Flow Bifurcation Research Articles

Numerical study of bifurcation blood flows using three different non-Newtonian constitutive models

In this work, a variational multiscale finite element formulation is used to study bifurcation flows of non-Newtonian fluids, using a representative simplified Carotid Artery geometry. In particular, the flow pattern and wall shear stress (WSS) computed using power-law, Cross, and Carreau–Yasuda models, are assessed. First, the formulation is validated by contrasting simulations of a benchmark test for bifurcation flows reported in the literature. After that, a study of blood flow through the carotid artery is presented. Hemodynamics conditions aimed to describe the flow behavior from diastole to systole of the cardiac cycle for healthy arteries and two specific conditions (60% carotid stenosis due to atherosclerosis and 20% increased bifurcation angle due to aging), are specifically analyzed. For each condition, the hemodynamics present different velocity fields that lead to distinctive distribution of WSS enable us to classified three regions, depending on their magnitude: low-WSS, medium-WSS and high-WSS. Results show that power-law flows predict lower wall shear stresses, especially in sections where geometry concentrates stresses, compared to those predicted using Cross and Carreau–Yasuda models. Overall, low-WSS are usually present in zones where stenosis develops even in healthy arteries, however, both geometries lead to a decrease of WSS magnitude in low-WSS regions, increasing the risk factor associated with plaque building.

Kolmogorov flow: Linear stability and energy transfers in a minimal low-dimensional model.

In this paper, we derive a four-mode model for the Kolmogorov flow by employing Galerkin truncation and the Craya-Herring basis for the decomposition of velocity field. After this, we perform a bifurcation analysis of the model. Though our low-dimensional model has fewer modes than past models, it captures the essential features of the primary bifurcation of the Kolmogorov flow. For example, it reproduces the critical Reynolds number for the supercritical pitchfork bifurcation and the flow structures of past works. We also demonstrate energy transfers from intermediate scales to large scales. We perform direct numerical simulations of the Kolmogorov flow and show that our model predictions match the numerical simulations very well.

Advective mass transport in two side-by-side liquid microspheres

Gaseous entrainment from a contaminated outer air stream into a pair of side-by-side homogeneous and heterogeneous micro-sized water drops is numerically examined for varied gap ratio (ratio of interfacial gap to radius), Reynolds number , Weber number , and liquid-phase Peclet number . For and , the separation–attachment induced momentum exchange and imposed non-uniform interfacial shear stress lead to breakup of the primary Hill’s vortex ring and create a significant secondary vortex ring in each drop, which together construct a dominant advective transport mechanism therein. Beneath a three-dimensional (3-D) topological separation line, the study identifies an active advective mass entrainment process that is led by the ‘inflow’ natured local dynamics of this primary–secondary vortex ring pair. Mechanistically, the secondary and primary vortex rings regulate species transfer into a drop by maintaining the spontaneous inflow-type counter-rotating motion along the 3-D separation line, whereby the is entrained; and near the attachment points/nodes, two vortices distinctly repulse entry by virtue of their ‘outflow’ natured local dynamics. The blockage effect and nozzle effect on flow approaching and passing the narrow neck that formed in the presence of a second drop lead to the asymmetric growth of both primary and secondary vortex rings via the locally weakened and enhanced near-interfacial air flow and imposed variable shear stress, which induce the occurrence of an asymmetric mass transfer phenomenon plus biased saturation. The , once entrained, rotates mostly along a spiral orbit of a primary vortex ring, owing to its higher strength. For increased , the transport process is reinforced following increased strength of the inflow paired secondary–primary vortex dynamics that enhanced the net entrainment rate and also advanced its transport to the vortex core via augmented convective flow plus radial diffusion. A narrow gap facilitated faster near-gap saturation, while the quantitative transport rate is decreased by virtue of the produced tapered primary–secondary vortex pairs, associated inner flow bifurcation, and changed topology of the separated wake, which appear similar to what develops for a larger single drop. The gap induced inner vortical structures are characterized by a weaker secondary vortex and a tapered primary vortex near the neck. For heterogeneous drop pairs, the influence of varying 3-D surface flow topology on the two interfaces and the impact of solid fraction ( , with being the radius of the solid core) on the created advective mechanism by the primary–secondary vortex ring pair and resultant transport are exclusively elucidated.

