Experiments on steady and oscillatory flows at moderate Reynolds numbers in a quasi-two-dimensional channel with a throat.

The study of steady and unsteady oscillatory static fluid pressures acting on the internal wall of a collapsible tube is essential for investigation of the complicated behavior observed when a flow is conveyed inside a tube. To examine the validity of two one-dimensional nonsteady theoretical flow models, this paper presents basic experimental observations of flow separation and reattachment and measured data on the static pressure distributions of the flow in a quasi-two-dimensional channel with a throat, together with information on the corresponding shape of the wall deflection and motion. For combinations of moderate Reynolds numbers and angles of the divergent segment of the channel, a smooth flow is separated from the wall downstream of the minimum cross section and reattached to the wall farther downstream. The measured data are compared with numerical results calculated by the two flow models.     

A one-dimensional viscous-inviscid strong interaction model for flow in indented channels with separation and reattachment

A new one-dimensional model is presented for the calculation of steady and unsteady flow through an indented two-dimensional channel with separation and reattachment. It is based on an interactive boundary layer approach, where the equations for the boundary layer flow near the channel walls and for an inviscid core flow are solved simultaneously. This approach requires no semi-empirical inputs, such as the location of separation and reattachment, which is an advantage over other existing one-dimensional models. Because of the need of an inviscid core alongside the boundary layers, the type of inflow as well as the length of the channel and the value of the Reynolds number poses some limitations on the use of the new model. Results have been obtained for steady flow through the indented channel of Ikeda and Matsuzaki. In further perspective, it is discussed how the present model, in contrast to other one-dimensional flow models, can be extended to calculate the flow in nonsymmetrical channels, by considering different boundary layers on each of the walls.     

Parameter study of simplified dragonfly airfoil geometry at Reynolds number of 6000

Aerodynamic study of a simplified Dragonfly airfoil in gliding flight at Reynolds numbers below 10,000 is motivated by both pure scientific interest and technological applications. At these Reynolds numbers, the natural insect flight could provide inspiration for technology development of Micro UAV’s and more. Insect wings are typically characterized by corrugated airfoils. The present study follows a fundamental flow physics study (Levy and Seifert, 2009), that revealed the importance of flow separation from the first corrugation, the roll-up of the separated shear layer to discrete vortices and their role in promoting flow reattachment to the aft arc, as the leading mechanism enabling high-lift, low drag performance of the Dragonfly gliding flight. This paper describes the effect of systematic airfoil geometry variations on the aerodynamic properties of a simplified Dragonfly airfoil at Reynolds number of 6000.The parameter study includes a detailed analysis of small variations of the nominal geometry, such as corrugation placement or height, rear arc and trailing edge shape.Numerical simulations using the 2D laminar Navier-Stokes equations revealed that the flow accelerating over the first corrugation slope is followed by an unsteady pressure recovery, combined with vortex shedding. The latter allows the reattachment of the flow over the rear arc. Also, the drag values are directly linked to the vortices’ magnitude. This parametric study shows that geometric variations which reduce the vortices’ amplitude, as reduction of the rear cavity depth or the reduction of the rear arc and trailing edge curvature, will reduce the drag values. Other changes will extend the flow reattachment over the rear arc for a larger mean lift coefficients range; such as the negative deflection of the forward flat plate. These changes consequently reduce the drag values at higher mean lift coefficients.The detailed geometry study enabled the definition of a corrugated airfoil geometry with enhanced aerodynamic properties, such as range and endurance factors, as compared to the nominal airfoil studied in the literature.     

Coupled oxygen transport analysis in the avascular wall of a coronary artery stenosis during angioplasty

