Wake development in staggered short cylinder arrays within a channel

Staggered arrays of short cylinders, known as pin?Cfins, are commonly used as a heat exchange method in many applications such as cooling electronic equipment and cooling the trailing edge of gas turbine airfoils. This study investigates the near wake flow as it develops through arrays of staggered pin fins. The height-to-diameter ratio was unity while the transverse spacing was kept constant at two cylinder diameters. The streamwise spacing was varied between 3.46 and 1.73 cylinder diameters. For each geometric arrangement, experiments were conducted at Reynolds numbers of 3.0e3 and 2.0e4 based on cylinder diameter and velocity through the minimum flow area of the array. Time-resolved flowfield measurements provided insight into the dependence of row position, Reynolds number, and streamwise spacing. Decreasing streamwise spacing resulted in increased Strouhal number as the near wake length scales were confined. In the first row of the bundle, low Reynolds number flows were mainly shear-layer-driven while high Reynolds number flows were dominated by periodic vortex shedding. The level of velocity fluctuations increased for cases having stronger vortex shedding. The effect of streamwise spacing was most apparent in the reduction of velocity fluctuations in the wake when the spacing between rows was reduced from 2.60 diameters to 2.16 diameters.     

Aerodynamic flow vectoring of a wake using asymmetric synthetic jet actuation

This paper reports an experimental investigation on the wake of a blunt-based, flat plate subjected to aerodynamic flow vectoring using asymmetric synthetic jet actuation. Wake vectoring was achieved using a synthetic jet placed at the model base 2.5?mm from the upper corner. The wake Reynolds number based on the plate thickness was 7,200. The synthetic jet actuation frequency was selected to be about 75?% the vortex shedding frequency of the natural wake. At this actuation frequency, the synthetic jet delivered a periodic flow with a momentum coefficient, C _??, of up to 62?%. Simultaneous measurements of the streamwise and transverse components of the velocity were performed using particle image velocimetry (PIV) in the near wake. The results suggested that for significant wake vectoring, vortex shedding must be suppressed first. Under the flow conditions cited above, C _?? values in the range of 10?C20?% were required. The wake vectoring angle seemed to asymptote to a constant value of about 30° at downstream distances, x/h, larger than 4 for C _?? values ranging between 24 and 64?%. The phase-averaged vorticity contours and the phase-averaged normal lift force showed that most of the wake vectoring is produced during the suction phase of the actuation, while the blowing phase was mostly responsible for vortex shedding suppression.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

Effect of streamwise spacing on periodic and random unsteadiness in a bundle of short cylinders confined in a channel

While flow across long tube bundles is considered classical data, pin-fin arrays made up of short tubes have become a growing topic of interest for use in cooling gas turbine airfoils. Data from the literature indicate that decreasing streamwise spacing increases heat transfer in pin-fin arrays; however, the specific mechanism that causes increased heat transfer coefficients remains unknown. The present work makes use of time-resolved PIV to quantify the effects of streamwise spacing on the turbulent near wake throughout various pin-fin array spacings. Specifically, proper orthogonal decomposition was used to separate the (quasi-) periodic motion from vortex shedding and the random motion from turbulent eddies. Reynolds number flow conditions of 3.0?×?10³ and 2.0?×?10⁴, based on pin-fin diameter and velocity at the minimum flow area, were considered. Streamwise spacing was varied from 3.46 pin diameters to 1.73 pin diameters while the pin-fin height-to-diameter ratio was unity and the spanwise spacing was held constant at two diameters. Results indicated that (quasi-) periodic motions were attenuated at closer streamwise spacings while the level of random motions was not strongly dependent on pin-fin spacing. This trend was observed at both Reynolds number conditions considered. Because closer spacings exhibit higher heat transfer levels, the present results imply that periodic motions may not contribute to heat transfer, although further experimentation is required.     

Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers

In view of the fact that large scale vortices play the substantial role of momentum transport in turbulent flows, large eddy simulation(LES) is considered as a better simulation model. However, the sub-grid scale(SGS) models reported so far have not ascertained under what flow conditions the LES can lapse into the direct numerical simulation. To overcome this discrepancy, this paper develops a swirling strength based the SGS model to properly model the turbulence intermittency, with the primary characteristics that when the local swirling strength is zero, the local sub-grid viscosity will be vanished. In this paper, the model is used to investigate the flow characteristics of zero-incident incompressible turbulent flows around a single square cylinder(SC)at a low Reynolds number range Re ∈ [103, 104]. The flow characteristics investigated include the Reynolds number dependence of lift and drag coefficients, the distributions of time-spanwise averaged variables such as the sub-grid viscosity and the logarithm of Kolmogorov micro-scale to the base of 10 at Re = 2 500 and 104, the contours of spanwise and streamwise vorticity components at t = 170. It is revealed that the peak value of sub-grid viscosity ratio and its root mean square(RMS) values grow with the Reynolds number. The dissipation rate of turbulent kinetic energy is larger near the SC solid walls.The instantaneous factor of swirling strength intermittency(FSI) exhibits some laminated structure involved with vortex shedding.     

Nonlinear evolution of instabilities behind spheres and disks

We have performed precise and systematic experiments with PIV in order to measure the velocity field in the wake of a solid sphere and of a disk in a water channel, in the range of intermediate Reynolds number in which stationary and oscillatory instabilities appear, including the hairpin shedding regime. From these experimental data, we study the modal decomposition of the streamwise vorticity in an unsteady case and we describe the full nonlinear evolution of the bifurcating branches. We compare these results with recent theoretical and numerical studies on instability in the vortex shedding process at these intermediate Reynolds numbers.     

Two- and three-dimensional numerical simulations of the clap–fling–sweep of hovering insects

The importance of three-dimensional effects for flapping wings is addressed by means of numerical simulation. In particular, the clap–fling–sweep mechanism is examined. The flow at the beginning of the downstroke is shown to be in reasonable agreement with the two-dimensional approximation. After the wings move farther than one chord length apart, three-dimensional effects become essential. Two values of the Reynolds number are considered. At Re=128, the spanwise flow from the wing roots to the wing tips is driven by the centrifugal forces acting on the mass of the fluid trapped in the recirculation bubble behind the wings. It removes the excess of vorticity and delays the periodic vortex shedding. At Re=1400, vortex breakdown occurs past the outer portion of the wings, and multiple vortex filaments are shed into the wake.     

Simulation of cross-flow-induced vibration of cylinder arrays by surface vorticity method

The surface vorticity method (SVM), which is a fast and practical grid-free two-dimensional (2-D) method, and a fluid–structure interaction model incorporating the effects of cylinder motions and displacements is used to simulate the vortex-induced vibration of cylinder arrays at sub-critical Reynolds number Re=2.67×10⁴. The SVM is found to be most suitable for simulating a 2-D cylinder row with large-amplitude vibrations where the vorticity field and the fluid forces of the cylinder row change drastically, and the effect of the stream on the transverse direction vibration is very significant. The fluidelastic instability of a flexible cylinder row at small pitch ratio is also investigated, and the critical reduced velocity of the cylinder row at a reduced damping parameter S_G=1.29 is calculated, which is in good agreement with experimental and analytical results of the unsteady model. Vortex-induced vibration of a staggered cylinder array is simulated using different structural parameters. When the cylinders are relatively more flexible, the flow pattern changes dramatically and the fluid–structure interaction has a dominant impact on the flow field. Compared with grid-based methods, the grid-free SVM is a fast and practical method for the simulation of the FIV of cylinder arrays due to vortex shedding at sub-critical Reynolds numbers.     

