Numerical simulation of the unsteady flow over an elliptic cylinder at different orientations

A numerical method is developed for investigating the two‐dimensional unsteady viscous flow over an inclined elliptic cylinder placed in a uniform stream of infinite extent. The direction of the free stream is normal to the cylinder axis and the flow field unsteadiness arises from two effects, the first is due to the flow field development following the start of the motion and the second is due to vortex shedding in the wake region. The time‐dependent flow is governed by the full conservation equations of mass and momentum with no boundary layer approximations. The parameters involved are the cylinder axis ratio, Reynolds number and the angle of attack. The investigation covers a Reynolds number range up to 5000. The minor–major axis ratio of the elliptic cylinder ranges between 0.5 and 0.6, and the angle of attack ranges between 0° and 90°. A series truncation method based on Fourier series is used to reduce the governing Navier–Stokes equations to two coupled infinite sets of second‐order differential equations. These equations are approximated by retaining only a finite number of terms and are then solved by approximating the derivatives using central differences. The results reveal an unusual phenomenon of negative lift occurring shortly after the start of motion. Various comparisons are made with previous theoretical and experimental results, including flow visualizations, to validate the solution methodology. Copyright © 2001 John Wiley & Sons, Ltd.     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.     

TANDEM CYLINDERS IN IMPULSIVELY STARTED FLOW

The impulsively started flow field for circular cylinders of equal diameter arranged in tandem was investigated using flow visualization and particle image velocimetry (PIV), over a longitudinal pitch ratio range ofL /D=1·0–3·0, and for Reynolds numbers from Re=1200–3800. The PIV technique was used to obtain a time history of the instantaneous in-plane vorticity field from the moment of impulsive start, from which the spatial and temporal development of the flow was studied. Measurements of vortex strength and vortex position relative to the cylinders were obtained from these data. Three types of fluid behaviour were identified based on L/D: single bluff-body behaviour when the cylinders are in contact, constrained streamwise growth and lateral expansion of the gap recirculation zones at small and intermediate L/D, and independent formation of recirculation zones similar to a single impulsively started circular cylinder at larger L/D.     

A phase averaged PIV study of circular and non-circular synthetic turbulent jets issuing from sharp edge orifices

An extensive experimental study using Particle Image Velocimetry (PIV) on synthetic jets issuing from different orifice shapes is reported. All data are phase and time averaged to derive mean velocity, half-velocity width and rms velocity profiles in the near field of the jet (0 < X/D < 7), at a Reynolds number around 10,000. Different non-circular orifice shapes as rectangular, square, elliptic and triangular are considered and results are compared to those of the circular orifice in order to investigate the effect of asymmetry on the turbulent flow field in view of mixing enhancement. The measurements are carried out on two orthogonal planes to capture three dimensional features of non-circular jets. Results show highest velocity decay rate for elongated orifices, especially the rectangular one, in comparison to the circular one, both in phase and time-averaged plots. Time averaged results show higher velocity decay rate of synthetic jets in comparison to those of continuous ones. It is also observed that, for X/D > 5, only profiles of circular and square jets become partially self-similar. For synthetic jets, higher turbulence content is measured for all orifice shapes at the centerline and close to the orifice exit in comparison to continuous jets.     

Suppression of force fluctuations in flow past an aerofoil

Force fluctuations on a solid body are associated with unsteadiness in the wake, e.g. vortex shedding. Therefore, the control of force fluctuations can be realised by suppressing the flow unsteadiness. A NACA0024 aerofoil closed with a round trailing edge is chosen to represent the solid body throughout this investigation, with the Reynolds number fixed at Re = 1000 and angle of attack α ≤ 15^o, at which the uncontrolled flow is two-dimensional. A linear optimal control is calculated by analysing the distribution of sensitivity of unsteadiness to control around the entire surface of the body. The nonlinear effects of the calculated control, which can be actuated through surface-normal suction and blowing across the surface of the aerofoil, are tested through two-dimensional direct numerical simulations. It is observed that a surface-normal velocity control with a maximum magnitude less than 8% of the free stream velocity completely suppresses unsteadiness at α = 10° with an overall drag reduction of 14% and a 138% increase of lift.     

Turbulent wake and vortex shedding for a stack partially immersed in a turbulent boundary layer

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake and Kármán vortex shedding for a cylindrical stack of aspect ratio AR=9 was investigated in a low-speed wind tunnel using thermal anemometry. The cross-flow Reynolds number was Re_D=2.3×10⁴, the jet Reynolds number ranged from Re_d=7.6×10³ to 4.7×10⁴, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-stack-height ratio of δ/H=0.5 at the location of the stack. From the behaviour of the turbulent wake and the vortex shedding, the flow around the stack could be classified into three regimes depending on the value of R, which were the downwash (R<0.7), cross-wind-dominated (0.7R<1.5), and jet-dominated (R1.5) flow regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields, as well as the variation of the Strouhal number and the power spectrum along the stack height.     