The coupled oxygen transport in the avascular wall of a coronary artery stenosis is studied numerically by solving the convection-diffusion equations. Two geometries replicating stenosis before and after percutaneous transluminal coronary angioplasty (PTCA) are used for the analysis. The results are compared to evaluate the effect of the degree of stenosis on oxygen transport. Important physiological aspects, such as oxygen consumption in the wall, oxygen carried by the hemoglobin, non-Newtonian viscosity of the blood, and supply of oxygen from the vasa vasorum are included. The results show that the PO2 in the medial region of the arterial wall is approximately 10mmHg. The oxygen flux to the wall increases in the flow acceleration region, whereas it decreases at the flow reattachment zone. Near the location of flow separation, there is a small rise followed by a sharp fall in the oxygen flux. The drop in the oxygen flux to the wall at the point of flow reattachment for pre-PTCA stenosis is four times that for post-PTCA stenosis. The minimum PO2 in the avascular wall, PO2,min, at this location decreases to approximately 6.0 and 4.2mmHg for post- and pre-PTCA stenosis, respectively. The drop in PO2,w and PO2,min at the point of flow reattachment for pre-PTCA is approximately 2 times that for post-PTCA stenosis. Thus, the present study quantifies the oxygen transport to the arterial wall before and after cardiovascular intervention.     

Comparison of LES of steady transitional flow in an idealized stenosed axisymmetric artery model with a RANS transitional model

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y(+) less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y(+) less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.     

Large eddy simulation of the unsteady flow-field in an idealized human mouth-throat configuration

The present study concerns the simulation and analysis of the flow field in the upper human respiratory system in order to gain an improved understanding of the complex flow field with respect to the process affecting drug delivery for medical treatment of the human air system. For this purpose, large eddy simulation (LES) is chosen because of its powerful performance in the transitional range of laminar and turbulent flow fields. The average gas velocity in a constricted tube is compared with experimental data (Ahmed and Giddens, 1983) and numerical data from Reynolds-averaged Navier-Stokes (RANS) equations coupled with low Reynolds number (LRN) κ-ω model (Zhang and Kleinstreuer, 2003) and LRN shear-stress transport κ-ω model (Jayaraju et al., 2007), for model validation. The present study emphasizes on the instantaneous flow field, where the simulations capture different scales of secondary vortices in different flow zones including recirculation zones, the laryngeal jet zone, the mixing zone, and the wall shear layer. It is observed that the laryngeal jet tail breaks up, and the unsteady motion of laryngeal jet is coupled with the unsteady distribution of secondary vortices in the jet boundary. The present results show that it is essential to study the unsteady flow field since it strongly affects the particle flow in the human upper respiratory system associated with drug delivery for medical treatment.     

Modelling and simulation of the behaviour of a biofluid in a microchannel biochip separator

This paper reports an investigation into the flow behaviour of a biofluid in a microchannel systems through conceptual analysis and modelling. The application is the design of a microfluidic chip developed for the separation of plasma from blood. The effect of key design features of the microchannels on the flow behaviour of the biofluid is explored. These include geometric features such as the constriction, bending channel, bifurcation and the channel length ratio between the main and side channels. The performance of each design is discussed in terms of separation efficiency of the red blood cells with respect to the rest of the medium. Particular phenomena such as the Fahraeus and Fahraeus-Lindqvist effects, the Zweifach-Fung bifurcation law and the cell-free layer are discussed. In this paper, the fluid is modelled as a single-phase flow assuming either Newtonian or Non-Newtonian behaviour to investigate the effect of the fluid viscosity on both flow and separation efficiency. For a flow rate-controlled Newtonian flow system, it is found that viscosity and outlet pressure have little effect on the velocity distribution through each of the microchannels. For a diluted fluid where the flow in the whole channel system is modelled with a uniform viscosity, less plasma is separated from blood than observed in the non-Newtonian case. This results in an increase in the flow rate ratio between the main and side channels. A comparison of Newtonian and non-Newtonian flows shows that both flows tend to behave identically with an increase in the shear strain rate.     

Dependence of adhesive behavior of neutrophils on local fluid dynamics in a region with recirculating flow

