Formation Of Vortical Structures Research Articles

Depletion of nonlinearity in two-dimensional turbulence

The strength of the nonlinearity is measured in decaying two-dimensional turbulence, by comparing its value to that found in a Gaussian field. It is shown how the nonlinearity drops following a two-step process. First a fast relaxation is observed on a timescale comparable to the time of formation of vortical structures, then at long times the nonlinearity relaxes further during the phase when the eddies merge to form the final dynamic state of decay. Both processes seem roughly independent of the value of the Reynolds number.

The Impact of Spinal Cord Nerve Roots and Denticulate Ligaments on Cerebrospinal Fluid Dynamics in the Cervical Spine

Cerebrospinal fluid (CSF) dynamics in the spinal subarachnoid space (SSS) have been thought to play an important pathophysiological role in syringomyelia, Chiari I malformation (CM), and a role in intrathecal drug delivery. Yet, the impact that fine anatomical structures, including nerve roots and denticulate ligaments (NRDL), have on SSS CSF dynamics is not clear. In the present study we assessed the impact of NRDL on CSF dynamics in the cervical SSS. The 3D geometry of the cervical SSS was reconstructed based on manual segmentation of MRI images of a healthy volunteer and a patient with CM. Idealized NRDL were designed and added to each of the geometries based on in vivo measurments in the literature and confirmation by a neuroanatomist. CFD simulations were performed for the healthy and patient case with and without NRDL included. Our results showed that the NRDL had an important impact on CSF dynamics in terms of velocity field and flow patterns. However, pressure distribution was not altered greatly although the NRDL cases required a larger pressure gradient to maintain the same flow. Also, the NRDL did not alter CSF dynamics to a great degree in the SSS from the foramen magnum to the C1 level for the healthy subject and CM patient with mild tonsillar herniation (∼6 mm). Overall, the NRDL increased fluid mixing phenomena and resulted in a more complex flow field. Comparison of the streamlines of CSF flow revealed that the presence of NRDL lead to the formation of vortical structures and remarkably increased the local mixing of the CSF throughout the SSS.

Wing performance and 3-D vortical structure formation in flapping flight

Numerical simulations of the three-dimensional flow around a modelled insect wing were performed to investigate the performance in flapping flight and to provide insight into the vortex dynamics and associated force generation. Different parameters relevant for three-dimensional flapping wing aerodynamics have been studied, notably the angle of attack in mid-stroke, the Rossby number, the Reynolds number and the stroke kinematic pattern. A parametric study has been made for these parameters, notably for the hovering flight regime. The leading-edge vortex is confirmed to be important for the gain in lift, it being larger and more stable at angles of attack larger than about 30°. At smaller angles of attack, the leading-edge vortex development is insufficient to increase the lift, instead the lift decreases. It is observed that the trend of the force development over the cycle and the effect of the angle of attack is similar for revolving and translating wings. However, a flapping wing motion with a revolving character has an important lift-enhancing effect, at a small penalty of drag. Although the variations in lift and drag with Reynolds number are found to be larger at lower Rossby numbers, the lift-enhancing effect of the revolving wing appears not strongly dependent on Reynolds number. Application of a ‘trapezoidal angle of attack’ pattern with increased angular rotation at stroke reversal showed a significant performance increase. It was further shown how the variation in lift and drag can be significantly influenced by introducing deviation in the stroke pattern. A comparison between the three-dimensional simulations and two-dimensional simulations (for forward flight conditions) displayed similar trends with respect to the influence of the angle of attack. However, the latter do not account for finite wing and tip vortex effects which were found to have an important impact on the LEV development.

Simulation and analysis of puffing instability in the near field of pure thermal planar plumes

The near-field unsteady behaviour of a buoyant plume is characterised by the puffing instability, which is a periodic formation of vortical structures (puffs) along the plume axis. In this study, a plume is generated from a finite-width fixed temperature planar source. The formation of puffs in the near-field is shown to be a result of the bulge forming instability in the lapping flow, which develops on the heated source region on either side of the plume axis. This paper reports on the three-dimensional direct numerical simulation of these near-field behaviours. The effect of the lapping flow velocity on the bulge forming instability is further investigated by modelling the boundary layer flow in the vicinity of the plume source by use of a channel flow with a heated floor section. The channel inlet velocity is controlled to vary the lapping flow velocity. The bulge formation is found to occur above a critical Reynolds number and below a critical Froude number, where the Froude number is defined as a measure of the lapping flow velocity. It is further found that with increasing Froude number the bulge forms further downstream, and there is the transition from a quasi-periodic to single periodic oscillation mode with a reduction in the oscillation amplitude.

