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.     

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

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

Validating CFD predictions of respiratory aerosol deposition: effects of upstream transition and turbulence

A number of computational fluid dynamics (CFD) studies have explored local deposition patterns of inhaled aerosols in the respiratory tract. These studies have highlighted the effects of multiple physiologic, geometric, and particle characteristics on deposition. However, very few studies have reported local or sub-branch quantitative comparisons to in vitro particle deposition data. The objective of this study is to numerically investigate the effects of transition and turbulence on highly localized particle deposition in a respiratory double bifurcation model in order to quantitatively validate CFD results. To perform the validations, local comparisons have been made to a specific in vitro case study of 10 microm particles depositing in a model of respiratory generations G3-G5. To achieve this objective, two geometric cases have been considered. The first case includes only the double bifurcation model. The second case includes a portion of the experimental particle delivery geometry, where transitional flow is expected. To evaluate the effectiveness of two-equation turbulence models in this system, the flow field solutions have been computed using laminar, standard k-omega, and low Reynolds number (LRN) k-omega approximations. Results indicate that even though the Reynolds number remained below the critical limit required for full turbulence, transition and turbulence have a significant impact on the flow field and local particle deposition patterns. For the experimental case considered, turbulence impacted the local deposition of 10 microm particles primarily by influencing the initial velocity and particle profiles. As such, both the laminar and LRN k-omega flow models provided good local quantitative matches to the in vitro deposition data, provided that the correct initial particle profile was specified. Implications of this study include the need for local quantitative validations of particle deposition results, the importance of correct inlet conditions, and the need to consider upstream effects in experimental and computational studies of the respiratory tract. Applications of these results to realistic respiratory geometries will require consideration on upstream flow conditions in the lung, transient flow, and intermittent turbulent structures.     

Turbulence Model Selection for Low Reynolds Number Flows

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

Application of large-eddy simulation to the study of pulsatile flow in a modeled arterial stenosis

The technique of large-eddy simulation (LES) has been applied to the study of pulsatile flow through a modeled arterial stenosis. A simple stenosis model has been used that consists of a one-sided 50 percent semicircular constriction in a planar channel. The inlet volume flux is varied sinusoidally in time in a manner similar to the laminar flow simulations of Tutty (1992). LES is used to compute flow at a peak Reynolds number of 2000 and a Strouhal number of 0.024. At this Reynolds number, the flow downstream of the stenosis transitions to turbulence and exhibits all the classic features of post-stenotic flow as described by Khalifa and Giddens (1981) and Lieber and Giddens (1990). These include the periodic shedding of shear layer vortices and transition to turbulence downstream of the stenosis. Computed frequency spectra indicate that the vortex shedding occurs at a distinct high frequency, and the potential implication of this for noninvasive diagnosis of arterial stenoses is discussed. A variety of statistics have been also extracted and a number of other physical features of the flow are described in order to demonstrate the usefulness of LES for the study of post-stenotic flows.     

Effects of vibration on steady flow downstream of a stenosis

A physical model was used to test the effects of vibrations on the position of transition to turbulence (zt) downstream of a constriction. Constrictions were inserted in a length of clear plastic (Tygon) tubing and vibrated. Water was the fluid medium and flow was visualized with India ink. The frequency and velocity of vibration were monitored. For a given constriction and flow velocity, there was a band of frequencies which caused zt to move upstream. This band corresponded to frequencies of flow disturbances as measured with a hot-film anemometer without vibration. Both flow-visualization and hot-film frequencies were correlated via a Strouhal number to the Reynolds number and contraction ratio of the flow. Values of zt decreased with increasing vibration amplitude. The critical Reynolds number for turbulence was also decreased by vibration. These results are of importance in the diagnosis of vascular disease and the design of physical models of stenotic flows.     

Simulation of turbulent airflow using a CT based upper airway model of a racehorse

Computational model for airflow through the upper airway of a horse was developed. Previous flow models for human airway do not hold true for horses due to significant differences in anatomy and the high Reynolds number of flow in the equine airway. Moreover, models that simulate the entire respiratory cycle and emphasize on pressures inside the airway in relation to various anatomical diseases are lacking. The geometry of the airway was created by reconstructing images obtained from computed tomography scans of a thoroughbred racehorse. Different geometries for inhalation and exhalation were used for the model based on the difference in the nasopharynx size during the two phases of respiration. The Reynolds averaged Navier-Stokes equations were solved for the isothermal flow with the standard k-epsilon model for turbulence. Transient pressure boundary conditions for the entire breathing cycle were obtained from past experimental studies on live horses. The flow equations were solved in a commercial finite volume solver. The flow rates, computed based on the applied pressure conditions, were compared to experimentally measured flow rates for model validation. Detailed analysis of velocity, pressure, and turbulence characteristics of the flow was done. Velocity magnitudes at various slices during inhalation were found to be higher than corresponding velocity magnitudes during exhalation. The front and middle parts of the nasopharynx were found to have minimum intraluminal pressure in the airway during inhalation. During exhalation, the pressures in the soft palate were higher compared to those in the larynx, epiglottis, and nasopharynx. Turbulent kinetic energy was found to be maximum at the entry to the airway and gradually decreased as the flow moved inside the airway. However, turbulent kinetic energy increased in regions of the airway with abrupt change in area. Based on the analysis of pressure distribution at different sections of the airway, it was concluded that the front part of the nasopharynx requires maximum muscular activity to support it during inhalation. During exhalation, the soft palate is susceptible to displacements due to presence of high pressures. These can serve as critical information for diagnosis and treatment planning of diseases known to affect the soft palate and nasopharynx in horses, and can potentially be useful for human beings.     

