The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Re_θ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.     

Numerical Simulation of the Flow in the Carotid Bifurcation

Pulsatile flow through the three-dimensional carotid artery bifurcation has been studied using the artificial-compressibility method. The part of the flow with large inertia bifurcates and creates a very steep velocity gradient on the divider walls. The flow near the nondivider walls slows down because of dilation of the cross section and strong adverse pressure gradient. The secondary flow in the bifurcation region, which is similar to the Dean vortex in a curved pipe, is strong and very complex. The region of separation is not closed for the cases of steady and pulsatile flow. The extent of this region is small and the streamlines are smooth except in the decelerating phase of systole. The change of common-internal bifurcation angle (25°± 15°) for fixed internal–external bifurcation angle of 50° has more effect on the shear on the bifurcation-internal carotid wall and less effect on the shear on the common-internal carotid wall. The mean wall shears are not sensitive to the input flow-rate waveform for constant mean flow, but the maximum wall shears are. Received 3 January 1997 and accepted 11 April 1997     

Large-scale tomographic particle image velocimetry using helium-filled soap bubbles

To measure large-scale flow structures in air, a tomographic particle image velocimetry (tomographic PIV) system for measurement volumes of the order of one cubic metre is developed, which employs helium-filled soap bubbles (HFSBs) as tracer particles. The technique has several specific characteristics compared to most conventional tomographic PIV systems, which are usually applied to small measurement volumes. One of them is spot lights on the HFSB tracers, which slightly change their position, when the direction of observation is altered. Further issues are the large particle to voxel ratio and the short focal length of the used camera lenses, which result in a noticeable variation of the magnification factor in volume depth direction. Taking the specific characteristics of the HFSBs into account, the feasibility of our large-scale tomographic PIV system is demonstrated by showing that the calibration errors can be reduced down to 0.1 pixels as required. Further, an accurate and fast implementation of the multiplicative algebraic reconstruction technique, which calculates the weighting coefficients when needed instead of storing them, is discussed. The tomographic PIV system is applied to measure forced convection in a convection cell at a Reynolds number of 530 based on the inlet channel height and the mean inlet velocity. The size of the measurement volume and the interrogation volumes amount to 750 mm × 450 mm × 165 mm and 48 mm × 48 mm × 24 mm, respectively. Validation of the tomographic PIV technique employing HFSBs is further provided by comparing profiles of the mean velocity and of the root mean square velocity fluctuations to respective planar PIV data.     

Multiphase non‐Newtonian effects on pulsatile hemodynamics in a coronary artery

Hemodynamic stresses are involved in the development and progression of vascular diseases. This study investigates the influence of mechanical factors on the hemodynamics of the curved coronary artery in an attempt to identify critical factors of non‐Newtonian models. Multiphase non‐Newtonian fluid simulations of pulsatile flow were performed and compared with the standard Newtonian fluid models. Different inlet hematocrit levels were used with the simulations to analyze the relationship that hematocrit levels have with red blood cell (RBC) viscosity, shear stress, velocity, and secondary flow. Our results demonstrated that high hematocrit levels induce secondary flow on the inside curvature of the vessel. In addition, RBC viscosity and wall shear stress (WSS) vary as a function of hematocrit level. Low WSS was found to be associated with areas of high hematocrit. These results describe how RBCs interact with the curvature of artery walls. It is concluded that although all models have a good approximation in blood behavior, the multiphase non‐Newtonian viscosity model is optimal to demonstrate effects of changes in hematocrit. They provide a better stimulation of realistic blood flow analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

Advantageous swirling flow in 45° end-to-side anastomosis

The effects of swirling flow on the flow field in 45° end-to-side anastomosis are experimentally investigated using a particle image velocimetry technique to reveal fluid dynamic advantages of swirling flow in the vascular graft. Non-swirling Poiseuille inlet flow unnecessarily induces pathological hemodynamic features, such as high wall shear stress (WSS) at the ‘bed’ side and large flow separation at the ‘toe’ side. The introduction of swirling flow is found to equalize the asymmetric WSS distribution and reduces the peak magnitude of WSS. In particular, the intermediate swirling intensity of S = 0.45 induces the most uniform axial velocity and WSS distributions compared with weaker or stronger swirling flows, which addresses the importance of proper selection of swirling intensity in the vascular graft to obtain optimum flow fields at the host vessel. In addition, swirling flow reduces the size of flow separation because it disturbs the formation of Dean-type vortices in secondary flow and inhibits secondary flow collision. The beneficial fluid dynamic features of swirling flow obtained in this study are helpful for designing better vascular graft suppressing pathological hemodynamic features in the recipient host vessel.     

