Mixing and entrainment in the near field of turbulent round jets

In this work, a methodology based on the analysis of single-camera, double-pulse PIV images is described and validated as a tool to characterize fiber-dispersed turbulent flows in large-scale facilities. The methodology consists of image pre-treatment (intensity adjustment, median filtering, threshold binarization and object identification by a recursive connection algorithm) and object-based phase discrimination used to generate two independent snapshots from one single image, one for the dispersed phase and one for the seeding. Snapshots are then processed to calculate the flow field using standard PIV techniques and to calculate fiber concentration and orientation statistics using an object-fitting procedure. The algorithm is tuned and validated by means of artificially generated images and proven to be robust against identified sources of error. The methodology is applied to experimental data collected from a fiber suspension in a turbulent pipe flow. Results show good qualitative agreement with experimental data from the literature and with in-house numerical data.     

Coherent structures and wavepackets in subsonic transitional turbulent jets

A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of Re = 105, which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous exper-imental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent struc-tures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The m = 0, 1 modes have high coherence of near-field pres-sure for both jets, while the coherence of m = 0 modes is enhanced greatly by heating. Based on the coherent struc-tures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heat-ing would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.     

Large eddy simulation and self-similarity analysis of the momentum spreading in the near field region of turbulent submerged round jets

Self-Similarity in turbulent round jets has been the object of investigation from several decades. The evolution of turbulent submerged jets is characterized by the presence of two regions: the region of flow establishment, or near field region (NFR) and the fully developed region (FDR), or far-field region (FFR). The momentum spreading in the FDR is known to be self-similar and few mathematical models have been presented in the past to describe it. The flow evolution in the NFR has been rarely studied since there is a certain consensus on the idea that the flow in the NFR is not self-similar. In this work, we study the flow evolution of a turbulent submerged round jet by means of large eddy simulation (LES) at several Reynolds numbers ranging from 2492 to 19,988. Three new self-similar laws are proposed to describe the flow evolution in the NFR, one for the initial region, called Undisturbed Region of Flow, (URF), and two for the final region, the potential core region (PCR). The numerical results presented in this work are also validated with the self-similar laws for the FDR proposed by Tollmien (1926) and Görtler (1942), and the experimental data of Hussein et al. (1994), and Panchapakesan and Lumley (1993), in the FDR; those of Davies et al. (1963), in the PCR; and van Hout et al. (2018), in the URF. The conclusion is that previous inability to find the self-similarity law in the NFR is due to the attempt to find a unique self-similar variable to describe the momentum spreading in both the URF and the PCR.     

Flow field characteristics in the near field region of particle-laden coaxial jets

The effects of solid particles on the flow structure in the near field region of a coaxial water jet are investigated non-intrusively using molecular tagging velocimetry. Glass beads of 240 μm and specific gravity SG of 2.46 are used at three volume loadings of γ_v=0.03, 0.06, and 0.09% in the central water jet with a Reynolds number of 4.1×10⁴. Measurements are acquired for four annular to central jet velocity ratios in the range 0.11≤ U _o/U _i≤1.15 at downstream distances up to six inner jet diameters and the results are analyzed for the effects of solid particles on the characteristics of flow. It is found that the addition of particles does not affect the mean fluid velocity profile in this region. The results also indicate a small and moderate enhancement of axial turbulent velocity and radial gradients of velocity fluctuations, respectively, due to the presence of particles.     

