The interactions between bloodstream and vascular structure on aortic dissecting aneurysmal model: A numerical study

Stent-graft implantation is an important means of clinical treatment for aortic dissecting aneurysm （ADA）. However, researches on fluid dynamics effects of stent were rare. Computer simulation was used to investigate the interactions between bloodstream and vascular structure in a stented ADA, which endures the periodic pulse velocity and pressure. We obtained and analyzed the flow velocity distribution, the wall displacement and wall stress in the ADA. By comparing the different results between a non-stented and a stented ADA, we found that the insertion of a vascular graft can make the location of maximum stress and displacement move from the aneurysm lumen wall to the artery wall, accompanied with a greatly decrease in value. These results imply that the placement of a stent-graft of any kind to oc-clude ADA will result in a decreased chance of rupture.     

Pulsatile flows in a lateral aneurysm anchored on a stented and curved parent vessel

We present particle tracking velocimetry measurements and flow visualization of pulsatile flow fields in a stented cerebrovascular lateral aneurysm model with a wide ostium anchored on a curved parent vessel. Among the stent parameters, the blocking ratioC _α ranging from 0% to 75% was selected to study its effect on the changes of intra-aneurysmal hemodynamics for the reference of minimally invasive endovascular aneurysm treatment. The Womersley number was 3.9 and the mean, peak, and minimal Reynolds numbers based on the bulk average velocity and diameter of the parent vessel were 600, 850, and 300, respectively. The results are characterized in terms of velocity vector field, coded streak images, region averaged velocity, vorticity, and wall shear stress. A critical range ofC _α related to the inflow location as well as the shape and number of intra-aneurysmal vortices is identified. The intra-aneurysmal flow activity, vortex strength, and wall shear stress are found to decrease with increasingC _α. Among theC _α examined,C _α=75% is the most favorable in attenuating the risk of aneurysmal rupture and promoting intra-aneurysmal thrombus.     

受支架支撑的血管管壁变形及应力分析

摘要：为了计算动脉粥样硬化和局部斑块形成的堵塞对血管壁工作状态的影响,本文根据血液流动的连续性方程、运动方程及管壁运动方程,在给定了血压波形函数的基础上,求得了狭窄血管管壁的径向位移及环向应力。分析了不同狭窄程度对血管壁变形及应力的影响;给出了不同狭窄情况下及局部斑块硬化程度不同时,血管植入支架所需的作用力。从而计算出了植入支架后血管壁的径向位移及应力状态。本文的研究结果可供临床上对狭窄血管植入支架后的变形与受力分析,和支架的正确安放参考,可避免发生堵塞严重或血管过渡硬化时,由于安放支架不当而使发生血管破裂的医疗事故。     

Tomographic particle image velocimetry investigation of the flow in a modeled human carotid artery bifurcation

Hemodynamic forces within the human carotid artery are well known to play a key role in the initiation and progression of vascular diseases such as atherosclerosis. The degree and extent of the disease largely depends on the prevailing three-dimensional flow structure and wall shear stress (WSS) distribution. This work presents tomographic PIV (Tomo-PIV) measurements of the flow structure and WSS in a physiologically accurate model of the human carotid artery bifurcation. The vascular geometry is reconstructed from patient-specific data and reproduced in a transparent flow phantom to demonstrate the feasibility of Tomo-PIV in a complex three-dimensional geometry. Tomographic reconstruction is performed with the multiplicative line-of-sight (MLOS) estimation and simultaneous multiplicative algebraic reconstruction (SMART) technique. The implemented methodology is validated by comparing the results with Stereo-PIV measurements in the same facility. Using a steady flow assumption, the measurement error and RMS uncertainty are directly inferred from the measured velocity field. It is shown that the measurement uncertainty increases for increasing light sheet thickness and increasing velocity gradients, which are largest near the vessel walls. For a typical volume depth of 6 mm (or 256 pixel), the analysis indicates that the velocity derived from 3D cross-correlation can be measured within ±2% of the maximum velocity (or ±0.2 pixel) near the center of the vessel and within ±5% (±0.6 pixel) near the vessel wall. The technique is then applied to acquire 3D-3C velocity field data at multiple axial locations within the carotid artery model, which are combined to yield the flow field and WSS in a volume of approximately 26 mm × 27 mm × 60 mm. Shear stress is computed from the velocity gradient tensor and a method for inferring the WSS distribution on the vessel wall is presented. The results indicate the presence of a complex and three-dimensional flow structure, with regions of flow separation and strong velocity gradients. The WSS distribution is markedly asymmetric confirming a complex swirling flow structure within the vessel. A comparison of the measured WSS with Stereo-PIV data returns an acceptable agreement with some differences in stress magnitude.     

