Effect of acoustic excitation on flow over a partially grooved circular cylinder

An experimental investigation was carried out on the flow over a partially grooved circular cylinder over a Reynolds number range of 3 × 10⁴ to 1.22 × 10⁵ with and without acoustic excitation. Without excitation the flow over the smooth half of the cylinder was observed to shift to higher subcritical regime. The flow over the groove half, however, is shifted to supercritical or transcritical flow regime. With excitation, on the smooth half it is the separated laminar shear layer which locks in with the excitation frequency, resulting in the shift from subcritical to supercritical or transcritical regimes. On the groove half excitation is not effective for the flow within the transcritical regime. With excitation, the lift is found to reverse its direction while the drag is nearly the same.This study is partly supported by a grant from the Committee of Research and Conference Grants. The University of Hong Kong     

Reynolds-number-effects in flow around a rectangular cylinder with aspect ratio 1:5

The paper reports on experiments carried out over a wide range of Reynolds numbers in a high pressure wind tunnel. The model was a sharp-edged rectangular cylinder with aspect ratio height/width 1:5 (width/span ratio 1:10.8), which was investigated in both basic orientations, lengthwise (4×10³<Re<4×10⁵) and perpendicular to the flow (2.7×10⁴<Re<6.4×10⁵). The Reynolds number is based on the height of the model normal to the flow. Steady and unsteady forces were measured with a piezoelectric balance. Thus along with steady (i.e. time averaged values) including the base pressure coefficient, also power spectra and probability density functions were measured yielding for example Strouhal numbers, higher statistical moments, etc. A response diagram for the vortex resonance phenomenon was taken for the natural bending motion of the slender model. If lift coefficient for constant angle of attack is plotted against Reynolds number, a significant Reynolds number effect is seen. For α=4°, the curve shows an inflection point and the lift varies between 0.3 and 0.6. For α=6° and 2° there are similar variations shifted to lower and higher values of Re, respectively. Probably the shapes of separation bubbles that depend on the Reynolds number are responsible for these effects. No Reynolds number effects were observed when the long side was normal to the flow, an orientation where reattachment at the side walls is not possible. Comparing both basic cases (α=0° and 90°), the interpretation of the probability distributions of lift force leads to the conclusion that the possibility of reattachment (α=0°) seems to enhance the degree of order in the vortex shedding process.     

Numerical investigations into effects of three-dimensional wake patterns on unsteady aerodynamic characteristics of a circular cylinder at Re=1.3×105

In contrast with a wide range of applications concerning flows around a circular cylinder at upper subcritical Reynolds numbers (Re), there is no systematic understanding about the fundamentals of so-called random flow patterns, and their effects on intermittent modulations in the time history of pressure or force, and the decrease in their spanwise correlations. This paper employed the large-eddy simulation (LES) technique to predict flows past a circular cylinder at Re=1.3×10⁵ and to provide images based on flow visualization that can clarify the physical mechanism responsible for these outcomes. A reasonably sufficient spanwise length was adopted for the numerical model by taking into consideration the effect of aspect ratios (the spanwise length to the diameter). We found that even at such high Res, a three-dimensional pattern of vortical field is present in the wake resulting in total force modulation and weak spanwise correlation, e.g., obvious oblique shedding. The whole development process of the three-dimensional wake is exhibited as a universal. The results revealed that local phase variations in primary vortex shedding are the starting points of three-dimensional wake patterns, which are induced by the “irregular” streamwise vortex. The three-dimensional near wake following local phase variations is associated with a successive evolution composed of certain stages in order. Quantitative analyses based on the time series of sectional lift coefficients show that intermittent increase in primary shedding periods and sectional lift streak divisions are closely related to local phase variations and vortex division in the development process of the three-dimensional pattern. In addition to the phase difference along the span, the three-dimensional pattern also weakens vortex shedding in cross sections perpendicular to the axis of the cylinder, resulting in modulation of the sectional lift coefficient.     

