Instability and sensitivity of the flow around a rotating circular cylinder

The two-dimensional flow around a rotating circular cylinder is studied at Re = 100. The instability mechanisms for the first and second shedding modes are analysed. The region in the flow with a role of ‘wavemaker’ in the excitation of the global instability is identified by considering the structural sensitivity of the unstable mode. This approach is compared with the analysis of the perturbation kinetic energy production, a classic approach in linear stability analysis. Multiple steady-state solutions are found at high rotation rates, explaining the quenching of the second shedding mode. Turning points in phase space are associated with the movement of the flow stagnation point. In addition, a method to examine which structural variation of the base flow has the largest impact on the instability features is proposed. This has relevant implications for the passive control of instabilities. Finally, numerical simulations of the flow are performed to verify that the structural sensitivity analysis is able to provide correct indications on where to position passive control devices, e.g. small obstacles, in order to suppress the shedding modes.

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First instability and structural sensitivity of the flow past two side-by-side cylinders

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.230 ◽

2014 ◽

Vol 749 ◽

pp. 627-648 ◽

Cited By ~ 18

Author(s):

M. Carini ◽

F. Giannetti ◽

F. Auteri

Keyword(s):

Bluff Body ◽

Passive Control ◽

Base Flow ◽

Circular Cylinders ◽

A Posteriori ◽

Instability Mechanism ◽

Structural Sensitivity ◽

Flow Past ◽

Structural Sensitivity Analysis ◽

Gap Spacing

AbstractThe onset of two-dimensional instabilities in the flow past two side-by-side circular cylinders is numerically investigated in the ranges $0.1\leq g\leq 3$ and $\mathit{Re}<100$, with $g$ being the non-dimensional gap spacing between the surfaces of the two cylinders and $\mathit{Re}$ the Reynolds number. A comprehensive, global stability analysis of the symmetric base flow is carried out, indicating that three harmonic modes and one steady antisymmetric mode become unstable at different values of $g$ and $\mathit{Re}$. These modes are known to promote distinct flow regimes at increasing values of $g$: single bluff-body, asymmetric, in-phase and antiphase synchronized vortex shedding. For each mode, the inherent structural sensitivity is examined in order to identify the core region of the related instability mechanism. In addition, by exploiting the structural sensitivity analysis to base flow modifications, a passive control strategy is proposed for the simultaneous suppression of the two synchronized shedding modes using two small secondary cylinders. Its effectiveness is then validated a posteriori by means of direct numerical simulations.

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The flow past a rapidly rotating circular cylinder

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1957.0157 ◽

1957 ◽

Vol 242 (1228) ◽

pp. 108-115 ◽

Cited By ~ 22

Keyword(s):

Boundary Layer ◽

Circular Cylinder ◽

Present Theory ◽

Stream Velocity ◽

Two Dimensional ◽

Rotating Circular Cylinder ◽

Flow Past ◽

Separating Flow ◽

Two Dimensional Flow ◽

Uniform Stream

This paper considers the two-dimensional flow past a circular cylinder immersed in a uniform stream, when the cylinder rotates about its axis so fast that separation in suppressed. The solution of the flow in the boundary layer on the cylinder is obtained in the form of a power series in the ratio of the stream velocity to the cylinder's peripheral velocity, and expressions are deduced for the value of the circulation and the torque on the cylinder. The terms calculated explicitly are sufficient to give reliable numerical values over the whole range of rotational speeds for which the postulate of non-separating flow is justifiable. The previously accepted theory, due to Prandtl, predicted that the circulation should not exceed a certain limit, while the present theory indicates that the circulation increases indefinitely with increase of rotaional speed. Strong arguments against the older theory are put forward, but the experimental evidence available is inconclusive.

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Flow Simulation Around a Rotating Circular Cylinder With Surface Roughness by the Vortex Method

Volume 2: Symposia, Parts A, B, and C ◽

10.1115/fedsm2003-45622 ◽

2003 ◽

Cited By ~ 1

Author(s):

Tetsuhiro Tsukiji ◽

Yuko Matsubara

Keyword(s):

Surface Roughness ◽

Circular Cylinder ◽

Flow Simulation ◽

Vortex Method ◽

Uniform Flow ◽

Speed Ratio ◽

Rotating Speed ◽

Rotating Circular Cylinder ◽

Two Dimensional Flow ◽

Good Agreement

The two-dimensional flow around a rotating circular cylinder with surface roughness in a steady uniform flow is investigated using a vortex method. The Reynolds number is 9500, while the rotating speed ratios of the peripheral velocity to the uniform velocity is 0–1.0. The surface roughness is distributed around the circular cylinder and its strength is 0.5% of the diameter. The viscous diffusion effects and the no-slip condition are considered. Before the calculation for a rotating circular cylinder with the surface roughness, the flow simulation for a circular cylinder in the steady uniform flow was conducted to confirm the present method. The development of the twin vortices and the velocity profiles behind the circular cylinder at the beginning of the calculation are compared with the previous experimental results. It is found that the calculated results are in good agreement with the experiments. The development of the vortices, the drag and the lift coefficients are computed by changing the rotating speed ratio for the circular cylinder both with the surface roughness and without it. The influence of the surface roughness and the rotating speed ratio on the vortex development, the drag and the lift coefficients are examined.

