Flows produced by the combined oscillatory rotation and translation of a circular cylinder in a quiescent fluid

2014 ◽  
Vol 764 ◽  
pp. 148-170 ◽  
Author(s):  
Christopher Koehler ◽  
Philip Beran ◽  
Marcos Vanella ◽  
Elias Balaras
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Bluff Body ◽  
Stokes Equations ◽  
Time Windows ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Immersed Boundary ◽  
Dimensionless Time ◽  
Quiescent Fluid

AbstractFlows produced by a circular cylinder undergoing oscillatory rotation and translation in a quiescent fluid have been studied via direct numerical simulations. The incompressible Navier–Stokes equations were solved for large dimensionless time windows using an immersed boundary method with adaptive Cartesian grid refinement. Parametric studies were conducted in two dimensions on the Reynolds number, Keulegan–Carpenter number and phase shift. In addition to the previously reported net thrust case (Blackburn et al., Phys. Fluids, vol. 11, 1999, pp. 4–6), the study catalogued the appearance of several streaming jet regimes with varying deflection angles, deflected and horizontal vortex shedding regimes, and a double mirrored jet regime with varying inter-jet angles, as well as several chaotic cases. Visualizations are presented to clarify each observed flow regime and to illustrate the parameter space. Connections are drawn between these canonical bluff-body deflected wakes and a similar phenomenon observed in aerofoils oscillating at high reduced frequencies in a cross-flow. Also, the discovery of the streaming jet regimes with varying deflection angles opens the door for using these flows as a low-Reynolds-number propulsive mechanism requiring only a two-degree-of-freedom actuator. Simulation results suggest that the flow phenomena observed in two dimensions persist in three dimensions, despite spanwise fluctuations.

scholarly journals The flow of viscous liquid past spinning bodies

1933 ◽  
Vol 142 (847) ◽  
pp. 491-508 ◽  
Keyword(s):  
Circular Cylinder ◽  
Viscous Liquid ◽  
Stokes Equations ◽  
Slow Motion ◽  
Two Dimensions ◽  
The Body ◽  
Three Dimensions ◽  
Stream Velocity ◽  
Flow Past ◽  
Spinning Bodies

The motion produced in a viscous liquid by a spinning sphere has been investigated for small values of the Reynolds’ number, using Stokes’ equations for slow motion, in which the inertia terms are neglected.* By combining the solution for this problem with that given by Stokes for the flow of a stream of viscous liquid past a fixed sphere, we obtain the solution for a stream flowing past a spinning sphere. Oseen introduced a modified system of equations, in which the inertia terms are partly taken into account, and obtained the solution for flow past a fixed sphere using these equations. The problem of the flow of viscous liquid past a fixed circular cylinder has been investigated by Lamb,§ using Oseen’s equations, and the additional solution required if the cylinder is rotating has been given by Oseen.║In the present paper the solution for flow past a spinning sphere is discussed, using Oseen’s equations. The flow of viscous liquid past a spinning body is physically equivalent to motion of the body through the liquid with combined translation and rotation. Now it is well known that in practice when a body moves through a liquid in such a manner, if there is rotation about an axis y perpendicular to the direction of motion x , then ther is a lift on the body in a direction perpendicular to both x and y ¶. In theoretical investigation , if we suppose that the motion is steady, we are restricted in three dimensions to a body rotating about an axis of symmetry, and in two dimensions to the circular cylinder. In these cases it is impossible to obtain a lift if we use Stokes' equations for slow motion. For since that equations are linear, the lift is the sum of the lifts due to the solution for flow past a fixed body and the solution for spin without flow, and these are both zero by symmetry. This argument does not apply to Oseen's equations, since we cannot have a solution for spin alone with no flow, the stream velocity being implied in the equations themselves. In the absence of a method for solving the complete hydrodynamcial equations, it is therefore of interest to investigate the flow of viscous liquid past spinning bodies, using Oseen's equations, and particularly to find whether a lift is obtained.

Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders

2013 ◽  
Vol 736 ◽  
pp. 414-443 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida ◽  
M. Iguchi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Vortex Method ◽  
The Self ◽  
Circular Cylinders ◽  
Far Field ◽  
Flow Past ◽  
Low Reynolds

AbstractThe long-time viscous flow about two identical rotating circular cylinders in a side-by-side arrangement is investigated using an adaptive numerical scheme based on the vortex method. The Stokes solution of the steady flow about the two-cylinder cluster produces a uniform stream in the far field, which is the so-called Jeffery’s paradox. The present work first addresses the validation of the vortex method for a low-Reynolds-number computation. The unsteady flow past an abruptly started purely rotating circular cylinder is therefore computed and compared with an exact solution to the Navier–Stokes equations. The steady state is then found to be obtained for $t\gg 1$ with ${\mathit{Re}}_{\omega } {r}^{2} \ll t$, where the characteristic length and velocity are respectively normalized with the radius ${a}_{1} $ of the circular cylinder and the circumferential velocity ${\Omega }_{1} {a}_{1} $. Then, the influence of the Reynolds number ${\mathit{Re}}_{\omega } = { a}_{1}^{2} {\Omega }_{1} / \nu $ about the two-cylinder cluster is investigated in the range $0. 125\leqslant {\mathit{Re}}_{\omega } \leqslant 40$. The convection influence forms a pair of circulations (called self-induced closed streamlines) ahead of the cylinders to alter the symmetry of the streamline whereas the low-Reynolds-number computation (${\mathit{Re}}_{\omega } = 0. 125$) reaches the steady regime in a proper inner domain. The self-induced closed streamline is formed at far field due to the boundary condition being zero at infinity. When the two-cylinder cluster is immersed in a uniform flow, which is equivalent to Jeffery’s solution, the streamline behaves like excellent Jeffery’s flow at ${\mathit{Re}}_{\omega } = 1. 25$ (although the drag force is almost zero). On the other hand, the influence of the gap spacing between the cylinders is also investigated and it is shown that there are two kinds of flow regimes including Jeffery’s flow. At a proper distance from the cylinders, the self-induced far-field velocity, which is almost equivalent to Jeffery’s solution, is successfully observed in a two-cylinder arrangement.

Effect of wall-mounted V-baffle position in a turbulent flow through a channel

2019 ◽  
Vol 29 (10) ◽  
pp. 3908-3937 ◽  
Author(s):  
Younes Menni ◽  
Ahmed Azzi ◽  
Ali J. Chamkha ◽  
Souad Harmand
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Simple Algorithm ◽  
Two Dimensions ◽  
Large Reynolds Number ◽  
Constant Property ◽  
Content Type

Purpose The purpose of this paper is to carry out a numerical study on the dynamic and thermal behavior of a fluid with a constant property and flowing turbulently through a two-dimensional horizontal rectangular channel. The upper surface was put in a constant temperature condition, while the lower one was thermally insulated. Two transverse, solid-type obstacles, having different shapes, i.e. flat rectangular and V-shaped, were inserted into the channel and fixed to the top and bottom walls of the channel, in a periodically staggered manner to force vortices to improve the mixing, and consequently the heat transfer. The flat rectangular obstacle was put in the first position and was placed on the hot top wall of the channel. However, the second V-shaped obstacle was placed on the insulated bottom wall, at an attack angle of 45°; its position was varied to find the optimum configuration for optimal heat transfer. Design/methodology/approach The fluid is considered Newtonian, incompressible with constant properties. The Reynolds averaged Navier–Stokes equations, along with the standard k-epsilon turbulence model and the energy equation, are used to control the channel flow model. The finite volume method is used to integrate all the equations in two-dimensions; the commercial CFD software FLUENT along with the SIMPLE-algorithm is used for pressure-velocity coupling. Various values of the Reynolds number and obstacle spacing were selected to perform the numerical runs, using air as the working medium. Findings The channel containing the flat fin and the 45° V-shaped baffle with a large Reynolds number gave higher heat transfer and friction loss than the one with a smaller Reynolds number. Also, short separation distances between obstacles provided higher values of the ratios Nu/Nu0 and f/f0 and a larger thermal enhancement factor (TEF) than do larger distances. Originality/value This is an original work, as it uses a novel method for the improvement of heat transfer in completely new flow geometry.

Numerical Simulation of Vortex Shedding Past a Circular Cylinder in a Cross-Flow at Low Reynolds Number With Finite Volume-Technique: Part 1 — Forced Oscillations

2007 ◽  
Author(s):  
Antoine Placzek ◽  
Jean-Franc¸ois Sigrist ◽  
Aziz Hamdouni
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Circular Cylinder ◽  
Finite Volume ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Cross Flow ◽  
Forced Oscillations ◽  
Lift And Drag ◽  
Wake Characteristics

The numerical simulation of the flow past a circular cylinder forced to oscillate transversely to the incident stream is presented here for a fixed Reynolds number equal to 100. The 2D Navier-Stokes equations are solved with a classical Finite Volume Method with an industrial CFD code which has been coupled with a user subroutine to obtain an explicit staggered procedure providing the cylinder displacement. A preliminary work is conducted in order to check the computation of the wake characteristics for Reynolds numbers smaller than 150. The Strouhal frequency fS, the lift and drag coefficients CL and CD are thus controlled among other parameters. The simulations are then performed with forced oscillations f0 for different frequency rations F = f0/fS in [0.50–1.50] and an amplitude A varying between 0.25 and 1.25. The wake characteristics are analysed using the time series of the fluctuating aerodynamic coefficients and their FFT. The frequency content is then linked to the shape of the phase portrait and to the vortex shedding mode. By choosing interesting couples (A,F), different vortex shedding modes have been observed, which are similar to those of the Williamson-Roshko map.

