Turbulent structure during transition to self-similarity in a round jet

 The developing turbulent region of a round jet was investigated using an improved implementation of digital particle image velocimetry (DPIV). The two-dimensional flow field in planes normal and parallel to the axial velocity was measured at locations between 15 and 30 diameters downstream, for two Reynolds numbers of 5500 and 16,000. The study consisted of instantaneous snapshots of the velocity and vorticity fields as well as measurements of velocity correlations up to third order. In this regime, the Reynolds number had a significant effect on both the instantaneous flow structure and the profiles of mean velocity across the jet. Coherent streamwise structures were present in the jet core for the lower Reynolds number. Additional structures whose evolution was governed by time scales two orders of magnitude larger than the convective scale inside the jet were observed in the entrainment field. The velocity correlations provided further support for the validity of DPIV turbulence measurements. The data was consistent with the equations of motion and momentum was conserved. DPIV measurements of turbulent kinetic energy components agreed with the hot-wire measurements of previous studies. Received: 27 November 1996/Accepted: 14 July 1997     

Experimental investigation of axisymmetric coaxial synthetic jets

Measurements were made in the near field of piston driven axisymmetric coaxial synthetic jets emanating from an orifice and a surrounding annulus of equal exit areas and cavity volumes. Piston velocity, amplitude, radial spacing between the orifice and the annulus, and exit angles had a strong influence on the dominant features of the flow. Flow visualization revealed three distinct topologies of the jet consisting of expanding, contracting and recirculating regions and doubling of the number of foci inside of the cavity compared to jet from the orifice alone. The direction of the swirl/rotation imposed on the mean flow was also dependent on the direction of the rotation of dominant foci. Interaction between flow from the orifice and the annulus amplified the azimuthal instability of ring vortices due to the periodic axial stretching and compression of the streamwise vortex filaments. Bifurcation of ring vortices into elliptical lobes reported earlier [S.V. Gaimella, V.P. Schroeder, Local heat transfer distributions in confined multiple air impingement, ASME Journal of Electronic Packaging 123 (3) (2001) 165–172] for single cavity jet was also observed in the coaxial jet. The number of cellular structures however was considerably larger than the single jet case. Large excursions of the jets from the plane of symmetry were observed. Power spectra exhibited sub-harmonic distribution of energy due to coalescence of the vortices. Growth of jet width and decay of centerline velocity were strongly influenced by the spacing and forcing frequency.     

Meandering jets in shallow rectangular reservoirs: POD analysis and identification of coherent structures

The effect of the shallowness on meandering jets in a shallow rectangular reservoir is investigated. Four meandering flows were investigated in an experimental shallow rectangular reservoir. Their boundary conditions were chosen to cover a large range of friction numbers (defined with the sudden expansion width). Due to the unsteady characteristics of the flows, a proper orthogonal decomposition (POD) of the fluctuating part of the surface velocity fields measured using Large-Scale Particle Image Velocity was used for discriminating the flow structures responsible for the meandering of the jet. Less than 1 % of the calculated POD modes significantly contribute to the meandering of the jet, and two types of instability are in competition in such a flow configuration. The sinuous mode is the dominant mode in the flow, and it induces the meandering of the flow, while the varicose mode is a source of local mixing and weakly participates to the flow. The fluctuating velocity fields were then reconstructed using the POD modes corresponding to 80 % of the total mean fluctuating kinetic energy, and the coherent structures were identified using the residual vorticity, their centres being localised using a topology algorithm. The trajectories of the structures centres emphasise that at high friction number the coherent structures are small and laterally paired in the near, middle and far fields of the jet, while with decreasing friction number, the structures merge into large horizontal vortices in the far field of the jet, their trajectories showing more variability in space and time. The analysis of the stability regime finally reveals that the sinuous mode is convectively unstable and may become absolutely unstable at the end of the reservoir when the friction number is small.     