Numerical investigations of a hydrogen impinging flame with different finite-rate chemical kinetic mechanisms

Large-eddy simulations (LES) of non-premixed hydrogen impinging flames using different chemical kinetics have been performed in this study. The work is mainly focused on the formation of vortical structures in the primary and wall jets, along with the analysis of heat transfer. The configuration corresponds to a laboratory hydrogen jet flame issuing from a circular nozzle which impinges on a downstream wall with a nozzle to plate distance of H/D=20. The numerical simulations were performed using the same subgrid scale model but different finite-rate chemical kinetic mechanisms. The results show appreciable differences in the predictions of vortex formation and near-wall heat transfer due to the influence of the chemical reactions on the flow field.

Analysis of Impinging Wall Effects on Hydrogen Non-Premixed Flame

Investigations of the flame–vortex and flame–wall interactions have been performed for hydrogen impinging non-premixed flame at a Reynolds number of 2000 and a nozzle-to-plate distance of 4 jet diameters by direct numerical simulation (DNS) and flamelet generated manifold (FGM) based on detailed chemical kinetics. The results presented in this study were obtained from simulations using a uniform Cartesian grid with 200 × 600 × 600 points. The spatial discretization was carried out using a sixth-order accurate compact finite difference scheme, and the discretized equations were advanced using a third-order accurate fully explicit compact-storage Runge–Kutta scheme. The results show that the inner vortical structures dominate the mixing of the primary jet for the nonbuoyant case, while outer vortical structures dominate over the inner vortical structures in the flow fields of the buoyant cases. The formation of vortical structures due to buoyancy has a direct impact on the flow patterns in both the primary and wall jet streams, which in turn affects the flame temperature and the near-wall heat transfer. It has been found that the buoyancy instability plays a key role in the formation of the much wider and higher value wall heat flux compared with the nonbuoyant case, while external perturbation does not play a significant role. The computational results show an increased wall heat flux with the presence of buoyancy.

Investigations of vortex formation in microbifurcations

The paper is dedicated to experimental studies and numerical simulations of viscous and viscoelastic flows in microchannels. The present work investigates separation phenomena and the formation of vortical structures in two microbifurcations with one closed branch: (1) Y-bifurcation with a square cross section and (2) T-bifurcation with trapezoidal sections and small aspect ratios depth/width. The main goal of the study is to characterize the dynamics of the vortex from the vicinity of Y-bifurcation and to emphasize the changes induced by the presence of elasticity on the local path lines. Velocity measurements and flow pattern visualizations of Newtonian fluid (deionized water) and weakly elastic polymer solution (low concentration of polyacrylamide in water) are obtained using a μPIV system. Numerical computations are performed in 2D and 3D flow configurations with the commercial FLUENT code. The Newtonian simulations offer very precise descriptions of the vortical structures for all flow regimes. In the case of polymer solution, the comparison between experimental data and numerical solutions for generalized Newtonian models prove the dominant role of elasticity in modifications induced on the vortical patterns in the analyzed microgeometries. The present topic is of great interest in developing novel microfluidic applications which require precise control of the hydrodynamics of viscoelastic fluids in the vicinity of complex geometries and patterned surfaces.

Particle image velocimetry measurements of vortex rings head-on collision with a heated vertical plate

We report particle image velocimetry measurements of the collision of a vortex ring with a heated wall kept at constant temperature. We consider the case when both the vortex ring and the thermal boundary layer generated by the vertical heated wall are stable and laminar prior to any interaction. The impingement process can be divided into two parts. (i) A ring-driven stage, where the vortex ring grows in diameter while approaching the wall and therefore it sweeps progressively an increased surface on the wall. (ii) A boundary layer-driven stage, where the vortex ring moves upward due to the thermal convective motion generated by the heated wall. In some cases, the head-on collision triggers the ring’s azimuthal instability as revealed by the formation of vortical structures arranged on a wavy starlike pattern and confirmed by flow visualizations. A single collision generates important velocity gradients and shear stresses along the wall accompanied with the creation of local vorticity normal to the vertical heated wall. Peak wall shear stresses occur near the point of impact of the vortex ring core.

