Effect of surface topology on the galloping instability of rectangular cylinders

The effect of geometry on the transverse galloping instability of rectangular cylinders was studied experimentally for Reynolds numbers between 1,000 and 10,000. In particular, a comparison was made between a rectangular cylinder with rounded corners and a smooth surface, and the same baseline geometry with added surface topology synthesized from two-dimensional Fourier-modes. The effects of the topology amplitude and wavelength were investigated. From measurements of the normal (galloping direction) force coefficient variation with angle-of-attack, it was found that the added surface topology generally had a destabilizing effect relative to the smooth cylinder. At the lowest Reynolds number, the smooth cylinder was stable, while the cylinders with added topology were unstable with respect to galloping. For Reynolds numbers from 5,000 to 10,000, the added topology did not cause a similar instability. However, there was a monotonic increase in the slope of the normal force coefficient at zero angle-of-attack with increasing surface height amplitude, thus moving the geometry closer to the instability threshold. This effect diminished as Reynolds number increased. Overall, for the range of parameters investigated herein, whenever the cylinders with topology were unstable to soft or hard galloping, the larger topology exhibited more favorable galloping resistance characteristics than the one with smaller topology. Topology wavelength was found to have no effect on the galloping behavior of the cylinder for Reynolds numbers below 7500, and a moderate increase in the normal force slope at zero angle of attack with decreasing wavelength for larger Reynolds numbers. The latter effect was associated with an increase in the angle of attack at which the cylinder could become unstable to hard galloping.     

Simulation of cross-flow-induced vibration of cylinder arrays by surface vorticity method

The surface vorticity method (SVM), which is a fast and practical grid-free two-dimensional (2-D) method, and a fluid–structure interaction model incorporating the effects of cylinder motions and displacements is used to simulate the vortex-induced vibration of cylinder arrays at sub-critical Reynolds number Re=2.67×10⁴. The SVM is found to be most suitable for simulating a 2-D cylinder row with large-amplitude vibrations where the vorticity field and the fluid forces of the cylinder row change drastically, and the effect of the stream on the transverse direction vibration is very significant. The fluidelastic instability of a flexible cylinder row at small pitch ratio is also investigated, and the critical reduced velocity of the cylinder row at a reduced damping parameter S_G=1.29 is calculated, which is in good agreement with experimental and analytical results of the unsteady model. Vortex-induced vibration of a staggered cylinder array is simulated using different structural parameters. When the cylinders are relatively more flexible, the flow pattern changes dramatically and the fluid–structure interaction has a dominant impact on the flow field. Compared with grid-based methods, the grid-free SVM is a fast and practical method for the simulation of the FIV of cylinder arrays due to vortex shedding at sub-critical Reynolds numbers.     

Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Measurements of transverse forces on circular cylinders undergoing vortex-induced vibration

Experiments have been carried out on a circular cylinder, with and without helical strakes, free to respond in a direction transverse to a water flow. The Reynolds number range was between 3×10³ and 2.1×10⁴, the mass ratio was just above 0.8 and the fraction of critical damping was approximately 2×10⁻⁴. Measurements are presented of the response, the transverse fluid force and the phase angle between the response and the force, all as a function of reduced velocity. The straked cylinder is observed to respond over a narrow range of reduced velocity and its maximum amplitude is decreased by just over 60%, compared with a plain cylinder. The familiar phase jump that occurs for a plain cylinder did not occur with the straked one, with the phase close to zero over the entire reduced velocity range where response to vortex shedding occurred.     

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.     

隔离板对流向振荡圆柱尾流旋涡脱落的抑制

用隔离板对直径为D, 沿流向振荡的圆柱后涡脱落进行抑制. 隔离板放于圆柱尾流中心线上,控制参数包括隔离板长度L/D以及隔离板前缘到柱体振荡中心的距离G/D. 实验的雷诺数范围Re=V_∞D/v=1.01×10⁴～1.69×10⁴,柱体折减振频范围f_eD/V_∞=0～0.03, 柱体振幅固定为A/D=0.2. 风洞烟线显示和热线测量结果表明:当 G/D位于一个有效区域内时,可有效抑制振荡柱体尾流的旋涡脱落. 该有效区的大小随着隔离板板长的增大而增大, 随着Re数和圆柱振荡频率的增大而减小.     

