Computational Analysis of Biological Fluid Flows Through Stenotic Artery

Blood flow dynamics are crucial in the development and progression of cardiovascular diseases. Computational modeling of blood circulation in arteries is vital for understanding disease symptoms and enhancing treatments. Aneurysms, stenoses, and atherosclerosis can change blood flow characteristics, leading to serious healthcomplications due to abnormal blood flow patterns and high wall shear stresses (WWS). Simulating these changes can help in detecting cardiovascular diseases early and managing them effectively. The commencement of the dissertation involves an effort to create a model of the 2D shape of a non-uniform artery wall that has a restricted segment, using a segmented function, which includes an obstruction of approximately 40%. The blood flow in the body follows a rhythmic pressure gradient that imitates the heart’s systolic and diastolic phases. Because blood behaves like a non-Newtonian fluid in certain situations, the Casson model for non-Newtonian fluids is used to account for the yield stress resulting from the formation of red blood cell aggregates at low shear rates. The Navier-Stokes equations, which describe incompressible and unsteady fluid flow, are expanded to include the non-Newtonian behavior of blood flow in radial coordinates. This is accomplished by including a temperature equation. To analyze the impact of stenosis over the flow, drug delivery agents such as copper (Cu) and alumina (Al2O3) nanoparticles with a concentration of about 0.03% are used. The concept of magnetohydrodynamics (MHD) involves applying a magnetic field to blood flow in an artery, taking into account the Hall current, to deliver magnetic drug carriers to a specific location within the bloodstream. The simulation of blood flow begins from a state of rest with zero velocity and temperature, using initial conditions to simplify the mathematical modeling process. On the symmetry axis, a zero radial gradient condition is applied to both velocity and temperature, while no-slip conditions are applied to the arterial wall. The complexity of the governing partial differential equations is removed by nondimensionalizing them. There are two cases to consider: the first case involves disregarding the long wavelength approach, which remains open issue for future consideration. The alternative scenario involves presenting the acquired dimensionless PDEs through the long-wavelength approximation and then applying a radial coordinate transformation to simplify them even further. Afterward, MATLAB software is utilized to execute the 2D explicit forward time central space (FTCS) differentiation method. Momentum and thermal analysis were done for blood, Cublood nanofluid, and Cu-Al2O3-blood hybrid nanofluid, along with wall shear stress (WWS) and local Nusselt number (Nulocal) evaluation.We proceed to revise the last batch of dimensional partial differential equations (PDEs) describing the behavior of non-Newtonian Cu-Al2O3-blood by incorporating magnetohydrodynamic (MHD) effects. Our approach involves converting the PDEs into a Reynolds-averaged Navier Stokes equation (RANS), which employs Reynolds averaging to account for turbulence in the mean flow. This is achieved by decomposing the flow variables into average and perturbed components. The equations for fluid dynamics include turbulent forces caused by eddy shear and molecular turbulence. These forces are accounted for using Boussinesq’s eddy-viscosity hypothesis, which is based on the average flow of the fluid. Additionally, the Zero-equation turbulence model, which is also called the algebraic turbulence model, is utilized by combining the principles of Prandtl mixing length and Boussinesq approximation. Turbulent flow is considered unsteady and fully developed, and flow properties are also modified using the Prandtl mixing length model with the laminar and turbulent effect contribution. The subsequent step involves making these equations nondimensional and then utilizing radial coordinate transformations. The resulting set of dimensionless partial differential equations that consists of Reynold and turbulent Prandtl numbers are then simulated using FTCS methodology. Additionally, the effect of various emerging parameters is analyzed through a graphical representation of the momentum equation for high Reynold numbers (Re = 42000, 46000). The last analysis involved flow momentum and pressure for the laminar flow scenario by considering blood as a Newtonian fluid. Using AutoCAD software, a 3D constricted artery with a 70% elliptical shaped stenosis was created. To proceed further, an ideal mesh was created using OpenFOAM’s blockMesh and snappyHexMesh tools. The simulation for laminar and incompressible flow has been conducted using the coFoam solver, which guarantees the convergence of the simulation at Courant number ≈ 0.2 < 1. Two different scenarios have been taken into account for the velocity inlet. Firstly, a parabolic velocity profile was used with a maximum inlet velocity of 0.003m/s. The outlet velocity was set to zero gradient and the inlet pressure was also set to zero. Secondly, we used a constant inlet velocity of 0.0137m/s for laminar flow with a Reynolds number of 200. We graphically analyzed the momentum and pressure of the fluid both at the center of the stricture and throughout the constriction arterial segment for both inlet velocity conditions.