The Effect of Constriction Size on the Pulsatile Flow in a Channel

1995 ◽  
Vol 117 (4) ◽  
pp. 571-576 ◽  
Author(s):  
Moshe Rosenfeld ◽  
Shmuel Einav
Keyword(s):  
Pulsatile Flow ◽  
Stokes Equations ◽  
Thrombus Formation ◽  
Propagation Speed ◽  
Navier Stokes ◽  
Flow Structures ◽  
Incoming Flow ◽  
Noninvasive Methods ◽  
Navier Stokes Equations ◽  
Potential Damage

The effect of the constriction size on the pulsatile flow in a channel is studied by solving the time-dependent incompressible Navier-Stokes equations. A pulsating incoming flow is specified at the upstream boundary and the flow is investigated for several constriction sizes. Large flow structures are developed downstream of the constriction even for very small constriction size. The flow structures consist of several vortices that are created in each cycle and propagate downstream until they are washed away with the acceleration of the incoming flow. Additional vortices are created by a vortex multiplication process. The strength and total number of vortices generated in each cycle increase with the severity of the constriction. The maximal size of the vortices as well as their propagation speed are independent of the constriction size. These findings may be used for devising noninvasive methods for detecting the severity of stenoses in blood vessels and the potential damage to blood elements and thrombus formation caused by vortices.

Numerical Investigation of Unsteady Incompressible 3D Turbulent Flow and Torque Transmission in Fluid Couplings

1994 ◽  
Author(s):  
L. Bal ◽  
A. Kost ◽  
M. Fiebig ◽  
N. K. Mitra
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Flow Structures ◽  
Optimized Design ◽  
Navier Stokes Equations ◽  
Reference Flow ◽  
Torque Transmission ◽  
Adequate Understanding ◽  
Volume Method ◽  
Good Agreement

The adequate understanding of the flow structure in fluid couplings is necessary for the optimized design of such devices. Up to now, empiricism plays an important role in design. Detailed studies of the unsteady 3D flow and torque transmission in fluid couplings were rarely carried out. In this paper the unsteady Reynolds time-averaged Navier-Stokes equations coupled with the k-ε model have been solved by a finite-volume method. The calculations were done by using boundary-fitted grids with non-staggered variable arrangement for a rotating frame of reference. Flow structures in fluid couplings were obtained. The results give insights into the physical process of torque transmission. A comparsion of the calculated torque transimission with the experimental measurements in the literature shows good agreement for low slip.

Geometrical Effects on Fluid Mixing of Pulsatile Flow in Convergent-Divergent Micromixer

2015 ◽  
Author(s):  
Arshad Afzal ◽  
Kwang-Yong Kim
Keyword(s):  
Pulsatile Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Geometrical Parameters ◽  
Navier Stokes Equations ◽  
Mixing Performance ◽  
Throat Width ◽  
Pulsatile Flows ◽  
Geometrical Effects ◽  
Diffusion Convection

Time-dependent pulsatile flows have been used by many researchers for fast and efficient mixing at micro-scale [1–2]. In a recent study, a convergent-divergent microchannel with sinusoidal walls showed a strong coupling with pulsatile flow for enhanced mixing performance over a short mixing length [3]. In the present study, effects of two geometrical parameters, i.e., the ratio of amplitude to wavelength and ratio of throat-width to depth on mixing performance, were analyzed with the Strouhal number and the ratio of pulsing amplitude to steady flow velocity at a fixed Reynolds number, Re = 0.5. The flow and mixing analyses were performed using unsteady Navier-Stokes equations and a diffusion-convection model for species concentration.

Three-Dimensional Flow and Pressure Patterns in a Hydrostatic Journal Bearing Pocket

1997 ◽  
Vol 119 (4) ◽  
pp. 711-719 ◽  
Author(s):  
M. J. Braun ◽  
M. B. Dzodzo
Keyword(s):  
Journal Bearing ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Regimes ◽  
Axial Direction ◽  
Outward Bound ◽  
Navier Stokes ◽  
Flow Structures ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations

The laminar flow in a hydrostatic pocket is described by a mathematical model that uses the three-dimensional Navier-Stokes equations written in terms of the primary variables, u, v, w, and p. Using a conservative formulation, a finite volume multiblock method is applied through a collocated, body fitted grid. The flow is simulated in a shallow pocket with a depth/length ratio of 0.02. The flow structures obtained and described by the authors in their previous two dimensional models are made visible in their three dimensional aspect for both the Couette, and the jet dominated flows. It has been found that both flow regimes formed central and secondary vortical cells with three dimensional corkscrew-like structures that lead the fluid on an outward bound path in the axial direction of the pocket. In the Couette dominated flow the position of the central vortical cell center is at the exit region of the capillary restrictor feedline, while in the jet dominated flow a flattened central vortical cell is formed in the downstream part of the pocket. It has also been determined that a fluid turn around zone occupies all the upstream space between the floor of the pocket and the runner, thus preventing any flow exit through the upstream exit of the pocket. The corresponding pressure distribution under the shaft for both flow regimes is presented as well. It was clearly established that both for the Couette, and the jet dominated cases the pressure varies significantly in the pocket in the circumferential direction, while its variation is less pronounced axially.

An analysis of aerodynamic forces on a delta wing

1996 ◽  
Vol 316 ◽  
pp. 173-196 ◽  
Author(s):  
Chien-Cheng Chang ◽  
Sheng-Yuan Lei
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Delta Wing ◽  
Leading Edge ◽  
Navier Stokes ◽  
Flow Structures ◽  
Aerodynamic Forces ◽  
Navier Stokes Equations ◽  
Lift And Drag ◽  
Secondary Vortices

The present study aims at relating lift and drag to flow structures around a delta wing of elliptic section. Aerodynamic forces are analysed in terms of fluid elements of non-zero vorticity and density gradient. The flow regime considered is Mα = 0.6 ∼ 1.8 and α = 5° ∼ 19°, where Mα denotes the free-stream Mach number and α the angle of attack. Let ρ denote the density, u velocity, and ω vorticity. It is found that there are two major source elements Re(x) and Ve(x) which contribute about 95% or even more to the aerodynamic forces for all the cases under consideration, \[R_e({\bm x})=-\frac{1}{2} {\bm u}^2 \nabla\rho \cdot \nabla\phi\quad {\rm and}\quad V_e ({\bm x}) = -\rho{\bm u}\times {\bm \omega}\cdot \nabla\phi,\] where θ is an acyclic potential, generated by the delta wing moving with unit velocity in the negative direction of the force (lift or drag). All the physical quantities are non-dimensionalized. Detailed force contributions are analysed in terms of the flow structures and the elements Re(x) and Ve(x). The source elements Re(x) and Ve(x) are concentrated in the following regions: the boundary layer in front of (below) the delta wing, the primary and secondary vortices over the delta wing, and a region of expansion around the leading edge. It is shown that Ve(x) due to vorticity prevails as the source of forces at relatively low Mach number, Mα < 0.7. Above about Mα = 0.75, Re(x) due to compressibility generally becomes the dominating contributor to the lift, while the overall contribution from Ve(x) decreases with increasing Mα, and even becomes negative at Mα = 1.2 for the lift, and at a higher Mα for the drag. The analysis is carried out with the aid of detailed numerical results by solving the Reynolds-averaged Navier–Stokes equations, which are in close agreement with experiments in comparisons of the surface pressure distributions.

Pulsatile Albumin Transport in Large Arteries: A Numerical Simulation Study

1996 ◽  
Vol 118 (4) ◽  
pp. 511-519 ◽  
Author(s):  
G. Rappitsch ◽  
K. Perktold
Keyword(s):  
Pulsatile Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Flow Region ◽  
Navier Stokes ◽  
Permeability Model ◽  
Navier Stokes Equations ◽  
Area Reduction ◽  
Stenosed Artery ◽  
Percent Area

Albumin transport in a stenosed artery configuration is analyzed numerically under steady and pulsatile flow conditions. The flow dynamics is described applying the incompressible Navier-Stokes equations for Newtonian fluids, the mass transport is modelled using the convection diffusion equation. The boundary conditions describing the solute wall flux take into account the concept of endothelial resistance to albumin flux by means of a shear dependent permeability model based on experimental data. The study concentrates on the influence of steady and pulsatile flow patterns and of regional variations in vascular geometry on the solute wall flux and on the ratio of endothelial resistance to concentration boundary layer resistance. The numerical solution of the Navier-Stokes equations and of the transport equation applies the finite element method where stability of the convection dominated transport process is achieved by using an upwind procedure and a special subelement technique. Numerical simulations are carried out for albumin transport in a stenosed artery segment with 75 percent area reduction representing a late stage in the progression of an atherosclerotic disease. It is shown that albumin wall flux varies significantly along the arterial section, is strongly dependent upon the different flow regimes and varies considerably during a cardiac cycle. The comparison of steady results and pulsatile results shows differences up to 30 percent between time-averaged flux and steady flux in the separated flow region downstream the stenosis.

