Algorithm for Solving Non-stationary Three-Dimensional Navier-Stokes Equations with Large Reynolds Numbers on Multiprocessor Systems

2011 ◽  
pp. 313-326 ◽  
Author(s):  
Nargozy T. Danaev ◽  
Dauren B. Zhakebaev ◽  
Abugamil U. Abdibekov
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Multiprocessor Systems ◽  
Navier Stokes Equations

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.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Self-similar behaviour of a rotor wake vortex core

2014 ◽  
Vol 740 ◽  
Author(s):  
Mohamed Ali ◽  
Malek Abid
Keyword(s):  
Vortex Core ◽  
Scaling Laws ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Azimuthal Velocity ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotating Blade ◽  
Self Similar

AbstractWe report a self-similar behaviour of solutions (obtained numerically) of the Navier–Stokes equations behind a single-blade rotor. That is, the helical vortex core in the wake of a rotating blade is self-similar as a function of its age. Profiles of vorticity and azimuthal velocity in the vortex core are characterized, their similarity variables are identified and scaling laws of these variables are given. Solutions of incompressible three-dimensional Navier–Stokes equations for Reynolds numbers up to $Re= 2000$ are considered.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

scholarly journals Energy spectrum in the dissipation range of fluid turbulence

1997 ◽  
Vol 57 (1) ◽  
pp. 195-201 ◽  
Author(s):  
D. O. MARTÍNEZ ◽  
S. CHEN ◽  
G. D. DOOLEN ◽  
R. H. KRAICHNAN ◽  
L.-P. WANG ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Turbulence ◽  
Theoretical Predictions ◽  
Dissipation Range ◽  
Good Agreement

High-resolution, direct numerical simulations of three-dimensional incompressible Navier–Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/kd)α exp[−βk/kd] is confirmed. The possible values of the parameters α and β, as well as their dependence on Reynolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A ‘bottleneck’-type effect is reported at k/kd≈4, exhibiting a possible transition from near-dissipation to far-dissipation.

scholarly journals Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 124 ◽  
Author(s):  
Masoud Jabbari ◽  
James McDonough ◽  
Evan Mitsoulis ◽  
Jesper Henri Hattel
Keyword(s):  
Projection Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Navier Stokes ◽  
Bottom Surface ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Main Vortex

In this paper, a first-order projection method is used to solve the Navier–Stokes equations numerically for a time-dependent incompressible fluid inside a three-dimensional (3-D) lid-driven cavity. The flow structure in a cavity of aspect ratio δ = 1 and Reynolds numbers ( 100 , 400 , 1000 ) is compared with existing results to validate the code. We then apply the developed code to flow of a generalised Newtonian fluid with the well-known Ostwald–de Waele power-law model. Results show that, by decreasing n (further deviation from Newtonian behaviour) from 1 to 0.9, the peak values of the velocity decrease while the centre of the main vortex moves towards the upper right corner of the cavity. However, for n = 0.5 , the behaviour is reversed and the main vortex shifts back towards the centre of the cavity. We moreover demonstrate that, for the deeper cavities, δ = 2 , 4 , as the shear-thinning parameter n decreased the top-main vortex expands towards the bottom surface, and correspondingly the secondary flow becomes less pronounced in the plane perpendicular to the cavity lid.

scholarly journals Inertial migration of a rigid sphere in three-dimensional Poiseuille flow

2015 ◽  
Vol 765 ◽  
pp. 452-479 ◽  
Author(s):  
Kaitlyn Hood ◽  
Sungyon Lee ◽  
Marcus Roper
Keyword(s):  
Particle Size ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Lateral Force ◽  
Navier Stokes ◽  
Rigid Sphere ◽  
Asymptotic Model ◽  
Navier Stokes Equations ◽  
Inertial Migration

AbstractInertial lift forces are exploited within inertial microfluidic devices to position, segregate and sort particles or droplets. However, the forces and their focusing positions can currently only be predicted by numerical simulations, making rational device design very difficult. Here we develop theory for the forces on particles in microchannel geometries. We use numerical experiments to dissect the dominant balances within the Navier–Stokes equations and derive an asymptotic model to predict the lateral force on the particle as a function of particle size. Our asymptotic model is valid for a wide array of particle sizes and Reynolds numbers, and allows us to predict how focusing position depends on particle size.

3D Simulation of Vortex Shedding Past Tapered Circular Cylinders in Subcritical Reynolds Numbers

2012 ◽  
Author(s):  
V. Tamimi ◽  
M. Zeinoddini ◽  
A. Bakhtiari ◽  
M. Golestani
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
High Reynolds

In this paper results from simulating the vortex shedding phenomena behind a fixed tapered circular cylinder, at relatively high Reynolds numbers, are reported. Ansys-CFX computational fluid dynamics model, based on solving three-dimensional (3D) incompressible transient Navier Stokes equations, is employed for this purpose. The geometries applied in the models resemble those used in wind tunnel experiments by other researchers. The taper slope along the cylinder span is uniform with a tangent of 24:1. The diameter at mid-span of the cylinder equals to 0.0389 m. The Reynolds number (based on the mid-span diameter) is around 29,000. The computational model has first been calibrated against experiments for uniform 3D cylinders as well as results from a Direct Numerical Simulation of turbulent wake with vortex shedding past a uniform circular cylinder, as obtained by other researchers. The main flow characteristics for tapered cylinders such as vortex dislocations and splitting, cellular vortex shedding, oblique vortex shedding and the variation of the vorticity patterns along the tapered cylinder could be obtained from the simulations.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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