Particle image velocimetry investigation on mixing enhancement of non-circular sharp edge nozzles

An experimental study using Particle Image Velocimetry (PIV) on free jets issuing from different orifice plate (OP) nozzles is reported. Mean velocity, turbulence intensity and higher order profiles relevant for large and small scale mixing are considered in the near field and interaction zone (0 < X/D < 20). This is done to determine mixing enhancement due to rectangular, squared, elliptic and triangular nozzles in comparison to circular nozzle results in two orthogonal planes. The effect of Reynolds number on the differences among the nozzle shapes is also considered by performing measurements just after laminar–turbulent transition (Re = 8000) and in the fully turbulent regime (Re = 35,000). The results at low Reynolds number show two classes of jets, i.e. at one side, those closer to axial-symmetric conditions, as circular, square and triangular jets, whereas on the other side those with elongated nozzles as rectangular and elliptic. The reason for the different behavior of the latter is connected to the phenomenon of axis-switching which allows a rearrangement of turbulence over the different velocity components and directions. However, for the highest Reynolds number investigated, all nozzles show similar behavior especially in the jet far field (X/D > 10), thus suggesting a significant Reynolds number dependence of the results.     

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

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

Smoke-wire flow visualization of the near-wake region behind a circular disc at low Reynolds numbers

The flow structures in the near field of the unducted wake region behind a circular disc for annular flow at low Reynolds numbers were studied by smoke-wire flow visualization technique. A twisted-dual-wire was employed to perform the time evolving visualization. Three typical characteristic flow modes: Q-tip, open-top toroid, and closed toroid, were identified in the near disc region. For Reynolds number between 130 and 390, the Q-tip flow mode which subject to a periodic up-down oscillatory motion was observed. The open-top toroid mode which experiences the expelling vortex shedding was found for Reynolds number between 390 and 455. The free separation surface turns around and merges to the central axisymmetric axis to form the conventionally observed toroidal recirculation bubble for Reynolds number higher than 455. The closed toroid mode exhibits both expelling and shear-layer vortex sheddings. With the identified flow modes at low Reynolds numbers, the recirculation contours, recirculation length, and the shedding frequency in each mode were measured and discussed.List of symbols B.R. blockage ratio (=D ² /D _a ² ) - D _a outer diameter of annular jet, 30 mm - D diameter of circular disc, 20 mm - f frequency of vortex shedding, Hz - L _r axial length of recirculation zone - R radius of circular disc, 10 mm - u _a average exit velocity of annular jet - ₀ stream function with value of zero - mass density of annular flow - u average axial velocity - r radial coordinate, originated from center of circular disk - r ₀ radial coordinate of the boundary of the recirculation zone - Re _a Reynolds number of annular jet based on the disc diameter - Z axial coordinate, originated from center of circular disk - w _max maximum half-width of the recirculation zone - St Strouhal number (=fD/D _a )     

Near-wake flow characteristics of a circular cylinder close to a wall

Flow characteristics in the near wake of a circular cylinder located close to a fully developed turbulent boundary layer are investigated experimentally using particle image velocimetry (PIV). The Reynolds number based on the cylinder diameter (D) is 1.2×10⁴ and the incident boundary layer thickness (δ) is 0.4D. Detailed velocity and vorticity fields in the wake region (0<x/D<6) are given for various gap heights (S) between the cylinder and the wall, with S/D ranging from 0.1 to 1.0. Both the ensemble-averaged (including the mean velocity vectors and Reynolds stress) and the instantaneous flow fields are strongly dependent on S/D. Results reveal that for S/D⩾0.3, the flow is characterized by the periodic, Kármán-like vortex shedding from the upper and lower sides of the cylinder. The shed vortices and their evolution are revealed by analyzing the instantaneous flow fields using various vortex identification methods, including Galilean decomposition of velocity vectors, calculation of vorticity and swirling strength. For small and intermediate gap ratios (S/D⩽0.6), the wake flow develops a distinct asymmetry about the cylinder centreline; however, some flow quantities, such as the Strouhal number and the convection velocity of the shed vortex, keep roughly constant and virtually independent of S/D.     