scholarly journals Modelling of the flow in front of the jet obstacle at variation of oncoming flow parameters

2021 ◽  
pp. 1-14
Author(s):  
Alexander Evgenyevich Bondarev ◽  
Artyom Evgenyevich Kuvshinnikov ◽  
Tatiana Nikolaevna Mikhailova ◽  
Irina Gennadievna Ryzhova ◽  
Lev Zalmanovich Shapiro
Keyword(s):  
Software Package ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Incoming Flow ◽  
Oncoming Flow ◽  
Input Flow ◽  
Navier Stokes Equations ◽  
Flow Parameters

The results of numerical simulation of the problem of interaction of supersonic flow with a jet obstacle under variation of input flow parameters are considered. The problem is solved in the system of Navier-Stokes equations. Laminar flows are considered. The qualitative flow pattern has been studied under the variation of incoming flow velocity and boundary layer thickness in the incoming flow. The calculations were performed using the OpenFOAM software package.

scholarly journals AN UNSTEADY ANALYSIS OF NONLINEAR TWO‐LAYERED 2D MODEL OF PULSATILE FLOW THROUGH STENOSED ARTERIES

2003 ◽  
Vol 8 (3) ◽  
pp. 229-246 ◽  
Author(s):  
P. K. Mandal
Keyword(s):  
Pulsatile Flow ◽  
Stokes Equations ◽  
Plasma Layer ◽  
Fluid Model ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Numerical Illustration ◽  
Navier Stokes Equations ◽  
Effective Measure ◽  
Two Fluid Model

The effects of red cell concentration and peripheral layer viscosity on physiological characteristics of pulsatile flow in presence of mild stenosis are investigated. The flowing blood is represented by a two‐fluid model, consisting of a core region of suspension of all the erythrocytes assumed to be non‐Newtonian (inhomogeneous Newtonian) and a peripheral plasma layer free from cells of any kind as a Newtonian fluid. In the realm of the flow characteristics of blood the viscosity is taken to be a function of hematocrit in a manner that it varies radially only in the central core characterising its non‐Newtonian behaviour while it remains constant in the plasma region. The arterial wall motion and its effect on local fluid mechanics is also incorporated in the present theoretical study. Finite difference scheme has been used to solve the unsteady Navier‐Stokes equations in cylindrical coordinates assuming axial symmetry under laminar conditions, so that the problem effectively becomes two‐dimensional. The nonlinear terms appearing in the Navier‐Stokes equations governing blood flow are accounted for. Finally, the numerical illustration presented at the end of the paper provides an effective measure of the flux, the resistive impedance and the wall shear stress quantitatively in order to validate the applicability of the present model.

scholarly journals Helicoidal particles in turbulent flows with multi-scale helical injection

2019 ◽  
Vol 869 ◽  
pp. 646-673 ◽  
Author(s):  
L. Biferale ◽  
K. Gustavsson ◽  
R. Scatamacchia
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Structural Parameters ◽  
Spherical Particles ◽  
Navier Stokes ◽  
Flow Structures ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Multi Scale ◽  
Preferential Sampling

We present numerical and theoretical results concerning the properties of turbulent flows with strong multi-scale helical injection. We perform direct numerical simulations of the Navier–Stokes equations under a random helical stirring with power-law spectrum and with different intensities of energy and helicity injections. We show that there exists three different regimes where the forward energy and helicity inertial transfers are: (i) both leading with respect to the external injections, (ii) energy transfer is leading and helicity transfer is sub-leading and (iii) both are sub-leading and helicity is maximal at all scales. As a result, the cases (ii)–(iii) give flows with Kolmogorov-like inertial energy cascade and tuneable helicity transfers/contents. We further explore regime (iii) by studying its effect on the kinetics of point-like isotropic helicoids, particles whose dynamics is isotropic but breaks parity invariance. We investigate small-scale fractal clustering and preferential sampling of intense helical flow structures. Depending on their structural parameters, the isotropic helicoids either preferentially sample co-chiral or anti-chiral flow structures. We explain these findings in limiting cases in terms of what is known for spherical particles of different densities and degrees of inertia. Furthermore, we present theoretical and numerical results for a stochastic model where dynamical properties can be calculated using analytical perturbation theory. Our study shows that a suitable tuning of the stirring mechanism can strongly modify the small-scale turbulent helical properties and demonstrates that isotropic helicoids are the simplest particles able to preferentially sense helical properties in turbulence.

