Experimental investigation of the flow around a radially vibrating circular cylinder

This work aims to develop a process for controlling a cylinder wake, especially the von Karman vortex street, in such way so as to drastically reduce the drag coefficient. A new technique for influencing the cylinder wake is proposed in the present experimental study. The flow around a circular cylinder is perturbed by temporarily changing the cylinder diameter. Experiments have been performed for Reynolds numbers in the range Re=9,500 to Re=31,500. Three values of the controlling frequencies are considered: fs₁=0.41, fs₂=0.54 and fs₃=0.73, in addition to the stationary case corresponding to a non-deformable cylinder, fs₀=0. The visualisation flow shows that the pulsing motion of the cylinder walls greatly influences both the near and far wake dynamics. A decrease of the drag is expected.

On the effect of flow direction on mixed convection from a horizontal cylinder

The influence of free stream direction on mixed (natural and forced) convective heat transfer from a circular cylinder is investigated. The cylinder, which has an isothermal surface, is placed with its axis horizontal and normal to the oncoming flow. The free stream direction varies between the vertically upward (parallel flow) and the vertically downward (contraflow) directions. The investigation is based on the time integration of the unsteady, two-dimensional equations of motion and energy until reaching steady conditions. The study is limited to Reynolds numbers up to Re = 40 and Grashoff numbers of Gr = Re². The results are compared with the available experimental data and the agreement is satisfactory.     

A note on the numerical simulations of flow past a wavy square-section cylinder

The flow past a square-section cylinder with a geometric disturbance is investigated by numerical simulations. The extra terms, due to the introduction of mapping transformation simulating the effect of disturbance into the transformed Navier-Stokes equations, are correctly derived, and the incorrect ones in the previous literature are pointed out and analyzed. Furthermore, the relationship between the vorticity, especially on the cylinder surface, and the disturbance is derived and explained theoretically. The computations are performed at two Reynolds numbers of 100 and 180 and three amplitudes of waviness of 0.006, 0.025 and 0.167 with another aim to explore the effects of different Reynolds numbers and disturbance on the vortex dynamics in the wake and forces on the body. Numerical results have shown that, at the mild waviness of 0.025, the Kairmain vortex shedding is suppressed completely for Re = 100, while the forced vortex dislocation is appeared in the near wake at the Reynolds number of 180. The drag reduction is up to 21.6% at Re = 100 and 25.7% at Re = 180 for the high waviness of 0.167 compared with the non-wavy cylinder. The lift and the Strouhal number varied with different Reynolds numbers and the wave steepness are also obtained.     

Effect of self-issuing jets along the span on the near-wake of a square cylinder

The study herein focuses on the vortex shedding characteristics and near-wake vorticity patterns of a square cylinder having self-issuing jets through holes along its span. Three different values of spacing between the consecutive holes λ with respect to the cylinder diameter D, i.e., λ/D = 1.5, 3 and 4 are studied experimentally via Digital Particle Image Velocimetry for the Reynolds number range extending from 200 to 1,000. It has been observed that the three-dimensionality of the wake flow depends on the spacing between the holes and Re number. For sufficiently low Reynolds numbers, the jet flows issuing from the holes yield a non-uniform distribution of mean flow characteristics like the shedding frequency and the formation length of vortices along the span of the cylinder when the spacing between jets along centerline is close to wavelength of the naturally existing three-dimensional wake instability. Additionally, for Re number up to 500, the self-issuing jets emanating from the holes show an indirect interaction with shear layers originating from upper and lower separation lines of the cylinder. However, for higher Re numbers of 750 and 1,000, they directly interact with and modify the vortices forming from the cylinder.     