Statistical analysis of the hydrodynamic pressure in the near field of compressible jets

This paper is devoted to the statistical characterization of the pressure fluctuations measured in the near field of a compressible jet at two subsonic Mach numbers, 0.6 and 0.9. The analysis is focused on the hydrodynamic pressure measured at different distances from the jet exit and analyzed at the typical frequency associated to the Kelvin–Helmholtz instability. Statistical properties are retrieved by the application of the wavelet transform to the experimental data and the computation of the wavelet scalogram around that frequency. This procedure highlights traces of events that appear intermittently in time and have variable strength. A wavelet-based event tracking procedure has been applied providing a statistical characterization of the time delay between successive events and of their energy level. On this basis, two stochastic models are proposed and validated against the experimental data in the different flow conditions     

The effects of acceleration in jets: kinematics of the near field vortices

Direct and large-eddy simulations (DNS/LES) of accelerating round jets are used to analyze the effects of acceleration on the kinematics of vortex rings in the near field of the jet (x/D < 12). The acceleration is obtained by increasing the nozzle jet velocity with time, in a previously established (steady) jet, and ends once the inlet jet velocity is equal to twice its initial value. Several acceleration rates (α = 0.02–0.6) and Reynolds numbers (Re _D = 500–20000) were simulated. Acceleration maps were used to make a detailed study of the kinematics of vortex rings in accelerating jets. One of the effects of the acceleration is to cause a number of new primary and secondary vortex merging events that are absent from steady jets. As the acceleration rate α increases, both the number of primary merging events between rings and the axial position where these take place decreases. The statistics for the speed of the starting ring that forms at the start of the acceleration phase for each simulation, agree well with the statistics for the “front” speed observed by Zhang and Johari (Phys Fluids 8:2185–2195, 1996). Acceleration maps and flow visualizations show that during the acceleration phase the near field coherent vortices become smaller and are formed at an higher frequency than in the steady jet, and their (mean) shedding frequency increases linearly with the acceleration rate. Finally, it was observed that the acceleration decreases the spreading rate of the jet, in agreement with previous experimental works.      

The near field behavior of turbulent gas jets in a long confinement

The present investigation reports on the near field behavior of gas jets in a long confinement and points out the differences between this type of jet flow and those of free jets and jets in a short confinement.The jet, with a diameter of 8.73 mm, is aligned concentrically with a tube of 125 mm diameter; thus giving a confinement area ratio of 205. The arrangement forms part of the test section of an open-jet wind tunnel and this gives a confinement length-to-jet diameter ratio of 1,700. Experiments are carried out with carbon dioxide, air and helium/air jets at different jet velocities. Mean velocity and turbulence measurements are made of the jet near field using a one-color, one-component laser doppler velocimeter operating in the forward scatter mode. In addition, the turbulent shear field of an air jet is examined in more detail using hot-wire anemometers.In view of the long confinement, the presence of the jet is not being felt immediately at the tunnel exit. Consequently, the air column inside the tunnel is first compressed by the jet and then slowly pushed out of the tunnel. This behavior causes the jet to spread rapidly and to decay quickly. As a result, an equilibrium turbulence field is established in the first two diameters of the jet. This equilibrium field bears striking similarity to that found in self-preserving, turbulent free jets and jets in short confinement and is independent of jet fluid densities and velocities. In terms of these characteristics, the near field of jets in a long confinement is very different from that found in free jets and jets in short confinements.     

The development of the large-scale structures in round impinging jets exiting long pipes at two Reynolds numbers

Measurements of the two-point and two-time correlation of the fluctuating wall pressure were performed in radial wall jets formed by impinging jets exiting a long pipe with Reynolds numbers of 23,300 and 50,000, and nozzle-to-plate distances of 2.0 diameters. The results from the two flows were compared to examine how the three-dimensionality and the development of the large-scale structures in the near field of the radial wall jet changed as the Reynolds number of the impinging jet varied. The measurements indicated that the large-scale structures were more two-dimensional, more periodic, and more prominent in the higher Reynolds number flow.This revised version was published online in November 2004 with corrections to the acknowledgement.     