Interaction between the near wake and the cross-section variation of a circular cylinder in uniform flow

The flow around a circular cylinder with a cross-section variation is experimentally investigated. Particle Image Velocimetry (PIV) is used to scrutinize the interaction of the cylinder’s wall with its near wake. The Reynolds number based on the cylinder’s diameter and freestream velocity is 80 × 10³, corresponding to the upper subcritical flow regime. At a forcing Strouhal number of St _f = 0.02, the maximum vorticity level around the cylinder is reduced by more than 50% as compared to its uncontrolled value. The topology of the bulk flow confined between the primary vortical structure and the cylinder surface is modified resulting in substantial drag reduction.     

The aerodynamics of a cylinder submerged in the wake of another

Flow-induced fluctuating lift (C_Lf) and drag (C_Df) forces and Strouhal numbers (St) of a cylinder submerged in the wake of another cylinder are investigated experimentally for Reynolds number (Re)=9.7×10³–6.5×10⁴. The spacing ratio L^⁎ (=L/D) between the cylinders is varied from 1.1 to 4.5, where L is the spacing between the cylinders and D is the cylinder diameter. The results show that C_Lf, C_Df and St are highly sensitive to Re due to change in the inherent nature of the flow structure. How the flow structure is dependent on Re and L^⁎ is presented in a flow structure map. Zdravkovich and Pridden (1977) observed a ‘kink’ in time-mean drag distribution at L^⁎≈2.5 for Re>3.1×10⁴, but not for Re≤3.1×10⁴. The physics is provided here behind the presence and absence of the ‘kink’ that was left unexplained since then.     

Numerical Simulation of the Negative Magnus Effect of a Two-Dimensional Spinning Circular Cylinder

Based on the finite volume method, the flow past a spinning circular cylinder at a low subcritical Reynolds number (Re =1 × 10 ⁵), high subcritical Reynolds number (Re =1.3 ×10 ⁵), and critical Reynolds number (Re =1.4 ×10 ⁵) were each simulated using the Navier-Stokes equations and the γ-Re _?? transition model coupled with the SST k?ω turbulence model. The system was solved using an implicit algorithm. The freestream turbulence intensity decay was effectively controlled by the source term method proposed by Spalart and Rumsey. The variations in the Magnus force as a function of the spin ratio, α were obtained for the three Reynolds numbers, and the flow mechanism was analyzed. The results indicate that the asymmetric transitions induced by spin affect the asymmetric separations at the top and bottom surfaces of the circular cylinder, which further affects the pressure distributions at the top and bottom surfaces of the circular cylinder and ultimately result in a negative Magnus force, whose direction is opposite to that of the classical Magnus force. This study is the first to use a numerical simulation method to predict a negative Magnus force acting on a spinning circular cylinder. At the low subcritical Reynolds number, the Magnus force remained positive for all spin ratios. At the high subcritical Reynolds number, the sign of the Magnus force changed twice over the range of the spin ratio. At the critical Reynolds number, the sign of the Magnus force changed only once over the range of the spin ratio. For relatively low spin ratios, the Magnus force significantly differed by Reynolds number; however, this variation diminished as the spin ratio increased.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

Time-averaged topological flow patterns and their influence on vortex shedding of a square cylinder in crossflow at incidence

Flow characteristics around the square cylinder and their influence on the wake properties are studied. Time-averaged flow patterns on the surfaces of square cylinder in a cross-stream at incidence are experimentally probed by surface-oil flow technique and analyzed by flow topology for Reynolds numbers between 3.9×10⁴ and 9.4×10⁴ as the incidence angle changes from 0° to 45°. Vortex shedding characteristics are measured by a single-wire hot-wire anemometer for Reynolds numbers between 5×10³ and 1.2×10⁵. The effects of topological flow patterns on the wake properties then are revealed and discussed. Flows around the square cylinder are identified as three categories: the subcritical, supercritical, and wedge flows according to the prominently different features of the topological flow patterns. The Strouhal number of vortex shedding, turbulence in the wake, and wake width present drastically different behaviors in different characteristic flow regimes. A critical incidence angle of 15° separates the subcritical and supercritical regimes. At the critical incidence angle the wake width and shear-layer turbulence present minimum values. The minimum wake width appearing at the critical incidence angle, which leads to the maximum Strouhal number, is due to the reattachment of one of the separated boundary layer to the lateral face of the square cylinder. If the Strouhal numbers are calculated based on the wake width instead of the cross-stream projection width of cylinder, the data in the subcritical and supercritical regimes are well correlated into two groups, which would approach constants at high Reynolds numbers.     