We have recently described patterns of adhesion of different types of leukocytes downstream of a backward facing step. Here the predicted fluid dynamics in channels incorporating backward facing steps are described, and related to the measured velocities of flowing cells, patterns of attachment and characteristics of rolling adhesion for neutrophils perfused over P-selectin. Deeper (upstream depth 300 microm, downstream depth 600 microm, maximum wall shear stress approximately 0.1 Pa) and shallower (upstream depth 260 microm, downstream depth 450 microm, maximum wall shear stress approximately 0.3 Pa) channels were compared. Computational fluid dynamics (CFD) predicted the presence of vortices downstream of the steps, distances to reattachment of flow, local wall shear stresses and components of velocity parallel and perpendicular to the wall. Measurements of velocities of perfused neutrophils agreed well with predictions, and suggested that adhesion to P-selectin should be possible in the regions of recirculating flow, but not downstream in re-established flow in the high shear channel. When channels were coated with a P-selectin-Fc chimaera, neutrophils were captured from flow and immobilised. Capture showed local maxima around the reattachment points, but was absent elsewhere in the high shear chamber. In the low shear chamber there was depression of adhesion just beyond the reattachment point because of expansion of flow and depletion of neutrophils near the wall. Inside the recirculation zones, adhesion decreased approaching the step because of an increasing, vertically upward velocity component. When channels were coated with P-selectin, neutrophils rolled in all regions, but lifted off the surface as they rolled backwards into low shear regions near the step. Rolling velocity in the recirculation zone was independent of shear stress, possibly because of the effects of vertical lift. We conclude that while local wall shear stress influences adhesive behavior, delivery of cells to the wall and their behavior after capture also depend on components of flow perpendicular to the wall.     

Modelling and simulation of the behaviour of a biofluid in a microchannel biochip separator

This paper reports an investigation into the flow behaviour of a biofluid in a microchannel systems through conceptual analysis and modelling. The application is the design of a microfluidic chip developed for the separation of plasma from blood. The effect of key design features of the microchannels on the flow behaviour of the biofluid is explored. These include geometric features such as the constriction, bending channel, bifurcation and the channel length ratio between the main and side channels. The performance of each design is discussed in terms of separation efficiency of the red blood cells with respect to the rest of the medium. Particular phenomena such as the Fahraeus and Fahraeus–Lindqvist effects, the Zweifach–Fung bifurcation law and the cell-free layer are discussed. In this paper, the fluid is modelled as a single-phase flow assuming either Newtonian or Non-Newtonian behaviour to investigate the effect of the fluid viscosity on both flow and separation efficiency. For a flow rate-controlled Newtonian flow system, it is found that viscosity and outlet pressure have little effect on the velocity distribution through each of the microchannels. For a diluted fluid where the flow in the whole channel system is modelled with a uniform viscosity, less plasma is separated from blood than observed in the non-Newtonian case. This results in an increase in the flow rate ratio between the main and side channels. A comparison of Newtonian and non-Newtonian flows shows that both flows tend to behave identically with an increase in the shear strain rate.     

Experimental analysis of the influence of stenotic geometry on steady flow.

We studied the flow behavior under steady flow conditions in four models of cylindrical stenoses at Reynolds numbers from 150 to 920. The flow upstream of the constrictions was always fully developed. The constriction ratios of the rigid tubes (D) to the stenoses (d) were d/D = 0.273; 0.505; 0.548; 0.786. The pressure drop at various locations in the stenotic models was measured with water manometers. The flow was visualized with a photoelasticity apparatus using an aqueous birefringent solution. We also studied the flow behavior at pulsatile flow in a dog aorta with a constriction of 71%. The flow through stenotic geometries depends on the Reynolds number of the flow generated in the tube and the constriction ratio d/D. At low d/D ratios, (with the increased constriction), the flow separation zones (recirculation zones, so-called reattachment length) and flow disturbances increased with larger Reynolds numbers. At lower values, eddies were generated. At high Re, eddies were observed in the pre-stenotic regions. The pressure drop is a function of the length and internal diameter of the stenosis, respective ratio of stenosis to the main vessel and the Reynolds numbers. At low Re-numbers and low d/D, distinct recirculation zones were found close to the stenosis. The flow is laminar in the distal areas. Further experiments under steady and unsteady flow conditions in a dog aorta model with a constriction of 71% showed similar effects. High velocity fluctuations downstream of the stenosis were found in the dog aorta. A videotape demonstrates these results.     

