Flow Bifurcation Research Articles

Study on bifurcation to chaos of surface tension gradient driven flow

As the primary heat and mass transfer mechanism in space through natural convection, surface tension gradient-driven convection is a complex nonlinear process concerning strong coupling between fluid flow and heat transfer. It is also a multiple parameter coupling process that exhibits complex spatial-temporal characteristics. Therefore, the mechanism of the surface tension gradient-driven convection becomes a hotspot in microgravity fluid physics. It also has many important applications, such as in space fluid and energy management. In this paper, recent experimental and numerical results on the transition of surface tension gradient-driven convection are reviewed, especially the nonlinear analysis on the flow bifurcations to chaos. There are several numerical methods to obtain the corresponding bifurcation diagrams. One is to integrate the model forward in time starting from different parameters and initial values, and others are to calculate the asymptotic flow states and bifurcation points directly. The direct numerical simulation method and time series analysis are widely used, but searching for bifurcation points from a large number of data is burdensome. Bifurcation points can be computed directly with the numerical bifurcation method, but such calculations are more difficult to implement than the direct numerical method.

Elastic instabilities and bifurcations in flows of wormlike micellar solutions past single and two vertically aligned microcylinders: Effect of blockage and gap ratios

This study presents an extensive numerical investigation on the flow characteristics of wormlike micellar (WLM) solutions past a single and vertically aligned two microcylinders placed in a microchannel in the creeping flow regime. The rheological behavior of the micellar solution is realized based on the two-species Vasquez–Cook–McKinley (VCM) constitutive model, which takes into account both the breakage and re-formation dynamics of micelles. For the case of single microcylinder, as the blockage ratio (ratio of the cylinder diameter to that of the channel height) is gradually varied, we find the existence of a flow bifurcation in the system, and also a gradual transition for a range of flow states, for instance, steady and symmetric or Newtonian like, steady and asymmetric, unsteady periodic and asymmetric, unsteady quasi-periodic and asymmetric, and, finally, unsteady quasi-periodic and symmetric. For the case of two microcylinders, we observe the presence of three distinct flow states in the system, namely diverging (D), asymmetric-diverging (AD), and converging (C) states as the intercylinder spacing in between the two cylinders is varied. Similar types of flow states are also observed in the recent experiments dealing with WLM solutions. However, we show that either this transition from one flow state to another in the case of a single microcylinder or the occurrence of any flow state in the case of two microcylinders is strongly dependent upon the values of the Weissenberg number and the nonlinear VCM model parameter ξ, which basically indicates how easy or hard it is to break a micelle. Based on the results and discussion presented herein for the single and two microcylinders, we hope this study will facilitate the understanding behind the formation of preferential paths or lanes during the flow of viscoelastic fluids through a porous media, which was seen in many prior experiments in the creeping flow regime.

Discordance of Tracer Transport and Particulate Matter Fate in a Baffled Clarification System

Abstract Large eddy simulation (LES) and coupled physical laboratory-scale modeling are performed to elucidate tracer transport and particulate matter (PM) fate in a baffled clarification system. Such baffled systems are common for urban water unit operations and processes. Flow hydrodynamic indices of these systems such as short-circuiting are often examined with measurement of inert tracer transport as a surrogate for chemical or PM transport and fate. Results of this study illustrate complex interactions between turbulent flow, tracer, and various PM diameters at the system scale. PM preferential accumulation and the discordance of PM transport with respect to flow hydrodynamics are observed based on the modeling results; otherwise not practical with physical model testing. Results demonstrate that baffling can promote system tracer mixing and improve volumetric utilization by extending the mean flow path through flow separation and bifurcation. The baffle tested produced high turbulence kinetic energy near the sedimentation floor and reduced PM separation (clarification) as compared to the unbaffled system used as a control. The unbaffled system in this study yields the highest PM separation, even though significant short-circuiting occurs during the residence time distribution (RTD) of the tracer. Further analysis demonstrates the mechanistic difference between the tracer transport and the finer suspended PM as compared to larger settleable and sediment PM diameters. Results illustrate that the tracer RTD, residence time (RT) and hydraulic efficiency indices are not reliable surrogates for PM or PM-bound chemical/pathogen separation. In addition, simulations suggest a site, system or condition-specific design approach given the coupled dependence on flow and design geometry.