Emeritus Professor Shan-Fu Shen,Cornell University

A numerical analysis of blood flow in a rigid artery has been performed to observe the variations in flow pattern and haemodynamic parameters under the influence of multiple (double) stenoses. The interspacing distance, degree of stenotic severity and Reynolds number of flow have been varied. It is found that two stenoses interact when the interspacing distance is lower than a critical value that corresponds to the redevelopment length of fully developed flow after the proximal stenosis. In the case of non-interacting stenoses the haemodynamic parameters, like the peak centreline velocity (representing the peak systolic velocity ratio in medical term), the maximum wall shear stress, region of low shear stress and the irrecoverable pressure drop at the stenosis site, repeat themselves at each individual stenosis. However, when the stenoses interact hydrodynamically because of their proximity, the parameters behave differently, which can lead to a different haemodynamic profile in the arteries and pose difficulties in their pathological interpretation. This work evaluates the influence of double stenoses on the variations in the key haemodynamic features under different degree of stenoses and interspacing distance between the stenoses.     

Mechanical, rheological, fatigue, and degradation behavior of PLLA, PGLA and PDGLA as materials for vascular implants

The biggest challenge in the treatment of arterial stenosis remains the issue of optimization of stent design. Despite continuous improvement in surgical techniques and use of intensive pharmacotherapy, the results of stent coronary interventions may be unsatisfactory, and long-term interaction of a metal implant with a blood vessel results in complications such as recurrent stenosis and thrombosis. Therefore, it is necessary to search for new materials and stent designs to obtain a stent capable of restoring flow in the vessel and disappearing after fulfilling its function. Such stent must also be compatible with the vessel wall to enable regeneration of new structure of endothelium and deeper artery layers damaged during implantation. Consequently, there is ongoing search for functional solutions with minimum effects of long-term implant-tissue interaction. In light of the above, the team investigated the possibility of using biodegradable polymers already mentioned in the literature as a construction material for vascular stent. The study used three polyhydroxyacids based on lactic acid and glycolic acid: poly(l-lactide), poly(lactide-co-glycolide) and poly(d,l-lactide-co-glycolide). The research focused on assessing changes in mechanical, thermomechanical, rheological, and fatigue properties during the process of hydrolytic degradation. The analysis also covered the rate of release of degradation products. The results of the conducted tests indicate the possibility of developing a vascular stent with biodegradable polymers.     

夹层动脉瘤及覆膜支架模型的流固耦合分析

腹主动脉瘤腹主动脉瘤(Abdominal Aortic Aneurysm,AAA)是危及病人生命的严重疾病,若主动脉瘤不加以治疗,瘤腔将不断长大而有破裂的危险,尽管目前对主动脉瘤的研究较多,但对主动脉夹层动脉瘤(Aortic Dissecting Aneruysm,ADA)的研究较少,本文在周期性脉动速度和压力条件下,对DNA内部流场及植入覆膜支架进行了流固耦合的数值模拟.得到了夹层动脉瘤内部流场的速度矢量分布,瘤壁上的位移、应力分布.同时对夹层动脉瘤植入覆膜支架前后进行了对比分析,覆膜支架的植入使得瘤壁上的最大应力和最大位移均从瘤腔壁面转移到管状动脉壁上,且数值大大下降,说明植入覆膜支架能很好的防止夹层动脉瘤破裂.     

Layered structure of turbulent plane wall jet

This paper investigates the layered structure of a turbulent plane wall jet at a distance from the nozzle exit. Based on the force balances in the mean momentum equation, the turbulent plane wall jet is divided into three regions: a boundary layer-like region (BLR) adjacent to the wall, a half free jet-like region (HJR) away from the wall, and a plug flow-like region (PFR) in between. In the PFR, the mean streamwise velocity is essentially the maximum velocity, and the simplified mean continuity and mean momentum equations result in a linear variation of the mean wall-normal velocity and Reynolds shear stress. In the HJR, as in a turbulent free jet, a proper scale for the mean wall-normal flow is the mean wall-normal velocity far from the wall and a proper scale for the Reynolds shear stress is the product of the maximum mean streamwise velocity and the velocity scale for the mean wall-normal flow. The BLR region can be divided into four sub-layers, similar to those in a canonical pressure-driven turbulent channel flow or shear-driven turbulent boundary layer flow. Building on the log-law for the mean streamwise velocity in the BLR, a new skin friction law is proposed for a turbulent wall jet. The new prediction agrees well with the correlation of Bradshaw and Gee (1960) over moderate Reynolds numbers, but gives larger skin frictions at higher Reynolds numbers.     

