scholarly journals Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers

2005 ◽  
Vol 2005 (3) ◽  
pp. 183-203 ◽  
Author(s):  
T. V. S. Sekhar ◽  
R. Sivakumar ◽  
T. V. R. Ravi Kumar
Keyword(s):  
Circular Cylinder ◽  
Drag Coefficient ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Flow Direction ◽  
Boundary Layer Separation ◽  
Pressure Fields ◽  
Correction Technique ◽  
Rear Stagnation Point

Steady incompressible flow around a circular cylinder in an external magnetic field that is aligned with fluid flow direction is studied forRe(Reynolds number) up to 40 and the interaction parameter in the range0≤N≤15(or0≤M≤30), whereMis the Hartmann number related toNby the relationM=2NRe, using finite difference method. The pressure-Poisson equation is solved to find pressure fields in the flow region. The multigrid method with defect correction technique is used to achieve the second-order accurate solution of complete nonlinear Navier-Stokes equations. It is found that the boundary layer separation at rear stagnation point forRe=10is suppressed completely whenN<1and it started growing again whenN≥9. ForRe=20and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing whenN≥3. The drag coefficient decreases for low values ofN(<0.1)and then increases with increase ofN. The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary withN. It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values ofN(<0.1)and rear pressure inversion occurs with further increase ofN. These results are in agreement with experimental findings.

Oscillatory flow past a circular cylinder in a rotating frame

1997 ◽  
Vol 345 ◽  
pp. 101-131
Author(s):  
M. D. KUNKA ◽  
M. R. FOSTER
Keyword(s):  
Circular Cylinder ◽  
Steady Flow ◽  
Stagnation Point ◽  
Oscillatory Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Temporal Integration ◽  
Oncoming Flow ◽  
Flow Past ◽  
Rear Stagnation Point

Because of the importance of oscillatory components in the oncoming flow at certain oceanic topographic features, we investigate the oscillatory flow past a circular cylinder in an homogeneous rotating fluid. When the oncoming flow is non-reversing, and for relatively low-frequency oscillations, the modifications to the equivalent steady flow arise principally in the ‘quarter layer’ on the surface of the cylinder. An incipient-separation criterion is found as a limitation on the magnitude of the Rossby number, as in the steady-flow case. We present exact solutions for a number of asymptotic cases, at both large frequency and small nonlinearity. We also report numerical solutions of the nonlinear quarter-layer equation for a range of parameters, obtained by a temporal integration. Near the rear stagnation point of the cylinder, we find a generalized velocity ‘plateau’ similar to that of the steady-flow problem, in which all harmonics of the free-stream oscillation may be present. Further, we determine that, for certain initial conditions, the boundary-layer flow develops a finite-time singularity in the neighbourhood of the rear stagnation point.

scholarly journals Computation of Pressure Fields around a Two-Dimensional Circular Cylinder Using the Vortex-In-Cell and Penalization Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seung-Jae Lee ◽  
Jun-Hyeok Lee ◽  
Jung-Chun Suh
Keyword(s):  
Circular Cylinder ◽  
Solid Body ◽  
Pressure Field ◽  
Stokes Equations ◽  
Computational Cost ◽  
Fixed Time ◽  
Computational Grids ◽  
Penalty Term ◽  
Pressure Fields ◽  
Wide Range

The vorticity-velocity formulation of the Navier-Stokes equations allows purely kinematical problems to be decoupled from the pressure term, since the pressure is eliminated by applying the curl operator. The Vortex-In-Cell (VIC) method, which is based on the vorticity-velocity formulation, offers particle-mesh algorithms to numerically simulate flows past a solid body. The penalization method is used to enforce boundary conditions at a body surface with a decoupling between body boundaries and computational grids. Its main advantage is a highly efficient implementation for solid boundaries of arbitrary complexity on Cartesian grids. We present an efficient algorithm to numerically implement the vorticity-velocity-pressure formulation including a penalty term to simulate the pressure fields around a solid body. In vorticity-based methods, pressure field can be independently computed from the solution procedure for vorticity. This clearly simplifies the implementation and reduces the computational cost. Obtaining the pressure field at any fixed time represents the most challenging goal of this study. We validate the implementation by numerical simulations of an incompressible viscous flow around an impulsively started circular cylinder in a wide range of Reynolds numbers: Re=40, 550, 3000, and 9500.

