Reduction In Wall Shear Stress Research Articles

β-Lapachone induces heart morphogenetic and functional defects by promoting the death of erythrocytes and the endocardium in zebrafish embryos

Backgroundβ-Lapachone has antitumor and wound healing-promoting activities. To address the potential influences of various chemicals on heart development of zebrafish embryos, we previously treated zebrafish embryos with chemicals from a Sigma LOPAC1280™ library and found several chemicals including β-lapachone that affected heart morphogenesis. In this study, we further evaluated the effects of β-lapachone on zebrafish embryonic heart development.MethodsEmbryos were treated with β-lapachone or dimethyl sulfoxide (DMSO) at 24 or 48 hours post fertilization (hpf) for 4 h at 28°C. Heart looping and valve development was analyzed by whole-mount in situ hybridization and histological analysis. For fractional shortening and wall shear stress analyses, AB and Tg (gata1:DsRed) embryos were recorded for their heart pumping and blood cell circulations via time-lapse fluorescence microscopy. Dextran rhodamine dye injection into the tail reticular cells was used to analyze circulation. Reactive oxygen species (ROS) was analyzed by incubating embryos in 5-(and 6-)-chloromethyl-2',7'-dichloro-dihydrofluorescein diacetate (CM-H2DCFDA) and recorded using fluorescence microscopy. o-Dianisidine (ODA) staining and whole mount in situ hybridization were used to analyze erythrocytes. TUNEL assay was used to examine DNA fragmentation.ResultsWe observed a linear arrangement of the ventricle and atrium, bradycardia arrhythmia, reduced fractional shortening, circulation with a few or no erythrocytes, and pericardial edema in β-lapachone-treated 52-hpf embryos. Abnormal expression patterns of cmlc2, nppa, BMP4, versican, and nfatc1, and histological analyses showed defects in heart-looping and valve development of β-lapachone-treated embryos. ROS production was observed in erythrocytes and DNA fragmentation was detected in both erythrocytes and endocardium of β-lapachone-treated embryos. Reduction in wall shear stress was uncovered in β-lapachone-treated embryos. Co-treatment with the NQO1 inhibitor, dicoumarol, or the calcium chelator, BAPTA-AM, rescued the erythrocyte-deficiency in circulation and heart-looping defect phenotypes in β-lapachone-treated embryos. These results suggest that the induction of apoptosis of endocardium and erythrocytes by β-lapachone is mediated through an NQO1- and calcium-dependent pathway.ConclusionsThe novel finding of this study is that β-lapachone affects heart morphogenesis and function through the induction of apoptosis of endocardium and erythrocytes. In addition, this study further demonstrates the importance of endocardium and hemodynamic forces on heart morphogenesis and contractile performance.

Influence of surgical arch reconstruction methods on single ventricle workload in the Norwood procedure

The study objective was to evaluate various types of Norwood arch reconstruction methods and to show the factors that affect the cardiac workload of the single ventricle. The Norwood procedure is one of the most challenging congenital heart surgeries. Several aortic arch reconstruction techniques have been reported to avoid recoarctation, ensure coronary perfusion, and improve long-term outcomes. Inside the arch, complicated turbulent flow is generated; however, little is known about the cause of the disadvantageous inefficient flow and the surgical techniques to avoid it. We created patient-specific computational hemodynamic models of 9 patients who underwent different types of arch reconstruction methods. Four patients had aortic atresia, and 5 patients had aortic stenosis. Flow profiles were defined by echocardiography data corrected with body surface area. Turbulent pulsatile flow was analyzed with the finite volume method. Flow energy loss was calculated to estimate cardiac workload, and wall shear stress was calculated to estimate vessel wall stiffness increase. Recoarctation and acute arch angles increased wall shear stress and energy loss. In the patients with aortic atresia, a longitudinal incision toward the descending aorta was effective in creating a smooth arch angle. In the patients with aortic stenosis, arch repair with the Damus-Kaye-Stansel procedure in a single anastomotic site was effective in creating sufficient anastomosis space and a smooth arch angle. Creation of a large anastomotic space and a smooth aortic arch angle reduced wall shear stress and energy loss, and should improve long-term cardiac performance after the Norwood procedure.