HYDRODYNAMIC DAMPING OF A CYLINDER AT β≈106

This paper describes delicate, but large-scale, experiments aimed at measuring the hydrodynamic damping of a circular cylinder oscillating in still water and transversely in a current. Attention is concentrated on the regime of very small Keulegan–Carpenter numbers, in which the drag coefficient is inversely proportional to the Keulegan–Carpenter number. Measurements in still water at β=650 000 and 1250 000 point to drag coefficients about twice those appropriate to two-dimensional laminar flow, in common with earlier measurements at β≈10⁵. In the presence of a slowly varying transverse current (generated by placing the cylinder at the node of standing waves of long period), the damping increased with the reduced velocity of the ambient flow at a rate that increased with the Reynolds number.     

Control of vortex formation from a vertical cylinder in shallow water: Effect of localized roughness elements

Vortex formation from a vertical cylinder in shallow water is controlled by placement of a narrow transverse strip of roughness elements on the bed (bottom surface). A technique of high-image-density particle image velocimetry is employed to obtain global, instantaneous representations of the flow patterns, which lead to phase- and time-averaged patterns of streamline topology and Reynolds stress on planes at and above the bed. Near the bed, the overall form of the streamline topology is maintained, even at larger heights of the roughness elements. With increasing height of the elements, the downstream saddle point is further displaced in the streamwise direction. Correspondingly, the streamwise extent of the negative pocket of the streamwise velocity component, i.e., the region of reverse flow along the bed surface, increases substantially in the streamwise direction. The Reynolds stress in the very near-wake, at locations upstream of the roughness elements, is significantly attenuated, even for small height of roughness. This attenuation occurs not only near the bed surface, but also at the midplane of the shallow water wake, and thereby indicates that the consequence of localized roughness is to exert a global influence. In fact, corresponding patterns of instantaneous velocity and vorticity indicate that consistent formation of large-scale vortices in the very near-wake region is attenuated with relatively small surface roughness on the bed. Downstream of the roughness elements, the patterns of Reynolds stress near the bed surface, as well as at the midplane of the water layer, are significantly altered relative to the case of no roughness. Near the bed, highly concentrated patterns of positive and negative Reynolds stress in the absence of roughness give way to lower-level regions of Reynolds stress in the form of alternating concentrations; the particular pattern depends on the height of the roughness elements. At the midplane of the water layer, the Reynolds stress patterns maintain their same overall form, but the extrema of the Reynolds stress concentrations are attenuated in magnitude and are shifted in the downstream direction, with increasing height of the roughness elements. These observations are complemented by patterns of instantaneous velocity and vorticity.     

Effect of transverse stream velocity in an incompressible boundary layer on the stability of the laminar flow regime

The stability of the laminar flow regime in the boundary layer developed on a wall is increased considerably by the relatively slight extraction of fluid from the wall [1–4]. In the theoretical study of this phenomenon, all the investigators known to the present authors have taken into account only the increase in the fullness of the velocity profile in the boundary layer with suction. Computations of the stability characteristics have been made on the assumption that there are no transverse velocities in the laminar boundary layer.We present below an analysis of the stability of the laminar boundary layer in the presence of a constant transverse velocity in the near-wall region (suction). The calculations made show the existence for a given velocity profile in the boundary layer of a relative suction velocity v=v such that with suction velocities greater than v the flow remains stable at all Reynolds numbers, while the method used in the cited references gives a definite finite critical Reynolds number, equal in our notation to the Reynolds number at v=0, for each relative suction velocity.It was found that with suction of fluid from the boundary layer the region of instability has finite dimensions, i.e., there exist lower and upper critical Reynolds numbers. The flow is stable if its Reynolds number is less than the lower, or greater than the upper values of the critical Reynolds number.The instability region diminishes with increase in the relative suction velocity, and at a value of this velocity which is specific for each value of the velocity profile the instability region degenerates into a point-the flow becomes absolutely stable. Thus, with distributed suction it is advisable to increase the relative suction velocity only to a definite magnitude corresponding to disappearance of the instability region. The computational results presented make it possible to estimate this velocity for velocity profiles ranging from a Blasius profile to an asymptotic profile. Specific calculations were made for a family of Wuest profiles, since under actual conditions with suction there always exists a starting segment of the boundary layer [1, 2].     