Mixed convection cooling of a heated circular cylinder by laminar upward-directed slot jet impingement

An experimental and numerical study has been carried out to investigate the heat transfer characteristics of a horizontal circular cylinder exposed to a slot jet impingement of air. A square-edged nozzle is mounted parallel with the cylinder axis and jet flow impinges on the bottom of the cylinder. The study is focused on low Reynolds numbers ranging from 120 to 1,210, Grashof numbers up to Gr = 10Re ² and slot-to-cylinder spacing from 2 to 8 of the slot width. The flow field is greatly influenced by the slot exit velocity and the buoyancy force due to density change. A Mach–Zehnder Interferometer is used for measurement of local Nusselt number around the cylinder at 10° interval. It is observed that the average Nusselt number decreases with increasing the jet spacing and increases with rising the Reynolds number. A finite volume method utilizing a curvilinear coordinate transformation is used for numerical modeling. The numerical results show good agreement with the experimental results. The flow and thermal field are seen to be stable and symmetric around the cylinder over the range of parameters studied.     

Flow past a cylinder: shear layer instability and drag crisis

Flow past a circular cylinder for Re=100 to 10⁷ is studied numerically by solving the unsteady incompressible two‐dimensional Navier–Stokes equations via a stabilized finite element formulation. It is well known that beyond Re ～ 200 the flow develops significant three‐dimensional features. Therefore, two‐dimensional computations are expected to fall well short of predicting the flow accurately at high Re. It is fairly well accepted that the shear layer instability is primarily a two‐dimensional phenomenon. The frequency of the shear layer vortices, from the present computations, agree quite well with the Re^0.67 variation observed by other researchers from experimental measurements. The main objective of this paper is to investigate a possible relationship between the drag crisis (sudden loss of drag at Re ～ 2 × 10⁵) and the instability of the separated shear layer. As Re is increased the transition point of shear layer, beyond which it is unstable, moves upstream. At the critical Reynolds number the transition point is located very close to the point of flow separation. As a result, the shear layer eddies cause mixing of the flow in the boundary layer. This energizes the boundary layer and leads to its reattachment. The delay in flow separation is associated with narrowing of wake, increase in Reynolds shear stress near the shoulder of the cylinder and a significant reduction in the drag and base suction coefficients. The spatial and temporal power spectra for the kinetic energy of the Re=10⁶ flow are computed. As in two‐dimensional isotropic turbulence, E(k) varies as k^?5/3 for wavenumbers higher than energy injection scale and as k^?3 for lower wavenumbers. The present computations suggest that the shear layer vortices play a major role in the transition of boundary layer from laminar to turbulent state. Copyright © 2004 John Wiley & Sons, Ltd.     

Flow past a square cylinder at low Reynolds numbers

Results are presented for the flow past a stationary square cylinder at zero incidence for Reynolds number, Re ? 150. A stabilized finite‐element formulation is employed to discretize the equations of incompressible fluid flow in two‐dimensions. For the first time, values of the laminar separation Reynolds number, Re_s, and separation angle, θ_s, at Re_s are predicted. Also, the variation of θ_s with Re is presented. It is found that the steady separation initiates at Re = 1.15. Contrary to the popular belief that separation originates at the rear sharp corners, it is found to originate from the base point, i.e. θ_s=180^° at Re = Re_s. For Re > 5, θ_s approaches the limit of 135 ^°. The length of the separation bubble increases approximately linearly with increasing Re. The drag coefficient varies as Re^?0.66. Flow characteristics at Re ? 40 are also presented for elliptical cylinders of aspect ratios 0.2, 0.5, 0.8 and 1 (circle) having the same characteristic dimension as the square and major axis oriented normal to the free‐stream. Compared with a circular cylinder, the flow separates at a much lower Re from a square cylinder leading to the formation of a bigger wake (larger bubble length and width). Consequently, at a given Re, the drag on a square cylinder is more than the drag of a circular cylinder. This suggests that a cylinder with square section is more bluff than the one with circular section. Among all the cylinder shapes studied, the square cylinder with sharp corners generates the largest amount of drag. Copyright © 2010 John Wiley & Sons, Ltd.     

