Instytut Podstawowych Problemów Techniki

Streszczenie:

Entrainment characteristics of a pure jet and buoyant jets in a stably-stratified ambient are compared with the help of laboratory experiments employing simultaneous particle image velocimetry and planar laser induced fluorescence techniques. For the buoyant jet, two cases of background stratification are considered, N = 0.4 s and 0.6 s, where N is the buoyancy frequency. Evolution of volume flux, Q, momentum flux, M, buoyancy flux, F, characteristic velocity, , width, , and buoyancy, with axial distance is quantified that helps in understanding the mean flow characteristics. Subsequently, two different methods are used for computing the entrainment coefficient, ; namely the standard entrainment hypothesis based on the mass conservation equation and energy-consistent entrainment relation proposed by van Reeuwijk and Craske (J Fluid Mech 782:333–355, 2015). It is observed that entrainment coefficient is constant for the pure jet ( 0.1) up until the point where the upper horizontal boundary starts to influence the flow. The entrainment coefficient for buoyant jets, , is not constant and varies with axial location before starting to detrain near the neutral layer. Near the source, 0.12 for both the values of N, while away from the source, N = 0.6 s exhibits a higher value of 0.15 in comparison to 0.13 for N = 0.4 s. During detrainment near the neutral layer, – 0.2 for N = 0.4 and – 0.3 for N = 0.6 . Importantly, close to the source, from standard entrainment hypothesis and energy-consistent relation are in reasonable match for pure jet and buoyant jets. However, far away from the source, the energy-consistent relation is ineffective in quantifying the entrainment coefficient in the pure jet and detrainment in buoyant jets. We propose ways in which the energy-consistent relation could be reconciled with standard entrainment hypothesis in the far-field region.

Słowa kluczowe:

Buoyant jet,Momentum,Buoyancy,Entrainment,Detrainment

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Streszczenie:

We report mean flow and turbulence characteristics of a buoyant jet evolving in a linearly stratified ambient with stratification strength ⁠. The velocity and density fields are captured experimentally using simultaneous particle image velocimetry and planar laser-induced fluorescence technique. We report our findings by strategically choosing four axial locations such that it covers different flow regimes; namely, momentum-dominated region, buoyancy-dominated region, neutral buoyant layer, and plume cap region. The results at these axial locations are presented as a function of the radial co-ordinate to provide a whole field picture of the flow dynamics. From the mean axial velocity and density fields, it is seen that the velocity and the scalar (density) widths are of the same magnitude in the momentum-dominated region but show significant difference in the buoyancy-dominated region and beyond. It is also seen that the axial velocity for the buoyant jet is consistently higher than pure jet at different axial locations due to buoyancy-aided momentum. With the help of turbulent kinetic energy (TKE) budget analysis, it is seen that the shear production (P) and TKE dissipation (⁠⁠) for a buoyant jet are higher compared to the case of pure jet at different axial locations, cementing the role of buoyancy and stratification on the flow dynamics. Further, it is observed that the buoyancy flux (B) aids and destroys TKE intermittently in the radial direction, and it is at least smaller than P, ⁠, and the mean flow buoyancy flux (F). Finally, the relative strength of the turbulent transport of momentum to that of scalar in the radial direction is quantified using the turbulent Prandtl number, ⁠. It is seen that   upto the neutral buoyant layer and 0.6 in the plume cap region. The current set of results obtained from experiments are first of its kind and elucidates various aspects of the flow which hitherto remained unknown and will also prove to be useful in testing numerical simulations for buoyancy-driven flows.

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Knowledge of turbulent mixing of pure jets and forced plumes in a stratified ambient is important for pollution mitigation, effluent discharge, and cloud dynamics. A fair number of experimental results on pure jets and forced plume in a uniform ambient are available in the literature. However, relatively fewer studies exist on the influence of stratification on the dynamics of a forced plume. The present study is an attempt to fill this gap by carrying out a detailed measurement and analysis directed at investigating the turbulence characterization and mixing behavior of a forced plume in a linearly stably stratified ambient with source Reynolds number, ℜ = W0D/ν = 3100, where W0 is the average flow velocity, D is the jet diameter, and ν is the kinematic viscosity. Stratification strength is characterized by the Brunt-Vaisala frequency N = √(−(g/ρb)[dρ/(dz)]), where dp/(dz) is the vertical density gradient, ρb is the bottom density, and g is the acceleration due to gravity. In this paper, results concerning the forced plume and its characteristic behavior in near- and far-field regions (z/D = 0-25) are presented. The mean and turbulence statistics of an evolving forced plume in a stratified ambient, with stratificiation strength N = 0.4 s-1, were measured using particle image velocimetry (PIV). The results are compared with that of a pure jet case (N = 0 s-1 and ℜ = 3100) to document the effect of stratification. From the experiments, some important results are as follows: (a) the centerline velocity decays at a lower rate in the case of a forced plume when compared to that of the pure jet, and it abruptly becomes zero in the neutral buoyant layer unlike the case of a pure jet where the centerline velocity keeps decreasing, (b) axial velocity for a forced plume in stratified ambient followed a Gaussian behavior, which is similar to that of pure jet, (c) the ambient stratification increases turbulence and mixing in a forced plume compared to a pure jet for the same source Reynolds number, due to the combined effects of buoyancy and initial momentum, and (d) turbulent kinetic energy and Reynolds stress were higher for the forced plume case due to the effect of buoyancy dominated momentum. The results from this study could be used as a test bed for validating numerical models related to shear-stratified flows.

