Unsteady Pulsatile Flow Research Articles

Effect of slip boundary conditions on unsteady pulsatile nanofluid flow through a sinusoidal channel: an analytical study

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number.

Unsteady pulsatile fractional Maxwell viscoelastic blood flow with Cattaneo heat flux through a vertical stenosed artery with body acceleration

In the current problem, we aim to discuss the heat transfer of pulsatile unsteady fractional Maxwell fluid (blood) flow through a vertical stenosed artery with body acceleration. The concept of fractional Cattaneo model will modify the energy equation. We will get the solutions using Laplace and finite Hankel transformations. The inverse of the transformed functions will be calculated numerically. It is observed that, the heat relaxation time causes a delay in the heat transfer until a critical time. In addition, the heat transfer increases sharply to take its maximum value at a critical value of time then it decreases to reach the steady state. Moreover, the blood velocity, the flow rate, and the shear stress continue to fluctuate during the time period due to the pulsatile phenomenon and body acceleration.

Numerical investigation of unsteady pulsatile Newtonian/non-Newtonian blood flow through curved stenosed arteries.

A numerical investigation of Newtonian/non-Newtonian unsteady pulsatile entry blood flow inside a 3D curved stenosed artery is presented. For considering the non-Newtonian effect (shear thinning or shear thickening behavior), the blood viscosity is characterized by the power-law model (Ostwald de Waele Equation). At the inlet of the artery, a realistic pulsatile waveform is utilized according to the experimental data reported by other researchers. This study belongs to the analysis of the curvature ratios, percentage and length ratio of stenosis, and blood thickening on hemodynamic characteristics of the flow. The results emphasize that the maximum wall shear stress happens near the stenosis neck and as expected, by decreasing the stenosis length, the maximum value of wall shear stress increases. In addition, the results indicate that the shear thickening fluid shows a more stable velocity profile rather than the shear thinning fluid flow.

Harvesting liquid stream energy from unsteady peristaltic flow induced pulsatile Flow-TENG (PF-TENG) using slipping polymeric surface inside elastomeric tubing

Flow in small size tubing or channels in multidisciplinary field such as Chemistry, medical and lab on chip sensors can be a potential candidate for energy scavenging. Recently, energy harvesting techniques have been developed utilizing the steady flow under induced pressure gradient in lab on chip device. Here, for the first-time harnessing energy from unsteady pulsatile water flow over hydrophobic polymeric surface attached in the inner wall of the elastic tubing that induces slip boundary and causes electrostatic potential difference in the electrical double layer of the solid-liquid interface is described. This work demonstrates peristaltic flow driven triboelectric nano-generator based on the flow contact electrification between the hydrophobic micro porous PVDF (mpPVDF) membrane and water stream flowing through elastic silicon tubing. The efficiency of the PF-TENG as energy harvester was evaluated using deionized water (PF.DIw-TENG), tap water (PF.Tw-TENG). The mechanistic approach is discussed for the generation of alternating current based on the relation between the hydrodynamics of pipe flow and adsorbed ions at the Electrical Double Layer (EDL). The generated voltage and short-circuit currents (Isc) are superior in PF.Tw-TENG, in particular, the maximum peak to peak values of voltage and Isc are 20.93 V and 1.67 μA, respectively, over PF.DIw-TENG. The PF.Tw-TENG shows greater efficiency over PF.DIw-TENG due to the presence of dissolved free mobile ions which can enhance the power output. Moreover, we verify the possibility of the PF-TENG as self-powered average volumetric flow rate sensor. The developed PF.TENG can be potentially applied for fluid dynamic monitoring of peristaltic flow involved in pharmaceuticals and food industries.

