Instability Of Jet Research Articles

Investigation of the shear-layer instabilities in supersonic impinging jets using dual-time velocity measurements

Motivated by applications in the propulsion industry, the fundamental study of phase-locked shear-layer instabilities in supersonic impinging jets has been of research interest for long time. While such flows have been experimentally investigated in various research studies using time-unresolved particle image velocimetry (PIV) techniques, the understanding of the shear-layer dynamics is limited, due to the absence of temporal information. Time-resolved PIV measurements for high-speed flows require a large bandwidth, which is challenging to achieve with the current state of technology. An alternate approach using time-unresolved double-PIV measurements is presented in the current study, which provides multiple samples of dual-time data, depicted in figure 1. Such data can be obtained using two co-visual PIV systems, triggered at a user-selectable time-offset, ∆t. As shown by Sikroria et al. (2020), the application of techniques like dynamic mode decomposition (DMD) on time-unresolved dual-time data provides valuable information about the flow structures governing the shear-layer instabilities. The experimental setup for such measurements in supersonic impinging jets, followed by the determination of the relevant dynamical flow structures from the data, will be presented in the conference.

Development of unsteady natural convection in a square cavity under large temperature difference

To investigate how the nonuniform fluid density distribution caused by large temperature variations affects the development of unsteady natural convection, we perform a series of direct numerical simulations of two-dimensional compressible natural convection in an air-filled square cavity. The cavity has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The simulations are done using a kinetic approach based on a modeled Boltzmann equation, from which the fully compressible Navier–Stokes–Fourier equations are recovered. No Boussinesq approximation or low Mach number approximation is made. An extra source term is introduced to adjust the fluid Prandtl number. Simulations are performed for a range of Rayleigh numbers (107−109) with a fixed dimensionless temperature difference of ε=0.6 to determine the critical Rayleigh number and study the development of unsteady flow. To illustrate the instability mechanism, instantaneous fluctuation field, time trace of temperature, and velocity at selected monitoring points, the spectrum and other statistics are presented and discussed. As expected, significant differences are observed between the instability of compressible natural convection and the Boussinesq-type natural convection. With a large temperature difference, the transition to unsteady flow is asymmetric for the flows near the hot wall and cold wall. For the Rayleigh number range we studied, the cold wall region is dominated by low-frequency impact instability of the boundary thermal jet at the bottom corner. For the hot wall region, besides the upper corner impact instability, a boundary layer instability featuring high-frequency oscillations is observed.

Extension Rate and Bending Instability of Electrospinning Jets: the Role of the Electric Field

Extension rates of an electrospinning jet, in the straight segment as well as in the first jet bend, subjected to different electric fields by changing the tip-to-collector distance (H) at a given applied voltage have been extensively studied through a model solution of poly(N-isopropylacrylamide) in the DMF solvent with a concentration of 17 wt %. Light scattering experiments were carried out to obtain the jet diameter profile along the straight jet (z direction), from which the profiles of the jet velocity vj(z) and the extension rate ε̇(z) (=dvj/dz) were subsequently derived on the assumption of negligible solvent evaporation. In addition, the jet-bending process was also monitored by high-speed video imaging to successfully obtain the axial velocity (z direction) and the lateral velocity of the first bend (wave), from which the extension rate of the first wave was calculated based on a simple equation for the spiral jet. In the straight jet section, the extension rate is found to be the highest at the Taylor cone apex (region I with ε̇I), and it rapidly decays to a relatively constant value in the main jet region (region II with ε̇II), followed by a significant drop to zero near the straight jet end (region III, ε̇III ∼ 0). The presence of the zero extension rate in region III is due to the effective air drag resisting the electric stretching when the fast flowing jet becomes too thin. As the nominal electric field is increased by a smaller H, ε̇II is enhanced. Both ε̇I and ε̇II are higher than the chain retraction rate τe–1 (∼370 s–1) for all the Hs studied, implying that the chain orientation/stretch has already taken place in the straight jet. The residence time of fluid elements in region III is short (<τe), so that the axial elastic strains developed in regions I and II survive downstream in the jet-bending region to stabilize the jet. Our video imaging with high frame rates (>5000 fps) reveals the formation of the “crumpling jet” section at the straight jet end, in which the excitation and relaxation of the dominant Fourier modes of the lateral perturbations of the jet occur in dynamic equilibrium to keep the feature of the straight jet on time average; the lateral perturbations are driven by the compressive force dominantly arising from the air drag (Fdrag). After the conflict between the Coulomb repulsive force (Fc) and the residual elastic tension (Felas), the crumpling jet section finally developed the first bend with a high frequency and a small wavelength, when the section at the jet end slightly shifts downstream. Our results show that both Fdrag and Felas should be taken into consideration at the onset of the jet bending (whipping) process; both promote locally the jet buckling at the straight jet end to generate the crumpling jet, and the latter resists the formation and growth of the first jet bend as well as promotes the shifting of the bending jet upstream. The maximum extension rate of the spiral-growing bend is found to be larger than τe–1. We concluded that the extension rate of the electrospinning jet, from the cone apex to the jet whipping, is position (or time)-dependent, and the process is extremely dynamic due to the fast flow, accompanied by subtle force perturbations along the spinning line.

