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Wakes and bluff bodies : Forced and free oscillations
Wind turbines’s wake and related studies
Localised states
Cavity Flows
Vortex breakdown — Swirling flow
Experimental techniques
Instabilities of diffusion flames

Wakes and bluff bodies : Forced and free oscillations

Abstract : This study investigates the nature of the dynamic response of an elastically mounted cylinder immersed in a free stream. A novel method is utilized, where the motion of the body during a free vibration experiment is accurately recorded, and then a second experiment is conducted where the cylinder is externally forced to follow this recorded trajectory. Generally, the flow response during both experiments is identical. However, particular regimes exist where the flow response is significantly different. This is taken as evidence of chaos in these regimes.

Abstract : This study investigates the free transverse flow-induced vibration (FIV) of an elastically mounted low-mass-ratio square cylinder in a free stream, at three different incidence angles : α = 0◦ , 20◦ and 45◦ . This geometric setup presents a body with an angle of attack, sharp corners and some afterbody, and therefore is a generic body that can be used to investigate a wide range of FIV phenomena. A recent study by Nemes et al. (J. Fluid Mech., vol. 710, 2012, pp. 102–130) provided a broad overview of the flow regimes present as a function of both the angle of attack α and reduced flow velocity U∗. Here, the focus is on the three aforementioned representative angles of attack : α = 0◦ , where the FIV is dominated by transverse galloping ; α = 45◦ , where the FIV is dominated by vortex-induced vibration (VIV) ; and an intermediate value of α = 20◦, where the underlying FIV phenomenon has previously been difficult to determine. For the α = 0◦ case, the amplitude of oscillation increases linearly with the flow speed except for a series of regimes that occur when the vortex shedding frequency is in the vicinity of an odd-integer multiple of the galloping oscillation frequency, and the vortex shedding synchronizes to this multiple of the oscillation frequency. It is shown that only odd-integer multiple synchronizations should occur. These synchronizations explain the ‘kinks’ in the galloping amplitude response for light bodies first observed by Bearman et al. (J. Fluids Struct., vol. 1, 1987, pp. 19–34). For the α = 45◦ case, the VIV response consists of a number of subtle, but distinctly different regimes, with five regimes of high-amplitude oscillations, compared to two found in the classic VIV studies of a circular cylinder. For the intermediate α = 20◦ case, a typical VIV ‘upper branch’ occurs followed by a ‘higher branch’ of very large-amplitude response. The higher branch is caused by a subharmonic synchronization between the vortex shedding and the body oscillation frequency, where two cycles of vortex shedding occur over one cycle of oscillation. It appears that this subharmonic synchronization is a direct result of the asymmetric body. Overall, the FIV of the square cylinder is shown to be very rich, with a number of distinct regimes, controlled by both α and U∗. Importantly, α controls the underlying FIV phenomenon, as well as controlling the types of possible synchronization between the oscillation and vortex shedding.

Abstract : The flow-induced vibrations of a circular cylinder, free to oscillate in the cross-flow direction and subjected to a forced rotation about its axis, are analysed by means of two- and three-dimensional numerical simulations. The impact of the symmetry breaking caused by the forced rotation on the vortex-induced vibration (VIV) mechanisms is investigated for a Reynolds number equal to 100, based on the cylinder diameter and inflow velocity. The cylinder is found to oscillate freely up to a rotation rate (ratio between the cylinder surface and inflow velocities) close to 4. Under forced rotation, the vibration amplitude exhibits a bell-shaped evolution as a function of the reduced velocity (inverse of the oscillator natural frequency) and reaches 1.9 diameters, i.e. three times the maximum amplitude in the non-rotating case. The free vibrations of the rotating cylinder occur under a condition of wake–body synchronization similar to the lock-in condition driving non-rotating cylinder VIV. The largest vibration amplitudes are associated with a novel asymmetric wake pattern composed of a triplet of vortices and a single vortex shed per cycle, the TCS pattern. In the low-frequency vibration regime, the flow exhibits another new topology, the U pattern, characterized by a transverse undulation of the spanwise vorticity layers without vortex detachment ; consequently, free oscillations of the rotating cylinder may also develop in the absence of vortex shedding. The symmetry breaking due to the rotation is shown to directly impact the selection of the higher harmonics appearing in the fluid force spectra. The rotation also influences the mechanism of phasing between the force and the structural response.

