Steady Flow Visualization in a Rigid Model of the Aortic Bifurcation: Application to Atherosclerosis

Hemodynamics have long been implicated in atherogenesis. The studiesreported here seek to explain the mechanisms for the formation ofatherosclerotic plaque in an aortic bifurcation. Flow studies were made ina model constructed from plexiglass to represent an aortic bifurcation. Under steady flow conditions at inflow Reynolds numbers of 80–1250,the streamline flow patterns and the boundary layer separation zones wereinvestigated in relation to the location of atherosclerotic plaques clinicallyfound at regions in the human aortic bifurcation. The streamline flowswere visualized by a slow injection of dye over the cross section of the tubeentrance and along the tube walls. The studies revealed a complex flowfield where secondary flows, induced by the centrifugal and viscous forces,cause the fluid to move towards the inner walls of the aortic bifurcation. The effect was more clearly seen with increasing Reynolds number. Boundary layer separation zones were observed to occur at the outercorners of the branching. The nature of the separation zone formed wasfound to be dependent on Reynolds number. The residence time of fluidparticles within such a separation zone was estimated by measuring thewashout time of a bolus of dye injected at strategic locations along the tubewalls. The residence time was found to decrease exponentially withincreasing Reynolds number. These observations provide strong support forthe role of flow separation in the accumulation of LDL and plateletaggregation within the aortic bifurcation.     

Flow in axisymmetrical glass model aneurysms

Experiments have been performed on the flow of water with a dye tracer in rigid glass models of axisymmetrical spherical aneurysms. Streamlines have been visualized, pressure drops over the surface of the bulbs have been measured, and a critical Reynolds number for the onset of turbulence in the aneurysms has been determined. Boundary layer separation and recirculating flow with closed streamlines was observed in all models for flow rates below those necessary for turbulence. Pressures on the aneurysm walls for both laminar and turbulent flow were found to be of the same order of magnitude as those immediately upstream and downstream with no large pressure differences over the bulb surfaces. An inviscid mathematical model of the flow field was developed and shown to give good agreement with experiment for high Reynolds number laminar flow. The use of a suitably defined critical Reynolds number as an aid in the decision to operate on fusiform aneurysms is noted, as well as the limitations imposed on the experimental and theoretical results by the neglect of flow periodicity and nonhomogeneity.     

Numerical modeling of pulsatile turbulent flow in stenotic vessels

Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-omega turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-epsilon turbulence model and the standard k-epsilon model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred.     

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.     

Analysis of hemodynamic fluid phase mass transport in a separated flow region

The mass transfer behavior in the recirculation region downstream of an axisymmetric sudden expansion was examined. The Reynolds number, 500, and Schmidt number, 3200, were selected to model the mass transfer of molecules, such as ADP, in the arterial system. In a first step the transient mass transport applying zero diffusive flux at the wall was analyzed using experiments and two computational codes. The two codes were FLUENT, a commercially available finite volume method, and FTSP, a finite element code developed at Graz University of Technology. The comparison of the transient wall concentration values determined by the three methods was excellent and provides a measure of confidence for computational mass transfer calculations in convection dominated, separated flows. In a second step the effect of the flow separation on the stationary mass transport applying a permeability boundary condition at the water-permeable wall was analyzed using the finite element code FTSP. The results show an increase of luminal ADP surface concentration in the upstream and in the downstream tube of the sudden expansion geometry in the range of six and twelve percent of the bulk flow concentration. The effect of flow separation in the downstream tube on the wall concentration is a decrease of about ten percent of the difference between wall concentration and bulk concentration occurring at nearly fully developed flow at the downstream region at a distance of 66 downstream tube diameters from the expansion. The decrease of ADP flux into the wall is in the range of three percent of the flux at the downstream region.     