On the stability and bifurcation of the non-rotating Boussinesq equation with the Kolmogorov forcing at a low Péclet number

This study examines the stability and potential bifurcations of a stratified shear flow governed by the non-rotating incompressible Boussinesq equation at a low Péclet number. For the ratio of the vertical scale to the horizontal scale of a stratified flow a∈[3/4,3/2), it is shown that there exists a threshold for the Reynold number Re above which the steady stratified shear flow driven by the Kolmogorov forcing becomes linearly unstable. As a result, the Boussinesq equation exhibits a Hopf bifurcation. To further determine the type of the Hopf bifurcation, the model is reduced to a low-order system whose numerical analyses reveal that the Hopf bifurcation is supercritical. That is, a stable periodic solution emerges, which describes an oscillating thermal convection in a highly stratified shear flow arising in the atmosphere or interior of many stellar systems with low Péclet numbers.

Application of pressure-sensitive paint for the characterization of mixing with various gases in T-type micromixers

In this study, the mixing of various gases in T-type micromixers was investigated using the pressure-sensitive paint technique. Three gases, namely nitrogen, argon, and helium, were mixed with oxygen at various flow speeds between 3 and 50 m/s. These three gases were selected because of their differences in terms of density, viscosity, and diffusion coefficients. Symmetric flow in the laminar flow regime and bifurcation flow in the engulfment flow regime were visualized through experimentation. Numerical simulation was also performed, and the numerical data were compared with the experimental data. A favorable agreement was obtained between the experimental and numerical results for the laminar flow regime. The effects of the properties of the mixed gases as well as the evolution of the mixing quality along the mixing channel in the T-type micromixer are discussed.

Flow bifurcation transitions of inelastic shear thinning fluids in a channel with sudden contraction and expansion

The bifurcation transitions from the symmetric to asymmetric flow regimes in shear thinning fluids in a channel with sudden contraction and expansion were studied by means of numerical simulations. On the example of the Carreau–Yasuda model, the bifurcation diagrams of shear thinning fluids with different viscosity flow curves were revealed along the critical Reynolds numbers of the bifurcation transitions. It was found that increase in variations of viscosity with shear rate leads to a noticeable decrease in critical Reynolds number and increase in dimensions of the angular vortices as compared to Newtonian fluids. The obtained results indicate the enhancement of flow instability of shear thinning fluids in channels with the variable cross-sections.

The effect of flood intermittency on bifurcations in fluviodeltaic systems: Experiment and theory

AbstractThe dimensions and organization of deltaic islands and channels dictate delta morphology. This study presents experimental results modelling deposition at a river mouth and flow bifurcation around delta islands. Mouth bar formation and channel bifurcation is achieved in a laboratory setting by alternating input of suspended load transport and bedload transport. These two modes of transport produce two characteristic deposits with different advection lengths. Suspended load transport creates a steep deposit far from the inlet, while bedload creates a low angle, levéed deposit near the inlet. This study found that flow bifurcations occur where the proximal and distal deposits encroach on one another; and determined that there is a relationship between the frequency of suspended load transport and the length to channel bifurcation. Frequent flooding causes shorter length to bifurcations, whereas infrequent flooding causes greater length to bifurcations. This work overturns the hitherto understood mechanism of bifurcation location as a function of only high‐transport conditions. Instead, the interactions between the sediment transport and deposition from normal flow and large‐scale flooding events dictate delta island morphology.

Bifurcations and chaos transition of the flow over an airfoil at low Reynolds number varying the angle of attack

The study of an airfoil at low Reynolds number regime was found to be a typical problem where the inception of bifurcations leads the flow evolution from a stationary or periodic behaviour to a purely chaotic one. The present work extends the present literature where numerical investigations of the flow field past two-dimensional symmetric airfoils were performed by fixing the incidence and changing the Reynolds number (Re). Conversely, here the Reynolds number was fixed at Re=1000 and the angle of attack (AoA) varied from 0∘ to 90∘. Different flow Modes and bifurcation phenomena are detected and, in addition, new non-linear phenomena are also identified. The latter consists of tripling period regimes and its bifurcations up to chaotic conditions. Moreover, for increasing AoA, an inverse transition from chaotic to periodic regimes is also observed. An in-depth study of these different flows is provided and new links with the time evolution of the forces acting on the airfoil, as well as with the wake structures observed, are offered. Phase portrait diagrams are evaluated through the time records of the lift force in order to highlight the eventual presence of limit cycles in the solutions. Accurate numerical simulations are performed with a Vortex Particle Method in a two-dimensional framework, using high spatial resolutions to solve in detail both the near-field and the far-field regions.

The role of oxygen transport in atherosclerosis and vascular disease.