An efficient simultaneous reconstruction technique for tomographic particle image velocimetry

To date, Tomo-PIV has involved the use of the multiplicative algebraic reconstruction technique (MART), where the intensity of each 3D voxel is iteratively corrected to satisfy one recorded projection, or pixel intensity, at a time. This results in reconstruction times of multiple hours for each velocity field and requires considerable computer memory in order to store the associated weighting coefficients and intensity values for each point in the volume. In this paper, a rapid and less memory intensive reconstruction algorithm is presented based on a multiplicative line-of-sight (MLOS) estimation that determines possible particle locations in the volume, followed by simultaneous iterative correction. Reconstructions of simulated images are presented for two simultaneous algorithms (SART and SMART) as well as the now standard MART algorithm, which indicate that the same accuracy as MART can be achieved 5.5 times faster or 77 times faster with 15 times less memory if the processing and storage of the weighting matrix is considered. Application of MLOS-SMART and MART to a turbulent boundary layer at Re _θ = 2200 using a 4 camera Tomo-PIV system with a volume of 1,000 × 1,000 × 160 voxels is discussed. Results indicate improvements in reconstruction speed of 15 times that of MART with precalculated weighting matrix, or 65 times if calculation of the weighting matrix is considered. Furthermore the memory needed to store a large weighting matrix and volume intensity is reduced by almost 40 times in this case.     

Comparison between computational fluid dynamics,fluid–structure interaction and computational structural dynamics predictions of flow-induced wall mechanics in an anatomically realistic cerebral aneurysm model

Haemodynamically induced stress plays an important role in the progression and rupture of cerebral aneurysms. The current work describes computational fluid dynamics (CFD), fluid–structure interaction (FSI) and computational structural dynamics (CSD) simulations in an anatomically realistic model of a carotid artery with two saccular cerebral aneurysms in the ophthalmic region. The model was obtained from three-dimensional (3D) rotational angiographic imaging data. CFD and FSI were studied under a physiologically representative waveform of inflow. The arterial wall was assumed elastic or hyperelastic, as a 3D solid or as a shell depending on the type of modelling used. The flow was assumed to be laminar, non-Newtonian and incompressible. The CFD, FSI and CSD models were solved with the finite elements package ADINA. Predictions of velocity field and wall shear stress (WSS) on the aneurysms made using CFD and FSI were compared. The CSD model of the aneurysms using complete geometry was compared with isolated aneurysm models. Additionally, the effects of hypertensive pressure on CSD aneurysm models are also reported. The vortex structure, WSS, effective stress, strain and displacement of the aneurysm walls showed differences, depending on the type of modelling used.     

局部扩张动脉管血液振荡流的切应力分布

本文求解局部缓慢扩张动脉管中血液振荡流的基本方程，得到血管内血液的流速与压力梯度的关系。通过导出压力梯度沿局部扩张管轴向的变化特性。建立利用扩张段上游血管均匀段中心流速波形确定局部扩张管中血液流的速度和切应力分布的方法，文章以人体颈动脉余弦扩张为例进行分析。详细讨论了局部扩张对血管壁切应力及其梯度分布的影响。数值结果表明，在与刚性均匀管中管壁切应力沿轴向保持不变不同，在局部扩张段，管壁切应力将随着血管半径的增大而减小，因而管壁切应力梯度一般不为零，甚至在某些位置达到相当大的数值。另外，随着血管扩张程度的增加，管壁切应力还将进一步减小，而且管壁切应力梯度也将进一步增大，血管扩张导致管壁切应力的这些变化将直接影响血管壁的结构和功能，使其产生适应性的变化。     

