Abstract In this paper, we have applied a recently-developed numerical technique to study the three-dimensional dynamics of a confined air bubble rising in shear thinning and shear-thickening power-law fluids. The method is a blend of Volume of Fluid and Level Set methods and incorporates a Sharp Surface Force Method (SSF) for surface tension forces by solving a second Pressure Poisson Equation (PPE). The gas-liquid interface is captured by an equation for the liquid volume fraction and advected using the geometry reconstruction method. The interface normal and curvature are computed using level-set and height function methods. The accurate representation of the interface and interfacial forces significantly suppressed the spurious velocities commonly observed with conventional volume of fluid method and the Continuum Surface Force (CSF). The algorithm is implemented in a in-house code called CUFLOW and runs on multiple GPUs platform. We explored the effects of fluid rheology, Bond number, and wall confinement on bubble’s transient shape, rise velocity, rise path, and generated vortex structures. The power-law index is varied from 0.25 to 1.50 covering shear-thinning and shear-thickening regimes. Three Bond numbers (Bo = 2, 10 and 50) and three confinement ratios (C r = 4, 6 and 8) are considered, and their impacts on bubble’s dynamics are analyzed. For the range of parameters examined here, bubble motion in a shear-thinning fluid is seen to be unsteady with significant shape oscillations. The bubble rises with a secondary motion in the cross-sectional plane along with its primary vertical rise. However, in the Newtonian and shear-thickening fluids, the bubble’s shape is seen to reach a steady-state in a relatively short time and rise with only minor deviations from the vertical path.

Abstract The accuracy of the continuous random walk (CRW) stochastic model for prediction of dispersion and deposition of suspended particles in inhomogeneous turbulent channel flows was explored. The Reynolds-averaged Navier-Stokes (RANS) equations in conjunction with the Reynolds Stress Transport model was used to evaluate the mean flow and RMS velocity fluctuation characteristics of a fully developed turbulent channel flow at shear Reynolds number of 219. Then, spherical particles with diameters ranging from 10 nm to 30 μm and dimensionless relaxation times of 10 −4 to 50 (in wall units) were uniformly introduced into the channel and their trajectories were evaluated by using the equation of particle motion including the Stokes drag and Brownian excitation. The particle laden flow was assumed to be sufficiently dilute so that the particle-particle collisions and the effects of particles on the flow could be ignored. To incorporate the effects of turbulence velocity fluctuations on particle motions, first, the Conventional-CRW stochastic model, which was originally proposed for homogenous turbulent flows, was used. The particles were tracked for the duration of 10,000 wall units of time and the deposition of particles on the walls was evaluated. By conducting ensemble averaging, the steady-state concentration profiles and deposition velocity of the particles were calculated. Comparison of the predicted results with the direct numerical simulation (DNS) and experimental data suggests that the deposition velocity was overestimated. In addition, unrealistic accumulation of fluid-point particles in the near-wall regions, and overestimation of the turbophoresis effects on finite-size particles were also observed. The poor agreement of the concentration profiles and deposition velocities resulting from the conventional (homogenous flow) CRW model with the experimental and the DNS data pointed to the lack of accuracy of the Conventional-CRW model in generating instantaneous fluid velocity fluctuations seen by ultrafine and finite-size particles in inhomogeneous turbulent flows. Then, the normalized Langevin equation with a drift correction term that was suggested by Bocksell and Loth [1] was used as an improved CRW model for applications to inhomogeneous flows. The simulations for the same range of particle sizes were repeated and the corresponding concentration profiles and the deposition velocity were evaluated. It was shown that the improved CRW model led to a reasonable uniform concentration profile for the ultrafine particles and the predicted concentration profiles of finite-size particles quantitatively matched with the DNS data. In addition, the evaluated deposition velocities from the improved CRW model were also in a good agreement with the experimental data and empirical model predictions.

