The dynamics of an axisymmetric turbulent jet in ambient turbulence interpreted from the passive scalar field statistics

Abstract

The effect of approximately homogeneous isotropic turbulence on the dynamics of an axisymmetric turbulent jet (Re = 10600 and 5800) in an ambient with a negligible mean flow is interpreted from the statistics of the passive scalar field. The ambient turbulence is generated by a random jet array and scalar concentrations are measured in orthogonal cross-sections of the jet using planar laser-induced fluorescence. Statistics of the scalar field of the jet in a turbulent ambient are compared to those in a quiescent ambient, using classical Eulerian averages and those conditioned on the jet centroid. A two-region model for the jet structure in ambient turbulence is proposed based on the centroidal statistics. Following the developing region of the jet, the ambient turbulence disrupts the jet structure, due to modulation of the jet interface, meandering of the jet by the large eddies and entrainment of the turbulent ambient fluid, resulting in a faster concentration decay and reduced entrainment compared to the quiescent ambient. Further downstream, once the ambient turbulence has destroyed the jet, only molecular and turbulent diffusion modify the scalar concentrations. The regions' relative lengths depend primarily on the relative turbulence intensity (ξ ) between the ambient and the jet, as assessed using the centroidal analysis, which removes the effect of the relative length scale (L ) on the jet behavior in the turbulent ambient. The centroidal scalar statistics reveal self-similarity and self-preservation in the mean scalar properties before jet break-up, which occurs abruptly once ξ > 0.5. The smaller scales of the ambient turbulence modulate the jet boundary and, when entrained lead to a wider range of centerline concentrations and, also rms concentrations, which are hypothesized to increase local concentration gradients within the jet and reduce the jet mixing. 42 velocity and the concentration. The rate of width growth is 43 increased (but less than the increase in the rate of decay of the 44 mean centerline properties) 8,[10][11][12]16 , while the mass flow rate 45 decreases. 11 Similarly, the velocity deficit in a wake decays 46 more quickly 17,18 and its width growth increases once the in-47 tegral scale of the ambient turbulence is larger than the width 48 of the wake. 19 49 The effect of the relative turbulence intensity and the rel-50 ative length scale between the ambient and the flow was ini-51 tially observed for boundary layers. 20 In wakes, the ambient 52 turbulence intensity is the dominant factor. 21,22 There is hy-53 pothesized to be little effect of the ambient turbulence on the 54 jet or plume flow close to the exit, where it is less intense 55 than the jet turbulence. However, its increasing impact with 56 downstream distance due to an increasing relative turbulence 57 intensity will result, at some point, in the break-up of the jet 58 and destruction of its structure. 9 After the jet structure is de-59 stroyed, a passive scalar will then only disperse due to detrain-60

On the scalar turbulent/turbulent interface of axisymmetric jets

“… (Sahebjam et al. 2022, also table 1), where the distances from the RJA to the jet centreline () were among those assessed by Perez-Alvarado (2016). This provided the velocity information of the RJA turbulence required to calculate the relative turbulence intensity and length scale between the ambient and the jet.…”

“…The values of increase with increasing relative turbulence intensity (figure 3 b ; also Perez-Alvarado 2016; Sahebjam et al. 2022), owing to external intermittency, induced by strong meandering, or the combination of external intermittency and the increased scalar fluctuations inside the jet due to the entrainment of external turbulence. Again, the conditional profiles should elucidate the mechanisms governing the increase of in a turbulent ambient.…”

“…Conditioning the average profiles relative to the distance from the interface accounts for the meandering path of the jet (Bisset et al 2002) and will, therefore, illustrate the importance of turbulent diffusion in increasing the concentration levels near the jet edge ( § 3.1). The values of φ rms increase with increasing relative turbulence intensity (figure 3b; also Perez-Alvarado 2016; Sahebjam et al 2022), owing to external intermittency, induced by strong meandering, or the combination of external intermittency and the increased scalar fluctuations inside the jet due to the entrainment of external turbulence. Again, the conditional profiles should elucidate the mechanisms governing the increase of φ rms in a turbulent ambient.…”

“…Reduced entrainment was later shown experimentally for a shallow jet in a co-flow (Gaskin, McKernan & Xue 2004) and more recently for momentum-driven and buoyant jets in approximately homogeneous turbulence (Khorsandi, Gaskin & Mydlarski 2013; Perez-Alvarado 2016; Lai, Law & Adams 2019). Sahebjam, Kohan & Gaskin (2022) proposed a two-region model for the evolution of a jet in approximately homogeneous turbulence generated by a random jet array (RJA) through a study of its centroidally averaged scalar field. The first region, albeit perturbed by the background turbulence (increased growth rate and concentration decay compared with the quiescent ambient), revealed self-preservation of the centroidally averaged first-order scalar statistics, whilst in the second region, the growth rate ceases and the jet is destroyed.…”

Effects of abundance, water temperature and light on the turbulence and mixing generated by fish schools of different sizes in quiescent water in a laboratory

“…The ratios of RMS velocity components, i.e., u rms /u i rms , v rms /u i rms andw rms /u i rms , are close to 1, which suggest that the turbulence generated by the fish is approximately isotropic for both abundances. The isotropy Homogeneity, isotropy and a negligible mean velocity are also characteristics of homogeneous isotropic turbulence with zero-mean flow, as generated in the laboratory using random jet arrays (Variano and Cowen, 2008;Khorsandi et al, 2013;Peŕez-Alvarado et al, 2016;Sahebjam et al, 2022) and oscillating grids (Hopfinger and Toly, 1976;Fernando and De Silva, 1993). However, the RMS velocities, Taylor-microscale Reynolds number and turbulence Reynolds number of the turbulent flow created by the fish are up to one order of magnitude smaller than those reported for the flows produced by random jet arrays and oscillating grids.…”