Theoretical Investigation of Equilibrium Dynamics in Braided Gravel Beds for the Preservation of a Sustainable Fluvial Environment

Gravel bars have an important role in the exchange between surface and subsurface waters, in preventing and mitigating riverbank erosion, in allowing the recreational use of rivers, and in preserving fluvial or riparian habitats for species of fishes, invertebrates, plants, and birds. In many cases, gravel bars constitute an important substrate for the establishment and development of ground flora and woody vegetation and guarantee higher plant diversity. A sustainable management of braided rivers should, therefore, ensure their ecological potential and biodiversity by preserving a suitable braiding structure over time. In the present study, we propose an analytical–numerical model for predicting the evolution of gravel bars in conditions of dynamical equilibrium. The model is based on the combination of sediment balance equation and a regression formula relating dimensionless unit bedload rate and stream power. The results highlight the dependence of the evolving sediment particles’ pattern on the ratio of initial macro-bedforms longitudinal dimension to river width, which determines the gradual transition from advective and highly braiding to diffusive transport regime. Specifically, the tendency to maintain braiding and flow bifurcation is associated with equilibrium average bed profiles and, therefore, equilibrium average stream power characterized by the maximum period that does not exceed transverse channel dimension.

Bifurcations in flows of complex fluids around microfluidic cylinders.

Flow around a cylinder is a classical problem in fluid dynamics and also one of the benchmarks for testing viscoelastic flows. The problem is of wide relevance to understanding many microscale industrial and biological processes and applications, such as porous media and mucociliary flows. In recent years, we have developed model microfluidic geometries consisting of very slender cylinders fabricated in glass by selective laser-induced etching. The cylinder radius is small compared with the channel width, which allows the effects of the stagnation points in the flow to dominate over the effects of squeezing between the cylinder and the channel walls. Furthermore, the cylinders are contained in high aspect ratio microchannels that render the flow field approximately two-dimensional (2D) and therefore conveniently permit comparison between experiments and 2D numerical simulations. A number of different viscoelastic fluids including wormlike micellar and various polymer solutions have been tested in our devices. Of particular interest to us has been the occurrence of a striking, steady-in-time, flow asymmetry that occurs for certain non-Newtonian fluids when the dimensionless Weissenberg number (quantifying the importance of elastic over viscous forces in the flow) increases above a critical value. In this perspective review, we present a summary of our key findings related to this novel flow instability and present our current understanding of the mechanism for its onset and growth. We believe that the same fundamental mechanism may also underlie some important non-Newtonian phenomena observed in viscoelastic flows around particles, drops, and bubbles, or through geometries composed of multiple bifurcation points such as cylinder arrays and other porous media. Knowledge of the instability we discuss will be important to consider in the design of optimally functional lab-on-a-chip devices in which viscoelastic fluids are to be used.

An experimental study on shear bands in sand using the orthogonal cutting setup

We study the evolution of shear bands in granular media subjected to very large deformations using the orthogonal cutting geometry. We perform our cutting experiments on Cauvery Delta sand with d50 of 0.45mm. We also capture images of the cutting process which allows us to perform a PIV analysis to determine the deformation in material around the cutting tool. In our experiments we observe that the dynamic angle of repose of the pile that forms in-front of the tool as cutting progresses, approaches the critical state friction angle of the material. We observe a flow bifurcation around the tool as the material begins to slip along planes which are oriented at an angle of π/4 – θ/2, θ being the dynamic angle of repose, to the cutting direction. This leads to formation of shear bands/velocity jumps which contain around 14 particles. A measurement of dilation angle within the shear bands indicate that material is in a critical state of deformation.