Simulation of the flow past a circular cylinder in the supercritical regime by blending RANS and variational-multiscale LES models

A strategy which blends a variational multiscale large eddy simulation (VMS-LES) model and a RANS model in a hybrid approach is investigated. A smooth blending function, which is based on the value of a blending parameter, is used for switching from VMS-LES to RANS. Different definitions of the blending parameter are investigated. The capabilities of the novel hybrid approach are appraised in the simulation of the flow around a circular cylinder at a Reynolds number 1.4×10⁵, based on the freestream velocity and on the cylinder diameter, in the presence of turbulent boundary-layer due to turbulent inflow conditions. A second study at Reynolds numbers from Re=6.7×10⁵ to 1.25×10⁶ is also presented. The effect of using the VMS-LES approach in the hybrid model is evaluated. Results are compared to those of other RANS, LES and hybrid simulations in the literature and with experimental data     

Experiment on smooth,circular cylinders in cross-flow in the critical Reynolds number regime

Experiments were conducted for 2D circular cylinders at Reynolds numbers in the range of 1.73 × 10⁵–5.86 × 10⁵. In the experiment, two circular cylinder models made of acrylic and stainless steel, respectively, were employed, which have similar dimensions but different surface roughness. Particular attention was paid to the unsteady flow behaviors inferred by the signals obtained from the pressure taps on the cylinder models and by a hot-wire probe in the near-wake region. At Reynolds numbers pertaining to the initial transition from the subcritical to the critical regimes, pronounced pressure fluctuations were measured on the surfaces of both cylinder models, which were attributed to the excursion of unsteady flow separation over a large circumferential region. At the Reynolds numbers almost reaching the one-bubble state, it was noted that the development of separation bubble might switch from one side to the other with time. Wavelet analysis of the pressure signals measured simultaneously at θ = ±90° further revealed that when no separation bubble was developed, the instantaneous vortex-shedding frequencies could be clearly resolved, about 0.2, in terms of the Strouhal number. The results of oil-film flow visualization on the stainless steel cylinder of the one-bubble and two-bubble states showed that the flow reattachment region downstream of a separation bubble appeared not uniform along the span of the model. Thus, the three dimensionality was quite evident.     

Dependence of flow classification on the Reynolds number for a two-cylinder wake

This work aims to investigate the dependence of flow classification on the Reynolds number (Re) for the wake of two staggered cylinders. The Re examined ranges from 1.5×10³ to 2.0×10⁴. The pitch ratio, P^⁎=P/d examined is 1.2–6.0 (d is the cylinder diameter), and angle (α) is 0–90°, where P is the center-to-center spacing between two cylinders and α is the angle between the incident flow and the line through the cylinder centers. Two single hotwires were used to measure simultaneously the fluctuating streamwise velocities (u) in the vortex streets generated by the two cylinders. The power spectral density functions and the Strouhal numbers were then obtained from the u signals, based on which the flow structure pattern or mode could be determined. Over two hundred configurations of two staggered cylinders have been examined for each Re. It is found that Re has an appreciable effect on the dependence of the flow mode on P^⁎ and α. The observation is connected to the Re effect on the generic features of a two-cylinder wake such as flow separation, boundary layer thickness, gap flow deflection and vortex formation length.     

