Session Z37: Turbulence: Jets

2.5D turbulence in non-Newtonian jets

We study the transition from 3D to 2D turbulence in planar jets of a power-law fluid at low Reynolds number. We use direct numerical simulations, in which we change the width of the computational domain, thus constraining the turbulent scale. We observe that the jet transitions from 3D to 2D turbulence as we reduce the width of the domain in the spanwise direction. We find a configuration with the simultaneous coexistence of 2D and 3D (or 2.5D) turbulence for intermediate domains. The analysis of the power spectrum shows the traditional Kolmogorov’s scaling for 3D turbulence, and we identify the inverse cascade in 2D turbulence, where energy is fed back onto the large scales. Cases with 2.5D turbulence show the 3D turbulence scaling close to the inlet, where the jet is thin, while flow structures far from the inlet follow a 2D-like behavior, due to their larger size. The bulk statistics follow almost the same power-law scaling obtained for turbulent Newtonian planar jets, but cases with a strong 2D turbulence activity show a sudden increase of the jet thickness far from the inlet, due to the large size 2D vortices.

    

Budgets of Turbulent Kinetic Energy in heated and cold rectangular jets

This work presents the budgets of turbulent kinetic energy in rectangular supersonic jets for heated and cold conditions. The analysis is based on high fidelity Large Eddy Simulations where the subgrid scale turbulence is modeled using Wall-Adapting Local Eddy Viscosity model. The jet nearfield results are validated with PIV data from the literature and are in good agreement. The budgets are calculated in the entirety of the computational domain and reveal anisotropy in turbulence statistics. It is shown that production and dilatation terms are the significant contributors to the local TKE gain and loss respectively. Other mechanisms responsible for the TKE transport are also explained and account for the diffusion and dissipation. Among the factors contributing to diffusion, velocity fluctuations play a significant role followed by pressure-velocity fluctuations and molecular transport. Contributions from subgrid scale activity are also presented. The TKE asymmetry in rectangular jets is explained by directly computing all terms in budget equation through this work.   

Interscale/Interspace Energy Transfers at the Turbulent/Non-turbulent Interface

Turbulent dissipation results from interscale/cascade interactions across a wide range of turbulence scales and plays a central role in turbulent shear flow development, such as jet growth rate. In this study, we investigate interscale and interspace energy transfer mechanisms at the turbulent/non-turbulent interface (TNTI) in a temporally developing turbulent jet using data from our own direct numerical simulations. The TNTI is a very sharp interface at the edge of the jet which marks the dynamic border between rotational and irrotational flow regions. We follow the method based on the Karman-Howard-Monin-Hill equation initiated by Zhou & Vassilicos (2020) and calculate interscale and interspace energy transport rates at the TNTI, however unlike them we do it conditionally on interface characteristics such as TNTI position relative to the centreline, orientation, curvature and/or local propagation speed relative to the fluid. Curvature and folds are expected to play an important role on entrainment, TNTI propagation and longevity which, in turn, depend on interscale and interspace energy transfers at the TNTI's vicinity. In this study, we try to draw the link between the structure and evolution of the TNTI and the interscale/interspace energy transfer mechanisms.   

Cyclostationary analysis of periodically forced turbulent jets

The forcing of turbulent flows is ubiquitous, from airfoil drag reduction to jet noise suppression. However, the mechanisms by which the forcing alters the turbulence are poorly understood. Recently, various statistically based tools (for example, POD, SPOD) have been successfully employed to study the effect of the forcing on the turbulence in these flows. However, in many forced flows, in addition to the strong deterministic tonal response, the underlying stochastic turbulence is modulated by the applied forcing and thus deviates from the stationarity assumption invoked in these analyses. We explore several strongly periodically forced turbulent jets using the cyclostationary framework that, while used heavily in signal processing and mechanics, is relatively unknown by the turbulence community. The cyclostationary framework provides a natural extension that allows for the statistics to vary periodically in time. Using several cyclostationary tools, including the Wigner-Ville spectrum and degree of cyclostationarity measure, we investigate how the statistics are modified as a function of the phase of the forcing and to what degree forced turbulence is cyclostationary.   