Abstract The present study theoretically carries out a derivation of the Korteweg–de Vries–Burgers (KdVB) equation and the nonlinear Schrödinger (NLS) equation for weakly nonlinear propagation of plane (i.e., one-dimensional) progressive waves in water flows containing many spherical gas bubbles that oscillate due to the pressure wave approaching the bubble. Main assumptions are as follows: (i) bubbly liquids are not at rest initially; (ii) the bubble does not coalesce, break up, extinct, and appear; (iii) the viscosity of the liquid phase is taken into account only at the bubble–liquid interface, although that of the gas phase is omitted; (iv) the thermal conductivities of the gas and liquid phases are dismissed. The basic equations for bubbly flows are composed of conservation equations for mass and momentum for the gas and liquid phases in a two-fluid model, the Keller-Miksis equation (i.e., the equation for radial oscillations as the expansion and contraction), and so on. By using the method of multiple scales and the determination of size of three nondimensional ratios that are wavelength, propagation speed and incident wave frequency, we can derive two types of nonlinear wave equations describing long range propagation of plane waves. One is the KdVB equation for a low frequency long wave, and the other is the NLS equation for an envelope wave for a moderately high frequency short carrier wave.

Abstract Impinging-jet injectors are commonly used in liquid propellant rocket engines. Two cylindrical liquid jets impinge at a certain angle and form a liquid sheet in the plane normal to the jets. When the Reynolds and Weber numbers are large, the liquid sheet becomes unstable and disintegrates into liquid ligaments and droplets. In the present study, we focus on cases with moderate injection velocities so that the liquid sheet remains unbroken. Detailed numerical simulations are performed using the adaptive multiphase flow solver, Basilisk. The volume-of-fluid method is used to resolve the gas-liquid interface. Grid-refinement studies are conducted to verify the formation of the liquid sheet is accurately captured in simulation. The numerical results are compared to the recent experimental measurement of the sheet thickness distribution by partial coherent interferometry and a good agreement is achieved.

Abstract Gas Carry-Under (GCU) is one of the two undesirable phenomena that occur in the GLCC ©,1 (Gas-Liquid Cylindrical Cyclone) separators when it operates even within the Operational Envelope (OPEN). Earlier studies have shown that maintaining a liquid level below the inlet of the GLCC under control configuration affects the GCU in GLCC. It has been identified that the tangential wall jet is the cause of gas entrainment within the GLCC and has been understood to change with liquid level maintained at the inlet. Also, it has been theorized that effective formation of the vortex formed in the lower part of the GLCC, or a stable gas core enhances the separation of gas entrained in the liquid. At present, there is no mechanistic model which captures these complex physical phenomena in the GLCC. This paper presents a newly developed mechanistic model which can predict the GCU for different flow conditions, fluid properties, and various liquid levels. The proposed model captures the various physical phenomena namely: saturated flow at the inlet, tangential wall jet phenomena, gas entrainment and vortex flow that results in separation of gas. The developed model has been compared with the extensive experimental data and is said to be in good agreement.

Abstract A particle-resolved simulation is performed on the motion of spherical particles with an eccentric internal mass distribution in laminar and turbulent vertical flows subjected to horizontal shear in order to examine the effects of mass eccentricity on the motion of particles in shear flows. A spherical shell/hollow particles with an inner spherical core is focused on as a typical example of mass eccentric particles. The Navier-Stokes equations and the Newton-Euler equations are solved for the fluid phase and the particles, respectively. An immersed boundary method is adopted to represent the shell particle. The Newton-Euler equations are solved using the body-fixed coordinate system and four quaternion parameters, considering the deviation of the mass center from the center of the spherical shell particle. Numerical results show that a particle tends to stop its rotation when the torque acting on the particle due to the gravity exceeds that due to the shear. It is found that the transverse migration of mass-eccentric particles becomes less vigorous in both laminar and turbulent flows since the effect of the Magnus force is also weakened for mass-eccentric particles. It is also found that the evolution of fluid kinetic energy is significantly affected by the mass-eccentricity of particles in laminar flows.

Abstract Gas Carry-Under (GCU) is one of the undesirable phenomena that exist in the Gas-Liquid Cylindrical Cyclone (GLCC) separators even within the liquid carry-over Operational Envelope (OE). In order to quantify the GCU, it is important to understand the cause of gas entrainment that occurs in the GLCC other than the incoming entrained gas within the liquid medium. The tangential inclined inlet of 27° with reduced area allows the stratified liquid flow to exit the inlet nozzle tangentially along the wall into the vertical lower part of the GLCC, whereby the liquid film spreads along the wall in an asymmetrical shape. The gas moves to the center of the GLCC and escapes through the gas leg. The liquid film flow is complex and turbulent exhibiting unevenness of the film thickness and asymmetrical velocity distribution. Experimental investigations show that the magnitude of liquid wall jet film tangential and axial velocity change as a function of length along the GLCC below the inlet of the GLCC. This wall jet film flowing down along the wall is the cause for gas entrainment and GCU. The experimental results show that the gas entrainment mechanism is not like the conventional jet entrainment as expected to be occurring in GLCC. The change in velocities of the wall jet film at various liquid heights maintained below the inlet results in varying gas entrainment at various inlet liquid levels and for fluid properties. The wall jet phenomena that takes places at the inlet has been discussed in detail and a mechanistic model capable of predicting the wall jet parameters has been presented in this paper. Further, a novel mechanistic model that is developed for the first time is also presented which can predict the gas entrainment at various liquid levels and flow conditions using the wall jet parameters as an input condition.