Asymmetric oscillation of pressurized dense gas-solid jet in a two-dimensional nozzle

The instability of pressurized dense gas-solid jets in a two-dimensional nozzle is experimentally studied using a high-speed camera, and the effects of the hopper pressure and the particle diameter on instability are considered. As particle velocity rises with hopper pressure, dense gas-solid jets become unstable and display an asymmetric oscillation, which is quasi-periodic and its frequency and evolution are further characterized. For particle diameters of d = 185 μm and 410 μm, the time-average frequencies increase linearly with the exit particle velocities. The asymmetric structures grow along the nozzle, and even undergo deformation and merging. The macroshot of the flow transition region between hopper and nozzle indicates that gas-solid separation generates fluctuations which will propagate both upstream and downstream. In the nozzle, fluctuations are amplified by the enhanced gas-solid interaction, evolving to the asymmetric structures.

Macrodrop-Impact-Mediated Fluid Microdispensing.

High‐resolution fluid dispensing techniques play a critical role in modern digital microfluidics, micro‐biosensing, and advanced fabrication. Though most of existing dispensers can achieve precise and high‐throughput fluid dispensing, they suffer from some inherent problems, such as specially fabricated dispensing micronozzles/microtips, large operating systems, low volume tunability, and poor performance for low surface tension liquids and liquids containing solid/liquid additives. Herein, the authors propose a facile, low‐frequency micro dispensing technique based on the Rayleigh–Plateau instability of singular liquid jets, which are stimulated by the air cavity collapse arising in the impact of microliter drops on non‐wetting surfaces. This novel dispensing strategy is capable to produce single microdrops of low‐viscosity liquids with a tunable volume from picoliters to nanoliters, and the operational surface tension range covers most laboratory solvents. The dispensing function is implemented without using small‐dimension nozzles/tips and enables handling diverse complex liquids. Moreover, the rather simple operating platform allows the integration of the whole dispensing function into a handy portable device with a low cost. Employing this microdispensing technique, the authors have controlled microchemical reactions, handled liquid samples in biological analysis, and fabricated smart materials and devices. The authors envision that this rational microdrop generator would find applications in various research areas.

Instability of the printing jet during the three-dimensional-printing process

Euler’s instability criterion is widely used in engineering to design a column. However, this criterion is not suitable for judging the instability of a three-dimensional printing process because the axial motion of the printing jet has to be considered. A variational principle is established, and an equivalent Eulerian load is obtained. The theoretical results show that a higher printing velocity makes the moving jet much more stable, and an experiment is designed to verify our theoretical prediction.

