Helical-mode excitation of lifted flames using piezoelectric actuators

 Experiments of helical excitation using piezoelectric actuators on jet flows and lifted flames are performed to enhance the understanding of the effects of vortical structures of various instability modes on the stabilization mechanism of the lifted flame. In addition to the common ring and braid structures, five or seven azimuthal fingers (or lobes) can be identified in the transverse image of the jet near field. Excitation with various helical modes enhances the azimuthal structures and entrainment in the near field. When helically excited with the asymmetric m=1 mode, one of the fingers is enhanced and may evolve into a strong streamwise vortex. The streamwise vortices generated in the braid region between the adjacent ring vortices may enhance fuel-air mixing due to additional azimuthal entrainment upstream of a lifted flame when helically excited with the m=1 mode. Therefore, the streamwise vortex serves as an additional path of high probability of premixed flammable layer for the upstream propagation of the lifted flame so that the flame base on one side of the lifted flame may extend farther upstream and the flame base is inclined. In addition to the inclined flame base, multiple-legs phenomenon is also observed in the flame base, which is strongly associated with fingers of the helical modes of the jet flow. Received: 21 August 1997/Accepted: 24 January 1999     

Vortex dynamics of turbulence–coherent structure interaction

We study the interaction between a coherent structure (CS) and imposed external turbulence by employing direct numerical simulations (DNS) designed for unbounded flows with compact vorticity distribution. Flow evolution comprises (i) the reorganization of turbulence into finer-scale spiral filaments, (ii) the growth of wave-like perturbations within the vortex core, and (iii) the eventual arrest of production, leading to the decay of ambient turbulence. The filaments, preferentially aligned in the azimuthal direction, undergo two types of interactions: parallel filaments pair to form higher-circulation “threads”, and anti-parallel threads form dipoles that self-advect radially outwards. The consequent radial transport of angular momentum manifests as an overshoot of the mean circulation profile—a theoretically known consequence of faster-than-viscous vortex decay. It is found that while the resulting centrifugal instability can enhance turbulence production, vortex decay is arrested by the dampening of the instability due to the “turbulent mixing” caused by instability-generated threads. Ensemble-averaged turbulence statistics show strong fluctuations within the core; these are triggered by the external turbulence, and grow even as the turbulence decays. This surprising growth on a normal-mode-stable vortex results from algebraic amplification through “linear transient growth”. Transient growth is examined by initializing DNS with the “optimal” modes obtained from linear analysis. The simulations show that the growth of transient modes reproduces the prominent dynamics of CS-turbulence interaction: formation of thread-dipoles, growth of core fluctuations, and appearance of bending waves on the column’s core. At the larger Reynolds numbers prevailing in practical flows, transient growth may enable accelerated vortex decay through vortex column breakdown.     

Helical Structures in the Near Field of a Turbulent Pipe Jet

We perform a finely resolved Large-eddy simulation to study coherent vortical structures populating the initial (near-nozzle) zone of a pipe jet at the Reynolds number of 5300. In contrast to ‘top-hat’ jets featured by Kelvin-Helmholtz rings with the non-dimensional frequency S t≈0.3?0.6, no high-frequency dominant mode is observed in the near field of a jet issuing from a fully-developed pipe flow. Instead, in shear layers we observe a relatively wide peak in the power spectrum within the low-frequency range (S t≈0.14) corresponding to the propagating helical waves entering with the pipe flow. This is confirmed by the Fourier transform with respect to the azimuthal angle and the Proper Orthogonal Decomposition complemented with the linear stability analysis revealing that this low-frequency motion is not connected to the Kelvin-Helmholtz instability. We demonstrate that the azimuthal wavenumbers m=1?5 contain the most of the turbulent kinetic energy and that a common form of an eigenmode is a helical vortex rotating around the axis of symmetry. Small and large timescales are identified corresponding to “fast” and “slow” rotating modes. While the “fast” modes correspond to background turbulence and stochastically switch from co- to counter-rotation, the “slow” modes are due to coherent helical structures which are long-lived and have low angular velocities, in agreement with the previously described spectral peak at low S t.     