Abstract Water-in-oil dispersion modeling is critical to assess the internal corrosion in pipelines, specifically for the oil and gas industry applications. In many oil transportation facilities, a small amount of water could be entrained in production fluids. Turbulence can break out the water into the form of tiny droplets. Under certain conditions in horizontal or inclined pipelines, water droplets can settle and contact the wall which may lead to CO 2 and/or O 2 or other forms of corrosion and damage the transport system integrity. In the present study, a novel transient approach has been developed that provides water concentrations across the pipe section. A one-dimensional transient finite-difference computational model has been used to determine concentration distribution in a vertical direction across the pipe. Calculated water fractions using the transient model is compared to experimental data and more comprehensive 3-D Computational Fluid Dynamics (CFD) approach for various flow conditions and watercuts that shows the viability of the simplified one-dimensional approach. The proposed model is capable of predicting water dispersion at different locations and could be utilized for various pipe-flow systems. Furthermore, water in the form of droplets or liquid film can result in corrosion when it wets the pipeline surface. Consequently, the calculated water concentration at the bottom of the pipe assists in determining wettability of the pipe surface by water and evaluating the corrosion risk along the pipeline.

Abstract This study experimentally investigates the mixing of a two-layer density-stratified fluid of water (upper layer) and aqueous sodium chloride (NaCl) solution (lower layer) induced by the interaction between a vortex ring and the density interface. The vortex ring, which consists of water, is launched from an orifice in the upper layer toward the density interface, after which its motion, along with the behavior of the lower fluid, is visualized through a planar laser-induced fluorescence method. The Atwood number that expresses the nondimensional density jump across the density interface is set at 0.0055, and the Reynolds number Re of the vortex ring is varied from 2050 to 3070. The visualization experiment clarifies that the vortex ring penetrating the density interface is bounced while collapsing in the lower fluid. Furthermore, it elucidates that the bounced upper fluid entrains the lower fluid into the upper layer by inducing a second vortex ring consisting of the lower fluid. Thus, this study reveals the effect of Re on the mixing of the upper and lower fluid induced by the launched vortex ring.

Abstract The purpose of this study is to clarify the formation characteristics and production conditions of two-layer droplets using coaxial nozzle. In this study, we focus on Newtonian fluid only to pay attention to the fundamental formation characteristics of two-layer droplet. Also, the three liquids flowing in the apparatus were assumed to have the same viscosity and density. First, theoretical equations concerning the outer diameters of the single layer droplet and the two-layer droplet were obtained, and a conditional expression for detaching both nozzles simultaneously from the nozzle in dripping was obtained. These theoretical equations were verified using numerical analysis. By analyzing with various parameters changed, the following six formation modes could be confirmed. 2 interface both dripping, 2 interface both jetting, Outer interface is jetting and The inner interface is dripping, 2 interface comes into contact and the encapsulated liquid is discharged to the outside, Two or more droplets are formed in the interior, Liquid droplets containing liquid droplets and liquid droplets not containing liquid droplets are alternately formed. The validity of each theoretical expression and conditional expression was also be confirmed.