LES-based Study of the Roughness Effects on the Wake of a Circular Cylinder from Subcritical to Transcritical Reynolds Numbers

This paper investigates the effects of surface roughness on the flow past a circular cylinder at subcritical to transcritical Reynolds numbers. Large eddy simulations of the flow for sand grain roughness of size k/D = 0.02 are performed (D is the cylinder diameter). Results show that surface roughness triggers the transition to turbulence in the boundary layer at all Reynolds numbers, thus leading to an early separation caused by the increased momentum deficit, especially at transcritical Reynolds numbers. Even at subcritical Reynolds numbers, boundary layer instabilities are triggered in the roughness sublayer and eventually lead to the transition to turbulence. The early separation at transcritical Reynolds numbers leads to a wake topology similar to that of the subcritical regime, resulting in an increased drag coefficient and lower Strouhal number. Turbulent statistics in the wake are also affected by roughness; the Reynolds stresses are larger due to the increased turbulent kinetic energy production in the boundary layer and separated shear layers close to the cylinder shoulders.     

A FLOW VISUALIZATION STUDY ON FEEDBACK CONTROL OF VORTEX SHEDDING FROM A CIRCULAR CYLINDER

This note presents flow visualization results to show the response of wake flows behind a cylinder to the feedback suppression and excitation. The experiments were conducted in a water channel and the feedback perturbations were introduced into the wake by oscillating the cylinder transverse to the oncoming flow. The visualization photographs directly illustrated the wake flows under the feedback suppression and excitation at Reynolds numbers up to 25% above the natural onset Reynolds number for vortex shedding.     

Vortex shedding and three-dimensional behaviour of flow past a cylinder confined in a channel

A numerical investigation of the flow past a circular cylinder centred in a two-dimensional channel of varying width is presented. For low Reynolds numbers, the flow is steady. For higher Reynolds numbers, vortices begin to shed periodically from the cylinder. In general, the Strouhal frequency of the shedding vortices increases with blockage ratio. In addition, a two-dimensional instability of the periodic vortex shedding is found, both empirically and by means of a Floquet stability analysis. The instability leads to a beating behaviour in the lift and drag coefficients of the cylinder, which occurs at a Reynolds number higher than the critical Reynolds number for the three-dimensional mode A-type instability, but lower than a Reynolds number for any mode B-type instability.     

Outer flow scaling of smooth and rough wall turbulent boundary layers

Mean velocity profiles in a zero pressure gradient turbulent boundary layer were measured on a hydraulically smooth surface and three different rough surfaces created from sand paper, perforated plate, and woven wire mesh. The physical size and geometry of the roughness elements were chosen to encompass both transitionally and fully rough flow regimes. The mean velocity profiles were measured using a Pitot tube in a subsonic wind tunnel, for Reynolds numbers (based on momentum thickness) ranging from 3,730 to 12,260. Three different outer velocity scales were used to analyze the defect profile. The results show that application of a so called mixed outer scale causes the velocity profile in the outer region to collapse onto the same curve for different Reynolds numbers and roughness conditions. Although the mixed scale collapses defect profiles on different surfaces, the effect of surface roughness is still observed in the outer region.     

The effect of riblets on laminar to turbulent transition

Experiments conducted on the effect of riblets on the laminar-to-turbulent transition of a flat plate in a water tunnel are reported. Transition was determined using a Laser Doppler Velocimeter (LDV). A smooth reference surface was compared to five riblet surfaces for a range of Reynolds numbers. Smooth surface transition Reynolds number was about 2.75 × 10⁶. All of the five tested riblet surfaces had lower transition Reynolds numbers. A critical roughness Reynolds number of about 6 was determined for one of the riblet surfaces. This is much lower than the generally accepted value of 25, considered safe for distributed roughness.     