CFD Analysis of Vortex Shedding in a Circular Cylinder: Flow Induced Vibration Design

2006 ◽  
Author(s):  
Nadeem Ahmed Sheikh ◽  
M. Afzaal Malik ◽  
Arshad Hussain Qureshi ◽  
M. Anwar Khan ◽  
Shahab Khushnood
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Boundary Layer Separation ◽  
The Body ◽  
Navier Stokes ◽  
Structural Vibrations ◽  
Flow Induced Vibration ◽  
Navier Stokes Equations ◽  
Implicit Approach

Flow past a blunt body, such as a circular cylinder, usually experiences boundary layer separation and very strong flow oscillations in the wake region behind the body at a discrete frequency that is correlated to the Reynolds number of the flow. The periodic nature of the vortex shedding phenomenon can sometimes lead to unwanted structural vibrations. The effect of vibrating instability of a single cylinder is investigated in a uniform flow using the power of computational methods. Fluid structure coupling procedure predicts the fluid forces responsible for structural vibrations. An implicit approach to the solution of the unsteady two-dimensional Navier-Stokes equations is used for computation of flow parameters. Calculations are performed in parallel using a domain re-meshing/deforming technique with efficient communication requirements. Results for the unsteady shedding flow behind a circular cylinder are presented with experimental comparisons, showing the feasibility of accurate, efficient, time-dependent estimation of shedding frequency and resulting vibrations.

Crossflow Over a Porous Circular Cylinder With Surface Blowing: CFD Analysis With Experimental Validation

2012 ◽  
Author(s):  
T. H. Reif ◽  
F. A. Kulacki
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Stagnation Point ◽  
Test Section ◽  
Free Stream ◽  
Absolute Error ◽  
Secondary Flows ◽  
Test Case ◽  
Positional Error ◽  
Rear Stagnation Point

Crossflow over a porous circular cylinder, with uniform blowing at the surface, was investigated experimentally and numerically. Two free stream conditions, Reynolds numbers 4,100 and 6,200, and five dimensionless blowing rate parameters (ratio of surface blowing to free stream velocity), 0.000 to 0.190, were studied experimentally. For simplicity, results for only one Reynolds number and three blowing cases are presented. A low speed wind tunnel was designed and constructed to give time-smoothed average velocities in the range of 61–122 cm/s. The tunnel was calibrated prior to the study. Velocity and pressure profiles were uniform up to 3.81 cm from the walls of the test section. Turbulence intensity, measured at the center of the test section, was 3.0% with an absolute error of 0.5%. Using hot wire anemometry, time-smoothed velocity profiles were measured at several radial and angular positions from the front to the rear stagnation point. The maximum absolute error in the velocity measurements was 12 cm/s and the positional error of the probe was 0.00254 cm. The numerical study employed the finite element method. The flow field was modeled as two-dimensional with half-symmetry. The unsteady, turbulent (k/ε) model had 2,160 elements and 2,287 nodes. Convergence and laminar flow was verified. When blowing was present, the numerical solution was found to give excellent agreement with the experiments in the entire flow field. For the no blowing test case, the agreement with the experiments was also excellent up to 20 deg from the rear stagnation point. Flow visualization, using smoke, was used to qualitatively study the large scale secondary flows in the wake region. These results helped explain the poorer agreement for the no blowing test case.

Suppression of Unsteady Vortex Shedding From a Circular Cylinder by Using a Passive Jet Flow Control Method

2014 ◽  
Author(s):  
Wenli Chen ◽  
Hui Li ◽  
Hui Hu
Keyword(s):  
Circular Cylinder ◽  
Flow Control ◽  
Stagnation Point ◽  
Vortex Shedding ◽  
Control Method ◽  
Aerodynamic Force ◽  
Jet Flow ◽  
Wake Flow ◽  
Cylinder Model ◽  
Rear Stagnation Point

A passive jet flow control method was employed to suppress the unsteady vortex shedding from a circular cylinder at the Reynolds number level of Re = (0.18∼1.1)×105. The passive jet flow control was achieved by blowing jets from the holes near the rear stagnation point of the cylinder, which are connected to the in-take holes located near the front stagnation point through channels embedded inside the cylinder. Since a part of the oncoming flow would inhale into the in-take holes, flow through the embedded channels, and blow out from the holes near the rear stagnation point to suppress/manipulate the alternating vortex shedding in the wake flow behind the circular cylinder, the present passive jet flow control method does not require any additional energy inputs for the flow control. In the present study, the aerodynamic force (i.e., both lift and drag) acting the circular cylinder model with and without the passive jet flow control were compared quantitatively at different Reynolds numbers (i.e., different inlet mean speed). It was found that, in addition to almost eliminating the fluctuations of the lift forces acting on the cylinder, the passive jet flow control method was also found to reduce the mean drag acting on the cylinder model greatly. The instantaneous vorticity distributions and corresponding streamline patterns were used to reveal the underlying physics about why and how the passive jet flow control method can be used to suppress the alternating vortex shedding and induce a symmetrical wake pattern behind the cylinder model.