PIV-based pressure fluctuations in the turbulent boundary layer

The unsteady pressure field is obtained from time-resolved tomographic particle image velocimetry (Tomo-PIV) measurement within a fully developed turbulent boundary layer at free stream velocity of U _???=?9.3?m/s and Re_???=?2,400. The pressure field is evaluated from the velocity fields measured by Tomo-PIV at 10?kHz invoking the momentum equation for unsteady incompressible flows. The spatial integration of the pressure gradient is conducted by solving the Poisson pressure equation with fixed boundary conditions at the outer edge of the boundary layer. The PIV-based evaluation of the pressure field is validated against simultaneous surface pressure measurement using calibrated condenser microphones mounted behind a pinhole orifice. The comparison shows agreement between the two pressure signals obtained from the Tomo-PIV and the microphones with a cross-correlation coefficient of 0.6 while their power spectral densities (PSD) overlap up to 3?kHz. The impact of several parameters governing the pressure evaluation from the PIV data is evaluated. The use of the Tomo-PIV system with the application of three-dimensional momentum equation shows higher accuracy compared to the planar version of the technique. The results show that the evaluation of the wall pressure can be conducted using a domain as small as half the boundary layer thickness (0.5??₉₉) in both the streamwise and the wall normal directions. The combination of a correlation sliding-average technique, the Lagrangian approach to the evaluation of the material derivative and the planar integration of the Poisson pressure equation results in the best agreement with the pressure measurement of the surface microphones.     

Dynamic NMR microscopy measurement of the dynamics and flow partitioning of colloidal particles in a bifurcation

The flow and distribution of Newtonian, polymeric and colloid suspension fluids at low Reynolds numbers in bifurcations has importance in a wide range of disciplines, including microvascular physiology and microfluidic devices. A bifurcation consisting of circular capillaries laser etched into a hard polymer with inlet diameter 2.50 ± 0.01 mm, bifurcating to a small diameter outlet of 0.76 ± 0.01 mm and a large diameter outlet of 1.25 ± 0.01 mm is examined. Four distinct fluids (water, 0.25%wt xanthan gum, 8 and 22%vol hard-sphere colloidal suspensions) are flowed at flow rates from 10 to 30 ml/h corresponding to Reynolds numbers based on the entry flow from 0.001 to 8. PGSE NMR techniques are applied to obtain dynamic images of the fluids inside the bifurcation with spatial resolution of 59 × 59 μm/pixel in plane over a 200-μm-thick slice. Velocity in all three spatial directions is examined to determine the impact of secondary flows and characterize the transport in the bifurcation. The velocity data provide direct measurement of the volumetric distribution of the flow between the two channels as a function of flow rate. Water and the 8% colloidal suspension show a constant distribution with increasing flow rate, the xanthan gum shows an increase in fluid going into the larger outlet with higher flow rate, and the 22% colloidal suspension shows a decrease in fluid entering the larger channel with higher flow rate. For the colloidal particle flow, the distribution of colloid particles down the capillary is determined by examining the spectrally resolved propagator for the oil inside the core–shell particles in a direction perpendicular to the axial flow. Using dynamic magnetic resonance microscopy, the potential for using magnetic resonance for “particle counting” in a microscale bifurcation is thus demonstrated.     

颈动脉分支的血流动力学数值模拟

采用有限元法数值模拟颈动脉分支的血流动力学。根据在体测量的实际尺寸来构造颈动脉分支的几何模型，以保持模型的解剖精确度；利用在体测量的颈内动脉和颈外动脉流量波形以及主颈动脉的压力波形来确定数值计算的边界条件，以保持数值计算的生理真实性。关注的重点是颈动脉窦内的局部血流形态、二次流和壁面剪应力。在心脏收缩的减速期和舒张期的某些时刻，颈动脉窦中部外侧壁面附近产生了流动分离，形成了一个低速回流区。该流动分离是瞬态的，导致了壁面剪应力的振荡，其振荡范围在-2～6dyn／cm^2之间。同时，颈动脉窦中部横截面内的二次流存在于整个心动周期，最大的二次流速度为同时刻轴向速度平均值的1／3左右。     

Numerical simulation of pulsatile non-Newtonian flow in the carotid artery bifurcation

Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact, however, the blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them, the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10 s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had verysimilar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.     