P-032 Vascular reconstruction devices shrink small cerebral aneurysms

Endovascular treatment of intracranial aneurysms (IAs) often includes the deployment of a vascular reconstruction device (VRD), particularly if the aneurysm has a wide neck or unfavorable dome to neck ratio,...

Influence of different computational approaches for stent deployment on cerebral aneurysm haemodynamics

Cerebral aneurysms are abnormal focal dilatations of artery walls. The interest in virtual tools to help clinicians to value the effectiveness of different procedures for cerebral aneurysm treatment is constantly growing. This study is focused on the analysis of the influence of different stent deployment approaches on intra-aneurysmal haemodynamics using computational fluid dynamics (CFD). A self-expanding stent was deployed in an idealized aneurysmatic cerebral vessel in two initial positions. Different cases characterized by a progression of simplifications on stent modelling (geometry and material) and vessel material properties were set up, using finite element and fast virtual stenting methods. Then, CFD analysis was performed for untreated and stented vessels. Haemodynamic parameters were analysed qualitatively and quantitatively, comparing the cases and the two initial positions. All the cases predicted a reduction of average wall shear stress and average velocity of almost 50 per cent after stent deployment for both initial positions. Results highlighted that, although some differences in calculated parameters existed across the cases based on the modelling simplifications, all the approaches described the most important effects on intra-aneurysmal haemodynamics. Hence, simpler and faster modelling approaches could be included in clinical workflow and, despite the adopted simplifications, support clinicians in the treatment planning.

An analysis of superhydrophobic turbulent drag reduction mechanisms using direct numerical simulation

Superhydrophobic surfaces combine hydrophobic surface chemistry with topological microfeatures. These surfaces have been shown to provide drag reduction in laminar and turbulent flows. In this work, direct numerical simulation is used to investigate the drag reducing performance of superhydrophobic surfaces in turbulent channel flow. Slip velocities, wall shear stresses, and Reynolds stresses are determined for a variety of superhydrophobic surface microfeature geometry configurations at friction Reynolds numbers of Reτ≈180, Reτ≈395, and Reτ≈590. This work provides evidence that superhydrophobic surfaces are capable of reducing drag in turbulent flow situations by manipulating the laminar sublayer. For the largest microfeature spacing, an average slip velocity over 80% of the bulk velocity is obtained, and the wall shear stress reduction is found to be greater than 50%. The simulation results suggest that the mean velocity profile near the superhydrophobic wall continues to scale with the wall shear stress and the log layer is still present, but both are offset by a slip velocity that is primarily dependent on the microfeature spacing.

Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms

AbstractFluid–structure interaction (FSI) analyses of cerebral aneurysm using patient‐specific geometry with uniform and pathological aneurysmal wall thickness models are carried out. The objective is to assess the influence of the wall thickness on the FSI and hemodynamics in aneurysms. Two aneurysm models that were reconstructured based on CT images are used. The arterial wall thickness is set to 0.3 mm for the non‐aneurysmal artery and to 0.05 mm for the aneurysmal wall based on experimental findings. Another set of aneurysm models with a uniform wall thickness of 0.3 mm for the entire model is used for comparison. The FSI simulations are carried out using the deforming‐spatial‐domain/stabilized space–time method with physiological inflow and pressure profiles. Computations with different aneurysmal wall thicknesses depict considerable differences in displacement, flow velocity and wall shear stress (WSS). The wall displacement for the pathological wall model is 61% larger than that of the uniform wall model. Consequently, the flow velocities in the aneurysm with the pathological wall model are lower, and that results in a 51% reduction in WSS on the aneurismal wall. Because low WSS on the aneurymal wall is linked to growth and rupture risk of aneurysm, the results suggest that using uniform wall thickness for the aneurysmal wall could underestimate risk in aneurysms. Copyright © 2009 John Wiley & Sons, Ltd.

