Simulation of liquid jet primary breakup: Dynamics of ligament and droplet formation

Primary atomization of liquid injected at high speed into still air is investigated to elucidate physical processes by direct numerical simulation. With sufficient grid resolution, ligament and droplet formation can be captured in a physically sound way. Ligament formation is triggered by the liquid jet tip roll-up, and later ligaments are also produced from the disturbed liquid core surface in the upstream. Ligament production direction is affected by gas vortices. Disturbances are fed from the liquid jet tip toward upstream through vortices and droplet re-collision. When the local gas Weber number is O(1), ligaments are created, thus the ligament or droplet scale becomes smaller as the bulk Weber number increases. Observation of droplet formation from a ligament provides insights into the relevance between the actual droplet formation and pinch-off from a slow liquid jet in laboratory experiments. In the spray, the dominant mode is the short-wave mode driven by propagative capillary wave from the ligament tip. An injection nozzle that is necessary for a slow jet is absent for a ligament, thus the long-wave (Rayleigh) mode is basically not seen without the effect of stretch. By the present simulation, a series of physical processes have been revealed. The present result will be extended to LES modeling in the future.     

Temporal analysis of breakup for a power law liquid jet in a swirling gas

The breakup mechanism and instability of a power law liquid jet are investigated in this study. The power law model is used to account for the non-Newtonian behavior of the liquid fluid. A new theoretical model is established to explain the breakup of a power law liquid jet with axisymmetric and asymmetric disturbances, which moves in a swirling gas. The corresponding dispersion relation is derived by a linear approximation, and it is applicable for both shear-thinning and shear-thickening liquid jets. Analysis results are calculated based on the temporal mode. The analysis includes the effects of the generalized Reynolds number, the Weber number, the power law exponent, and the air swirl strength on the breakup of the jet. Results show that the shear-thickening liquid jet is more unstable than its Newtonian and shear-thinning counterparts when the effect of the air swirl is taken into account. The axisymmetric mode can be the dominant mode on the power law jet breakup when the air swirl strength is strong enough, while the non-axisymmetric mode is the domination on the instability of the power liquid jet with a high We and a low Re _n . It is also found that the air swirl is a stabilizing factor on the breakup of the power law liquid jet. Furthermore, the instability characteristics are different for different power law exponents. The amplitude of the power law liquid jet surface on the temporal mode is also discussed under different air swirl strengths.     

A numerical study of an annular liquid jet in a compressible gas medium

An annular liquid jet in a compressible gas medium has been examined using an Eulerian approach with mixed-fluid treatment. The governing equations have been solved by using highly accurate numerical methods. An adapted volume of fluid method combined with a continuum surface force model was used to capture the gas–liquid interface dynamics. The numerical simulations showed the existence of a recirculation zone adjacent to the nozzle exit and unsteady large vortical structures at downstream locations, which lead to significant velocity reversals in the flow field. It was found that the annular jet flow is highly unstable because of the existence of two adjacent shear layers in the annular configuration. The large vortical structures developed naturally in the flow field without external perturbations. Surface tension tends to promote the Kelvin–Helmholtz instability and the development of vortical structures that leads to an increased liquid dispersion. A decrease in the liquid sheet thickness resulted in a reduced liquid dispersion. It was identified that the liquid-to-gas density and viscosity ratios have opposite effects on the flow field with the reduced liquid-to-gas density ratio demoting the instability and the reduced liquid-to-gas viscosity ratio promoting the instability characteristics.     

The breakup and atomization of a viscous liquid jet

Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet. With respect to the spatial growing disturbance mode, the numerical results obtained from the solution of the dispersion equation reveal that a dimensionless parameterJ _e exists. AsJ _e>1, the axisymmetric disturbance mode is most unstable; and whenJ _e<1, the asymmetric disturbances come into being, their growth rate increases with the decrease, ofJ _e, till one of them becomes the most unstable disturbance. The breakup of a low-speed liquid jet results from the developing of axisymmetric disturbances, whose instability is produced by the surface tension; while the atomization of a high-speed liquid jet is brought about by the evolution of nonaxisymmetric disturbance, whose instability is caused by the aerodynamic force on the interface between the jet and the ambient gas. The project supported by the National Natural Science Foundation of China     

Sonic annular jet in a counterstreaming supersonic flow

When sonic annular jets encounter a supersonic flow, two interaction regimes are possible with open or closed central separation regions. When the flow regimes change, there is an abrupt change in the separation of the shock wave from the nozzle and of the pressure in the central separation region, and hysteresis is also observed. The flow regimes with open central separation region are stationary and can be calculated numerically on the basis of Euler's equations fairly accurately.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–180, September–October, 1979.     

