Modeling transition to turbulence in eccentric stenotic flows

Mean flow predictions obtained from a host of turbulence models were found to be in poor agreement with recent direct numerical simulation results for turbulent flow distal to an idealized eccentric stenosis. Many of the widely used turbulence models, including a large eddy simulation model, were unable to accurately capture the poststenotic transition to turbulence. The results suggest that efforts toward developing more accurate turbulence models for low-Reynolds number, separated transitional flows are necessary before such models can be used confidently under hemodynamic conditions where turbulence may develop.     

A fluid dynamics approach to bioreactor design for cell and tissue culture

The problem of controlling cylindrical tank bioreactor conditions for cell and tissue culture purposes has been considered from a flow dynamics perspective. Simple laminar flows in the vortex breakdown region are proposed as being a suitable alternative to turbulent spinner flask flows and horizontally oriented rotational flows. Vortex breakdown flows have been measured using three-dimensional Stereoscopic particle image velocimetry, and non-dimensionalized velocity and stress distributions are presented. Regions of locally high principal stress occur in the vicinity of the impeller and the lower sidewall. Topological changes in the vortex breakdown region caused by an increase in Reynolds number are reflected in a redistribution of the peak stress regions. The inclusion of submerged scaffold models adds complexity to the flow, although vortex breakdown may still occur. Relatively large stresses occur along the edge of disks jutting into the boundary of the vortex breakdown region.     

From individuals to aggregations: the interplay between behavior and physics

This paper analyses the processes by which organisms form groups and how social forces interact with environmental variability and transport. For aquatic organisms, the latter is especially important-will sheared or turbulent flows disrupt organism groups? To analyse such problems, we use individual-based models to study the environmental and social forces leading to grouping. The models are then embedded in turbulent flow fields to gain an understanding of the interplay between the forces acting on the individuals and the transport induced by the fluid motion. Instead of disruption of groups, we find that flows often enhance grouping by increasing the encounter rate among groups and thereby promoting merger into larger groups; the effect breaks down for strong flows. We discuss the transformation of individual-based models into continuum models for the density of organisms. A number of subtle difficulties arise in this process; however, we find that a direct comparison between the individual model and the continuum model is quite favorable. Finally, we examine the dynamics of group statistics and give an example of building an equation for the spatial and temporal variations of the group-size distribution from the individual-based simulations. These studies lay the groundwork for incorporating the effects of grouping into models of the large scale distributions of organisms as well as for examining the evolutionary consequences of group formation.     

Effect of turbulent models on left ventricle diastolic flow patterns simulation

Abstract

Vortex structures, as one of the most important features of cardiac flow, have a crucial impact on the left ventricle function and pathological conditions. These swirling flows are closely related to the presence of turbulence in left ventricle which is investigated in the current study. Using an extended model of the left heart, including a fluid-structure interaction (FSI) model of the mitral valve with a realistic geometry, the effect of using two numerical turbulent models, k-ε and Spalart-Allmaras (SA), on diastolic flow patterns is studied and compared with results from laminar flow model. As a result of the higher dissipation rate in turbulent models (k-ε and SA), vortices are larger and stronger in the laminar flow model. Comparing E/A ratio in the three models (Laminar, k-ε, and SA) with experimental data from healthy subjects, it is concluded that the results from k-ε model are more accurate.     

Flow in a mechanical bileaflet heart valve at laminar and near-peak systole flow rates: CFD simulations and experiments

Time-accurate, fully 3D numerical simulations and particle image velocity laboratory experiments are carried out for flow through a fully open bileaflet mechanical heart valve under steady (nonpulsatile) inflow conditions. Flows at two different Reynolds numbers, one in the laminar regime and the other turbulent (near-peak systole flow rate), are investigated. A direct numerical simulation is carried out for the laminar flow case while the turbulent flow is investigated with two different unsteady statistical turbulence modeling approaches, unsteady Reynolds-averaged Navier-Stokes (URANS) and detached-eddy simulation (DES) approach. For both the laminar and turbulent cases the computed mean velocity profiles are in good overall agreement with the measurements. For the turbulent simulations, however, the comparisons with the measurements demonstrate clearly the superiority of the DES approach and underscore its potential as a powerful modeling tool of cardiovascular flows at physiological conditions. The study reveals numerous previously unknown features of the flow.     

