Modeling transition to turbulence in eccentric stenotic flows

Mean flow predictions obtained from a host of turbulence models were found to be in poor agreement with recent direct numerical simulation results for turbulent flow distal to an idealized eccentric stenosis. Many of the widely used turbulence models, including a large eddy simulation model, were unable to accurately capture the poststenotic transition to turbulence. The results suggest that efforts toward developing more accurate turbulence models for low-Reynolds number, separated transitional flows are necessary before such models can be used confidently under hemodynamic conditions where turbulence may develop.     

Augmentation of sickling process due to turbulent blood flow.

The purpose of this study was to determine if the fluid mechanical stresses associated with turbulent blood flow can contribute to the sickling process. Blood from seven patients with sickle cell disease was subjected to intermediate and high levels of turbulent flow in vitro. Turbulence was quantitated by hot film anemometry. Control samples showed 20 +/- 3% sickled cells. Cells subjected to intermediate levels of turbulent flow showed 26 +/- 4% sickling (P less than 0.01); and blood subjected to high intensities of turbulence showed 31 +/- 4% sickling (P less than 0.01). A quantitative count by electronmicroscopy, performed in one patient, showed polymerization of the hemoglobin indicative of sickling in more cells subjected to turbulence than in the control sample. A turbulence-reducing agent, polyethylene oxide, diminished the augmentation of the sickling process as it reduced turbulence at comparable Reynolds numbers. These results support the hypothesis that a deleterious effect upon hemoglobin SS erythrocytes may occur due to the mechanical stresses of turbulent flow. The agitation associated with turbulent flow presumably modifies the stabilizing factors of the intracellular colloidal solution of hemoglobin, thereby contributing to sol-gel transformation. Such hydrodynamic stresses may supplement the previously described factors which contribute to sickle cell crises.     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

Turbulence detection in a stenosed artery bifurcation by numerical simulation of pulsatile blood flow using the low-Reynolds number turbulence model

The pulsatile blood flow in a partially blocked artery is significantly altered as the flow regime changes through the cardiac cycle. This paper reports on the application of a low-Reynolds turbulence model for computation of physiological pulsatile flow in a healthy and stenosed carotid artery bifurcation. The human carotid artery was chosen since it has received much attention because atherosclerotic lesions are frequently observed. The Wilcox low-Re k-omega turbulence model was used for the simulation since it has proven to be more accurate in describing transition from laminar to turbulent flow. Using the FIDAP finite element code a validation showed very good agreement between experimental and numerical results for a steady laminar to turbulent flow transition as reported in a previous publication by the same authors. Since no experimental or numerical results were available in the literature for a pulsatile and turbulent flow regime, a comparison between laminar and low-Re turbulent calculations was made to further validate the turbulence model. The results of this study showed a very good agreement for velocity profiles and wall shear stress values for this imposed pulsatile laminar flow regime. To explore further the medical aspect, the calculations showed that even in a healthy or non-stenosed artery, small instabilities could be found at least for a portion of the pulse cycle and in different sections. The 40% and 55% diameter reduction stenoses did not significantly change the turbulence characteristics. Further results showed that the presence of 75% stenoses changed the flow properties from laminar to turbulent flow for a good portion of the cardiac pulse. A full 3D simulation with this low-Re-turbulence model, coupled with Doppler ultrasound, can play a significant role in assessing the degree of stenosis for cardiac patients with mild conditions.     

The effect of a turbulent jet on gas transport during oscillatory flow

Axial mass transport due to the combined effects of flow oscillation and a turbulent jet was studied both experimentally and with a simple theoretical model. The experiments show that the distance over which turbulence enhances transport is greatly increased by flow oscillation, and is particularly sensitive to tidal volume. The jet flow rate and jet configuration are relatively less important. To analyze the results, the region influenced by the jet is divided into two zones: a near field in which the time-mean flow velocities are larger than the turbulent fluctuations, and a far field where the time-mean flow is essentially zero. In the far field, axial mass transport is increased due to the turbulence which decays in strength away from the jet. When oscillatory flow is superimposed upon the steady jet flow, the turbulence in the far field interacts with the flow oscillations to augment the transport of turbulence energy and of mass. This transport enhancement is modeled by introducing an effective axial diffusivity analogous to that used in laminar oscillatory flow.     