The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions

In the abdominal segment of the human aorta under a patient's average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 < or = Rem < or = 300, corresponding to a range of peak Reynolds numbers 262.5 < or = Repeak < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.     

Laminar and turbulent flow in the mammalian aorta: Reynolds number

Laminar to turbulent flow transition in the mammalian aorta is generally characterized by Reynolds number. When dimensional analysis is applied to obtain the Reynolds number in allometric form, it is found that this number is not invariant of body weight but is approximately proportional to body length dimensions. This implies that flow in the aorta of large mammals is turbulent and laminar in smaller mammals during most of ventricular ejection. Since Reynolds number is defined for steady flow through rigid tubes, it may not reflect the actual fluid behavior of pulsatile flow in compliant vessels such as the aorta. In addition, turbulence is frequency dependent. The larger compliance of the aorta and the slower heart rate in larger mammals and the shorter entrance length and higher heart rate in smaller mammals lead to equal prevalence of turbulence. The consequence is that the aortic flow waveforms remain similar in all mammals.     

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.     

Computational modeling and validation of human nasal airflow under various breathing conditions

The human nose serves vital physiological functions, including warming, filtration, humidification, and olfaction. These functions are based on transport phenomena that depend on nasal airflow patterns and turbulence. Accurate prediction of these airflow properties requires careful selection of computational fluid dynamics models and rigorous validation. The validation studies in the past have been limited by poor representations of the complex nasal geometry, lack of detailed airflow comparisons, and restricted ranges of flow rate. The objective of this study is to validate various numerical methods based on an anatomically accurate nasal model against published experimentally measured data under breathing flow rates from 180 to 1100 ml/s. The numerical results of velocity profiles and turbulence intensities were obtained using the laminar model, four widely used Reynolds-averaged Navier-Stokes (RANS) turbulence models (i.e., k-ε, standard k-ω, Shear Stress Transport k-ω, and Reynolds Stress Model), large eddy simulation (LES) model, and direct numerical simulation (DNS). It was found that, despite certain irregularity in the flow field, the laminar model achieved good agreement with experimental results under restful breathing condition (180 ml/s) and performed better than the RANS models. As the breathing flow rate increased, the RANS models achieved more accurate predictions but still performed worse than LES and DNS. As expected, LES and DNS can provide accurate predictions of the nasal airflow under all flow conditions but have an approximately 100-fold higher computational cost. Among all the RANS models tested, the standard k-ω model agrees most closely with the experimental values in terms of velocity profile and turbulence intensity.     

Effects of oral airway geometry characteristics on the diffusional deposition of inhaled nanoparticles

The deposition of ultrafine aerosols in the respiratory tract presents a significant health risk due to the increased cellular-level response that these particles may invoke. However, the effects of geometric simplifications on local and regional nanoparticle depositions remain unknown for the oral airway and throughout the respiratory tract. The objective of this study is to assess the effects of geometric simplifications on diffusional transport and deposition characteristics of inhaled ultrafine aerosols in models of the extrathoracic oral airway. A realistic model of the oral airway with the nasopharynx (NP) included has been constructed based on computed tomography scans of a healthy adult in conjunction with measurements reported in the literature. Three other geometries with descending degrees of physical realism were then constructed with successive geometric simplifications of the realistic model. A validated low Reynolds number k-omega turbulence model was employed to simulate laminar, transitional, and fully turbulent flow regimes for the transport of 1-200 nm particles. Results of this study indicate that the geometric simplifications considered did not significantly affect the total deposition efficiency or maximum local deposition enhancement of nanoparticles. However, particle transport dynamics and the underlying flow characteristics such as separation, turbulence intensity, and secondary motions did show an observable sensitivity to the geometric complexity. The orientation of the upper trachea was shown to be a major factor determining local deposition downstream of the glottis and should be retained in future models of the respiratory tract. In contrast, retaining the NP produced negligible variations in airway dynamics and could be excluded for predominantly oral breathing conditions. Results of this study corroborate the use of existing diffusion correlations based on a circular oral airway model. In comparison to previous studies, an improved correlation for the deposition of nanoparticles was developed based on a wider range of particle sizes and flow rates, which captures the dependence of the Sherwood number on both Reynolds and Schmidt numbers.     