Reacting, Circular Mixing Layers in Transition to Turbulence

The evolution of a reacting, circular mixing layer - a model of round-jet flow - in its transition to turbulence was studied by direct numerical simulation. An economical Fourier pseudospectral method was combined with the third-order Adams-Bashforth scheme to integrate Navier-Stokes and scalar transport equations. The Reynolds number based on initial mixing-layer diameter and velocity difference was 1600. The initially thin mixing layer encloses a cylindrical core of fuel that mixes and reacts with the surrounding oxidizer. Both fast and finite-rate reactions were examined. The stages in transition are characterized by roll-up of the mixing layer into a sequence of vortex rings, pairing of adjacent rings, azimuthal instability, and breakdown to a disordered (turbulent) state. Reaction surfaces in the fast reaction limit become extended, folded and pinched off at various times corresponding to the dynamics of the vortices observed in the simulations. When the equivalence ratio is O(1) or smaller,the progress of reaction is determined by the dynamics of vortex rings. For larger ratios there is a qualitative difference: Initially, the flame is located well outside the rings and is relatively unaffected. Following breakdown to turbulence, there is a steep increase in flame surface area resulting in a noticeable change in fuel consumption rate. At smaller reaction rates (small Damkohler numbers), the reaction zones are diffuse and fill the vortical (mixed) regions. Product accumulates in and its presence raises the temperature of vortex cores, but reaction rates remain low due to low reactant concentrations. Reaction rates are highest in the braids between vortex rings where scalar dissipation rates and compressive strain rates show the highest values. This revised version was published online in July 2006 with corrections to the Cover Date.     

Large-Eddy Simulations of Forced Three-Dimensional Impinging Jets

Large-eddy simulations of the flow field around twin three-dimensional impinging jets were carried out to simulate the near-ground hover configuration of a vertical takeoff and landing (VTOL) aircraft. Both the impinging jet and the upwash caused by the collision of the wall jets are modeled in this study. The evolution of the vortical structures in the impinging jet flow field, due to the introduction of axisymmetric and azimuthal perturbations at the jet exit, has been investigated. The vortical structures formed in the jet shear layer due to azimuthal forcing, show significant three-dimensional vortex stretching effects when compared to the structures formed during axisymmetric forcing. Breakdown of the large-scale structures into smaller vortices also occurs much earlier during azimuthal forcing. When compared to the upwash formed during axisymmetric forcing, the azimuthally perturbed jet forms an upwash that is less coherent and results in a weaker upload or lift-off force on the aircraft undersurface. Comparison with available experimental data indicates good agreement for the centerline velocity decay, the wall pressure variation and the phase speed of the vortical structures.     

Mode spectra of natural disturbances in a circular jet and the effect of acoustic forcing

A modal spectrum technique was used to study coherent instability modes (both axisymmetric and azimuthal) triggered by naturally occurring disturbances in a circular jet. This technique was applied to a high Reynolds number (400,000) jet for both untripped (transitional) and tripped (turbulent) nozzle exit boundary layers, with both cases having a core turbulence level of 0.15%. The region up to the end of the potential core was dominated by the axisymmetric mode, with the azimuthal modes dominating further downstream. The growth of the azimuthal modes was observed closer to the nozzle exit for the jet with a transitional boundary layer. Whether for locally parallel flow or slowly diverging flow, even at low levels of acoustic forcing, the inviscid linear theory is seen to be inadequate for predicting the amplitude of the forced mode. In contrast, the energy integral approach reasonably predicts the evolution of the forced mode.     

The 3D Transition to Turbulence in Wake Flows by Means of Direct Numerical Simulation

The three-dimensional transition to turbulence in flows around bodies of non-rectangular configuration has been analysed physically by performing direct numerical simulation to solve the system of Navier-Stokes equations. The successive stages of 3D transition, beyond the first bifurcation, have been detected first in the incompressible regime, for a circular cylinder configuration. The generation of streamwise vorticity, organised according to spanwise periodic cells has been associated with the development of large-scale coherent spanwise undulations of the originally rectilinear (nominally 2D) alternating vortex rows. The wavelengths of these undulations have been determined as a function of Reynolds number. As this parameter increases, a further inherent change of the flow transition is obtained and analysed, the natural vortex dislocations pattern. Beyond this change, the increase of Reynolds number yields an abrupt shortening of the spanwise wavelength and the flow undergoes another transition step, whose critical Reynolds number is evaluated by the present DNS approach in association with the Ginzburg-Landau model. Therefore, the linear and non-linear parts of the flow transition have been quantified by means of the amplitude evolution versus time obtained by the present DNS, in conjunction with the mentioned global oscillator model. This revised version was published online in July 2006 with corrections to the Cover Date.     