Slot/slots air jet impinging cooling of a cylinder for different jets–cylinder configurations

Heat transfer characteristics of a slot/slots jet air impinging on a cylinder have been experimentally investigated for two different orientations of slot/slots jet plan with respect to cylinder axis. The experiments were carried out to study the effects of orientation of slot/slots jet plan with respect to cylinder axis on the rate of heat transfer from the cylinder. Two different jet–cylinder configurations were studied: (1) single slot jet aligned with cylinder axis (slot length = cylinder length), and (2) multiple slot jets equally spaces distributed orthogonal to cylinder axis (each slot length = cylinder diameter and sum of slots lengths = cylinder length). For each configuration, parametric effects of Reynolds numbers (Re) ranging from 1,000 to 10,000, dimensionless slot widths (W/d) ranging from 0.125 to 0.5, and dimensionless slot orifice-to-cylinder spacing (Z/W) ranging from 1 to 12 on local and average Nusselt numbers around cylinder surface have been investigated. The results showed that: (1) cooling the cylinder by multiple slots jets situated orthogonal to cylinder axis gave more uniform surface temperature distributions and higher heat transfer rate than the case of cooling the cylinder by single slot jet aligned with cylinder axis, (2) for both configurations the Nusselt number around the cylinder increased with increasing Re and W/d, and (3) for both configurations there was a certain Z/W in the range 4<Z/W<6 at which the stagnation and mean Nusselt number were maximum. Correlations for the mean Nusselt numbers around cylinder surface have been presented for both configurations. Comparisons between the correlations predictions and the present and other previous experimental data have been conducted.     

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Adjoint formulation is employed for the optimal control of flow around a rotating cylinder, governed by the unsteady Navier–Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time‐dependent. Since the numerical control problem is ill‐posed, regularization is employed. An empirical logarithmic law relating the regularization coefficient to the Reynolds number was derived for 60?Re?140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re=60 to Re=1000. The results obtained by the computational optimal control method agree with previously obtained experimental and numerical observations. A significant reduction of the amplitude of the variation of the drag coefficient is obtained for the optimized values of the rotation rate. Copyright © 2002 John Wiley & Sons, Ltd.     

Finite element analysis of two- and three-dimensional flows around square columns in tandem arrangement

Two- (2D) and three-dimensional (3D) finite element analyses for flow around two square columns in tandem arrangement were performed with various column spacings and Reynolds numbers. The computed values were compared with the wind-tunnel results in terms of the aerodynamic characteristics of the leeward column. In most 2D computations, strong vortices were formed behind the windward column, irrespective of widely changed Reynolds numbers. This was different from the experimental phenomena of equivalent spacing, so that the computed time-averaged pressure coefficients were not identical to the experimental values except when the distance between the two columns was adequately wide or narrow. On the other hand, in 3D computation, distinct differences in flow structures behind the column were observed between Reynolds numbers of 10³ and 10⁴ and the pressure coefficient in the 3D analysis with Re=10⁴ agreed well with the experimental value. Thus, the effectiveness of 3D computations and Reynolds number effects on the flow around two square columns have been confirmed. © 1998 John Wiley & Sons, Ltd.     

Motion of tracer particles in supersonic flows

 Factors that may act on particle motion in high-speed flow are investigated. The classical expressions of drag coefficient C _D for a sphere are reviewed. Then, a drag expression is proposed, extending Cunningham’s method to higher velocities and Knudsen numbers. This law, valid from continuum to free molecule conditions, for Re≲200 and M≲1 (where Re and M are, respectively, the Reynolds and Mach numbers based on relative velocity), is used to compare calculated and experimental values of the drag coefficient, as well as the particle velocities across an oblique shock wave. Calculated results are found to be in agreement with experiments. Received: 3 June 1997/Accepted: 16 August 1998     

