Simulation of liquid micro-jet in free expanding high-speed co-flowing gas streams

We present the development of an experimentally validated computational fluid dynamics model for liquid micro jets. Such jets are produced by focusing hydrodynamic momentum from a co-flowing sheath of gas on a liquid stream in a nozzle. The numerical model based on laminar two-phase, Newtonian, compressible Navier–Stokes equations is solved with finite volume method, where the phase interface is treated by the volume of fluid approach. A mixture model of the two-phase system is solved in axisymmetry using?~?300,000 finite volumes, while ensuring mesh independence with the finite volumes of the size 0.25 µm in the vicinity of the jet and drops. The numerical model is evaluated by comparing jet diameters and jet lengths obtained experimentally and from scaling analysis. They are not affected by the strong temperature and viscosity changes in the focusing gas while expanding at nozzle outlet. A range of gas and liquid-operating parameters is investigated numerically to understand their influence on the jet performance. The study is performed for gas and liquid Reynolds numbers in the range 17–1222 and 110–215, and Weber numbers in the range 3–320, respectively. A reasonably good agreement between experimental and scaling results is found for the range of operating parameters never tackled before. This study provides a basis for further computational designs as well as adjustments of the operating conditions for specific liquids and gases.     

Modelling compressible gas flow near the nozzle of a gas atomiser using a new unified model

In this paper, a unified numerical model is used to simulate the compressible gas flow, during the process of atomisation of liquid, near the atomiser nozzle in gas-only case studies. The flow of the under-expanded gas jets is studied, by analyzing the pressure field, density field and the spatial distribution of Mach number of the gas. The simulated predictions of gas status at the nozzle exit, the radial profile of Pitot pressure, aspiration pressure, and the spatial distribution of the density gradient, are compared with relevant experimental results and an analytical correlation, in order to validate and verify the application of this unified model in the numerical simulation of the gas dynamic behavior during gas atomisation. The simulation results show that the compressible gas flow near the nozzle of a discrete jet atomiser is different from that in a typical annular slit atomiser. Unlike existing models, this new formulation has the potential to be used in future to simulate the simultaneous flow of compressible gas and a weakly compressible liquid metal stream.     

Temporal analysis of power law liquid jets

In this paper we investigate the breakup mechanisms of power law liquid jets. The viscosity of the liquid is represented the Carreau-Yasuda model, and the surface tension of the liquid jet has a variation (gradient) along the jet axial direction. The surface tension gradient may be introduced by the thermal disturbance of the jet surface as it comes of out an orifice. The Carreau-Yasuda fluid has a power law viscosity bounded by two plateaus, the higher plateau at zero strain rate, μ₀, and the lower plateau at the infinite strain rate, μ_∞. The governing equation for the surface profile of the liquid jet is derived in the forms of a partial differential equation (PDE), as well as an ordinary differential equation (ODE). The PDE and ODE are solved for various cases of Carreau-Yasuda fluid to study the effect of fluid properties on jet breakup. The effects of various parameters on the instability behavior are studied in comparison with two Newtonian jets with upper and lower bound viscosities, μ₀ and μ_∞. A number of quantitative conclusions and sensitivities on the instability behavior of non-Newtonian jets are investigated. It is found that the jet breakup mechanism depends on the properties of the fluid as well as the wave number of the thermal disturbance that causes the surface tension gradient. In contrast to the Newtonian liquid where the jet surface profile has the same frequency as the surface tension gradient, the nonlinear nature of the Carreau-Yasuda constitutive behavior may enable the jet surface profile at frequencies higher than that of the surface tension gradient. This leads to significant surface profile oscillation within one wavelength of the surface tension gradient and the generation of small satellite drops. It is worth noting that at a small wave number the breakup time for the Carreau-Yasuda fluid maybe shorter than that of the Newtonian jet with μ_∞, although the Newtonian jet has a lower viscosity.     

Time-resolved dynamics of laser-induced micro-jets from thin liquid films

Laser-induced forward transfer (LIFT) is a high-resolution direct-write technique, which can print a wide range of liquid materials without a nozzle. In this process, a pulsed laser initiates the expulsion of a high-velocity micro-jet of fluid from a thin donor film. LIFT involves a novel regime for impulsively driven free-surface jetting in that viscous forces developed in the thin film become relevant within the jet lifetime. In this work, time-resolved microscopy is used to study the dynamics of the laser-induced ejection process. We consider the influence of thin metal and thick polymer laser-absorbing layers on the flow actuation mechanism and resulting jet dynamics. Both films exhibit a mechanism in which flow is driven by the rapid expansion of a gas bubble within the liquid film. We present high-resolution images of the transient gas cavities, the resulting ejection of high aspect ratio external jets, as well as the first images of re-entrant jets formed during LIFT. These observations are interpreted in the context of similar work on cavitation bubble formation near free surfaces and rigid interfaces. Additionally, by increasing the laser beam size used on the polymer absorbing layer, we observe a transition to an alternate mechanism for jet formation, which is driven by the rapid expansion of a blister on the polymer surface. We compare the dynamics of these blister-actuated jets to those of the gas-actuated mechanism. Finally, we analyze these results in the context of printing sensitive ink materials.     