Symmetry-induced high-moment turbulent velocity scaling laws of a spatially evolving turbulent round jet

A direct numerical simulation (DNS) of a spatially evolving turbulent round jet is conducted at Re₀ = 3500 in a very large box using a fully turbulent pipe flow as an inlet to analyze classical and new scaling laws from the near up to the far-field. This simulation couples a DNS of a turbulent pipe flow with a DNS of a turbulent jet flow. Furthermore, symmetry analysis is performed on the multi-point moment equations (MPME) to derive turbulent scaling laws up to statistical moments of arbitrary order n for a spatially evolving turbulent round jet. The analysis unveils that the scaling law exponents of the higher moments are only dependent on the exponents of the first and second moments. The validation of the scaling laws with the DNS data reveal that the decay constants grow exponentially with n and that the scaling laws are fully described by five parameters. Further investigations show that the normalized instantaneous axial moments up to the tenth order are extremely well represented by a Gaussian function of the radius η = r/z. The prefactors of these exponents show a non-linear behavior in n. This suggests the existence of a statistical symmetry which, if confirmed, can only be found in the MPME rather than in the Navier-Stokes equations alone.   

Effect of external turbulence on the entrainment and interface of axisymmetric jets

The effect of zero-mean-flow background turbulence on the topology of the scalar turbulent/turbulent interface (TTI) of a round jet is investigated and compared to the traditional turbulent/non-turbulent interface (TNTI) using planar laser-induced fluorescence. The intensity of the external turbulence, generated by a random jet array (RJA), is systematically varied by changing the distance between the RJA sheet and the jet exit. The TTI and TNTI outlines are detected by applying a low-magnitude threshold to high-Schmidt number scalar concentration fields. The thickness of the interfacial layer, as interpreted from the gradient of the conditionally averaged scalar profiles along the interface-normal coordinates, is an increasing function of the background turbulence intensity. Compared to the quiescent ambient, background turbulence leads to a ‘rougher’ interface, as is evident by its higher tortuosity, higher fractal exponent, and the lowered occurrence of zero-curvature surface elements. Lastly, the spatially averaged scalar skewness profiles indicate a net reduction in the entrainment rate into the jet in the presence of external turbulence.

    

A new scaling for turbulent, twin round jets

The flow field due to a pair of identical uniform round jets emerging from ports in a plane wall depend on the jet velocity U_j, port diameter d and port separation S.  At Reynolds numbers U_jd/ν that are O(1000) or larger, these jets will breakdown into turbulence.  The jets grow downstream and merge to have an elliptical cross-section that will develop into a single circular jet downstream.  From LES of such configurations at Re of 25 000, and 230 000 of two experiments, in close quantitative agreement,  over the range 2 ≤ S ≤ 8, we observed the mean axial velocity to rise to a peak U₀ at distance L₀ from the inflow plane wall, and thereafter to fall off smoothly.  U₀ decreases and L₀ increases with S.  For all nozzle spacings, a similar development was observed:  Scaled, configuration centerline velocity U_c/U₀ is a function of distance x/L₀ only, and is essentially independent of S/d and Re.   Since U₀ and L₀ linearly on inflow plane parameters, near-fields of all twin round jets can be predicted from one solution.   

Conditional statistics of the passive scalar field of an axisymmetric turbulent jet in the turbulent ambient

The dynamics of an axisymmetric turbulent jet in an approximately homogeneous isotropic turbulent ambient with no mean flow is studied experimentally. The passive scalar field of the jet is measured using the planar laser-induced fluorescence technique. The statistics are conditioned on the jet centroid and are compared to those of the jet in a quiescent ambient. A two-region model for the jet structure in the turbulent ambient is proposed, based on the conditional statistics. In the first region, the mean scalar properties are self-similar and self-preserving despite the external disturbance. The entrainment and the mixing of the jet are reduced compared to those in a quiescent ambient. In the second region, the jet structure is destroyed, and the width growth stops due to the cessation of the entrainment. The relative turbulence intensity between the ambient and the jet characterizes the transition between the two regions and the critical value of 0.5 indicates the onset of breakup.

    

On the coexistence of elastic and inertial regimes in viscoelastic turbulent jets

Jets and puffs are a simplified representation of many natural, biological and industrial flows. A striking example is the puff of air exhaled by an individual; the emitted breath carries a large number of small-size droplets of biological fluid, which are all potential virus carriers. The turbulent flow in the exhaled puff determines the dispersion of these droplets; understanding of the turbulent flow allowed for scientifically-grounded prevention guidelines. In our work, we use direct numerical simulations to study the dynamics of Newtonian and non-Newtonian turbulent round jets at relatively high Reynolds number. The non-Newtonian fluid is viscoelastic and is represented using an Oldroyd-B model. We are interested in how fluid elasticity modifies the flow; to this aim we consider viscoelastic fluids having different polymer relaxation times. We will report how the non-Newtonian contribution modifies the bulk jet statistics, as for instance the centerline velocity and jet thickness, and the turbulent flow. Turbulent kinetic energy power spectra show the contribution from the polymers: a new decay rate appears in addition to the classic $-5/3$ observed in Newtonian turbulence.