Numerical study of the effects occurring near a circular cylinder in stratified fluid flows with short buoyancy periods

Flow around a two-dimensional circular cylinder of a stratified fluid with periods buoyancy T_b = 25.2 and 6.28 sec is studied numerically over a wide range of Reynolds and Froude numbers. It is found that in the presence of a perturbation ahead of a cylinder which moves downstream with increasing Reynolds number, the salinity isolines have the shape of a semi-circular comb with sharp teeth. The shape change of the attached waves and the occurrence of fluid layers of different densities in the cylinder wake are studied. In flows with a buoyancy period T_b = 6.28 sec at Reynolds numbers Re < 60, stagnant zones are found in the cylinder wake, and at Re > 60, these zones are absent.     

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

This paper describes a numerical study of the two‐dimensional and three‐dimensional unsteady flow over two square cylinders arranged in an in‐line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross‐sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time‐averaged and spanwise‐averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender‐body regime (G < 0.5), the reattach regime (G < 4) and co‐shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.     

Aerodynamic characteristics of a square cylinder with a rod in a staggered arrangement

The aerodynamic characteristics of a square cylinder with an upstream rod in a staggered arrangement were examined. The pressure measurement was conducted in a wind tunnel at a Reynolds number of Re_D=82,000 (based on the width of the square cylinder) and the flow visualization was carried out in a water tunnel with the hydrogen bubble technique at Re_D=5,200. When the rod and the square cylinder were in tandem, the reduction of drag was mainly caused by the increase of the rear suction pressure. When the staggered angle was introduced, the shield and disturbance effect of the rod on the square cylinder diminished, which results in the increase of the cylinder drag. The side force induced by the staggered angle is small (the maximum value is 20% of the drag of the isolate square cylinder). There were six different flow modes with various staggered angles and spacing ratios, and the corresponding flow patterns are presented in present paper.     

Viscous oscillatory flow around a circular cylinder at low Keulegan–Carpenter numbers and frequency parameters

The results of a numerical study of the viscous oscillating flow around a circular cylinder at low Keulegan–Carpenter numbers (KC) and frequency parameters (β) are presented in this paper. The finite element method was used for the solution of the Navier–Stokes equations in the formulation where the streamfunction and vorticity are the field variables. The computation was conducted at Keulegan–Carpenter numbers extending up to KC=15 and frequency parameters ranging between β=6 and 100. At low values of the Keulegan–Carpenter number the flow remains symmetrical. As the Keulegan–Carpenter number is increased over a certain value which depends also on the frequency parameter, asymmetries appear in the flow which are eventually amplified and lead finally to complex vortex-shedding patterns, some of which are markedly different from those observed at higher frequency parameters. The solution revealed that although for certain values of KC and β the shedding of vortices is periodic, there also exists a complicated flow regime in which the flow is not periodic but switches between different modes in consecutive cycles of flow oscillation. For the various flow cases examined, the traces of the hydrodynamic forces are presented and the hydrodynamic coefficients and RMS values of the in-line force are compared with experimental evidence. © 1998 John Wiley & Sons, Ltd.     

On the development of Taylor vortices in a vertical annulus with a heated rotating inner cylinder

A numerical study has been conducted to determine the heat transfer characteristics and flow patterns which develop around a rotating, heated vertical cylinder enclosed within a stationary concentric cylinder. A tall annulus (aspect ratio of 10) with fixed, adiabatic horizontal end-plates and a radius ratio of 0·5 has been considered. Furthermore, the effect that the introduction of buoyancy forces by heating the inner cylinder has on the development of the Taylor vortex flow is examined. It is observed that the formation of the Taylor vortices is delayed until the rotational parameter σ = Gr/Re² has a value below unity for any given Reynolds number Re which is above the critical value Re_crit for the formation of Taylor vortices in an isothermal flow. Also, the Taylor cells first appear at the top of the annulus. As σ is gradually decreased below unity, bifurcations to other states are observed. The final structure of the secondary flow is noticeably distorted in the mixed-convection mode, with the size of the Taylor cells varying greatly along the height of the annulus. This distortion diminishes as σ is further decreased, until the isothermal flow pattern is nearly recovered below σ = 0·01.     