Słowa kluczowe:

jet, forced plume, stratification, buoyancy frequency, Brunt-Vaisala frequency, turbulent kinetic energy, particle image velocitmetry

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The vertical release of a lighter buoyant fluid, commonly referred to as a forced plume, into dense environment is a common occurrence in ocean and atmosphere. Such releases may have heterogeneity in them in form of particles with varied size, shape, and volume fraction. Normally in field conditions, the particle size ranges from a few microns to millimetres, and the volume fraction ranges from %. In this study, the effects of low values of (corresponding to a two-way coupled system) on the dynamics and structure of a plume umbrella cloud formed in a linearly stratified ambient were examined. Spherical particles with mean diameter μ, density, , and were injected along with the lighter plume fluid. Due to the phenomena of “particle fall-out” and “particle re-entrainment”, it was observed that a plume trough characterized by radius, , and depth, , forms below the neutral buoyant layer of an umbrella cloud. The plume trough formation is linked to the draw-down of the fluid from the neutral buoyant layer by the sedimenting particles. This trough either sustains or collapses depending on the plume conditions at the source, namely, the diameter , fluid buoyancy, , vertical velocity, , and . In all the experiments, and were kept constant while and were varied. The experiments revealed that the sustaining and collapsing trough regimes could be qualitatively demarcated based on a source effective Richardson number, , that accounts for the combined effect of and . It was found that when , the plume trough collapses, otherwise it is sustained. However, failed to predict the variations in and and hence was unsuitable for quantifying the plume trough. Therefore, it was established that the characteristics of a plume trough (i.e. and ) depend independently on the particle volume fraction and source Richardson number , while the demarcation of the trough regimes could be done using . For a constant , with an increase in the trough radius, , was found to decrease. In contrast, increases for a sustaining trough and decreases for a collapsing trough. For a constant , a decrease in caused both and to increase irrespective of a sustaining or collapsing plume trough. Using equations of motion for sedimenting particles, an analytical expression for the trough radius, , was formulated that accurately explains the experimental results. A relation for trough radius, , that elucidates the dynamics of particle re-entrainment was also obtained. If a particle is within the value of it is re-entrained into the plume, otherwise settles at the bottom. These results provide useful information needed for modeling particle-laden forced plumes.

Słowa kluczowe:

Forced plume, Particles, Umbrella cloud, Richardson number, Plume trough

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Streszczenie:

This paper presents the results of laboratory experiments conducted to study the effects of varying ambient stratification strengths, characterized by the buoyancy frequency

Słowa kluczowe:

Buoyant plume,Buoyancy frequency,Maximum height,Spreading height,Mixing,Radial intrusion,Richardson number

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Streszczenie:

We present results of laboratory experiments conducted to study the evolution, growth, and spreading rate of a dispersed particle-laden plume produced by a constant inflow into a density varying environment. Particles having mean size, μm, density , volume fraction, 0–0.7 % , were injected along with the lighter buoyant fluid into a linearly stratified medium. It was observed that a particle-laden plume intruding at the neutral density layer is characterized by four spreading regimes: (i) radial momentum flux balanced by the inertia force; (ii) inertia buoyancy regime; (iii) fluid-particle inertia regime, and (iv) viscous buoyancy regime. Regimes (i), (ii), and (iv) are similar to that of a single-phase plume, for which . The maximum height, , for was observed to be consistently lower than the single-phase case. An empirical parameterization was developed for the maximum height for particle-laden case, and was found to be in very good agreement with the experimental data. In the inertia buoyancy regime, the radial spread of the plume, , for , advanced in time as which is slower compared to the single-phase plume that propagates at . Due to the presence of particles, ‘particle fall out’ effect occurs, which along with the formation of a secondary umbrella region inhibits the spreading rate and results in slower propagation of the particle-laden plume. The effect of particles on spreading height of plume, , and thickness of the plume, , were also studied, and these results were compared with the single-phase case. Overall from these experiments, it was found that the evolution, growth, and spread of dispersed particle-laden plume is very different from that of the single-phase plume, and presence of low concentration of particles () could have significant effects on the plume dynamics.

Słowa kluczowe:

Plume, Particles, Maximum height, Radial intrusion, Plume thickness

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