Session X44: Jets: General

Analysis of the Fractal Dimension of the Edge Boundary of a Helium Plume in Air During Laminar to Turbulent Transition

Schlieren imaging was used to observe the behavior of a metered helium plume as it transitioned from laminar to turbulent flow in an air environment. A high-speed camera was used to record the plume's behavior, edge position, and shape during transition. Jet Reynolds numbers were calculated for the plume as it transitioned from laminar to turbulent flow. Trends in the fractal behavior of the density fluctuations of the plume and edge characteristics were studied during transition as a function of Reynolds number. The spatially resolved fractal dimension of the density contours visualized in schlieren was estimated using pointwise mass methods, while the whole flow fractal dimension was estimated using box counting. The results gathered from the experimentation were used to validate estimates of turbulent kinetic energy (TKE) from correlated image velocimetry (CIV) based velocity extraction. CIV results for TKE in jet flow agree with jet behaviors in literature from CFD. Uncertainty in the fractal measurement due to limited image resolution prevents drawing strong conclusions on the spatial variation.   

Wake and thrust characteristics of low Reynolds number, parallel twin single-pulsed round jets

Individual single-pulsed jets are used for propulsion and locomotion by a number of aquatic animals such as squid and jellyfish. Although perhaps less known, some aquatic animals use arrangements of several pulsed jets for the same purpose. Salps and siphonophores form colonies that maneuver as a single organism by individually modulating their jet strength and timing. Arrangements of pulsed jets can therefore provide an alternative means of propulsion and maneuverability for aquatic vehicles. In general, we can define a pulsed jet as a fixed volume of fluid ejected through an orifice over a finite time interval on a periodic or aperiodic basis. In this work, we investigate the effect of interjet spacing and timing on the wake and thrust characteristics behind low Reynolds number (Re = 350), parallel twin single-pulsed round jets ejected from a wall. We conduct direct numerical simulations using the open source highly parallelized Xcompact3D solver (Bartholomew et al., 2020). The total thrust decreases as the interjet spacing is reduced due to the modification of the pressure field between the jets, as observed in the experimental work of Athanassiadis & Hart (2016). The generated vortex rings approach each other and decay throughout their streamwise evolution. By contrast, a vortex rebound effect is observed in the case of twin plane jets. Varying the interjet timing results in more complex vortex dynamics in the wake and induces a force couple at the wall that can be leveraged for rotational maneuvers.   

High-speed PIV measurements of the near-field of coaxial, round jets

A coaxial jet is characterized by two mixing layers, i.e. between inner and outer jet, and between outer jet and quiescent ambient. For a given nozzle geometry, the ratio between outer and inner jet velocities, r_u, as well as absolute jet exit velocities are important. They strongly affect the flow field and in particular the structure of vortices generated by wake and shear instabilities. Here, we measured the near-field flow dynamics of a coaxial, round water jet using high-speed particle image velocimetry (PIV). The inner and outer jets were issued from a long tube and a constant area annulus, respectively. Vortex generation, convection velocities, and vortex interaction between the mixing layers were studied. Measurements were performed for r_u = 0.66, 1, and 1.32 for which wake instabilities due to finite lip thickness become important. For each case, the dominating instability mode was investigated and spatial maps of governing Strouhal numbers indicated the extent of coherent vortices prior to their break-up. Vortex strengths and sizes based on instantaneous swirling strength maps are presented. In addition, mean velocity and Reynolds shear stress jumps across ensemble averaged instantaneous internal and external interfaces were determined.   

Water entry of spheres with entry-axis channels

In this study, we modify the classical water entry sphere by including impact axis channels that permit flow passage through the impactor center. Perturbations to the classical impactor are critical for aligning fundamental investigations with real-world use. Impactors begin as slightly hydrophobic phenolic resin spheres, which are made superhydrophobic with surface coatings. Through-channels have various diameters and inlet/outlet tapers. Flow through the channels creates a trailing jet behind the impactor. Interactions of the trailing jet with the cavity wall result in a shallower pinch-off with a smaller cavity due to a hastened pinch-off. In comparison with solid, intact spheres, impactors with channels suppress the formation of air-entraining cavities. We propose a drag model for the channeled impactors and observe that channeled impactors experience more drag than their intact counterparts, a result of shear in the channel and a modified stagnation surface.   