Three-dimensional 12-velocity multiple-relaxation-time lattice Boltzmann model of incompressible flows

In order to improve the computational efficiency of multiple-relaxation-time lattice Boltzmann model (MRT), a 12-velocity multiple-relaxation-time lattice Boltzmann model (iD3Q12 MRT model) for three-dimensional incompressible flows is proposed in this work by using an inversion method. This model has higher computational efficiency than the commonly used D3Q13 MRT model in principle. In numerical simulations, the accuracy and stability of iD3Q12 MRT model are validated by simulating different flows, including steady Poiseuille flow driven by pressure, unsteady pulsatile flow driven by periodic pressure and lid-driven cavity flow. We also compare the iD3Q12 MRT model with the 13-velocity multiple-relaxation-time lattice Boltzmann model(He-Luo D3Q13 MRT model). For the Poiseuille flow and pulsatile flow, the numerical solutions of the iD3Q12 MRT model agree well with the analytical solutions. In terms of accuracy, the iD3Q12 MRT model and He-Luo D3Q13 MRT model are used to simulate Poiseuille flow with different parameters. The global relative errors of the two models are identical. Similarly, we also simulate the pulsatile flow to calculate the global relative errors of flow fields at different times and different lattice spacing. It is found that the global relative errors of the iD3Q12 MRT model are smaller than those of the He-Luo D3Q13 MRT model, and both models have the second-order spatial accuracy. Furthermore, we also simulate the pulsatile flow by changing the lattice spacing or relaxation time when the maximal pressure drop of the channel is increased, and it is found that the global relative errors calculated by the iD3Q12 MRT model are smaller than those by the He-Luo D3Q13 MRT model in most cases, but the iD3Q12 MRT model diverges when the maximal pressure drop of the channel is large. This indicates that the iD3Q12 MRT model is more accurate than the He-Luo D3Q13 MRT model in simulating unsteady pulsatile flow, but less stable. For the lid-driven cavity flow, the results show that the numerical results of the iD3Q12 MRT model agree well with those given by Ku et al [Ku H C, Hirsh R S, Taylor T D 1987 J. Comput. Phys. 70 439]. In terms of stability, the iD3Q12 MRT model is quantitatively less stable than He-Luo D3Q13 MRT model.

An Unsteady Pulsatile Flow of Some MHD Non-Newtonian Nanofluids with Hall Current and Ion Slip Through a Porous Medium

An Unsteady Pulsatile Flow of Some MHD Non-Newtonian Nanofluids with Hall Current and Ion Slip Through a Porous Medium

Effects of nanoparticles (Cu, TiO[formula omitted], Al[formula omitted]O[formula omitted]) on unsteady blood flow through a curved overlapping stenosed channel

In this letter, we have explored the effects of nanoparticles on unsteady pulsatile blood flow through a curved overlapping stenosed channel. The governing differential equations are derived for the given physical problem and this contains momentum and energy equations along with suitable boundary conditions. An explicit finite difference technique has been used to calculate the numerical results of the given differential equations. The numerical results for different values of curved parameter (Rc), nanoparticles (Cu, TiO2, Al2O3) and Grashof numbers (Gr) are calculated in order to analyze the effects of these parameters on blood flow pattern. A notable deviation in the results of blood flow pattern has been observed with the comparison of pure blood with nano-fluids. It is further noted that the curved parameter (Rc) of a channel has a great influence on velocity profile, flow rate and impedance/resistance to flow. It is also extracted from the velocity profiles that the shape of the velocity curves reduces to symmetric pattern for the higher values of the curved parameters (Rc). Similarly, the magnitude of temperature profiles is constricted due to the insertion of nanoparticles within blood. Moreover, streamlines are also calculated in order to analyze the effects of nanoparticles inside the circulating regions of the flow field.

Nanoparticles (Cu, [formula omitted], [formula omitted]) analysis on unsteady blood flow through an artery with a combination of stenosis and aneurysm

A theoretical and numerical study of unsteady pulsatile blood flow through an artery with a combination of stenosis and aneurysm containing nano-particles (Cu, TiO2,Al2O3) has been discussed in this article. The transport equations comprise momentum and energy partial differential equations with physiologically realistic boundary conditions. The bi-directional, non-linear, coupled differential equations are simplified by using the assumption of mild stenotic condition. The coupled differential equations are solved numerically by using robust finite difference method. The effects of nano-particles along with aneurysm on blood flow rate, wall shear stress and impedance are discussed in detail through graphs. Similarly, the graphical results of nano-particles fluid show notable deviation when compared with pure blood profiles. At the end, it is also concluded from the calculated results that both source/sink β parameter and Grashof number (Gr) facilitates the blood to maximize its flow within the vessel and minimize the hemodynamic factors such as wall shear and impedance. The circulating regions inside the flow field are also investigated through instantaneous patterns of streamlines for different parameters of interest.

