Unsteady circulatory flow about a circular cylinder with suction

Summary The complete Navier-Stokes equations which describe the unsteady flow of a viscous incompressible fluid when an infinite circular cylinder is given an impulsive twist, and simultaneously a constant suction velocity is imposed on the cylinder, are integrated using Laplace transforms. It is found that points which are at a greater distance from the cylinder are nearer to steadiness than points which are closer to the cylinder. Unsteady flow through a concentric annulus has also been considered.     

Steady circulatory flow about a rotating circular cylinder with uniformly distributed suction at the surface

An exact solution for steady circulatory flow about an infinite porous circular cylinder rotating with a given angular velocity in an incompressible non-Newtonian second-order fluid that is also rotating so that a given circulation is maintained at infinity, is investigated. Using the Coleman-Noll model for the fluid, it is found that when circulation, velocity, vorticity and pressure are affected by non-Newtonian effects due to second-order terms in the constitutive equation of the fluid even at the first-order approximation or the series solution used, torque is independent of these effects even when the second-order approximation is considered.     

Flow past a circular cylinder over a free surface: Interaction between the near wake and the free surface deformation

Air-flow around a circular cylinder placed above a free surface and liquid flow under the free surface were investigated experimentally in a wind/wave tunnel. The cylinder spanned the tunnel test-section and was oriented normal to the freestream direction. The main objective of this study was to investigate the interaction of the cylinder wake with the free surface. The flow structure was analyzed for various gap widths, H, between the cylinder and the free surface using a digital particle image velocimetry (PIV) system with a spatial resolution of 2048×2048 pixels. The Reynolds number based on the cylinder diameter was 3.3×10³. For each experimental condition, 400 instantaneous velocity fields were measured and ensemble-averaged to obtain spatial distributions of the mean velocity and turbulence statistics. The results showed that the cylinder near-wake inclined upward due to the influence of the free surface elevation. Vortices were shed, even at a small gap ratio of H/D=0.25, where D is the cylinder diameter. Strong jet-like flow appeared in the gap beneath the cylinder. At a gap ratio of H/D=0.50, the jet flow exhibited a quasi-periodic vibration with a period of 2–3 s. The free surface deformation was caused by the pressure difference in the air-flow immediately above it. As the gap ratio increased, the inclination angle of the wake and the height of the free surface elevation decreased gradually. The liquid flow under the free surface followed a convective flow motion, and the range of the convection depended on the gap width between the cylinder and the free surface.     

Flow of wormlike micelle solutions past a confined circular cylinder

In this paper, we present the results of an investigation into the flow of a series of viscoelastic wormlike micelle solutions past a confined circular cylinder. Although this benchmark flow has been studied in great detail for polymer solutions, this paper reports the first experiments to use a viscoelastic wormlike micelle solution as the test fluid. The flow kinematics, stability and pressure drop were examined for two different wormlike micelle solutions over a wide range of Deborah numbers and cylinder to channel aspect ratios. A combination of particle image velocimetry and pressure drop measurements were used to characterize the flow kinematics, while flow-induced birefringence measurements were used to measure the micelle deformation and alignment in the flow. The pressure drop was found to decrease initially due to the shear thinning of the test fluid before increasing at higher flow rates as elastic effects begin to dominate the flow. Above a critical Deborah number, an elastic instability was observed for just one of the test fluids studied, the other remained stable for all Deborah number tested. Flow-induced birefringence and velocimetry measurements showed that observed instability originates in the extensional flow in the wake of the cylinder and appears not as periodic counter-rotating vortices as has been observed in the flow of polymer solutions past circular cylinders, but as a chaotic rupture event in the wake of the cylinder that propagates axially along the cylinder. Reducing the cylinder to channel aspect ratio and the degree of shearing introduced by the channel walls had a weak impact on the stability of the flow. These measurements, when taken in conjunction with previous work on flow of wormlike micelle solutions through a periodic array of cylinders, definitively show that the instability can be attributed to a breakdown of the wormlike micelle solutions in the extensional flow in the wake of the cylinder.     