scholarly journals Flow past a circular cylinder on a β-plane

1982 ◽  
Vol 306 (1496) ◽  
pp. 533-556 ◽  
Keyword(s):  
Aspect Ratio ◽  
Circular Cylinder ◽  
Large Scale ◽  
Flow Direction ◽  
Water Channel ◽  
Unsteady Flows ◽  
Boundary Layer Separation ◽  
Coriolis Parameter ◽  
The North ◽  
Flow Past

With a view to obtaining a fuller understanding of the interactions between topography and large-scale geophysical flows, a series of laboratory investigations have been performed on the flow past a right circular cylinder in a rotating water channel. For large-scale flows on a spherical Earth the variation of the Coriolis parameter, F = 2Ωsinϕ , with latitude, ϕ, is commonly written (Pedlosky 1979) as F = f + β 0 y where f = 2Ωsinϕ o , β o = 2Ωcosϕ o /R E , y is the distance to the north from the reference latitude ϕ o , and R E and Ω( = 7.29 x 10 -5 s-1 ) are the radius and rotation rate of the Earth respectively. In this paper we shall discuss laboratory experiments in which the variation of F can be simulated. We shall refer to those studies in which β = 0 (i.e. the Coriolis parameter is uniform over the latitudinal extent of the region under investigation) as f-plane experiments. Models for which β o is non-zero will be referred to as β-plane experiments. In the experiments the β-effect has been simulated by tilting the upper and lower surfaces of the channel so that the depth of the fluid varies in the cross-stream direction. Flow patterns have been obtained over a range of five independent non-dimensional parameters: Rossby and Ekman numbers, cylinder aspect ratio, β-parameter and flow direction (‘eastward’ or ‘westward’). A dramatic difference in downstream behaviour is found between f-plane, β-plane westward and /plane eastward flows. In particular, the β-plane eastward flows are characterized by bunching and pinching of streamlines in the wake region, the generation of damped stationary Rossby waves and downstream acceleration. Compared with f-plane flows the β-effect is shown to inhibit boundary layer separation from the cylinder for eastward flow and to enhance the separation for westward flow. Data are presented from all cases to show the asymmetry of the downstream flows and the transitions from fully attached to unsteady flows. Under otherwise identical conditions the downstream extent of the separated bubble region is much greater for β-plane westward flow than, in turn, for f-plane and β-plane eastward flows. In addition, the data indicate that the size of the bubble increases with increasing Rossby number and decreases with increasing Ekman number and cylinder aspect ratio. For eastward flow the bubble size decreases with increasing β-parameter and for westward flow it increases with increasing β-parameter. Unsteady flows are investigated and instances of asymmetrical vortex shedding are presented.

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

2021 ◽  
Vol 929 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida
Keyword(s):  
Circular Cylinder ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Drag Coefficient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Initial Flow ◽  
Penalization Method ◽  
Brinkman Penalization Method

The initial flow past an impulsively started translating circular cylinder is asymptotically analysed using a Brinkman penalization method on the Navier–Stokes equations. The asymptotic solution obtained shows that the tangential and normal slip velocities on the cylinder surface are of the order of $1/\sqrt {\lambda }$ and $1/\lambda$ , respectively, within the second approximation of the present asymptotic analysis, where $\lambda$ is the penalization parameter. This result agrees with the estimation of Carbou & Fabrie (Adv. Diff. Equ., vol. 8, 2003, pp. 1453–1480). Based on the asymptotic solution, the influence of the penalization parameter $\lambda$ is discussed on the drag coefficient that is calculated using the adopted three formulae. It can then be found that the drag coefficient calculated from the integration of the penalization term exhibits a half-value of the results of Bar-Lev & Yang (J. Fluid Mech., vol. 72, 1975, pp. 625–647) as $\lambda \to \infty$ .