Particle Image Velocimetry Measurements of the Flow-Diverting Effects of a New Generation of the eCLIPs Implant for the Treatment of Intracranial Bifurcation Aneurysms

Flow diverters (FDs) for the endovascular treatment of intracranial aneurysms are effective for sidewall aneurysms, but their use at a bifurcation is problematic because FDs only partially cover the aneurysm neck and impede flow into a daughter branch; they are thus not employed routinely in this anatomy. eCLIPs was developed as a non-tubular implant to completely cover the neck of an aneurysm and serve as a coil retention device necessary for the adequate treatment of wide-neck bifurcation aneurysms. eCLIPs has shown some flow diversion effects in bifurcation anatomy but not equal to those exhibited by clinically accepted flow diverters in sidewall anatomy. A new generation of eCLIPs implant, the eCLIPs bifurcation flow diverter (eBFD), with higher metal coverage, was developed to achieve a similar flow diversion as a Pipeline Embolization Device (PED), a prototypical FD. Particle image velocimetry was used to capture the fluid dynamics and velocity reduction within silicone aneurysm replicas. A circulatory mimicking loop was developed to circulate the flow through the silicone models. All generations of eCLIPs implants had some flow-diverting effect, with increasing metal coverage density of the implant proportionately increasing the flow diversion effect. The eBFD, with a metal density of 35%, showed greater flow diversion than PED, with 30% metal density, for bifurcation anatomy. The eBFD showed similar reduction of flow in a bifurcation anatomy to PED in a sidewall, both sufficient to permit early thrombosis of the aneurysm. Thus, the eBFD can potentially provide sufficient flow diversion for the treatment of bifurcation aneurysms to avoid adjunctive coiling.

Evolution of stationary flows of a viscous incompressible fluid in a plane diffuser

For the classical formulation of the Jeffery-Hamel problem of the stationary flows of a viscous incompressible fluid in a plane diffuser the solutions are found. The bifurcation of the basic single-mode flow into flows containing sectors of flow and outflow (multi-mode flows) is found. The second bifurcation point (the bifurcation of three mode flow into four and five modes flows) is analyzed as well as the third one. The values of Reynolds number corresponding to the bifurcation points are calculated. The dependence of first bifurcation value vs. the half-expansion angle is presented.

Optical Method for Simultaneous High-Resolution Measurement of Heat and Fluid Flow: The Case of Rayleigh-Bénard Convection

An optical system combining phase-shifting interferometry (PSI) and particle image velocimetry (PIV) is built and verified with simultaneous two-dimensional temperature- and velocity-field measurements of a convective flow. The well-known Rayleigh-B\'enard convection in laminar regime in a cubical cavity filled with water is chosen as the experimental validation case. Three-, four-, and six-bucket temporal phase-shifting equations using a rotating polarizer method are tuned under different light-source power conditions, first without PIV, to produce high-resolution phase-shifted data. The results showed that the three-bucket phase-shifting equation is the most robust method over a wide range of laser powers, while the PIV tracers decreased the PSI precision from 1.5% in the case without tracers to 3.0% when seeded at 0.02 wt%. The temporal and spatial resolution of the PSI measurement is 0.1 s and 6.47 $\ensuremath{\mu}\mathrm{m}$, respectively. Owing to the combined PSI and PIV technique, both temperature and velocity characteristics are obtained, unveiling the existence of several flow bifurcations as the Rayleigh number is increased up to $1.06\ifmmode\times\else\texttimes\fi{}{10}^{5}$. This optical setup is a potential paradigm shift in heat- and fluid-flow visualization, while having a great potential in biosensor development for concurrent velocity-, concentration-, and temperature-field measurements of aerosols and flows with multicomponent species.