Hidden intermittency and a DNS of a turbulent round jet at a high Reynolds number

In experiments and simulations of turbulent round jets, similarity is observed primarily for the mean velocity. Using symmetry methods, we calculate similarity-type scaling laws for arbitrarily high moments of velocity from the infinite set of moment equations. Most centrally, symmetry theory provides moment-based scaling on instantaneous rather than fluctuation velocities. To prove its validity, a large-scale direct numerical simulation (DNS) of a turbulent jet flow was conducted at Re=3500 and a box length of z/D=75. As an inlet, a fully turbulent pipe flow is utilized to obtain similarity at small z. Nearly perfect similarity is observed in the z/D=25−65 range and this is especially true for U_z-moments up to order n=10. In matching theory and DNS data, we found that U_z-moments show Gaussian-like curves that get increasingly narrower with n, and this n-dependence is non-linear. The two statistical symmetries describing non-Gaussianity and intermittency, which were central for high-order moments in near-wall turbulence, are broken for turbulent jets. Instead, we find a new statistical symmetry, which, like the other two, is also based on the linearity of the moment equation.   

A Theory of Turbulent Jets Via Lie Symmetry Analysis

A theory of turbulent jets (plane --TPJ, and axisymmetric -- TAJ) is developed using Lie symmetry analysis (LSA) resolving failings of current theories -- due to inappropriate application of boundary layer approximation. Applying LSA with translational and dilatational transformations to the Navier-Stokes equations yields a new family of scaling laws for key flow measures: mean streamwise and lateral velocities U and V , Reynolds shear stress R=〈-u'v'〉, mean pressure P, etc. In comparison to classical theory, we find that TPJ spreads more slowly with streamwise coordinate x, and TAJ spreads faster; and whereas classically△P=P-P_∞ = 0 (P_∞ -- ambient), our theory predicts a pressure deficit △P= -〈v' ²〉< 0 (also experimentally observed). Consequently, the total streamwise momentum flux J_T  increases with x, i.e., J_T (x) >1 – a condition that all jet flows must satisfy. Trivially, the pressure deficit integral across the jet is balanced by a commensurate increase in J_T . Most experiments and theories fail this condition. Those experiments showing J_T >1  also validate many of our predictions, including profiles of U, V and R which match measurements well in both jets. In TPJ, we predict: b∼x^0.91 (half-width), Q_m ∼x^0.52 (mass flux), J_T ∼x^0.13,  and  centerline  U_c ∼x^-0.39 ,V_c ∼x^-0.48 and R_c ∼x^-0.87. In TAJ: b∼x^1.23, Q_m ∼x^1.34, J_T ∼x^0.22, U_c ∼x^-1.12, V_c ∼x^-0.89, R_c ∼x^-2.01. Rigorously designed and accurately measured free jet experiments and simulations, and deeper explanation of the mechanisms involved, are clearly needed.   

Azimuthal acoustic modes and their impact on an axisymmetric jet

An experimental study is conducted to investigate the impact of azimuthal acoustic forcing on an axisymmetric jet. Understanding the effect of such asymmetric forcing is crucial, as it emulates conditions in annular combustion chambers such as gas turbines or jet engines, where coupling between the unsteady heat release and acoustic waves propagating azimuthally as travelling or standing modes, can have a destructive effect. While various studies have investigated the effect of axisymmetric forcing, those studying the impact of asymmetric azimuthal forcing are minimal. Recently, the response of a jet placed in a standing azimuthal acoustic wave oriented normally to the jet was investigated and jet bifurcation into two or more momentum streams was observed. Here, the effect of travelling azimuthal acoustic waves on the jet development is investigated. To this effect, a novel experimental rig was commissioned and characterized. The jet was also subjected to axisymmetric forcing at the preferred mode. Flow visualization and planar PIV were used to discern the jet's structure and evolution. Preliminary results will be presented to show the changes of the jet's spreading rate in the far field. Instantaneous snapshots will also be used to understand both the jet's spreading rate and its orientation, which in similar studies have been shown to strongly depend on the phase of the azimuthal forcing and induced axisymmetric jet modes.   