Direct Numerical Simulation of a Square Jet Ejected Transversely into an Accelerating, Laminar Main Flow

A numerical simulation of a square jet ejected transversely into a laminar boundary-layer flow was performed at a jet-to-main-flow velocity ratio of 9.78 and jet Reynolds number of 6330. The jet consisted of a single pulse with a duration equal to the time required for the jet fluid to travel 173 jet widths. A strongly-favourable streamwise pressure gradient was applied to the boundary layer and produced a freestream acceleration that is above the typical threshold required for relaminarization. The results of the simulation illustrate the effect of the favourable streamwise pressure gradient on the flowfield created by the transverse jet. Notably, the horseshoe vortex system created upwind of the jet remains steady in time and does not induce noticeable fluctuations in the jet flow. The upwind and downwind shear layers of the jet roll-up through a Kelvin–Helmholtz-like instability into discrete shear-layer vortices. Jet vorticity in the upwind and downwind shear layers accumulates near the corners of the jet and produces two sets of vortex pairs, the former of which couple with the shear-layer vortices to produce large, counter-rotating vortices in the freestream, while the latter are unstable and periodically produce hairpin vortices in the main-flow boundary layer and elongated vortices in the freestream behind the jet. The departure of the jet flowfield from the vortical structures typically observed in transverse jets illustrates the substantive effect of the favourable streamwise pressure gradient on the flowfield created by the jet.     

Experimental investigation of a blunt trailing edge flow field with application to sound generation

The unsteady lift generated by turbulence at the trailing edge of an airfoil is a source of radiated sound. The objective of the present research was to measure the velocity field in the near wake region of an asymmetric beveled trailing edge in order to determine the flow mechanisms responsible for the generation of trailing edge noise. Two component velocity measurements were acquired using particle image velocimetry. The chord Reynolds number was 1.9 × 10⁶. The data show velocity field realizations that were typical of a wake flow containing an asymmetric periodic vortex shedding. A phase average decomposition of the velocity field with respect to this shedding process was utilized to separate the large scale turbulent motions that occurred at the vortex shedding frequency (i.e., those responsible for the production of tonal noise) from the smaller scale turbulent motions, which were interpreted to be responsible for the production of broadband sound. The small scale turbulence was found to be dependent on the phase of the vortex shedding process implying a dependence of the broadband sound generated by the trailing edge on the phase of the vortex shedding process.     

Separated flow structures around a cylindrical obstacle in a narrow channel

A detailed experimental study is performed on the separated flow structures around a low aspect-ratio circular cylinder (pin-fin) in a practical configuration of liquid cooling channel. Distinctive features of the present arrangement are the confinement of the cylinder at both ends, water flow at low Reynolds numbers (Re = 800, 1800, 2800), very high core flow turbulence and undeveloped boundary layers at the position of the obstacle. The horseshoe vortex system at the junctions between the cylinder and the confining walls and the near wake region behind the obstacle are deeply investigated by means of Particle Image Velocimetry (PIV). Upstream of the cylinder, the horseshoe vortex system turns out to be perturbed by vorticity bursts from the incoming boundary layers, leading to aperiodical vortex oscillations at Re = 800 or to break-away and secondary vorticity eruptions at the higher Reynolds numbers. The flow structures in the near wake show a complex three-dimensional behaviour associated with a peculiar mechanism of spanwise mass transport. High levels of free-stream turbulence trigger an early instabilization of the shear layers and strong Bloor–Gerrard vortices are observed even at Re = 800. Coalescence of these vortices and intense spanwise flow inhibit the alternate primary vortex shedding for time periods whose length and frequency increase as the Reynolds number is reduced. The inhibition of alternate vortex shedding for long time periods is finally related to the very large wake characteristic lengths and to the low velocity fluctuations observed especially at the lowest Reynolds number.     

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.     