Vortex generation in pulsatile flow through arterial bifurcation models including the human carotid artery

Visualization experiments were performed to elucidate the complicated flow pattern in pulsatile flow through arterial bifurcations. Human common carotid arteries, which were made transparent, and glass-models simulating Y- and T-shaped bifurcations were used. Pulsatile flow with wave forms similar to those of arterial flow was generated with a piston pump, elastic tube, airchamber, and valves controlling the outflow resistance. Helically recirculating flow with a pattern similar to that of the horseshoe vortex produced around wall-based protuberances in circular tubes was observed in pulsatile flow through all the bifurcations used in the present study. This flow type, which we shall refer to as the horseshoe vortex, has also been demonstrated to occur at the human common carotid bifurcation in steady flow with Reynolds numbers above 100. Time-varying flows also produced the horseshoe vortex mostly during the decelerating phase. Fluid particles of dye solution approaching the bifurcation apex diverged, divided into two directions perpendicularly, and then showed helical motion representing the horseshoe vortex formation. While this helical flow was produced, the stagnation points appeared on the wall upstream of the apex. Their position was dependent upon the flow distribution ratio between the branches in the individual arteries. The region affected by the horseshoe vortex was smaller during pulsatile flow than during steady flow. Lowering the Reynolds number together with the Womersley number weakened the intensity of helical flow. A separation bubble, resulting from the divergence or wall roughness, was observed at the outer or inner wall of the branch vessels and made the flow more complicated.     

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.     

Application and validation of the lattice Boltzmann method for modelling flow-related clotting

The purpose of this paper is to present a simple clotting model, based on residence time and shear stress distribution, that can simulate the deposition over time of enzyme-activated milk in an in vitro system. Results for the model are compared with experiments exhibiting clot deposition in the region of a sharp-edged stenosis. The milk experiments have been shown to be a valuable analogue for the experimental representation of flow-induced blood clotting, particularly in the context of separation of hydrodynamic from biochemical factors. The facility to predict the flow-induced clotting of the blood analogue, in which the chemistry reduces to what is effectively a zeroth order reaction, gives confidence in this physics-based approach to simulation of the final part of the coagulation cascade. This type of study is a necessary precursor to the development of a complex, multi-factorial, biochemical model of the process of thrombosis. In addition to the clotting simulations, comparisons are reported between the computed flow patterns prior to clot deposition and flow visualisation studies. Excellent agreement of hydrodynamic parameters is reported for a Reynolds number of 100, and qualitative agreement is seen for the complex, disturbed flow occurring at a physiologically relevant Reynolds number of 550. The explicit, time-stepping lattice Boltzmann approach may have particular merit for the transitional flow at this higher Reynolds number.     

Particle-Image Velocimetry and Force Measurements of Leading-Edge Serrations on Owl-Based Wing Models

High-resolution Particle-Image Velocimetry （PIV） and time-resolved force measurements were performed to analyze the impact of the comb-like structure on the leading edge of barn owl wings on the flow field and overall aerodynamic performance. The Reynolds number was varied in the range of 40,000 to 120,000 and the range of angle of attack was 0° to 6° for the PIV and -15° to ＋20° for the force measurements to cover the full flight envelope of the owl. As a reference, a wind-tunnel model which possessed a geometry based on the shape of a typical barn owl wing without any owl-specific adaptations was built, and measurements were performed in the aforementioned Reynolds number and angle of attack： range. This clean wing model shows a separation bubble in the distal part of the wing at higher angles of attack. Two types of comb-like structures, i.e., artificial serrations, were manufactured to model the owl＇s leading edge with respect to its length, thickness, and material properties. The artificial structures were able to reduce the size of the separation region and additionally cause a more uniform size of the vortical structures shed by the separation bubble within the Reynolds number range investigated, resulting in stable gliding flight independent of the flight velocity. However, due to increased drag coefficients in conjunction with similar lift coefficients, the overall aerodynamic performance, i.e., lift-to-drag ratio is reduced for the serrated models. Nevertheless, especially at lower Reynolds numbers the stabilizing effect of the uniform vortex size outperforms the lower aerodynamic performance.     

