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.     

Near wall characteristics of flow over grooved circular cylinder

An experimental investigation was made of the flow over a grooved circular cylinder of different aspect ratios. Based on the drag coefficient, Strouhal number and mean shear stress, three flow regimes of subcritical, critical and supercritical were found, all of which are below the subcritical Reynolds number of a smooth cylinder. Boundary layer characteristics within the different flow regimes were measured. The shift of the boundary layer away from the grooves and an estimated change in the virtual origin are used to establish the similarity of the flow characteristics of grooved and smooth cylinders.Now at Development and Planning Division, Hong Kong Electric Co. Ltd., Hong Kong     

Fluctuating lift on a circular cylinder: review and new measurements

Apart from providing some new experimental data the paper reviews previous investigations concerning fluctuating lift acting on a stationary circular cylinder in cross-flow. In particular, effects of Reynolds number in the nominal case of an infinitely long and nonconfined cylinder in a smooth oncoming flow are discussed. The Reynolds number range covered is from about Re=47 to 2×10⁵, i.e., from the onset of vortex shedding up to the end of the subcritical regime. At the beginning of the subcritical regime (Re≃0.3×10³) a spanwise correlation length of about 30 cylinder diameters is indicated, the correlation function being based on near-cylinder velocity fluctuations in outer parts of the separated shear layer. In between Reynolds numbers 1.6×10³ and 20×10³, an approximate 10-fold increase in the sectional r.m.s. lift coefficient is indicated. This range contains a fundamental change-over from one flow state to another, starting off at Re≃5×10³ and seemingly fully developed at Re≃8×10³.     

Unsteady force measurements in sphere flow from subcritical to supercritical Reynolds numbers

The flow over a smooth sphere is examined in the Reynolds number range of 5.0 × 10⁴ < Re < 5.0 × 10⁵ via measurements of the fluctuating forces and particle image velocimetry measurements in a planar cut of the velocity field. Comprehensive studies of the statistics and spectra of the forces are presented for a range of subcritical and supercritical Reynolds numbers. While the subcritical lateral force spectra are dominated by activity corresponding to the large-scale vortex shedding frequency at a Strouhal number of approximately 0.18, there is no such peak apparent in the supercritical spectra, although resolution effects may become important in this region. Nor does the large-scale vortex shedding appear to have a significant effect on the drag force fluctuations at either sub- or super-critical Reynolds numbers. A simple double spring model is shown to capture the main features of the lateral force spectra. The low-frequency force fluctuations observed in earlier computational studies are shown to have important implications for statistical convergence, and in particular, the apparent mean side force observed in earlier studies. At least one thousand dimensionless time units are required for reasonable estimates of the second and higher moments below the critical Reynolds number and even more for supercritical flow, stringent conditions for computational studies. Lastly, investigation of the relationship between the motion of the instantaneous wake shape, defined via the local position where the streamwise velocity is equal to half the freestream value, and the in-plane lateral force for subcritical flow reveals a significant negative correlation throughout the near wake, which is shown to be related to a structure inferred to arise from the large-scale vortex shedding convecting downstream at 61% of the freestream velocity. In addition to its utility in understanding basic sphere flow, the apparatus is also a testbed that will be used in future studies, examining the effect of both static and dynamic changes to the surface morphology.     

Prediction of unsteady,separated boundary layer over a blunt body for laminar,turbulent, and transitional flow

The focus of this paper is to study the ability of unsteady RANS‐based CFD to predict separation over a blunt body for a wide range of Reynolds numbers particularly the ability to capture laminar‐to‐turbulent transition. A perfect test case to demonstrate this point is the cylinder‐in‐crossflow for which a comparison between experimental results from the open literature and a series of unsteady simulations is made. Reynolds number based on cylinder diameter is varied from 10⁴ to 10⁷ (subcritical through supercritical flow). Two methods are used to account for the turbulence in the simulations: currently available eddy–viscosity models, including standard and realizable forms of the k–ε model; and a newly developed eddy–viscosity model capable of resolving boundary layer transition, which is absolutely necessary for the type and range of flow under consideration. The new model does not require user input or ‘empirical’ fixes to force transition. For the first time in the open literature, three distinct flow regimes and the drag crisis due to the downstream shift of the separation point are predicted using an eddy–viscosity based model with transition effects. Discrepancies between experimental and computational results are discussed, and difficulties for CFD prediction are highlighted. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 × 10³ to 6.5 × 10⁵ to study the effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics. In the subcritical range of Re (<2 × 10⁵), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 × 10⁵), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag. Received: 8 September 1998 / Accepted: 1 January 2000     

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.     

