Solution of a problem on the interaction mechanics of a free liquid jet with a flat plate, body and with other jet has been achieved by means of a graphic-analytical method, developed by author of the given article. This method has allowed physically adequately and visually to describe the flow field near the streamlined surface and to give expressions for quantitative evaluation of the jet pressure profile onto this surface. This method is equally correct for both a flat jet and a jet with a round cross-section. Analysis of the flow field has allowed to detect a jet component, induced by the body fore part in the unrestricted fluid stream and determining the body form drag. Besides that, it has been ascertained that a friction also induces the jet component in the potential boundary layer. It has been introduced a new notion of the stream total head vector, determining an origin of the possible jet flow in the stream.
A cavity hollowed out on a free liquid surface is relaxing, forming an intense liquid jet. Using a model experiment where a short air pulse sculpts an initial large crater, we depict the different stages in the gravitational cavity collapse and in the jet formation. Prior eversion, all cavity profiles are found to exhibit a shape similarity. Following hollow relaxation, a universal scaling law establishing an unexpected relation between the jet eruption velocity, the initial cavity geometry and the liquid viscosity is evidenced experimentally. On further analysing the jet forms we demonstrate …
Penetration process and an instability on a liquid jet impinging to a stream of the same fluid in a channel is focused. The jet penetrated into the stream is wrapped by entrained air, and coalesces with the stream when the air sheath around the jet collapses. We introduce instability arisen on the jet and the vigorous effect of the entrained-air sheath on the dynamic behavior of the jet in this fluid dynamics video.
The analytical solution of heated laminar vertical jet in a liquid with power-law temperature dependence of density was obtained in the skin-layer approximation for certain values of Prandtl number. Cases of point and linear sources were considered.
We conduct a series of experiments with a special interest on a penetration process and instabilities arisen on a liquid jet impinged to a liquid of the same kind flowing in a channel. The impinged jet penetrates into the flowing bath accompanying with entrainment of the ambient immiscible gas, which results in the impinged jet wrapped by the entrained gas as a 'sheath.' This sheath formation enables the impinged jet to survive in the fluid in the channel without coalescing until the entrained-air sheath breaks down. Occasionally a 'cap' of the entrained air is formed at the tip of the penetra…
It is generally accepted that the Worthington jet occurs when a droplet impacts onto a liquid pool. However, in this experimental study of the impact of viscous droplets onto a less-viscous liquid pool, we identify another jet besides the Worthington jet, forming a two-jet phenomenon. The two jets, a surface-climbing jet and the Worthington jet, may appear successively during one impact event. By carefully tuning the impact condition, we find that the two-jet phenomenon is jointly controlled by the droplet-pool viscosity ratio, the droplet Weber number, and the droplet-pool miscibility. The me…
A liquid jet may develop different types of instabilities, like the so-called Rayleigh-Plateau instability, which breaks the jet into droplets. However, another type of instabilities may appear when we electrify a liquid jet and induce some charge at his surface. Among them, the most common is the so-called Whipping Instability, which is characterized by violent and fast lashes of the jet. In the submitted fluid dynamic video(see http://hdl.handle.net/1813/11422), we will show an unstable charged glycerine jet in a dielectric liquid bath, which permits an enhanced visualization of the instabil…
In this fluid dynamics video, we present a visualization of the primary atomization of a turbulent liquid jet injected into a turbulent gaseous crossflow. It is based on a detailed numerical simulation of the primary atomization region of the jet using a finite volume, balanced force, incompressible LES/DNS flow solver coupled to a Refined Level Set Grid (RLSG) solver to track the phase interface position. The visualization highlights the two distinct breakup modes of the jet: the column breakup mode of the main liquid column and the ligament breakup mode on the sides of the jet and highlights…