Effects of salinity and temperature on drag reduction characteristics of polymers in straight circular pipes

It has been nearly 60 years since Toms [Toms, B.A., 1949 first discovered the tremendous reduction in wall shear stress caused by the addition of small amount of linear macromolecules to a flowing fluid. This drag reduction phenomenon corresponds to an increase in pumpability of a fluid by the additive. Therefore the application of this phenomenon can be found in many areas of the oil and gas industry; including well completion, workover, drilling operations, and hydraulic fracturing. The turbulent flow prevails in such operations. The eddy currents and velocity fluctuations in turbulent motion produce increased pressure drops and thus, limit the maximum obtainable fluid flow rate. This results in a problem particularly in hydraulic fracturing where higher flow rates are desired. Employing the commercially available drag reducing fluids can overcome this limitation. Salinity and temperature are among the factors that affect the extent of drag reduction. Other factors include polymer type and concentration, molecular weight and distribution, solvent chemistry, pH, ionic strength, molecular conformation, flow geometry, and degree of mechanical shearing. Despite the widespread use of brine solutions as base fluids in fracturing the deep hot formations, the effects of temperature and salinity on the drag reduction characteristics of polymers have received the least attention. Most studies on drag reduction have considered either water or salt-free base fluids at ambient temperatures. Therefore, the aim of the present study is to experimentally investigate the effects of salinity and temperature on the extent of drag reduction of polymers flowing in straight circular pipes. Two commonly used anionic polyacrylamides; Nalco ASP-700 and ASP-820 are used in this study: ASP-700 is an analog of partially hydrolyzed polyacrylamide (PHPA), while ASP-820 is a sulfonate-containing polyacrylamide. A 1/2-in. OD flow loop with a 15-ft straight tubing is used. Flow tests are conducted to determine the optimum concentrations of ASP-700 and ASP-820 polymers. It is found that the optimum concentration for both polymers is 0.07% (vol.). To investigate the effect of temperature, tests are conducted with fresh water at 72, 100 and 130 °F. Additional tests are conducted at ambient temperature and with 2% KCl brine and synthetic sea water to investigate the effect of salinity on drag reduction of ASP-700 and ASP-820. It is found that both polymers are quite effective drag reducers in circular straight pipes. Drag reduction in the range of 30–80% is noticed. Both temperature and salinity have significant effect on their drag reduction characteristics. Due to differences in their composition and potentially molecular weight variances, both polymers show different characteristics in the presence of salt and at elevated temperatures. Within the conditions studied, ASP-700 is found to be better than ASP-820 at providing drag reduction. Correlations to predict drag reduction at either temperature or salinity are developed. These results are presented and discussed in detail.

Direct numerical simulations of turbulent flows over superhydrophobic surfaces

Direct numerical simulations (DNSs) are used to investigate the drag-reducing performance of superhydrophobic surfaces (SHSs) in turbulent channel flow. SHSs combine surface roughness with hydrophobicity and can, in some cases, support a shear-free air–water interface. Slip velocities, wall shear stresses and Reynolds stresses are considered for a variety of SHS microfeature geometry configurations at a friction Reynolds number of Reτ ≈ 180. For the largest microfeature spacing studied, an average slip velocity over 75% of the bulk velocity is obtained, and the wall shear stress reduction is found to be nearly 40%. The simulation results suggest that the mean velocity profile near the superhydrophobic wall continues to scale with the wall shear stress but is offset by a slip velocity that increases with increasing microfeature spacing.

PL10. Accelerated Intimal Hyperplasia Distal to a Focal Stenosis: A New Paradigm in Vein Graft Remodeling

Despite the relative uniformity of the surgical trauma at the time of implantation, vein grafts (VG) demonstrate significant focality in their lesion development. With an established link between the local hemodynamics and intimal hyperplasia (IH) development, we explored the impact of wall shear stress (WSS) on lesion progression using a novel focal stenosis VG model. The current paradigm suggests that reductions in WSS enhance the hyperplastic response, however, results from this study challenge this by demonstrating a critical WSS threshold above which IH formation is markedly elevated.

