Comparative study of Newtonian and Non-Newtonian blood flow through a stenosed carotid artery

Abstract

A numerical simulation to investigate the Non-Newtonian modeling effects on physiological flows in a three dimensional idealized stenosed carotid artery with 75% severity (by area) is taken from patient specific model. The wall vessel is considered to be rigid. Oscillatory physiological and parabolic velocity profile has been imposed for inlet boundary condition. Where the physiological waveform was performed using a Fourier series with sixteen harmonics. The investigation has a Reynolds number range of 94 to 1120. Low Reynolds number k − ω model is used as governing equation. The investigation has been carried out to characterize two Non-Newtonian constitutive equations of blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has been investigated also to study the physics of fluid. The results of Newtonian model are compared with the Non-Newtonian models. The numerical results are presented in terms of pressure, wall shear stress distributions and the streamlines contours. At early systole pressure differences between Newtonian and Non-Newtonian models are observed at pre-stenotic, throat and immediately after throat regions. In the case of wall shear stress, some differences between Newtonian and Non-Newtonian models are observed when the flows are the minimum such as at early systole or diastole. It is known that blood is Bingham plastic fluid. So the viscosity of blood will decrease with increase in shear rate and when shear rate will be greater than 100 then viscosity will be constant. The viscosity of Newtonian model is less than that of non-Newtonian model when shear rate is less than 100, but viscosity of all models is equal when shear rate is equal to 100. When Reynolds number is very low then pressure and WSS of Newtonian model will be less than that of non-Newtonian model but opposite scenario will be seen for velocity distribution. Since early systole and diastole there are comparatively low Reynolds numbers, the results of Newtonian and non-Newtonian condition may be different at early systole and diastole. On the other hand maximum Reynolds number is seen at peak systole. So the results of Newtonian and non Newtonian condition follow each other at peak systole. Again the velocity of the throat region is high for any time instant. So the results of Newtonian and non Newtonian condition may be same at the throat region but different at the pre and post stenotic region. The results of pressure, WSS, and velocity distribution are discussed below with respective figure.