Random-mass disorder in the critical Gross-Neveu-Yukawa models

An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum phase transitions of the symmetry-breaking type in Dirac materials such as graphene and the surfaces of topological insulators are described by relativistic (2+1)-dimensional quantum field theories of the Gross-Neveu-Yukawa (GNY) type. We study the universal critical properties of the chiral Ising, XY, and Heisenberg GNY models perturbed by quenched random-mass disorder, both uncorrelated or with long-range power-law correlations. Using the replica method combined with a controlled triple epsilon expansion below four dimensions, we find a variety of new finite-randomness critical and multicritical points with nonzero Yukawa coupling between low-energy Dirac fields and bosonic order parameter fluctuations, and compute their universal critical exponents. Analyzing bifurcations of the renormalization-group flow, we find instances of the fixed-point annihilation scenario—continuously tuned by the power-law exponent of long-range disorder correlations and associated with an exponentially large crossover length—as well as the transcritical bifurcation and the supercritical Hopf bifurcation. The latter is accompanied by the birth of a stable limit cycle on the critical hypersurface, which represents the first instance of fermionic quantum criticality with emergent discrete scale invariance.

PROFOUND ENDOTHELIAL DYSFUNCTION AS A CAUSE OF STROKE IN COVID-19: A CASE REPORT

SESSION TITLE: Medical Student/Resident Signs and Symptoms of Chest Disease Posters SESSION TYPE: Med Student/Res Case Rep Postr PRESENTED ON: October 18-21, 2020 INTRODUCTION: There are recent reports of neurological manifestations (NMs) from COVID-191. We present a healthy male who developed multiple strokes likely from direct endothelial dysfunction (ED). CASE PRESENTATION: 66M with GERD presents with 5 days of cough, fever, and chills. He was febrile and hypoxic. Work-up revealed CRP 19 mg/dL, ferritin 594 ng/mL, D-dimer 2.01 mg/L, positive COVID-19 PCR, and normal lipid panel. He had wheezing and no NMs. He was treated with antibiotics, enoxaparin, and oxygen. On day 14 he acutely developed altered mental status, aphasia, and unilateral weakness. CT head revealed acute left ischemic infarct. CTA head/neck revealed proximal left ICA dissection. Aspirin and Atorvastatin were given. Further studies revealed D-dimer 0.4 mg/L, no inheritable hypercoagulopathy, and negative TTE and lower extremity venous duplex. MRI brain confirmed multiple acute infarcts. Left ICA thrombectomy and stent placement were performed. It was found that there was a pseudo-dissection with a ruptured plaque and an overlying thrombus resulting in a 75% stenosis. DISCUSSION: Arterial complications from COVID-19 have recently been reported.3 Studies from Wuhan, China showed that 36.7% of COVID-19 patients had NMs, most commonly dizziness (16.8%) and headache (13.1%); 5.7% had acute ischemic stroke. These patients had severe respiratory symptoms and developed neurologic signs in 1-2 days.1 Another study revealed that stroke occurred in elevated CRP (51.1 vs 12.1 ng/L) and D-dimer (6.9 vs 0.5 mg/L)2. It is believed that the virus directly invades and injures endothelial cells (ECs), changes prothrombotic factors, and promotes a hypercoagulable state secondary to a profound inflammatory response4. ACE-2-receptors on ECs are used for viral adhesion. Viral replication causes EC apoptosis, which promotes vasoconstriction, organ ischemia, tissue edema, and microvascular prothrombotic sequelae.5 In our case, COVID-19 had profound ED distal to the carotid artery bifurcation. Arterial bifurcations are sites of turbulent blood flow that are athero-prone.6 The stroke occurred in the setting of moderate elevations of D-dimer, suggesting an alternate mechanism.2 Plaque rupture occurred with prophylactic anticoagulation and normal lipid panel. At the time of the stroke, D-dimer and inflammatory markers largely normalized. His late onset NMs indicate that prothrombotic sequelae and ED persist after the cytokine storm has improved.1 Further studies are needed to investigate the duration of cytokine storm and prothrombotic state, and appropriate screening measures. CONCLUSIONS: Clinicians must be cognizant of NMs from COVID-19 such as thromboembolic strokes from direct ED. Reference #1: 1. Mao L et al. Neurologic Manifestations of Hospitalized Patients With Coronavirus Disease 2019 in Wuhan, China. JAMA Neurol. Epub 2020 Apr 10. Reference #2: 2. Li Y, Wang M, Zhou Y, Chang J. Acute Cerebrovascular Disease Following COVID-19: A Single Center, Retrospective, Observational Study. Available at SSRN: https://ssrn.com/abstract=3550025. 2020 Mar 3. Reference #3: 3. Oxley, Thomas et al. Large-Vessel Stroke as a Presenting Feature of Covid-19 in the Young. N Engl J Med. Epub 2020 Apr 28. 4. Connors JM, Levy JH. COVID-19 and its implications for thrombosis and anticoagulation. Blood. Epub 2020 Apr 27. 5. Ferrario CM et al. Effect of angiotensin-converting enzyme inhibition and angiotensin II receptor blockers on cardiac angiotensin-converting enzyme 2. Circulation. 2005;111:2605-10. 6. Ku DN, Giddens DP, Zarins CK, Glagov S. Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque location and low oscillating shear stress. Atherosclerosis. 1985 May-Jun; 5:293-302 DISCLOSURES: No relevant relationships by Krishna Akella, source=Web Response No relevant relationships by Luke Alessi, source=Web Response No relevant relationships by David Capone, source=Web Response No relevant relationships by Olga McAbee, source=Web Response No relevant relationships by Heidi Roppelt, source=Web Response No relevant relationships by Fredric Weinbaum, source=Web Response No relevant relationships by Daisy Young, source=Web Response