An experimental study of fluctuating lift on a square-section cylinder oscillating transversely in a uniform stream

Experiments on a square-section cylinder fixed and forced to oscillate transversely in a uniform stream were conducted in a water tank. The Reynolds number of the experiments is in the range of 3·10³ to 10⁴, the amplitude to side length ratioA/D is up to 0.7 and the range of reduced velocity is 4.5<V _r <12. This study aims at investigating the lock-in phenomenon, the fluctuating lift and the phase shift between fluctuating lift and displacement of the oscillating cylinder. The problems on the aeroelastic instability relating to present experimental results have been discussed. The flow visualization clearly shows that there are drastic changes of vortex-shedding from cylinder at the resonance point and the upper end of the lock-in range. The results of the flow visualization give better understanding of the physical mechanism of the phase shift. Project supported by National Natural Science Foundation of China     

LES of incompressible heat and fluid flows past a square cylinder at high Reynolds numbers

This paper presents large eddy simulation (LES) results of incompressible heat and fluid flows around a square cylinder (SC) at zero incident angle at high Reynolds numbers (Re) in the range from 1.25×10⁵ to 3.5×10⁵. LES results are obtained on the basis of swirling strength based sub-grid model, and a higher order upwind scheme developed with respect to the Taylor expansion. It was found that, for the zero incident SC wake flows at a Reynolds number in the range {Re₅ = Re/10⁵ ∈ [1.25, 3.5]}, the Strouhal number equals to 0.1079, completely independent of the Reynolds number; the coefficient of drag is around 1.835 with an uncertainty of about 1.9%, almost non-sensitive to the Re. When Re is beyond 3.0×10⁵, the time-averaged peak value of sub-grid viscosity is over 340, implying that the role of sub-grid model is crucial in some regions where vortex motion is active and vortex interaction is intense. The time–spanwise (t-z) averaged sub-grid viscosity ratio profiles and the profiles of fluctuations of the sub-grid viscosity ratio and velocity components at four locations downstream of the SC are presented. The fields of the t-z averaged sub-grid viscosity ratio, and the instantaneous fields of streamwise and spanwise vorticities are also reported and discussed. The predicted mean Nusselt number is compared with empirical correlations, revealing that swirling strength based LES has its potential in predicting natural and industrial flows.     

CONTROL OF FLOW PAST BLUFF BODIES USING ROTATING CONTROL CYLINDERS

Computational results for control of flow past a circular cylinder using small rotating cylinders are presented. A well-proven stabilized finite-element method, that has been applied to various flow problems earlier, is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The formulation is first applied to study flow past an isolated rotating cylinder. Excellent match with experimental results, reported earlier, is observed. It is found that in purely two-dimensional flows, very high lift coefficients can be realized. However, it is observed, via three-dimensional Navier–Stokes simulations, that the end-effects and centrifugal instabilities along the cylinder span lead to a loss of lift and increase in drag. The aspect ratio of the cylinder plays an important role. The flow past a bluff body with two rotating control cylinders is studied using 2-D numerical simulations. The effect of the Reynolds number is studied by carrying out simulations for Re=10²and 10⁴. Finite element meshes with an adequate number of grid points are employed to resolve the flow in the gap between the main and control cylinders. Two values of the gap are considered: 0·01D and 0·075 D, where D is the diameter of the main cylinder. It is observed that when the control cylinders rotate at high speed, such that the tip speed is 5 times the free-stream speed, the flow at Re=100 achieves a steady state. For Re=10⁴, even though the flow remains unsteady, the wake is highly organized and narrower compared to the one without control. The results are in good agreement with the flow-visualization studies conducted by other researchers for bluff bodies using similar control concepts. In all the cases, a significant reduction in the overall drag coefficient and the unsteady aerodynamic forces acting on the main cylinder is observed. Results are also presented for the power requirements of the system for translation and rotation. It is found that the coefficient of power required for the rotation of control cylinders is significant for Re=100 but negligible for Re=10⁴flow. The size of the gap is found to be more critical for the Re=10⁴flows. This study brings out the relevance of the gap as a design parameter for such flow control devices.     

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.     

Stationärer Stoff- und Wärmeübergang an stationär quer angeströmten Zylindern

The steady forced convection mass and heat transfer from circular cylinders has been investigated. The full mass transport differential equation has been integrated numerically. The employed velocity distributions are known [1]. The most important result is reproduced in a correlation for the mass transfer, which regards the turbulence intensity in the flow of the cylinders. This mass transfer law is proofed theoretically and experimentally in the range of Schmidt numbers from Sc=0.73 up to S=3.3×10⁴; however it is valid for 0≤Sc∞. It can be used for all values of Re Sc greater than Re Sc=7.3×10^?5 and for all values of the Reynolds number less than the critical value, Re_kr. The critical Reynolds number, Re_kr, is a known function of the turbulence intensity [1]. For values of Re Sc less than Re Sc=7.3 x10^?5 the mass transfer can be predicted by an analytical equation that based on Oseen type linearization of the differential equation. The conditions are illustrated, which allow to calculate the quantities for heat transfer by means of the correlations for the mass transfer.     