CFD prediction of the trajectory of a liquid jet in a non-uniform air crossflow

This paper describes a predictive numerical modelling methodology for calculation of deflection and deformation of liquid jets in air crossflows. The methodology combines Jet Embedding (JE) with Volume-of-Fluid (VOF) in a computational fluid dynamics (CFD) based approach. The combined JE/VOF methodology applies the JE concept of modelling the air and liquid phases in separate but linked models, with a representation of the liquid column embedded in the crossflow model. The crossflow is modelled in a CFD calculation using CFX4.2 and the separate jet model is written in FORTRAN 77. A multi-fluid implementation of the VOF technique, in CFX4.2, is used to model deformation of the liquid column cross-section in a series of two-dimensional models along the column trajectory. The crossflow, jet and deformation calculations are linked by an iterative procedure which advances from the nozzle exit in a series of time-steps. The JE/VOF methodology is used to make a prediction of a time-average trajectory of a deflected liquid column, with a progressively deformed cross-section, in an air crossflow. The prediction demonstrates that the JE/VOF methodology is capable of producing a physically realistic result.     

Large-eddy simulation of vortex breakdown in compressible swirling jet flow

Vortex breakdown in a compressible swirling jet flow is investigated by large-eddy simulation (LES) using the approximate deconvolution model. Conditions are chosen similar to recent experimental investigations by Liang and Maxworthy [Liang H, Maxworthy T. An experimental investigation of swirling jets. J Fluid Mech 2005;525:115] for incompressible flow. LES results are presented for two simulations of a swirling jet at Mach number Ma = 0.6 with and without inflow forcing by imposed linear instability disturbances. Both the forced and the self-excited jet show three-dimensional helical waves developing in the jet breakdown zone. The features observed in the two simulations are compared to each other as well as to the experiments with respect to flow statistics and instability behaviour. Both simulations show favourable qualitative agreement with the experiment.     

Application of Compact Schemes to Large Eddy Simulation of Turbulent Jets

We present 3-D large eddy simulation (LES) results for a turbulent Mach 0.9 isothermal round jet at a Reynolds number of 100,000 (based on jet nozzle exit conditions and nozzle diameter). Our LES code is part of a Computational Aeroacoustics (CAA) methodology that couples surface integral acoustics techniques such as Kirchhoff's method and the Ffowcs Williams– Hawkings method with LES for the far field noise estimation of turbulent jets. The LES code employs high-order accurate compact differencing together with implicit spatial filtering and state-of-the-art non-reflecting boundary conditions. A localized dynamic Smagorinsky subgrid-scale (SGS) model is used for representing the effects of the unresolved scales on the resolved scales. A computational grid consisting of 12 million points was used in the present simulation. Mean flow results obtained in our simulation are found to be in very good agreement with the available experimental data of jets at similar flow conditions. Furthermore, the near field data provided by the LES is coupled with the Ffowcs Williams–Hawkings method to compute the far field noise. Far field aeroacoustics results are also presented and comparisons are made with experimental measurements of jets at similar flow conditions. The aeroacoustics results are encouraging and suggest further investigation of the effects of inflow conditions on the jet acoustic field.     

DNS for flow separation control around an airfoil by pulsed jets

Direct numerical simulation (DNS) for flow separation and transition around a NACA-0012 airfoil with an attack angle of 4° and Reynolds number of 100,000 has been reported in our previous paper. The details of flow separation, formation of the detached shear layer, Kelvin-Helmholtz instability (inviscid shear layer instability) and vortex shedding, interaction of nonlinear waves, breakdown, and re-attachment are obtained and analyzed. The power spectral density of pressure shows the low frequency of vortex shedding caused by the Kelvin-Helmholtz instability still dominates from the leading edge to trailing edge. Based on our understanding on the flow separation mechanism, we try to reveal the mechanism of the flow separation control using blowing jets and then optimize the jets. DNS simulations for flow separation control by blowing jets (pulsed and pitched and skewed jets) are reported and analyzed. The effects of different unsteady blowing jets on the surface at the location just before the separation points are studied. The length of separation bubble is significantly reduced (almost removed) after unsteady blowing technology is applied. The mechanism of early transition caused by the blowing jets was found. A blowing jet with K-H frequency, sharp shape function (very small mass blowing), pitching and skewing obtained the best efficiency based on the increase of the ratio of lift over drag and decrease of blowing mass flow. In this work, a DNS code with high-order accuracy and high-resolution developed by the computational fluid dynamics group at University of Texas at Arlington is applied.     