POD analysis of flow structures in a scale model of a ventilated room

Measurements with particle image velocimetry have been carried out in a scale model of the Annex 20 room. Data were taken in a plane near the inlet. The flow consisted of a wall jet (Re=5,000) and a low-velocity region below the jet. POD was used to analyze dominant flow structures. The analysis showed that the flow some of the time has flow structures very different from the mean velocity field. A time-resolved data series was projected onto the orthonormal basis derived from the POD for analysis of the time variation of the POD amplitudes.     

Accuracy of tomographic particle image velocimetry data on a turbulent round jet

Tomographic particle image velocimetry (Tomo-PIV) was applied on a turbulent round air jet to quantitatively assess the accuracy of velocity gradients obtained in the self-similar turbulent region. The jet Reynolds number based on the nozzle diameter (d) was Re_d = 3000. Mean velocity, turbulent intensities, and Reynolds shear stress at the center plane of the jet were measured. In addition, statistical results of Tomo-PIV along the axial direction were assessed by performing a separate set of two-dimensional two-component PIV experiments on a “side view” plane along the jet axis. Moreover, the probability distribution functions of four components of the measured velocity gradients in the axial and radial directions were validated by these “side view” planar PIV data. The root mean square of the velocity divergence values relative to the norm of the velocity gradient tensor was 0.36. Furthermore, the on- and off-diagonal components of the velocity gradients satisfied the axisymmetric isotropy conditions. The divergence error in the data affected only areas with low gradient magnitude. Therefore, turbulent structures in the regions with intense vorticity and dissipation can be closely monitored. On this basis, the joint pdfs of the invariants of the velocity gradient and strain and rotation tensor rates were produced and compared well with those in isotropic turbulence studies.     

An investigation of forced structures in turbulent jet flows

In many cases, turbulence is superimposed on an unsteady organized motion of a mean flow. In the past, these turbulent flows have been studied by time or ensemble averaging methods and some decomposition techniques such as proper orthogonal decomposition (POD). In this study, a new decomposition technique called the turbulence filter will be used to decompose the forced turbulent jet flows. By using the turbulence filtering technique, the fluctuating (turbulent) part and the more organized (forced) part of the velocity field are analyzed. Within this context several experiments on organized turbulent jet flow have been carried out. In the experiments, variable frequency and amplitude oscillation are imposed on a 1D jet. An elliptical plate was used in order to obtain sinusoidal forcing. The axial distance, Reynolds number and the forcing frequency of the signal were varied. The multiple hot wires (six probes) were used to investigate the evolution of the signal along the radial distance. The obtained results of the turbulence filter are compared with those of phase-averaging and POD techniques. The eigenmodes of the data are also evaluated by using the POD method. Received: 31 July 1998/Accepted: 19 January 2000     

Effect of initial conditions on a circular jet

 Two circular jets are considered. One issues from a contraction with a laminar top-hat velocity profile. The other exits from a pipe with a fully developed turbulent mean velocity profile. In spite of the significantly different initial conditions, spectra of axial and radial velocity fluctuations in the far field (x≳30d, where d is the jet diameter) collapse over scales ranging from the Kolmogorov length scale to a length scale characterizing the organized motion. This agreement is consistent with the observation that, at the measurement station, the large-scale anisotropy is unchanged between the two flows. Received: 21 September 2000/Accepted: 5 March 2001     

Investigation on time scales in a low Reynolds number jet flow using particle-tracking velocimetry

The near flow field of an axisymmetric water jet at Reynolds numbers between 2000 and 5000 is investigated using Particle-Tracking Velocimetry. Measurements are taken in the longitudinal section (along the mean flow) and in cross-sections (orthogonal to the mean flow). From the former, correlation coefficients of the two in-plane velocity components in a Lagrangian framework are obtained: thus Lagrangian integral scales can be computed. Those of the streamwise velocity (axial) component increase on moving away from the centreline, whereas the opposite happens for the vertical velocity (radial) component: integral time scales of the two components are almost equal at the interface between jet and ambient fluids. On the other hand, integral scales are almost constant or increase slightly with the axial direction. In cross-sections, fluid ejection and injection from the jet centreline are observed to be connected to counter-rotating vortices (mushroom): their number and size change with Reynolds number in agreement with results from other authors. The maximum ejection velocity (orthogonal to the mean jet flow), at 3 nozzle diameters downstream of the outlet, is found to be one half of the mean outlet velocity.     