Study of the transition regime of forced capillary breakup of a liquid jet

The results of a study of capillary breakup of thin liquid jets subjected to a random external acoustic field are reported.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–74, July–August, 1995.     

Nonlinear instability of an annular liquid sheet exposed to gas flow

Nonlinear instability and breakup of an annular liquid sheet has been modeled in this paper. The liquid sheet is considered to move axially and is exposed to co-flowing inner and outer gas streams. Also, the effect of outer gas swirl on sheet breakup has been studied. In the developed model a perturbation expansion method has been used with the initial magnitude of the disturbance as the perturbation parameter. This is a comprehensive model in that other geometries of planar sheet and a coaxial jet can be obtained as limiting cases of very large inner radius and inner radius equal to zero, respectively. In this temporal analysis, the effect of liquid Weber number, initial disturbance amplitude, inner gas-to-liquid velocity ratio, outer gas-to-liquid velocity ratio and outer gas swirl strength on the breakup time is investigated. The model is validated by comparison with earlier analytical studies for the limiting case of a planar sheet as well as with experimental data of sheet breakup length available in literature. It is shown that the linear theory cannot predict breakup of an annular sheet and the developed nonlinear model is necessary to accurately determine the breakup length. In the limiting case of a coaxial jet, results show that gas swirl destabilizes the jet, makes helical modes dominant compared to the axisymmetric mode and decreases jet breakup length. These results contradict earlier linear analyses and agree with experimental observations. For an annular sheet, it is found that gas flow hastens the sheet breakup process and shorter breakup lengths are obtained by increasing the inner and the outer gas velocity. Axially moving inner gas stream is more effective in disintegrating the annular sheet compared to axially moving outer gas stream. When both gas streams are moving axially, the liquid sheet breakup is quicker compared to that with any one gas stream. In the absence of outer gas swirl, the axisymmetric mode is the dominant instability mode. However, when outer gas flow has a swirl component higher helical modes become dominant. With increasing outer gas swirl strength, the maximum disturbance growth rate increases and the most unstable circumferential wave number increases resulting in a highly asymmetric sheet breakup with shorter breakup lengths and thinner ligaments.     

Planar jet flow of a radiating gas

Propagation of a laminar jet of a thermodynamically equilibrious gray gas is examined in the boundary layer theory approximation. The one-dimensional radiative energy transport is accounted for in the P ₁ approximation of the spherical harmonic method. Numerical solution of the problem is made under additional simplifying assumptions for various values of the radiation parameters to illustrate the radiation effect. The method and the computational scheme used are applicable to the study of complex jet flows of a radiating gas.The author thanks Yu. P. Lun'kin for his assistance in posing the problem and for his continued interest in the study.     

A cross-correlation velocimetry technique for breakup of an annular liquid sheet

A novel experimental technique for studying the stability of the breakup of a two-phase flow is presented. High-speed backlit photography is used to capture realisations of the unstable mixing layer, and the edge velocity is derived in order to measure the effects of parameters such as gas/liquid momentum ratio, Reynolds and Weber Number. This has traditionally been an edge detection problem that introduces additional uncertainty. Here, a cross-correlation solution is presented, which overcomes the limitations of threshold techniques. Practical application is demonstrated for an atomising annular liquid sheet under several conditions. Sensitivity due to edge blurring and noise is quantified by artificial analysis. Sensitivity analysis shows accuracy and precision to permit sub-pixel precise velocity and stability measurements up to 0.6 sheet thicknesses from the nozzle exit at the conditions studied.     