Turbulence modeling in three-dimensional stenosed arterial bifurcations

Under normal healthy conditions, blood flow in the carotid artery bifurcation is laminar. However, in the presence of a stenosis, the flow can become turbulent at the higher Reynolds numbers during systole. There is growing consensus that the transitional k-omega model is the best suited Reynolds averaged turbulence model for such flows. Further confirmation of this opinion is presented here by a comparison with the RNG k-epsilon model for the flow through a straight, nonbifurcating tube. Unlike similar validation studies elsewhere, no assumptions are made about the inlet profile since the full length of the experimental tube is simulated. Additionally, variations in the inflow turbulence quantities are shown to have no noticeable affect on downstream turbulence intensity, turbulent viscosity, or velocity in the k-epsilon model, whereas the velocity profiles in the transitional k-omega model show some differences due to large variations in the downstream turbulence quantities. Following this validation study, the transitional k-omega model is applied in a three-dimensional parametrically defined computer model of the carotid artery bifurcation in which the sinus bulb is manipulated to produce mild, moderate, and severe stenosis. The parametric geometry definition facilitates a powerful means for investigating the effect of local shape variation while keeping the global shape fixed. While turbulence levels are generally low in all cases considered, the mild stenosis model produces higher levels of turbulent viscosity and this is linked to relatively high values of turbulent kinetic energy and low values of the specific dissipation rate. The severe stenosis model displays stronger recirculation in the flow field with higher values of vorticity, helicity, and negative wall shear stress. The mild and moderate stenosis configurations produce similar lower levels of vorticity and helicity.     

Three-dimensional visualization of stationary flow behind artificial heart valves]

The visualization and quantitative analysis of flow offers a possibility for the hydrodynamic characterization of artificial heart valves. Different types of valves can be compared if velocity profile and the turbulent shear stress caused by the prosthesis are known. The tracer technique was selected, since it permits visualization also of turbulent flow through the valve. With the aid of a simple optical device the three-dimensional flow pattern behind the valve is determinable. The main features of the method are: The regions of interest can easily be identified. Velocity profiles can be determined and shear stress and turbulence intensities estimated. The experimental setup is simple, calibration is not necessary, and it can be used for turbulent flows. The method can be used only with transparent fluids and vessels; measurements in blood are not possible. Because of the large number of measuring points required the method is very time-consuming. The use of an automatic picture analyzing system would make it possible to increase the number of pictures processed, and thus increase resolution. The velocity profile of a three-finger-valve, the TAD 29, was established at a distance of 20 mm from the ring, and compared with known profiles from the literature. The valve has an opening angle of 70 degrees. All typical regions for the flow of an artificial heart valve, such as jet, stagnation gone, backflow and turbulence were demonstrated.     

Two-equation turbulence modeling of pulsatile flow in a stenosed tube

The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.     

A model of constant-flow ventilation in a dog lung

A semiempirical model of constant-flow ventilation (CFV) is developed to test the hypothesis that a three-zone serial model with the following characteristics can explain the adequate CO2 transport observed during CFV: 1) a zone of jet recirculation immediately downstream of the catheter in which convection dominates; 2) a zone influenced by turbulence but with little or no bulk flow; and 3) a peripheral zone, free of turbulence, in which transport is governed by molecular and augmented diffusion. Interactions between turbulent eddies and cardiogenic oscillations are included using a modification of Taylor dispersion theory according to the formulation of Kamm et al. Predicted values for arterial PCO2 are reasonably similar to experimental results for He-O2, air, and SF6-O2 mixtures for catheter flow rates from 0.2 to 1.6 l/s. Specific impedance to gas exchange was found to be largest immediately proximal to the end of turbulent mixing zone, where transport is governed by low-level eddy mixing and molecular diffusion. Simulations suggest that, during CFV, cardiogenic oscillations augment gas exchange primarily by promoting turbulent eddy dispersion in the distal airways and by extending the length of the turbulent mixing zone. Even small displacements of the catheter are shown to have a dramatic effect on gas exchange.     

Computational simulations of airflow in an in vitro model of the pediatric upper airways

In order to understand mechanisms of gas and aerosol transport in the human respiratory system airflow in the upper airways of a pediatric subject (male aged 5) was calculated using Computational Fluid Dynamic techniques. An in vitro reconstruction of the subject's anatomy was produced from MRI images. Flow fields were solved for steady inhalation at 6.4 and 8 LPM. For validation of the numerical solution, airflow in an adult cadaver based trachea was solved using identical numerical methods. Comparisons were made between experimental results and computational data of the adult model to determine solution validity. It was found that numerical simulations can provide an accurate representation of axial velocities and turbulence intensity. Data on flow resistance, axial velocities, secondary velocity vectors, and turbulent kinetic energy are presented for the pediatric case. Turbulent kinetic energy and axial velocities were heavily dependant on flow rate, whereas turbulence intensity varied less over the flow rates studied. The laryngeal jet from an adult model was compared to the laryngeal jet in the pediatric model based on Tracheal Reynolds number. The pediatric case indicated that children show axial velocities in the laryngeal jet comparable to adults, who have much higher tracheal Reynolds numbers than children due to larger characteristic dimensions. The intensity of turbulence follows a similar trend, with higher turbulent kinetic energy levels in the pediatric model than would be expected from measurements in adults at similar tracheal Reynolds numbers. There was reasonable agreement between the location of flow structures between adults and children, suggesting that an unknown length scale correlation factor could exist that would produce acceptable predictions of pediatric velocimetry based off of adult data sets. A combined scale for turbulent intensity as well may not exist due to the complex nature of turbulence production and dissipation.     