Intermittency and stochastic modeling of hydrodynamic pressure fluctuations in the near field of compressible jets

The intermittent statistics of the pressure fluctuations measured in the near field of a compressible jet are investigated under several flow conditions. An experiment is carried out in a semi-anechoic chamber on a single stream compressible jet at Mach numbers varying from 0.5 to 0.9 and measuring the fluctuating pressure in several positions in the near field. The main quantities analyzed are the intermittent time and the energy amplitude of events that are extracted from the experimental data through a wavelet-based tracking algorithm. As an extension of a previous paper (Camussi et al., 2017), low order statistical moments (mean and variance) and Probability Distribution Functions are parametrized in terms of three relevant quantities characterizing the jet flow physics: the Mach number, the radial distance from the jet axis and the axial position. It is observed that the non-dimensional statistical quantities are weakly dependent upon the flow conditions allowing for simple stochastic models to be introduced on the basis of suitable fittings of averaged statistical properties and of the Probability Distribution Functions.     

Absolute instability in variable density round jets

This is a brief report on the properties of round jets of different densities issuing into the ambient air. Different densities were obtained by premixing helium and air in various proportions. We show that these jets have two types of behaviour depending on the density ratio between the jet and the ambient fluids, one characterized by very sharp peaks in the power spectral density of the velocity in the near field of the jet, and another with broadened and much less prominant spectral peaks. We examine the possibility that the first state corresponds to absolute instability, and the second to convective instability. It appears that the nature of instability can be changed from absolute to convective by very simple means reminiscent of similar possibilities in low Reynolds number wakes of circular cylinders. Flow visualization reveals that the low-density jets intermittently breakdown, and spread spectacularly, beyond a certain small axial distance.     

Coherent and random structure in reacting jets

Combustion rate and stability are strongly related to the interaction of fluid dynamics with the combustion process in reactive flow systems. The ability to control the combustion depends on the understanding of this interaction. This paper describes the use of the Planar Laser Induced Fluorescence (PLIF) technique to get insight into these processes, by looking at the coherent and random structures of a combusting jet. The coherent structures educed by phase-locked averaging are significantly different from instantaneous pictures, which are highly three dimensional. The PLIF images clarify the relationship between the large-scale structures and the generation of small-scale turbulence.     

Measurement of the turbulent diffusivity in the near field of variable density jets using conditional velocimetry

Pulsed laser Mie scattering and laser Doppler velocimetry (LDV), both conditioned on the origin of the seed particles, have been successively performed in turbulent jets with variable density. In the early stages of the jet developments, significant differences are measured between the ensemble average LDV data obtained by jet seeding and those obtained by seeding the ambient air. Careful analysis of the marker statistics shows that this difference is a quantitative measure of the turbulent mixing. The good agreement with gradient–diffusion modelling suggests the validity of a general diffusion equation where the velocities involved are expressed in terms of ensemble conditional Favre averages. This operator accounts for all events (including intermittent ones) and for variations in the density of the marked fluid whose velocity is still specified by the binary origin of the marker.List of symbols D_L laminar diffusivity, m²/s - D_T turbulent diffusivity, m²/s - d diameter of the jet nozzle, m - F_r Froude number - J diffusion vector, m/s - k global sensitivity of the detection system for one particle (signal level) - N_P number of seed particles in the probe volume - N_P,i number of seed particles in sample i - N_P⁽ⁱ⁾ value of N_P in channel i - N_B number of Doppler bursts - count rate of bursts, s^–1 - N_v number of validated Doppler bursts - count rate of validated bursts, s^–1 - N_id number of ideal particles - N_id* number of marked ideal particles - P* probability that an ideal particle be marked by a seed particle - P(z) probability density function for z, m³/kg - probability to have k seed particles in the probe volume - probability of having k seed particle conditioned on a given value of z - r radial coordinate, m - R =⁽¹⁾/⁽²⁾, density ratio - S₁ local signal level with jet seeding - S₁⁽¹⁾ reference signal level in pure stream 1 with jet seeding - s₁ = S_1/S₁⁽¹⁾, normalized signal - v_c volumic capacity of the probe volume, m³ - V velocity vector, m/s - V_x axial velocity component, m/s - V_r radial velocity component, m/s - V_P particulate velocity vector, m/s - V_Pj velocity vector of particle j, m/s - V_Pij velocity vector of the jth particle in sample i, m/s - V_i velocity vector of the marked flow for realization i, m/s - V_1,i velocity vector of the flow such it is marked in realization i by particles issuing only from stream 1, m/s - x axial coordinate, m - Y_i local mass fraction of species i - Z mixture fraction:local mass fraction of jet fluid - Z_i mixture fraction for realization iGreek local density, kg/m³ - _i local density for realization i, kg/m³ - ⁽¹⁾ density in stream 1 (density of the jet fluid), kg/m³ - ₁ time of flight of jet seed particles to reach the probe volume, s - _B duration of a Doppler burst, sAverages <A> ensemble average of A - Ā time average of A - Favre average, , ( ) the present notation is only due to printing problems - A Favre fluctuation,      