Large Eddy Simulation and Reynolds-Averaged Navier-Stokes modeling of flow in a realistic pharyngeal airway model: an investigation of obstructive sleep apnea

Computational fluid dynamics techniques employing primarily steady Reynolds-Averaged Navier-Stokes (RANS) methodology have been recently used to characterize the transitional/turbulent flow field in human airways. The use of RANS implies that flow phenomena are averaged over time, the flow dynamics not being captured. Further, RANS uses two-equation turbulence models that are not adequate for predicting anisotropic flows, flows with high streamline curvature, or flows where separation occurs. A more accurate approach for such flow situations that occur in the human airway is Large Eddy Simulation (LES). The paper considers flow modeling in a pharyngeal airway model reconstructed from cross-sectional magnetic resonance scans of a patient with obstructive sleep apnea. The airway model is characterized by a maximum narrowing at the site of retropalatal pharynx. Two flow-modeling strategies are employed: steady RANS and the LES approach. In the RANS modeling framework both k-epsilon and k-omega turbulence models are used. The paper discusses the differences between the airflow characteristics obtained from the RANS and LES calculations. The largest discrepancies were found in the axial velocity distributions downstream of the minimum cross-sectional area. This region is characterized by flow separation and large radial velocity gradients across the developed shear layers. The largest difference in static pressure distributions on the airway walls was found between the LES and the k-epsilon data at the site of maximum narrowing in the retropalatal pharynx.     

An experimental investigation on the multiphase flows and turbulent mixing in a flat-panel photobioreactor for algae cultivation

Keeping an appropriate mixing state of the multiphase flows in photobioreactors (PBRs) is a key issue for the optimal design and operation of the PBRs. In the present study, an experimental investigation is conducted to quantify the turbulent mixing of multiphase flows inside a flat-panel PBR and its consequential effects on the performance of the PBR for algae cultivation. While a high-resolution particle image velocity (PIV) system is used to achieve detailed flow field measurements to quantify the unsteady behaviors of the multiphase flows and turbulent mixing inside the PBR, algae cultures are also grown in the same PBR under the same test conditions. Detailed flow field measurement results are correlated with the algae growth performance in order to elucidate the underlying physics and explore/optimize design paradigms. The measurement results reveal that even though the airflow rate that is supplied to the PBR plays a dominant role in determining the characteristics of the turbulent mixing in the PBR, the geometric positioning of the aeration inlets also significantly contributes to the turbulent mixing. These differences in turbulent mixing cause differences in algae productivity within the PBR, clearly effecting efficiency of the PBR.     

Environmental variability and the initiation of dispersal: turbulence strongly increases seed release

Dispersal is a critical process in ecology. It is an important biological driver of, for example, invasions, metapopulation dynamics, spatial pattern formation and pathogen movement. Much is known about the effect of environmental variability, including turbulence, on dispersal of diaspores. Here, we document experimentally the strong but under-explored influence of turbulence on the initiation of dispersal. Flower heads of two thistle species (Carduus nutans and Carduus acanthoides) with ripe seeds were exposed to series of laminar and turbulent air flows of increasing velocity in a wind tunnel. Seed release increased with wind speeds for both laminar and turbulent flows for both species. However, far more seeds were released, at significantly lower wind speeds, during turbulent flows. These results strongly suggest a need for more quantitative studies of abscission in the field, as well as dispersal models that incorporate variability in the diaspore release phase.     

Effect of geometrical assumptions on numerical modeling of coronary blood flow under normal and disease conditions

Shear stress plays a pivotal role in pathogenesis of coronary heart disease. The spatial and temporal variation in hemodynamics of blood flow, especially shear stress, is dominated by the vessel geometry. The goal of the present study was to investigate the effect of 2D and 3D geometries on the numerical modeling of coronary blood flow and shear stress distribution. We developed physiologically realistic 2D and 3D models (with similar geometries) of the human left coronary artery under normal and stenosis conditions (30%, 60%, and 80%) using PROE (WF 3). Transient blood flows in these models were solved using laminar and turbulent (k-ω) models using a computational fluid dynamics solver, FLUENT (v6.3.26). As the stenosis severity increased, both models predicted a similar pattern of increased shear stress at the stenosis throat, and in recirculation zones formed downstream of the stenosis. The 2D model estimated a peak shear stress value of 0.91, 2.58, 5.21, and 10.09 Pa at the throat location under normal, 30%, 60%, and 80% stenosis severity. The peak shear stress values at the same location estimated by the 3D model were 1.41, 2.56, 3.15, and 13.31 Pa, respectively. The 2D model underestimated the shear stress distribution inside the recirculation zone compared with that of 3D model. The shear stress estimation between the models diverged as the stenosis severity increased. Hence, the 2D model could be sufficient for analyzing coronary blood flow under normal conditions, but under disease conditions (especially 80% stenosis) the 3D model was more suitable.     