Atherosclerosis and vascular disease of larger arteries are often associated with hypoxia within the layers of the vascular wall. In this review, we begin with a brief overview of the molecular changes in vascular cells associated with hypoxia and then emphasize the transport mechanisms that bring oxygen to cells within the vascular wall. We focus on fluid mechanical factors that control oxygen transport from lumenal blood flow to the intima and inner media layers of the artery, and solid mechanical factors that influence oxygen transport to the adventitia and outer media via the wall's microvascular system—the vasa vasorum (VV). Many cardiovascular risk factors are associated with VV compression that reduces VV perfusion and oxygenation. Dysfunctional VV neovascularization in response to hypoxia contributes to plaque inflammation and growth. Disturbed blood flow in vascular bifurcations and curvatures leads to reduced oxygen transport from blood to the inner layers of the wall and contributes to the development of atherosclerotic plaques in these regions. Recent studies have shown that hypoxia-inducible factor-1α (HIF-1α), a critical transcription factor associated with hypoxia, is also activated in disturbed flow by a mechanism that is independent of hypoxia. A final section of the review emphasizes hypoxia in vascular stenting that is used to enlarge vessels occluded by plaques. Stenting can compress the VV leading to hypoxia and associated intimal hyperplasia. To enhance oxygen transport during stenting, new stent designs with helical centrelines have been developed to increase blood phase oxygen transport rates and reduce intimal hyperplasia. Further study of the mechanisms controlling hypoxia in the artery wall may contribute to the development of therapeutic strategies for vascular diseases.

Experimental investigation on fire smoke bifurcation flow in longitudinal ventilated tunnels

SummaryInvestigation of smoke bifurcation flow has been receiving more attentions, however, delicate quantitative analyses on different regions of the bifurcation flow have rarely been addressed. In this study, a series of small‐scale experiments were conducted to investigate smoke bifurcation flow in longitudinal ventilated tunnels. Results show that when longitudinal ventilation velocity increases to a certain value, the smoke bifurcation phenomenon emerges, and a low‐temperature region forms in the center of the tunnel. Similar to the natural conditions, smoke development under relatively strong ventilation can also be subdivided into four regions. With the increase of ventilation velocity, the ceiling impact region, side wall impact region, and convergence region of two smoke streams move further downstream, indicating that the bifurcation phenomenon becomes more evident. A simple model is proposed based on theoretical analysis and experimental phenomenon to predict two characteristic lengths of smoke bifurcation flow: the offset distance of ceiling impact region and the length of low‐temperature region. Both characteristic lengths increase with ventilation velocity and can be well correlated with the dimensionless ventilation velocity defined in Equation (2) ( V′). The results of this work could provide references for both tunnel ventilation designers and fire science researchers.

Effect of sinus size and position on hemodynamics during pulsatile flow in a carotid artery bifurcation

Background and objectivesHemodynamics plays a crucial role in the progression of atherosclerosis and the treatment of arterial diseases. Stroke is one of the arterial diseases and a leading cause of death worldwide. Hemodynamics in the carotid artery plays a vital role in the stroke. The common carotid artery bifurcates into the internal carotid artery and the external carotid artery. Carotid sinus, a slightly dilated area, exists in the internal carotid artery just after the bifurcation and acts as a pressure receptor and regulator. The location and size of the sinus can vary in different people; the change in sinus size and location may affect the hemodynamics. It is necessary to study the shift in hemodynamics due to changes in sinus size and position on atherosclerosis. The change in flow behavior may suggest the probable sites of backflow and low wall shear stress, and therefore the sites prone to atherosclerosis. MethodsThe model of the carotid artery has been constructed using patient data. Transient computational fluid dynamics simulations have been performed using a finite volume method for the numerical solution in a three-dimensional computational domain using ANSYS Fluent 19.2. Pulsatile flow is specified at the inlet boundary. The coupled scheme is used for the pressure-velocity coupling. The second-order discretization scheme is used for pressure interpolation and second-order upwind scheme is used for the discretisation of momentum equation. The temporal term is discretized using the first-order implicit scheme. ResultsThe effect of sinus size and location on the overall flow behavior, wall shear stress, and secondary flow are presented. Results show that the outer wall of bifurcation has low wall shear stress and bigger recirculation as compared with that on the inner wall of bifurcation. Numerical results obtained for varying sinus size and position are shown in graphs and contours, including wall shear stress, secondary flow, and velocity streamlines. ConclusionNumerical results reveal that sinus away from bifurcation, and larger diameter sinus has more recirculation and low wall shear stress. Therefore, the person having sinus away from bifurcation and larger sinus diameter are more susceptible to plaque formation.