Abstract : This paper presents the results of an in-depth study of the flow past a streamwise oscillating cylinder, examining the impact of varying the amplitude and frequency of the oscillation, and the Reynolds number of the incoming flow. These findings are presented in a framework that shows that the relationship between the frequency of vortex shedding fs and the amplitude of oscillation A* is governed by two primary factors : the first is a reduction of fs proportional to a series in A*2 over a wide range of driving frequencies and Reynolds numbers ; the second is nonlinear synchronization when this adjusted fs is in the vicinity of N = (1 - fs/fd)-1, where N is an integer. Typically, the influence of higher-order terms is small, and truncation to the first term of the series (A*2) well represents the overall trend of vortex shedding frequency as
a function of amplitude. However, discontinuous steps are overlaid on this trend due to the nonlinear synchronization. When fs is normalized by the Strouhal frequency fSt (the frequency of vortex shedding from an unperturbed cylinder), the rate at which fs/fSt decreases with amplitude, at least for fd/fSt = 1, shows a linear dependence on the Reynolds number. For a fixed Re = 175, the truncated series shows that the rate of decrease of fs/fSt with amplitude varies as (2 - fd/fSt)-1/2 for 1 < or egal fd/fSt < or egal 2, but is essentially independent of fd/fSt for fd/fSt < 1. These trends of the rate of decrease of fs with respect to amplitude are also used to predict the amplitudes of oscillation around which synchronization occurs. These predicted amplitudes are shown to fall in regions of the parameter space where synchronized modes occur. Further, for the case of varying fd/fSt, a very reasonable prediction of the amplitude of oscillation required for the onset of synchronization to the mode where fs = 0.5fd is given. In a similar manner, amplitudes at which fs = 0 are calculated, predicting where the natural vortex shedding is completely supplanted by the forcing. These amplitudes are found to coincide approximately with those at which the onset of a symmetric vortex shedding mode is observed. This result is interpreted as meaning that the symmetric shedding mode occurs when the dynamics crosses over from being dominated by the vortex shedding to being dominated by the forcing.

Abstract : This study examines the influence of angle of attack of a square section cylinder on the cylinder’s flow-induced vibration, where the direction of the vibration is transverse to the oncoming flow. Our experiments, which traversed the velocity–angle of attack parameter space in considerable breadth and depth, show that a low-mass ratio body can undergo combinations of both vortex-induced vibration and galloping. When the body has an angle of attack that makes it symmetric to the flow, such as when it assumes the square or diamond orientation, the two mechanisms remain independent. However, when symmetry is lost we find a mixed mode response with a new branch of vortex-induced oscillations that exceeds the amplitudes resulting from the two phenomena independently.
The oscillations of this higher branch have amplitudes larger than the ‘upper branch’ of vortex-induced vibrations and at half the frequency. For velocities above this resonant region, the frequency splits into two diverging branches. Analysis of the amplitude response reveals that the transition between galloping and vortex-induced vibrations occurs over a narrow range of angle of incidence. Despite the rich set of states found in the parameter space the vortex shedding modes remain very similar to those found previously in vortex-induced vibration.

Abstract : The modification of a cylinder wake by streamwise oscillation of the cylinder at the vortex shedding frequency of the unperturbed cylinder is reported. Recent numerical simulations [J. S. Leontini, D. Lo Jacono, and M. C. Thompson, “A numerical study of an inline oscillating cylinder in a free stream,” J. Fluid Mech. 688, 551–568 (2011)10.1017/jfm.2011.403] showed that this forcing results in the primary frequency decreasing proportionally to the square of the forcing amplitude, before locking to a subharmonic at higher amplitudes. The experimental results presented here show that this behavior continues at higher Reynolds numbers, although the flow is three-dimensional. In addition, it is shown that this behavior persists when the body is a square cross section, and when the frequency of forcing is detuned from the unperturbed cylinder shedding frequency. The similarity of the results across Reynolds number, geometry, and frequency suggests that the physical mechanism is applicable to periodic forcing of the classic von Kármán vortex street, regardless of the details of the body which forms the street.

