both.
Methods
A backward facing step [2] was modelled using open source finite volume software OpenFOAM. Large eddy simulation (LES) was performed using a Smagorinsky eddy viscosity model as a means to predict transitional flow. Two blood analogs were considered, one Newtonian and one shear-thinning. The Newtonian analog assumed a constant viscosity µ = 0.0035 kg/m/s whilst the shear-thinning analog was implemented using a Carreau rheology model with viscosity µ∞ = 0.0035 kg/m/s. Transitional behaviour was observed by varying the Reynolds number from Re=50 to Re=3400 for both analogs. Velocity fluctuations were plotted over time at the reattachment point to observe the transition to turbulence.
Results
For Re=50, the recirculation zone length was reduced by 56% in the shear-thinning analog compared to the Newtonian, in fair agreement with [3] (difference 7%). Velocity traces over time showed that at low Re both analogs were very similar without fluctuations. Increasing Re to 1200 resulted in small velocity fluctuations for both analogs. At Re=1800 fluctuations were much greater in the Newtonian analog, which was assumed to mean transition to turbulence had occurred. The fluctuations were smaller and less frequent with the shear-thinning analog, assumed to mean transition had not yet occurred. Qualitative comparison of velocity fields showed that the flow fields were the same, but at different Re.
Discussions
The transition to turbulence was delayed by Re=300 for the shear thinning fluid. Hence, the velocity fields were similar at Re=1800 and Re=2100 for the Newtonian and shear-thinning analogs respectively. To conclude, accounting for the transition to turbulence by using an LES model with a shear-thinning blood analog may give a clearer depiction of the damaging shear stresses present in transitional blood flow. Currently a multiphase model considering RBCs and proteins is being developed, and validated experimentally, with the aim of simulating flow through real medical devices.
References
[1] L. Antigua and D. Steinman, (2009). Biorheology, 46(2)
[2] B. F. Armaly et al, (1982). J. Fluid Mech, 127
[3] H. Choi and A. I. Barakat, (2005). Biorheology, 42
Blood is a multiphase, non-Newtonian fluid which exhibits shear-thinning behaviour at low shear rates. It is often simplified as Newtonian, but this results in incorrect predictions of behaviour in blood contacting medical devices, and in diseased arteries, where flow becomes turbulent and eddies orders of magnitude larger than red blood cells (RBCs) are present [1]. The purpose of this project is to consider the multiphase nature of blood and create a numerical model for the design and analysis of medical devices. The aim of this work was to calculate the velocity fields over a backward facing step with Newtonian and shear-thinning blood analogs, finding the transition in both.
Methods
A backward facing step [2] was modelled using open source finite volume software OpenFOAM. Large eddy simulation (LES) was performed using a Smagorinsky eddy viscosity model as a means to predict transitional flow. Two blood analogs were considered, one Newtonian and one shear-thinning. The Newtonian analog assumed a constant viscosity µ = 0.0035 kg/m/s whilst the shear-thinning analog was implemented using a Carreau rheology model with viscosity µ∞ = 0.0035 kg/m/s. Transitional behaviour was observed by varying the Reynolds number from Re=50 to Re=3400 for both analogs. Velocity fluctuations were plotted over time at the reattachment point to observe the transition to turbulence.
Results
For Re=50, the recirculation zone length was reduced by 56% in the shear-thinning analog compared to the Newtonian, in fair agreement with [3] (difference 7%). Velocity traces over time showed that at low Re both analogs were very similar without fluctuations. Increasing Re to 1200 resulted in small velocity fluctuations for both analogs. At Re=1800 fluctuations were much greater in the Newtonian analog, which was assumed to mean transition to turbulence had occurred. The fluctuations were smaller and less frequent with the shear-thinning analog, assumed to mean transition had not yet occurred. Qualitative comparison of velocity fields showed that the flow fields were the same, but at different Re.
Discussions
The transition to turbulence was delayed by Re=300 for the shear thinning fluid. Hence, the velocity fields were similar at Re=1800 and Re=2100 for the Newtonian and shear-thinning analogs respectively. To conclude, accounting for the transition to turbulence by using an LES model with a shear-thinning blood analog may give a clearer depiction of the damaging shear stresses present in transitional blood flow. Currently a multiphase model considering RBCs and proteins is being developed, and validated experimentally, with the aim of simulating flow through real medical devices.
References
[1] L. Antigua and D. Steinman, (2009). Biorheology, 46(2)
[2] B. F. Armaly et al, (1982). J. Fluid Mech, 127
[3] H. Choi and A. I. Barakat, (2005). Biorheology, 42
| Original language | English |
|---|---|
| Publication status | Submitted - 19 Dec 2017 |
| Event | 8th World Congress of Biomechanics - The Convention Centre Dublin, Dublin, Ireland Duration: 8 Jul 2018 → 12 Jul 2018 http://wcb2018.com |
Conference
| Conference | 8th World Congress of Biomechanics |
|---|---|
| Country/Territory | Ireland |
| City | Dublin |
| Period | 8/07/18 → 12/07/18 |
| Internet address |