Session L11: Jets: Turbulent and Variable Density

Modeling Variable-Density Jets with Co-Flow Using BHR

The two-fluid jet in a co-flow has two similarity breaking features which make it more interesting, and challenging, than the simple self-similar jet. First, it transitions from strong jet to weak jet, and second, from shear driven to buoyancy driven. These two simultaneous mechanisms make it a strong test for a turbulence model. The Extreme Fluids team at Los Alamos National Laboratory has an on-going experimental campaign examining an $\text{SF}_{6}$ jet injected downwards into a co-flowing air stream. Using simultaneous PIV/PLIF they have obtained measurements of important turbulence quantities, including the Reynolds stresses, and the velocity-density correlations. In the current work, these measurements are used to validate the BHR turbulence model. The BHR model (Besnard et al., 1992) is a variable-density turbulence model similar to the LRR model for shear flows, but with additional transport equations for $\bar{\rho}a_{i}=\overline{\rho'u_{i}''}$ and $b=\overline{\rho'v'}$. Here we examine both the conventional model form, as well as a new version (Schwarzkopf et al., 2016) which include two length-scale equations: one for the dissipation scale, and one for the turbulent transport scale.   

Investigation of mean flow and turbulence for a variable-density jet near transition

Plumes can vary widely in size and speed in geophysical systems, with Reynolds numbers (Re) extending from thousands to billions. Concurrently, their densities also have significant deviations, resulting in Richardson numbers (Ri) from negligible levels to near one. To investigate a range of these flow conditions more closely, a laboratory-scale experiment considered helium jets exhausting into air. The tests considered Re from 1500 to 10000 and Ri magnitudes near 0.001, which encompasses a series of jet conditions near the exit, including laminar, transitioning, and turbulent flow. Using particle image velocimetry (PIV), instantaneous velocity fields were acquired, and these were used to determine the mean velocity, entrainment, and turbulent statistics. The laminar jet showed very little development or entrainment, with only minor fluctuations. Turbulent jets had rapid flow development, nearing fully-developed conditions earlier than similar non-buoyant jets. For the transitioning jet, the entrainment and turbulent stresses were significantly larger than even the fully turbulent jet, with axial normal stresses more than doubled. Examining the instantaneous flow fields, these increases coincided with large, non-axisymmetric eddies in the shear layer.   

Low-order Description and Conditional Averaging in a Transitional Variable-Density Jet

A vertically oriented jet is investigated using particle image velocimetry to identify characteristics of the flow that contribute to the distribution of turbulent kinetic energy and development of Reynolds shear stresses. Experiments with three different gases air, argon and helium| as the jet and a range of exit velocities were performed to allow for variety of the Reynolds and Richardson numbers. Five cases are examined in total. Proper orthogonal decomposition is applied to assess the energy distribution of all cases with respect to the number of modes. Reconstruction of the Reynolds shear stresses using 50\% of the total turbulent kinetic energy is performed. Quadrant analysis with respect to the Reynolds shear stress is also performed for insight into the entrainment of the jet. Reynolds shear stresses are dominant in Q1 - advancing ejections and Q3 - impeding entrainment and exhibit negligible contributions from the remaining two quadrants. POD is able to identify most dominant structures and transition effects within the basis. Via quadrant analysis, advancing ejection and impeding entrainment further describe the streamwise development of each jet.   

Eulerian and Lagrangian accelerations in the intermediate field of turbulent circular jets.

Particle tracking velocimetry is used to study the structure of various acceleration components, vorticity, and strain within the intermediate field of a circular jet at Re $=$6000. The total acceleration is decomposed into three sets: a) streamwise-radial; b) tangential-normal; and c) local-convective components. Probability density function (PDF) and joint PDFs of each set are characterized at various radial locations within a streamwise band contained within 16 and 17 pipe diameters. Results show that the acceleration components are described by two distributions; one of them exhibits symmetry and heavy tails, while the other is best fitted by a power-law type. The PDF tails are heavier with increasing the radial distance. The growing departure from the Gaussian distribution is a result of the comparatively increase in turbulence promoted by the mean shear of the jet. The variation of third and fourth moments between the streamwise-tangential and the radial-normal accelerations indicates the anisotropy of the jet. Although joint PDFs show distinctive distribution and depend on the distance from the jet core, the relative angles between the Lagrangian acceleration with velocity, vorticity and strain show similar PDF across radial distances.   