The role of vorticity in the near field development of sharp-edged,rectangular, wall jets

Experimental results on the near field development of a turbulent rectangular wall jet with aspect ratio 10 that issues from a sharp-edged orifice at Re_h ∼ 23,000 are presented and discussed, in comparison with results obtained in a free jet with identical initial conditions. Hot wire X-probe measurements on cross plane grids provide information on the 3D characteristics of the flow field. This work, besides presenting the main features of the jet, focuses on the effect of vorticity on the development of specific flow field characteristics. Mean vorticity components were estimated by interpolation and derivation from the mean and turbulent velocity measurements and the symmetries of the flow field were imposed by suitable averaging. Several terms of the axial vorticity equation are presented and discussed to uncover some complex flow physics, related e.g. to axis switching and the formation of a dumbbell shape of the jet outline, in the early stages of development.     

Similarity solutions of round jets and plumes

Theκ-εturbulence model,considering the effect of buoyancy on turbulentkinetic energy and its dissipation rate,is adopted to present a mathematical model forround plumes and jets.There are similarity solutions in the uniform environment.Taking into account the conservation of momentum and heat flux.Finite AnalyticMethod is applied to obtain the similarity functions of velocity,temperature andturbulent kinetic energy.The agreement between the calculated and experimental datais good.     

A visual study in the near field of turbulent jets and implications for estimating accidental discharges

A series of dye flow visualization experiments are carried out in water to study the visible flow features in the near field of turbulent jets and to assess their usefulness in estimating the discharge rate of a turbulent jet in a homogeneous medium. The jet Reynolds numbers are 0.3–2.2 × 10⁵. The large eddies at the core of the flow and the smaller eddies at the edge show disparate, independent length scales. Their convection speeds are more than an order of magnitude apart. Discharge rate estimates based on large-scale core features are useful. However, their reliability depends on a priori knowledge of the state of the bulk flow upstream of the discharge location. A useful method for estimating discharge rates based on the small-scale outer edge features is not obvious.     

Particle modulations to turbulence in two-phase round jets

The particle modulations to turbulence in round jets were experimentally studied by means of two-phase velocity measurements with Phase Doppler Anemometer （PDA）. Laden with very large particles, no significant attenuations of turbulence intensities were measured in the farfields, due to small two-phase slip velocities and particle Reynolds number. The gas-phase turbulence is enhanced by particles in the near-fields, but it is significantly attenuated by the small particles in the far-fields. The smaller particles have a more profound effect on the attenuation of turbulence intensities. The enhancements or attenuations of turbulence intensities in the far-fields depends on the energy production, transport and dissipation mechanisms between the two phases, which are determined by the particle prop- erties and two-phase velocity slips. The non-dimensional parameter CTI is introduced to represent the change of turbulence intensity.     