Turbulent flow evaluation of the venous needle during hemodialysis

Arteriovenous (AV) grafts and fistulas used for hemodialysis frequently develop intimal hyperplasia (IH) at the venous anastomosis of the graft, leading to flow-limiting stenosis, and ultimately to graft failure due to thrombosis. Although the high AV access blood flow has been implicated in the pathogenesis of graft stenosis, the potential role of needle turbulence during hemodialysis is relatively unexplored. High turbulent stresses from the needle jet that reach the venous anastomosis may contribute to endothelial denudation and vessel wall injury. This may trigger the molecular and cellular cascade involving platelet activation and IH, leading to eventual graft failure. In an in-vitro graft/needle model dye injection flow visualization was used for qualitative study of flow patterns, whereas laser Doppler velocimetry was used to compare the levels of turbulence at the venous anastomosis in the presence and absence of a venous needle jet. Considerably higher turbulence was observed downstream of the venous needle, in comparison to graft flow alone without the needle. While turbulent RMS remained around 0.1 m/s for the graft flow alone, turbulent RMS fluctuations downstream of the needle soared to 0.4-0.7 m/s at 2 cm from the tip of the needle and maintained values higher than 0.1 m/s up to 7-8 cm downstream. Turbulent intensities were 5-6 times greater in the presence of the needle, in comparison with graft flow alone. Since hemodialysis patients are exposed to needle turbulence for four hours three times a week, the role of post-venous needle turbulence may be important in the pathogenesis of AV graft complications. A better understanding of the role of needle turbulence in the mechanisms of AV graft failure may lead to improved design of AV grafts and venous needles associated with reduced turbulence, and to pharmacological interventions that attenuate IH and graft failure resulting from turbulence.     

河流鱼类产卵场紊动能计算与分析

通过对鱼类产卵场地形分析,认为水流能量损失是鱼类产卵场形成的重要原因之一,这种能量损失主要是由于特殊河道地貌形成的水流紊动而产生的.在此基础上探索性地推导了考虑这种河道水流能量损失的明渠非恒定流方程.以中华鲟为例,对产卵场河段进行了三维水流数值模拟,计算了产卵河段紊动能的分布,探讨了中华鲟产卵行为与水流紊动之间的关系,结果表明产卵区因紊动产生的能量损失明显大于非产卵区.以期为保护中华鲟和其他鱼类产卵场水力学环境提供参考.     

Numerical simulations of the pulsating flow of cerebrospinal fluid flow in the cervical spinal canal of a Chiari patient

The flow of cerebrospinal fluid (CSF) in a patient-specific model of the subarachnoid space in a Chiari I patient was investigated using numerical simulations. The pulsating CSF flow was modeled using a time-varying velocity pulse based on peak velocity measurements (diastole and systole) derived from a selection of patients with Chiari I malformation. The present study introduces the general definition of the Reynolds number to provide a measure of CSF flow instability to give an estimate of the possibility of turbulence occurring in CSF flow. This was motivated by the fact that the combination of pulsating flow and the geometric complexity of the spinal canal may result in local Reynolds numbers that are significantly higher than the commonly used global measure such that flow instabilities may develop into turbulent flow in these regions. The local Reynolds number was used in combination with derived statistics to characterize the flow. The results revealed the existence of both local unstable regions and local regions with velocity fluctuations similar in magnitude to what is observed in fully turbulent flows. The results also indicated that the fluctuations were not self-sustained turbulence, but rather flow instabilities that may develop into turbulence. The case considered was therefore believed to represent a CSF flow close to transition.     

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.     