Flow structure of wake behind a rotationally oscillating circular cylinder

Flow around a circular cylinder oscillating rotationally with a relatively high forcing frequency has been investigated experimentally. The dominant parameters affecting this experiment are the Reynolds number (Re), oscillation amplitude (θ_A), and frequency ratio F_R=f_f/f_n, where f_f is the forcing frequency and f_n is the natural frequency of vortex shedding. Experiments were carried out under conditions of Re=4.14×10³, 0°θ_A60° and 0.0F_R2.0. Rotational oscillation of the cylinder significantly modified the flow structure in the near-wake. Depending on the frequency ratio F_R, the cylinder wake showed five different flow regimes, each with a distinct wake structure. The vortex formation length and the vortex shedding frequency were greatly changed before and after the lock-on regime where vortices shed at the same frequency as the forcing frequency. The lock-on phenomenon always occurred at F_R=1.0 and the frequency range of the lock-on regime expanded with increasing oscillation amplitude θ_A. In addition, the drag coefficient was reduced when the frequency ratio F_R was less than 1.0 (F_R<1.0) while fixing the oscillation amplitude at θ_A=30°. When the oscillation amplitude θ_A was used as a control parameter at a fixed frequency ratio F_R=1.0 (lock-on regime), the drag reduction effect was observed at all oscillation amplitudes except for the case of θ_A=30°. This type of active flow control method can be used effectively in aerodynamic applications while optimizing the forcing parameters.     

Vortex shedding from a circular cylinder with a slit and concave rear surface

Vortex shedding from short circular cylinders with a slit was studied using a flow visualization and amplitude spectrum analysis of a thermoanemometry probe signal. It was found that a circular cylinder with a slit and concave rear surface produces stronger vortices than other bluff cylinders but that these vortices are very vulnerable to the end wall conditions. It was established that two small splitter plates (tails) fixed directly behind the cylinder at the end walls effectively isolate the vortices shed from the cylinder from the end wall boundary layer effects. For this arrangement a perfect regularity of vortex shedding and almost constant Strouhal number were achieved in the Reynolds number test range of about 250 to 43,000.On a leave from Technical University, 60965 Poznan, Piotrowo 3, Poland.     

Flow of non-Newtonian fluid contained in a fixed circular cylinder due to the longitudinal oscillation of a concentric circular cylinder

Summary The flow of a Reiner-Rivlin fluid between two coaxial porous circular cylinders has been studied. The inner cylinder performs a steady oscillation while the outer one is fixed.The exact solution of this problem has been obtained and approximate solutions for the two extreme cases, very small and very high frequencies, have been derived.     

Magnetic induction strength on surface of a ferro-medium circular cylinder

Based on the Ampere molecular current hypothesis and the Biot–Savart law,a magnetic model on the metal magnetic memory(MMM) testing of a specimen is proposed.Relation between magnetic flux leakage(MFL) and magnetization of a ferro-medium circular cylinder is set up.We can predict magnetization of material according to the MFL on surface of the circular cylinder.     

Flow of a particulate suspension in the wake of a circular cylinder

Measurements are reported for the average local particulate velocity and concentration distributions in the wake of a cylinder immersed in a stream containing a polydisperse aerosol. The wake centerline defects and transverse distributions were determined for both parameters. It was found that the particulate centerline defect persists a considerable distance downstream of the cylinder before fully developed conditions are satisfied. Transverse particulates and gaseous velocity distributions assume a Gaussian profile at the same point downstream. The charge-to-mass ratio throughout the wake region was equal to the free stream value for all experimental conditions and was of such a magnitude to permit the electrostatic effects to be neglected in the governing equations. Gaseous and particulate transport properties were identified in the wake.     