We find that a liquid jet can bounce off a bath of the same liquid if the bath is moving horizontally with respect to the jet. Previous observations of jets rebounding off a bath (e.g. Kaye effect) have been reported only for non-Newtonian fluids, while we observe bouncing jets in a variety of Newtonian fluids, including mineral oil poured by hand. A thin layer of air separates the bouncing jet from the bath, and the relative motion replenishes the film of air. Jets with one or two bounces are stable for a range of viscosity, jet flow rate and velocity, and bath velocity. The bouncing phenomen…
This paper is associated with a poster winner of a 2019 American Physical Society Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.P0020
A spontaneous breakup of a liquid jet results in the formation of a chain of droplets, which is a daily observed phenomenon, such as in the raining process and under an open water-faucet. We here report inkjet printing experiments for the formation of droplets which are inconsistent with existing theories and thereafter propose a novel concept of surface area minimization to address the droplet-formation condition. The novel concept is also capable of predicting the formation of satellite and subsatellite droplets, which cannot be comprehended by the classic Rayleigh theory for the formation o…
We investigate motion of a gas-liquid interface in a test tube induced by a large acceleration via impulsive force. We conduct simple experiments in which the tube partially filled with a liquid falls under gravity and impacts a rigid floor. A curved gas-liquid interface inside the tube reverses and eventually forms an elongated jet (i.e. the so-called a focused jet). In our experiments, there arises either vibration of the interface or increment in the velocity of a liquid jet accompanied by the onset of cavitation in the liquid column. These phenomena cannot be explained by considering press…
This paper experimentally investigates the effect of viscosity on the outcomes of collisions between a regular stream of droplets and a continuous liquid jet. A broad variation of liquid viscosity of both the drop and the jet liquid is considered, keeping other material properties unchanged. To do so, only two liquid types were used: aqueous glycerol solutions for the drop and different types of silicone oil for the jet liquid. Combining these liquids, the viscosity ratio λ = μdrop/μjet was varied between 0.25 and 3.50. The collision outcomes were classified in the form of regime maps leading …
Liquid jets issued from a non-circular orifice exhibit oscillation owing to the surface tension. When the orifice has an $n$-fold rotational symmetry, a material cross section of the jet interchanges two symmetric shapes alternately. This oscillation, called axis switching, is a superposition of two ripples oppositely propagating in the azimuthal direction around the axis. In this study, we used computer simulations to demonstrate that we can pick up one of the two ripples by adjusting the initial velocity profile of the orifice. As a result of the single wave propagation in the azimuth, the j…
Collisions between a stream of drops and a continuous jet of a different liquid are experimentally investigated. In contrast to previous studies, our work focuses on the effects of liquid miscibility and wettability on the collision outcomes. Thus, miscible and immiscible liquids providing total and partial wetting are used. We show that, as long as the jet surface tension is smaller than the drop surface tension, the drops can be encapsulated by the jet, providing the so-called drops-in-jet structure. The transitions between the different regimes remain similar in nature with a capillary frag…
we report an ultrafast synchrotron x-ray phase contrast imaging study of the primary breakup mechanism of a coaxial air-assisted water jet. We demonstrate that there exist great similarities in the phenomenology of primary breakup with that of the secondary breakup. Especially, a membrane-mediated breakup mechanism dominates the breakup process for a wide range of air speeds. This finding reveals the intrinsic connections of these two breakup regimes and has deep implications on the unified theoretical approach in treating the breakup mechanism of high speed liquid jet.
