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.     

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     

Effect of ventilation on the flowfield around a sphere

The flowfield around a sphere with and without ventilation was investigated in a wind tunnel over a range of Reynolds numbers in an incompressible flow. At supercritical Re, the pressure drag of a sphere can be nearly nullified by venting only 2% of the frontal area of the sphere to the base through a smooth internal duct. The drag reduction is achieved by increased pressures in the separated flow region close to the base. At high Re, the vent flow breaks through the near wake and brings about symmetry in the global flowfield. When the internal shear is increased by using a rough internal duct, the base pressure is unchanged, but the external flow is accelerated to velocities beyond that achieved by the potential flow around the basic sphere. The findings can be explained by a flow model in which the near wake is aerodynamically streamlined by a pair of counterrotating vortex rings at the base. A roughness element can be made to partially destroy the vortex system at the base and result in a steady asymmetric wake. A 1.2 mm diameter wire placed at 70° was found to overtrip the boundary layer and completely destroy the vortex system. Simultaneously, the turbulent separation is advanced and the drag increased.At subcritical Re, ventilation marginally increases static pressures all over the surface. Since the large pressure differential between the windward and leeward sides is not reduced, the internal flow has a rapid acceleration to a velocity close to that of the free stream. The reverse flow associated with the near wake forces the vent flow to rest within itself and the wake profile is unchanged. The main features of subcritical flow around the basic sphere are retained in spite of ventilation. The upstream effects of ventilation are greater for subcritical flow than for supercritical flow.The work reported was carried out under a study grant from the German Academic Exchange Service (DAAD) in Bonn. The authors wish to thank the Director of DAAD in Bonn for the same. Thanks are due to Dr. F. R. Grosche and colleagues at DLR in Göttingen who assisted in the design, fabrication and wind tunnel testing of the sphere model. Thanks are also due to Prof. D. G. Mabey, visiting Professor, Imperial College, London for useful discussions. The many useful discussions with the research advisors of the first author viz., Dr. P. R. Viswanath of National Aerospace Laboratories and Prof. A. Prabhu of Indian Institute of Science, Bangalore are acknowledged with thanks. The support given by the Head, Experimental Aerodynamics Division, National Aerospace Laboratories is thankfully acknowledged.     

LES and RANS for Turbulent Flow over Arrays of Wall-Mounted Obstacles

Large-eddy simulation (LES) has been applied to calculate the turbulent flow over staggered wall-mounted cubes and staggered random arrays of obstacles with area density 25%, at Reynolds numbers between 5 × 10³ and 5 10⁶, based on the free stream velocity and the obstacle height. Re = 5 × 10³ data were intensively validated against direct numerical simulation (DNS) results at the same Re and experimental data obtained in a boundary layer developing over an identical roughness and at a rather higher Re. The results collectively confirm that Reynolds number dependency is very weak, principally because the surface drag is predominantly form drag and the turbulence production process is at scales comparable to the roughness element sizes. LES is thus able to simulate turbulent flow over the urban-like obstacles at high Re with grids that would be far too coarse for adequate computation of corresponding smooth-wall flows. Comparison between LES and steady Reynolds-averaged Navier-Stokes (RANS) results are included, emphasising that the latter are inadequate, especially within the canopy region.     

The ultra-low Reynolds number airfoil wake

Lift force and the near wake of an NACA 0012 airfoil were measured over the angle (α) of attack of 0°–90° and the chord Reynolds number (Re _c ), 5.3 × 10³–5.1 × 10⁴, with a view to understand thoroughly the near wake of the airfoil at low- to ultra-low Re _c . While the lift force is measured using a load cell, the detailed flow structure is captured using laser-Doppler anemometry, particle image velocimetry, and laser-induced fluorescence flow visualization. It has been found that the stall of an airfoil, characterized by a drop in the lift force, occurs at Re _c  ≥ 1.05 × 10⁴ but is absent at Re _c  = 5.3 × 10³. The observation is connected to the presence of the separation bubble at high Re _c but absence of the bubble at ultra-low Re _c , as evidenced in our wake measurements. The near-wake characteristics are examined and discussed in detail, including the vortex formation length, wake width, spanwise vorticity, wake bubble size, wavelength of K–H vortices, Strouhal numbers, and their dependence on α and Re _c .     