Surface breakup of a non-turbulent liquid jet injected into a high pressure gaseous crossflow

We employ detailed numerical simulations to understand the physical mechanism underlying the surface breakup of a non-turbulent liquid jet injected transversely into a high pressure gaseous crossflow under isothermal conditions. The numerical observations reveal the existence of shear instability on the jet periphery as the primary destabilization mechanism. The temporal growth of such azimuthal instabilities leads to the formation of interface corrugations, which are eventually sheared off of the jet surface as sheet-like structures. The sheets next undergo disintegration into ligaments and drops during the surface breakup process. The proposed instability mechanism is inherently an inviscid mechanism, contrary to the previously suggested mechanism of surface breakup (known as “boundary layer stripping”), which is relied on a viscous interpretation. The numerically obtained length and time scales of the shear instabilities on the jet laterals are compared with the results of Behzad et al. (2015) on temporal linear stability analyses of a jet in crossflow at near the nozzle. The stability characteristics of the most amplified modes (i.e., the wavenumber and the corresponding growth rate) obtained from the numerical simulations and the stability analyses are in good agreement.     

Effect of the wake on flow in an annular jet

The flow of an annular jet in a channel is studied. The effect of the Mach number of the wake on the structure of the jet is determined. It is shown that with a near-sonic velocity a reorganization occurs in the mode of flow from an open to a closed base region accompanied by a reduction in the level of pressure pulsations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 74–79, November–December, 1974.     

Special characteristics of the breakup of liquid drops with a high gas pressure

In a majority of power plants, the conversion of a liquid fuel into combustion products takes place at high pressure and with a high velocity of the motion of the gas. It is natural that in the choice of the working scheme of the process account must be taken of the effect of possible changes in the characteristics of the atomization process of a liquid fuel, connected with a change in the density of the gas. Of particular importance is the effect of perturbations of the pressure and the velocity on the behavior of liquid drops in a high-density gas flow. The number of communications in which such questions are discussed is very limited, since an overwhelming number of experiments were made at atmospheric pressure [1–7]. Only articles [8, 9] give qualitative concepts with respect to the effect of perturbations of the pressure on the breakup of drops with a gas pressure up to 30 atm. From the information given in [8, 9] it is difficult to form a judgment with respect to the change in the critical conditions and the time parameters of the process of the breakup of drops with a rise in the initial pressure (density) of the gas.     

水动力作用下低速射流碎化的数值模拟

为研究射流在水动力作用下的碎化特性,采用有限体积法对轴对称坐标下Navier-Stokes方程进行了求解,考虑重力和表面张力的影响,并通过Volume-of-Fluid法与Level-Set法成功捕捉到界面的不稳定发展、变形及射流碎化过程,分析了流场内部速度场和压力场分布,结果表明,射流碎化长度随Re/We“5数呈指数型增加,最后探讨了射流速度、直径及周围流体密度、粘性等参量对射流的碎化过程的影响规律.     

液体环轴对称抛洒首次破碎的理论分析

对于水和无水乙醇环形轴对称抛洒实验的首次破碎结果的分析表明，在给定实验条件下，液体密度大约是气体的1000倍，液体首次破碎的过程分2个阶段:首先，界面不稳定性非线性发展，液体尖钉在惯性力和空气阻力的作用下，拉伸变细变长；然后在射流不稳定性的作用下，断裂成液体珠串。这个理论分析给出的首次破碎的平均液体直径与实验结果基本一致。理论分析表明，无水乙醇破碎液滴的平均直径比水液滴小，是无水乙醇表面张力值仅为水的1/3的一个必然结果。     

Momentum transfer in a vertical down flow liquid jet ejector: case of self gas aspiration and emulsion flow

Momentum transfer in a vertical liquid jet contactor consisting of an ejector supported in a vertical column has been studied, using three different liquids as motive fluids, and air as the entrained gas.On the basis of macroscopic momentum and energy balance, an overall loss factor is derived. Moreover, an empirical correlation is proposed to predict the mass flow rate of entrainment by the liquid jet system. Finally, an expression to predict the volumetric flow rate of the carried fluid available at a pressure higher than atmospheric, is given.