Abstract : The experimental research reported here employs particle image velocimetry to extend the study of Nazarinia et al. (2009a), recording detailed vorticity fields in the near-wake of a circular cylinder undergoing combined translational and rotational oscillatory motions. The focus of the present study is to examine the effect of the ratio between the cross-stream translational and rotational velocities and frequencies on the synchronization of the near- wake structures for multiple phase differences between the two motions. The frequencies are fixed close to that of the natural frequency of vortex shedding. The results are presented for a fixed amplitude of rotational oscillation of 1 rad and a range of ratios between the translational and rotational velocities (V_R) = [0.25,0.5,1.0,1.5] and for a range of frequency ratios (F_R) = [0.5, 1.0, 2.0]. In particular, it was found that varying the V_R value changed the near-wake structure. The results show that at the lower value of V_R = 0.25, for all of the phase differences examined, the vortices are shed in a single-row 2S mode aligned in the medial plane with a slight offset from the centreline and also synchronized with the combined oscillatory motion. As V_R increases the vortex shedding mode changes from a 2S single-row to a 2S double-row structure and eventually back to the single-row (at V_R = 0.5). Increasing V_R further resulted in the loss of lock-on over the range of negative phase angles and a transition from the 2S to P+S mode for the in-phase case. There was transition back to the 2S wake mode with a further decrease in \phi. For higher V_R the range of desynchronization increased. In the second and third parts of this paper it is shown that the occurrence of unlocked wake flow as the phase angle is varied is greater when the frequency ratio between the imposed oscillatory motions and the natural vortex shedding frequency F_RN is higher than unity. The vortices are synchronized in the near-wake at F_RN values less than unity and unlocked when F_RN > 1.0. In particular, the near-wake structures have also been shown to be synchronized for F_R = 0.5 and unlocked for F_R = 2.0.

Abstract : Simulations of a cylinder undergoing externally controlled sinusoidal oscillations in the free stream direction have been performed. The frequency of oscillation was kept equal to the vortex shedding frequency from a fixed cylinder, while the amplitude of oscillation was varied, and the response of the flow measured. With varying amplitude, a rich series of dynamic responses was recorded. With increasing amplitude, these states included wakes similar to the Kármán vortex street, quasiperiodic oscillations interleaved with regions of synchronized periodicity (periodic on multiple oscillation cycles), a period-doubled state and chaotic oscillations. It is hypothesized that, for low to moderate amplitudes, the wake dynamics are controlled by vortex shedding at a global frequency, modified by the oscillation. This vortex shedding is frequency modulated by the driven oscillation and amplitude modulated by vortex interaction. Data are presented to support this hypothesis.

Abstract : A study of the flow past an oscillatory rotating cylinder has been conducted, where the frequency of oscillation has been matched to the natural frequency of the vortex street generated in the wake of a stationary cylinder, at Reynolds number 300. The focus is on the wake transition to three-dimensional flow and, in particular, the changes induced in this transition by the addition of the oscillatory rotation. Using Floquet stability analysis, it is found that the fine-scale three-dimensional mode that typically dominates the wake at a Reynolds number beyond that at the second transition to three-dimensional flow (referred to as mode B) is suppressed for amplitudes of rotation beyond a critical amplitude, in agreement with past studies. However, the rotation does not suppress the development of three-dimensionality completely, as other modes are discovered that would lead to three-dimensional flow. In particular, the longer-wavelength mode that leads the three-dimensional transition in the wake of a stationary cylinder (referred to as mode A) is left essentially unaffected at low amplitudes of rotation. At higher amplitudes of oscillation, mode A is also suppressed as the two-dimensional near wake changes in character from a single- to a double- row wake ; however, another mode is predicted to render the flow three-dimensional, dubbed mode D (for double row). This mode has the same spatio-temporal symmetries as mode A.

Abstract : The flow behind a cylinder undergoing forced combined oscillatory motion has been studied. The motion consists of two independent oscillations : cross-stream translation and rotation. Previous studies have extensively investigated the effect of these motions individually on cylinder wakes ; however, the investigation of their combined effect is new. The motivation lies in its application to vortex-induced vibration and its suppression and to biomimetic motion. The focus is on the effect of the phase difference between the two motions. The results show that there is an unexpected loss of synchronization of the wake for a finite range of phase differences.