One-information suboptimal control repercussion on the fine structure of wall turbulence

The suboptimal control with the cost function directly connected to the wall shear and introduced for a while has been revisited through direct numerical simulations of high temporal and spatial resolution. Its effect on the fine structure of the wall turbulence has been analyzed in details, essentially through the spanwise vorticity transport mechanism. It is shown that only half of the viscous sublayer is mainly affected by the control. The actuation efficiency is limited in terms of the wall shear stress reduction, but is high as long as the turbulent wall activity is concerned. The wall shear stress is reduced due both to the reduction of the shear production in the viscous sublayer and to the contribution of the turbulent body force. The dissipation involving in the streamwise vorticity fluctuations transport equation increases significantly and overcomes the production in a thin layer near the wall leading to a drastic diminution of the turbulent wall shear stress fluctuations.

Increased shear stress with upregulation of VEGF-A and its receptors and MMP-2, MMP-9, and TIMP-1 in venous stenosis of hemodialysis grafts

Venous injury and subsequent venous stenosis formation are responsible for hemodialysis graft failure. Our hypothesis is that these pathological changes are in part related to changes in wall shear stress (WSS) that results in the activation of matrix regulatory proteins causing subsequent venous stenosis formation. In the present study, we examined the serial changes in WSS, blood flow, and luminal vessel area that occur subsequent to the placement of a hemodialysis graft in a porcine model of chronic renal insufficiency. We then determined the corresponding histological, morphometric, and kinetic changes of several matrix regulatory proteins including VEGF-A, its receptors, matrix metalloproteinase (MMP)-2, MMP-9, tissue inhibitor of matrix metalloproteinase (TIMP)-1, and TIMP-2. WSS was estimated by obtaining blood flow and luminal vessel area by performing phase-contrast MRI with magnetic resonance angiography in 21 animals at 1 day after graft placement and prior to death on day 3 (n = 7), day 7 (n = 7), and day 14 (n = 7). At all time points, the mean WSS at the vein-to-graft anastomosis was significantly higher than that at the control vein (P < 0.05). WSS had a bimodal distribution with peaks on days 1 and 7 followed by a significant reduction in WSS by day 14 (P < 0.05 compared with day 7) and a decrease in luminal vessel area compared with control vessels. By day 3, there was a significant increase in VEGF-A and pro-MMP-9 followed by, on day 7, increased pro-MMP-2, active MMP-2, and VEGF receptor (VEGFR)-2 (P < 0.05) and, by day 14, increased VEGFR-1 and TIMP-1 (P < 0.05) at the vein-to-graft anastomosis compared with control vessels. Over time, the neointima thickened and was composed primarily of alpha-smooth muscle actin-positive cells with increased cellular proliferation. Our data suggest that hemodialysis graft placement leads to early increases in WSS, VEGF-A, and pro-MMP-9 followed by subsequent increases in pro-MMP-2, active MMP-2, VEGFR-1, VEGFR-2, and TIMP-1, which may contribute to the development of venous stenosis.

Streamwise development of turbulent boundary-layer drag reduction with polymer injection

Zero-pressure-gradient turbulent boundary-layer drag reduction by polymer injection has been studied with particle image velocimetry. Flow fields ranging from low to maximum drag reduction have been investigated. A previously developed technique – the (1 −y/δ) fit to the total shear stress profile – has been used to evaluate the skin friction, drag reduction and polymer stress. Current results agree well with the semi-log plot of drag reductionvs. normalized polymer flux which has been used by previous workers and can be used as a guide to optimize the use of polymer from a single injector. Detailed flow-field statistics show many special features that pertain to polymer flow. It is shown that the mean velocity responds quickly to the suddenly reduced wall shear stress associated with polymer injection. However, it takes a much longer time for the entire Reynolds shear stress profile to adjust to the same change. The Reynolds shear stress profiles in wall units can be higher than unity and this unique feature can be used to further judge whether the flow is in equilibrium. The streamwise evolution of drag reduction magnitude is used to divide the flow into three regions: development region; steady-state region; and depletion region. The polymer stress is estimated and found to be proportional to drag reduction in the depletion region, but not necessarily so in the other regions. The interaction between injected polymer and turbulent activity in a developing boundary-layer flow is dependent upon the flow history and it produces an equally complex relationship between polymer stress and drag reduction. The stress balance in the boundary layer and the dynamical contribution of the various stresses to the total stress are evaluated and it is seen that the polymer stresses can account for up to 25% of the total stress. This finding is in contrast to channel flows with homogeneous polymer injection where the polymer stress is found to account for up to 60% of the total stress.