Bifurcations of Periodic Solutions of a Hamiltonian System with a Discrete Symmetry Group

An autonomous Hamiltonian system with two degrees of freedom that is invariant under the Klein four-group of linear canonical automorphisms of the extended phase space of the system is studied. A sequence of symplectic transformations of the monodromy matrix of the symmetric periodic solution of this system is constructed. Using these transformations, the structure and bifurcation of the phase flow in the vicinity of this solution is investigated. It is shown that the bifurcations corresponding to the multiple period increase are different for the solutions with double symmetry and the solutions with a single symmetry. An example of critical periodic solutions of the family of doubly symmetric orbits of the plane circular Hill problem is discussed. The majority of tedious analytical calculations are performed using packages for the computation of Grobner bases and for the work with polynomial ideals in the computer algebra system Maple.

Bifurcation phenomena for incompressible laminar flow in expansion channel to study Coanda effect

The present study analyzes the symmetry breaking and Hopf bifurcation of incompressible laminar flow through two-dimensional expansion channel with different expansion ratios. The governing momentum and mass conservation equations are solved by SIMPLE algorithm (pressure based solver) in Ansys workbench 14.1. It investigates the values of critical Reynolds number for symmetry breaking bifurcation and Hopf bifurcation using three different mesh refinements. Three different types of expansion channels have been used to analyze the bifurcation phenomena. The flow is assumed to be viscous, unsteady, laminar and Newtonian. It is observed that increase in expansion ratio causes a decrease of critical Reynolds number (Recr).

The effect of rotation on the thermal-solutal capillary-buoyancy flow in a shallow annular pool with various capillary ratios

In order to understand the effect of pool rotation on the thermal-solutal capillary-buoyancy convection at various capillary ratios, a series of three-dimensional simulations are performed in a rotating shallow annular pool filled with silicon-germanium melt and subjected to radial temperature and solute concentration gradients under normal gravity. The capillary ratios are Rσ=−0.5, −0.8, −1.25 and −2, while Taylor number ranges from Ta = 0 to 1200. Three types of basic flows are obtained at different capillary ratios. The pool rotation diversely affects the structures of the basic flow and further varies the destabilization mechanisms. The pool rotation enhances the flow stability at Ta < 400 and reduces the flow stability at Ta > 400 with Rσ=−0.5 and −0.8, while it always stabilizes the basic flow at Rσ=−1.25 and −2. The evolution of flow pattern depends remarkably on the Taylor number and the capillary ratio. Multiple flow bifurcations occur at small capillary ratios or high Taylor numbers, which results from the coupling of various driven forces. The reverse transition process is observed at Rσ=−0.5 and −0.8 with Taylor numbers slightly larger than the turning point. Meanwhile, abundant oscillatory flow patterns are shown. The effects of pool rotation on their characteristics are discussed.

A Spatiotemporal exploration and 3D modeling of blood flow in healthy carotid artery bifurcation from two modalities: Ultrasound-Doppler and phase contrast MRI

In the present study, we investigated the velocity profile over the carotid bifurcation in ten healthy volunteers by combining velocity measurements from two imaging modalities (PC-MRI and US-Doppler) and hemodynamic modeling in order to determine the optimal combination for the most realistic velocity estimation. The workflow includes data acquisition, velocity profile extraction at three sites (CCA, ECA and ICA), the arterial geometrical model reconstruction, a mesh generation and a rheological modeling. The results showed that US-Doppler measurements yielded higher velocity values as compared to PC-MRI (about 26% shift in CCA, 52% in ECA and 53% in ICA). This implies higher simulated velocities based on US-Doppler inlet as compared to simulated velocities based on PC-MRI inlet. Overall, PC-MRI inlet based simulations are closer to measurements than US-Doppler inlet based simulations. Moreover, the measured velocities showed that blood flow keeps a parabolic sectional profile distal from CCA, ECA and ICA, while being quite disturbed in the carotid sinus with a significant decrease in magnitude making this site very prone to atherosclerosis.

Freight transportation planning for regular and hazmat materials with simplified risk functions

Routing regular and dangerous commodities in railway freights transportation is discussed in this paper. Based on a link-based modeling approach, a mixed integer nonlinear programing model is developed. The model takes into account weather stability conditions of urban and rural areas and spatial distribution of risk at yards and around links as it impacts these zones along the routes. This paper also discusses the advantages of using bifurcation of flows on risk-cost tradeoffs and route planning decisions. The widely used nonlinear risk function is linearized and then the problem was solved to optimality using a commercial software. Results of the experiments on two hypothetical networks and one based on the rail network of the Province of Québec in Canada are presented and analyzed. Routing decisions associated with both variants of the proposed model with bifurcation of the material flows are compared to obtain managerial insights on the model in solving hazmat freight routing problems.