Electrostatically driven synthetic microjet arrays as a propulsion method for micro flight

A novel propulsion method suitable for micromachining is presented that takes advantage of Helmholtz resonance, acoustic streaming, and eventually flow entrainment and thrust augmentation. In this method, an intense acoustic field is created inside the cavity of a Helmholtz resonator. Flow velocities at the resonator throat are amplified by the resonator and create a jet stream due to acoustic streaming. These jets are used to form a propulsion system. In this paper a system hierarchy incorporating the new method is described and the relevant governing equations for the Helmholtz resonator operation and acoustic streaming are derived. These equations can predict various device parameters such as cavity pressure amplitude, exit jet velocity and generated thrust. In a sample embodiment, an electrostatic actuator is used for generation of the initial acoustic field. The relevant design parameters for the actuator are discussed and an equivalent circuit model is synthesized for the device operation. The circuit model can predict the lowest order system resonance frequencies and the small signal energy conversion efficiency. A representative resonator performance is simulated and it is shown that velocities above 16 m/s are expected at jet nozzles. The calculated delivered thrust by this resonator with 0.7 m diaphragm displacement amplitude is 3.3 N at the resonance frequency.     

Numerical simulation of impact of a jet on a wall

A computing technique for simulating the impact of a high-speed liquid jet on a wet wall is implemented. Such an impact generates shock waves in the jet, in the liquid layer on the wall, and in the gas surrounding the liquid. Also, the interphase boundary is strongly deformed by such an impact. The technique is based on the Constrained Interpolation Profile-Combined Unified Procedure (CIP-CUP) method combined with the dynamically adaptive Soroban grids. The gas-dynamic equations describing the liquid and gas flow are integrated without an explicit separation of the liquid-gas boundary. Such an approach is shown to be efficient for the considered problems. It allows us to obtain solutions without oscillations near the interfaces (including the case where they interact with the shock waves). For illustrative purposes, we provide the computational results for several one-dimensional and twodimensional problems with the typical features of the impact of a high-speed liquid jet on a wall, as well as a comparison with the known analytical and numerical solutions. The computational results for the problem of the impact of a high-speed liquid jet on a wall covered by a thin liquid layer are also presented.     

Prediction of penetration depth in a plunging water jet using soft computing approaches

The flow characteristics of the plunging water jets can be defined as volumetric air entrainment rate, bubble penetration depth, and oxygen transfer efficiency. In this study, the bubble penetration depth is evaluated based on four major parameters that describe air entrainment at the plunge point: the nozzle diameter (D _N), jet length (L _j), jet velocity (V _N), and jet impact angle (θ). This study presents artificial neural network (ANN) and genetic expression programming (GEP) model, which is an extension to genetic programming, as an alternative approach to modeling of the bubble penetration depth by plunging water jets. A new formulation for prediction of penetration depth in a plunging water jets is developed using GEP. The GEP-based formulation and ANN approach are compared with experimental results, multiple linear/nonlinear regressions, and other equations. The results have shown that the both ANN and GEP are found to be able to learn the relation between the bubble penetration depth and basic water jet properties. Additionally, sensitivity analysis is performed for ANN, and it is found that D _N is the most effective parameter on the bubble penetration depth.     

Numerical simulation of vortical flows in the near field of jets from notched circular nozzles

The vortex dominated flows in the near field of jets from notched circular nozzles are investigated using direct numerical simulation. The nozzles studied include a normal circular nozzle, a V-shaped notched nozzle, and an A-shaped notched nozzle, all with the same circular cross-section. The vortical structures resulting from these different circular nozzles are visualized by using a numerical dye visualization technique. Results for the V-shaped notched nozzle are compared with available experimental measurements using laser-induced fluorescence techniques. In addition to azimuthal vortex rings created because of the shear-layer between the jet and the ambient fluid, the computations also reveal streamwise vortex pairs both inside and outside the vortex rings that spread outward as the vortex rings move downstream. Comparisons of the three different nozzles show that, unlike in the case of the circular nozzle where the streamwise vortex pairs emerge evenly along the nozzle lip, streamwise vortex pairs for the notched circular nozzles are produced only at peak and trough locations. Analysis of the mixing characteristics of the three types of nozzles shows that the notches in the nozzle exit significantly enhance jet mixing.     

