Numerical investigation of steady suction control of flow around a circular cylinder

This paper numerically investigates the effectiveness of the control of steady suction on a stationary circular cylinder with several isolated suction holes on the surface at a subcritical Reynolds number. The control effectiveness as a function of the azimuthal position, spanwise spacing and suction flow rate of the suction holes on the control of the aerodynamic forces on the cylinder and the suppression of alternate vortex shedding are taken into account. The study of the azimuthal location of the suction holes indicates that azimuthal angles of θ=90° and 270°, which are close to the separation point, provide the most substantial decreases in the aerodynamic forces. When restricted to the most effective azimuthal angle, a remarkable control effectiveness can be achieved when the axial spacing between two neighboring suction holes is less than a minimum value even under a small suction momentum coefficient. However, if the axial spacing exceeds the minimum spacing, the control effectiveness will not be saturated even under a very large suction momentum coefficient. Thus, the cause of the effective aerodynamic force control is suggested to be a result of obvious three-dimensional phenomenon in the near wake, which is characterized by the generation of a convergent flow between two neighboring suction hole sections and a stronger, larger three-dimensional vortex pair adjacent to the convergent flow. It has been suggested that this strongly three-dimensional flow pattern is induced by the strong interaction between two neighboring but counter-rotating three-dimensional vortices separately produced by two neighboring suction holes. Moreover, the effects of such three-dimensional flow patterns are investigated in detail based on variations in the flow field and sectional aerodynamic forces in different cross sections. Finally, the upper limit of the axial spacing between two neighboring suction holes to form such a three-dimensional flow pattern is suggested to be between 0.75 D and 1.5 D when the suction flow rate exceeds a certain value.     

Numerical study of the effects of particles on the near wake around a circular cylinder

In this work, we investigate the dynamics of the near wake in a turbulent flow going past a circular cylinder with/without particles at a moderate Reynolds number using a direct numerical simulation method. High-order finite-deference schemes are applied to solve for the bulk fluid properties, and a Lagrangian approach is adopted to track the individual particles. The single-phase flow is analysed and validated using previous experimental data. Two converged states, U- and V-shaped, are observed in the near wake, which are consistent with the experimental results. For the two-phase flow, the addition of smaller particles shortens the length of the recirculation region and causes a V-shaped profile to form behind the circular cylinder. Furthermore, the particles increase the drag force from the circular cylinder and suppress the vortex shedding frequency. An increase in the turbulent statistics in the very near wake and a decrease in the turbulent statistics further downstream are also observed.     

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder atRe=200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number. The project supported by the State Key Fundamental Research Project of “Large Scale Scientific Computation Research” (G199903281)     

Spanwise correlations in the wake of a circular cylinder and a trapezoid placed inside a circular pipe

The spanwise correlation of a circular cylinder and a trapezoidal bluff body placed inside a circular pipe in fully developed turbulent regime is studied using hotwire anemometer. The present configuration possesses complex fluid structure interaction owing to the following features: high blockage effect; low aspect ratio of the body; upstream turbulence and interaction of axisymmetric flow with a two dimensional bluff body. The spatial correlation of such configuration is seldom reported in the literature. Results are presented for Reynolds number of Re_D=1×10⁵. Three different blockage ratios (0.14, 0.19 and 0.28) are considered in the present study. Correlation coefficient is observed to improve with increase in blockage ratio. Compared to a circular cylinder, a trapezoidal bluff body possesses high correlation length. The near wall effects tend to increase the phase drift, which is reflected in low correlation coefficients close to the pipe wall. The results show that the simultaneous effect of curvature, low aspect ratio and upstream turbulence reduces the correlation coefficients significantly as compared to unconfined and confined (parallel channel) flows. The low frequency modulations with a circular cylinder are higher for lower blockage ratios. The three-dimensionality of vortex shedding for trapezoid with a blockage ratio of 0.28 was observed to be lower compared to circular cylinder and all other blockage ratios. Low frequency modulations were found to be responsible for weak vortex shedding from a circular cylinder compared to a trapezoidal bluff body. The vortex shedding is observed to be nearly two dimensional in case of a trapezoidal bluff body of blockage ratio 0.28.     

Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number

Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations and at 300 for the three-dimensional simulations, and the reduced velocity is varied by changing the structural stiffness. The in-line centre-to-centre distance is varied from 1.5 to 8.0 diameters, and the results are compared to that of a single isolated flexible cylinder with the same structural characteristics, m^?=2.0 and ζ=0.007. The calculations show that significant changes occur in the dynamic behaviour of the cylinders, when comparing the flow around the tandem arrangements to that around an isolated cylinder: for the tandem arrangements, the lock-in boundaries are wider, the maximum displacement amplitudes are greater and the amplitudes of vibration for high reduced velocities, outside the lock-in, are very significant. The main responsible for these changes appears to be the oscillatory flow in the gap between the cylinders.     

Effect of blockage on spanwise correlation in a circular cylinder wake

A short series of experiments was conducted with the aim of assessing the possible effect of tunnel blockage on spanwise correlation lengths measured in the near-wake of a circular cylinder. The results indicate that increasing blockage acts to increase spanwise correlation. This finding has important implications for the conduct and reporting of both physical and numerical experiments on bluff-body wake flows.     

Experimental investigation of the effect of Reynolds number on flow structures in the wake of a circular parachute canopy

In the present study, an experimental study was conducted to characterize the effect of Reynolds number on flow structures in the turbulent wake of a circular parachute canopy by utilizing stereoscopic particle image velocime- try （Stereo-PIV） technique. The parachute model tested in the present study was attached by 28 nylon suspension lines and placed horizontally at the test section center of the wind tunnel. The obtained results showed that with the in- crease of Reynolds number, the intensities of the vortices near the downstream region of the canopy skirt were found to increase accordingly. However, the increase of Reynolds number did not result in a significant change in ensemble- averaged normalized x-component of the velocity, ensembleaveraged normalized vorticity, normalized Reynolds stress, and normalized turbulent kinetic energy distributions in the turbulent wake of the circular parachute canopy. The obtained results are very useful to further our understanding about the unsteady aerodynamics in the wake of flexible circular parachute canopies and to constitute a reference for CFD computation.     

Effects of large spanwise wavelength on the wake of a sinusoidal wavy cylinder

The wake of a sinusoidal wavy cylinder with a large spanwise wavelength λ/D_m (=3.79–7.57) and a constant wave amplitude a/D_m=0.152, where D_m is the mean diameter of the cylinder, is investigated using three dimensional (3D) large eddy simulation (LES) at a subcritical Reynolds number Re=3×10³, based on incoming free-stream velocity (U_∞) and D_m. Attention is paid to assimilating the effects of λ/D_m on the cylinder wake, including vortex shedding frequency, spanwise vortex formation length, streamwise velocity distribution, flow separation angle, 3D vortex structure, and turbulent kinetic energy (TKE) distribution. Based on the predominant role of λ/D_m in the near wake modification, three regimes are identified, i.e., regime I at λ/D_m<6.0, regime II at λ/D_m≈6.0 and regime III at λ/D_m>6.0. A dramatic decrease in fluid forces is observed at λ/D_m=6.06, about 16% and 93% reduction in time-averaged drag and fluctuating lift, respectively, compared to those of a smooth cylinder. We identified, for the first time, an optimum λ/D_m (=6.06) for the wavy cylinder with relatively large λ/D_m (>3.5) in the subcritical flow regime. The underlying mechanisms of force reduction are discussed, including the flow characteristics at the three λ/D_m regimes. A comparison is also made between the results of λ/D_m effects on the near wakes of a circular and a square cylinder.     

Induced parallel vortex shedding from a circular cylinder at Re of O(10) by using the cylinder end suction technique