Structure detection and analysis of non-circular impinging jets in a semi-confined array configuration

The flow structure generated by circular and oblate shaped nozzles for an impinging confined 7-by-7 jet array is investigated. Instantaneous velocity fields, obtained from Digital Particle Image Velocimetry (DPIV) along the crossflow direction are analyzed using Proper Orthogonal Decomposition (POD). Also, a vortex detection algorithm is used to locate and quantify the nature of the instantaneous vortices within the flow. The results show that an oblate shaped nozzle when oriented with its major axis aligned with the exhaust flow has flow characteristics resulting in increased turbulent kinetic energy. This has potential for increased surface transport.     

Population,characteristics and kinematics of vortices in a confined rectangular jet with a co-flow

Vortex behavior and characteristics in a confined rectangular jet with a co-flow were examined using vortex swirling strength as a defining characteristic. On the left side of the jet, the positively (counterclockwise) rotating vortices are dominant, while negatively rotating vortices are dominant on the right side of the jet. The characteristics of vortices, such as population density, average size and strength, and deviation velocity, were calculated and analyzed in both the cross-stream direction and the streamwise direction. In the near-field of the jet, the population density, average size and strength of the dominant direction vortices show high values on both sides of the center stream with a small number of counter-rotating vortices produced in the small wake regions close to jet outlet. As the flow develops, the wake regions disappear, these count-rotating vortices also disappear, and the population of the dominant direction vortices increase and spread in the jet. The mean size and strength of the vortices decrease monotonically with streamwise coordinate. The signs of vortex deviation velocity indicate the vortices transfer low momentum to high-velocity region and high momentum to the low velocity region. The developing trends of these characteristics were also identified by tracing vortices using time-resolved particle image velocimetry data. Both the mean tracked vortex strength and size decrease with increasing downstream distance overall. At the locations of the left peak of turbulent kinetic energy, the two-point spatial cross-correlation of swirling strength with velocity fluctuation and concentration fluctuation were calculated. All the correlation fields contain one positively correlated region and one negatively correlated region although the orientations of the correlation fields varied, due to the flow transitioning from wake, to jet, to channel flow. Finally, linear stochastic estimation was used to calculate conditional structures. The large-scale structures in the velocity field revealed by linear stochastic estimation are spindle-shaped with a titling stream-wise major axis.     

Numerical study of unsteady flow and heat transfer of circular tangential direction jets flowing over the inner cylinder surface in the annular chamber

In order to understand the dynamics of vortices on heat transfer, the unsteady flow field of tangential direction jets flowing in the annular chamber is numerically investigated by scale-adaptive simulation (SAS). The jet Reynolds number is 332,000 based on the jet’s diameter and inflow velocity for a specific geometric model. The analogy theory is used to obtain the convective heat transfer coefficient distribution on the hub surface. Spectral analysis via fast Fourier transform (FFT) is used to analyze frequency information that flows inside the chamber. The proper orthogonal decomposition (POD) method is performed on the velocity field in the chamber and the convective heat transfer coefficient on the hub surface using a snapshot method. The fast Fourier transform helps find the dominant frequency of the unsteady flow in the chamber. The time sequence of velocity fields on the radial plane shows the presence of cyclic flapping of the jet. The proper orthogonal decomposition analysis indicates that the unsteady periodic flow phenomenon in the chamber and unsteady heat transfer on the hub surface are mainly related to the dynamics of the counter-rotating vortices caused by the jet.     