Abstract The rheological properties of a suspension depend on particle shape, spatial arrangement of the particles and hydrodynamic interactions as well as the concentration of the particles. So far, we proposed a two-way coupling numerical scheme to evaluate the effects of particle rotation on the rheological properties. This particle rotation decreases the fluid resistance. However, these studies were conducted on the condition that suspended particles were homogeneously distributed. Therefore, the particles in this study are randomly scattered in a suspension for better practical applications. Pressure-driven suspension flow simulations were conducted to consider the effects of inertia on the relationship between spatial arrangement of the particles and the rheological properties of a suspension. The channel width and axial length were set 400 μm and 1620 μm, respectively, and periodic boundary conditions were applied in the flow direction. The rigid spherical particles whose diameter was 20 μm were randomly scattered in the channel as an initial condition. The concentration of the suspension was set 1.02% for dilute assumption, and the suspension flows with the Reynolds number from 2 to 128 were reproduced in order to investigate the inertial effects of the suspended particles on the rheological properties. The rheological properties of the suspension were evaluated in terms of power-law index (non-Newtonian index). The velocity profile of a suspension for low Reynolds number conditions exhibited almost parabolic. This indicates the suspension behaves as a Newtonian fluid. For higher Reynolds number conditions, on the other hand, the lift force on the particles increased and they migrated toward the equilibrium y-axis position, where the lift force is zero. These changes in the y-axis position of the particles caused a change in microstructure of the suspension, which were followed by a change in macroscopic rheological properties. Owing to these microstructure changes, the non-Newtonian (thixotropic) properties were enhanced as the Reynolds number increased.

Abstract Slurries and sludges across the United States Department of Energy (DOE) complex rank among the most rheologically interesting. Their composition is heterogeneous, spanning a very broad range of particle sizes, densities, and interparticle forces. All exhibit shear thinning, some have yield stresses, and many are thixotropic. Despite the variety, these complex fluids are often represented using the historic Bingham fluid model, which fits higher shear rate data to a simple straight line. The intercept provides a yield stress, which has been a key design parameter in construction of large-scale waste processing facilities. However, many radioactive wastes are simply not Bingham fluids, and this representation extrapolates poorly across low to intermediate shear rates that are characteristic of typical processing conditions. Indeed, processing shear rates as high as 200 1/s, which has been a typical minimum shear rate used in fitting the Bingham fluid model, are seldom encountered in nuclear waste processing. Therefore, more realistic rheological models are necessary to accurately predict waste processing performance. Pacific Northwest National Laboratory (PNNL) recently re-evaluated the rheology of reconstituted Hanford REDOX (reduction-oxidation) process sludge waste against a wide variety of rheological models including the Bingham, Cross, Cross with yield stress, Carreau, biviscous, Herschel-Bulkley (which includes a power law dependence), Casson, and Gay models. They found that all of the models provided a closer fit than the Bingham model and that the biviscous model and Cross with yield stress model were convincing. However, reconstituted Hanford REDOX sludge waste is but one type of DOE waste and a direct contrast, and comparison of these three models against undiluted, unmixed tank waste (actual not simulant) has not been performed previously. Therefore, the purpose of this paper is to evaluate the rheology of actual tank waste with these more accurate rheological models. In this paper, we evaluate select rheological data for slurry samples from Hanford’s AZ-101, AZ-102, and SY-101 waste tanks. In each of these cases, we find that Cross’ model with yield stress and the biviscous model significantly outperform the Bingham fluid model. Furthermore, the AZ-101 data also shows that the shear stress peak at startup significantly exceeds the Bingham yield stress, which is commonly observed in the initial moments of rheological measurements on simulants. Remarkably, Cross’ model may empirically accommodate an initial spike in shear stress at modest shear rates. These are important observations because computational and analytical fluid dynamics simulations rely on rheological constitutive models for accurately and conservatively predicting waste processing performance. These findings suggest the need for better rheological modeling of and validation against radioactive waste.

Abstract The key mechanism that sustains fluid turbulence flowing through a channel is examined using the Lagrangian experiment, done in a direct numerical simulation (DNS) of the turbulent fluid flow and that being damped by addition of a small amount of small particles. The results indicate large contribution of the fluctuations of large-scale fluid motions, which are seen as their multi-directionality and multi-dimensionality, to sustenance of wall turbulence. Small-scale fluid turbulence structures, such as vortices and packets of them, are seen to induce the fluctuations of large-scale fluid motions.

Abstract In the present paper, a high-temperature packed bed energy storage system of volume 175,000m 3 is numerically investigated. The system is a underground packed bed of truncated conical shape, which comprises of rocks as a storage medium and air as a heat transfer fluid. A one-dimensional, two-phase model is developed to simulate the transient behavior of the storage. The developed model is used to conduct a parametric study with a wide range of design parameters to investigate the change in performance during both charging and discharging operation. Results show that the model satisfactorily predicts the dynamic behavior, and the truncated conical shaped storage with a rock diameter of 3cm, insulation thickness up to 0.6m and charging-discharging rate of 553kg/s leads to lower thermal losses and higher energy efficiencies. The paper provides useful insight into the transient performance and efficiency of a large-scale packed bed energy storage system within the range of parameters investigated.