Imaging of flame behavior in flickering methane/air diffusion flames

During this study, flow visualization through the use of imaging provided visual data of the events that occurred as the flame oscillated. Imaging was performed in two different ways: 1) the first method was phase-locked imaging to capture a detailed history by simply advancing the phase angle during each image capture, 2) the second method involved high-speed imaging to gather visual image data of a natural or forced oscillating flame. For visualization, two items were considered. The first one was the shape of the flame envelope as it evolved during one oscillation cycle. From the data gathered, it was confirmed that the flame stretched in the vertical direction before quenching in the region near its center. The second consideration was imaging of the oxidizer (air) in the region immediately outside the flame. This was done by imaging the laser light reflected from particles seeded into the flow, which revealed formation of vortical structures in those regions where quenching had occurred. It was noted that quenching took place primarily by the entrainment of fresh non-reacting air into the flame. The quenching process was in turn responsible for the oscillatory behavior.

Large-scale instability in a sheared nonhelical turbulence: Formation of vortical structures

We study a large-scale instability in a sheared nonhelical turbulence that causes generation of large-scale vorticity. Three types of the background large-scale flows are considered, i.e., the Couette and Poiseuille flows in a small-scale homogeneous turbulence, and the "log-linear" velocity shear in an inhomogeneous turbulence. It is known that laminar plane Couette flow and antisymmetric mode of laminar plane Poiseuille flow are stable with respect to small perturbations for any Reynolds numbers. We demonstrate that in a small-scale turbulence under certain conditions the large-scale Couette and Poiseuille flows are unstable due to the large-scale instability. This instability causes formation of large-scale vortical structures stretched along the mean sheared velocity. The growth rate of the large-scale instability for the "log-linear" velocity shear is much larger than that for the Couette and Poiseuille background flows. We have found a turbulent analogue of the Tollmien-Schlichting waves in a small-scale sheared turbulence. A mechanism of excitation of turbulent Tollmien-Schlichting waves is associated with a combined effect of the turbulent Reynolds stress-induced generation of perturbations of the mean vorticity and the background sheared motions. These waves can be excited even in a plane Couette flow imposed on a small-scale turbulence when perturbations of mean velocity depend on three spatial coordinates. The energy of these waves is supplied by the small-scale sheared turbulence.

COMBUSTION OF NORMAL AND LOW CALORIFIC FUELS IN HIGH TEMPERATURE AND OXYGEN DEFICIENT ENVIRONMENT

Combustion characteristics of two different gaseous fuels (a low calorific value fuel and methane fuel) have been examined using high temperature and low oxygen concentration combustion air. The momentum flux ratio between the fuel jet and the combustion airflow was kept constant to provide similarity in mixing between the different experimental cases to understand the role of fuel jet property on combustion. Direct flame photography, 2-D Particle image velocimetry (PIV), Light Emission Spectroscopy and chemiluminescent NOX analyzer was used as the diagnostics. These diagnostics allowed information on global flame features, mean and rms components of axial and radial velocity, axial strain rates and vorticity, the spatial distribution of combustion intermediate species, such as, OH and CH, and overall NOX emission levels. The results indicate a slower mixing during high temperature air combustion with low calorific value fuel as compared to methane fuel. The results showed higher turbulence levels and higher axial strain rates for low calorific fuel jets as compared to methane fuel jet during the high temperature air combustion condition. This results in less intense (or mild) combustion conditions with the result of increased flame length and volume and lower NOX emissions. Even for the normal methane fuel high temperature and oxygen deficient combustion conditions provided lower NOX emission. Furthermore, the high temperatures obtained for methane combustion provided lower vorticity and axial strain rates than the low calorific value fuel due to the suppression of vortical structure formation from the stronger heat release. In the case of low calorific value fuel, higher fuel jet velocity into low-density high temperature air leads to longer jet length. This jet causes a local stagnation to the upstream cross-flow to create local higher value of turbulence levels immediately upstream of the jet. The spatial distribution of the flame generated radicals (OH and CH) revealed significant ignition delay of the LCV fuel jet and a far more uniform distribution of the intermediate species. The methane fuel jet showed a prolonged reaction zone and faster ignition at high temperature and oxygen deficient conditions when compared to normal temperature air combustion of methane.