Development of a turbulent boundary layer after a step from smooth to rough surface

The flow developing downstream of a step change from smooth to rough surface condition is studied in the light of Townsend’s wall similarity hypothesis. Previous studies seem to support the hypothesis for channel and pipe flows, but there are considerable controversies about its application to boundary layers and in particular to surface roughness formed by spanwise bars. It has been suggested that this controversy arises from insufficient separation of scales between the boundary layer thickness and the roughness length scale. An experimental investigation has therefore been undertaken where the flow evolves from a fully developed smooth wall boundary layer at high Reynolds numbers over a step in surface roughness (Re _θ = 13,400 at the step). The flow is mapped through the development of the internal layer until the flow is fully developed over the rough wall. The internal layer is found to grow as δ ∼ X ^0.73, and after about 15 boundary layer thicknesses at the step, the internal layer has reached the outer edge of the incoming layer. At the last rough wall measurement station, the Reynolds number has grown to Re _θ ≈ 32,600 and the ratio of boundary layer to roughness length scales is δ/k ≈ 140. The outer layer differences between the smooth and the rough wall data were found to be sufficiently small to conclude that for this setup the Townsend’s wall similarity hypothesis appears to hold.     

Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers

 The lift force experienced by a spinning sphere moving in a viscous fluid, with constant linear and angular velocities, is measured by means of a trajectographic technique. Measurements are performed in the range of dimensionless angular velocities γ=aω/V lying between 1 and 6, and in the range of Reynolds numbers Re=2aV/ν lying between 10 and 140 (a sphere radius, ω angular velocity, V relative velocity of the sphere centre, ν fluid kinematic viscosity). A notable departure from the theoretical relationship at low Reynolds number, C _L =2γ, is obtained, the ratio C _L /γ being found to significantly decrease with increasing γ and increasing Re. The following correlation is finally proposed to estimate the lift coefficient in the range 10<Re<140: C _L ≅0.45+(2γ−0.45) exp (−0.075γ^0.4 Re ^0.7) Received: 20 May 1996/Accepted: 9 November 1997     

The effects of freestream turbulence on the drag coefficient of a sphere

The effects of freestream turbulence intensity and integral length scale as freestream turbulent parameters on the drag coefficient of a sphere were experimentally investigated in a closed circuit wind tunnel. The Reynolds number, Re = Ud/ν, was varied from 2.2 × 10⁴ to 8 × 10⁴ by using spheres with diameter d of 20, 51 and 102 mm in addition to altering the freestream velocity, U. The freestream turbulence intensity Tu and flow integral length scale Λ were manipulated by the utilization of orifice perforated plates. The proper combination of orifice perforated plate hole diameter, sphere size, and sphere location along the center line of the wind tunnel enabled the independent alterations of turbulence intensity and relative integral length scale (Λ/d) from 1.8% to 10.7% and from 0.1 to 2.6, respectively, at each studied Reynolds number. Results show that over the range of conditions studied, the drag always decreases with increasing Tu and, the critical Reynolds number at which the drag coefficient is dramatically reduced is decreased by increasing Tu. Most interestingly, the drag at any particular Re and Tu may be significantly lowered by reducing Λ/d; this is particularly the case at high Re and Tu.     

Dynamical deformation of a flat liquid–liquid interface

The passage of solid spheres through a liquid–liquid interface was experimentally investigated using a high-speed video and PIV (particle image velocimetry) system. Experiments were conducted in a square Plexiglas column of 0.1 m. The Newtonian Emkarox (HV45 50 and 65% wt) aqueous solutions were employed for the dense phase, while different silicone oils of different viscosity ranging from 10 to 100 mPa s were used as light phase. Experimental results quantitatively reveal the effect of the sphere’s size, interfacial tension and viscosity of both phases on the retaining time and the height of the liquid entrained behind the sphere. These data were combined with our previous results concerning the passage of a rising bubble through a liquid–liquid interface in order to propose a general relationship for the interface breakthrough for the wide range of Mo ₁/Mo ₂ ∈ [2 × 10⁻⁵–5 × 10⁴] and Re ₁/Re ₂ ∈ [2 × 10⁻³–5 × 10²].     

The effect of support position and turbulence intensity on the flow near the surface of a sphere

The flow near the surface of a sphere was studied, using a flow visualization technique, for Reynolds numbers from about 4×10⁴ to 2.5×10⁵. It was concluded that the presence of a crossflow support substantially disturbed the flow near the surface of the sphere, especially at supercritical Reynolds numbers. Photographs of the flow patterns around spheres with crossflow supports, and with rear supports, have been presented. Also, measurements were made which show the way in which the turbulence intensity of the free stream influenced the angle of separation at various Reynolds numbers.