Computation of high Reynolds number flow around a circular cylinder with surface roughness

Incompressible high-Reynolds-number flows around a circular cylinder are analyzed by direct integration of the Navier-Stokes equations using finite-difference method. A generalized coordinate system is used so that a sufficient number of grid points are distributed in the boundary layer and the wake. A numerical scheme which suppresses non-linear instability for calculations of high-Reynolds-number flows is developed. The computation of an impulsively started flow at Re = 1200 is compared with corresponding experimental observations, and excellent agreements are obtained.A series of computations are carried out on the flow around a circular cylinder with surface roughness. The height of the roughness in these computations is 0.5% of the diameter. The range of Reynolds numbers is from 10³ to 10⁵; no turbulence model is employed. Sharp reduction of drag coefficient is observed near Re = 2 × 10⁴, which indicates that the critical Reynolds number is captured in the present computation.     

Transient free convection about a horizontal circular cylinder in a porous medium

The method of matched asymptotic expansions is employed for investigating the growth of the free convection boundary-layer on a horizontal circular cylinder which is embedded in a porous medium. It is assumed that the Rayleigh number is large, but finite, and the time of investigation is short. It is shown that the solution contains terms that are absent from the solution based on the boundary-layer approximation and that vortices form at both sides of the cylinder. The development of the plume region near the top of the cylinder, as well as the local and average Nusselt numbers, are evaluated and presented in graphical form.     

Influence of single rectangular groove on the flow past a circular cylinder

In the present study, flow control mechanism of single groove on a circular cylinder surface is presented experimentally using Particle image velocimetry (PIV). A square shaped groove is patterned longitudinally on the surface of the cylinder with a diameter of 50 mm. The flow characteristics are studied as a function of angular position of the groove from the forward stagnation point of the cylinder within 0° ≤ θ ≤ 150°. In the current work, instantaneous and time-averaged flow data such as vorticity, ω streamline, Ψ streamwise, u/U_o and transverse, v/U_o velocity components, turbulent kinetic energy, TKE and RMS of streamwise, u_rms and transverse, v_rms velocity components are utilized in order to present the results of quantitative analyses. Furthermore, Strouhal numbers are calculated using Karman vortex shedding frequency, f_k obtained from single point spectral analysis. It is concluded that a critical angular position of the groove, θ = 80° is observed. The flow separation is controlled within 0° ≤ θ < 80°. At θ = 80°, the flow separation starts to occur in the upstream direction. The instability within the shear layer is also induced on grooved side of the cylinder with frequencies different than Karman vortex shedding frequency, f_k.     

Hydrodynamics of flow over a transversely oscillating circular cylinder beneath a free surface

In this paper, hydrodynamic force coefficients and wake vortex structures of uniform flow over a transversely oscillating circular cylinder beneath a free surface were numerically investigated by an adaptive Cartesian cut-cell/level-set method. At a fixed Reynolds number, 100, a series of simulations covering three Froude numbers, two submergence depths, and three oscillation amplitudes were performed over a wide range of oscillation frequency. Results show that, for a deeply submerged cylinder with sufficiently large oscillation amplitudes, both the lift amplitude jump and the lift phase sharp drop exist, not accompanied by significant changes of vortex shedding timing. The near-cylinder vortex structure changes when the lift amplitude jump occurs. For a cylinder oscillating beneath a free surface, larger oscillation amplitude or submergence depth causes higher time-averaged drag for frequency ratio (=oscillation frequency/natural vortex shedding frequency) greater than 1.25. All near-free-surface cases exhibit negative time-averaged lift the magnitude of which increases with decreasing submergence depth. In contrast to a deeply submerged cylinder, occurrences of beating in the temporal variation of lift are fewer for a cylinder oscillating beneath a free surface, especially for small submergence depth. For the highest Froude number investigated, the lift frequency is locked to the cylinder oscillation frequency for frequency ratios higher than one. The vortex shedding mode tends to be double-row for deep and single-row for shallow submergence. Proximity to the free surface would change or destroy the near-cylinder vortex structure characteristic of deep-submergence cases. The lift amplitude jump is smoother for smaller submergence depth. Similar to deep-submergence cases, the vortex shedding frequency is not necessarily the same as the primary-mode frequency of the lift coefficient. The frequency of the induced free surface wave is exactly the cylinder oscillation frequency. The trends of wave length variation with the Froude number and frequency ratio agree with those predicted by the linear theory of small-amplitude free surface waves.     