Review of Experimental Work in Biomimetic Foils

Significant progress has been made in understanding some of the basic mechanisms of force production and flow manipulation in oscillating foils for underwater use. Biomimetic observations, however, show that there is a lot more to be learned, since many of the functions and details of fish fins remain unexplored. This review focuses primarily on experimental studies on some of the, at least partially understood, mechanisms, which include 1) the formation of streets of vortices around and behind two- and three-dimensional propulsive oscillating foils; 2) the formation of vortical structures around and behind two- and three-dimensional foils used for maneuvering, hovering, or fast-starting; 3) the formation of leading-edge vortices in flapping foils, under steady flapping or transient conditions; 4) the interaction of foils with oncoming, externally generated vorticity; multiple foils, or foils operating near a body or wall.

Secondary Instabilities In Shock-inducedTransition To Turbulence

Richtmyer-Meshkovinstability(RMI)occurswhereveradensitygradientisimpulsively accelerated, e.g., by a shock wave. Misalignment between pressure and density gradients leads to baroclinic production of vorticity, the latter resulting in formation of vortical structures after the shock wave passage. The vortex-dominated evolutionof theflow eventuallyleads to turbulence.In the processof RMI-induced transition to turbulence, several secondary instabilities could develop in the flow, driven, e.g., by shear (Kelvin-Helmholtz) or by density-pressure gradient misalignment (secondary baroclinic instability). The exact nature of the secondary instabilities has been the subject of some discussion in the literature, with different authors observing shear-induced and baroclinic secondary instabilities. To resolve the issue, we have undertaken an experimental study of a Mach 1.2 shockaccelerated column of heavy gas (sulfur hexafluoride) immersed in a lighter gas (air). For visualization and quantitative analysis purposes, we use planar laserinducedfluorescence of acetone tracer pre-mixedwith the heavy gas, which makes it possible to resolve the small-scale (down to 12 microns) structure of the flow. Our observations of the RMI-driven flow around the gas column show the presence of two apparently distinct secondary instabilities: instability inside the vortex cores as well as the instability along the outer edge of the primary vortex spirals of the heavy gas. The former is consistent with the reports of baroclinic instability, while the latter is likely shear-induced.

Cyclic transition to turbulence in rigid abdominal aortic aneurysm models

The hydrodynamic stability of cyclic flows inside rigid abdominal aortic aneurysm (AAA) models was investigated. Rectified sine waveforms were used to simulate aortic flow conditions (Remean = 1600–2100 and α = 7.2–12.2). Depending on the bulge geometry (D/d and L/d ratios), AAA flows can be broadly classified into three regimes, namely types A, B and C, respectively. While type A has no vortex formation, type B and C have distinctive laminar vortical structures that are very different from one another. The type of flow regimes would also determine where and when the transition to turbulence would occur and the portion of the cycle at which the flow remains turbulent in the bulge. The stability characteristics of types B and C are obtained from the linear stability analysis performed on the unsteady velocity profiles measured at different phases of a cycle. Based on the linear stability analyses, instability is found to initiate in the bulge for types B and C through the formation of vortical structures. Instability grows progressively during the acceleration phase and transition to turbulence in the bulge occurs shortly after the commencement of the deceleration phase in all cases investigated. The mechanisms of transition to turbulence for types B and C are discussed. Although transition to turbulence appears in all the cases investigated here, fully laminar flows in types B and C are predicted to exist by the linear stability theory under extreme flow conditions. Finally, the in vivo biological implications of the in vitro results were discussed.