On the outer flow field and `episodic' entrainment in a round turbulent jet

We study a round turbulent jet at a Reynolds number of 2400 using Direct Numerical Simulation (DNS), with focus on the flow field outside the turbulent core and on its relevance to the entrainment process. Using DNS flow imagery, we present a detailed analysis of this outer flow field, which is found to exhibit considerable order in sub-regions whose location near the jet boundary varies with time. This order is shown to be largely governed, at any given time, by the vorticity field associated with elements of the coherent structures within the turbulent core at the time. This is particularly clear in the simpler cases, where the coherent vorticity on the core side of the boundary of the jet is (e.g.) of only one sign, and the instantaneous outer flow velocities are inversely proportional to the radial distance from an effective vortex center as required by the Biot-Savart relation. Interestingly, the outer flow velocities can be as high as more than a third of the mean centerline velocity. Such high velocities are shown to appear as part of strong inrush events, and their intermittent occurrence in space and time favors an episodic view of the entrainment process.   

High-speed imaging of submerged jet: visualization analysis using proper orthogonality decomposition.

In the present study, the submerged jet at low Reynolds numbers was visualized using laser induced fluoresce and high-speed imaging in a water tank. Well-controlled calibration was made to determine linear dependency region of the fluoresce intensity on its concentration. Subsequently, the jet fluid issuing from a circular pipe was visualized using a high-speed camera. The animation sequence of the visualized jet flow field was supplied for the snapshot proper orthogonality decomposition (POD) analysis. Spatio-temporally varying structures superimposed in the unsteady fluid flow were identified, e.g., the axisymmetric mode and the helical mode, which were reflected from the dominant POD modes. The coefficients of the POD modes give strong indication of temporal and spectral features of the corresponding unsteady events. The reconstruction using the time-mean visualization and the selected POD modes was conducted to reveal the convective motion of the buried vortical structures.   

Vortex structures in the near field of a transversely forced jet

We investigate the effect of transverse acoustic forcing on the formation of vortex structures in the near field of an axisymmetric jet using stereoscopic particle image velocimetry. The jet is placed at different locations between the pressure anti-node and node within a standing wave, and velocity and vorticity fields were measured in the $x-r$ plane. At the pressure anti-node, the jet response exhibited an axisymmetric mode, $m=0$, as harmonic fluctuations in pressure and the streamwise velocity components result in the periodic formation of vortex rings at the forcing frequency. As the jet was moved away from the anti-node, the shear layer roll-up and resulting vortex structures become increasingly asymmetric and three-dimensional due to time-varying spatial pressure gradients across the jet exit. The location where the transverse and streamwise velocity fluctuations were of equal magnitude coincided with sudden change in the jet response, characterised by shear layer roll-up and resulting vortex structures either side of the jet being in anti-phase. At the pressure node, harmonic transverse oscillations of the jet were observed forming vortices of equal circulation on either side of the jet in anti-phase. Meandering of the potential core was also observed.   

Effect of large density ratios on turbulence budgets in buoyant jets with coflow

Turbulence statistics and energy transport budgets have been measured in two fully turbulent jets with coflow at density ratios of $s=1.2$ \& 4.2 to improve our understanding of variable-density mixing in turbulent flows. The exit Reynolds number was matched for both flows at $\sim$20,000 and simultaneous planar PIV and acetone PLIF measurements were acquired so the coupled evolution of the velocity and density statistics could be examined in terms of density-weighted average quantities. Measurements were taken over 10,000 snapshots of the flow at three locations to assure statistical convergence, and the spatial resolution (288 $\mu$m) is well below the Taylor microscale. Variable-density effects caused changes in both the magnitude and distribution of the evolving turbulence, with differences most pronounced within the jet half-width. As the jet tends toward pseudo self-similarity, a new scaling based on effective diameter and density successfully scales the energy budgets of the two jets, but significant differences were still seen in the core. For the high density ratio jet, the turbulent kinetic energy production is negative on the centerline, as opposed to slightly positive, leading to large changes in advection and diffusion. A mechanism for these differences is proposed.