Ballooning dispersal in arthropod taxa with convergent behaviours: dynamic properties of ballooning silk in turbulent flows

We present a new model of ballooning behaviour in arthropods in which draglines are regarded as being extendible and completely flexible. Our numerical simulations reveal that silk draglines within turbulent flows can become twisted and stretched into highly contorted shapes. Ballooners are therefore predicted to have little control over their aerodynamic drag and their dispersal within the atmospheric boundary layer. Dragline length is crucial only at lift-off. This prediction runs counter to that of Humphrey who suggested that the length of rigid draglines can be used to control dispersal. In contrast with Humphrey's model, the new model accounts naturally for the large distances travelled by some ballooners.     

Theory to Predict Shear Stress on Cells in Turbulent Blood Flow

Shear stress on blood cells and platelets transported in a turbulent flow dictates the fate and biological activity of these cells. We present a theoretical link between energy dissipation in turbulent flows to the shear stress that cells experience and show that for the case of physiological turbulent blood flow: (a) the Newtonian assumption is valid, (b) turbulent eddies are universal for the most complex of blood flow problems, and (c) shear stress distribution on turbulent blood flows is possibly universal. Further we resolve a long standing inconsistency in hemolysis between laminar and turbulent flow using the theoretical framework. This work demonstrates that energy dissipation as opposed to bulk shear stress in laminar or turbulent blood flow dictates local mechanical environment of blood cells and platelets universally.     

Numerical simulation of the cardiovascular system

In this article, we aim at giving a non-technical overview of some mathematical models currently used in the numerical simulation of the cardiovascular system. A hierarchy of models for blood flows in large arteries is briefly described as well as an electromechanical model for the heart. We discuss some possible applications of the numerical simulations of such models, for example the optimization of prostheses. We also address the issue of the data assimilation for the calibration of the models.     

Magneto-inertial fusion with laser compression of a magnetized spherical target

The paper is devoted to the principles of magneto-inertial fusion and laser-plasma methods of generation of a Megagauss field during spherical implosion of a magnetized target. A model based on a magnetic confinement system, namely, a cusp configuration with inertial compression of the target by a laser driver, is developed. The dynamics of plasma in a cusp compressed under the effect of laser beams is precalculated. Analytical and numerical estimates of the particle number and magnetic field intensity during magneto-inertial plasma compression are obtained. The problems of irradiation of a spherically closed volume by a high-energy laser pulse are discussed.     

Two-dimensional MHD simulations of a plasma focus with allowance for the acceleration mechanism for neutron generation

The problem is formulated and a numerical model is developed for calculating MHD flows in plasma-focus (PF) devices. An implicit (with respect to the magnetic field) difference scheme and a method for its numerical implementation are proposed. The scheme allows one to describe plasma flows with drastically different densities and, therefore, to take into account the presence of a vacuum region behind the PF current sheath. Taking into account this region is important to numerically simulate the focusing process and adequately describe the acceleration mechanism for the generation of fast ions and fusion neutrons. The results of calculations are compared with the experimental data on the plasma dynamics in two different types of PF device. A model of accelerated ions is proposed to estimate the contribution of the acceleration mechanism to the total neutron yield. The neutron yield calculated in the framework of this model for three different geometries of the PF chamber at currents of 0.5–1.5 MA differs from the measured values by less than a factor of 2.     

Direct visualizations of air flow in the human upper airway using in-vitro models

A better understanding of airflow characteristics in the upper airway(UA) is crucial in investigating obstructive sleep apnea(OSA), particle sedimentation, drug delivery, and many biomedical problems. Direct visualization of air flow patterns in in-vitro models with realistic anatomical structures is a big challenge. In this study, we constructed unique half-side transparent physical models of normal UA based on realistic anatomical structures. A smoke-wire method was developed to visualize the air flow in UA models directly. The results revealed that the airflow through the pharynx was laminar but not turbulent under normal inspiration, which suggested that compared with turbulent models, a laminar model should be more suitable in numerical simulations. The flow predicted numerically using the laminar model was consistent with the observations in the physical models. The comparison of the velocity fields predicted numerically using the half-side and complete models confirmed that it was reasonable to investigate the flow behaviors in UA using the half-side model. Using the laminar model, we simulated the flow and evaluated the effects of UA narrowing caused by rostral fluid shift on pharyngeal resistance. The results suggested that fluid shift could play an important role in the formation of hypopnea or OSA during sleep.     

