Assessing the Disturbed Flow and the Transition to Turbulence in the Arteriovenous Fistula

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Simone Stella ◽  
Christian Vergara ◽  
Luca Giovannacci ◽  
Alfio Quarteroni ◽  
Giorgio Prouse
Keyword(s):  
Velocity Field ◽  
Arteriovenous Fistula ◽  
Stokes Equations ◽  
Computational Study ◽  
Color Doppler ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Shear Stresses ◽  
Angle Of Incidence ◽  
Disturbed Flow

The arteriovenous fistula (AVF) is the main form of vascular access for hemodialysis patients, but its maintenance is very challenging. Its failure is mainly related to intimal hyperplasia (IH), leading to stenosis. The aim of this work was twofold: (i) to perform a computational study for the comparison of the disturbed blood dynamics in different configurations of AVF and (ii) to assess the amount of transition to turbulence developed by the specific geometric configuration of AVF. For this aim, we reconstructed realistic three-dimensional (3D) geometries of two patients with a side-to-end AVF, performing a parametric study by changing the angle of incidence at the anastomosis. We solved the incompressible Navier–Stokes equations modeling the blood as an incompressible and Newtonian fluid. Large eddy simulations (LES) were considered to capture the transition to turbulence developed at the anastomosis. The values of prescribed boundary conditions are obtained from clinical echo-color Doppler (ECD) measurements. To assess the disturbed flow, we considered hemodynamic quantities such as the velocity field, the pressure distribution, and wall shear stresses (WSS) derived quantities, whereas to quantify the transition to turbulence, we computed the standard deviation of the velocity field among different heartbeats and the turbulent kinetic energy.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

scholarly journals Doubly localized states in plane Couette flow

2014 ◽  
Vol 758 ◽  
pp. 1-4 ◽  
Author(s):  
Bruno Eckhardt
Keyword(s):  
Couette Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Linear Instability ◽  
Localized States ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Plane Couette Flow ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

AbstractMuch of our understanding of the transition to turbulence in flows without a linear instability came with the discovery and characterization of fully three-dimensional solutions to the Navier–Stokes equation. The first examples in plane Couette flow were periodic in both spanwise and streamwise directions, and could explain the transitions in small domains only. The presence of localized turbulent spots in larger domains, the spatiotemporal decoherence on larger scales and the ability to trigger turbulence with pointwise perturbations require solutions that are localized in both directions, like the one presented by Brand & Gibson (J. Fluid Mech., vol. 750, 2014, R3). They describe a steady solution of the Navier–Stokes equations and characterize in unprecedented detail, including an analytic computation of its localization properties. The study opens up new ways to describe localized turbulent patches.

Direct Numerical Simulation of Effects of Small Angle of Incidence on Honji Instability

2011 ◽  
Author(s):  
Kun Yang ◽  
Liang Cheng ◽  
Hongwei An ◽  
Ming Zhao
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Angle Of Incidence ◽  
Navier Stokes Equations ◽  
Small Incidence ◽  
Inclination Angles

This paper concerns Honji instability generated around a circular cylinder in an oscillatory flow with a small oblique angle. In this study, direct numerical simulation has been conducted for an oscillatory flow past a stationary cylinder with small incidence angles (α) of 5° and 10° at KC number of 2 and β number of 200. The three-dimensional Navier-Stokes equations are solved using the Petrov-Galerkin finite element method. Flow structures around the cylinder are visualized through using streamlines, velocity vectors and vorticity contours. Honji instability has been captured at both chosen inclination angles. However Honji vortex pairs are asymmetric at α = 5° and 10° due to the inclination of the oscillation direction and can only be observed during the flow reversal. It is also found that the flow inclination appears to suppress the three-dimensional instability.

Turbulent Rayleigh–Bénard convection in a near-critical fluid by three-dimensional direct numerical simulation

2009 ◽  
Vol 619 ◽  
pp. 127-145 ◽  
Author(s):  
G. ACCARY ◽  
P. BONTOUX ◽  
B. ZAPPOLI
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Thermal Balance ◽  
Transition To Turbulence ◽  
Convective Structures ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper presents state of the art three-dimensional numerical simulations of the Rayleigh–Bénard convection in a supercritical fluid. We consider a fluid slightly above its critical point in a cube-shaped cell heated from below with insulated sidewalls; the thermodynamic equilibrium of the fluid is described by the van der Waals equation of state. The acoustic filtering of the Navier–Stokes equations is revisited to account for the strong stratification of the fluid induced by its high compressibility under the effect of its own weight. The hydrodynamic stability of the fluid is briefly reviewed and we then focus on the convective regime and the transition to turbulence. Direct numerical simulations are carried out using a finite volume method for Rayleigh numbers varying from 106 up to 108. A spatiotemporal description of the flow is presented from the convection onset until the attainment of a statistically steady state of heat transfer. This description concerns mainly the identification of the vortical structures in the flow, the distribution of the Nusselt numbers on the horizontal isothermal walls, the structure of the temperature field and the global thermal balance of the cavity. We focus on the influence of the strong stratification of the fluid on the penetrability of the convective structures in the core of the cavity and on its global thermal balance. Finally, a comparison with the case of a perfect gas, at the same Rayleigh number, is presented.