Finite element solution of viscous jet flows with surface tension

A finite element method is used to study the effect of Reynolds number and surface tension on the expansion and contraction of jets of Newtonian liquids. For values of Reynolds numbers (based on tube diameter), below 14 the jets expand, and when Re > 14 the jets contract. For higher Reynolds numbers the jet diameter approaches a limiting value. It is also found that the surface tension has a considerable effect on low Reynolds number jet flows, becoming negligible at higher Reynolds numbers. As an example, if the surface tension parameter $\text{σ}\text{η}\text{u}$ is equal to unity, the creeping flow jet expansion is reduced by 4% relative to the case with no surface tension but when Re is equal to 20 and 50 the final jet diameters increase by only 0.2%. The calculated jet shapes are compared with available experimental results.     

Numerical investigations in Rayleigh breakup of round liquid jets with VOF methods

Simulations of the growth of a capillary instability and of the breakup of a jet were carried out using a one-fluid model to describe the two-phase flow motion and a VOF approach to capture the interface. The model considered each phase as fictitious sub-domains and accounted implicitly for jump conditions at the interface through a unique set of equations for which a source term of surface tensions appeared in momentum equations. The predominance of capillary effects in the breakup mechanism required to accurately describe the surface tension contribution. The Brackbill surface model was chosen because of its simplicity to represent tension forces, although it was known to generate parasitic currents susceptible to limit its precision. The flow incompressibility was ensured with an augmented Lagrangian method in case of sequential calculations and by a predictor/corrector approach for 3D simulations that required parallel computations. As a first step, the numerical methods were validated by simulating the growth of a capillary instability and comparing results to those predicted by the Rayleigh theory for capillary instabilities. The consistency of the Brackbill surface tension model and the accuracy of the methods were evaluated via a convergence study. As a second step, the simulation of a jet breakup was carried out using water as injected liquid and compressed carbon dioxide as surrounding medium. It was shown that the simulation predicted accurately the breakup length and the droplet size evidenced experimentally in literature.     

Optimal Jet Finder

We describe a FORTRAN 77 implementation of the optimal jet definition for identification of jets in hadronic final states of particle collisions. We discuss details of the implementation, explain interface subroutines and provide a usage example. The source code is available from http://www.inr.ac.ru/~ftkachov/projects/jets/.

Program summary

Title of program: Optimal Jet Finder (OJF_014)Catalogue identifier: ADSBProgram Summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSBProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: Any computer with the FORTRAN 77 compilerTested with: g77/Linux on Intel, Alpha and Sparc; Sun f77/Solaris (thwgs.cern.ch); xlf/AIX (rsplus.cern.ch); MS Fortran PowerStation 4.0/Win98Programming language used: FORTRAN 77Memory required: ∼1 MB (or more, depending on the settings)Number of bytes in distributed program, including examples and test data: 251 463Distribution format: tar gzip fileKeywords: Hadronic jets, jet finding algorithmsNature of physical problem: Analysis of hadronic final states in high energy particle collision experiments often involves identification of hadronic jets. A large number of hadrons detected in the calorimeter is reduced to a few jets by means of a jet finding algorithm. The jets are used in further analysis which would be difficult or impossible when applied directly to the hadrons. Grigoriev et al. [hep-ph/0301185] provide a brief introduction to the subject of jet finding algorithms and a general review of the physics of jets can be found in [Rep. Prog. Phys. 36 (1993) 1067].Method of solution: The software we provide is an implementation of the so-called optimal jet definition (OJD). The theory of OJD was developed by Tkachov [Phys. Rev. Lett. 73 (1994) 2405; 74 (1995) 2618; Int. J. Mod. Phys. A 12 (1997) 5411; 17 (2002) 2783]. The desired jet configuration is obtained as the one that minimizes , a certain function of the input particles and jet configuration.Restrictions on the complexity of the program: The size of the largest data structure the program uses is (maximal number of particles in the input) × (maximal number of jets in the output) × 8 bytes. (For the standard settings <1 MB). Therefore, there is no memory restriction for any conceivable application for which the program was designed.Typical running time: The running time depends strongly on the physical process being analyzed and the parameters used. For the benchmark process we studied, , with the average number of ∼80 particles in the input, the running time was <10−2s on a modest PC (per event with n_tries=1). For a fixed number of jets the complexity of the algorithm grows linearly with the number of particles (cells) in the input, in contrast with other known jet finding algorithms for which this dependence is cubic. The reader is referred to Grigoriev et al. [hep-ph/0301185] for a more detailed discussion of this issue.     