Aerodynamic loading on a cylinder behind an airfoil

The interaction between the wake of a rotor blade and a downstream cylinder holds the key to the understanding and control of electronic cooling fan noise. In this paper, the aerodynamic characteristics of a circular cylinder are experimentally studied in the presence of an upstream NACA 4412 airfoil for the cylinder-diameter-based Reynolds numbers of Re_d=2,100–20,000, and the airfoil chord-length-based Reynolds numbers of Re_c=14,700–140,000. Lift and drag fluctuations on the cylinder, and the longitudinal velocity fluctuations of the flow behind the cylinder were measured simultaneously using a load cell and two hot wires, respectively. Data analysis shows that unsteady forces on the cylinder increase significantly in the presence of the airfoil wake. The dependence of the forces on two parameters is investigated, that is, the lateral distance (T) between the airfoil and the cylinder, and the Reynolds number. The forces decline quickly as T increases. For Re_c<60,000, the vortices shed from the upstream airfoil make a major contribution to the unsteady forces on the cylinder compared to the vortex shedding from the cylinder itself. For Re_c>60,000, no vortices are generated from the airfoil, and the fluctuating forces on the cylinder are caused by its own vortex shedding.     

Numerical simulations of laminar flow over a 3D backward-facing step

A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier–Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100⩽Re⩽ 800. © 1997 John Wiley & Sons, Ltd.     

Stability of flow past a cylinder: Energy budget of eigenmodes

Global linear stability analysis of the flow past a circular cylinder at the onset of primary wake instability is carried out. The real and imaginary parts of the most unstable eigenmode, responsible for vortex shedding, are very similar but associated with a spatial shift in the vortex structures. This shift results in the convection of vortices that are observed in the unsteady flow, which is actually a consequence of global absolute instability. The kinetic energy density, associated with the most unstable eigenmode, is studied. At the onset of the instability the energy density of the disturbance field is found to be stronger in the far wake compared with the near wake. With increase in Re the region where the disturbance is strong moves upstream closer to the cylinder. However, the maximum value of the kinetic energy density of the disturbance lies outside the recirculation zone even for Re upto 100. A linearized mechanical energy equation for the time evolution of the kinetic energy density of the disturbance is utilized to examine the energy budget of the most unstable eigenmode at various Re. It is found that the most significant contribution to the growth rate of the disturbance arises from the transfer of the energy due to the strain rate of the base flow to the perturbation. The stabilizing effect of the viscous dissipation increases with increase in Re, but saturates for Re beyond ～70. Copyright © 2009 John Wiley & Sons, Ltd.     

Computation of Vortex Shedding and Radiated Sound for a Circular Cylinder: Subcritical to Transcritical Reynolds Numbers

The Lighthill acoustic analogy combined with Reynolds-averaged Navier–Stokes flow computations are used to investigate the ability of existing technology to predict the tonal noise generated by vortex shedding from a circular cylinder for a range of Reynolds numbers (100 < Re < 5 million). Computed mean drag, mean coefficient of pressure, Strouhal number, and fluctuating lift are compared with experiment. Two-dimensional calculations produce a Reynolds number trend similar to experiment but incorrectly predict many of the flow quantities. Different turbulence models give inconsistent results in the critical Reynolds number range (Re≈ 100000). The computed flow field is used as input for noise prediction. Two-dimensional inputs overpredict both noise amplitude and frequency; however, if an appropriate correlation length is used, predicted noise amplitudes agree with experiment. Noise levels and frequency content agree much better with experiment when three-dimensional flow computations are used as input data. Received 5 May 1998 and accepted 28 September 1998