Parametric study of a model for determining the liquid flow-rates from the pressure drop and water hold-up in oil–water flows

A flow-pattern-dependent model, traditionally used for calculation of pressure drop and water hold-up, is accustomed for calculation of the liquid production rates in oil–water horizontal flow, based on the known pressure drop and water hold-up. The area-averaged steady-state one-dimensional two-fluid model is used for stratified flow, while the homogeneous model is employed for dispersed flow. The prediction errors appear to be larger when the production rates are calculated instead of pressure drop and water hold-up. The difference in the calculation accuracies between the direct and inverse calculation is most probably caused by the different uncertainties in the measured values of the input variables and a high sensitivity of the calculated phase flow-rates on even small change of the water hold-up for certain flow regimes. In order to locate the source of error in the standard two-fluid model formulation, several parametric studies are performed. In the first parametric study, we investigate under which conditions the momentum equations are satisfied when the measured pressure drop and water hold-up are imposed. The second and third parametric studies address the influence of the interfacial waves and drop entrainment on the model accuracy, respectively. These studies show that both interfacial waves and drop entrainment can be responsible for the augmentation of the wall-shear stress in oil–water flow. In addition, consideration of the interfacial waves offers an explanation for some important phenomena of the oil–water flow, such as the wall-shear stress reduction.

Experimental and computational studies on the flow fields in aortic aneurysms associated with deployment of AAA stent-grafts

Pulsatile flow fields in rigid abdominal aortic aneurysm (AAA) models were investigated numerically, and the simulation results are found in good agreement with particle image velocimetry (PIV) measurements. There are one or more vortexes in the AAA bulge, and a fairly high wall shear stress exists at the distal end, and thus the AAA is in danger of rupture. Medical treatment consists of inserting a vascular stent-graft in the AAA, which would decrease the blood impact to the inner walls and reduce wall shear stress so that the rupture could be prevented. A new computational model, based on porous medium model, was developed and results are documented. Therapeutic effect of the stent-graft was verified numerically with the new model.

Characteristics of the response of the iliac artery to wall shear stress in the anaesthetized pig

The functional significance of shear stress-induced vasodilatation in large conduit arteries is unclear since changes in the diameter have little effect on the resistance to blood flow. However, changes in diameter have a relatively large effect on wall shear stress which suggests that the function of flow-mediated dilatation is to reduce wall shear stress. The mean and pulsatile components of shear stress vary widely throughout the arterial system and areas of low mean and high amplitude of wall shear stress are prone to the development of atheroma. In this study, using an in vivo model with the ability to control flow rate and amplitude of flow independently, we investigated the characteristics of the response of the iliac artery to variations in both the mean and amplitude of wall shear stress. The results of this study confirm that increases in mean wall shear stress are an important stimulus for the release of nitric oxide by the endothelium as indicated by changes in arterial diameter and show for the first time, in vivo, that increases in the amplitude of the pulsatile component of shear stress have a small but significant inhibitory effect on this response. A negative feedback mechanism was identified whereby increases in shear stress brought about by increases in blood flow are reduced by the release of nitric oxide from the endothelium causing dilatation of the artery, thus decreasing the stimulus to cell adhesion and, through a direct action of nitric oxide, inhibiting the process of cell adhesion. The results also provide an explanation for the uneven distribution of atheroma throughout the arterial system, which is related to the ratio of pulsatile to mean shear stress and consequent variability in the production of NO.