Abstract : Previous two-dimensional numerical studies have shown that a circular cylinder undergoing both oscillatory rotational and translational motions can generate thrust so that it will actually self-propel through a stationary fluid. Although a cylinder undergoing a single oscillation has been thoroughly studied, the combination of the two oscillations has not received much attention until now. The current research reported here extends the numerical study of Blackburn et al. Phys. Fluids 11, L4 (1999) both experimentally and numerically, recording detailed vorticity fields in the wake and using these to elucidate the underlying physics, examining the three-dimensional wake development experimentally, and determining the three-dimensional stability of the wake through Floquet stability analysis. Experiments conducted in the laboratory are presented for a given parameter range, confirming the early results from Blackburn et al. Phys. Fluids 11, L4 (1999). In particular, we confirm the thrust generation ability of a circular cylinder undergoing combined oscillatory motions. Importantly, we also find that the wake undergoes three-dimensional transition at low Reynolds numbers Re=100 to an instability mode with a wavelength of about two cylinder diameters. The stability analysis indicates that the base flow is also unstable to another mode at slightly higher Reynolds numbers, broadly analogous to the three-dimensional wake transition mode for a circular cylinder, despite the distinct differences in wake/mode topology. The stability of these flows was confirmed by experimental measurements.

Wind turbines’s wake and related studies

Abstract : Analysis of the helical vortices measured behind a model wind turbine in a water channel are reported. Phase-locked measurements using planar particle image ve- locimetry are taken behind a Glauert rotor to investigate the evolution and breakdown of the helical vortex structures. Existing linear stability theory predicts helical vortex filaments to be susceptible to three unstable modes. The current work presents tip and root vortex evolution in the wake for varying tip speed ratio and shows a breaking of the helical symmetry and merging of the vortices due to mutual inductance between the vortical filaments. The merging of the vortices is shown to be steady with rotor phase, however, small-scale non-periodic meander of the vortex positions is also ob- served. The generation of the helical wake is demonstrated to be closely coupled with the blade aerodynamics, strongly influencing the vortex properties which are shown to agree with theoretical predictions of the circulation shed into the wake by the blades. The mutual inductance of the helices is shown to occur at the same non-dimensional wake distance

Abstract : The vortical near wake of a model horizontal
axis wind turbine has been investigated experimentally in a
water channel. The objective of this work is to study vortex
interaction and stability of the helical vortex filaments
within a horizontal axis wind turbine wake. The experimental model is a geometrically scaled version of the
Tjæreborg wind turbine, which existed in western Denmark
in the late 1980s. Here, the turbine was tested in both the
upwind and downwind configurations. Qualitative flow
visualisations using hydrogen bubble, particle streakline
and planar laser-induced fluorescence techniques were
combined with quantitative data measurements taken using
planar particle image velocimetry. Vortices were identified
using velocity gradient tensor invariants. Parameters that
describe the helical vortex wake, such as the helicoidal
pitch, and vortex circulation, were determined for three tip
speed ratios. Particular attention is given here to the root
vortex, which has been investigated minimally to date.
Signatures of the coherent tip vortices are seen throughout
the measurement domain ; however, the signature of the
root vortex is only evident much closer to the rotor plane,
irrespective of the turbine configuration. It is postulated
that the root vortex diffuses rapidly due to the effects of the
turbine support geometries.

Localised states

Abstract : Three-dimensional convection in a binary mixture in a porous medium heated from below is studied. For negative separation ratios steady spatially localized convection patterns are expected. Such patterns, spatially localized in two dimensions, are computed and numerical continuation is used to examine their growth and proliferation as parameters are varied. The patterns studied have the form of a core region with four extended side-branches and can be stable. A physical mechanism behind the formation of these unusual structures is suggested.

Abstract : Numerical continuation is used to compute branches of time-independent, spatially localized convectons in an imposed vertical magnetic field focusing on values of the Chandrasekhar number Q in the range 10 < Q < 103. The calculations reveal that convectons initially grow by nucleating additional cells on either side, but with the build-up of field outside owing to flux expulsion, the convectons are able to transport more heat only by expanding the constituent cells. Thus, at large Q and large Rayleigh numbers, convectons consist of a small number of broad cells.