Effects of nanoparticles (Cu (Copper), Silver (Ag)) and slip on unsteady blood flow through a curved stenosed channel with aneurysm

The present article is concerned with the slip effects on unsteady pulsatile blood flow through a curved channel containing nano-particles in the presence of stenosis and aneurysm. The nano-particles momentum and thermal energy equations are developed using curvilinear co-ordinates. The suitable slip boundary conditions are imposed at the channel walls. Employing mild stenotic condition, the governing differential equations are solved numerically using a robust explicit finite difference scheme. The effects of slip on various hemo-dynamical variables such as velocity, flow rate, wall shear stress and resistance to flow are shown through plots. The effects of nano-scale particles and thermo fluid parameters on flow and heat transfer characteristics of blood have been discussed in detail in this article. The flow patterns are also shown through plotting streamlines. Calculated results reveal that velocity, flow rate and shear stress increase while resistance to flow decreases with greater volume fraction of nanoparticles. The current work has many applications in the field of nano-pharmacological transport phenomena, a new and exciting area of modern medical fluid dynamics which is used to integrate the coupled diffusion and nano-scale drug delivery mechanisms.

NUMERICAL SIMULATION OF TIME-DEPENDENT NON-NEWTONIAN NANOPHARMACODYNAMIC TRANSPORT PHENOMENA IN A TAPERED OVERLAPPING STENOSED ARTERY

Nanofluids are becoming increasingly popular in novel hematological treatments and also advanced nanoscale biomedical devices. Motivated by recent developments in this area, a theoretical and numerical study is described for unsteady pulsatile flow, heat and mass transport through a tapered stenosed artery in the presence of nanoparticles. An appropriate geometric expression is employed to simulate the overlapping stenosed arterial segment. The Sisko non-Newtonian model is employed for hemodynamic rheology. Buongiorno’s formulation is employed to model nanoscale effects. The two-dimensional non-linear, coupled equations are simplified for the case of mild stenosis. An explicit forward time central space (FTCS) finite difference scheme is employed to obtain a numerical solution of these equations. Validation of the computations is achieved with another numerical method, namely the variational finite element method (FEM). The effects of various emerging rheological, nanoscale and thermofluid parameters on flow and heat/mass characteristics of blood are shown via several plots and discussed in detail. The circulating regions inside the flow field are also investigated through instantaneous patterns of streamlines. The work is relevant to nanopharmacological transport phenomena, a new and exciting area of modern medical fluid dynamics which integrates coupled diffusion, viscous flow and nanoscale drug delivery mechanisms.

Study of pulsatile pressure-driven electroosmotic flows through an elliptic cylindrical microchannel with the Navier slip condition

This paper aims to study an unsteady electric field-driven and pulsatile pressure-driven flow of a Newtonian fluid in an elliptic cylindrical microchannel with Navier boundary wall slip. The governing equations of the slip flow and distributions of electric potential and charge densities are the modified Navier-Stokes equations, the Poisson equation and the Nernst-Planck equations, respectively. Analytical and numerical analyses based on the Mathieu and modified Mathieu equations are performed to investigate the interplaying effects of pulsatile pressure gradients and the slip lengths on the electroosmotic flow.

A parallel monolithic approach for fluid-structure interaction in a cerebral aneurysm