Unsteady PTV velocity field past an airfoil solved with DNS: Part 1. Algorithm of hybrid simulation and hybrid velocity field at <Emphasis Type="Italic">Re</Emphasis> ≈ 10<Superscript>3</Superscript>

We develop a hybrid unsteady-flow simulation technique combining direct numerical simulation (DNS) and particle tracking velocimetry (PTV) and demonstrate its capabilities by investigating flows past an airfoil. We rectify instantaneous PTV velocity fields in a least-squares sense so that they satisfy the equation of continuity, and feed them to the DNS by equating the computational time step with the frame rate of the time-resolved PTV system. As a result, we can reconstruct unsteady velocity fields that satisfy the governing equations based on experimental data, with the resolution comparable to numerical simulation. In addition, unsteady pressure distribution can be solved simultaneously. In this study, particle velocities are acquired on a laser-light sheet in a water tunnel, and unsteady flow fields are reconstructed with the hybrid algorithm solving the incompressible Navier–Stokes equations in two dimensions. By performing the hybrid simulation, we investigate nominally two-dimensional flows past the NACA0012 airfoil at low Reynolds numbers. In part 1, we introduce the algorithm of the proposed technique and discuss the characteristics of hybrid velocity fields. In particular, we focus on a vortex shedding phenomenon under a deep stall condition (α = 15°) at Reynolds numbers of Re = 1000 and 1300, and compare the hybrid velocity fields with those computed with two-dimensional DNS. In part 2, the extension to higher Reynolds numbers is considered. The accuracy of the hybrid simulation is evaluated by comparing with independent experimental results at various angles of attack and Reynolds numbers up to Re = 10⁴. The capabilities of the hybrid simulation are also compared with two-dimensional unsteady Reynolds-Averaged Navier–Stokes (URANS) solutions in part 2. In the first part of these twin papers, we demonstrate that the hybrid velocity field approaches the PTV velocity field over time. We find that intensive alternate vortex shedding past the airfoil, which is predicted by the two-dimensional DNS, is substantially suppressed in the hybrid simulation and the resultant flow field is similar to the PTV velocity field, which is projection of the three-dimensional velocity field on the streamwise plane. We attempt to identify the motion that originates three-dimensional flow patterns by highlighting the deviation of the PTV velocity field from the two-dimensional governing equations at each snapshot. The results indicate that the intensive spots of the deviation appear in the regions in which three-dimensional instabilities are induced in the shear layer separated from the pressure side.     

3-D measurements of separated flow over rigid plates with spanwise periodic cambering at low Reynolds number

Measurements of the flow field around a flat plate and rigid plates with spanwise periodic cambering were performed using volumetric three-component velocimetry (V3V) at a Reynolds numbers of 28,000 at α=12° where the flow is fully separated. The Reynolds normal and shear stresses, and the streamwise, spanwise and normal components of the vorticity vector are investigated for three-dimensionality. Flow features are discussed in context of the periodic cambering and corresponding aerodynamic force measurements. The periodic cambering results in spanwise variation in the reversed-flow region, Reynolds stresses and spanwise vorticity. These spanwise variations are induced by streamwise and normal vortices of opposite directions of rotation. Moreover, measurements were carried out for the cambered plates at α=8°, where a long separation bubble exists, to further understand the behavior of the streamwise and normal vortices. These vortices become more organized and increase in strength and size at the lower angle of attack. It is also speculated that these vortices contribute to the increase in lift at and beyond the onset of stall angle of attack.     

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.     

Time resolved flow-field measurements of a turbulent mixing layer over a rectangular cavity

High Reynolds number, low Mach number, turbulent shear flow past a rectangular, shallow cavity has been experimentally investigated with the use of dual-camera cinematographic particle image velocimetry (CPIV). The CPIV had a 3 kHz sampling rate, which was sufficient to monitor the time evolution of large-scale vortices as they formed, evolved downstream and impinged on the downstream cavity wall. The time-averaged flow properties (velocity and vorticity fields, streamwise velocity profiles and momentum and vorticity thickness) were in agreement with previous cavity flow studies under similar operating conditions. The time-resolved results show that the separated shear layer quickly rolled-up and formed eddies immediately downstream of the separation point. The vortices convect downstream at approximately half the free-stream speed. Vorticity strength intermittency as the structures approach the downstream edge suggests an increase in the three-dimensionality of the flow. Time-resolved correlations reveal that the in-plane coherence of the vortices decays within 2–3 structure diameters, and quasi-periodic flow features are present with a vortex passage frequency of ~1 kHz. The power spectra of the vertical velocity fluctuations within the shear layer revealed a peak at a non-dimensional frequency corresponding to that predicted using linear, inviscid instability theory.     