Numerical Investigation of the Flow Past a Rotating Golf Ball and Its Comparison with a Rotating Smooth Sphere

Large-eddy simulations are conducted for a rotating golf ball and a rotating smooth sphere at a constant rotational speed at the subcritical, critical and supercritical Reynolds numbers. A negative lift force is generated in the critical regime for both models, whereas positive lift forces are generated in the subcritical and supercritical regimes. Detailed analysis on the flow separations on different sides of the models reveals the mechanism of the negative Magnus effect. Further investigation of the unsteady aerodynamics reveals the effect of rotating motion on the development of lateral forces and wake flow structures. It is found that the rotating motion helps to stabilize the resultant lateral forces for both models especially in the supercritical regime.     

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.     

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.     

Experiments on the flow past long circular cylinders in a shear flow

This paper describes an experimental investigation of the flow past circular cylinders, with the mean flow perpendicular to the cylinder axis, at conditions that yield a strong three-dimensional behaviour. The experiments were carried out in the subcritical regime. Long cylinders with end plates were subjected to shear flow with a linear velocity profile in the spanwise direction generated by means of a curved gauze. It was concluded that spanwise cellular structures of vortex shedding emerged in the wake, more clearly for some boundary conditions than others. These structures are characterised by a portion of spanwise length, a cell, having constant shedding frequency over a time average, which implies that there were no vortex dislocations inside that cell during that time. These features were studied using flow visualisation and hot-film anemometry. Spectra of the local shedding frequency are shown, revealing the effect of the shear parameter (=0.02 and 0.04) and aspect ratio L/D (=20.6 and 8) on the stability and geometry of the cells at several Reynolds numbers in the range of 3.13×10³Re_m1.25×10⁴.     

FLUID FORCES AND DYNAMICS OF A HYDROELASTIC STRUCTURE WITH VERY LOW MASS AND DAMPING

In this paper we present some central new results from a study of the dynamics and fluid forcing on an elastically mounted rigid cylinder, constrained to oscillate transversely to a free stream. With very low damping, and with a low specific mass that is around 1% of the value used in the classic study of Feng (1968), we show that the cylinder excitation regime extends over a large range of normalized velocity (around four times that found by Feng), with a large amplitude which is around twice that of Feng. Four distinct regions of response are identified, namely the initial excitation region, the “upper branch” (of very high amplitude response), the “lower branch” (of moderate amplitude response), and the desynchronization region. There are distinct differences in the character of mode transitions, as follows. As normalized velocity is increased, there is a hysteretic jump from an initial excitation regime to the upper branch, whereas the jump from the upper to the lower branch involves an intermittent switching, which is illustrated by plotting the instantaneous phase between lift force and displacement using the Hilbert transform. Contrary to classical “lock-in”, whereby the oscillation frequency matches the structural natural frequency, we find that the oscillation frequency increases markedly above the natural frequency, through the excitation regime. Finally, we present the first lift force measurements for such a freely vibrating cylinder experiment, yielding a maximum lift coefficient of around 4·5, whereas a maximum drag coefficient of 6·0 is also measured. The lift is comparable, but somewhat higher, than the forces measured (C_L∼2·0) in the equivalent free-vibration experiments of Hoveret al.(1997), involving force-feedback and on-line computer-simulation of the modelled structure. Both the lift and drag maxima exhibit at least a five-fold increase over the stationary cylinder case. Perhaps the largest effect is found for the fluctuating drag, which is found to be upto 100 times that measured for a static cylinder.     

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.     

Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers

The transition from supercritical to subcritical open channel flow is characterised by a strong dissipative mechanism called a hydraulic jump. A hydraulic jump is turbulent and associated with the development of large-scale turbulence and air entrainment. In the present study, some new physical experiments were conducted to characterise the bubbly flow region of hydraulic jumps with relatively small Froude numbers (2.4 < Fr₁ < 5.1) and relatively large Reynolds numbers (6.6 × 10⁴ < Re < 1.3 × 10⁵). The shape of the time-averaged free-surface profiles was well defined and the longitudinal profiles were in agreement with visual observations. The turbulent free-surface fluctuation profiles exhibited a peak of maximum intensity in the first half of the hydraulic jump roller, and the fluctuations exhibited some characteristic frequencies typically below 3 Hz. The air–water flow properties showed two characteristic regions: the shear layer region in the lower part of the flow and an upper free-surface region above. The air–water shear layer region was characterised by local maxima in terms of void fraction and bubble count rate. Other air–water flow characteristics were documented including the distributions of interfacial velocity and turbulence intensity. The probability distribution functions (PDF) of bubble chord time showed that the bubble chord times exhibited a broad spectrum, with a majority of bubble chord times between 0.5 and 2 ms. An analysis of the longitudinal air–water structure highlighted a significant proportion of bubbles travelling within a cluster structure.     

Drag characteristics of longitudinal and transverse riblets at low dimensionless spacings

A surface grooved with microscopic riblets aligned parallel to the flow is an effective means to reduce the turbulent skin friction up to 10% compared to a smooth surface. The maximum drag reduction is found for a dimensionless rib spacing s ⁺ in the range of 15–17. For s ⁺ < 10, a linear behaviour of the drag reduction curve is predicted by viscous theory. This linear slope of the drag reduction curve is in contradiction to Schlichting’s postulation of a hydraulically smooth behaviour of small-scale roughness in a turbulent flow. This regime of evanescent dimensionless rib spacings is investigated experimentally by direct wall shear stress measurements in a fully developed channel flow. Additionally, a numerical calculation of the viscous flow over riblets was carried out to predict the drag reducing behaviour. The experimental results show a linear drag reducing behaviour down to s ⁺ = 0.3, which is in good agreement with the numerical results of the viscous simulation. The postulation of Schlichting’s hydraulically smooth regime of a rough surface was not confirmed, neither for a riblet surface nor for a surface geometry with grooves oriented perpendicular to the flow. In the latter case, the drag increases as a quadratic function of the roughness height.     

Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.     

Numerical investigation on flow around circular cylinders in tandem arrangement at a subcritical Reynolds number

Three-dimensional fluid computations have been performed to investigate the flows around two circular cylinders in tandem arrangements at a subcritical Reynolds number, Re=2.2×10⁴. The center-to-center space between the cylinders was varied from twice the cylinder diameter to five times that, and the flows and fluid-dynamic forces obtained from the simulations are compared with the experimental results reported in the literature. Special attention is paid to the characteristics of the vortices shed from the upstream cylinder such as the convection, the impingement onto the downstream cylinder and the interaction with the vortices from the downstream cylinder. The effects of the vortices from the upstream cylinder on the fluid-dynamic forces acting on the downstream cylinder are discussed.     

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.     

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.     

Large-Eddy Simulation of transcritical flows

The present study uses the LES code AVBP, developed at CERFACS, to simulate transcritical flows. Real gas effects are accounted for by the use of a cubic equation of state, in conjunction with appropriate viscosity and thermal conductivity coefficients. First a single nitrogen round jet at supercritical pressure injected in a gaseous reservoir is simulated. Two cases are considered, one demonstrating a transcritical injection (high density injection), the other being directly injected at supercritical temperature (lower density injection). Comparison with available measurements shows good agreement. Finally, the simulation of a reacting case from the Mascotte bench (ONERA) is performed, consisting in a single coaxial injector injecting transcritical oxygen and supercritical hydrogen in a 60 bar chamber. Mean flow characteristics are in good agreement with the experimental observations of OH^* emission, whereas temperature comparisons are more difficult to interpret. To cite this article: T. Schmitt et al., C. R. Mecanique 337 (2009).