Abstract A parallel fully-coupled numerical algorithm has been developed for the fluid-structure interaction problem in a cerebral artery with aneurysm. For the fluid part of the problem, an Arbitrary Lagrangian-Eulerian formulation based on the side-centered unstructured finite volume method is employed for the governing incompressible Navier–Stokes equations. The deformation of the solid domain is governed by the constitutive laws for the nonlinear Saint Venant-Kirchhoff material and the classical Galerkin finite element method is used to discretise the governing equations in a Lagrangian frame. The time integration method for the structure domain is based on the Newmark type generalized − α method while the second-order backward difference (BDF2) is used in the fluid domain. A special attention is given to construct an algorithm obeying the local/global discrete geometric conservation laws (DGCL) in order to conserve fluid volume at machine precision when the fluid domain is entirely enclosed by solid domain boundary. Therefore, a compatible kinematic boundary condition is applied at the interface between the solid and fluid domains. The parallel implementation of the present fully coupled unstructured fluid-structure solver is based on the PETSc library and a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains is utilized for the resulting fully coupled system. The proposed algorithm is initially validated for a pressure pulse propagating in a flexible tube and the mass conservation accuracy is tested for a thin elastic sphere filled with an incompressible fluid in a circular tube. Then the numerical method is applied to a complicated problem involving unsteady pulsatile blood flow in a cerebral artery with aneurysm as a realistic fluid-structure interaction problem encountered in biomechanics. Various hemodynamic quantities of interest like fluid velocities, blood pressure and wall shear stresses (WSS) are computed as well as the time dependent artery wall deformations.

Influence of Slip Condition on Unsteady Pulsatile Flow through a Porous Medium in a Circular Pipe

Influence of Slip Condition on Unsteady Pulsatile Flow through a Porous Medium in a Circular Pipe

Particulate suspension effect on peristaltically induced unsteady pulsatile flow in a narrow artery: Blood flow model

This work is concerned with theoretically investigating the pulsatile flow of a fluid with suspended particles in a flow driven by peristaltic waves that deform the wall of a small blood artery in the shape of traveling sinusoidal waves with constant velocity. The problem formulation in the wave frame of reference is presented and the governing equations are developed up to the second-order in terms of the asymptotic expansion of Womersley number which characterizes the unsteady effect in the wave frame. We suppose that the flow rate imposed, in this frame, is a function versus time. The analytical solution of the problem is achieved using the long wavelength approximation where Reynolds number is considered small with reference to the blood flow in the circulatory system. The present study inspects novelties brought about into the classic peristaltic mechanism by the inclusion of Womersley number, and the critical values of concentration and occlusion on the flow characteristics in a small artery with flexible walls. Momentum and mass equations for the fluid and particle phases are solved by means of a perturbation analysis in which the occlusion is a small parameter. Closed form solutions are obtained for the fluid/particle velocity distributions, stream function, pressure rise, friction force, wall shear stress, instantaneous mechanical efficiency, and time-averaged mechanical efficiency. The physical explanation of the Segré–Silberberg effect is introduced and the trapping phenomenon of plasma for haemodilution and haemoconcentration cases is discussed. It has been deduced that the width of the closed plasma streamlines is increased while their number is minimally reduced in case of haemoconcentration. This mathematical problem has numerous applications in various branches in science including blood flow in small blood vessels. Several results of other models can be deduced as limiting cases of our situation.

UNSTEADY MAGNETOHYDRODYNAMIC BLOOD FLOW IN A POROUS-SATURATED OVERLAPPING STENOTIC ARTERY — NUMERICAL MODELING

Unsteady pulsatile flow of blood through a porous-saturated, tapered and overlapping stenotic artery in the presence of magnetic field is examined theoretically and computationally. The power law constitutive model is employed to simulate hameo-rheological characteristics. The governing equation is derived assuming the flow to be unsteady, laminar, uni-directional and one-dimensional (1D). A robust, finite difference method is employed for the solution of the governing equation, subject to appropriate boundary conditions. Based on this solution, an extensive quantitative analysis is performed to analyze the effects of blood rheology, body acceleration, magnetohydrodynamic parameter, permeability parameter and arterial geometrical parameters of stenosis on various quantities of interest such as axial velocity, flow rate, resistance impedance and wall shear stress. The computations demonstrate that velocity, flow rate and shear stress increase while resistance to flow decreases with greater permeability parameter. Additionally, the effects of magnetic field are observed to be converse to those of permeability i.e., flow is decelerated and resistance is increased, demonstrating the powerful utility of exploiting magnetic fields in hemodynamic flow control (e.g., intra-corporeal surgical procedures). Furthermore, the size of trapped bolus of fluid is also found to be reduced for large values of the permeability parameter indicating that progressively more porous media circumvent bolus growth.