Abstract : Numerical continuation is used to compute branches of spatially localized structures in convection in an imposed vertical magnetic field. In periodic domains with finite spatial period, these branches exhibit slanted snaking and consist of localized states of even and odd parity. The properties of these states are analysed and related to existing asymptotic approaches valid either at small amplitude (Cox and Matthews, Physica D, vol. 149, 2001, p. 210), or in the limit of small magnetic diffusivity (Dawes, J. Fluid Mech., vol. 570, 2007, p. 385). The transition to standard snaking with increasing domain size is explored.

Abstract : The origin and properties of time-independent spatially localized binary fluid convection in a layer of porous material heated from below are studied. Different types of single and multipulse states are computed using numerical continuation, and the results related to the presence of homoclinic snaking of single and multipulse states.

Cavity flows

Abstract : The turbulent flow inside a rotating channel provided with transverse ribs along
one wall is studied by means of two-dimensional time-resolved particle image velocimetry.
The measurement set-up is mounted on the same rotating disk with the
test section, allowing to obtain the same accuracy and resolution as in a non-rotating
rig. The Reynolds number is 15 000, and the rotation number is 0.38. As the ribbed
wall is heated, both the Coriolis force and the centrifugal force play a role in the
fluid dynamics. The mean velocity fields highlight the major impact of the rotational
buoyancy (characterized by a buoyancy number of 0.31) on the flow along the leading
side of the duct. In particular, since the flow is directed radially outward, the
near-wall layers experience significant centripetal buoyancy. The recirculation area
behind the obstacles is enlarged to the point of spanning the whole inter-rib space.
Also the turbulent fluctuations are significantly altered, and overall augmented, with
respect to the non-buoyant case, resulting in higher turbulence levels far from the rib.
On the other hand the centrifugal force has little or no impact on the flow along the
trailing wall. Vortex identification, proper orthogonal decomposition, and two-point
correlations are used to highlight rotational effects, and in particular to determine
the dominant scales of the turbulent unsteady flow, the time-dependent behavior of
the shear layer and of the recirculation bubble behind the wall-mounted obstacles,
the lifetime and advection velocity of the coherent structures.

Abstract : An experimental investigation of the recirculation zone formed downstream of a forward facing step immersed in a turbulent boundary layer has been undertaken using particle image velocimetry. Bluff body flow is observed with the fixed separation point located at the leading edge of the step. The recirculation region dimensions are characterised over a range of Reynolds numbers (1400–19 000), with Reh based on the step height and the free stream velocity. Turbulent perturbations are produced in the free shear layer which develops between the recirculating flow close to the step and the free stream flow. Contour maps of amplification factor, streamwise perturbation velocity and Reynolds stresses are constructed, providing insight into optimal placement of structures within such topographical features. The mechanisms affecting the reattachment distance, namely the turbulent mixing within the boundary layer and the velocity deficit in the boundary layer, are discussed.

Abstract : “Oseen-Poiseuille” equations are developed from an asymptotic formulation of the three-dimensional Navier-Stokes equations in order to study the influence of weak inertia on flows between rough surfaces. The impact of the first correction on macroscopic flow due to inertia has been determined by solving these equations numerically. From the numerical convergence of the asymptotic expansion to the three-dimensional Navier-Stokes flows, it is shown that, at the macroscopic scale, the quadratic correction to the Reynolds equation in the weak-inertial regime vanishes generalizing a similar result in porous media.

Vortex breakdown — Swirling flow

Abstract : Experiments were conducted to determine the effectiveness of controlling vortex break- down in a confined cylindrical vessel using a small rotating disk, which was flush-mounted into the opposite endwall to the rotating endwall driving the primary recirculating flow. The results show that the control disk, with relatively little power input, can modify the azimuthal and axial flow significantly, changing the entire flow structure in the cylinder. Co-rotation was found to precipitate vortex breakdown onset whereas counter-rotation delays it. Furthermore, for the Reynolds number range over which breakdown normally exists, co-rotation increases the bubble radial and axial dimensions, while shifting the bubble in the upstream direction. By contrast, counter-rotation tends to reduce the size of the bubble, or completely suppress it, while shifting the bubble in the downstream direction. These effects are amplified substantially by the use of larger control disks and higher rotation ratios. A series of numerical simulations close to the onset Reynolds number reveals that the control disk acts to generate a rotation-rate invariant local positive or negative azimuthal vorticity source away from the immediate vicinity of the control disk but upstream of breakdown. Advection of this source along streamlines, modifies the strength of the azimuthal vorticity ring, which effectively controls whether the flow reverses on the axis, and thus, in turn, whether vortex breakdown occurs. The vorticity source generated by the control disk scales approximately linearly with rotation ratio and cubically with disk diameter ; this allows the observed variation of the critical Reynolds number to be approximately predicted.

