Introduction
Biomechanical engineering is a promising multidisciplinary field. It involves several academic disciplines as physics, computational sciences, and medicine, aiming to improve the quality of diagnosis limiting invasive procedures and offering alternative ways of treatment.
The study of the circulatory system under normal and pathological conditions is one of the most important elements in the field of biomechanical engineering. Hemodynamic is one of the major and larger systems connecting several structures at different scales in the human body. The development of high-quality tools enabling a more extended comprehension of this system and its structures is then a main objective in biomechanical engineering, allowing to investigate the complications encountered in cardiovascular diseases, to study alternative surgical procedures and extrapolating its consequences via simulations. Thanks to the reliability of contemporary computational and physical modelling techniques, simulations show up to be a good substitute for experimental studies, which in most of cases are too expensive and time-consuming.
Many researchers are considered blood as a bio-fluid that can behave as Newtonian fluid when it flows through arteries of human body [1-3]. From the state of art, it seems to be appropriate to model blood as a Newtonian fluid when it flows in narrow arteries. Some researchers were dealt with the flow in narrow arteries as a biological porous flow (e.g. GUO [4] at 1980 s). Where some biological capillaries are examined being a porous media that is led to build a model of porous.
The mathematical modelling was presented by Song et al. [5] to treat the blood flow in the narrow arteries as porous medium. They showed that the increase in the threshold significantly increases the frictional resistance. Others researchers have considered the porous media based energy equations to compute the distribution of temperature in the body of tissue phantoms[6]. In general, a porous medium is a material volume that consists in a solid material with an interconnected void space that can be simply characterized via the volume fraction of voids immersed in the solid space [7-9]. Most studies of the flow in porous media have used the Darcy law that can be define as a relationship between the velocity of flow to the pressure gradient across the porous medium according to mathematical modelling [10]. In addition permeability is represented one of the porous medium’s parameters that is the measure of flow conductivity in the porous medium [11]. Tortuosity and curvature vessel are considered an important for the combination of the fluid and the porous medium which is represented the hindrance to flow diffusion imposed by local boundaries or local viscosity. Where tortuosity is considered an important when it is related to the medical applications [8]. In recent decades, CFD analysis is become a popular tool to analyse medical applications. [12, 13] have used porous media to model aneurysm coiling. An ideal geometry was applied by [14, 15] to calculate the properties of blood flow. In addition, a model is showed by [16-18] to implement porous medium representation on aneurysm diverting stent.
A numerical analysis is presented by [19] to assess blood hemodynamic inside the unruptured aneurysm. They presented a model (coiled aneurysm) as a porous volume with porosity and permeability related to the coil size and compactness value to study the effect of endovascular embolization. The results of this study demonstrated that smaller coil diameter can be led to less flow circulation within the aneurysm, in which it can be increased the chances of thrombosis compactness value. The CFD analysis will be introduced in this paper as a method to overcome the most limitations and difficulties of porous flow. To permit modelling of fluid flow such as blood flow through an elbow artery various useful features can be provided. The further analysis of the flow through an elbow vessel as a porous media is explored in this numerical test. The aim is to show how the characteristics of flow will take a location inside of curvature vessel after the blood flow has been released. The effect of the different diameter of geometry will also be studied. The numerical simulations of blood flow models are examined and compared with experimental data available in the literature.