Absolute instability of double annular jets: local stability analysis

The paper presents the local linear stability analysis of the double annular jets. The calculations show that the first absolutely unstable helical mode can be generated in the non-swirling annular jets by the back-flow in the central recirculation zone or sufficiently strong back-flow in the external recirculation zone. The influence of the back-flow magnitude on the frequency, growth rate and eigenfunctions of the first helical mode is discussed. The calculations are completed with an analysis of the influence of the swirl intensity in the internal and external jets on the characteristics of the first absolutely unstable helical mode.

Temporal instability of surfactant-laden compound jets with surface viscoelasticity

When compound jets are covered with surfactant on both interfaces, the property of those interfaces will be viscoelastic, unlike the Newtonian fluid interface. In this paper, the effects of surface viscoelasticity are principally studied through linear stability analysis and calculated using the Chebyshev spectral collocation method. Both surface elasticity and viscosity have properties to make the jet more stable, but the physical effects behind the two influencing mechanisms are different. When the inner and outer interfaces are separately covered with surfactant, the variations of surface viscoelastic parameters affect the growth rate and dominant wavenumber differently. In addition, the sensitivity of the maximum growth rate to the surface viscoelastic parameters depends on which interface the surfactant covers. A significant increase in the surface shear viscosity reduces the influence of surface elasticity on the maximum growth rate. The long-wave assumption was adopted to derive a one-dimensional dispersion equation in an algebraic form. The comparison between the simplified expression and the numerical results validated the applicability of the one-dimensional model in the vicinity of small wavenumber.

Stability of a Viscous Liquid Jet in a Coaxial Twisting Compressible Airflow

Based on the linear stability analysis, a mathematical model for the stability of a viscous liquid jet in a coaxial twisting compressible airflow has been developed. It takes into account the twist and compressibility of the surrounding airflow, the viscosity of the liquid jet, and the cavitation bubbles within the liquid jet. Then, the effects of aerodynamics caused by the gas–liquid velocity difference on the jet stability are analyzed. The results show that under the airflow ejecting effect, the jet instability decreases first and then increases with the increase of the airflow axial velocity. When the gas–liquid velocity ratio A = 1, the jet is the most stable. When the gas–liquid velocity ratio A &gt; 2, this is meaningful for the jet breakup compared with A = 0 (no air axial velocity). When the surrounding airflow swirls, the airflow rotation strength E will change the jet dominant mode. E has a stabilizing effect on the liquid jet under the axisymmetric mode, while E is conducive to jet instability under the asymmetry mode. The maximum disturbance growth rate of the liquid jet also decreases first and then increases with the increase of E. The liquid jet is the most stable when E = 0.65, and the jet starts to become more easier to breakup when E = 0.8425 compared with E = 0 (no swirling air). When the surrounding airflow twists (air moves in both axial and circumferential directions), given the axial velocity to change the circumferential velocity of the surrounding airflow, it is not conducive to the jet breakup, regardless of the axisymmetric disturbance or asymmetry disturbance.

Effect of tabs on transverse jet instabilities, structure, vorticity dynamics and mixing

Abstract

Linear instability of an annular liquid jet with gas velocity oscillations

Pressure fluctuation produced in liquid rocket engines affects atomization of the annular liquid jet in the combustion chamber. A linear stability analysis of an annular liquid jet under acoustic oscillations was conducted in this work. Parametric instability was applied to study the problem, and the oscillations of the gas velocity were considered. The Floquet theory was used to solve the disturbance, from which the dispersion equation containing the coefficients of the infinite order matrix was derived; the order of the coefficient matrix affected the accuracy of the results. There were several unstable regions in the wavenumber range, obtained by solving the dispersion matrix. When the gas velocity oscillated, the amplitude of the surface wave displacement also oscillated. In various unstable regions, the growth of the surface wave of the annular liquid sheet was also different, but the crest never passed through the equilibrium position, which was more complicated than in the planar liquid sheet. Increasing oscillation frequency contributed to an increase in the wavenumber corresponding to the unstable area. Increasing the oscillation amplitude increased the maximum growth rate. The effect of physical parameters on the instability of the annular liquid jet was also discussed.