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Characteristics of two-dimensional flow around a rotating circular cylinder near a plane wall

Physics of Fluids ◽

10.1063/1.2738608 ◽

2007 ◽

Vol 19 (6) ◽

pp. 063601 ◽

Cited By ~ 36

Author(s):

Ming Cheng ◽

Li-Shi Luo

Keyword(s):

Circular Cylinder ◽

Plane Wall ◽

Two Dimensional ◽

Dimensional Flow ◽

Rotating Circular Cylinder ◽

Two Dimensional Flow

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Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder

Journal of Fluid Mechanics ◽

10.1017/s0022112085002725 ◽

1985 ◽

Vol 158 ◽

pp. 447-488 ◽

Cited By ~ 123

Author(s):

H. M. Badr ◽

S. C. R. Dennis

Keyword(s):

Circular Cylinder ◽

Differential Equations ◽

Numerical Study ◽

Separated Flow ◽

Time Dependent ◽

Initial Development ◽

Rotation Rates ◽

Finite Set ◽

Small Times ◽

Two Dimensional Flow

A numerical study is made of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with constant speed. The governing partial differential equations in two space variables and time are reduced to sets of time-dependent equations in one space variable by means of Fourier analysis. By truncating the Fourier series to a finite number of terms, a finite set of differential equations is solved to give an approximation to the theoretical flow. The solutions are obtained by numerical methods. Results are given for the initial development with time of the asymmetrical wake at the rear of the cylinder at Reynolds numbers R [ges ] 200, based on the diameter of cylinder, and at small rotation rates. The detailed results show the formation of a Kármán vortex street. The time development of this separated flow is compared in detail at R = 200 with recent experimental results. The details of the formation and movement of the vortices behind the cylinder and the velocity profiles in several locations are virtually identical in the experimental and theoretical studies. The variations with time of the lift, drag and moment exerted by the fluid on the cylinder are determined both by calculations and by means of approximate analytical expressions. The agreement between these results at small times is excellent.

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Flow-induced vibration of a rotating circular cylinder at high reduced velocities and high rotation rates

Ocean Engineering ◽

10.1016/j.oceaneng.2021.109562 ◽

2021 ◽

Vol 238 ◽

pp. 109562

Author(s):

Adnan Munir ◽

Ming Zhao ◽

Helen Wu ◽

Feifei Tong

Keyword(s):

Circular Cylinder ◽

Flow Induced Vibration ◽

Rotation Rates ◽

Rotating Circular Cylinder

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Three-dimensional instability of the flow around a rotating circular cylinder

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.334 ◽

2013 ◽

Vol 730 ◽

pp. 5-18 ◽

Cited By ~ 36

Author(s):

Jan O. Pralits ◽

Flavio Giannetti ◽

Luca Brandt

Keyword(s):

Circular Cylinder ◽

Critical Reynolds Number ◽

Three Dimensional ◽

Stationary Flow ◽

Rotating Cylinder ◽

Neutral Curve ◽

Qualitative Comparison ◽

Rotation Rates ◽

Rotating Circular Cylinder ◽

Dimensional Instability

AbstractThe two-dimensional stationary flow past a rotating cylinder is investigated for both two- and three-dimensional perturbations. The instability mechanisms are analysed using linear stability analysis and the complete neutral curve is presented. It is shown that the first bifurcation in the case of the rotating cylinder occurs for stationary three-dimensional perturbations, confirming recent experiments. Interestingly, the critical Reynolds number at high rotation rates is lower than that for the stationary circular cylinder. The spatial characteristics of the disturbance and a qualitative comparison with the results obtained for linear flows suggest that the stationary unstable three-dimensional mode could be of hyperbolic nature.

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Low Reynolds number flow around and heat transfer from a heated circular cylinder

International Review of Applied Sciences and Engineering ◽

10.1556/irase.1.2010.1-2.3 ◽

2010 ◽

Vol 1 (1-2) ◽

pp. 15-20 ◽

Cited By ~ 1

Author(s):

B. Bolló

Keyword(s):

Reynolds Number ◽

Circular Cylinder ◽

Lift Coefficient ◽

Reynolds Numbers ◽

Low Reynolds Numbers ◽

Reynolds Number Flow ◽

Two Dimensional Flow ◽

Number Flow ◽

Low Reynolds ◽

Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

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