Abstract In the present study, we numerically manipulate the mean velocity profile of a turbulent channel flow and assess the friction drag reduction performance by using resolvent analysis. Building on the implication obtained from Kühnen et al. ( Nat. Phys. , Vol. 14, 2017, pp. 386–390) that modifying mean velocity profile flat leads to significant drag reduction, we first introduce two functions for turbulent mean velocity, which can express ‘flattened’ profiles: one is derived based on the turbulent viscosity model proposed by Reynolds & Tiederman ( J. Fluid Mech. , Vol. 658, 2010, pp. 336–382), and the other is based on the mean velocity profile of laminar flow. These functions are used as the mean velocity profile for the resolvent analysis, and the flatness of the resulting profiles is characterized by two different measures. As a result, we confirm that, friction drag reduction is achieved if the turbulent mean velocity profile is ‘flattened’. However, we also find that the flatness of the mean velocity profile in the center of the channel alone is not enough to evaluate the drag reduction performance.

Abstract Active fluids refer to the fluids that contain self-propelled particles such as bacteria or micro-algae, whose properties differ fundamentally from the passive fluids. Such particles often exhibit an intermittent motion; with high-motility “run” periods separated by low-motility “tumble” periods. The average motion can be modified with external stresses, such as nutrient or light gradient, leading to a directed movement called chemotaxis and phototaxis, respectively. Using cyanobacterium Synechocystis sp.PCC 6803 , a model micro-organism to study photosynthesis, we track the bacterial response to light stimuli, under isotropic and non-isotropic conditions. In particular, we investigate how the intermittent motility is influenced by illumination. We find that just after a rise in light intensity, the probability to be in the run state increases. This feature vanishes after a typical time of about 1 hour, when initial probability is recovered. Our results are well described by a model based on the linear response theory. When the perturbation is anisotropic, the characteristic time of runs is longer whatever the direction, similar to what is observed with isotropic conditions. Yet we observe a collective motion toward the light source (phototaxis) and show that the bias emerges because of more frequent runs towards the light.

Abstract Vortex generators/turbulent promoters generate the longitudinal vortices which introduce the better mixing of the fluid with fluid circulation and enhance heat transfer. In this research, experimental investigations have been carried out to study the effect of delta winglet vortex generator (DWVG) in the core of the pipe on heat transfer and flow behavior. In this experiment, two pairs of delta winglet vortex generators (DWVG) were printed on the upside and downside of the thin plate using 3D printing technology in a ring and then placed in the core of the pipe to generate longitudinal vortices. Middle plate was very thin. The effect of heights (H = 5mm, 10mm, 15mm and 20mm) of DWVG for 10° angle of attack and 15mm spacing between leading edges of VG pairs on heat transfer and pressure drop was studied. The experiments were conducted for a fully developed turbulent flow of air in the range of Reynolds numbers (Re) 5000–25000. The influence of the DWVGs on heat transfer and pressure drop was investigated in terms of the Nusselt number (Nu) and friction factor (f). The experimental results indicate that DWVG in the core of the tube results in a considerable increase in Nu with some pressure penalty. It is found that DWVG increase Nu considerably only when H is over 10mm. Nu increases with Re and H. Friction factor decreases with Re but increase with H. The thermal performance enhancement (TPE) was noticed decreasing with Re. TPE could be obtain up to 1 only when the height is over 10mm for Re ≤ 7500. The experimental results show that the DWVG in the core of the pipe is not a good option to enhance the heat transfer at a higher Re.

Abstract Difficulty in capturing heat transfer characteristics for liquid metals is commonplace because of their low molecular Prandtl number (Pr). Since these fluids have very high thermal diffusivity, the Reynolds analogy is not valid and creates modeling difficulties when assuming a turbulent Prandtl number (Pr t ) of near unity. Baseline problems have used direct numerical simulations (DNS) for the channel flow and backward facing step to aid in developing a correlation for Pr t . More complex physics need to be considered, however, since correlation accuracy is limited. A tight lattice square rod bundle has been chosen for DNS benchmarking because of its presence of flow oscillations and coherent structures even with a relatively simple geometry. Calculations of the Kolmogorov length and time scales have been made to ensure that the spatial-temporal discretization is sufficient for DNS. In order to validate the results, Hooper and Wood’s 1984 experiment has been modeled with a pitch-to-diameter (P/D) ratio of 1.107. The present work aims at validating first- and second-order statistics for the velocity field, and then analyzing the heat transfer behavior at different molecular Pr. The effects of low Pr flow are presented to demonstrate how the normalized mean and fluctuating heat transfer characteristics vary with different thermal diffusivity. Progress and future work toward creating a full DNS database for liquid metals are discussed.