Instantaneous structure and statistical feature of unsteady flow in a channel obstructed by a square rod

A two-dimensional numerical computation has been made for an unsteady flow in a channel obstructed by an inserted square rod. The results of the computation made for the flow with a parabolic inlet velocity profile at a specific value of channel Reynolds number are analyzed in detail. The obtained results reveal that momentum transfer is enhanced due to the apparent shear stress resulting from the nonzero value of cross-correlation between the streamwise and normal components of fluctuating velocity, , just as in turbulent shear flows, although the studied flow is quite different from turbulent flows in the sense that it is highly periodical and therefore free from randomness. This periodicity leads to a quick recovery of the velocity defect in some region of the wake of the rod. Special attention is paid to the time variation of flow structure. The crisscross motion of the Karman vortex previously found to occur is discussed again, and how it appears is explained in terms of the interaction between the Karman vortex and the disturbed wall shear layer. In the discussion of this relationship, wavering motion of the separation vorticity layers formed on both sides of the rod and the periodic formation of an isolated vortex island from the lifted tip of the wall vorticity layer are analyzed. The vortex island is found to play an important role not only for the occurrence of the crisscross motion of Karman vortex but also for the generation of the nonzero value of .     

Vortex dynamics mechanisms of separated boundary layer in a highly loaded low pressure turbine cascade

This paper investigates the vortex dynamics in the suction-side boundary layer on an aero-engine low pressure turbine blade at two different Reynolds numbers at which short and long laminar separation bubbles occur. Different vortical patterns are observed and investigated through large eddy simulation (LES). The results show that at the higher Reynolds number, streamwise streaks exist upstream of separation line. These streaks initiate spanwise undulation in the form of vortex tubes, which roll-up and shed from the shear layer due to the Kelvin–Helmholtz instability. The vortex tubes alternately pair together and eventually distort and break down to small-scale turbulence structures near the mean reattachment location and convect into a fully turbulent boundary layer. At the lower Reynolds number, streamwise streaks are strong and the separated flow is unable to reattach to the blade surface immediately after transition to turbulence. Therefore, bursting of short bubbles into long bubbles can occur, and vortex tubes have larger diameters and cover a part of the blade span. In this case vortex pairing does not occur and vortex shedding process is promoted mainly by flapping phenomenon. Moreover, the results of dynamic mode decomposition (DMD) analysis show a breathing motion as a source of unsteadiness in the separation location, which is accompanied by the flapping phenomenon.     

Closed-loop-manipulated wake of a stationary square cylinder

Vortex shedding from a fixed rigid square cylinder in a cross flow was manipulated by perturbing the cylinder surface using piezo-ceramic actuators, which were activated by a feedback hot-wire signal via a proportional–integral–derivative (PID) controller. The manipulated flow was measured at a Reynolds number (Re) of 7,400 using particle image velocimetry (PIV), laser-induced fluorescence (LIF) flow visualisation, two-component laser Doppler anemometry (LDA), hot wires and load cells. It is observed that the vortex circulation, fluctuating streamwise velocity, lift and drag coefficients and mean drag coefficient may decrease by 71%, 40%, 51%, 42% and 20%, respectively, compared with the unperturbed flow, if the perturbation velocity of the cylinder surface is anti-phased with the flow lateral velocity associated with vortex shedding. On the other hand, these quantities may increase by 152%, 90%, 60%, 67% and 37%, respectively, given in-phased cylinder surface perturbation and vortex shedding. Similar effects are obtained at Re=3,200 and 9,500, respectively. The relationship between the perturbation and flow modification is examined, which provides insight into the physics behind the observation.     

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.