Mammalian cell damage in a novel membrane bioreactor

The experimental study has assessed a novel membrane bioreactor for mammalian cell culture. In the absence of a gas phase, the key features of cell damage associated with laminar and turbulent flow have been identified. The bioreactor employs a dimpled membrane in order to enhance transverse mixing in a narrow channel, but a fall in viable cell density has been observed at Reynolds numbers above Re = 83. In the laminar flow regime wall shear is the critical mechanism and an accurate calculation of shear rate in a complex channel has been achieved using the Reynolds analogy. Flow generating a wall shear rate in excess of 3000 s(-1) has been shown to cause damage. Power dissipation measurements have been used to distinguish between laminar and turbulent flow and also to predict Kolmogorov eddy lengths. An additional turbulent bulk stress damage mechanism at higher Reynolds numbers (Re > 250) results in a very rapid fall in viable cell density.     

Pulsatile flow in fusiform models of abdoiminal aortic aneurysms: flow fields, velocity patterns and flow-induced wall stresses

As one important step in the investigation of the mechanical factors that lead to rupture of abdominal aortic aneurysms, flow fields and flow-induced wall stress distributions have been investigated in model aneurysms under pulsatile flow conditions simulating the in vivo aorta at rest. Vortex pattern emergence and evolution were evaluated, and conditions for flow stability were delineated. Systolic flow was found to be forward-directed throughout the bulge in all the models, regardless of size. Vortices appeared in the bulge initially during deceleration from systole, then expanded during the retrograde flow phase. The complexity of the vortex field depended strongly on bulge diameter In every model, the maximum shear stress occurred at peak systole at the distal bulge end, with the greatest shear stress developing in a model corresponding to a 4.3 cm AAA in vivo. Although the smallest models exhibited stable flow throughout the cycle, flow in the larger models became increasingly unstable as bulge size increased, with strong amplification of instability in the distal half of the bulge. These data suggest that larger aneurysms in vivo may be subject to more frequent and intense turbulence than smaller aneurysms. Concomitantly, increased turbulence may contribute significantly to wall stress magnitude and thereby to risk of rupture.     

Suggestions for the operation of radial flow cells in cell adhesion and biofouling studies

An analysis of the radial flow cell is presented to show that the assumption of creeping laminar flow should be used cautiously. Simple models which account for the influence of fluid inertial forces over most of the width of the plate are reviewed. A modified Reynolds number is introduced which may be used to test the validity of the creeping flow solution.     

Laser-Doppler measurements of velocities just downstream of a collapsible tube during flow-induced oscillations

The flow field less than one diameter downstream of the end of a collapsible tube executing self excited oscillations was examined using a two-component fiber-optic laser-Doppler anemometer. The time-averaged Reynolds number of the flow was 11,000. With the tube oscillating periodically, results obtained during many cycles of oscillation were combined to yield surface plots of the axial component over the cross section at 16 phases of the cycle. By combining measurements obtained with the laser probe in two different orientations, secondary flow vectors over the cross section were likewise constructed for 16 phases. The measurements showed strongly phasic turbulence intensity, with the phase of high intensity coinciding with the time of maximal tube collapse. Reverse flow occurred during much of the cycle, at places in the cross section that agree with our previous observations of laminar and turbulent steady flow through a rigid simulated collapsed tube.     

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

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

Velocity profiles in annular perfusion chamber measured by laser-Doppler velocimetry

p6e fluid flow in the annular perfusion chamber of Baumgartner developed to study platelet vessel wall interaction was examined with laser-Doppler velocimetry. A laminar and stable flow with a Reynolds number of less than or equal to 50 was measured at flow rates up to 3 ml s-1. No turbulence was found. The wall shear rate directly determined from measured velocity profiles agreed well with theory. The experiments underlined the necessity to work with vessels of uniform thickness and a smooth surface.     

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.     

Finite element analysis of two dimensional steady flow in model arterial bifurcation

The purpose of the investigation reported in this paper is to determine theoretically the fluid dynamic field in models of common iliac arterial bifurcation and to identify the flow features which might influence the predominant occurrence of atherosclerotic lesions at such sites. This has been accomplished by numerically simulating fluid flow through 90 degrees symmetric bifurcations with branch-to-trunk area ratios of 0.8-1.414 and for Reynolds numbers ranging from 100 to 400. The analysis predicts flow reversal along the outer wall in models with area ratios over unity for high Reynolds number range, while no flow reversal occurred in models with area ratio below unity; a low shear zone along the outer wall and high shear stresses at the divider lip. Adverse pressure gradients are observed along the outer wall downstream of the corner point, the magnitudes increased with Reynolds number for a given branch to area ratio. Biological implication of the results is discussed with specific reference to the sites of atherosclerotic lesions found in man for these geometries.