In the present work, the objective is to attempt to induce parallel vortex shedding at a moderately high Reynolds number (=1.578 × 10⁴) by using the cylinder end suction method, and measure the associated aerodynamic parameters.We first measured the aerodynamic parameters of a single circular cylinder without end suction, and showed that the quantities measured are in good agreement with equivalent data in the published literature. Next, by using different amount of end suction which resulted in increasing the cylinder end velocity by 1%, 2% and 2.5%, we were able to show that the above corresponded to the situation of under suction, optimal suction and over suction, respectively. With optimal suction, we demonstrated that the end suction method works at Re = 1.578 × 10⁴. The shape of the primary vortex shed became straighter than when there is no end suction, and parameters like cylinder surface pressure distribution, drag force per unit span, as well as vortex shedding frequency all showed negligible spanwise variation. Further careful analyses showed that when compared to the naturally existing curved vortex shedding, with parallel vortex shedding the mid-span drag per unit span became slightly smaller, but the drag averaged over the cylinder span became slightly larger. For cylinder surface pressure, it was found that cylinder end effects mainly influenced the surface pressure in the angular ranges −180°  β < −60° and 60° < β  180°. Without end suction, the cylinder surface pressure in the above ranges was found to increase (become less negative) slightly with |z/d|, but such increase disappeared when optimal end suction was applied, and the cylinder surface pressure distribution became spanwise location independent. As for the vortex shedding frequency (Strouhal number), although the Strouhal number showed spanwise variation when there is no end suction and negligible spanwise variation when optimal suction was applied, the difference between the spanwise averaged Strouhal number was quite negligible. With under suction, the spanwise dependence of various aerodynamic parameters existed, but was found to be not as significant as when no end suction was applied at all. With over suction, the flow situation was found to be practically no change from the optimal suction situation.     

Centrifugal instability and the rib vortices in the cylinder wake

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v _θ)∂v _θ/∂r−1 is derived, wherev _θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China     

Numerical investigation of the turbulent energy budget in the wake of freely oscillating elastically mounted cylinder at low reduced velocities

We present a numerical study of the turbulent kinetic energy budget in the wake of cylinders undergoing Vortex-Induced Vibration (VIV). We show three-dimensional Large Eddy Simulations (LES) of an elastically mounted circular cylinder in the synchronization regime at Reynolds number of Re=8000. The Immersed Boundary Method (IBM) is used to account for the presence of the cylinder. The flow field in the wake is decomposed using the triple decomposition splitting the flow variables in mean, coherent and stochastic components. The energy transfer between these scales of motions are then studied and the results of the free oscillation are compared to those of a forced oscillation. The turbulent kinetic energy budget shows that the maximum amplitude of VIV is defined by the ability of the mean flow to feed energy to the coherent structures in the wake. At amplitudes above this maximum amplitude, the energy of the coherent structures needs to be fed additionally by small scale, stochastic energy in form of backscatter to sustain its motion. Furthermore, we demonstrate that the maximum amplitude of the VIV is defined by the integral length scale of the turbulence in the wake.     

Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder

The steady mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder in a stream flowing vertically upwards is numerically studied for both cases of heated and cooled cylinders. The governing partial differential equations are transformed into dimensionless forms using an appropriate transformation and then solved numerically using the Keller-box method. The comparison between the solutions obtained and those for a Newtonian fluid is found to be very good. Effects of the mixed convection and elasticity parameters on the skin friction and heat transfer coefficients for a fluid having the Prandtl number equal to one are also discussed. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point. However, for a sufficiently cold cylinder there will not be a boundary layer.     

Three-dimensional evolution of vortices and early features of coherent structure in the turbulent wake behind a 2-D circular cylinder

3-D evolution of Kármán vortex filaments and vortex filaments in braid regions in the turbulent wake of a 2-D circular cylinder is investigated numerically based on inviscid vortex dynamics by analyzing the response of the initially 2-D spanwise vortex filaments to periodic spanwise disturbance of varying magnitude, wavelength and initial phase angles. Our results reveal a kind of 3-D vortex system in the wake which consists of large scale horseshoe-shaped vortices and small scale γ-shaped vortex filaments as well as vortex loops. The mechanism and the dynamic process about the generation of streamwise vortical structure and the 3-D coherent structure are reported. currently published in the Chinese Edition of Acta Mechanica Sinica, Vol.25, No.3, 1993 The project supported by National Natural Science Foundation of China and the National Basic Research Project “Nonlinear Science”     

Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary

Two-degree-of-freedom vortex-induced vibrations (VIV) of a circular cylinder close to a plane boundary are investigated numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the Arbitrary Lagrangian Eulerian (ALE) scheme with a k-ω turbulence model closure. The numerical model is validated against experimental data of VIV of a cylinder in uniform flow and VIV of a cylinder close to a plane boundary at low mass ratios. The numerical results of the vibration mode, vibration amplitude and frequency agree well with the experimental data. VIV of a circular cylinder close to a plane boundary is simulated with a mass ratio of 2.6 and gap ratios of e/D=0.002 and 0.3 (gap ratio is defined as the ratio of gap between the cylinder and the bed (e) to cylinder diameter (D)). Simulations are carried out for reduced velocities ranging from 1 to 15 and Reynolds numbers ranging from 1000 to 15 000. It is found that vortex-induced vibrations occur even if the initial gap ratio is as small as e/D=0.002, although reported research indicated that vortex shedding behind a fixed circular cylinder is suppressed at small gap ratios (e/D<0.3 or 0.2). It was also found that vibration amplitudes are dependant on the bouncing back coefficient when the cylinder hits the plane boundary. Three vortex shedding modes are identified according to the numerical results: (i) single-vortex mode where the vortices are only shed from the top of the cylinder; (ii) vortex-shedding-after-bounce-back mode; (iii) vortex-shedding-before-bounce-back mode. It was found that the vortex shedding mode depends on the reduced velocity.     

The effect of slip distribution on flow past a circular cylinder

A slip boundary has been shown to have a significant impact on flow past bluff bodies. In this work and using a circular cylinder as a model system, the effects of various slip configurations on the passing flow are investigated. A theoretical analysis using matched-asymptotic expansion is first performed in the small-Reynolds number regime following Stokes and Oseen. A slip boundary condition is shown to lead to only higher-order effects (~1/ln(Re)) on the resulting drag coefficient. For higher Reynolds numbers (100–500), the effects of five types of symmetric slip boundary conditions, namely, no slip, fore-side slip, aft-side slip, flank slip, and all slip on the flow field and pertinent parameters are investigated with numerical simulations. Detailed results on the flow structure and force distribution are presented. Flank slip is found to have the best effect for drag reduction with comparable coverage of slip area. For asymmetric slip distributions, torque and lift are found to generally occur.     

Effect of the domain spanwise periodic length on the flow around a circular cylinder

We assess the effect of the choice of spanwise periodic length on simulations of the flow around a fixed circular cylinder. The Reynolds number is set to 400 because, at this value, both lift coefficient and shedding frequency show significant drop due to three-dimensional flow structures. From the analysis of the three-dimensionalities of the wake and of the integral quantities such as Strouhal number, RMS of lift coefficient and energy contained in the three-dimensional portion of the flow we obtain an estimate of the minimum spanwise length to satisfactorily represent the flow. Furthermore, we observe a distinct wake behavior when the spanwise length is approximately the mode B instability wavelength.     

Experimental investigation on wake characteristics behind a yawed square cylinder

The wake vortical structures of a square cylinder at different yaw angles to the incoming flow ($\alpha =$0°, 15°, 30° and 45°) are studied using a one-dimensional (1D) hot-wire vorticity probe at a Reynolds number (Re) of about 3600. The results are compared with those obtained in a yawed circular cylinder wake. The Strouhal number (St_N) as well as the mean drag coefficient ($C_{D_N}$), normalized by the velocity component normal to the cylinder axis, follow the independent principle (IP) satisfactorily up to $\alpha =$40°. Using the phase-averaging analysis, both the coherent and the remaining contributions of velocity and vorticity are quantified. The flow patterns of the coherent spanwise vorticity (${\omega }_z$) display obvious Kármán vortex streets and their maximum concentrations decrease as $\alpha$ increases. Similar phenomena are also shown in the coherent contours of the streamwise ($u$) and transverse ($v$) velocities as well as the Reynolds shear stress ($uv$). The contours of the spanwise velocity ($w$) and Reynolds shear stress ($uw$), however, experience an increasing trend for the maximum concentrations with increasing yaw angle. These results indicate an enhancement of the three-dimensionality of the wake and the reduction of vortex shedding strength as $\alpha$ increases. While general similarities to the wake behind a yawed circular cylinder are found in terms of flow features, some differences between the two wakes at different yaw angles are highlighted.     

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.