A model of particle capture by bryozoans in turbulent flow: significance of colony form

A hydrodynamic model was developed to examine particle capture by lophophores of encrusting bryozoans. Particle capture rate is predicted to increase with increasing speed of the feeding current. There should be a large feeding advantage when lophophores are tightly packed and excurrents are vented through chimneys. This prediction contradicts conclusions of an earlier model study and suggests that selection for colony integration has a basis in the acquisition of food. If lophophores are not tightly packed, particle-capture patterns depend on two key ratios: the advection ratio (feeding current velocity to shear velocity) and the separation ratio (lophophore spacing to lophophore diameter). At high separation ratios, particle capture rates should be fairly uniform among zooids. At high advection ratios, lophophores located near the upstream colony edge should experience higher rates of particle capture. Rates of particle capture in turbulent flows should greatly exceed those in laminar flows (of identical speed) when excurrent waters are locally remixed into the flow above lophophores. However, when lophophores are tightly packed and excurrents are vented through chimneys, feeding rates should be identical in turbulent and laminar flows. Thus, colonies that vent excurrents through chimneys may be uniquely able to exploit weak laminar flows.     

Characterization of erythrocyte membrane tension for hemolysis prediction in complex flows

Hemolysis is a persistent issue with blood-contacting devices. Many experimental and theoretical contributions over the last few decades have increased insight into the mechanisms of hemolysis in both laminar and turbulent flows, with the ultimate goal of developing a comprehensive, mechanistic hemolysis model. Many models assume that hemolysis scales with a resultant, scalar stress representing all components of the fluid stress tensor. This study critically evaluates this scalar stress hypothesis by calculating the response of the red blood cell membrane to different types of fluid stress (laminar shear and extension, and three turbulent shear and extension cases), each with the same scalar stress. It was found that even though the scalar stress is the same for all cases, membrane tension varied by up to three orders of magnitude. In addition, extensional flow causes constant tension, while tank-treading in shear flow causes periodic tension, with tank-treading frequency varying by three orders of magnitude among the cases. For turbulent flow, tension also depends on eddy size. It is concluded, therefore, that scalar stress alone is inadequate for scaling hemolysis. Fundamental investigations are needed to establish a new index of the fluid stress tensor that provides reliable hemolysis prediction across the wide range of complex flows that occur in cardiovascular devices.     

Prediction of mechanical damage to animal cells in turbulence

In previous work a model was proposed for estimation of disruption of animal cells in turbulent capillary flows using information about the hydrodynamics, and cell mechanical properties determined by micromanipulation. The model assumed that the capillary flow consists of a laminar sublayer and a homogeneous turbulent region, and within the latter eddies of sizes similar to or smaller than the cells interact with those cells, causing local surface deformations. The proposed mechanism of cell damage was that such deformations result in an increase in membrane tension and surface energy, and that a cell disrupts when its bursting membrane tension and bursting surface energy are exceeded. The surface energy of the cells was estimated from the kinetic energy of appropriate sized eddies. To test the model, cells were disrupted in turbulent flows in capillaries at mean energy dissipation rates ranging from 800 to 2×10⁴ Wkg^–1. The model assumed that the specific lysis rate is almost independent of the number of passes, which was verified by the experimental data. The implication was that despite the damage the cell mechanical properties did not change markedly during multiple recirculations through the capillaries. On average the model underestimated the cell disruption by about 15%. Although the model gave reasonably good predictions, it lacks proper explanation of the independence of the specific lysis rate on the number of passes. In this paper it is shown that this problem can be resolved in principle by consideration of the localisation of the energy dissipation in turbulent capillary flows. The necessity of further modelling of cell-turbulence interactions is demonstrated.     

Far-field analysis of coupled bulk and boundary layer diffusion toward an ion channel entrance.

We present a far-field analysis of ion diffusion toward a channel embedded in a membrane with a fixed charge density. The Smoluchowski equation, which represents the 3D problem, is approximated by a system of coupled three- and two-dimensional diffusions. The 2D diffusion models the quasi-two-dimensional diffusion of ions in a boundary layer in which the electrical potential interaction with the membrane surface charge is important. The 3D diffusion models ion transport in the bulk region outside the boundary layer. Analytical expressions for concentration and flux are developed that are accurate far from the channel entrance. These provide boundary conditions for a numerical solution of the problem. Our results are used to calculate far-field ion flows corresponding to experiments of Bell and Miller (Biophys. J. 45:279, 1984).