Experiments on stability and oscillatory behavior of planar buoyant plumes

Experiments on the onset of buoyant instabilities leading to periodic formation of vortical structures in planar buoyant plumes of helium and helium/air mixtures injected into quiescent air are reported for a range of nozzle widths (w=20–70 mm), plume fluid densities (pure helium to that approaching air), and velocities at the nozzle exit. First, the plume parameters corresponding to the onset of the oscillatory instability were experimentally determined by varying the nozzle exit velocity for different nozzle widths and plume fluid densities in two different nozzle configurations. These configurations corresponded to a freestanding rectangular nozzle and a rectangular nozzle surrounded by a flat plate in the plane of the nozzle exit. The observed plume behavior in the near field was characterized as nonoscillatory, transitional, or pulsatile. The onset of pulsations in the near field of these buoyant plumes (within a height of two nozzle widths) was best correlated in terms of the plume source Reynolds number and the plume fluid to ambient density ratio. It was also found that the boundary conditions surrounding the nozzle exit had an influence on the onset of plume instability in the near field. Specifically, at a given plume to the ambient density ratio, the plumes with flat plate surround were found to transition to the oscillatory state at a lower value of the threshold velocity and therefore are less stable than the plumes originating from freestanding nozzles. Subsequently, the plume oscillation frequencies were measured as a function of plume width, plume source velocity, and the density ratio for a range of these parameters. The plume oscillation frequency was found to correlate well in terms of the nondimensional parameters, Strouhal number, S=(fw)/Vp, and Richardson number, Ri=[(ρ∞−ρp)gw]/ρ∞Vp2, yielding a correlation S=0.55Ri0.45 determined for 1<Ri<102. This correlation is somewhat different from that of the axisymmetric buoyant plumes, which can be attributed to the differences in mixing rates and the strength of the local buoyancy flux in planar and axisymmetric plumes. The vortical structures formed in the unstable plumes also exhibit several distinct vortex pair modes. The centers of the formed vortex pairs, in general, do not remain colinear and distort with respect to each other when compared with the axisymmetric plume vortex rings, which are toroidal. The convection speeds of the vortex pair centers were also measured and reported in this study.

Flow-combustion interactions in the near field of high Damköhler number non-premixed exothermic jets

The flow in the near-field of high Damkohler number, exothermic planar jets is analyzed using highresolution two-dimensional simulations. The focus of the analysis is the experimentally observed, and yet unexplained, tendency of the flame to locate itself outside the region of vortical structures and to experience minimum convolution by them. The Lagrangian transport element method is used to resolve the unsteady and unaveraged post-transitional flow. The reacting field is represented by an infinite reaction rate model based on the Schvab-Zeldovich formulation. Results indicate that the flame behavior in the jet near field is controlled by the presence of a wake region just downstream the nozzle wall and the interaction of this region with combustion exothermicity. The wake region is contaminated by vorticity from the upstream boundary layers. This vorticity experiences a maximum away from the initial location of the flame that is constrained by the diffusion of the previously unmixed reactants. The region of most intense vorticity gets destabilized in a shear layer mode leading to the formation of vortical structures that, in the absence of exothermicity, convolute the flame. When exothermic energy is present, volumetric expansion pushes the flame and the developing shear layer away from one another, diminishing and delaying their interaction. This behavior is expected to become more pronounced with increasing combustion exothermicity and decreasing Reynolds number. The upstream physical arragement of the nozzle is also important because it controls the nature of the boundary layers. Finally, it is suggested that under most conditions, nonunity stoichiometry, preferential diffusion effects, and the presence of a weak coflow have a secondary impact on this phenomenon.