Structure of near wall turbulence downstream of a wall mounted protrusion: an interesting Reynolds stress suppression phenomena

A local suppression in the generation of near wall Reynolds stress is achieved by modifying the buffer region and sublayer (y ⁺ <30) of a turbulent pipe flow with a 16.4 wall unit high wall mounted protrusion. Multi-component, multi-point, time resolved laser Doppler velocimetry measurements are made in the undisturbed and modified ARL/PSU glycerin tunnel pipe flow at a Reynolds number of approximately 10000. A downstream converging flow field is produced by the divergence of the approaching mean flow around the protrusion. A pair of counter-rotating vortices, 15 wall units in diameter with common flow down, are generated by the protrusion and also contribute to the wall directed flow convergence. The convergence region is 15 wall units high and more than 100 wall units long and appears to decouple the near wall region from the outer turbulent wall layer. Locally, turbulent velocity fluctuations in the form of Reynolds stress producing events, sweeps and ejections, are retarded within this region. This results in a reduction in near wall uv Reynolds stress and local wall shear. Interestingly, the counter-rotating vortices act to increase turbulent diffusion in a manner which is uncorrelated with Reynolds stress generation.     

Application of the lattice Boltzmann method to flow in aneurysm with ring‐shaped stent obstacles

To resolve the characteristics of a highly complex flow, a lattice Boltzmann method with an extrapolation boundary technique was used in aneurysms with and without transverse objects on the upper wall, and results were compared with the non‐stented aneurysm. The extrapolation boundary concept allows the use of Cartesian grids even when the boundaries do not conform to Cartesian coordinates. To ease the code development and facilitate the incorporation of new physics, a new scientific programming strategy based on object‐oriented concepts was developed. The reduced flow, smaller vorticity magnitude and wall shear stress, and smaller du/dy near the dome of the aneurysm were observed when the proposed stent obstacles were used. The height of the stent obstacles was more effective to reduce the vorticity near the dome of the aneurysm than the width of the stent. The rectangular stent with 20% height‐of‐vessel radius was observed to be optimal and decreased the magnitude of the vorticity by 21% near the dome of the aneurysm. Copyright © 2008 John Wiley & Sons, Ltd.     

Flowfields in lateral aneurysm models arising from parent vessels with different curvatures using PTV

 Pulsatile and steady flowfields in a lateral aneurysm model arising from the parent vessel with radius of curvature to vessel diameter ratios of 2.5, 5, and ∞ are presented in terms of particle tracking velocimetry (PTV) measurements and flow visualization. The steady-flow case has a Reynolds number of 600 and the pulsatile-flow one has a Womersley number of 3.9 and Reynolds number of 600. It is found that there exist two opposite vortices and a single vortex in the aneurysms arising from a straight and a curved parent vessel, respectively. The intra-aneurysmal flow velocity, vorticity, and wall shear stresses increase with increasing curvature of the parent vessel. It is suggested from the present results that the lateral aneurysm arising from a straight or small-curvature parent vessel has a tendency to thrombosis whereas the lateral aneurysm arising from a large-curvature parent vessel is more risky. Received: 14 August 1996/Accepted: 17 January 1997     

Effects of an asymmetrical confined flow on a rectangular cylinder

The effects of an asymmetric confined flow on a cylinder of rectangular cross-section are investigated and discussed. Experiments are performed in a wind tunnel by placing cylinders of different cross-sections at various elevations from the floor of the test-section. The Reynolds number is varied within the range 6×10³–4×10⁴. Forces exciting the cylinder are measured by built-in dynamometers placed inside the cylinder structure. The flow is characterized by mean and fluctuating local velocity components to define the inflow distribution and the ensuing wake region. The mean dimensionless force coefficients are then calculated and analyzed. The frequency analysis of the force components acting on the cylinder provides the dynamic characterization of the loading and of the wake shedding. The experimental results highlight that the presence of the wall strongly influences the system dynamics also when the cylinder is placed at a relatively large elevation from the wall itself. The cylinder aspect ratio governs effects of the wall condition on the force coefficients and the Strouhal number.     