Abstract The hydrodynamic boundary layer encountered in many practical engineering systems is turbulent in nature and known to play a significant role in governing the induced friction drag and species transport. In turbulent boundary layer flows, heat transfer is often involved which increases flow complexity due to the influence of buoyancy. When the buoyant force is sufficiently large in magnitude, thermals carrying heated fluid are known to detach and rise from the wall. Literature review shows that in mixed convection, thermals have been primarily identified through qualitative flow visualizations and there is a scarcity of their quantitative assessment. Furthermore, the evolution of thermals in the boundary layer with respect to flow inertia and viscous shear is not well-understood. Hence, there is a need for a better understanding of the dynamics of thermals in mixed convection turbulent boundary layer flow. The objective of this study is to experimentally investigate the three-dimensional nature of thermals rising from a turbulent boundary layer flow over a heated smooth horizontal flat plate. Experiments were performed in a closed loop low-disturbance wind tunnel with a test section featuring a 1 m long heated bottom wall. The multi-plane particle image velocimetry (PIV) technique was used to capture images in multiple planes with respect to the turbulent boundary layer mean flow direction for three-dimensional characterization. The measurements were conducted at Richardson numbers (Ri) of 0.3, 1.0, and 2.0. Flow visualization images are used to describe the nature of thermals and the dynamical processes involved during their interaction with bulk boundary layer flow. An image processing algorithm to detect thermals is then detailed and applied to experimental images. The performance of the new algorithm is then assessed in its ability to detect thermals.

Abstract This focus of this study is to understand the relationship between the fluid properties present in and the geometric parameters of stenoses developed in end-stage renal disease (ESRD) patients, after creation of an arteriovenous fistula (AVF). Stenosis is the leading cause of failure in AVF creation and maturation. A fistula is meant to provide an access point for hemodialysis treatment necessary for ESRD patients, but large failure rates in fistula creation and maturation cause reoccurring problems for patients and a disproportionately high amount of spending on ESRD patient care. In the United States alone, ESRD patients account for 1% of the Medicare patient population, but the Centers for Medicare & Medicaid Services spent $35.4 billion, 7.2% of the 2016 Medicare budget on their treatment (United States Renal Data System, 2018 Annual Report). This study uses CFD to simulate blood flowing through venous stenoses of varying lengths and initial flow conditions. Computational modeling allows for specific control of geometric conditions as well as simple generation of resulting properties, such as wall shear stress, that are difficult to acquire in vivo. For this study, five different geometric models were constructed to represent straight vascular segments with varying lengths of stenosis. Each vessel was 4-millimeters in diameter with a 2-millimeter diameter stenosis. The lengths of the inlet and outlet vessel segments adjacent to the stenosis were each four times the vessel diameter. Stenosis lengths of 5, 15, 30, 45 and 60-millimeters were used. Vessels were treated as rigid tubes, and the geometries were created using PTC Creo Parametric (PTC Inc., Needham, MA), a commercially available CAD software. CFD analysis of the flow through the vessel segments was performed using ANSYS Fluent (ANSYS, Inc., Canonsburg, PA) for each geometric model with a range of boundary conditions. The working fluid was blood, treated as a Newtonian fluid for the shear rates present, with dynamic viscosity of 2.55 × 10 −3 kg/m-s and density of 1060 kg/m 3 . To model the range of pressure experienced by vessels during the cardiac cycle, simulations were performed using a range of pressure values at the vessel inlet. The boundary condition used at the inlet was a static pressure ranging from 50 to 160 mmHg in increments of 10 mmHg for each geometric model. Outflow pressure values of 10, 15, and 20mmHg were used on the outlet boundary. As expected, flow rate through the system was found to increase linearly with inlet pressure for each geometry and outlet pressure. Flow rate decreased logarithmically as stenosis length increased for each inlet and outlet pressure. Flow rate through the system also decreased as outflow pressure increased, as it would in the presence of further downstream blockages in patients. The data collected here shows under which flow conditions different stenosis geometries can result in a failed fistula, as well as under which conditions the stenosis alone will not prevent the fistula from providing the required flow for dialysis treatment.