Numerical simulation of flow around a square cylinder in uniform-shear flow

This paper presents results obtained from a numerical simulation of a two-dimensional (2-D) incompressible linear shear flow over a square cylinder. Numerical simulations are performed, using the lattice Boltzmann method, in the ranges of 50⩽Re⩽200 and 0⩽K⩽0.5, where Re and K are the Reynolds number and the shear rate, respectively. The effect of the shear rate on the frequency of vortex shedding from the cylinder, and the lift and drag forces exerted on the cylinder are quantified together with the flow patterns around the cylinder. The present results show that vortex structure behind the cylinder is strongly dependant on both the shear rate and Reynolds number. When Re=50, a small K can disturb the steady state and cause an alternative vortex shedding with uneven intensity. In contrast, a large value of K will suppress the vortex shedding from the cylinder. When Re>50, the differences in the strength and size of vortices shed from the upper and lower sides of the cylinder become more pronounced as K increases. Vortex shedding disappears when K is larger than a critical value, which depends on Re. The flow patterns around the cylinder for different Re tend towards self-similarity with increasing K. The lift and drag forces exerted on the cylinder, in general, decrease with increasing K. Unlike a shear flow past a circular cylinder, the vortex shedding frequency past a square cylinder decreases with increasing the shear rate. A significant reduction of the drag force occurs in the range 0.15<K<0.3.     

Control of mean and fluctuating forces on a circular cylinder at high Reynolds numbers

A narrow strip is used to control mean and fluctuating forces on a circular cylinder at Reynolds numbers from 2.0 × 10⁴ to 1.0 × 10⁵. The axes of the strip and cylinder are parallel. The control parameters are strip width ratio and strip position characterized by angle of attack and distance from the cylinder. Wind tunnel tests show that the vortex shedding from both sides of the cylinder can be suppressed, and mean drag and fluctuating lift on the cylinder can be reduced if the strip is installed in an effective zone downstream of the cylinder. A phenomenon of mono-side vortex shedding is found. The strip-induced local changes of velocity profiles in the near wake of the cylinder are measured, and the relation between base suction and peak value in the power spectrum of fluctuating lift is studied. The control mechanism is then discussed from different points of view. The project supported by the National Natural Science Foundation of China (10172087 and 10472124). The English text was polished by Yunming Chen.     

The effect of a small isolated roughness element on the forces on a sphere in uniform flow

The effect of an isolated roughness element on the forces on a sphere was examined for a Reynolds number range of 5 × 10⁴ < Re < 5 × 10⁵ using a novel sting-mounted sphere apparatus. The roughness element was a circular cylinder, and its width and height was varied to be 1, 2, and 4% of the sphere diameter. At subcritical Re, a lateral force is produced in the direction of the roughness, while at supercritical Re, the force is in the opposite direction. This is caused by asymmetric boundary layer separation, as shown using particle image velocimetry. At supercritical Re, a roughness element that is only 1% the sphere diameter produces a lift to drag ratio of almost one. It was found that the isolated roughness element has the largest effect on the lateral forces when it is located between a streamwise angle of about 40° and 80°. In addition to the mean forces, the unsteady forces were also measured. It was found that at subcritical Re, vortex shedding is aligned to the plane of the roughness element. In addition, the probability distribution of the forces was nearly Gaussian for subcritical Re, but for supercritical Re, the skewness and kurtosis deviate from Gaussian, and the details are dependent on the roughness size. A simple model developed for the vortical structure formed behind the roughness element can be extended to explain aspects of nominally smooth sphere flow, in which external disturbances perturb the sphere boundary layer in an azimuthally local sense. These results also form the basis of comparison for an investigation into the effectiveness of a moving isolated roughness element for manipulating sphere flow.     

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.