Numerical study on the effect of initial flow velocity on liquid film thickness of accelerated slug flow in a micro tube

Numerical simulation of air–water slug flows accelerated from steady states with different initial velocities in a micro tube is conducted. It is shown that the liquid film formed between the gas bubble and the wall in an accelerated flow is significantly thinner than that in a steady flow at the same instantaneous capillary number. Specifically, the liquid film thickness is kept almost unchanged just after the onset of acceleration, and then gradually increases and eventually converges to that of an accelerated flow from zero initial velocity. Due to the flow acceleration, the Stokes layer is generated from the wall, and the instant velocity profile can be given by superposition of the Stokes layer and the initial parabolic velocity profile of a steady flow. It is found that the velocity profile inside a liquid slug away from the bubble can be well predicted by the analytical solution of a single-phase flow with acceleration. The change of the velocity profile in an accelerated flow changes the balance between the inertia, surface tension and viscous forces around the meniscus region, and thus the resultant liquid film thickness. By introducing the displacement thickness, the existing correlation for liquid film thickness in a steady flow (Han and Shikazono, 2009) is extended so that it can be applied to a flow with acceleration from an arbitrary initial velocity. It is demonstrated that the proposed correlation can predict liquid film thickness at Re < 4600 within the range of ±10% accuracy.     

Two-phase structure above hot surfaces in jet impingement boiling

Jet impingement boiling is very efficient in cooling of hot surfaces as a part of the impinging liquid evaporates. Several studies have been carried out to measure and correlate the heat transfer to impinging jets as a function of global parameters such as jet subcooling, jet velocity, nozzle size and distance to the surface, etc. If physically based mechanistic models are to be developed, studies on the fundamentals of two-phase dynamics near the hot surface are required. In the present study the vapor–liquid structures underneath a subcooled (20 K) planar (1 mm × 9 mm) water jet, impinging the heated plate vertically with a velocity of 0.4 m/s, were analyzed by means of a miniaturized optical probe. It has a tip diameter of app. 1.5 μm and is moved toward the plate by a micrometer device. The temperature controlled experimental technique enabled steady-state experiments in all boiling regimes. The optical probe data provides information about the void fraction, the contact frequencies and the distribution of the vapor and liquid contact times as a function of the distance to the surface. The measured contact frequencies range from 40 Hz at the onset of nucleate boiling to nearly 20,000 Hz at the end of the transition boiling regime. Due to condensation in the subcooled jet vapor disappears at a distance to the surface of app. 1.2 mm in nucleate boiling. This vapor layer becomes smaller with increasing wall superheat. In film boiling a vapor film thickness of 8 ± 2 μm was found.     

LDV measurements in lateral model aneurysms of various sizes

 Laser Doppler velocimetry (LDV) measurements are presented of three-dimensional flow fields in lateral model aneurysms arising from a straight parent vessel at a 90° angle. The flow considered was pulsatile and the aneurysm wall was rigid. The mean, peak, and minimal Reynolds numbers based on the bulk average velocity and diameter of the parent vessel were 550, 790, and 375, respectively. Comparisons among present in vitro studies, previous in vitro studies, computational simulations, and in vivo studies were made. It was found that the inflow angle into the lateral aneurysm, the maximum wall shear stress acting on the distal lip of the lateral aneurysm, and the intra-aneurysmal vortical motion increased with decreasing aneurysm size. This fact together with the impingement bifurcation of the inflow at the aneurysm dome provide possible hemodynamic factors for the rupture of the lateral aneurysm at small critical size. Received: 15 March 1996/Accepted: 13 March 1997     

动脉中非平稳流动壁面剪切力及其Hilbert-Huang变换

本文通过数值方法求解均匀动脉中的非平稳脉动流,给出了通过测量非平稳脉动血流量确定壁面切应力的方法.作为算例,采用实测的大鼠颈总动脉流量信号,求出了均匀动脉壁面切应力波形.进一步对求得的切应力波形进行经验模态分解(EMD),得到了切应力波形的各内在模态(IMF),以及Hilbert幅值谱.从切应力波形经Hilbert-Huang变换得到的IMF和Hilbert谱图可以明显地看出切应力各频率成分的物理意义.所得结果为进一步深入研究非平稳脉动切应力与血管重建的关系提供了一种方法学基础.     

