Title:

LES of pulsatile flow in the models of arterial stenosis and aneurysm

The Large Eddy Simulation (LES) technique is used to simulate the different types of Newtonian and nonNewtonian pulsatile blood flow in a constricted as well as in a dilated channel to gain insight of the transitiontoturbulent blood flow due to the arterial stenosis and aneurysm. In the stenosed model, a cosine shape stenosis is placed at the upper wall of a 3D channel which reduces the crosssectional area, whereas the aneurysm which is also placed at the upper wall dilates the channel crosssectional area. In LES, a tophat spatial gridfilter is applied to the NavierStokes equations of motion to separate the large scale flows, which carry the majority of the energy, from the small scale known as subgrid scale (SGS).The large scale flows are resolved fully while the unresolved SGS motions are modelled using two different dynamic models to determine the Smagorinsky constant at each time step. Initially, an additive sinusoidal pulsatile velocity profile is used at the inlet of the model stenosis to generate the unsteady oscillating flow and a comparison is made between the results obtained by the additive and nonadditive pulsation. Secondly, the physiological pulsatile flow in the same model stenosis is investigated, where the physiological pulsation is generated at the inlet using the first four harmonics of the Fourier series of pressure pulse. A comparison between the LES and the coarse Direct Numerical Simulation (DNS) results is drawn and the effects of the various harmonics of pressure pulse, length and percentage of the stenosis on the flow field are examined. Transitiontoturbulent physiological flow through the model of a double stenosis and an aneurysm is also investigated. Finally, the physiological pulsatile flow in a model of single stenosis is investigated using the various nonNewtonian blood viscosity models and the results are compared with the Newtonian model. For the additive sinusoidal pulsation case the maximum ratio of the SGS to molecular viscosity is 0.709 and for the nonadditive case is 0.78 while Re =2000. The shape of the poststenotic recirculation region is totally different between the additive and nonadditive case. In the additive case the upper wall pressure drop is larger than the nonadditive case. Due to the large amplitude of the oscillation, transition happens earlier and the peak turbulent kinetic energy occurs at the postlip of the stenosis. The intensity of the turbulent kinetic energy is higher in the additive sinusoidal pulsation case than the physiological pulsation. The maximum contribution of the SGS motion to the large scale motion is 37.4 percent for the first harmonic physiological pulsation while 97 percent contribution from the first four harmonics case for Re =2000. The centreline turbulent kinetic energy is slightly higher in the first harmonic case than the first four harmonics. For the higher area reduction of the stenosis, the stress drop at the upper wall, the maximum shear stress at the lower wall and the turbulent kinetic energy increased. The intensity of the shear stress and the turbulent kinetic energy decreased when the length of the stenosis is increased. The break frequency of the energy spectra found from 5/3 to 10/3 for the velocity fluctuations and from 5/3 to 7/3 for the pressure fluctuations. Due to the presence of the second stenosis, the stress drop, the adverse pressure gradient and the turbulent intensity of the flow enhance significantly. Inside the aneurysm a large recirculation region exists and the flow is turbulent for a asymmetric aneurysm and maximum turbulent intensity occurs between the centre and the ending segment of the aneurysm. Owing to the effects of the nonNewtonian viscosity, the length of the poststenotic recirculation region increased as well as the streamwise velocity and the turbulent kinetic energy decreased.