Abstract : The free surface flow in a circular cylinder driven by a rotating bottom disk is studied experimentally using particle image velocimetry. Results are compared with computational results assuming a stress-free surface. A dye visualization study by Spohn et al. “Observations of vortex breakdown in an open cylindrical container with a rotating bottom,” Exp. Fluids 14, 70 (1993), as well as several numerical computations, has found a range of different vortex breakdown structures in this flow. We confirm the existence of a transition where the top of the breakdown bubble crosses from the axis to the surface, which has previously only been found numerically. We employ a technique by Brøns et al. “Topology of vortex breakdown bubbles in a cylinder with rotating bottom and free surface,” J. Fluid Mech. 428, 133 (2001) to find the corresponding bifurcation curve in the parameter plane, which has hitherto only been used on numerical data. The bifurcation curve located here agrees well with previous numerical simulations. For low values of the Reynolds number we find a regime with vortex breakdown that has not been previously identified. Experiments deviate substantially from computations, indicating the importance of surface effects in this regime.

Abstract : Effective control of vortex breakdown in a cylinder with a rotating lid was achieved with small rotating rods positioned on the stationary lid. After validation with accurate measurements using a novel stereoscopic particle image velocimetry (SPIV) technique, analysis of numerical simulations using a high-order spectral element method has been undertaken. The effect of a finite length rod creates additional source terms of vorticity as the rod rotates. These additional source terms and their spatial locations influence the occurrence of the vortex breakdown.

Abstract : This article is devoted to the study of an incompressible viscous flow of a fluid partly enclosed in a cylin- drical container with an open top surface and driven by the constant rotation of the bottom wall. Such type of flows belongs to a group of recirculating lid-driven cavity flows with geometrical axisymmetry and of the prescribed boundary conditions of Dirichlet type—no-slip on the cavity walls. The top surface of the cylindrical cavity is left open with an imposed stress-free boundary condition, while a no-slip con- dition with a prescribed rotational velocity is imposed on the bottom wall. The Reynolds regime corresponds to transitional flows with some incursions in the fully laminar regime. The approach taken here revealed new flow states that were investigated based on a fully three-dimensional solution of the Navier–Stokes equations for the free-surface cylindrical swirling flow, without resorting to any symmetry property unlike all other results available in the literature. Theses solutions are obtained through direct numerical simulations based on a Legendre spectral element method.

Abstract : Unsteady incompressible viscous flows of a fluid partly enclosed in a cylindrical container with an open top surface are presented in this article. These moving free-surface flows are generated by the steady rotation of the solid bottom end wall. Such type of flows belongs to a group of recirculating lid-driven cavity flows with geometrical axisymmetry. The top surface of the cylindrical cavity is left open so that the free surface can freely deform. The Reynolds regime corresponds to unsteady transitional flows with some incursions in the fully laminar regime. The approach taken here revealed new nonaxisymmetric flow states that are investigated based on a fully three-dimensional solution of the Navier–Stokes equations for the free-surface cylindrical swirling flow without resorting to any symmetry property unlike all other results available in the literature. The results are compared with those of Bouffanais and Lo Jacono “Transitional cylindrical swirling flow in presence of a flat free surface,” Comput. Fluids 38, 1651 (2009) corresponding to the exact same parameters but with a flat-and-fixed top free surface. These solutions are obtained through direct numerical simulations based on a highly accurate Legendre spectral element method combined with a moving-grid technique.