A numerical investigation of the effects of the spanwise length on the 3-D wake of a circular cylinder

The numerical prediction of vortex-induced vibrations has been the focus of numerous investigations to date using tools such as computational fluid dynamics. In particular, the flow around a circular cylinder has raised much attention as it is present in critical engineering problems such as marine cables or risers. Limitations due to the computational cost imposed by the solution of a large number of equations have resulted in the study of mostly 2-D flows with only a few exceptions. The discrepancies found between experimental data and 2-D numerical simulations suggested that 3-D instabilities occurred in the wake of the cylinder that affect substantially the characteristics of the flow. The few 3-D numerical solutions available in the literature confirmed such a hypothesis. In the present investigation the effect of the spanwise extension of the solution domain on the 3-D wake of a circular cylinder is investigated for various Reynolds numbers between 40 and 1000. By assessing the minimum spanwise extension required to predict accurately the flow around a circular cylinder, the infinitely long cylinder is reduced to a finite length cylinder, thus making numerical solution an effective way of investigating flows around circular cylinders. Results are presented for three different spanwise extensions, namely πD/2, πD and 2πD. The analysis of the force coefficients obtained for the various Reynolds numbers together with a visualization of the three-dimensionalities in the wake of the cylinder allowed for a comparison between the effects of the three spanwise extensions. Furthermore, by showing the different modes of vortex shedding present in the wake and by analysing the streamwise components of the vorticity, it was possible to estimate the spanwise wavelengths at the various Reynolds numbers and to demonstrate that a finite spanwise extension is sufficient to accurately predict the flow past an infinitely long circular cylinder.     

A SERIES IN 1/√Re TO REPRESENT THE STROUHAL–REYNOLDS NUMBER RELATIONSHIP OF THE CYLINDER WAKE

In this Brief Note, we show that shedding frequency data is well collapsed, over a large range of Re from 50 up to at least 140,000, by using a Strouhal number that depends upon an effective wake width, which includes not only the physical body diameter, but also a characteristic width of the separating shear layers. The use of this effective wake width also leads to a new formulation for the relationship between Strouhal number (S) versus Reynolds number (Re) for the cylinder wake, which may be expressed as an expansion in powers of (1/√Re): EquationTruncated two-term or three-term series have much less error-of-fit when compared with the traditional S–Re relationships commonly in use. A good test of any S–Re functional relationship is now made possible by comparison with Henderson's numerical data for two-dimensional laminar shedding, over a much larger range of Re (up to Re=1000) than is possible to obtain experimentally. It seems significant that even a two-term fit, given by S=0·2698 −1·0271/√Re has one order of magnitude less error than the traditional three-term fit. By using such √Re-formulae in both the laminar and 3-D wake turbulent regimes, we may accurately represent S–Re data over a large range of Re, although the validity of these representations at these higher Re needs further support. In summary, this Brief Note not only provides physical support for the use of such S–Re relationships as shown above, but also demonstrates that these formulations fit the data closer than traditional S–Re expressions.     

The wake of falling disks at low Reynolds numbers

We visualized the wake structure of circular disks falling vertically in quiescent water.The evolution of the wake was shown to be similar to the flow patterns behind a fixed disk.The Reynolds number,Re = Ud/ν,is in the range of 40 200.With the ascension of Reynolds numbers,a regular bifurcation occurred at the first critical Reynolds number Re c 1,leading to a transition from an axisymmetric wake structure to a plane symmetric one;A Hopf bifurcation took place at the second critical Reynolds number Re c 2,as the wake structure became unsteady.Plane symmetry of the wake structure was first lost as periodic vortex shedding appeared,but recovered at higher Reynolds number.The difference between the two critical Reynolds numbers was found to be shape-dependent,as we compared our results for thin discs with those for other falling bodies,such as spheres and cones.This observation could be understood in terms of the instability mechanism of the vortical structure.     

Flow past a circular cylinder over a free surface: Interaction between the near wake and the free surface deformation

Air-flow around a circular cylinder placed above a free surface and liquid flow under the free surface were investigated experimentally in a wind/wave tunnel. The cylinder spanned the tunnel test-section and was oriented normal to the freestream direction. The main objective of this study was to investigate the interaction of the cylinder wake with the free surface. The flow structure was analyzed for various gap widths, H, between the cylinder and the free surface using a digital particle image velocimetry (PIV) system with a spatial resolution of 2048×2048 pixels. The Reynolds number based on the cylinder diameter was 3.3×10³. For each experimental condition, 400 instantaneous velocity fields were measured and ensemble-averaged to obtain spatial distributions of the mean velocity and turbulence statistics. The results showed that the cylinder near-wake inclined upward due to the influence of the free surface elevation. Vortices were shed, even at a small gap ratio of H/D=0.25, where D is the cylinder diameter. Strong jet-like flow appeared in the gap beneath the cylinder. At a gap ratio of H/D=0.50, the jet flow exhibited a quasi-periodic vibration with a period of 2–3 s. The free surface deformation was caused by the pressure difference in the air-flow immediately above it. As the gap ratio increased, the inclination angle of the wake and the height of the free surface elevation decreased gradually. The liquid flow under the free surface followed a convective flow motion, and the range of the convection depended on the gap width between the cylinder and the free surface.     