In this paper, breakup of liquid jet is simulated using smoothed particle hydrodynamics (SPH) which is a meshless Lagrangian numerical method. For this aim, flow governing equations are discretized based on SPH method. In this paper, SPHysics open source code has been utilized for numerical solutions. Therefore, the mentioned code has been developed by adding the surface tension effects. The proposed method is then validated using dam break with obstacle problem. Finally, simulation of twodimensional liquid jet flow is carried out and its breakup behavior considering one-phase flow is investig…
The present study aims to investigate the role of injector geometry, particularly injector tube length to diameter ratio (L/D) in liquid jet stability and breakup in presence of crossflow. Water is injected into a crossflow of air. Aerodynamic Weber number (We) and liquid Reynolds number (Rel) are systematically varied to observe various breakup modes. Bag breakup and surface stripping is observed for different operating conditions. Time-resolved jet trajectory images are processed using Proper Orthogonal Decomposition (POD) algorithm. POD mode shapes and corresponding Power Spectral Density (…
This Letter presents the novel experimental observation of long and narrow jets shooting out in disconnecting large elongated bubbles. We investigate this phenomenon by carrying out experiments with various viscosities, surface tensions, densities and nozzle radii. We propose a universal scaling law for the jet velocity, which unexpectedly involves the bubble height to the power 3/2. This anomalous exponent suggests an energy focusing phenomenon. We demonstrate experimentally that this focusing is purely gravity-driven and independent of the pinch-off singularity.
The present work develops a compressible VOF-LPT coupled solver in OpenFOAM and utilizes it to simulate a LJICF numerically. This methodology helps accurately predict a complex primary breakup in the Eulerian framework and the secondary atomization of spherical droplets using a computationally efficient LPT method. The coupled solver with AMR is rigorously validated for a liquid jet in crossflow at varying operating conditions. We have further carried out a thorough investigation to study the effect of momentum flux ratio and weber number on the various flow features and liquid jet break-up ph…
Multiphase Smoothed Particle Hydrodynamics (SPH) method has been used to study the jet breakup phenomena. It has been shown that this method is well capable of capturing different jet breakup characteristics. The value obtained for critical Weber number here in transition from dripping to jetting is a very good match to available values in literature. Jet breakup lengths are also agreeing well with several empirical correlations. Successful usage of SPH, as a comparably fast CFD solver, in jet breakup analysis helps in speeding up the numerical study of this phenomenon.
A three-dimensional round liquid jet within a low-speed coaxial gas flow is numerically simulated and explained via vortex dynamics ($λ_2$ method). The instabilities on the liquid-gas interface reflect well the vortex interactions around the interface. Certain key features are identified for the first time. Two types of surface deformations are distinguished, which are separated by a large indentation on the jet stem: First, those near the jet start-up cap are encapsulated inside the recirculation zone behind the cap. These deformations are directly related to the dynamics of the growing cap a…
Many natural and technical processes deal with the turbulent mixing and heat transfer in the jet of mutually immiscible liquids, which represent an important class of the modern multiphase systems dynamics. The differential equations for axisymmetrical two-dimensional stationary flow and the integral correlations in a cylindrical coordinate system are considered for the free and confined jets. The parameters of the turbulent mixing in a free jet and in two-phase flow in a chamber are modelled and analyzed. One example is also done for high-temperature flow of the liquid metal melt cooled by wa…
As a bubble bursts at a liquid-air interface, a tiny liquid jet rises and can release the so-called \textit{jet drops}. In this paper, the size of the top jet drop produced by a bubble bursting is investigated experimentally. We determine, and discuss, the first scaling law enabling the determination of the top jet drop size as a function of the corresponding mother bubble radius and the liquid properties (viscosity, surface tension, density), along with its regime of existence. Furthermore, in the aim of decoupling experimentally the effects of bubble collapse and jet dynamics on the drop det…
We study a liquid jet that breaks up into drops in an external co-flowing liquid inside a confining microfluidic geometry. The jet breakup can occur right after the nozzle in a phenomenon named dripping or through the generation of a liquid jet that breaks up a long distance from the nozzle, which is called jetting. Traditionally, these two regimes have been considered to reflect the existence of two kinds of spatiotemporal instabilities of a fluid jet, the dripping regime corresponding to an absolutely unstable jet and the jetting regime to a convectively unstable jet. Here, we present quanti…
Liquid-fueled Oblique Detonation Stabilized by a Transverse Jet
Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所）；City University of Hong Kong（香港城市大学）；University of Chinese Academy of Sciences（中国科学院大学）
A general scaling of the evolution of an exploding liquid jet under an ultra short and intense X-ray pulse from a X-ray free electron laser (XFEL) is proposed. A general formulation of the conservation of energy for blasts in vacuum partially against a deformable object leads to a compact expression that governs the evolution of the gap produced by the explosion. The theoretical analysis contemplates two asymptotic stages for small and large times from the initiation of the blast. A complete dimensional analysis of the problem and an optimal collapse of experimental data reveal that the univer…
We investigate the collision of a continuous liquid jet with a regular stream of immiscible droplets. The immiscible liquids, namely silicon oil for the continuous jet and an aqueous glycerol solution for the drop stream, are selected to enable the total wetting of the drops by the jet liquid. Four different regimes are experimentally identified: drops in jet, encapsulation without satellites, encapsulation with satellites from the jet liquid and mixed fragmentation. The drops in jet regime, potentially of great interest for new applications, corresponds to a regular stream of drops embedded i…
A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which exploits the hydrodynamic similarity solution for thin film flow. The approximate solution may provide a valuable basis for assessing flow and heat transfer in more complex settings.