Numerical simulation of steady turbulent flow through trileaflet aortic heart valves—II. Results on five models

Turbulent flow simulations are run for five aortic trileaflet valve geometries, ranging from a valve leaflet orifice area of 1.1 cm² (Model A1—very stenotic) to 5.0 cm² (Model A5—natural valve). The simulated data compares well with experimental measurements made downstream of various aortic trileaflet valves by Woo (PhD Thesis, 1984). The location and approximate width and length of recirculation regions are correctly predicted. The less stenotic valve models reattach at the end of the aortic sinus region, 1.1 diameters downstream of the valve. The central jet exiting the less stenotic valve models is not significantly different from fully developed flow, and therefore recovers very quickly downstream of the reattachment point. The more stenotic valves disturb the flow to a greater degree, generating recirculation regions large enough to escape the sinuses and reattach further downstream. Peak turbulent shear stress values downstream of the aortic valve models which approximated prosthetic valves are 125 and 300 N m⁻², very near experimental observations of 150 to 350 N m⁻². The predicted Reynolds stress profiles also present the correct shape, a double peak profile, with the location of the peak occuring at the location of maximum velocity gradient, which occurs near the recirculation region. The pressure drop across model A2 (leaflet orifice area 1.6 cm²) is 20 mmHg at 1.6 diameters downstream. This compares well with values ranging from 19.5 to 26.2 mmHg for valves of similar orifice areas. The pressure drop decreases with decreasing valve stenosis, to a negligible value across the least stenotic valve model. Based on the good agreement between experimental measurements of velocity, shear stress and pressure drop, compared to the simulated data, the model has the potential to be a valuable tool in the analysis of heart valve designs.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube.

A numerical and experimental investigation of unsteady entry flow in a 90 degrees curved tube is presented to study the impact of the non-Newtonian properties of blood on the velocity distribution. The time-dependent flow rate for the Newtonian and the non-Newtonian blood analog fluid were identical. For the numerical computation, a Carreau-Yasuda model was employed to accommodate the shear thinning behavior of the Xanthan gum solution. The viscoelastic properties were not taken into account. The experimental results indicate that significant differences between the Newtonian and non-Newtonian fluid are present. The numerical results for both the Newtonian and the non-Newtonian fluid agree well with the experimental results. Since viscoelasticity was not included in the numerical code, shear thinning behavior of the blood analog fluid seems to be the dominant non-Newtonian property, even under unsteady flow conditions. Finally, a comparison between the non-Newtonian fluid model and a Newtonian fluid at a rescaled Reynolds number is presented. The rescaled Reynolds number, based on a characteristic rather than the high-shear rate viscosity of the Xanthan gum solution, was about three times as low as the original Reynolds number. Comparison reveals that the character of flow of the non-Newtonian fluid is simulated quite well by using the appropriate Reynolds number.     

Coupled oxygen transport analysis in the avascular wall of a post-angioplasty coronary artery stenosis

The coupled oxygen transport in the avascular wall of a coronary artery stenosis is studied by numerically solving the convection-diffusion equations. Geometry, replicating residual stenosis after percutaneous transluminal coronary angioplasty (PTCA), is used for the analysis. Important physiological aspects, such as oxygen consumption in the wall, oxygen carried by the hemoglobin, non-Newtonian viscosity of the blood, and supply of oxygen from the vasa vasorum are included. Mean blood flow rate in the lumen is varied from basal to hyperemic conditions. The results show that the P(O2) in the medial region of the arterial wall is approximately 10 mmHg. The oxygen flux to the wall increases in the flow acceleration region, whereas it decreases at the flow reattachment zone. Near the location of flow separation there is a small rise and a sharp fall in the oxygen flux. The minimum P(O2) in the avascular wall, P(O2, min ), at the point of flow reattachment reduces to approximately 6 mmHg for a 300 micron wall thickness. For a thinner wall of 200 micron, the P(O2, min ) at the location of flow reattachment increases to 6 times that of a 300 micron wall. The P(O2, min ) in the wall decreases by 60% when volumetric oxygen consumption is increased by 30% for the same avascular wall thickness.     