A One-Continuum Approach for Mutual Interaction of Fluids and Structures

2015 ◽  
Vol 31 (6) ◽  
pp. 745-755 ◽  
Author(s):  
I. Farahbakhsh ◽  
H. Ghassemi ◽  
F. Sabetghadam
Keyword(s):  
Circular Cylinder ◽  
Immersed Boundary Method ◽  
Simulation Method ◽  
Immersed Boundary ◽  
Continuum Approach ◽  
Fluid Structure ◽  
Driven Cavity ◽  
Basic Equations ◽  
Definition Of ◽  
Quiescent Fluid

ABSTRACTA new simulation method for solving fluid-structure two-way coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A new definition of velocity-vorticity formulation aids us to introduce an immersed boundary method that does not require a force term to impose the no-slip condition on the solid boundaries. The proposed method is easy to implement and apply for two-way fluid-structure interaction problems. The dynamics of a falling and rising circular cylinder in a quiescent fluid as well as the motion of a circular cylinder in a lid-driven cavity are considered to evaluate the capabilities of the presented method.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

The Flow of A Falling Ellipse: Numerical Method and Classification

2015 ◽  
Vol 31 (6) ◽  
pp. 771-782 ◽  
Author(s):  
R.-J. Wu ◽  
S.-Y. Lin
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Correction Method ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Two Dimensional ◽  
Inertia Moment ◽  
Navier Stokes Equations ◽  
Direct Forcing ◽  
Ib Method

AbstractA modified direct-forcing immersed-boundary (IB) pressure correction method is developed to simulate the flows of a falling ellipse. The pressure correct method is used to solve the solutions of the two dimensional Navier-Stokes equations and a direct-forcing IB method is used to handle the interaction between the flow and falling ellipse. For a fixed aspect ratio of an ellipse, the types of the behavior of the falling ellipse can be classified as three pure motions: Steady falling, fluttering, tumbling, and two transition motions: Chaos, transition between steady falling and fluttering. Based on two dimensionless parameters, Reynolds number and the dimensionless moment of inertia, a Reynolds number-inertia moment phase diagram is established. The behaviors and characters of five falling regimes are described in detailed.

Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation

1994 ◽  
Vol 261 ◽  
pp. 95-134 ◽  
Author(s):  
J. Feng ◽  
H. H. Hu ◽  
D. D. Joseph
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Steady Motion ◽  
Vertical Channel ◽  
Periodic Oscillation ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Fluid Particle ◽  
Initial Value ◽  
Circular Particle

This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.

Numerical Simulation of Flow in a Wavy Wall Microchannel Using Immersed Boundary Method

2020 ◽  
Vol 13 (2) ◽  
pp. 118-125
Author(s):  
Mithun Kanchan ◽  
Ranjith Maniyeri
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Immersed Boundary ◽  
Solid Boundary ◽  
Wavy Wall ◽  
Dirac Delta ◽  
Boundary Method

Background: Fluid flow in microchannels is restricted to low Reynolds number regimes and hence inducing chaotic mixing in such devices is a major challenge. Over the years, the Immersed Boundary Method (IBM) has proved its ability in handling complex fluid-structure interaction problems. Objectives: Inspired by recent patents in microchannel mixing devices, we study passive mixing effects by performing two-dimensional numerical simulations of wavy wall in channel flow using IBM. Methods: The continuity and Navier-Stokes equations governing the flow are solved by fractional step based finite volume method on a staggered Cartesian grid system. Fluid variables are described by Eulerian coordinates and solid boundary by Lagrangian coordinates. A four-point Dirac delta function is used to couple both the coordinate variables. A momentum forcing term is added to the governing equation in order to impose the no-slip boundary condition between the wavy wall and fluid interface. Results: Parametric study is carried out to analyze the fluid flow characteristics by varying amplitude and wavelength of wavy wall configurations for different Reynolds number. Conclusion: Configurations of wavy wall microchannels having a higher amplitude and lower wavelengths show optimum results for mixing applications.

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