The wake flow control behind a circular cylinder using ion wind

Active and passive flow control methods have been studied for decades, but there have been only a few studies of flow control methods using ion wind, which is the bulk motion of neutral molecules driven by locally ionized air from a corona discharge. This paper describes an experimental study of ion wind wake control behind a circular cylinder. The experimental conditions consisted of a range of electrohydrodynamic numbers—the ratio of an electrical body force to a fluid inertial force—from 0 to 2 and a range of Reynolds numbers from 4×10³ to 8×10³. Pressure distributions over the cylinder surface were measured and flow visualizations were carried out using a smoke-wire method. The flow visualizations confirmed that ion wind significantly affects the wake structure behind a circular cylinder, and that the pressure drag can be dramatically reduced by superimposing ion wind.List of symbols BR blockage ratio - C _d coefficient of the pressure drag - C _p coefficient of the surface pressure, 2(p–p ₀)/(U ₀ ²) - C _pb coefficient of the base surface pressure, 2(p _b–p ₀)/(U ₀ ²) - D diameter of the cylinder - D _P pressure drag - d _p diameter of particle - E the electric field - F _e Coulombian force (qE) - F _v viscous force - H wire-to-cylinder spacing - I total electric current (A) - L the axial length of cylinder (m) - N _EHD electrohydrodynamic number - p _b base pressure of cylinder at =180° - p ₀ reference static pressure at 10D upstream - q the charge on the particle - R radius of the cylinder - V applied voltage (kV) - U ₀ mean flow velocity (m/s) - ion mobility in air (m²/(s V)) - ₀ permittivity of free space - viscosity of fluid (kg/ms) - density of fluid (kg/m³) - installation angle of a wire electrode (°)     

Evolution of global enstrophy in cylinder wake controlled by Lorentz force

The Okubo-Weiss function is correlated with the fluid particle compression, deformation and vorticity, which provides a simple way to characterize different regions of a flow-field. In the present paper, it shows mathematically that the global integration of Okubo-Weiss function is always equal to zero for a two dimensional incompressible flow with no-slip boundaries. To validate the conclusion, a flow passing a circular cylinder con- trolled by the electromagnetic force is calculated numerically as an example. Distributions of global enstrophy, total squared strain and Okubo-Weiss function in the controlled flow field are discussed. The influence of Lorentz force on the distribution is analyzed.     

Optimal control applied to water flow using second order adjoint method

This paper presents an optimal control applied to water flow using the first and second order adjoint equations. The gradient of the performance function with respect to control variables is analytically obtained by the first order adjoint equation. It is not necessary to compute the Hessian matrix directly using the second order adjoint equation. Two numerical studies have been performed to show the adaptability of the present method. The performance of the second order adjoint method is compared with that of the weighted gradient method, Broyden–Fletcher–Goldfarb–Shanno method and Lanczos method. The precise forms of the adjoint equations and the gradient to use for the minimisation algorithm are derived. The computation by the Lanczos method is shown as superior to those of the other methods discussed in this paper. The message passing interface library is used for the communication of parallel computing.     

Instability of cylinder wake under open-loop active control

Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimensional control input created by an electromagnetic actuator located on the cylinder surface,adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number representing the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926 D and 0.822 D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode transformation.All of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force.     

Numerical simulation of force and wake mode of an oscillating cylinder

The turbulent flow behind a circular cylinder subjected to forced oscillation is numerically studied at a Reynolds number of 5500 by using three-dimensional Large Eddy Simulations (3-D LES) technique with the Smagorinsky model. The filtered equations are discretised using the finite volume method with an O-type structured grid and a second-order accurate method in both time and space. Firstly, the main wake parameters of a stationary cylinder are examined and compared in the different grid resolutions. Secondly, a transversely oscillating cylinder with a constant amplitude in a uniform flow is investigated. The cylinder oscillation frequency ranges between 0.75 and 0.95 of the natural Kármán frequency, and the excitation amplitude is moderate, 50% of the cylinder diameter. The flow characteristics of an oscillating cylinder are numerically examined and the corresponding wake modes are captured firstly in 3-D LES at Re=5500. A transition between different wake modes is firstly investigated in a set of numerical simulations.     