Energy Separation and Acoustic Interaction in Flow Across a Circular Cylinder

2001 ◽  
Vol 123 (4) ◽  
pp. 682-687 ◽  
Author(s):  
R. J. Goldstein ◽  
Boyong He
Keyword(s):  
Wind Tunnel ◽  
Circular Cylinder ◽  
Stagnation Point ◽  
Energy Separation ◽  
Acoustic Measurements ◽  
Velocity Measurements ◽  
Acoustic Interaction ◽  
Strong Energy ◽  
Separation Mechanisms ◽  
Rear Stagnation Point

Energy separation in a flow around an adiabatic circular cylinder is investigated using a surface-mounted thermocouple. Energy separation mechanisms in different regions around the cylinder are discussed. Velocity measurements near the rear stagnation point and acoustic measurements indicate that shedding vortices and the wind tunnel intrinsic resonant acoustics can strengthen each other when their frequencies match producing strong energy separation.

Circular cylinder vortex-synchronization control with a synthetic jet positioned at the rear stagnation point

2010 ◽  
Vol 662 ◽  
pp. 232-259 ◽  
Author(s):  
LI HAO FENG ◽  
JIN JUN WANG
Keyword(s):  
Circular Cylinder ◽  
Stagnation Point ◽  
Large Scale ◽  
Water Channel ◽  
Excitation Frequency ◽  
Synthetic Jet ◽  
Reynolds Stresses ◽  
Flow Topology ◽  
Wake Vortices ◽  
Rear Stagnation Point

The flow over a circular cylinder controlled by a two-dimensional synthetic jet positioned at the mean rear stagnation point has been experimentally investigated in a water channel at the cylinder Reynolds number Re = 950. This is an innovative arrangement and the particle-image-velocimetry measurement indicates that it can lead to a novel and interesting phenomenon. The synthetic-jet vortex pairs induced near the exit convect downstream and interact with the vorticity shear layers behind both sides of the cylinder, resulting in the formation of new induced wake vortices. The present vortex synchronization occurs when the excitation frequency of the synthetic jet is between 1.67 and 5.00 times the natural shedding frequency at the dimensionless stroke length 99.5. However, it is suggested that the strength of the synthetic-jet vortex pair plays a more essential role in the occurrence of vortex synchronization than the excitation frequency. In addition, the wake-vortex shedding is converted into a symmetric mode from its original antisymmetric mode. The symmetric shedding mode weakens the interaction between the upper and lower wake vortices, resulting in a decrease in the turbulent kinetic energy produced by them. It also has a significant influence on the global flow field, including the velocity fluctuations, Reynolds stresses and flow topology. However, their distributions are still dominated by the large-scale coherent structures.

Three dimensional stagnation point flow into a corner

1975 ◽  
Vol 344 (1639) ◽  
pp. 489-507 ◽  
Keyword(s):  
Stagnation Point ◽  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Plane Flow ◽  
Stagnation Line ◽  
Concave Corner ◽  
Point Motion ◽  
The Cross

The principal features of the three dimensional laminar motion produced when a viscous incompressible fluid impinges on a corner, formed by two infinitely long planes meeting at an angle (π 2α), are discussed mainly for the almost-planar configuration, where the slight cranking of the planes promotes flow in the third direction. On the face of it, there seem to be two quite distinct flows possible when α becomes small. One is the known two dimensional stagnation-point motion with the stagnation line at a right angle to the line of intersection. The other is in effect a three dimensional sink-flow, with fluid approaching the stagnation point radially in the cross-flow plane, which is normal to the line of intersection, while accelerating away from it, parallel to the line of intersection. (This flow can also be considered as an axisymmetric stagnation point motion with the line of intersection as the axis of symmetry and all flow direction reversed.) The explanation of this apparent non-uniqueness is that the first major alteration in the characteristics of the viscous and inviscid steady flowfields occurs while α is still small, due essentially to the interactions between the breakdown of the linearization procedure and the emergence of transverse viscous forces close to the corner. Specifically, the critical value of α is 0(l/lnR e) where Re, a characteristic Reynolds number of the motion, is assumed to be large. In that regime, for a concave corner, the pattern of the flow develops non-linearly away from the planar form, for a = 0, toward the completely different kind of motion corresponding to the sink-flow phenomenon. The flow in the corner is derived numerically and exhibits a partial reversal in the direction of the cross-plane velocity when the corner angle is sufficiently increased. New exact solutions of the Navier-Stokes equations are also proposed for the sink-flows at arbitrary positive values of α , the solution as -α > 0 + being precisely that obtained as a In Re becomes large and positive. In contrast, for the convex corner the effect of increasing the inclination ( —α ) is to compress the boundary layer substantially, and the cross-plane flow is always outward.

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