Kink instability of triangular jets in the solar atmosphere

Context. It is known that hydrodynamic triangular jets (i.e. the jet with maximal velocity at its axis, which linearly decreases at both sides) are unstable to anti-symmetric kink perturbations. The inclusion of the magnetic field may lead to the stabilisation of the jets. Jets and complex magnetic fields are ubiquitous in the solar atmosphere, which suggests the possibility of the kink instability in certain cases. Aims. The aim of the paper is to study the kink instability of triangular jets sandwiched between magnetic tubes (or slabs) and its possible connection to observed properties of the jets in the solar atmosphere. Methods. A dispersion equation governing the kink perturbations is obtained through matching of analytical solutions at the jet boundaries. The equation is solved analytically and numerically for different parameters of jets and surrounding plasma. The analytical solution is accompanied by a numerical simulation of fully non-linear magnetohydrodynamic (MHD) equations for a particular situation of solar type II spicules. Results. Magnetohydrodynamic triangular jets are unstable to the dynamic kink instability depending on the Alfvén Mach number (the ratio of flow to Alfvén speeds) and the ratio of internal and external densities. When the jet has the same density as the surrounding plasma, only super-Alfvénic flows are unstable. However, denser jets are also unstable in a sub-Alfvénic regime. Jets with an angle to the ambient magnetic field have much lower thresholds of instability than field-aligned flows. Growth times of the kink instability are estimated to be 6−15 min for type I spicules and 5−60 s for type II spicules matching with their observed lifetimes. The numerical simulation of full non-linear equations shows that the transverse kink pulse locally destroys the jet in less than a minute in type II spicule conditions. Conclusions. Dynamic kink instability may lead to the full breakdown of MHD flows and consequently to an observed disappearance of spicules.

Interfacial instability and transition of jetting and dripping modes in a co-flow focusing process

The breakup dynamics of coaxial liquid interfaces into compound droplets in a co-flow focusing process is studied systematically. In experiments, the jetting and dripping modes downstream the focusing orifice are identified within the parametric regime where a coaxial liquid cone can be established steadily, and the phase diagram is plotted under different flow rates of inner, outer, and driving liquids. The force balance for the jet interface is analyzed numerically to explore the critical conditions for the jetting-dripping transition. It is found that the instability of the inner interface is much easier to trigger the modes transition, and the transition criterion is decided by the balance of inertia force, shear stress, and interfacial tension at the local inner jet. The linear spatiotemporal instability analysis is further carried out to study the convective and absolute instabilities of the coaxial jets. The effects of main process parameters on jet instability are accessed, and the boundary between the absolute/convective instabilities is further compared with the experimental and numerical results, which achieves good agreement. Finally, the energy budget analysis of the instability of coaxial liquid jets is performed to provide more understanding of physical mechanisms for the mode transition.

On the mechanism of the influence of medium density on the supersonic core length of an underexpanded jet

Exhaustion of a supersonic underexpanded air jet into air–helium and air–sulfur hexafluoride mixtures is studied experimentally. The air jet escapes from a convergent circular nozzle in the range of moderate Reynolds numbers covering the laminar and transitional regimes of the jet flow. The experiments are performed with “cold” and heated jets in a low-pressure jet setup, which allows the Reynolds number of the jet exhaustion from the nozzle, the jet pressure ratio, and the density of the gas surrounding the jet to be maintained independently. A Pitot tube is used to measure the supersonic core length of the air jet as a function of the density of the ambient medium whereto the jet exhausts. In addition, the spatial distributions of the amplitude–frequency characteristics of acoustic oscillations generated by the jet in the ambient space are measured by a moving sensor of pressure fluctuations. The effect of the ratio of the underexpanded air jet density to the ambient medium density on the supersonic core length is demonstrated. It is shown that the mechanism of influence of the ambient medium density is associated with a change in the conditions for the global instability of the underexpanded air jet and, in particular, the conditions for generation of the screech tone.