Control of 3D turbulent boundary layer separation caused by a wing–body junction

Abstract In three-dimensional flows, boundary layer separation leads to the formation of vortical structures formed by the rolling up of the viscous flow sheet previously confined in a thin layer attached to the wall. Several characteristics of the vortex flow development have negative effects; for example, it may be responsible for unsteadiness or generating unwanted vibration or noise. There are several ways to alter the properties of the vortex or to eliminate it as an organized structure. The objective of this paper is to present two different vortex control approaches. The first solution involves a modification of the pressure field induced by the obstacle by altering its geometry with a strake. The second solution, which can be called active control, consists of suction through an aperture located near the separation line. In this study, we have considered the incompressible three-dimensional boundary layer separation induced by an obstacle mounted perpendicular to a flat plate. The tests were conducted in the F2 subsonic wind tunnel of the ONERA Fauga-Mauzac center. The test section has a cross sectional area of 1.8 × 1.4 m2 and the upstream velocity of the flow was 50 m/s. The surface flow properties have been characterized by using a viscous coating which allows the visualization of the skin friction line patterns. The essential part of the study has been devoted to Laser Doppler Velocimetry (LDV) measurements. The plane of symmetric flow ahead of the leading edge has been qualified by using 3D laser velocimetry in the forward scatter mode. Results show that the geometrical extent of the separation region is reduced and the primary separation line is much closer to the model's leading edge when considering the configuration with a strake. Using an active control system, with suction through a hole located in the plane of symmetry in front of the obstacle's leading edge, the vortex size is reduced and its location displaced towards the origin of the obstacle.

Three-Dimensional Structure of Lifted, Turbulent-Jet Flames

Previous planar imaging measurements in lifted, turbulent jet flames provide evidence for the three-dimensionality of these flows and the importance of flame propagation in the azimuthal direction normal to the image plane. The primary objective of the present paper is to obtain data in a plane normal to the flow direction that will provide a better understanding of the three-dimensional features of the flow. In addition, the results of the previous measurements were limited to a Reynolds number of 7,000. imaging data at a Reynolds number of 12,100 will be presented to extend the previous findings to a higher Reynolds number regime. Images of the radial cross section in the low Reynolds number flame show that considerable asymmetry and structure exist. At upstream locations, the flame is typically not continuous around the circumference of the jet but consists of multiple flame segments. Farther downstream, the flame extends over a larger percentage of the circumference with breaks confined to smaller lengths along the circumference. The CH chemiluminescence images show numerous breaks in the flame sheet. These breaks coincide with outward bulges in the flame sheet that result from the formation of vortical structures in the jet shear layer. The images clearly show the three-dimensionality of the flow, since the breaks in the flame are localized to the area of the bulges and do not extend around the circumference of the central jet. Many of the same features found in the lower Reynolds number flame are also seen at the higher Reynolds number. Consistent with the larger turbulence scales existing farther downstream where this flame is stabilized, the flame surface is more convoluted and breaks in the flame sheet are more extensive. Rapid discontinuous jumps upstream by the flame are seen considerably more often than in the lower Reynolds number flame, which is indicative of the higher turbulence levels and greater three dimensionality of this flame.

Experimental studies on flow transition of a plane wall jet

SummaryFlow transition in the developing region of a plane wall jet is studied experimentally by means of hot-wire measurements. The Reynolds number, based on the jet exit velocity and nozzle exit height, varies from 3 x 102 to 3 x 104 in the investigations. The results indicate that the most important factor causing wall jet flow to change from the initial exit state to the final turbulent state is the rapid increase of turbulent intensity from the formation of vortical structures and their interactions with the wall. Data also shows that the transition process of the wall jet depends on the Reynolds number in the operating range. When the Reynolds number is greater than 2000, the mean velocity distribution of the wall jet changes directly from a top-hat profile at the nozzle exit to a turbulent profile in the turbulent developed region. When the Reynolds number is smaller than 2000, Glauert's laminar velocity profile is found between the nozzle exit and the turbulent region. It is also found that the transition will be delayed and the transition region prolonged with the decrease of the Reynolds number.

Flow visualization and the three-dimensional flow in an axial-flow pump

Surface flow visualization on an axial-flow pump results in patterns of the skin-friction lines on various surfaces and these patterns provide important insight into the topology of the three-dimensional flowfield. In particular, critical points and lines within the patterns give characteristics of three-dimensi onal separation and the formation of vortical structures. Here, oil-paint tests show the topology for the formation of horseshoe vortices, the structure of three-dimensional corner separation, the initial development of a rotor tip leakage vortex, and the development of other important secondary flows. Surface flow visualization can also provide information concerning boundary-layer transition. In summary, the surface flow visualization experiment presented in this article allows one to give a fairly detailed description of the complex flow within an axial-flow pump.