Aortoiliac hemodynamic and morphologic adaptation to chronic spinal cord injury

Reduced lower limb blood flow and resistive hemodynamic conditions potentially promote aortic inflammation and aneurysmal degeneration. We used abdominal ultrasonography, magnetic resonance imaging, and computational flow modeling to determine the relationship between reduced infrarenal aortic blood flow in chronic spinal cord injury (SCI) subjects and risk for abdominal aortic aneurysm (AAA) disease. Aortic diameter in consecutive SCI subjects (n = 123) was determined via transabdominal ultrasonography. Aortic anatomic and physiologic data were acquired via magnetic resonance angiography (MRA; n = 5) and cine phase-contrast magnetic resonance flow imaging (n = 4) from SCI subjects whose aortic diameter was less than 3.0 cm by ultrasonography. Computational flow models were constructed from magnetic resonance data sets. Results were compared with those obtained from ambulatory control subjects (ultrasonography, n = 129; MRA/phase-contrast magnetic resonance flow imaging, n = 6) who were recruited at random from a larger pool of risk factor-matched individuals without known AAA disease. Age, sex distribution, and smoking histories were comparable between the SCI and control groups. In the SCI group, time since injury averaged 26 +/- 13 years (mean +/- SD). Aortic diameter was larger (P < .01), and the prevalence of large (> or = 2.5 cm; P < .01) or aneurysmal (> or = 3.0 cm; P < .05) aortas was greater in SCI subjects. Paradoxically, common iliac artery diameters were reduced in SCI subjects (< 1.0 cm; 48% SCI vs 26% control; P < .0001). Focal preaneurysmal enlargement was noted in four of five SCI subjects by MRA. Flow modeling revealed normal flow volume, biphasic and reduced oscillatory flow, slower pressure decay, and reduced wall shear stress in the SCI infrarenal aorta. Characteristic aortoiliac hemodynamic and morphologic adaptations occur in response to chronic SCI. Slower aortic pressure decay and reduced wall shear stress after SCI may contribute to mural degeneration, enlargement, and an increased prevalence of AAA disease.

Numerical Analysis of Wall Slip Effects on Flow of Newtonian and Non-Newtonian Fluids in Macro and Micro Contraction Channels

We performed numerical simulation to investigate the effects of wall slip on flow behaviors of Newtonian and non-Newtonian fluids in macro and micro contraction channels. The results show that the wall slip introduces different vortex growth for the flow in micro channel as compared to that in macro channel, which are qualitatively in agreement with experimental results. The effects of slip on bulk flow behaviors depend on rheological property of the fluid. For Newtonian fluid, the wall slip always reduces the vortex length, while for non-Newtonian fluid, the strength of the slip determines whether the vortex length is reduced or increased. Analyses on the velocity and stress fields confirm the channel size dependent phenomena, such as the reduction of wall shear stress with the decrease in channel size. With the increase in average shear rate, the Newtonian fluid shows the reduction of wall shear stress that increases in the same trend with slip velocity-wall shear stress function, while for non-Newtonian fluid, the effect of the slip is suppressed by shear thinning effect and, therefore, the reduction of wall shear stress is less sensitive to the change in average shear rate and slip velocity-wall shear stress function.

Effects of iodinated contrast media on common carotid and brachial artery blood flow and wall shear stress

The aim of our study was to evaluate the effect of the intravenous contrast media iomeprol on wall shear stress, blood flow and vascular parameters in the common carotid and brachial artery. Thirty outpatients undergoing thoracic or abdominal spiral CT scans were studied. The internal diameter and flow velocity of the common carotid and brachial artery were evaluated by ultrasound, and blood viscosity was measured before and after low osmolality iomeprol (Iomeron 350) injection. The wall shear stress, blood flow and pulsatility index were calculated. To test the differences between groups, the Wilcoxon rank test and Mann Whitney U test were applied. Blood viscosity decreased slightly, but significantly after contrast media (4.6+/-0.7 vs. 4.5+/-0.7 mPa.s, P = 0.02). Contrarily, blood flow and wall shear stress did not change in the common carotid artery, but significantly decreased in the brachial artery (0.9+/-0.4 vs. 0.6+/-0.3 ml/s, P < 0.0001, and 41.5+/-13.9 vs. 35.3+/-11.0 dynes/cm2, P < 0.002, respectively), whereas the pulsatility index significantly increased in the brachial artery (5.0+/-3.3 vs. 7.5+/-5.3, P < 0.001). Iomeprol injection causes blood flow and wall shear stress reduction of the brachial artery; the rise in the pulsatility index suggests an increase in peripheral vascular resistance. Further investigation is needed to evaluate whether these modifications can be clinically relevant.