An image analysis method as applied to study the space-temporal evolution of waves in an annular gas-liquid flow

The secondary instability of the surface of a liquid film sheared by an intensive gas flow was first discovered using high-speed modification of the laser-induced fluorescence method. To study the space-temporal evolution of waves of different types, we used image analysis tools, in particular, the Canny method. As a result, we obtained the quantitative characteristics for both wave types and the phenomenon of the back slope instability of primary waves.     

Application of the image-analysis method to studies of the space-time wave evolution in an annular gas-liquid flow

A secondary instability of the surface of a liquid film sheared by an intense gas flow was found for the first time by our team using the high-speed modified laser-induced fluorescence method. An image-analysis toolkit (in particular, the Canny method) was used for studying space-time evolution of various types of waves. As a result, quantitative characteristics of both the types of waves and the characteristics of the instability phenomena of back slopes of primary waves were obtained.     

An experimental and numerical study of the structure and stability of laminar opposed-jet flows

Experiments, simulations, and numerical bifurcation analysis are used to study the incompressible flow between two opposed tubes with disks mounted at their exits. The experiments in this axisymmetric geometry show that for low and equal Reynolds numbers, Re, at both nozzles, the flow remains symmetric about the plane halfway through the nozzle exits and the stagnation plane is located halfway between the two jets. When Re is increased past a critical value, asymmetric flow fields are obtained even when the momentum fluxes of the two opposed streams are equal. For unequal Re at the jet exits, when the fixed velocity (and the corresponding Reynolds number, Re₁) of one stream is low, the stagnation plane location, SPL, changes smoothly with the Re₂. For high enough Re₁, a hysteretic jump of SPL is observed. Particle Image Velocimetry and flow visualization demonstrate that within the hysteretic range, the two stable flow fields are anti-symmetric. The experimental setup is also studied with transient incompressible flow simulations using a spectral element solver. It is found that to accurately model the flow, we either need to extend the domain into the nozzles, or impose experimental velocity profiles at the nozzle exits. As in the experiments asymmetric flows are obtained past a critical Re. Finally, bifurcation analysis using a Newton-Picard method shows that the transition from symmetric to asymmetric flows results from the loss of stability of the symmetric flows at a pitchfork bifurcation.     

Computations of Explosive Boiling in Microgravity

Dynamics of the explosive growth of a vapor bubble in microgravity is investigated by direct numerical simulation. A front tracking/finite difference technique is used to solve for the velocity and the temperature field in both phases and to account for inertia, viscosity, and surface deformation. The method is validated by comparison of the numerical results with the available analytical formulations such as the evaporation of a one-dimensional liquid/vapor interface, frequency of oscillations of capillary waves, and other numerical results. Evolution of a three-dimensional vapor nucleus during explosive boiling is followed and a fine scale structure similar to experimental results is observed. Two-dimensional simulations yield a similar qualitative instability growth.     

Pneumatic dispensing of nano- to picoliter droplets of liquid metal with the StarJet method for rapid prototyping of metal microstructures

This study presents a new, simple and robust, pneumatically actuated method for the generation of liquid metal micro droplets in the nano- to picoliter range. The so-called StarJet dispenser utilizes a star-shaped nozzle geometry that stabilizes liquid plugs in its center by means of capillary forces. Single droplets of the liquid metal can be pneumatically generated by the interaction of the sheathing gas flow in the outer grooves of the nozzle and the liquid metal. For experimental validation, a print head was build consisting of silicon chips with a star-shaped nozzle geometry and a heated actuator (up to 280°C). The silicon chips are fabricated by Deep Reactive Ion Etching (DRIE). Chip designs with different star-shaped geometries were able to generate droplets with diameters in the range of the corresponding nozzle diameters. The StarJet can be operated in two modes: Either continuous droplet dispensing mode or drop on demand (DoD) mode. The continuous droplet generation mode for a nozzle with 183?μm diameter shows tear-off frequencies between 25 and 120?Hz, while droplet diameters remain constant at 210?μm for each pressure level. Metal columns were printed with a thickness of 0.5–1.0?mm and 30?mm height (aspect ratio >30), to demonstrate the directional stability of droplet ejection and its potential as a suitable tool for direct prototyping of the metal microstructures.