A liquid metal flow in the form of a submerged round jet entering a square duct in the presence of a transverse magnetic field is studied experimentally. A range of high Reynolds and Hartmann numbers is considered. Flow velocity is measured using electric potential difference probes. A detailed study of the flow in the duct's cross-section about seven jet's diameters downstream of the inlet reveals the dynamics, which is unsteady and dominated by high-amplitude fluctuations resulting from instability of the jet. The flow structure and fluctuation properties are largely determined by the value …
In this fluid dynamics video, Ray-tracing data visualization technique was used to obtain realistic and detailed flow motions during impinging of two liquid jets. Different patterns of sheet and rim configurations were presented to shed light into the underlying physics, including liquid chain, closed rim, open rim, unstable rim and flapping sheet. In addition, stationary asymmetrical waves were observed and compared with existing theories. The generation of stationary capillary wave in respect to the liquid rim were explained by the classic shallow water wave theory. The atomization process c…
The primary breakup of a planar liquid jet is explored via direct numerical simulation (DNS) of the incompressible Navier-Stokes equation with level-set and volume-of-fluid interface capturing methods. PDFs of the local radius of curvature and the local cross-flow displacement of the liquid-gas interface are evaluated over wide ranges of the Reynolds number ($Re$), Weber number ($We$), density ratio and viscosity ratio. The temporal cascade of liquid-structure length scales and the spread rate of the liquid jet during primary atomization are analyzed. The formation rate of different surface st…
A liquid jet can stably bounce off a sufficiently soft gel, by following the contour of the dimple created upon impact. This new phenomenon is insensitive to the wetting properties of the gels and was observed for different liquids over a wide range of surface tensions, $γ$ = 24--72 mN/m. In contrast, other jet rebound phenomena are typically sensitive to $γ$: jet rebounds off a hard solid (e.g. superhydrophobic surface) or another liquid are possible only for high and low $γ$ liquids, respectively. This is because an air layer must be stabilized between the two interfaces. For a soft gel, no …
A three-dimensional color-fluid lattice Boltzmann model for immiscible two-phase flows is developed in the framework of a three-dimensional 27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27 versions of three sub-operators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu--Valocchi--Kang perturbation operator, and a Latva-Kokko--Rothman recoloring operator. A D3Q27 version of an enhanced equilibrium distribution function is also incorporated into this model to improve the Galilean invariance. Three types of numerical tests, namely, a static droplet, a…
This fluid dynamics video presents the gravity-driven jets induced by the relaxation of large prolate bubbles or large holes at a free liquid surface. It shows that the jet developing inside a bubble can be strong enough to give rise to liquid projections shooting out way above the free surface.