Flow characteristics around a circular cylinder subjected to vortex-induced vibration near a plane boundary

Although vortex-induced vibration (VIV) has been extensively studied, much of existing literature deals with uniform flow in the absence of a boundary. The VIV flow field of a structure close to a boundary generally remains unexplored, but it can have important engineering implications, such as pipeline scour if the boundary is an erodible seabed. In this paper, laboratory experiments are performed to investigate the flow characteristics of an elastically mounted circular cylinder undergoing VIV, and a rigid plane boundary is considered to simplify the problem. The initial gap-to-diameter ratio is fixed at 0.8, and six different reduced velocities are considered. The velocity field is measured using a high resolution particle image velocimetry (PIV) system, which has several advantages over traditional PIV systems, including high sampling rate and the ability to mitigate scatter of laser light near the boundary, allowing accurate measurements at the viscous sublayer. This paper presents the vibration amplitude and oscillation frequency for different V_r; in addition, the mean velocity field, turbulence characteristics, vortex behavior, gap flow velocity, and normal/shear stresses on the boundary were measured/calculated, leading to new insights on the flow field behavior.     

The turbulent wake of a circular cylinder rotating about the streamwise axis

This paper presents measurements in the turbulent wake of a circular cylinder rotating with its axis normal to the free-stream velocity; in other words, the axis of rotation was parallel to the streamwise direction. All three mean velocities and six Reynolds stresses were obtained at three positions downstream of the cylinder, with and without rotation of the free-stream. Most emphasis is given to the latter results because of the better flow quality. The ratio of the circumferential velocity of the cylinder to the free-stream velocity — the swirl number — had a maximum value of 0.6. Measurements for two combinations of the free-stream and angular velocities showed the velocity deficit in the wake to be a multi-valued function of the swirl number, implying that the rotation affected the separation of the cylinder's boundary layer in a complex manner. In the turbulent wake, the rotation did not significantly alter the magnitudes of the normal stresses, but caused large changes to the shape of the profiles of the axial and cross-stream normal stresses. Eventually, the primary (cross-stream) shear stress became almost entirely positive, but there was no corresponding change to the (cross-stream) gradient of the streamwise mean velocity. Despite these alterations to the turbulence, the rotationally-activated generation terms in the Reynolds transport equations never dominated the terms that are common to the wakes of rotating and non-rotating cylinders.This work was supported by the Australian Research Council. Most of the data acquisition software was written by Mr J. J. Smith.     

Flow around a circular cylinder—structure of the near wake shear layer

The separated shear layer in the near wake of a circular cylinder was investigated using a single hot wire probe, with special attention given to the shear layer instability characteristics. Without end plates to force parallel vortex shedding, the critical Reynolds number for the onset of the instability was 740. The present data, together with all previously published data, show that the ratio of the instability frequency f_sl to the vortex shedding frequency f_v varies as Re^0.65, which is in agreement with the Re^0.67 dependence obtained by Prasad and Williamson [1997, J Fluid Mech 333:375–402]. However, the distribution of f_sl/f_v and the spectra of the longitudinal velocity fluctuation (u) suggest that, on either side of Re=5,000, the shear layer exhibits lower and upper subcritical regimes, in support of the observations by Norberg [1987, publication no. 87/2, Chalmers University of Technology, Sweden] and Prasad and Williamson [1997, J Fluid Mech 343:235–265]. The spectra of u provide strong evidence for the occurrence of vortex pairing in wake shear layers, suggesting that the near wake develops in a similar manner to a mixing layer.