Session S07: Turbulence: Jets (5:45pm - 6:30pm CST)

A compressible Lagrangian flow in an incompressible turbulent water jet

A large-scale Lagrangian study based on Particle Tracking Velocimetry has been completed on an incompressible turbulent round water jet spreading freely into water with a Taylor-based Reynolds number $Re_\lambda \simeq 260$. A particular tracer seeding only in the core of the jet is used. Based on tracer velocities, the mean velocity field is computed and compared with the self-similar velocity field known through Eulerian measurements. This measured field, still self-similar, is the same for the axial velocity but presents important discrepancies for the radial velocity. Actually, because we are using a particular core seeding, the entrained part of the flow, which is mainly radial, is not completely tagged. Therefore discrepancies for the radial velocity are observed between the jet flow and the Lagrangian tracer flow. By taking into account this particular inhomogeneous seeding, a new divergence-free model is proposed and successfully gives the tracer velocity field. Finally a diffusive model is also proposed to obtain quantitative relations between compressibility, entrainment and turbulent fluctuations.   

Analysis of velocity gradient tensor in a turbulent planar jet with triple decomposition

Local turbulent motions are investigated with a triple decomposition, which decomposes a velocity gradient tensor into three components representing an irrotational straining motion, a rotating motion, and a shearing motion. Analysis based on the triple decomposition is applied to direct numerical simulation data of a temporally evolving incompressible planar jet. Averages of the norm of the decomposed tensors show that the shearing motion is dominant in the turbulent region, while fluid motions outside the jet comprise solely of the irrotational straining motion. Internal shear layers are detected with local maxima of the magnitude of the vorticity vector associated with the shearing motion. An averaged flow pattern around the shear layers shows that velocity rapidly changes across the shear layers, whose thickness is about 10 times the Kolmogorov scale. Moreover, a biaxial strain acts on the shear layers, where the direction of compression is perpendicular to the shear layers. It is confirmed that the Burgers vortex layer predicts well the relation between the shear layer thickness and the intensity of the biaxial strain. A comparison between the turbulent planar jet and homogeneous isotropic turbulence confirms that the velocity jump and thickness of the shear layer scale with Kolmogorov velocity and length scales in both flows.   

Entrainment in negatively buoyant jets and fountains

Turbulent negatively buoyant jets (NBJs) occur when the buoyancy of a jet opposes its initial momentum. A vertically aligned NBJ discharged from a round source will be decelerated by the opposing buoyancy force until its axial momentum is reduced to zero, reaching a stagnation point. Here the flow reverses direction and returns annularly towards the source, mixing with the opposing fluid and forming a fountain. The flow during the initial stage will be referred to as a `negatively buoyant jet', while the fully developed, quasi-steady, stage will be considered a `fountain'. The present experimental investigation uses 2D particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) to obtain data during both the NBJ and fountain stages, for source Froude and Reynolds numbers in the ranges $15\leq Fr_o\leq30$ and $4500\leq Re_o\leq 6000$. The study examines how classical integral models typically applied to jets and plumes can be used to describe fountains and NBJs, and we investigate different approaches to describing entrainment between the inner and outer flow regions.   

DNS of crossflow jet subject to a very strong Favorable Pressure Gradient

Incompressible jets transversely issuing into a spatially-developing turbulent boundary layer (SDTBL) is one of the most challenging types of three dimensional flows due to its fluid-dynamic complexity and technological applications; for instance, film cooling of turbine blades, chimney plumes and fuel injection. In this study, Direct Numerical Simulation (DNS) of a jet in a crossflow under different streamwise pressure gradients (zero and favorable pressure gradient, hereafter ZPG and FPG) is carried out. The goal is to accurately model the interaction between the wall-normal jet with the incoming SBTBL in order to examine the physics behind the thermal coherent structures in crossflow jets at different streamwise pressure gradients (ZPG vs. FPG) and velocity ratios (VR = 0.5 and 1). The analysis is performed by prescribing accurate turbulent information (instantaneous velocity and temperature) at the inlet of a computational domain for simulations of SDTBL. The methodology is based on the Dynamic Multiscale Approach (DMA) by Araya et al. (JFM, Vol. 670, pp. 581-605, 2011). The major effect of strong FPG on crossflow jets has been identified as a rapid damping process of the counter-rotating vortex pair system (CVP) and a more quickly recovery of the skin friction coefficient.   

Critical Point Identification and Classification Methods for Jets in Turbulent Crossflow

The complex interconnected vortex systems present in jets in cross-flow are important in understanding both the far-field development and entrainment. As identified in previous works, the presence of high turbulence intensity inflow increases the shear layer expansion and reduces the lee-side wake region where vortex systems are dominant. Stereoscopic particle image velocimetry data is collected in the $x-y$ plane of a jet (center-plane) for low ($3-5\%$) and high ($15-20\%$) turbulence intensity inflow. Critical point analysis is performed on each instantaneous flow-field and classified through the characteristic equation of the deformation tensor. Shear layer vortices are identified through the $q$-criterion and compared across cases. Statistics of changes in size and spread characterize the influence of inflow velocity and turbulence intensity. Critical points within the lee-side wake region are identified to identify changes to the unstable focus and wake region. Further characterization of all critical points through eigenvalues of the deformation tensor is used to identify changes in the interaction with turbulent inflow.   