Mass and momentum transport in the near field of swirling turbulent jets. Effect of swirl rate

Local transport of the flow momentum and scalar admixture in the near-field of turbulent swirling jets (Re = 5,000) has been investigated by using a combination of the particle image velocimetry and planar laser-induced fluorescence methods. Advection and turbulent and molecular diffusions are evaluated based on the measured distributions of the mean velocity and concentration and the Reynolds stresses and fluxes. As has been quantified from the data, the flow swirl intensifies the entrainment of the surrounding fluid and promotes mass and momentum exchange in the outer mixing layer. A superimposed swirl results in the appearance of a wake/recirculation region at the jet axis and, consequently, the formation of an inner shear layer. In contrast to the scalar admixture, the momentum exchange in the inner shear layer is found to be strongly intensified by the swirl. For the jet with the highest considered swirl rate, a substantial portion of the surrounding fluid is found to enter the unsteady central recirculation zone, where it mixes with the jet that is issued from the nozzle. The contribution of the coherent velocity fluctuations, which are induced by large-scale vortex structures, to the turbulent transport has been evaluated based on triple decomposition, which was based on proper orthogonal decomposition analysis of the velocity data sets. For the considered domain of the jet with the highest swirl rate and vortex breakdown, the contributions of detected helical vortex structures, inducing pressing vortex core, to the radial fluxes of the flow momentum and the scalar admixture are found to locally exceed 65% and 80%, respectively.     

The stability of low Reynolds number round jets

Multigrid cross-correlation digital particle image velocimetry (MCCDPIV) is used to investigate the stability and structure of low Reynolds number axisymmetric jets. The in-plane velocities, out-of-plane vorticity and some of the components of the Reynolds stress tensor are measured. Two Reynolds numbers based on the orifice outlet diameter are examined (680 and 1,030) at two different positions: one close to the orifice, ranging from 2D ₀ to 5D ₀ (D ₀ is the orifice diameter); and the other further from the orifice, ranging from 10D ₀ to 14.4D ₀. The results show that the lower Reynolds number jet (Re=680) is marginally unstable in the near-orifice region and is best described as laminar. Further downstream some intermittent structures are observed in the jet, and the growth in integrated turbulent kinetic energy with axial position indicates that the jet is also unstable in this region. For the higher Reynolds number jet (Re=1,030) the increasing size and intensity of vortical structures in the jet in the near-orifice region observed from the MCCDPIV data and the growth in integrated turbulent kinetic energy indicate that the jet is unstable. Further downstream this jet is best described as transitional or turbulent. From flow visualisation images in the near-orifice region it seems that, for both Reynolds numbers, shear layer roll-up occurs when the jet exits the orifice and enters the quiescent fluid in the tank, resulting in vortical structures that appear to grow as the jet proceeds. This is indicative of instability in both cases and is consistent with previous flow visualisation studies of low Reynolds number round jets. Discrepancies observed between the flow visualisation results and the MCCDPIV data is addressed. On the basis of flow visualisation results it is generally assumed that round jets are unstable at very low Reynolds number, however the present work shows that this assertion may be incorrect.     

Evaluation of stochastic particle dispersion modeling in turbulent round jets

ODT (one-dimensional turbulence) simulations of particle-carrier gas interactions are performed in the jet flow configuration. Particles with different diameters are injected onto the centerline of a turbulent air jet. The particles are passive and do not impact the fluid phase. Their radial dispersion and axial velocities are obtained as functions of axial position. The time and length scales of the jet are varied through control of the jet exit velocity and nozzle diameter. Dispersion data at long times of flight for the nozzle diameter (7 mm), particle diameters (60 and 90 µm), and Reynolds numbers (10, 000–30, 000) are analyzed to obtain the Lagrangian particle dispersivity. Flow statistics of the ODT particle model are compared to experimental measurements. It is shown that the particle tracking method is capable of yielding Lagrangian prediction of the dispersive transport of particles in a round jet. In this paper, three particle-eddy interaction models (Type-I, -C, and -IC) are presented to examine the details of particle dispersion and particle-eddy interaction in jet flow.