Numerical simulation of an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder

This article presents a numerical investigation of turbulent flow in an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder. The governing equations were discretized by the finite-volume method and SIMPLER method was applied to solve the equations on a staggered grid. The turbulent flow was numerically simulated using the standard k–ε, Abe–Kondoh–Nagano (AKN) and Shear Stress Transport (SST) turbulence models. The comparisons made between numerical results and experimental measurements showed that the SST model is superior to other models in the present calculation.Computations were performed for three different Reynolds numbers of 6000, 10 000 and 20 000 based on the cylinder diameter. To our knowledge, this study represents the first numerical investigation of the present flow configuration. The computational results were validated with the available experimental data of reattachment length, mean velocity distribution and wall static pressure coefficient in the turbulent blunt circular cylinder flows. Further, other characteristics of the flow, such as turbulent kinetic energy, pressure, streamlines, and the velocity vectors are discussed.The results show that the main characteristics of the turbulence flow in the separation region, such as reattachment length or velocity profiles, are nearly independent of the Reynolds number. The obtained results showed that a secondary separation bubble may appear in the main separation bubble near the leading edge. Furthermore, it was found that the turbulent kinetic energy has a large effect on the formation of the secondary bubble.     

BOUNDARY TREATMENT AND AN EFFICIENT PRESSURE ALGORITHM FOR INTERNAL TURBULENT FLOWS USING THE PDF METHOD

The generalized Langevin model, which is used to model the motion of stochastic particles in the velocity–composition joint probability density function (PDF) method for reacting turbulent flows, has been extended to incorporate solid wall effects. Anisotropy of Reynolds stresses in the near-wall region has been addressed. Numerical experiments have been performed to demonstrate that the forces in the near-wall region of a turbulent flow cause the stochastic particles approachi ng a solid wall to reverse their direction of motion normal to the wall and thereby, leave the near-wall layer. This new boundary treatment has subsequently been implemented in a full-scale problem to prove its validity. The test problem considered here is that of an isothermal, non-reacting turbulent flow in a two-dimensional channel with plug inflow and a fixed back-pressure. An efficient pressure correction method, developed in the spirit of the PISO algorithm, has been implemented. The pressure correction strategy is easy to implement and is completely consistent with the time- marching scheme used for the solution of the Lagrangian momentum equations. The results show remarkable agreement with both k–ϵ and algebraic Reynolds stress model calculations for the primary velocity. The secondary flow velocity and the turbulent moments are in better agreement with the algebraic Reynolds stress model predictions than the k– ϵ predictions. © 1997 by John Wiley & Sons, Ltd.     

Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method

A turbulent channel flow and the flow around a cubic obstacle are calculated by the moving particle semi‐implicit method with the subparticle‐scale turbulent model and a wall model, which is based on the zero equation RANS (Reynolds Averaged Navier‐Stokes). The wall model is useful in practical problems that often involve high Reynolds numbers and wall turbulence, because it is difficult to keep high resolution in the near‐wall region in particle simulation. A turbulent channel flow is calculated by the present method to validate our wall model. The mean velocity distribution agrees with the log‐law velocity profile near the wall. Statistical values are also the same order and tendency as experimental results with emulating viscous layer by the wall model. We also investigated the influence of numerical oscillations on turbulence analysis in using the moving particle semi‐implicit method. Finally, the turbulent flow around a cubic obstacle is calculated by the present method to demonstrate capability of calculating practical turbulent flows. Three characteristic eddies appear in front of, over, and in the back of the cube both in our calculation and the experimental result that was obtained by Martinuzzi and Tropea. Mean velocity and turbulent intensity profiles are predicted in the same order and have similar tendency as the experimental result. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental Investigation on Turbulent Structure of Drag Reducing Channel Flow with Blowing Polymer Solution from the Wall