Negative wake in the uniform flow past a cylinder

The upstream/downstream streamline shift and the associated negative wake generation (streamwise velocity overshoot in the wake) in a viscoelastic flow past a cylinder are studied in this paper, for the Oldroyd-B, UCM, PTT, and FENE-CR fluids, using the Discrete Elastic Viscous Split Stress Vorticity (DEVSS-ω) scheme (Dou HS, Phan-Thien N (1999). The flow of an Oldroyd-B fluid past a cylinder in a channel: adaptive viscosity vorticity (DAVSS-ω) formulation. J Non-Newtonian Fluid Mech 87:47–73). The numerical algorithm is a parallelized unstructured Finite Volume Method (FVM), running under a distributed computing environment through the Parallel Virtual Machine (PVM) library. It is demonstrated that both the normal stress and its gradient are responsible for the negative wake generation and streamline shifting. Fluid extensional rheology plays an important role in the generation of the negative wake. The negative wake can occur in flows where the fluid extensional viscosity does not increase rapidly with strain rate. The formation of the negative wake does not depend on whether the streamlines undergo an upstream or a downstream shift. Shear-thinning viscosity weakens the velocity overshoot and while shear-thinning first normal stress coefficient enhances the velocity overshoot. Wall proximity is not necessary for the velocity overshoot; however, it enhances the strength of the negative wake. For the Oldroyd-B fluid, the ratio of the solvent viscosity to the zero-shear viscosity plays an important role in the streamline shift. In addition, mesh dependent behaviour of normal stresses along the centreline at high De in most cylinder/sphere simulations is due to the convection of normal stress from the cylinder to the wake, which results in the maximum of the normal stress being located off the centreline by a short distance at high De.     

Characterization by proper-orthogonal-decomposition of the passive controlled wake flow downstream of a half cylinder

This study focuses on the flow modifications generated by a flat plate stabilizer placed downstream of a half-cylinder compared to the wake formation without the plate. For moderate Reynolds number, a snapshot proper-orthogonal-decomposition method based on particle-image-velocimetry (PIV) is used to analyze the complex dynamics of the flows and to highlight typical swirl formation mechanisms. Using this tool, the near-wake structures, the kinetic aspects, the energy contributions, the degree of organization of the structures and their temporal behaviour are identified. A strong link between the Strouhal number, the mean vorticity and the Total Energy is observed. The interference of the shear layer with the stabilizer has an atypical influence on the wake characteristics.     

The influences of wall Lorentz force and field Lorentz force on the cylinder drag reduction

In this paper,the effects of Lorentz force on drag reduction for a circular cylinder have been studied experimentally and numerically.Based on its effects on drag reduction,the Lorentz force is found to be classified into two parts:one acts directly on the cylinder,named as the wall Lorentz force,and the other called the field Lorentz force acts on the fluid inside the boundary layer.The wall Lorentz force leads to the generation of a thrust,whereas the field Lorentz force results in drag increase.Since the former dominates the drag variation,the drag would reduce accordingly and even turn into negative (thrust) with the application of Lorentz force.     

The velocity field of the turbulent very near wake of a circular cylinder

Hot-wire measurements were conducted in the very near wake (x/d10) of a circular cylinder at a Reynolds number based on cylinder diameter, Re _d of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.This study has been funded by the NASA-Ames University Consortium Cooperative Agreement, NCC2-5003. We wish to thank Patrick Beaudan for providing us with the LES results for comparison and Parviz Moin for his interest in and encouragement of this experiment to provide validation data for the LES. We also wish to thank loseph Murray for his help with the look-up-table data reduction program.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

Optimal control of two-dimensional nonaxisymmetric temperature field in a hollow cylinder with thermoelastic stress restrictions

Institute of Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lvov. Translated from Prikladnaya Mekhanika, Vol. 31, No. 6, pp. 42–49, June, 1995.     

Formation of discontinuities in the wake of a cylinder in a stratified flow

The results of an experimental investigation of continuously stratified flow past a cylinder are presented. It is shown that interfaces with an elevated value of the density gradient (discontinuities) are formed in the wake.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 20–26, January–February, 1993.     