Study on the effect of steady,simple pulsatile and physiological pulsatile flows through a stenosed artery

In the present paper, the comparison of steady, simple pulsatile flow and physiological pulsatile flow on flow reversal zone and hemodynamic wall parameters [wall shear stress (WSS) and oscillatory shear index (OSI)] for the progression of the disease, atherosclerosis has been investigated numerically. The governing equations have been solved by finite volume method. For the numerical analysis, Womersley number, Reynolds number and percentage of restriction are taken as 10, 100 and 50 % respectively. From this study it is revealed that the separated flow from the stenosis strongly depends on inlet flow situations, the maximum chance of deposition of plaque material due to streamline contour is higher at time step t* = 0.75 for simple pulsatile flow and at time step t* = 0 for physiological pulsatile flow and this chance is lower in case of steady flow. The effect of WSS on the disease is higher in physiological pulsatile flow compared to steady as well as simple pulsatile flow. The maximum possibility of initiation as well as progression for atherosclerosis in arterial wall due to high WSS takes place at t* = 0.25 for physiological pulsatile flow. OSI indicates same length of separation for two cases of transient flow, but the rate of cyclic departure of WSS is higher in case of physiological pulsatile flow.     

窦部对称狭窄对颈动脉内流场影响的数值研究

以颈动脉分岔血管为例，采用数值方法研究了窦部环缩狭窄之后的流场分布情况，并和正 常血管情况下的流场分布进行了比较. 结果表明，采用环缩方式给颈动脉分岔血管施加对称 的狭窄改变了颈动脉窦内流场，特别是壁面剪应力的分布规律. 低剪应力区出现在狭窄段之 后的窦内，并且沿整个周向均匀分布. 根据低剪应力和动脉粥样硬化的关系，指出： 若人为地给颈动脉窦内施加对称狭窄，则脂质沉积将在狭窄下游的窦内沿周向轴对称 发展. 为了更真实地反映颈动脉窦内的狭窄，建议根据动脉血管中的实际狭窄情况，采用非 对称的狭窄分布模式.     

A carbon nanotube sensor for wall shear stress measurement

A novel carbon nanotube (CNT) sensor is being developed to measure the mean and fluctuating wall shear stress (WSS) in a turbulent boundary layer. The CNT WSS sensor is based on the thermal principle and featured by high spatial and temporal resolutions (in the order of nm and kHz, respectively), low power consumption (in the order of μW), and a compact fabrication process compared with traditional WSS measurement sensors. The CNT WSS-sensing element was characterized in detail before its calibration. The CNT sensor was operated under a constant temperature (CT) operation mode and an overheat ratio range of −0.15 to −0.19 and calibrated in a fully developed turbulent channel flow. It has been observed for the first time in a macroscopic flow that the sensor output power is approximately proportional to the 1/3 powered WSS, as expected for a thermal-principle-based WSS sensor, and the wall shear stress measurement is demonstrated for a low Reynolds number flow.     

A Parallel 3D Unsteady Flow Analysis in an Asymmetrically Constricted Vessel

In this study, parallel computation of unsteady incompressible flow in an asymmetrically constricted 3D vessel has been presented. A time accurate cell centered finite volume method (FVM) in conjunction with pseudo-compressibility technique and Roe's flux difference splitting of nonlinear terms has been employed for solving the Navier-Stokes (NS) equations on the multiple instruction multiple data (MIMD) machine VPP700. The influence of Reynolds' number ( Re ) and the Strouhal number ( St ) on flow dynamic factors like wall pressure (WP), wall shear stress (WSS), central axis velocity (CAV), etc., have been analyzed. Three-dimensional (3D) features in the formation and detachment of separation zones, which are sensitive to both Re and St have been noticed on the diverging wall of the constriction.