Numerical study of unsteady blood flow through a vessel using Sisko model

A mathematical study for two-phase unsteady pulsatile flow of blood through a vessel in the presence of body acceleration is presented in this paper. The blood in the core region is modeled as a non-Newtonian fluid while in the peripheral region it is described as a Newtonian fluid. The effects of body acceleration are also taken into account in this study. The continuity and momentum equations are used to model the proposed problem in terms of a nonlinear partial differential equation. This equation along with initial and boundary conditions is made dimensionless and then solved numerically using finite difference method. The behavior of various flow quantitates is analyzed through a parametric study.

Pulsatile Flow of Blood in a Vessel Using an Oldroyd-B fluid

Abstract This paper is concerned with the effects of body acceleration on an unsteady pulsatile flow of blood in a vessel. The non-Newtonian behavior of blood is modeled by the constitutive equation of an Oldroyd-B fluid. The behavior of the blood is assumed as an Oldroyd-B fluid in the core and a viscous fluid in the periphery. This new model predicts the relaxation and retardation phenomena in a pulsatile flow. Our interest lies in investigating the effects of stress relaxation and retardation in unsteady pulsatile flow of an Oldroyd-B fluid. The modeled equations are normalized and solved numerically using finite difference method. The results are graphically displayed and influence of the pertinent parameter on various physical quantities of interest is analyzed.

14-velocity and 18-velocity multiple-relaxation-time lattice Boltzmann models for three-dimensional incompressible flows

In this paper, 14-velocity and 18-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) models are proposed for three-dimensional incompressible flows. These two models are constructed based on the incompressible LBGK model proposed by He et al. (2004) and the MRT LB model proposed by d’Humières et al. (2002), which have advantages in the computational efficiency and stability, respectively. Through the Chapman–Enskog analysis, the models can recover to three-dimensional incompressible Navier–Stokes equations in the low Mach number limit. To verify the present models, the steady Poiseuille flow, unsteady pulsatile flow and lid-driven cavity flow in three dimensions are simulated. The simulation results agree well with the analytical solutions or the existing numerical results. Moreover, it is found that the present models show higher accuracy than d’Humières et al. model and better stability than He et al. model.

Quantitative Assessment of Turbulence and Flow Eccentricity in an Aortic Coarctation: Impact of Virtual Interventions.

Turbulence and flow eccentricity can be measured by magnetic resonance imaging (MRI) and may play an important role in the pathogenesis of numerous cardiovascular diseases. In the present study, we propose quantitative techniques to assess turbulent kinetic energy (TKE) and flow eccentricity that could assist in the evaluation and treatment of stenotic severities. These hemodynamic parameters were studied in a pre-treated aortic coarctation (CoA) and after several virtual interventions using computational fluid dynamics (CFD), to demonstrate the effect of different dilatation options on the flow field. Patient-specific geometry and flow conditions were derived from MRI data. The unsteady pulsatile flow was resolved by large eddy simulation including non-Newtonian blood rheology. Results showed an inverse asymptotic relationship between the total amount of TKE and degree of dilatation of the stenosis, where turbulent flow proximal the constriction limits the possible improvement by treating the CoA alone. Spatiotemporal maps of TKE and flow eccentricity could be linked to the characteristics of the jet, where improved flow conditions were favored by an eccentric dilatation of the CoA. By including these flow markers into a combined MRI-CFD intervention framework, CoA therapy has not only the possibility to produce predictions via simulation, but can also be validated pre- and immediate post treatment, as well as during follow-up studies.

Effects of unsteadiness and non-Newtonian rheology on blood flow through a tapered time-variant stenotic artery

A two-dimensional model is used to analyze the unsteady pulsatile flow of blood through a tapered artery with stenosis. The rheology of the flowing blood is captured by the constitutive equation of Carreau model. The geometry of the time-variant stenosis has been used to carry out the present analysis. The flow equations are set up under the assumption that the lumen radius is sufficiently smaller than the wavelength of the pulsatile pressure wave. A radial coordinate transformation is employed to immobilize the effect of the vessel wall. The resulting partial differential equations along with the boundary and initial conditions are solved using finite difference method. The dimensionless radial and axial velocity, volumetric flow rate, resistance impedance and wall shear stress are analyzed for normal and diseased artery with particular focus on variation of these quantities with non-Newtonian parameters.