Investigation of how agitation during precipitation,and subsequent processing affects the particle size distribution and separation of α-lactalbumin enriched whey protein precipitates

In this work, α-lactalbumin (α-la) rich precipitate particles are formed and aged in a batch stirred-tank from a whey protein concentrate (WPC) dispersion. Precipitation of the proteins occurs during a period of acid-addition followed by an ageing period. This study investigates how stirred-tank impeller agitation and subsequent processing, by means of passing precipitate suspensions through a capillary tube or a partially open ball-valve, affect particle size and composition. Precipitate particles are largely unaffected when subjected to laminar capillary tube flow. However, as flow becomes transitional and thereafter turbulent, particle breakage increases, especially for precipitates formed and aged under mild agitation conditions. Precipitates passed through the ball-valve experience even greater particle size reduction as a sharp geometrical transition results in highly turbulent flow. Moreover, particles formed and aged under low shear conditions, though initially larger, are in fact weaker and fragment to a greater extent during turbulent processing through the ball-valve. This has process design implications for separation processes where particle size is important, as shear history can influence particle toughness. Substantial size reduction of particles can best be mitigated by identifying regions of high turbulence or sudden changes in flow geometry, and by redesigning these regions so as to reduce these effects.     

The effect of turbulent motion on the diffusion of microorganisms

The effect of turbulent fluid motion on the diffusion of simple organisms is discussed. The net reproduction rate and the turbulent flow are assumed to be Gaussian-correlated random variables. For homogeneous istropic turbulence, simple equations for the average concentration of the organisms are derived in terms of the energy density of the fluid. It is shown that the effective diffusivity generated by the motion is positive-definite, and is independent of the helicity of the flow.     

Turbulent flow of red cells in dilute suspensions. Effect on kinetics of O2 uptake.

The turbulent flow properties of dilute (0.06% by volume) suspensions of human red blood cells in 4-mm-bore glass tubing were estimated by laser anemometry. The flow properties of the dilute red cell suspension were similar to those of a dilute suspension of polystyrene spheres (0.5 micron diameter) in isotonic NaCl solution. Flow was found to be laminar when the Reynolds number was below 2,000, transitional in the range of Reynolds numbers from 2,000 to 3,000, and fully turbulent above Reynolds number 3,000. These results differ from previous studies of more concentrated red cell suspensions. The length scales of the turbulence were also estimated: at a Reynolds number near 4,000 the macroscale is about 1.25 mm, the Taylor microscale is about 0.85 mm, and the Kolmogoroff scale is near 0.075 mm. The results are discussed in relation to previous measurements of the rate of oxygen uptake by dilute red cell suspensions in the flow-type rapid reaction apparatus. Our results suggest that under the conditions of most of these oxygen uptake measurements, the turbulent flow is characterized by eddies about 1 mm across, mixing with each other on a time scale of about 45 ms. Since most of the reported oxygen uptake measurements involve a similar time scale, it is possible that an effective "unstirred layer" influenced the reported rate of oxygen uptake.     

Orientation and food search behaviour of a deep sea lobster in turbulent versus laminar odour plumes

New Zealand scampi (Metanephrops challengeri) is a commercially important deep-water lobster species that is caught by bottom trawling on areas of muddy seafloor on the continental shelf below 300 m. Efforts are being made to develop lower impact potting methods to harvest scampi, however, they can only be caught when out of their burrows and searching for food. This emergent food searching behaviour appears to be associated with periods of higher tidal flow. Such water flow will increase turbulence along the sea floor, which has been observed to improve the efficiency of chemosensory food searching in some lobster species. Consequently, this study examined the food search behaviour of scampi in response to odours from two types of bait (mackerel and mussel) in both turbulent and laminar flows. Scampi were more efficient at foraging in the turbulent flow than in the laminar flow, using shorter search paths in response to both types of bait. Scampi in the turbulent flow reached the mussel bait 44% faster and with lower mean heading angles than in laminar flow. However, there was no difference between the flow regimes for the mackerel bait. The pattern of orientation behaviour was similar under both flow regimes, suggesting that the scampi were using the same orientation strategy, but it was more accurate in turbulent flows. The results show that the foraging efficiency of scampi improves in turbulent conditions and that this may explain their increased emergent behaviour during periods of higher tidal flows.     

Measurement of turbulence intensity in the center of the canine ascending aorta with a hot-film anemometer

The blood flow velocity near the central axis of the canine ascending aorta was measured with a hot-film anemometer. The cardiac output and the heart rate were controlled at will by means of an extracorporeal circulation and by atrial pacing. The turbulent component of the blood flow velocity was calculated using an ensemble average technique. Ensemble average turbulent intensity was also calculated to show the time course of turbulence in the aorta. The ratio of the mean turbulence intensity to the time mean sectional average velocity in the aorta was constant in most animals regardless of the changes in fluid mechanical parameters. The correlation between the frequency parameter and the relative mean turbulence intensity was weakly positive. The power spectrum of the turbulence was also calculated.