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Zusammenfassung Die Strömung nahe der Oberfläche einer Kugel wurde untersucht, indem die Stromlinien sichtbar gemacht wurden. Die Untersuchungen wurden durchgeführt für Reynoldszahlen von etwa 4×10⁴ bis 2,5×10⁵. Die Ergebnisse zeigten, daß die Anwesenheit einer Halterung quer zur Strömung diese in der Nähe der Kugeloberfläche wesentlich störte, besonders bei überkritischen Reynoldszahlen. Photographien des Strömungsverlaufes um die Kugel sowohl mit einer Halterung quer zur Stromrichtung als auch mit einer anderen hinter der Kugel werden gezeigt. Außerdem wurden Messungen durchgeführt, die zeigen, in welcher Weise die Intensität der Turbulenz der freien Strömung den Ablösungswinkel bei verschiedenen Reynoldszahlen beeinflußt.

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Nomenclature C _D drag coefficient (total drag/dynamic head × projected area) - C _Dc critical drag coefficient. IfC _D<D _Dc, the flow pattern is considered subcritical. - h distance (s. Fig. 1) - Nu Nusselt number - R radius of the sphere - Re Reynolds number - Re _c Reynolds number at whichC _D=C _Dc - Tu turbulence intensity component in the direction of the freestream flow - _s average angle from the stagnation point to the separation circle measured in the horizontal plane - _sc critical separation angle. If _s<_sc, the flow pattern is considered subcritical. In this investigation _sc 92°     

Tomographic and time resolved PIV measurements on a finite cylinder mounted on a flat plate

Tomographic and time resolved PIV measurements were performed to examine the 3D flow topology and the flow dynamic above the upper surface of a low-aspect ratio cylinder at Re ≈ 1 ×  10⁵. This generic experiment is of fundamental interest because it represents flow features which are relevant to many applications such as laminar separation bubbles and turbulent reattachment. At Re  ≈ 1 × 10⁵, laminar separation bubbles arise on the side of the cylinder. Furthermore, on the top of the cylinder a separation with reattachment is of major interest. The tomographic PIV measurement, which allows to determine all three velocity components in a volume instantaneously, was applied to examine the flow topology and interaction between the boundary layer and wake structures on the top of the finite cylinder. In the instantaneous flow fields the tip vortices and the recirculation region becomes visible. However, it is also observed that the flow is quite unsteady due to the large separation occurring on the top of the cylinder. In order to study the temporal behaviour of the separation, time resolved PIV was applied. This technique allows capturing the dynamic processes in detail. The development of vortices in the separated shear layer is observed and in addition regions with different dominant frequencies are identified.     

Roughness induced forced convective laminar-transitional micropipe flow: energy and exergy analysis

Variable fluid property continuity, Navier–Stokes and energy equations are solved for roughness induced forced convective laminar-transitional flow in a micropipe. Influences of Reynolds number, heat flux and surface roughness, on the momentum-energy transport mechanisms and second-law of thermodynamics, are investigated for the ranges of Re = 1–2,000, Q = 5–100 W/m² and ε = 1–50 μm. Numerical investigations put forward that surface roughness accelerates transition with flatter velocity profiles and increased intermittency values (γ); such that a high roughness of ε = 50 μm resulted in transitional character at Re _tra = 450 with γ = 0.136. Normalized friction coefficient (C _f^*) values showed augmentation with Re, as the evaluated C _f^* are 1.006, 1.028 and 1.088 for Re = 100, 500 and 1,500, respectively, at ε = 1 μm, the corresponding values rise to C _f^* = 1.021, 1.116 and 1.350 at ε = 50 μm. Heat transfer rates are also recorded to rise with Re and ε; moreover the growing influence of ε on Nusselt number with Re is determined by the Nu _ε=50 μm/Nu _ε=1 μm ratios of 1.086, 1.168 and 1.259 at Re = 500, 1,000 and 1,500. Thermal volumetric entropy generation values decrease with Re and ε in heating; however the contrary is recorded for frictional volumetric entropy generation data, where the augmentations in are more considerable when compared with the decrease rates of      

On the Reynolds number scaling of vorticity production at no-slip walls during vortex-wall collisions

Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z μ Re^0.8{Z\propto{\rm Re}^{0.8}} and P μ Re^2.25{P\propto {\rm Re}^{2.25}} for 5 × 10² ≤ Re ≤ 2 × 10⁴ and Z μ Re^0.5{Z\propto{\rm Re}^{0.5}} and P μ Re^1.5{P\propto{\rm Re}^{1.5}} for Re ≥ 2 × 10⁴ (with Re based on the velocity and size of the dipole). A critical Reynolds number Re _c (here, Re_c ? 2×10⁴{{\rm Re}_c\approx 2\times 10^4}) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following scaling relations are obtained: Z μ Re^3/4, P μ Re^9/4{Z\propto{\rm Re}^{3/4}, P\propto {\rm Re}^{9/4}} , and dP/dt μ Re^11/4{\propto {\rm Re}^{11/4}} in agreement with the numerically obtained scaling laws. For Re ≥ Re _c the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate boundary-layer theory, this yields: Z μ Re^1/2{Z\propto{\rm Re}^{1/2}} and P μ Re^3/2{P\propto {\rm Re}^{3/2}}.     