Computational Fluid Dynamics: Hemodynamic Changes in Abdominal Aortic Aneurysm After Stent-Graft Implantation

The aim of this study was to demonstrate quantitatively and qualitatively the hemodynamic changes in abdominal aortic aneurysms (AAA) after stent-graft placement based on multidetector CT angiography (MDCT-A) datasets using the possibilities of computational fluid dynamics (CFD). Eleven patients with AAA and one patient with left-side common iliac aneurysm undergoing MDCT-A before and after stent-graft implantation were included. Based on the CT datasets, three-dimensional grid-based models of AAA were built. The minimal size of tetrahedrons was determined for grid-independence simulation. The CFD program was validated by comparing the calculated flow with an experimentally generated flow in an identical, anatomically correct silicon model of an AAA. Based on the results, pulsatile flow was simulated. A laminar, incompressible flow-based inlet condition, zero traction-force outlet boundary, and a no-slip wall boundary condition was applied. The measured flow volume and visualized flow pattern, wall pressure, and wall shear stress before and after stent-graft implantation were compared. The experimentally and numerically generated streamlines are highly congruent. After stenting, the simulation shows a reduction of wall pressure and wall shear stress and a more equal flow through both external iliac arteries after stenting. The postimplantation flow pattern is characterized by a reduction of turbulences. New areas of high pressure and shear stress appear at the stent bifurcation and docking area. CFD is a versatile and noninvasive tool to demonstrate changes of flow rate and flow pattern caused by stent-graft implantation. The desired effect and possible complications of a stent-graft implantation can be visualized. CFD is a highly promising technique and improves our understanding of the local structural and fluid dynamic conditions for abdominal aortic stent placement.

Numerical experiments on wall turbulence at low Reynolds number

A direct numerical simulation of a turbulent channel flow, with regularly spaced two-dimensional roughness elements mounted at the wall and perpendicular to the flow direction, was performed at a very low Reynolds number of Re
940 based on the centerline velocity and the full channel height. Using the lattice Boltzmann numerical algorithm, all essential scales were resolved with about 19·106 grid points (1155 x 129 x 128 in the x1, x2 and x3 directions). The computed results confirm the existence of turbulence at such a low Reynolds number. Turbulence persisted over the entire computation time, which was sufficiently long to prove its self-maintenance. By examination of statistical features of the flow across the anisotropy-in variant map, it was found that these coincide with conclusions emerging from the analysis of transition and breakdown to turbulence in a laminar boundary layer exposed to small, statistically stationary, neutrally stable axisymmetric disturbances with the stream wise intensity component ( u'1) lower than the intensities in the normal ( u'1) and span wise directions u'1< u'2 = u'3. To further support the concept and the results of
theoretical considerations of the laminar to turbulent transition process in wall-bounded flows using statistical techniques and to demonstrate its great potential for engineering, an additional simulation was performed of a plane channel flow with regularly spaced riblet elements mounted at the wall and aligned parallel with the flow direction. The supplementary simulation was done at a Reynolds number of Re = 6584 using about 250·106 grid points (4096 x 257 x 240). Analysis of the simulation results carried out across the flow region located in the mid plane between the riblet elements confirms the central result which lies in the root of the statistical dynamics of the velocity fluctuations in wall-bounded flows: when the velocity fluctuations close to the wall tend towards the one-component state, so that the stream wise intensity component is much larger than the intensities in the normal and span wise directions, u'1< u'2 = u'3, the turbulent dissipation rate vanishes at the wall, leading to a significant reduction of the wall shear stress. For the simulated flow case the local value of wall shear stress reduction was found to exceed the wall shear stress reduction SR
92% which corresponds to a fully developed laminar channel flow with smooth walls at the same Reynolds number.