Experimental techniques

Abstract : When investigating flow structures, and especially flow transitions, research projects often seek to increase insight using complementary numerical and physical experiments. Obtaining exact Reynolds number correspondence can frequently be difficult in experiments, particularly when relatively low values are required. Often, available test facilities were designed and optimised for a specific velocity range, meaning they have restrictions on the minimum flow velocity. This study describes a device to reduce the flow velocity locally in an open surface water channel. The underlying idea is to divert a controlled fraction of the incoming flow from the working section by increasing the pressure there, resulting in reduced velocity. This idea is realised using a ‘sub-channel’ that can be inserted into the main test chamber, with a variable porosity perforated screen at its downstream end. This study assesses and optimises the flow quality inside this structure, such as usable test section length, uniformity of the velocity profiles and turbulence intensity. The results demonstrate that the device creates high quality low Reynolds number flows, which is exemplified with the canonical circular cylinder in cross-flow.

Abstract : We have developed a new method for contrast microangiography of the rat renal circulation using synchrotron radiation. The method was applied to determine responses of the renal arterial vasculature to angiotensin II and electrical stimulation of the renal nerves (RNS). Iodinated contrast agent was administered directly into the renal artery of pentobarbital-anesthetized rats before and during 1) intravenous infusion of angiotensin II (1.6 microg kg^-1 min^-1) or 2) its vehicle, or 3) RNS at 2 Hz. Images were obtained at 30 Hz, before and during these treatments, and vascular caliber was determined by use of a newly developed algorithm described herein. Up to four levels of branching could be observed simultaneously along the arterial tree, comprising vessels with resting diameter of 28–400 microm. Vessel diameter was not significantly altered by vehicle infusion (3.1 \pm 3.5% change) but was significantly reduced by angiotensin II (-24.3 \pm 3.4%) and RNS (-17.1 \pm 3.8%). Angiotensin II-induced vasoconstriction was independent of vessel size, but RNS-induced vasoconstriction was greatest in vessels with a resting caliber of 100–200 microm and least in vessels with a resting caliber 40–100 microm. In conclusion, the method we describe herein provides a new approach for assessing responses of the renal arterial circulation to vasoactive factors along several orders of branching.

Abstract : A method is proposed that allows three- dimensional (3D) two-component measurements to be made by means of particle image velocimetry (PIV) in any volume illuminated over a finite thickness. The method is based on decomposing the cross-correlation function into various contributions at different depths. Because the technique is based on 3D decomposition of the correlation function and not reconstruction of particle images, there is no limit to particle seeding density as experienced by 3D particle tracking algorithms such as defocusing PIV and tomographic PIV. Correlations from different depths are differentiated by the variation in point spread function of the lens used to image the measurement volume over that range of depths. A number of examples are demonstrated by use of synthetic images which simulate micro-PIV experiments. These examples vary from the trivial case of Couette flow (linear variation of one velocity component over depth) to a general case where both velocity components vary by different complex functions over the depth. A final validation—the measurement of a parabolic velocity profile over the depth of a microchannel flow—is presented. The same method could also be applied using a thick light sheet in macro-scale PIV and in a stereo configuration for 3D three-component PIV.

Abstract : A novel, accurate and simple stereo particle image velocimetry (SPIV) technique utilising three cam- eras is presented. The key feature of the new technique is that there is no need of a separate calibration phase. The calibration data are measured concurrently with the PIV data by a third paraxial camera. This has the benefit of improving ease of use and reducing the time taken to obtain data. This third camera also provides useful velocity information, considerably improving the accuracy of the resolved 3D vectors. The additional redundancy provided by this third perspective in the stereo reconstruction equations suggests a least-squares approach to their solution. The least-squares process further improves the utility of the technique by means of the reconstruction residual. Detailed error analysis shows that this residual is an accurate predictor of resolved vector errors. The new technique is rigorously validated using both pure translation and rotation test cases. However, while this kind of validation is standard, it is shown that such validation is substantially flawed. The case of the well-known confined vortex breakdown flow is offered as an alternative validation. This flow is readily evaluated using CFD methods, allowing a detailed comparison of the data and evaluation of PIV errors in their entirety for this technique.

Abstract : A technique capable of simultaneous measurement of free-surface topography and velocity vector field data is presented. This technique offers substantial benefits of both reduced complexity and enhanced accuracy over all other techniques known to offer the same measurements. The flow behind a circular cylinder at low Reynolds numbers is measured using this technique. The velocity and vorticity fields as well as Strouhal number closely match the expected results. The free-surface topography, which can be related to the pressure field, exhibits an intimate relationship to the vorticity field.