Analysis of air layer shape formed by air injection at the bottom of flat plate

Air lubrication drag reduction has been proven to be a workable drag reduction technology in laboratory and for the full ship scales. The bottom air layer shape and coverage are the key factors affecting the drag reduction effect, which cannot be controlled well in actual sea conditions. This study presents the experimental investigation on the air-water mixed flow shape at the lower surface of a flat plate. The air layer shapes are captured by an image system under different air flow rates and velocities. Four distinct air-water mixed flow are classified, referred to as dispersed bubble flow (DBF), mixture flow (MF), air layer flow (ALF) and bifurcation flow (BF). The ALF regime should be considered as the best way for the drag reduction, because the air layer flow is relatively stable and the air layer coverage is large and uniform under flat plate. In addition, the attitude of the plate has a great influence on the air-water mixed flow shape on the lower surface of the flat plate. The tail trim of the plate would suppress the longitudinal diffusion of the air bubbles, and the heel will shift the air-water mixed shape.

Forced Convection Laminar Pulsating Flow in a 90-deg Bifurcation

Abstract Numerical investigation of laminar forced convection of pulsating flow in a 90-deg bifurcation was performed with the finite volume method. The inlet velocity varies sinusoidally with time while constant wall temperature is utilized. The working fluid is air with constant properties and the numerical work is conducted for a range of the Reynolds numbers (100–2000), dividing flowrates (0.3–0.7) and Strouhal numbers (0.1–10). It is observed that the amplitudes of oscillating heat transfer are damped as the value of the Strouhal number increases. The average value of Nu number rises for higher Reynolds number and the dividing flowrate for the downstream wall of the y-channel branch. As the value of the dividing flowrate increases from 0.3 to 0.7, heat transfer is less effective in the vicinity of the branch at the Reynolds number of 500. The effects of the Reynolds number on the average Nu number variation is more pronounced for the y-branch wall for different values of dividing flowrates. Resonant type behavior of average Nu number is obtained for the y-branch channel for diving flowrates of 0.3 and 0.5.

Evolution of deepwater turbidite bedforms in the Huaguang channel–lobe transition zone revealed by 3D seismic data in the Qiongdongnan Basin, South China Sea