Effects of nozzle configuration on flash boiling fuel sprays of twin-orifice nozzle with aviation kerosene

To investigate the effects of nozzle configuration on flash boiling fuel sprays of the twin-orifice nozzle with aviation kerosene, five different two-dimensional transparent slit nozzles with various orifices’ diameter ratio and expansion chamber's aspect ratio are fabricated and studied. Both internal two-phase flow and near-nozzle fuel jet under subcooled and superheated conditions are studied via a high-speed camera with backlit measurement and image processing methods. The experimental results indicate that the bubbles nucleation from cavitation at the inlet-orifice wall can accumulate within the expansion chamber with enhanced bubble growth and aggregation under higher-level superheated conditions, which can significantly promote the fuel atomization and evaporation. In addition, a smaller orifices’ diameter ratio leads to larger in-nozzle bubble volumes within the twin-orifice nozzle, while the internal bubble inception may be inhibited by increasing the expansion chamber's aspect ratio. Furthermore, decreasing the orifices’ diameter ratio can promote the flash boiling process, while better-quality spray at flare flash boiling state may be facilitated by the near-nozzle mechanical breakup. The nozzle with a lower expansion chamber's aspect ratio has a larger spray cone angle and weaker jet instability, benefited from larger bubble volume and higher effective bubble rate, which accelerates the bubble disruption and fulfills the potential of in-nozzle flash boiling on near-nozzle jet disintegration.

A Numerical Study of the Global Instability in Counter-Current Homogeneous Density Incompressible Round Jets

The paper focuses on a global instability phenomenon in counter-current round jets issuing from co-axial nozzles. Three different configurations that differ in a way of the counter flow generation are investigated. Besides typical configurations used in experimental and numerical research performed so far, in which suction applied in an annular nozzle is a driving force for the counterflow, a novel set-up is proposed where the annular nozzle is oriented in the opposite direction and placed above the main one. Such a configuration eliminates the suction of fluid from the main jet, which in previous research was found to have a destructive impact on the occurrence of the global flow instability. The research is performed using a large eddy simulation (LES) method and the computations are carried out applying a high-order numerical code, the accuracy of which has been proven in previous works and also in the present research through comparisons with available experimental data. The research is complemented by the linear stability analysis which supports the LES results and formulated conclusions. In agreement with a number of the previous works it has been shown that the global modes can be triggered only when the velocity ratio (I) between the main jet velocity and the velocity of the jet issuing from the annular nozzle is above a certain threshold level (I_{text {cr}}). It has been shown that in the classical configurations of the co-axial nozzles the range of Ige I_{text {cr}} for which the global instability phenomenon exists is very narrow and it disappears for larger velocity ratios. Reasons for that have been identified through detailed scrutiny of instantaneous flow pictures. In the new set-up of the nozzles the global instability persists for a significantly wider range of I. It has been shown that I_{text {cr}} depends on both the momentum thickness of the mixing layer formed between the counter-current streams and the applied configuration of the nozzles. The LES results univocally showed that the latter factor decides on the type of the instability mode (Mode I or Mode II) that emerges in the flow, as it directly influences on a length of the region where the counter-current streams are parallel allowing the growth of short or long wave disturbances characteristic for Mode I and Mode II, respectively.

Modulated rotating waves and triadic resonances in spherical fluid systems: The case of magnetized spherical Couette flow

The existence of triadic resonances in the magnetized spherical Couette system is related to the development of modulated rotating waves, which are quasiperiodic flows understood in terms of bifurcation theory in systems with symmetry. In contrast to previous studies in spherical geometry, the resonant modes are not inertial waves but related to the radial jet instability, which is strongly equatorially antisymmetric. We propose a general framework in which triadic resonances are generated through successive Hopf bifurcations from the base state. The study relies on an accurate frequency analysis of different modes of the flow, for solutions belonging to two different bifurcation scenarios. The azimuthal and latitudinal nonlinear coupling among the resonant modes is analyzed and interpreted using spherical harmonics, and the results are compared with previous studies in spherical geometry.