O(2)‐symmetry breaking bifurcation: with application to the flow past a sphere in a pipe

The steady, axisymmetric laminar flow of a Newtonian fluid past a centrally‐located sphere in a pipe first loses stability with increasing flow rate at a steady O(2)‐symmetry breaking bifurcation point. Using group theoretic results, a number of authors have suggested techniques for locating singularities in branches of solutions that are invariant with respect to the symmetries of an arbitrary group. These arguments are presented for the O(2)‐symmetry encountered here and their implementation for O(2)‐symmetric problems is discussed. In particular, how a bifurcation point may first be detected and then accurately located using an ‘extended system’ is described. Also shown is how to decide numerically if the bifurcating branch is subcritical or supercritical. The numerical solutions were obtained using the finite element code ENTWIFE. This has enabled the computation of the symmetry breaking bifurcation point for a range of sphere‐to‐pipe diameter ratios. A wire along the centerline of the pipe downstream of the sphere is also introduced, and its effect on the critical Reynolds number is shown to be small. Copyright © 2000 John Wiley & Sons, Ltd.     

Experimental study on surface wave and film breakdown of falling liquid film flow

In order to evaluate characteristics of the liquid film flow and their influences on heat and mass transfer, measurements of the instantaneous film thickness using a capacitance method and observation of film breakdown are performed. Experimental results are reported in the paper. Experiments are carried out at Re = 250–10000, T _in = 20–50°C and three axial positions of vertically falling liquid films for film thickness measurements. Instantaneous surface waveshapes are given by the interpretation of the test data using the cubic spline method. The correlation of the mean film thickness versus the film Reynolds number is also given by fitting the test data. It is revealed that the surface wave has nonlinear behavior. Observation of film breakdown is performed at Re = 1.40 × 10³–1.75 × 10⁴ and T _in = 85–95°C. From experimental results, the correlation of the film breakdown criterion can be obtained as follows: Bd = 1.567 × 10⁻⁶ Re ^1.183     

Aerodynamic forces and flow fields of a two-dimensional hovering wing

This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (α _A) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping are found to be more sensitive to changes in α _A than in Re. In fact, a subtle change in α _A may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient around α _A = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at α _A = 30° and a neutral wake structure at α _A = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering motion only, the unique force characteristics observed here, particularly their strong dependence on α _A, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics to help them to stay aloft and maneuver. An erratum to this article can be found at     

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.     

Secondary flow patterns and mixing in laminar pulsating flow through a curved pipe

Mixing by secondary flow is studied by particle image velocimetry (PIV) in a developing laminar pulsating flow through a circular curved pipe. The pipe curvature ratio is η = r ₀/r _c  = 0.09, and the curvature angle is 90°. Different secondary flow patterns are formed during an oscillation period due to competition among the centrifugal, inertial, and viscous forces. These different secondary-flow structures lead to different transverse-mixing schemes in the flow. Here, transverse mixing enhancement is investigated by imposing different pulsating conditions (Dean number, velocity ratio, and frequency parameter); favorable pulsating conditions for mixing are introduced. To obviate light-refraction effects during PIV measurements, a T-shaped structure is installed downstream of the curved pipe. Experiments are carried out for the Reynolds numbers range 420 ≤ Re_st ≤ 1,000 (Dean numbers 126.6 ≤ Dn ≤ 301.5) corresponding to non-oscillating flow, velocity component ratios 1 ≤ (β = U _max,osc/U _m,st) ≤ 4 (the ratio of velocity amplitude of oscillations to the mean velocity without oscillations), and frequency parameters 8.37 < (α = r ₀(ω/ν)^0.5) < 24.5, where α² is the ratio of viscous diffusion time over the pipe radius to the characteristic oscillation time. The variations in cross-sectional average values of absolute axial vorticity (|ζ|) and transverse strain rate (|ε|) are analyzed in order to quantify mixing. The effects of each parameter (Re_st, β, and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζ _P |/|ζ _S |) and dimensionless transverse strain rates (|ε _P |/|ε _S |) during a complete oscillation period.     

Experimental study of the laminar-turbulent transition on a blunt cone

Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M _∞ = 6, and unit Reynolds number in the interval Re _∞,1 = 5.79 · 10⁶–5.66 · 10⁷ m^?1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re _∞,R ≈ 1.3 · 10⁵ beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.