Quantification of the spatial evolution of Eulerian and Lagrangian timescales within a turbulent jet

An experimental study of an axisymmetric jet was conducted to determine the dependence of statistical parameters and timescales on the axial and radial location. Particle tracking velocimetry techniques were implemented to create three component trajectories in three dimensional space. With the interrogation volume, ranging from the exit of the jet up to 50 diameters downstream in the axial direction, characterization of important parameters as the plume develops is achievable. Examination of the second-order structure function at various locations reveals strong dependence of the universal scaling constant on the axial and radial position within the jet. Analysis of the spatial and temporal velocity correlations provide the Eulerian and Lagrangian integral timescales, both of which are also functions of location. Further, these scales differ from one another, implying that the advecting flow affects the spatial and temporal large scale coherence in unique manners. Insight into these characteristics of the flow is relevant to the dispersion and transport phenomenon of the large scale dynamics within the jet.   

RANS-calibrated resolvent models of turbulent jets

For turbulent jets, resolvent modes computed using a linear eddy-viscosity model show quantitative agreement with structures educed using spectral proper orthogonal decomposition of large-eddy simulation (LES) data. To make these models predictive, the amplitudes of the resolvent modes and their correlations need to be determined. We pose an optimization approach where the coefficients are determined by matching first-order statistics available from Reynolds-Averaged Navier-Stokes (RANS) computations, with the ultimate aim of a fully RANS-based approach to predicting the dominant coherent structures. We examine such models for a Mach 0.4, isothermal, turbulent round jet at $Re=450,000$. For example, using only the turbulent kinetic energy (TKE) field from RANS, we find that a drastically reduced model (i.e. $10^1-10^2$ degrees of freedom) can correctly infer Reynolds stresses, and other quantities that are not directly available from RANS such as turbulence intensities and pressure fluctuations. We validate the latter quantities through comparison with LES data.   

Reynolds number effect on jet control and its scaling

This work aims to investigate experimentally the effect of Reynolds number \textit{Re} on the mixing effectiveness of a turbulent jet manipulated using a single unsteady radial minijet. A novel artificial intelligence (AI) control system has been developed to manipulate the turbulent jet. The \textit{Re }examined is 8000-50000 based on the time-averaged jet exit velocity $\overline {U_{j} } $ \begin{figure}[htbp] \centerline{\includegraphics[width=0.13in,height=0.19in]{030820201.eps}} \label{fig1} \end{figure} and the nozzle exit diameter $D$. The control parameters include the mass flow rate ratio $C_{m}$ of the minijet to main jet, the frequency ratio $f_{e}$/$f_{\mathrm{0}}$ of the minijet excitation frequency $f_{e}$ to the preferred-mode frequency $f_{\mathrm{0\thinspace }}$of main jet, the duty cycle $\alpha ,$ and the diameter ratio $d$/$D$ of the minijet to the main jet. Jet mixing is quantified using $K_{e}$/$K_{\mathrm{0}}$, where $K $is the decay rate of the jet centreline mean velocity, and subscripts $e$ and 0 denote the manipulated and unforced jets, respectively. Empirical scaling analysis of the AI-obtained experimental data reveals that the relationship $K_{e} = g_{\mathrm{1}}$ ($C_{m}$, $f_{e}$/$f_{\mathrm{0}}$, $\alpha $, $d$/\textit{D, Re, K}$_{\mathrm{0}})$ may be reduced to $K_{e}$/$K_{\mathrm{0}} \quad = \quad g_{\mathrm{2}}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.19in,height=0.17in]{030820202.eps}} \label{fig2} \end{figure} $(\zeta ),$ where $\zeta \quad = \quad \frac{\sqrt {MR} }{\alpha }\left( {\frac{d}{D}} \right)^{n}\frac{1}{Re}\left( {\frac{f_{e} }{f_{0} }} \right)^{m}$ ($n$ and $m$ are power indices) \begin{figure}[htbp] \centerline{\includegraphics[width=1.04in,height=0.28in]{030820203.eps}} \label{fig3} \end{figure} ,$\sqrt {MR} \equiv C_{m} \frac{D}{d}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.71in,height=0.23in]{030820204.eps}} \label{fig4} \end{figure} and $g_{\mathrm{2}}$ is approximately a linear function. The scaling law is discussed, along with the physical meanings of the dimensionless parameters $K_{e}$/$K_{0}$, $\zeta $, $\frac{\sqrt {MR} }{\alpha }\left( {\frac{d}{D}} \right)^{n}\frac{1}{Re}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.69in,height=0.27in]{030820205.eps}} \label{fig5} \end{figure} and $\left( {\frac{f_{e} }{f_{0} }} \right)^{m}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.33in,height=0.28in]{030820206.eps}} \label{fig6} \end{figure} .   

Exploring the anisotropy of a jet in cross-flow

Motivated by difficulties in accurately modeling volcanic plumes in the atmosphere, the anisotropic characteristics of an experimental scale jet in cross-flow are examined. Experiments were conduced on a round jet of air exiting a wind tunnel floor, varying the jet to cross-flow velocity ratio. Data are collected using a stereo PIV system allowing access to three components of velocity on a vertical plane oriented streamwise to the cross-flow, centered on the jet exit. Two data sets are collected with either a passive or active grid present at the wind tunnel inlet allowing for the effect of cross-flow turbulence intensity to be examined in two distinct regimes. With an aim towards informing model selection and flow specific parameter tuning, the anisotropy parameter $F$ is examined on radial profiles along the centerline. Identified areas of increased anisotropy are further explored via Anisotropy Invariant Mapping, which allows for the anisotropy tensor to be characterized by its invariants. The development in space of the state of anisotropy is used to refine coefficients in both linear and non-linear return to anisotropy models for the transport of anisotropy tensor.