Hydraulic and statistical study of metastable phenomena in PWR rod bundles

The analysis of fuel rod bundle flows constitutes a key element of Pressurized-Water Reactors (PWR) safety studies. The present work aims at improving our understanding of nefarious reorganisation phenomena observed by numerous studies in the flow large-scale structures. 3D simulations allowed identifying two distinct reorganisations consisting in a sign change for either a transverse velocity in rod-to-rod gaps or for a subchannel vortex. A Taylor “frozen turbulence” hypothesis was adopted to model the evolution of large-scale 3D structures as transported-2D. A statistical method was applied to the 2D field to determine its thermodynamically stable states through an optimization problem. Similarities were obtained between the PWR coherent structures and the stable states in a simplified 2D geometry. Further, 2D simulations allowed identifying two possible flow bifurcations, each related to one of the reorganisations observed in 3D simulations, laying the foundations for a physical explanation of this phenomenon.

Interior structural bifurcation of 2D symmetric incompressible flows

The structural bifurcation of a 2D divergence free vector field $ \mathbf{u}(\cdot, t) $ when $ \mathbf{u}(\cdot, t_0) $ has an interior isolated singular point $ \mathbf{x}_0 $ of zero index has been studied by Ma and Wang [23]. Although in the class of divergence free fields which undergo a local bifurcation around a singular point, the ones with index zero singular points are generic, this class excludes some important families of symmetric flows. In particular, when $ \mathbf{u}(\cdot, t_0) $ is anti-symmetric with respect to $ \mathbf{x}_0 $, or symmetric with respect to the axis located on $ \mathbf{x}_0 $ and normal to the unique eigendirection of the Jacobian $ D\mathbf{u}(\cdot, t_0) $, the vector field must have index 1 or -1 at the singular point. Thus we study the structural bifurcation when $ \mathbf{u}(\cdot, t_0) $ has an interior isolated singular point $ \mathbf{x}_0 $ with index -1, 1. In particular, we show that if such a vector field with its acceleration at $ t_0 $ both satisfy the aforementioned symmetries then generically the flow will undergo a local bifurcation. Under these generic conditions, we rigorously prove the existence of flow patterns such as pairs of co-rotating vortices and double saddle connections. We also present numerical evidence of the Stokes flow in a rectangular cavity showing that the bifurcation scenarios we present are indeed realizable.

Evaluation of the Influence of Anomalies on the Flow of Non-Newtonian Fluid in Carotid Bifurcation by the PIV Method

The blood flow in anomalous carotid bifurcation is associated with stroke. Changed character of the flow, especially the occurrence of vortex structures, has showed a high correlation with thrombus formation and the development of atherosclerotic changes. The purpose of this work is to perform comparative model measurements of the flow inside the internal carotid bifurcation and to evaluate the influence of the geometry - stenosis, aneurysm on changes in the interaction of the fluid with the wall surface, i.e. on the local hemodynamic. The study uses the Global Imaging Methods for visualization and measurement of the phantom blood flow. The evaluation of the measured dataset and their subsequent analysis confirms the impact on the origin and development of pathological changes.

On the spectral instability and bifurcation of the 2D-quasi-geostrophic potential vorticity equation with a generalized Kolmogorov forcing

In this article, the spectral instability and the associated bifurcations of the shear flows of the 2D quasi-geostrophic equation with a generalized Kolmogorov forcing are investigated. To determine the linear instability of the basic shear flow, we write the corresponding eigenvalue problem as a system of finite difference equations whose nontrivial solutions are expressed in the form of continued fractions. By a rigorous analysis of these continued fractions, we prove the existence of a number Rc such that if the control parameter R, which is proportional to the Reynolds number and the intensity of the curl of forcing, is over Rc, then the basic shear flow loses its stability. To shed light on the bifurcation involved in the loss of stability of the basic shear flow, a natural method is used to reduce the quasi-geostrophic equation to a system of ordinary differential equations. Based on numerical experiments on the coefficients of this reduced system, we show that both supercritical and subcritical Hopf bifurcations occur depending on the frequency of the generalized Kolmogorov forcing. Moreover, we investigate the double Hopf bifurcations which occur at critical aspect ratios. Our results show that in the double Hopf bifurcation case, two periodic solutions, one stable and the other unstable, bifurcate on R>Rc.