The theoretical model of turbidite bedform evolution has been verified based on laboratory tests and outcrop surveys. However, the evolution of the bedforms associated with flow regime variation within the channel–lobe transition zone (CLTZ) is poorly documented and generally extremely poorly understood. In this study, a combination of seismic sedimentological and topographic analyses, based on high-resolution 3D seismic data within the Qiongdongnan Basin of the South China Sea, was used. Continuous bedforms varied with the depositional elements within the CLTZ of the Huaguang leveed channel system along the flow direction. The depositional elements within the CLTZ change from the main channel to the distributary channels as well as to the sub-distributary channels. Numerous bifurcation and confluence points of gravity flows illustrated the complexity of the drainage network within the CLTZ. The average asymmetry index of the bedforms increased from 0.8 to 1.6, with the average wavelength increasing from 803 m to 1545 m along the thalweg of the channels. Crevasse splays at the starting reach of the CLTZ are likely to form the initial state of the new CLTZ in the future, because the slope gradient starting from the avulsion point was higher than that inside the channel. The deep scours at the bifurcation points and high steps at the confluence points demonstrate the critical roles of supercritical flows and hydraulic jumps in reworking the bedforms of the CLTZ. The high steps at confluence points were simultaneously formed along the margin and thalweg of the main channel. The acceleration mechanisms of flow velocity forming the high steps were the increase of the elevation difference along the internal slope of the main channel margin and promotion of discharge along the main channel thalweg. This paper presents newly completed deepwater observations of the present seafloor bedforms based on the turbidity currents within the CLTZ. These observations update the evolution model of local supercritical flows and hydraulic jumps under the global decreasing trend of the Froude numbers within CLTZs.

Modeling Lahars on a Poorly Eroded Basaltic Shield: Karthala Volcano, Grande Comore Island

Lahars impose significant secondary hazards on highly populated volcanic islands by remobilising volcanic ash deposits. Karthala, on Grande Comore Island, is a basaltic shield volcano with sporadic occurrence of ash-forming phreatic eruptions. In 2005, two mildly explosive episodes emplaced tephra blankets on the summit area. Heavy precipitation subsequently triggered the repetitive occurrence of small-volume secondary lahars up to 2012. These lahars impacted the settlements at the foot of Karthala, damaging roads and hundreds of houses, affecting thousands of inhabitants. This study aims at gaining insights into the effectiveness of two simple tools to reproduce the lahars’ extent in this data-poor context. To understand the physical characteristics of the lahars, we first documented the extent and characteristics of the debris deposits at the foot of Karthala volcano and in the ravines that guided the flows. Our observations suggest that the debris was emplaced by small-scale (volumes ≤105 m³), rain-triggered and predominantly low sediment concentration lahars. The spatial extent of the deposits served to calibrate and compare numerical lahar simulations from the widely used volume-limited LaharZ model with results from Q-LavHA, a recent probabilistic flow model originally developed for lava flows. Our comparison demonstrates that LaharZ outperforms Q-LavHA for small-scale lahar simulations. While Q-LavHA has features that mitigate some limitations of LaharZ, such as its ability to simulate flow bifurcations and the transition from constrained to unconstrained flow, it typically underestimates the actual inundated area. Nevertheless, both models show rather poor performance, encountering difficulties in delineating lahar flow paths due to the smooth topography of the volcanic edifice. We therefore also evaluated the potential to increase simulation accuracy by updating a 10-meter resolution Digital Elevation Model (DEM) with channel topography measurements. While this approach led to improved simulation accuracies for both models compared to using un-adapted DEMs, it did not prevent simulations to miss the hazard-prone position of settlements actually affected by the hazard. This study helps inform numerical volcanic flow simulation strategies on young and poorly dissected volcanic edifices, such as basaltic shields, and forms a basis for further developing numerical simulation tools more adapted to these particular environmental settings.

Bifurcated Crustal Channel Flow and Seismogenic Structures of Intraplate Earthquakes in Western Yunnan, China as Revealed by Three‐Dimensional Magnetotelluric Imaging