A numerical and experimental analysis of the flow field in a two-dimensional model of the human carotid artery bifurcation

Axial velocities were measured in an enlarged, two-dimensional, rigid model of the carotid artery bifurcation by means of a laser-Doppler anemometer, under both steady and unsteady flow conditions. Also a numerical model was developed, based on the finite element approximation of the Navier-Stokes and continuity equations. From this study it appeared that the numerically predicted velocities agree well with the experimentally obtained values. Besides, the bifurcation hardly influenced the upstream flow in the main branch (common carotid artery), high velocity gradients were observed at the divider walls of the daughter branches (internal and external carotid arteries) and large zones with reversed flow were present near the nondivider walls of these branches. For steady flow the maximal diameter of this zone at the entrance of the internal carotid artery (carotid sinus) was about 25% of the local diameter of this branch. For unsteady flow this zone was absent during the initial phase of flow acceleration and maximal at the end of flow deceleration with a maximal diameter of about 50% of the local diameter of the carotid sinus.     

Pause point spectra in DNA constant-force unzipping

Under constant applied force, the separation of double-stranded DNA into two single strands is known to proceed through a series of pauses and jumps. Given experimental traces of constant-force unzipping, we present a method whereby the locations of pause points can be extracted in the form of a pause point spectrum. A simple theoretical model of DNA constant-force unzipping is presented, which generates theoretical pause point spectra through Monte Carlo simulation of the unzipping process. The locations of peaks in the experimental and theoretical pause point spectra are found to be nearly coincident below 6000 basepairs for unzipping the bacteriophage lambda-genome. The model only requires the sequence, temperature, and a set of empirical basepair binding and stacking energy parameters, and the good agreement with experiment suggests that pause point locations are primarily determined by the DNA sequence. The model is also used to predict pause point spectra for the bacteriophage phi X174 genome. The algorithm for extracting the pause point spectrum might also be useful for studying related systems which exhibit pausing behavior such as molecular motors.     

Experimental design methodology applied to the study of channel dimensions on the elution of red blood cells in gravitational field flow fractionation

Field flow fractionation (FFF) separation techniques have gained considerable success with micron-sized species. Living red blood cells (RBCs) of any origin have emerged as ideal models for cell separation development. Their elution mode is now described as “Lift-Hyperlayer”. Certain separator dimension parameters are known to play a key role in the separation and band spreading process. Systematic studies of channel dimensions effects on RBC retention, band spreading, peak capacity and on a novel parameter described as “Particle Selectivity” were set up by means of a two-level factorial experimental design. From experimental results and statistical calculations it is confirmed that channel thickness plays a major role in retention ratio, peak variance, peak capacity and particle selectivity. Channel breadth strongly influences plate height, with lower impact on peak capacity and particle selectivity. Retention ratio, peak variance and peak capacity observed results are modulated by second-order interactions between channel dimensions. Preliminary rules for channel configurations are therefore set up and depend on separation goals. It is shown that a very polydisperse population is best disentangled in a thin and narrow channel whatever its length. If a mixture of many different micron-sized species is considered (each of limited polydispersities); a thick and broad channel should be preferred, with length modulating peak capacity to disentangle this polymodal mixture.     

Physiological modulation of voltage-dependent inactivation in the cardiac muscle L-type calcium channel: a modelling study

The inactivation of the L-type Ca²⁺ current is composed of voltage-dependent and calcium-dependent mechanisms. The relative contribution of these processes is still under dispute and the idea that the voltage-dependent inactivation could be subject to further modulation by other physiological processes had been ignored. This study sought to model physiological modulation of inactivation of the current in cardiac ventricular myocytes, based upon the recent detailed experimental data that separated total and voltage-dependent inactivation (VDI) by replacing extracellular Ca²⁺ with Mg²⁺ and monitoring L-type Ca²⁺ channel behaviour by outward K⁺ current flowing through the channel in the absence of inward current flow. Calcium-dependent inactivation (CDI) was based upon Ca²⁺ influx and formulated from data that was recorded during β-adrenergic stimulation of the myocytes. Ca²⁺ influx and its competition with non-selective monovalent cation permeation were also incorporated into channel permeation in the model. The constructed model could closely reproduce the experimental Ba²⁺ and Ca²⁺ current results under basal condition where no β-stimulation was added after a slight reduction of the development of fast voltage-dependent inactivation with depolarization. The model also predicted that under β-adrenergic stimulation voltage-dependent inactivation is lost and calcium-dependent inactivation largely compensates it. The developed model thus will be useful to estimate the respective roles of VDI and CDI of L-type Ca²⁺ channels in various physiological and pathological conditions of the heart which would otherwise be difficult to show experimentally.