Measurements in the near flow field of an isosceles triangular turbulent free jet

The near field mean flow and turbulence characteristics of a turbulent jet of air issuing from a sharp-edged isosceles triangular orifice into still air surroundings have been examined experimentally using hot-wire anemometry and a pitot-static tube. For comparison, some measurements were made in an equilateral triangular free jet and in a round free air jet, both of which also issued from sharp-edged orifices. The Reynolds number, based on the orifice equivalent diameter, was 1.84×10⁵ in each jet. The three components of the mean velocity vector, the Reynolds normal and primary shear stresses, the one-dimensional energy spectra of the streamwise fluctuating velocity signals and the mean static pressure were measured. The mean streamwise vorticity, the half-velocity widths, the turbulence kinetic energy and the local shear in the mean streamwise velocity were obtained from the measured data. It was found that near field mixing in the equilateral triangular jet is faster than in the isosceles triangular and round jets. The mean streamwise vorticity field was found to be dominated by counter-rotating pairs of vortices, which influenced mixing and entrainment in the isosceles triangular jet. The one-dimensional energy spectra results indicated the presence of coherent structures in the near field of all three jets and that the equilateral triangular jet was more energetic than the isosceles triangular and round jets.     

Investigation of downstream and sideline subsonic jet noise using Large Eddy Simulation

The sound fields radiated by Mach number 0.6 and 0.9, circular jets with Reynolds numbers varying from 1.7×10³ to 4×10⁵ are investigated using Large Eddy Simulations. As the Reynolds number decreases, the properties of the sound radiation do not change significantly in the downstream direction, whereas they are modified in the sideline direction. At low Reynolds numbers, for large angles downstream from the jet axis, the acoustic levels are indeed remarkably lower and a large high-frequency part of the sound spectra vanishes. For all Reynolds numbers, the downstream and the sideline sound spectra both appear to scale in frequency with the Strouhal number. However their peak amplitudes vary following two different velocity exponents according to the radiation direction. The present observations suggest the presence of two sound sources: a Reynolds number-dependent source, predominant for large radiation angles, connected to the randomly-developing turbulence, and a deterministic source, radiating downstream, related to a mechanism intrinsic to the jet geometry, which is still to be comprehensively described. This view agrees well with the experimental results displaying two distinguishable components in turbulent mixing noise [1, 2].     

Flow behaviour of turbulent nozzle jets issuing from bevelled collars

An experiment was conducted to investigate turbulent, low-speed air jets issuing from bevelled and non-bevelled circular collared-nozzle configurations. The collar-to-nozzle expansion ratio used was three and Reynolds number was approximately 20,000. Detailed mean flow velocity fields and velocity spectra of the resultant jet flows at different collar lengths and bevel angles were evaluated using hot-wire anemometry along both axial and radial directions of the jets. Centreline velocity decay was shown to be augmented when either collar length or bevel angle was increased, with the collar length playing a more dominant role. Results also showed that bevelled collared-jets vectored towards the longer collar-length region, the extent to which was enhanced when the collar length or bevel angle was increased. The study demonstrated that a bevelled collar exit could be used as an additional control device on top of the collar length to achieve finer jet flow control in terms of jet momentum vectoring and asymmetric jet spread.     

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES) method at a Reynolds number Re = 8 500. The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric. The proper orthogonal decomposition(POD) analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1% of the turbulent kinetic energy, and hence their impact on the wake dynamics is studied. The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point. The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction. In addition, the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.     

Analysis and reconstruction of a pulsed jet in crossflow by multi-plane snapshot POD

In this work, snapshot proper orthogonal decomposition (POD) is used to study a pulsed jet in crossflow where the velocity fields are extracted from stereoscopic particle image velocimetry (SPIV) results. The studied pulsed jet is characterized by a frequency f = 1 Hz, a Reynolds number Re _j  = 500 (based on the mean jet velocity ${\overline{U}_{j}}$  = 1.67 cm/s and a mean velocity ratio of R = 1). Pulsed jet and continuous jet are compared via mean velocity field trajectory and Q criterion. POD results of instantaneous, phase-averaged and fluctuating velocity fields are presented and compared in this paper. Snapshot POD applied on one plane allows us to distinguish an organization of the first spatial eigenmodes. A distinction between “natural modes” and “pulsed modes” is achieved with the results obtained by the pulsed and unforced jet. Secondly, the correlation tensor is established with four parallel planes (multi-plane snapshot POD) for the evaluation of volume spatial modes. These resulting modes are interpolated and the volume velocity field is reconstructed with a minimal number of modes for all the times of the pulsation period. These reconstructions are compared to orthogonal measurements to the transverse jet in order to validate the obtained three-dimensional velocity fields. Finally, this POD approach for the 3D flow field reconstruction from experimental data issued from planes parallel to the flow seems capable to extract relevant information from a complex three-dimensional flow and can be an alternative to tomo-PIV for large volume of measurement.     