Computational hemodynamic investigation of a new bileaflet mechanical heart valve

SIMULATION ◽  
2019 ◽  
Vol 96 (5) ◽  
pp. 459-469
Author(s):  
Belkhiri Khellaf ◽  
Boumeddane Boussad
Keyword(s):  
Heart Valve ◽  
Heart Valves ◽  
Stokes Equations ◽  
Thrombus Formation ◽  
Mechanical Heart Valve ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Blood Damage ◽  
Flow Through

In this paper, we perform a numerical analysis for simulating steady, two-dimensional, laminar blood flow through our proposed design, known as the Butterfly mechanical heart valve, where the leaflets are fully opened. Blood has been assumed to be Newtonian and non-Newtonian fluid using the Casson model for shear-thinning behavior. A non-uniform Cartesian grid generation technique is presented to generate a two-dimensional grid for the irregular geometry of the Butterfly valve. The governing Navier–Stokes equations of flow, written in a stream function–vorticity formulation, are solved by the finite difference method with hybrid differencing of the convective terms. The computed results show that the blood’s non-Newtonian nature significantly affects the flow field with the existence of recirculation and consequently stagnation causing thrombus formation, as well as an increase of the shear stress along the wall, which contributes to hemolytic blood damage. The results demonstrate that the model is capable of predicting the hemodynamic features most interesting to physiologists. It can be used to assess thromboembolic problems occurring with heart valves and in the design of cardiac prostheses.

scholarly journals FEATURES OF MODELING THE FLOW AROUND THE HELICOPTER MAIN ROTOR TAKING INTO ACCOUNT ARBITRARY BLADES MOTION

2019 ◽  
Vol 22 (3) ◽  
pp. 25-34
Author(s):  
V. A. Vershkov ◽  
B. S. Kritsky ◽  
R. M. Mirgazov
Keyword(s):  
Turbulence Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Incoming Flow ◽  
Main Rotor ◽  
Thrust Coefficient ◽  
Navier Stokes Equations ◽  
Ansys Cfx ◽  
Sst Turbulence Model ◽  
Helicopter Main Rotor

The article considers the problem of the flow around the helicopter main rotor taking into account blades flapping in the plane of rotation and in the plane of thrust as well as the elastic blades deformation. The rotor rotation is modeled by the method of converting Navier-Stokes equations from a fixed coordinate system associated with the incoming flow into a rotating system associated with the rotor hub. For axial flow problems, this makes it possible to formulate the problem as stationary at a constant rotational speed of rotor. For a mode of skewed flow around the rotor in the terms of incident flow in this system it is necessary to solve the non-stationary problem. To solve the problem, the method of deformable grids is used, in which the equations are copied taking into account the grid nodes motion determined in accordance with the spatial blades motion, and SST turbulence model is used for closure. The results of the test calculations of the main rotor aerodynamic characteristics with and without blade flapping are presented in this paper. The coefficients of the main rotor thrust cT and the blades hinge moments mh are compared. The calculations were carried out in the CFD software ANSYS CFX (TsAGI License No. 501024). The flow around a four-bladed main rotor of a radius of 2.5 meters is modeled in the regime of skewed flow. The speed of the incoming flow came to 85 m/s under normal atmospheric conditions. The rotor was at an angle of attack of −10˚. To calculate the rotor motion without taking into account the flapping movements, we used the nonstationary system of Navier-Stokes equations with the closure with SST turbulence model. The calculation was being carried out until the change in the maximum value of the rotor thrust during one revolution became less than 1%. For modeling flapping blade movements, the control laws and equations describing the angle of blade flapping as a function from its azimuth angle obtained from the experiment were used. The procedure for reconstructing the grid according to a given law was conducted using standard grid deformation methods presented in the ANSYS CFX software. When solving the nonstationary Navier-Stokes equations, a dual time step was used. The obtained results show that accounting of the effect of flapping movements and cyclic control of the blades has an impact on the character of changing the main rotor thrust coefficient during one revolution and significantly changes the shape of the graph of the hinge moment coefficient of each blade.

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