Instabilities of diffusion flames

Abstract : Systematic experiments have been undertaken to study the parameter dependence of cellular instability and in particular the scaling of the resulting cell size in CO2-diluted H2–O2 jet diffusion flames. Cellular flames are known to arise near the extinction limit when reactant Lewis numbers are relatively low. The Lewis numbers of the investigated near-extinction mixtures, based on the initial mixture strength φm and ambient conditions, varied in the ranges [1.1–1.3] for oxygen and [0.25–0.29] for hydrogen (φm is defined here as the fuel-to-oxygen mass ratio, normalized by the stoichiometric ratio). The experiments were carried out both in an axisymmetric jet (AJ) burner and in a two-dimensional slot burner known as a Wolfhard–Parker (WP) burner with an oxidizer co-flow (mostly 100% O2) of fixed low velocity. First, the region of cellular flames adjacent to the extinction limit was characterized in terms of initial H2 concentration and fuel jet velocity, with all other parameters fixed. Then, the wavelength of the cellular instability, i.e., the cell size, was determined as a function of the fuel jet velocity and the initial mixture strength φm. For conditions not too close to extinction, this wavelength is found to increase with the square root of the vorticity thickness of the jet shear layer and roughly the 1/5 power of φm. Very close to extinction, this scaling breaks down and will likely switch to a scaling with the flame thickness, i.e., involving the Damköhler number.

Abstract : Abstract
A unique burner was constructed to experimentally realize a one-dimensional unstrained planar non- premixed flame, previously considered only in idealized theoretical models. One reactant, the fuel mixture in the current experiments, is supplied through a porous plug at the bottom of the combustion chamber and flows vertically up towards the horizontal flame. The crux of the design is the introduction of the oxidizer from above in such a way that its diffusion against the upward product flow is essentially one-dimensional, i.e., uniform over the burner cross-section. This feature was implemented by introducing the oxidizer into the burner chamber from the top through an array of 625 closely spaced hypodermic needles, and allowing the hot products to escape vertically up through the space between the needles. Due to the injection of oxidizer through discrete tubes, a three-dimensional ‘‘injection layer’’ exists below the exit plane of the oxidizer supply tubes. Experimental evidence suggests that this layer is thin and that oxidizer is supplied to the flame by 1-D counterdiffusion, producing a nearly unstrained flame. To characterize the burner, flame position measurements were conducted for different compositions and flowrates of H2–CO2 and O2–CO2 mixtures. The measured flame locations are compared to an idealized one-dimensional model in which only diffusion of oxidizer against the product flow is considered. The potential of the new burner is demonstrated by a study of cellular structures forming near the extinction limit. Consistent with previous investigations, cellular instabilities are shown to become more prevalent as the initial mixture strength and/ or the Damköhler number are decreased. As the extinction limit is approached, the number of cells was observed to decrease progressively.

Abstract : Systematic experiments with CO2 diluted H2–O2 circular jet diffusion flames have been undertaken to study the formation of cellular flames, which occur for relatively low reactant Lewis numbers and near the extinction limit. The jet Reynolds number for all experiments was about 500, based on the centreline velocity, jet diameter and ambient fuel properties. The Lewis numbers, based on the initial mixture strength φ and ambient conditions of the investigated near-extinction mixtures, vary in the range 1.1–1.3 for oxygen and 0.25–0.29 for hydrogen (φ is defined here as the fuel-to-oxygen molar ratio normalized by the stoichiometric value). Various conditions near the extinction limit were investigated by fixing the fuel composition (H2–CO2 mixture), and systematically lowering the oxygen concentration in the co-flowing oxidizer stream past the point where cellular structures formed, until extinction occurred. The observed different instability states were correlated with the initial mixture strength and the proximity to the extinction limit.
The parameter space for cellularity was found to increase with decreasing initial mixture strength. For a given initial mixture strength, several cellular states were found to co-exist near the extinction limit, and the preferred number of cells (the azimuthal wave number) was observed to decrease with decreasing oxygen concentration (Damköhler number). These trends are consistent with previous theoretical work and our own stability analysis that will be reported elsewhere.