A thermal LBM-LES model in body-fitted coordinates: Flow and heat transfer around a circular cylinder in a wide Reynolds number range

In order to apply the lattice Boltzmann method (LBM) for modeling passive heat transfer at high Reynolds numbers, a number of models were proposed by introducing the large eddy simulation (LES) into the LBM framework to improve numerical stability. Our study finds that the generalized form of interpolation-supplemented LBM (GILBM), likewise, can locally modify the dimensionless relaxation time, thus enhancing the numerical stability at high Reynolds numbers. Given additional advantages of the GILBM in dealing with complicated geometries and improving computing accuracy, a thermal LBM-LES model in body-fitted coordinates is established in this paper. Numerical validation is performed by investigating the flow and heat transfer around a circular cylinder over a wide range of Reynolds numbers. The obtained results agree well with both experimental and numerical data in the previous work. Meanwhile, the effects of Reynolds number and Prandtl number on thermodynamic features of flow past a circular cylinder are revealed. It is found out that when the Reynolds number exceeds the critical value, the local Nusselt number fluctuates rapidly in a specific region of the rear cylinder surface affected by the Prandtl number. In the near-wake region, the temperature field exhibits significant dependence on the Prandtl number at moderate Reynolds numbers, while such effects turn to be slight at high Reynolds numbers.     

Global stability analysis of axisymmetric boundary layer over a circular cylinder

This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier–Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi’s iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.     

Simulation of turbulent flows around a circular cylinder using nonlinear eddy-viscosity modelling: steady and oscillatory ambient flows

Steady incident flow past a circular cylinder for sub- to supercritical Reynolds number has been simulated as an unsteady Reynolds-averaged Navier–Stokes (RANS) equation problem using nonlinear eddy-viscosity modelling assuming two-dimensional flow. The model of Craft et al. (Int. J. Heat Fluid Flow 17 (1996) 108), with adjustment of the coefficients of the ‘cubic’ terms, predicts the drag crisis at a Reynolds number of about 2×10⁵ due to the onset of turbulence upstream of separation and associated changes in Strouhal number and separation positions. Slightly above this value, at critical Reynolds numbers, drag is overestimated because attached separation bubbles are not simulated. These do not occur at supercritical Reynolds numbers and drag coefficient, Strouhal number and separation positions are in approximate agreement with experimental measurements (which show considerable scatter). Fluctuating lift predictions are similar to sectional values measured experimentally for subcritical Reynolds numbers but corresponding measurements have not been made at supercritical Reynolds numbers. For oscillatory ambient flow, in-line forces, as defined by drag and inertia coefficients, have been compared with the experimental values of Sarpkaya (J. Fluid Mech. 165 (1986) 61) for values of the frequency parameter, β=D²/νT, equal to 1035 and 11240 and Keulegan–Carpenter numbers, KC=U₀T/D, between 0.2 and 15 (D is cylinder diameter, ν is kinematic viscosity, T is oscillation period, and U₀ is the amplitude of oscillating velocity). Variations with KC are qualitatively reproduced and magnitudes show best agreement when there is separation with a large-scale wake, for which the turbulence model is intended. Lift coefficients, frequency and transverse vortex shedding patterns for β=1035 are consistent with available experimental information for β≈250−500. For β=11240, it is predicted that separation is delayed due to more prominent turbulence effects, reducing drag and lift coefficients and causing the wake to be more in line with the flow direction than transverse to it. While these oscillatory flows are highly complex, attached separation bubbles are unlikely and the flows probably two dimensional.     

Characteristics of the near wake of a cylinder at low Reynolds numbers

An experimental study has been made of the near wake of two two-dimensional bluff bodies, a circular cylinder and a flat ribbon in the regimes corresponding to the 2-D steady and 2-D periodic wake. Velocity measurements from both hot-wire and laser Doppler anemometry are compared. Detailed measurements of the velocity field in air in the near wake, in isothermal conditions, are presented. The evolutions of the mean longitudinal velocity and the rms transverse velocity fluctuation on the center line can be plotted in a universal form whatever the value of the Reynolds number. These measurements show also that the onset of the instability is related to a critical value of an interaction term characteristic of the strength of the shear layers and the shear layer spacing at the end of the recirculation zone.     

HYDRODYNAMIC DAMPING OF A CYLINDER AT β≈10

This paper describes delicate, but large-scale, experiments aimed at measuring the hydrodynamic damping of a circular cylinder oscillating in still water and transversely in a current. Attention is concentrated on the regime of very small Keulegan–Carpenter numbers, in which the drag coefficient is inversely proportional to the Keulegan–Carpenter number. Measurements in still water at β=650 000 and 1250 000 point to drag coefficients about twice those appropriate to two-dimensional laminar flow, in common with earlier measurements at β≈10⁵. In the presence of a slowly varying transverse current (generated by placing the cylinder at the node of standing waves of long period), the damping increased with the reduced velocity of the ambient flow at a rate that increased with the Reynolds number.