Additives influence thermocavitation-induced microjets

The study of thermocavitation jetting is relevant for several applications, including needle-free injection and 3D printing. A laser focused on the closed end of a glass microchannel filled with liquid induces cavitation (bubble growth and collapse) and forms microjets traveling outside the microchannel. The maximum bubble size is proportional to the amount of absorbed optical energy and also depends on the liquid filling volume. We studied a nozzle-free rectangular channel that can produce jets with distinct shapes and breakup behaviour. The interplay between instabilities such as axis-switching, bubble collapse, and capillary instability led to a slender jet of ~50 µm diameter and ~17 m/s velocity, which was identified as suitable for needle-free injection and investigated further. We also tested solutions of three different types of additives: surfactants, viscous, and viscoelastic additives of varying concentrations to assess their influence on the formation and breakup of the jet. We observed that viscous and viscoelastic additives delay jet breakup, but surfactants had no measurable effect. Moreover, the presence of the viscous additives led to slower (~13 m/s) and thinner (~30 µm) jets.    

High-speed schlieren imaging of a highly-efficient atmospheric plasma jet

This study presents an extensive flow visualization of a highly-efficient microwave plasma jet. This atmospheric jet is a helium plasma plume exiting from a glass capillary tube with an inner diameter of 0.9 mm which passes through a gap region of an evanescent-mode cavity resonator. The specific design of the cavity concentrates the electric field mainly over the critical gap, and thus breakdowns the gas molecules even at very low values of input microwave power. The plasma jet is generated at 2.45 GHz with an input power in the range 0.5 to 10 W. A Z-type high-speed schlieren imaging system is used to investigate the hydrodynamic characteristics of the jet within the steady gas flow rate of 1 to 7 SLPM, both with and without the presence of plasma. We characterize the jet flow in terms of its core size and spread size, shear layer unsteadiness, and mixing of the helium jet with the surrounding air. The use of a knife-edge in radial and axial orientations provides the density gradient field perpendicular to it. We also present two-point correlation maps of the density gradient fields in both radial and axial directions to quantify the spatial coherence of the jetting flow and its mixing with the ambient air. This benchmarking study provides detailed flow visualization of this efficient atmospheric plasma jet that can later be used to optimize its performance for various applications including plasma actuation for flow control and propulsion in fluid dynamics settings.   

Computational Investigation of the Developing Jet from an Open Test Section Wind Tunnel

Open test section wind tunnels offer distinct advantages in the study of unsteady gusts which travel at convective speeds in contrast to closed test sections where the disturbances travel at the speed of sound. Matching such configurations in computational studies bring additional challenges in terms of domain, boundary conditions, and the scales that must be resolved. This study focuses on the validation of a high-fidelity simulation of an open test section low-speed unsteady wind tunnel facility and analysis of the resulting flow physics. Results from a Delayed Detached Eddy Simulation matching the entire wind tunnel facility are compared to experimental measurements at steady and unsteady conditions. After validating the computational setup, further analysis of the behaviors of the pressure and velocity fields in the wind tunnel setup are investigated which are impractical to measure experimentally. The simulation results allow for a more complete understanding of the overall setup, including coupling of velocity fluctuations in the jet core to structures in the shear layers and the effects of global pressure fluctuations on the core during unsteady operation of the wind tunnel.   

Coherent structures in supersonic twin-rectangular jet flow

Supersonic jet noise is a major cause of hearing impairment among aviation personnel working on aircraft carriers. While the mechanisms of noise generation are increasingly well-understood in axisymmetric jets, these mechanisms may have only limited applicability to jets from military-style nozzles. For example, in a twin-rectangular jet, which lacks azimuthal symmetry, coherent structures are not azimuthal Fourier modes. Rather, the D₂ symmetry of the nozzle imposes reflection symmetries on these structures about the major and minor axes. Recent investigations into twin-rectangular jets have focused on the highly energetic screech phenomenon, and the coherent structures responsible for it. As a step towards a global understanding of twin-rectangular jet physics, D₂-symmetric spectral proper orthogonal decomposition (SPOD) is performed on data from a large-eddy simulation of a Mach 1.5, nominally ideally-expanded, unforced twin-rectangular jet. The energy spectrum consists of a mixture of discrete tones and broadband turbulence. To control spectral leakage while ensuring adequate statistical convergence, a recently developed adaptive-multitaper version of SPOD is used. Dominant three-dimensional coherent structures at a broad range of frequencies of interest are cataloged and analyzed.