On the interaction of Taylor bubbles rising in two-phase co-current slug flow in vertical columns: turbulent wakes

An experimental study on the interaction between Taylor bubbles rising through a co-current flowing liquid in a vertical tube with 32 mm of internal diameter is reported. The flow pattern in the bubble's wake was turbulent and the flow regime in the liquid slug was either turbulent or laminar. When the flow regime in the liquid slug is turbulent (i) the minimum distance between bubbles above which there is no interaction is 5D-6D; (ii) the bubble's rising velocity is in excellent agreement with the Nicklin relation; (iii) the experimental values of the bubble length compare well with theoretical predictions (Barnea 1990); (iv) the distance between consecutive bubbles varied from 13D to 16D and is insensitive to the liquid Reynolds number. When the flow regime in the liquid slug is laminar (i) the wake length is about 5D-6D; (ii) the minimum distance between bubbles above which there is no interaction is higher than 25D; (iii) the bubble's rising velocity is significantly smaller than theoretical predictions. These results were explained in the light of the findings of Pinto et al. (1998) on coalescence of two Taylor bubbles rising through a co-current liquid. Received: 2 February 2000 / Accepted: 15 March 2001     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (∼1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e∼9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.     

Momentum and heat transport in a finite-length cylinder wake

This paper reports an experimental study of turbulent momentum and heat transport in the wake of a wall-mounted finite-length square cylinder, with its length-to-width ratio L/d = 3–7. The cylinder was slightly heated so that heat produced could be considered as a passive scalar. A moveable three-wire probe (a combination of an X-wire and a cold wire) was used to measure velocity and temperature fluctuations at a Reynolds number of 7,300 based on d and the free-stream velocity. Measurements were performed at 10 and 20d downstream of the cylinder at various spanwise locations. Results indicate that L/d has a pronounced effect on Reynolds stresses, temperature variance and heat fluxes. The downwash flow from the free end of the cylinder acts to suppress spanwise vortices and, along with the upwash flow from the cylinder base, makes the finite-length cylinder wake highly three-dimensional. Reynolds stresses, especially the lateral normal stress, are significantly reduced as a result of suppressed spanwise vortices at a small L/d. The downwash flow acts to separate the two rows of spanwise vortices further apart from the wake centerline, resulting in a twin-peak distribution in temperature variance. While the downwash flow entrains high-speed fluid into the wake, responsible for a small deficit in the time-averaged streamwise velocity near the free end, it does not alter appreciably the distribution of time-averaged temperature. It has been found that the downwash flow gives rise to a counter-gradient transport of momentum about the central region of the wake near the free end of the cylinder, though such a counter-gradient transport does not occur for heat transport.     

An experimental investigation of flow past a dual step cylinder

Flow development in the wake of a dual step cylinder has been investigated experimentally using Laser Doppler Velocimetry and flow visualization. The dual step cylinder model is comprised of a large diameter cylinder (D) mounted at the mid-span of a small diameter cylinder (d). The experiments have been performed for a Reynolds number (Re _D ) of 1,050, a diameter ratio (D/d) of 2, and a range of large cylinder aspect ratios (L/D). The results show that the flow development is highly dependent on L/D. The following four distinct flow regimes can be identified based on vortex dynamics in the wake of the large cylinder: (1) for L/D ≥ 15, three vortex shedding cells form in the wake of the large cylinder, one central cell bounded by two cells of lower frequency, (2) for 8 < L/D ≤ 14, a single vortex shedding cell forms in the wake of the large cylinder, (3) for 2 < L/D ≤ 6, vortex shedding from the large cylinder is highly three-dimensional. When spanwise vortices are shed, they deform substantially and attain a hairpin shape in the near wake, (4) for 0.2 ≤ L/D ≤ 1, the large cylinder induces vortex dislocations between small cylinder vortices. The results show that for Regimes I to III, on the average, the frequency of vortex shedding in the large cylinder wake decreases with L/D, which is accompanied by a decrease in coherence of the shed vortices. In Regime IV, small cylinder vortices connect across the large cylinder wake, but these connections are interrupted by vortex dislocations. With decreasing L/D, the frequency of dislocations decreases and the dominant frequency in the large cylinder wake increases toward the small cylinder shedding frequency.     

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