Evolution analysis of the main mechanisms of the jet/vortex interaction

A new analysis method of the jet/vortex interaction is presented to better understand the effect of each vortical structure on the others composing the jet and even on itself. Vortical structures are isolated from each other and the velocity field they produce is calculated by means of the Biot–Savart law. The structure influence on each another is then distinguished from the others by using its velocity field in the calculation of the vorticity momentum equations. Based on 3D‐datafields provided by a large‐eddy‐simulation (LES) of the interaction between a Lamb–Oseen vortex and a turbulent round jet, a post‐processing tool educes the vortical structures and quantifies the different vorticity momentum equations terms. The study has been limited to the first steps of the interaction regime when there are still few vortical structures so that the subsequent analysis of the post‐process results remains simple enough to be performed. The present method confirmed the intensification of azimuthal structures as they roll up around the main vortex. Core disturbance of the latter was found to be initially caused by those structures and not by core dynamic instabilities, which become dominant with the appearance of non‐linear mechanisms. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental characterization of the instability of the vortex ring. Part I: Linear phase

The results of experiments performed to study the linear phase of the instability of vortex rings are presented. The experiments were performed in water. The vortex rings are generated by pushing water through the cylindrical nozzle of a pipe submerged in an aquarium. The experiments were made with the help of planar laser induced fluorescence as well as 2D2C and 2D3C particle image velocimetry. They show the straining field causing the instability, and for the first time experimentally the growth of a band of linear unstable modes. They also confirm previous studies concerning the shape of the instability and theories predicting the number of waves and the bandwidth of unstable modes. However, the measurement of the growth rate shows the influence of viscous damping, and consequently, the limit of the theories based on the hypothesis of an ideal fluid.     

Three-dimensional numerical simulation of a vortex ring impacting a bump

A vortex ring impinging on a three-dimensional bump is studied using large eddy simulation for a Reynolds number Re = 4 × 10⁴ based on the initial translation speed and diameter of the vortex ring. The effects of bump height on the vortical flow phenomena and the underlying physical mechanisms are investigated. Based on the analysis of the evolution of vortical structures, two typical kinds of vortical structures, i.e., the wrapping vortices and the hair-pin vortices, are identified and play an important role in the flow state evolution. The circulation of the primary vortex ring reasonably elucidates some typical phases of flow evolution. Furthermore, the mechanism of flow transition from laminar to turbulent state has been revealed based on analysis of turbulent kinetic energy.     

Direct Numerical Simulation of the Three-Dimensional Transition to Turbulence in the Incompressible Flow around a Wing

The onset of the secondary instability and the successive steps ofthe 3D transition to turbulence are examined in the flow around a wing of NACA0012 section, constant along the spanwise direction. The wing is placed in a uniform flow upstream, at 20° of incidence and at the Reynolds number of 800. The spanwise length is equal to four chords. The objectives of this study are the identification of the three-dimensional transition mechanism and the development of the early stages of turbulence in the present class of unsteady aerodynamic flows. A detailed processing of the DNS signals carried out by an appropriate conditional sampling allows the identification of the physical mechanisms related to the birth of turbulence and to the non-linear interaction with the 3D coherent structures in the near region.     

Instability of the flow around an impacting sphere

Results from an experimental and numerical study of the flow generated by a sphere immersed in fluid, impacting normally without rebound on a solid wall, are presented. The parameters are the running distance before impact and the sphere Reynolds number. For running lengths less than 7.5 diameters, the sphere wake before impact is axisymmetric in the form of an attached vortex ring. After impact, this ring overtakes the sphere and spreads out along the wall. For Reynolds numbers below 1000, the flow remains axisymmetric at all times. For higher values, perturbations of azimuthal wavenumbers 20–25 are observed on the vortex ring, leading to a breakdown of the flow. We analyse different hypotheses concerning the origin of this instability, with the conclusion that a centrifugal instability mechanism is likely to be acting in this flow. Comparisons are made with the flow involving an isolated vortex ring approaching a wall. Numerical simulations of this case have revealed that two distinct instability mechanisms are operating, one of which appears to be similar to the centrifugal instability observed for the sphere impact.     

Simulations of two-dimensional turbulence on the connection machine

The two-dimensional Navier-Stokes equations with a large scale instability of the Kuramoto-Sivashinsky type, describing marginally negative eddy-viscosity situations, is simulated on a Connection Machine CM-2. Up to millions of time steps at the resolution 256² and tens of thousands at the resolution 1024² are performed. A linear growth phase, a disorganized inverse cascade phase and a structured vortical phase are successively observed. In the vortical phase monopolar and multipolar structures are proliferating and display strongly depleted nonlinearities.     

Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble

The deformation and instability of a low-density spherical bubble induced by an incident and its reflected shock waves are studied by using the large eddy simulation method. The computational model is firstly validated by experimental results from the literature and is further used to examine the effect of incident shock wave strength on the formations and three-dimensional evolutions of the vortex rings. For the weak shock wave case (Ma?=?1.24), the baroclinic effect induced by the reflected shock wave is the key mechanism for the formation of new vortex rings. The vortex rings not only move due to the self-induced effect and the flow field velocity, but also generate azimuthal instability due to the pressure disturbance. For the strong shock wave case (Ma?=?2.2), a boundary layer is formed adjacent to the end wall owing to the approach of vortex ring, and unsteady separation of the boundary layer near the wall results in the ejection and formation of new vortex rings. These vortex rings interact in the vicinity of the end wall and finally collapse to a complicated vortex structure via azimuthal instability. For both shock wave strength cases, the evolutions of vortex rings due to the instability lead to the formation of the complicated structure dominated by the small-scale streamwise vortices.     

Continuous Mode Transition in High-speed Boundary-layers

Mode interaction is studied via direct numerical simulations of a Mach 4.5 boundary layer with discrete and continuous modes imposed at the inflow. An approximate decoupling procedure is developed to create separate vortical, acoustic and entropic continuous mode components. Oblique horizontal vorticity modes induce boundary layer disturbances that grow with downstream distance, similarly to their incompressible counterpart. One salient difference is that a low frequency vorticity mode, alone, is found to induce transition by spawning two-dimensional, unstable discrete modes. The discrete modes are non-linearly excited at high harmonics of the inlet perturbation. Adding a Mack second mode, in addition to the vorticity mode, causes even earlier transition, suggesting that, in supersonic flow, unstable discrete modes play a crucial role in breakdown of boundary-layer streaks.     

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.     

Obstacle-induced spiral vortex breakdown

An experimental investigation on vortex breakdown dynamics is performed. An adverse pressure gradient is created along the axis of a wing-tip vortex by introducing a sphere downstream of an elliptical hydrofoil. The instrumentation involves high-speed visualizations with air bubbles used as tracers and 2D Laser Doppler Velocimeter (LDV). Two key parameters are identified and varied to control the onset of vortex breakdown: the swirl number, defined as the maximum azimuthal velocity divided by the free-stream velocity, and the adverse pressure gradient. They were controlled through the incidence angle of the elliptical hydrofoil, the free-stream velocity and the sphere diameter. A single helical breakdown of the vortex was systematically observed over a wide range of experimental parameters. The helical breakdown coiled around the sphere in the direction opposite to the vortex but rotated along the vortex direction. We have observed that the location of vortex breakdown moved upstream as the swirl number or the sphere diameter was increased. LDV measurements were corrected using a reconstruction procedure taking into account the so-called vortex wandering and the size of the LDV measurement volume. This allows us to investigate the spatio-temporal linear stability properties of the flow and demonstrate that the flow transition from columnar to single helical shape is due to a transition from convective to absolute instability.     

Power-Spectral density estimate of the Bloor-Gerrard instability in flows around circular cylinders

There have been differences in the literature concerning the power law relationship between the Bloor-Gerrard instability frequency of the separated shear layer from the circular cylinder, the Bénard-von Kármán vortex shedding frequency and the Reynolds number. Most previous experiments have shown a significant degree of scatter in the measurement of the development of the shear layer vortices. Shear layers are known to be sensitive to external influences, which can provide a by-pass transition to saturated growth, thereby camouflaging the fastest growing linear modes. Here, the spatial amplification rates of the shear layer instabilities are calculated using power-spectral density estimates, allowing the fastest growing modes rather than necessarily the largest structures to be determined. This method is found to be robust in determining the fastest growing modes, producing results consistent with the low scatter results of previous experiments.     

Three-dimensional instability on the interaction between a vortex and a stationary sphere

We present direct numerical simulations of the interaction between a vortex ring and a stationary sphere for Re = 2,000. We analyze the vortex dynamics of the ring as it approaches the sphere surface, and the boundary layer formed on the surface of the sphere undergoes separation to form a secondary vortex ring. This secondary vortex ring can develop azimuthal instabilities, which grow rapidly as it interacts with the primary ring. The azimuthal instabilities on both rings are characterized by analysis of the azimuthal component decomposition of the axial vorticity.