Turbulent drag reducing flow with blowing polymer solution from the channel wall was investigated experimentally using particle image velocimetry (PIV). Experiments were carried out with varying conditions of blowing polymer solution (e.g. weight concentration of polymer solution). Reynolds number based on the channel height and mean velocity was set to 20000 and 40000. When the polymer solution was blown from the channel wall, streamwise velocity fluctuation little increased, but wall-normal velocity fluctuation, Reynolds shear stress and correlation coefficient decreased significantly only near the blower wall. This behavior corresponds to the decrease of the ejection and sweep in the near-wall region observed by the investigation of instantaneous velocity map. On the contrary, this characteristic behavior was not observed at a position away from the blower wall (y/(H/2) > 0.4) and the scatter plot was almost the same as that of the water flow in this region. These results suggest that there are two regions in the drag reducing flow with blowing polymer solution from the wall; one is a non-Newtonian region which exists near the blower wall, and the other is a Newtonian region at a distance from the wall. The non-Newtonian region plays a key role in the drag reduction by the blowing polymer solution.     

A two-fluid model for pulsatile flow in catheterized blood vessels

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.     

A bypass wake induced laminar/turbulent transition

The process of laminar to turbulent transition induced by a von Karman vortex street wake, was studied for the case of a flat plate boundary layer. The boundary layer developed under zero pressure gradient conditions. The vortex street was generated by a cylinder positioned in the free stream. An X-type hot-wire probe located in the boundary layer, measured the streamwise and normal to the wall velocity components. The measurements covered two areas; the region of transition onset and development and the region where the wake and the boundary layer merged producing a turbulent flow. The evolution of Reynolds stresses and rms-values of velocity fluctuations along the transition region are presented and discussed. From the profiles of the Reynolds stress and the mean velocity profile, a ‘negative' energy production region along the transition region, was identified. A quadrant splitting analysis was applied to the instantaneous Reynolds stress signals. The contributions of the elementary coherent structures to the total Reynolds stress were evaluated, for several x-positions of the near wall region. Distinct regions in the streamwise and normal to the wall directions were identified during the transition.     

Numerical studies of fluid flow through tubes with double constrictions

The flow fields in the neighbourhood of double constrictions in a circular cylindrical tube were studied numerically. The effects on the streamline, velocity and vorticity distributions as the flow passes through the constrictions in the tube were studied in the Reynolds number range 5–200. Double constrictions with dimensionless spacing ratios of 1, 2, 3 and ∞ were studied for a 50% constriction. It is noted that when the Reynolds number is below 10, no recirculation region is formed in the above constricted flow. For Reynolds numbers greater than 10, a recirculation region forms downstream of each of the constrictions. For constriction spacing ratios of 1, 2, and 3, when the Reynolds number is high, a recirculation region spreads between the valley of the constrictions. The recirculation region formed between the two constrictions has a diminishing effect on the generation of wall vorticity near the second constriction area. In general, the peak value of wall vorticity is found slightly upstream of each of the constrictions. When the Reynolds number is increased, the peak wall vorticity value increases and its location is moved upstream. Maximum wall vorticity generated by the first constriction is found to be always greater than the maximum wall vorticity generated by the second constriction. The extent of this spreading of the recirculation region from the first constriction and its effects on the second constriction depend on the constriction spacing ratio and the flow Reynolds number.     

倾斜吹吸控制下湍流边界层减阻的直接数值模拟

雷诺切应力是壁湍流高摩擦阻力的重要来源, 有理论认为可以通过壁面生成负雷诺应力(数值上为正)的方式来削弱湍流流场中雷诺应力的分布, 以此获得流动减阻. 而通过对雷诺平均运动方程的法向二次积分, 可以发现壁面生成正雷诺应力(数值上为负)对壁面摩擦阻力系数才有负贡献. 文中在湍流边界层流动的控制区域下边界设置一系列倾斜狭缝, 利用该装置通过周期性吹吸的方法产生壁面生成正(负)雷诺应力, 并采用直接数值模拟方法考察和验证上文提到的减阻理论. 文中采用的湍流边界层流动模型, 其流动雷诺数(基于外流速度及动量损失厚度)从300 发展到860. 文中通过多组数值模拟算例, 考察了射流强度和频率对壁面摩擦阻力系数的影响, 并对比了壁面生成正或负雷诺应力对流动的影响. 研究表明, 壁面生成正雷诺应力控制的减阻率能达到3.26, 而壁面生成负雷诺应力控制的减阻效果较壁面生成正雷诺应力控制的要差; 壁面生成的正雷诺应力对壁面摩擦阻力有负贡献, 而壁面生成的负雷诺应力对壁面摩擦阻力有正贡献; 通过考察控制的收支比, 发现控制方案不能获得能量净收益.