From everyday experience, we all know that a solid edge can deflect a liquid flowing over it significantly, up to the point where the liquid completely sticks to the solid. Although important in pouring, printing and extrusion processes, there is no predictive model of this so-called "teapot effect". By grazing vertical cylinders with inclined capillary liquid jets, we here use the teapot effect to attach the jet to the solid and form a new structure: the liquid helix. Using mass and momentum conservation along the liquid stream, we first quantitatively predict the shape of the helix and then …
Illuminating a water solution with a focused continuous wave laser produces a strong local heating of the liquid that leads to the nucleation of bubbles, also known as thermocavitation. During the growth of the bubble, the surrounding liquid is expelled from the constraining microfluidic channel through a nozzle, creating a jet. The characteristics of the resulting liquid jet was imaged using ultra-fast imaging techniques. Here, we provide a phenomenological description of the jet shapes and velocities, and compare them with a Boundary Integral numerical model. We define the parameter regime, …
In this fluid dynamics video prepared for the APS-DFD Gallery of Fluid Motion we study the collision of two identical viscous jets at different jet speeds and collision eccentricities. The dynamics of the jet motion are slowed down by orders of magnitude using a synchronized strobe effect coupled with precise timing control of the perturbation frequency imposed on one of the jets. Our results show that different shapes and morphologies appear as we change the collision eccentricity. At low jet speeds ($We_j = 45$) viscous threads and filaments are formed as the jets begin to impinge on each ot…
Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid into a strip, the process of counter-propagating waves interaction is numerically simulated. The nonlinear solitary waves on the surface can separately propagate along or against the direction of electric field without distortion. At the same time, the shape of the oppositely traveling waves can be distorted as the result of their interaction. In the problem…
We have used the integral form of the conservation equations, to find a cubic formula for the drop size in liquid sprays in cross flows. Similar to our work on axial liquid sprays, the energy balance dictates that the initial kinetic energy of the gas and injected liquid be distributed into the final surface tension energy, kinetic energy of the gas and droplets, and viscous dissipation incurred. Kinetic energy of the cross flow is added to the energy balance. Then, only the viscous dissipation term needs to be phenomenologically modelled. The mass and energy balance for the spray flows render…
We analyze both numerically and experimentally the stability of the steady jetting tip streaming produced by focusing a liquid stream with another liquid current when they coflow through the orifice of an axisymmetric nozzle. We calculate the global eigenmodes characterizing the response of this configuration to small-amplitude perturbations. In this way, the critical conditions leading to the instability of the steady jetting tip streaming are determined. The unstable perturbations are classified according to their oscillatory character and to the region where they are originated (convective …
Helped by the careful analysis of their experimental data, Worthington (1897) described roughly the mechanism underlying the formation of high-speed jets ejected after the impact of an axisymmetric solid on a liquid-air interface. In this work we combine detailed boundary-integral simulations with analytical modeling to describe the formation and break-up of such Worthington jets in two common physical systems: the impact of a circular disc on a liquid surface and the release of air bubbles from an underwater nozzle. We first show that the jet base dynamics can be predicted for both systems us…
The injection of liquid fuel at supercritical pressures is a relevant topic in combustion, but usually overlooked. In the past, the wrong assumption whereby the liquid experiments a fast transition to a supercritical state was made, thus neglecting any role of two-phase interface dynamics in the early stages of the atomization process. However, recent studies have shown that local thermodynamic phase equilibrium and mixing between the involved species allow the coexistence of both phases in this pressure range. In this work, a Volume-of-Fluid method adapted to variable-density real fluids is u…
In this fluid dynamics video prepared for the APS-DFD Gallery of Fluid Motion we study the Kelvin-Helmholtz instability for both Newtonian and viscoelastic jets. The nonlinear dynamics of the jet motion are slowed down by orders of magnitude using a synchronized strobe effect coupled with precise timing control of perturbation frequencies. Our results show that at high wave-numbers the imposed perturbations initially grow linearly with time and the jet axis remains straight while the Kelvin-Helmholtz wave amplitude grows and rolls up into bags that encapsulate the central jet within themselves…