A computational study of the topology of vortex breakdown

1991 ◽  
Vol 435 (1894) ◽  
pp. 321-337 ◽  
Keyword(s):  
Topological Structure ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Computational Study ◽  
Double Helix ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Streamwise Direction ◽  
Navier Stokes Equations ◽  
Axial Velocity Distribution

A fully three-dimensional numerical simulation of vortex breakdown using the unsteady, incompressible Navier–Stokes equations has been performed. Solutions to four distinct types of breakdown are identified and compared with experimental results. The computed solutions include weak helical, double helix, spiral, and bubble-type breakdowns. The topological structure of the various breakdowns as well as their interrelationship are studied. The data reveal that the asymmetric modes of breakdown may be subject to additional breakdowns as the vortex core evolves in the streamwise direction. The solutions also show that the freestream axial velocity distribution has a significant effect on the position and type of vortex breakdown.

scholarly journals Distal Placement of an End-to-Side Bypass Graft Anastomosis: A 3-D Computational Study

2005 ◽  
Author(s):  
John R. DiCicco ◽  
Ayodeji O. Demuren
Keyword(s):  
Stokes Equations ◽  
Computational Study ◽  
Bypass Graft ◽  
Three Dimensional ◽  
Rate Equations ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Shear Rates ◽  
Lower Shear ◽  
Hexahedral Elements

A three-dimensional (3-D) computational fluid dynamics study of shear rates around distal end-to-side anastomoses has been conducted. Three 51% and three 75% cross-sectional area reduced 6 mm cylinders were modeled each with a bypass cylinder attached at a 30 degree angle at different placements distal to the constriction. Steady, incompressible, Newtonian blood flow was assumed, and the full Reynolds-averaged Navier-Stokes equations and turbulent kinetic energy and specific dissipation rate equations were solved on a locally structured multi-block mesh with hexahedral elements. Consequently, distal placement of an end-to-side bypass graft anastomosis was found to have an influence on the shear rate magnitudes. For the 75% constriction, closer placements produced lower shear rates near the anastomosis. Hence, there is potential for new plaque formation and graft failure.

Fine-scale structure of thin vortical layers

1998 ◽  
Vol 364 ◽  
pp. 297-318
Author(s):  
TAKASHI ISHIHARA ◽  
YUKIO KANEDA
Keyword(s):  
Velocity Field ◽  
Fourier Spectrum ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Scale Structure ◽  
Navier Stokes ◽  
Small Scale ◽  
Planar Jet ◽  
Exponential Decay Rate ◽  
Vortical Layer

A class of exact solutions of the Navier–Stokes equations is derived. Each of them represents the velocity field v=U+u of a thin vortical layer (a planar jet) under a uniform strain velocity field U in three-dimensional infinite space, and provides a simple flow model in which nonlinear coupling between small eddies plays a key role in small-scale vortex dynamics. The small-scale structure of the velocity field is studied by numerically analysing the Fourier spectrum of u. It is shown that the Fourier spectrum of u falls off exponentially with wavenumber k for large k. The Taylor expansion in powers of the coordinate (say y) in the direction perpendicular to the vortical layer suggests that the solution may be well approximated by a function with certain poles in the complex y-plane. The Fourier spectrum based on the singularities is in good agreement with that obtained numerically, where the exponential decay rate is given by the distance of the poles from the real axis of y.

Derivation of a Thin Film Equation by a Direct Approach

1996 ◽  
Vol 63 (2) ◽  
pp. 467-473
Author(s):  
F. Y. Huang ◽  
C. D. Mote
Keyword(s):  
Thin Film ◽  
Velocity Field ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Film Structure ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Thin Film Equations ◽  
Thin Film Equation

A new model of the thin viscous fluid film, constrained between two translating, flexible surfaces, is presented in this paper: The unsteady inertia of the film is included in the model. The derivation starts with the reduced three-dimensional Navier-Stokes equations for an incompressible viscous fluid with a small Reynolds number. By introduction of an approximate velocity field, which satisfies the continuity equation and the no-slip boundary conditions exactly, into weighted integrals of the three-dimensional equations over the film thickness, a two-dimensional thin film equation is obtained explicitly in a closed form. The 1th thin film equation is obtained when the velocity field is approximated by 21th order polynominals, and the three-dimensional viscous film is described with increasing accuracy by thin film equations of increasing order. Two cases are used to illustrate the coupling of the film to the vibration of the structure and to show that the second thin film equation can be applied successfully to the prediction of a coupled film-structure response in the range of most applications. A reduced thin film equation is derived through approximation of the second thin film equation that relates the film pressure to transverse accelerations and velocities, and to slopes and slope rates of the two translating surfaces.

Prediction of the three-dimensional flow field and bed shear stresses in a regulated river in mid-Norway

2010 ◽  
Vol 41 (2) ◽  
pp. 145-152 ◽  
Author(s):  
Nils Rüther ◽  
Jens Jacobsen ◽  
Nils Reidar B. Olsen ◽  
Geir Vatne
Keyword(s):  
Cross Sections ◽  
Water Surface ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Surface Profile ◽  
Free Water ◽  
Regulated River ◽  
Shear Stresses ◽  
Three Dimensional Flow ◽  
Dimensional Flow

This study evaluates the use of two Computational Fluid Dynamics (CFD) techniques in calculating the three-dimensional flow and bed shear stress distribution in a regulated river reach near Trondheim, Norway. The two different CFD codes being used in this study are: one commercial FLOW-3D and an in-house program, SSIIM, developed by the third author (NRBO). One of the primary differences between the programs is that FLOW-3D uses an orthogonal, structured grid, while SSIIM uses a non-orthogonal unstructured grid. Flow-3D computes the location of the free water surface based on a volume of fluid method. In the current study, the water surface profile was computed using a 1D backwater computation with SSIIM. Both programs use first- or second-order schemes for the convective term in the Navier–Stokes equations, and the study investigated both options for the two different models. The computed results were compared to ADCP measurements obtained from three cross sections of the river. The comparison showed a good agreement between calculated and measured velocities when using higher-order discretization schemes. Using a first-order upwind scheme, the results deteriorated somewhat due to false diffusion. The results of this current study could be beneficial for the estimation of fluvial erosion, which causes severe damages to riverine areas.

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