An experimental study on unsteady turbulent near wake of a rectangular cylinder in channel flow

 Unsteady turbulent near wake of a rectangular cylinder in channel flow has been studied experimentally with a laser Doppler velocimetry (LDV). The time-averaged and phase-averaged statistics were measured for the cylinders having various width-to-height ratios, b/h. It is shown that the turbulent intensities on the centerline of the channel have their maxima near the rear stagnation point of a recirculation region. The contours of coherent vorticity and streamline reproduce clearly the shed vortices from the cylinder observed by the flow visualization. The characteristics of the flow field, which depends on b/h, are discussed and the significant contribution of the coherent structure to the flow field is clarified. Moreover, the turbulent kinetic energy budget has been examined. Received: 19 January 1998/Accepted: 21 July 1998     

Wavelet multi-scale analysis of the circular cylinder wake under synthetic jets control

The wavelet method is used to study the multi-scale vortical structures of the flow around a circular cylinder without and with synthetic jet control at Re = 950. The velocity field is decomposed into 9 wavelet components, including one approximation component and 8 detail components. The first component shows the flow characteristics at low frequency. The dominant components represent large-scale vortical structures in the flow and they show similar distributions for the same wake pattern. Other detail components reflect the characteristics of relatively small-scale structures. The individual vortex dynamics underlying the complex flow can be extracted and thus reconstructed by the approximation and dominant components. Thus, we show an effective approach to reveal the flow physics from the complex flow.     

Effect of finite depth of stratified flow on turbulence formation in the wake of a cylinder

The experimental results of investigating the effect of the finite depth of a linearly stratified flow channel on turbulence formation associated with the horizontal motion of a cylinder are presented. The limits of the interval of internal Froude numbers and dimensionless channel depths (with respect to the cylinder diameter) corresponding to local instabilites in the disturbed flow density distribution, leading to the formation of turbulence, are found. The dynamics of formation of the turbulent zones and their evolution are investigated. Unsteady periodic regimes are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 160–163, September–October, 1990.The authors are grateful to A. T. Onufriev for his interest in their work.     

The turbulent flow field around a circular cylinder

The flow field around a circular cylinder mounted vertically on a flat bottom has been investigated experimentally. This type of flow occurs in several technical applications, e.g. local scouring around bridge piers. Hydrogen bubble flow visualization was carried out for Reynolds numbers ranging from 6,600 to 65,000. The main flow characteristic upstream of the cylinder is a system of horse-shoe vortices which are shed quasi-periodically. The number of vortices depends on Reynolds number. The vortex system was found to be independent of the vortices that are shed in the wake of the cylinder. The topology of the separated flow contains several separation and attachment lines which are Reynolds number dependent. In the wake region different flow patterns exist for each constant Reynolds number.     

Drag force on a free surface-piercing yawed circular cylinder in steady flow

The force distribution on a surface-piercing yawed cylinder surface differs significantly from that on a surface-piercing vertical cylinder. The established numerical model for flow past the surface-piercing yawed cylinder with yaw angles from −45° to 45° was solved by the standard large-eddy simulation (LES) methodology. Six cases at intervals of ±15° relative to the vertical were studied at the Reynolds number of 27 000 and the Froude number of 0.8 based on the cylinder diameter and free-stream velocity, among which the drag forces on four cylinders with yaw angles from −15° to 30° were tested for the validation of the LES approach. The results revealed that the time-averaged total drag coefficient for all cases increases with the increase of yaw angle compared to that of the surface-piercing vertical cylinder, even over 2.5 for the ±45°-yawed cylinders. The sectional drag coefficients for the negatively yawed cylinders are much greater than that for the vertical cylinder, and much less for the positively yawed cylinders. The unbalanced hydrostatic pressures on the inclined section are mainly responsible for those increment and decrement. Once the hydrostatic pressure was removed, the sectional drag coefficient on the mid-span of the positively yawed cylinder increases from the top section to the bottom, and decreases for the negatively yawed cylinder. The corresponding integrated total drag coefficient decreases with the increase of the yaw angle to ±15°, then increases with the further increase of the magnitude of yaw angle.     

Streamwise evolution of an inclined cylinder wake

The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Re_d of 7,200 based on free stream velocity (U _∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to [`(v<sup>2</sup>)] \overline{{v^{2}}} is remarkable at x/d = 10 and 20 and significantly larger than that to [`(u²)] \overline{{u^{2}}} and [`(w<sup>2</sup>)]. \overline{{w^{2}}}. This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to [`(u²)] \overline{{u^{2}}} and [`(v²)] \overline{{v^{2}}} decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for a larger α.