AbstractBased on broadband magnetotelluric data collected in western Yunnan, we obtain a three‐dimensional crustal resistivity model, which reveals seismogenic structures of Yingjiang and Longling earthquakes. Our model suggests a bifurcation of the crustal flow in western Yunnan, with a southwestern branch running into the Tengchong Block north of the Dayingjiang Fault and a southeastern branch flowing into the Baoshan Block. The Yingjiang region features an upper and midcrustal resistive body above 20‐km depth, surrounded by conductors in the midcrust. Six moderate earthquakes in Yingjiang occurred in the transition zone between the resistive and conductive structures. These earthquakes occurred in the context of a right‐lateral accommodation zone between the Nabang and Binglangjiang Faults and in the presence of the southwestern branch of the crustal flow, which provides a mechanical decoupling under the rigid high‐resistive upper crust. Beneath the Longling area, a high‐resistive structure extends through the entire crust, but a zone of low resistivity is embedded in the depth range of 10–25 km where the 1976 M7.3 earthquake occurred. The high‐resistive body provides a blockage to the previously proposed crustal channel flow along the Gaoligong shear zone and may accumulate sufficient stress. The Longling strong earthquakes may result from the sinistral strike‐slip motion of the Ruili‐Luxi Fault in the framework of the north to northeast trending compressive stress. The blockage to the crustal channel flow along the Gaoligong shear zone by the high‐resistivity zone in Longling could be an important factor to produce the north to northeast trending compressive stress field in Longling area.

Methodology for Voltage Stability Analysis Using Hopf Bifurcation and Continuation Power Flow Simulator

The search for the Hopf bifurcation point in power systems can be made as the load is increased by small steps, and a power flow is solved for every load until a pair of purely imaginary eigenvectors has been found (zero real part). However, a search through successive power flows is time-consuming and does not guarantee that the Hopf bifurcation point will be found. This paper proposes a methodology and strategies that mitigate these problems. To increase the possibility of finding the Hopf bifurcation point, a continuation power flow is used to stablish search paths as the loading is incremented according to a fraction of the maximum loading point of the power system. It is only at specific converged continuation power flow that the dynamic state Jacobian matrix is constructed and has its eigenvalues computed. To facilitate the understanding and application of the proposal, it is used the MATPOWER (version 7.0) computer program and two available power systems.

Electrically driven toroidal Moffatt vortices: experimental observations

Abstract

Unsteady characteristics of laminar free convection in an enclosure in the presence of power law fluid at Ra = 107

The present study deals with an unsteady laminar free convection inside the annuli confined between an outer square enclosure and an inner circular cylinder. The annuli are filled with non-Newtonian power law fluids. The inner cylinder is located at three positions along the vertical center line. The unsteadiness arising due to bifurcation of flow from steady state is also reported in this study. The flow characteristics were found to be steady in nature in case of shear thickening fluid. However, most of the cases in the shear thinning fluid regime are found to be unsteady in nature with periodic and non-periodic fluctuations. The bifurcation of the flow from steady to unsteady state is mainly governed by the location of the cylinder as well as the characteristics of non-Newtonian fluid. The Bernard cells arising due to very high convective flow at Ra = 107 are also observed in the flow fields.

Heterogeneous partition of cellular blood-borne nanoparticles through microvascular bifurcations

Blood flowing through microvascular bifurcations has been an active research topic for many decades, while the partitioning pattern of nanoscale solutes in the blood remains relatively unexplored. Here we demonstrate a multiscale computational framework for direct numerical simulation of the nanoparticle (NP) partitioning through physiologically relevant vascular bifurcations in the presence of red blood cells (RBCs). The computational framework is established by embedding a particulate suspension inflow-outflow boundary condition into a multiscale blood flow solver. The computational framework is verified by recovering a tubular blood flow without a bifurcation and validated against the experimental measurement of an intravital bifurcation flow. The classic Zweifach-Fung (ZF) effect is shown to be well captured by the method. Moreover, we observe that NPs exhibit a ZF-like heterogeneous partition in response to the heterogeneous partition of the RBC phase. The NP partitioning prioritizes the high-flow-rate daughter branch except for extreme (large or small) suspension flow partition ratios under which the complete phase separation tends to occur. By analyzing the flow field and the particle trajectories, we show that the ZF-like heterogeneity in the NP partition can be explained by the RBC-entrainment effect caused by the deviation of the flow separatrix preceded by the tank treading of RBCs near the bifurcation junction. The recovery of homogeneity in the NP partition under extreme flow partition ratios is due to the plasma skimming of NPs in the cell-free layer. These findings, based on the multiscale computational framework, provide biophysical insights to the heterogeneous distribution of NPs in microvascular beds that are observed pathophysiologically.