Experimental Study of the Vortex-Induced Vibration of Drilling Risers under the Shear Flow with the Same Shear Parameter at the Different Reynolds Numbers

A considerable number of studies for VIV under the uniform flow have been performed. However, research on VIV under shear flow is scarce. An experiment for VIV under the shear flow with the same shear parameter at the two different Reynolds numbers was conducted in a deep-water offshore basin. Various measurements were obtained by the fiber bragg grating strain sensors. Experimental data were analyzed by modal analysis method. Results show several valuable features. First, the corresponding maximum order mode of the natural frequency for shedding frequency is the maximum dominant vibration mode and multi-modal phenomenon is appeared in VIV under the shear flow, and multi-modal phenomenon is more apparent at the same shear parameter with an increasing Reynolds number under the shear flow effect. Secondly, the riser vibrates at the natural frequency and the dominant vibration frequency increases for the effect of the real-time tension amplitude under the shear flow and the IL vibration frequency is the similar with the CF vibration frequency at the Reynolds number of 1105 in our experimental condition and the IL dominant frequency is twice the CF dominant frequency with an increasing Reynolds number. In addition, the displacement trajectories at the different locations of the riser appear the same shape and the shape is changed at the same shear parameter with an increasing Reynolds number under the shear flow. The diagonal displacement trajectories are observed at the low Reynolds number and the crescent-shaped displacement trajectories appear with an increasing Reynolds number under shear flow in the experiment.     

Flush mounted hot film anemometer measurement of wall shear stress distal to a tri-leaflet valve for Newtonian and non-Newtonian blood analog fluids

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.     

Mathematical modelling of flow through an irregular arterial stenosis.

A mathematical model of flow through an irregular arterial stenosis is developed. The model is two-dimensional and axi-symmetric with the stenosis outline obtained from a three-dimensional casting of a mildly stenosed artery. Agreement between modelled and experimental pressure drops (obtained from an axi-symmetric machined stenosis with the same profile) is excellent. Results are also obtained for a smooth stenosis model, similar to that used for most mathematical modelling studies. This model overestimates the pressure drop across the stenosis, as well as the wall shear stress and separation Reynolds number. Also, the smooth model predicts one instead of three recirculation zones present in the irregular model. The original stenosis is modified to increase the severity from 48 and 87% areal occlusion, while maintaining the same general shape. This has the effect of increasing the pressure drop by an order of magnitude and decreasing the number of recirculation zones to one, with a lower separation Reynolds number.     

Turbulence Model Selection for Low Reynolds Number Flows

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Re_θ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.     

Steady flow through a double converging-diverging tube model for mild coronary stenoses

Velocity profiles and the pressure drop across two mild (62 percent) coronary stenoses in series have been investigated numerically and experimentally in a perspex-tube model. The mean flow rate was varied to correspond to a Reynolds number range of 50-400. The pressure drop across two identical (62 percent) stenoses show that for low Reynolds numbers the total effect of two stenoses equals that of two single stenoses. A reduction of 10 percent is found for the higher Reynolds numbers investigated. Numerical and experimental results obtained for the velocity profiles agree very well. The effect of varying the converging angle of a single mild (62 percent) coronary stenosis on the fluid flow has been determined numerically using a finite element method. Pressure-flow relation, especially with respect to relative short stenoses, is discussed.     

Numerical simulation of steady flow in a model of the aortic bifurcation.

The governing equations of steady flow of an incompressible viscous fluid through a 3-D model of the aortic bifurcation are solved with the finite element method. The effect of Reynolds number on the flow was studied for a range including the physiological values (200 < or = Re < or = 1600). The symmetrical bifurcation, with a branch angle of 70 degrees and an area ratio of 0.8, includes a tapered transition zone. Secondary flows induced by the tube curvature are observed in the daughter tubes. Transverse currents in the transition zone are generated by the combined effect of diverging and converging walls. Flow separation depends on both the Reynolds number and the inlet wall shear.     

Parallel-plate flow chamber for studies of 3D flow-endothelium interaction

Flow induced shear stress influences vascular cellular biology and pathophysiology in numerous ways. Previous in vitro studies on interactions between flow and endothelial cells using parallel-plate flow chambers involve two-dimensional flows, whereas flows in larger vessels are commonly three-dimensional. We have constructed a parallel plate flow chamber with a backward facing step aligned oblique to the axis of the chamber. Flow visualisation by steady injection of ink through a hypodermic tube reveals swirling flow in the recirculation region downstream of the step. At given angles of the step, theta; (to the axis of the chamber), the pitch of the swirl and the width of the separation region, as measured in the direction perpendicular to the step, increase with the Reynolds number (Re). On the other hand, at given values of Re, reduction of theta; results in increases in the swirl pitch but decreases in the width of the separation zone. Furthermore, clearance time of ink from the separation region is shorter with an oblique step than a perpendicular one at given Re. Computer simulation confirms the 3D swirling flow created by the oblique step and provides detailed distribution of wall shear stresses in the flow chamber.     

Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows

Effects of the non-Newtonian viscosity of blood on a flow in a coronary arterial casting of man were studied numerically using a finite element method. Various constitutive models were examined to model the non-Newtonian viscosity of blood and their model constants were summarized. A method to incorporate the non-Newtonian viscosity of blood was introduced so that the viscosity could be calculated locally. The pressure drop, wall shear stress and velocity profiles for the case of blood viscosity were compared for the case of Newtonian viscosity (0.0345 poise). The effect of the non-Newtonian viscosity of blood on the overall pressure drop across the arterial casting was found to be significant at a flow of the Reynolds number of 100 or less. Also in the region of flow separation or recirculation, the non-Newtonian viscosity of blood yields larger wall shear stress than the Newtonian case. The origin of the non-Newtonian viscosity of blood was discussed in relation to the viscoelasticity and yield stress of blood.     

Measurement of steady-flow instability and turbulence levels in Dacron vascular grafts.

Fluid dynamic properties of Dacron vascular grafts were studied under controlled steady-flow conditions over a Reynolds number range of 800 to 4500. Knitted and woven grafts having nominal diameters of 6 mm and 10 mm were studied. Thermal anemometry was used to measure centerline velocity at the downstream end of the graft; pressure drop across the graft was also measured. Transition from laminar flow to turbulent flow was observed, and turbulence intensity and turbulent stresses (Reynolds normal stresses) were measured in the turbulent regime. Knitted grafts were found to have greater pressure drop than the woven grafts, and one sample was found to have a critical Reynolds number (Rc) of less than one-half the value of Rc for a smooth-walled tube.     

Low Reynolds number equi-bifurcation flow in a two-dimensional channel

The fluid flow in some physiological vessels such as the blood flow in blood vessels and the air flow through bronchi and bronchioles in the lungs undergoes a large number of bifurcations. The understanding of the bifurcation flow is of importance for a better comprehension of its effect in the blood and the air circulatory systems of the living body. The Reynolds number of flow in large blood vessels and bronchi is high and fluid inertia plays a dominant role in the bifurcation flow in such vessels. In small caliber blood vessels such as arterioles and capillaries, and bronchioles, the Reynolds number of flow is quite low and the effect of fluid inertia is negligible compared to the pressure and shear forces. In order to have a quantitative understanding of the bifurcation flow at low Reynolds numbers, the low Reynolds number equi-bifurcation flow in a two-dimensional channel at zero bifurcation angle is studied based on the Stokes approximation. The solution of the problem is posed as an infinite series, where the truncated version is used in numerical calculations. The results of this analysis is discussed in connection with the bifurcation flow of blood in small caliber blood vessels and that of the air in bronchioles in the lung.     

Experimental investigation of branch flow ratio, angle, and Reynolds number effects on the pressure and flow fields in arterial branch models

An experimental investigation was carried out to acquire an understanding of local pressure changes and flow along the main lumen of arterial branch models similar to the femoral artery of man with three different branch angles (30, 60, and 90 deg) and side branch to the main lumen diameter ratio of 0.4. Effects of branch to main lumen flow rate ratios and physiological Reynolds numbers were found to be significant on the local pressure changes, while that of branch angle was also found to be important. The flow visualization study revealed that the flow separated in the main lumen near the branch junction when the pressure rise coefficient along the main lumen was above a critical value (i.e., 0.35 - 0.46), which was observed to be a function of the Reynolds number. The critical value of the branch to main lumen flow rate ratio was found to be about 0.38 - 0.44 also depending on the Reynolds number. Time averaged pressure distributions for pulsatile flow were similar in trend to steady flow values although they differed somewhat in detail in the main lumen in the branch region.