Magnetic inhibition of the recollimation instability in relativistic jets

ABSTRACT In this paper, we describe the results of three-dimensional relativistic magnetohydrodynamic simulations aimed at probing the role of regular magnetic field on the development of the instability that accompanies recollimation of relativistic jets. In particular, we studied the recollimation driven by the reconfinement of jets from active galactic nuclei (AGN) by the thermal pressure of galactic coronas. We find that a relatively weak azimuthal magnetic field can completely suppress the recollimation instability in such jets, with the critical magnetization parameter σcr &amp;lt; 0.01. We argue that the recollimation instability is a variant of the centrifugal instability (CFI) and show that our results are consistent with the predictions based on the study of magnetic CFI in rotating fluids. The results are discussed in the context of AGN jets in general and the nature of the Fanaroff–Riley morphological division of extragalactic radio sources in particular.

Onset of temporal dynamics within a low reynolds-number laminar fluidic oscillator

We investigate the onset of temporal dynamics of a fluidic oscillator (FO) in the laminar regime at very low Reynolds number (Re=Uhi/ν, where U and hi are the velocity and channel height at inlet, and ν is the kinematic viscosity of the fluid). Both two- and spanwise-periodic-three-dimensional simulations are performed using high-order spectral element methods to characterise the flow inside the FO cavity and the outcoming jet. While the flow remains steady and symmetric for sufficiently low Re, the two-dimensional FO undergoes a symmetry-breaking Hopf bifurcation at ReH2=75.7 that results in a space-time symmetric periodic solution. The remnant space-time symmetry is later broken in a pitchfork bifurcation of limit cycles at ReP2=294.2. Taking three-dimensionality into consideration results in an early spanwise-invariance disruption at about Re3≃68 of wavelength 13hi that retards the onset of the oscillation to ReH3=82.1. This effect is little representative of actual FO implementations, which are typically much narrower than the wavelength of the spanwise instability observed at these low Re. Contrary to what happens with FOs in the turbulent oscillatory regime, the oscillation frequency of the output jet in the laminar regime is found to decrease with Re. The mechanism that drives the oscillation, however, remains the same: as the high speed flow inside the cavity attaches to one of the internal walls through the Coandă effect, the feedback channels divert part of the momentum back, which pushes the incoming flow against the opposite wall. The alternate deviation of the flow inside the cavity to one or the other side results in the periodic flipping of the output jet. The pressure contribution to net momentum at the end of the feedback channels is found to be double that of the advective momentum flux at the early time-periodic regime but both become comparable as Re is increased. The jet sweeping angle amplitude is more pronounced for the two-dimensional FO as compared to three-dimensional at a fixed given Re, the Coandă effect being only partially fulfilled in the latter case. In both cases the sweep amplitude increases with Re. The instability of the output jet, which becomes slightly chaotic already at very low Re, is responsible for triggering the cavity instability that drives the oscillation slightly earlier than it would, should outside noise be suppressed altogether.

An experimental study of recoil capillary waves and break up of vertically flowing down water jets

Break up of water jets under gravity is a ubiquitous phenomenon. The role of surface tension on the instability of uniform water jets was recognised long ago by Plateau and Rayleigh. According to the Plateau–Rayleigh theory, external (or internal) perturbation waves create necks and bulges all along the uniform jet length. The perturbation waves of wavelengths larger than a certain value keep growing with time and ultimately cause the continuous jet to break up into individual drops. The effect of external perturbation waves was investigated experimentally, in most cases under gravity, and found to confirm the essentials of the theory. Recently, the idea of recoil capillary waves as a possible internal source of perturbations was emphasised. According to this idea, immediately after the break up of the jet, the tip of the remaining continuous jet (after a drop is detached) recoils. Its effect travels upstream as a recoil capillary wave which gets reflected at the mouth of the jet-issuing nozzle. The reflected capillary wave travels downstream along the jet with its Doppler-shifted wavelength as a reinforcing perturbation wave and, as a result, affecting the break up length of the jet. We set up and perform an experiment to verify the existence of these tip contraction recoil capillary waves. The results of our experiment support the existence of these recoil capillary waves. However, the effect of these capillary waves on the jet break up length is found to be small.