Swirling and Impinging Effects in an Annular Nonpremixed Jet Flame

The effects of swirl and downstream wall confinement on an annular nonpremixed flame were investigated using direct numerical simulation (DNS). Fully three-dimensional parallel DNS was performed employing high-order numerical methods and high-fidelity boundary conditions to solve governing equations for variable-density flow and finite-rate Arrhenius chemistry. Three swirl numbers have been examined: 0 (without swirl), 0.4 and 0.8, while the effects of downstream wall confinement have been examined for swirl numbers 0 and 0.4. Results have been presented in terms of instantaneous and time-averaged flow quantities, which have also been analysed using energy spectra and proper orthogonal decomposition (POD). Effects of swirl on the fluid dynamic behaviour of the annular nonpremixed flame were found to be significant. The fluid dynamic behaviour of the flame is greatly affected by the interaction between the geometrical recirculation zone (GRZ) near the jet nozzle exit due to the annular configuration, the central recirculation zone (CRZ) associated with swirl, the unsteady vortical structures in the jet column due to the shear instability, and the downstream wall confinement. Depending on the degree of swirl, the GRZ near the burner mouth and the CRZ may co-exist or one zone may be overwhelmed by another. At a moderate swirl number, the co-existence leads to a flame with strong reaction attached to the burner mouth; while at a high swirl number, the CRZ dominates over the GRZ. The precessing vortex core was observed to exist in the swirling flow fields. The Nusselt number distribution of the annular impinging flames differs from that of round impinging jets. The POD analysis revealed that wall effects on the flow field are mainly associated with the higher mode numbers.     

Performances of LES and RANS Models for Simulation of Complex Flows in a Coaxial Jet Mixer

Flow and mixing processes in a classical coaxial jet mixer have been investigated numerically. Calculations have been performed using three Large Eddy Simulation models and three unsteady RANS models. The time averaged mixture fraction and axial velocity, their rms values and energy spectra are compared with LIF and LDA measurements for both j- and r-modes of the jet mixer flow. A special attention is paid to the ability of different models to reproduce unsteady effects. The analysis demonstrates the superiority of the LES method with the dynamic mixed SGS model (DMM) with respect to other RANS and LES models.     

On coherent structures and mixing characteristics in the near field of a rotating-pipe jet

Mixing characteristics and coherent structures populating the near-nozzle area of a rotating-pipe jet at the Reynolds number of 5300 were studied by Large-eddy simulation (LES). The swirl rate, defined as the ratio of the tangential velocity of the inner pipe wall to the bulk axial velocity, varied from 0 to 1, corresponding to a weak-to-moderate swirl intensity, insufficient to induce reverse flow near the nozzle. The visualization shows that for the non-swirling jet the near-wall streaky structures generated in the pipe interact with the shear layer, evolving into hairpin-like structures that become tilted at low rotation rates. For higher swirl, they cannot be recognized as they are destroyed at the nozzle exit. No large-scale coherent structures akin to Kelvin–Helmholtz vortical rings in the ‘top-hat’ jets are identifiable close to the nozzle. Using the single and joint probability density functions of velocity and passive scalar (temperature) fields we quantify the events responsible for the intensive entrainment at various swirl numbers. The isosurface of the temperature field indicates the meandering and precessing motion of the rotating jet core at the axial distance of 6D downstream, where D is the diameter of the pipe. The Fourier analysis with respect to the azimuthal angle and time reveals an interplay between the co- and counter-rotating modes. These findings explain the previously detected but not fully clarified phenomenon of the weakly counter-rotating jet core at low swirl rates.