Radial Liquid Sheet Research Articles

Response to comment on “Stability of a moving radial liquid sheet: Time-dependent equations” [Phys. Fluids 35, 099101 (2023)

In a recent comment, Mehring and Gyurkovich show that in our derivation of the time-dependent equations, we have neglected the perturbed term in the interface location while applying the kinematic boundary condition. When the neglected term is incorporated in the analysis, the time-dependent equation for the sinuous mode is different from our original expression. They conclude that the instability predicted by the original model does not exist for their new model. We show that, on the contrary, the new model predicts spatial growth of sinuous disturbance that depends on forcing frequency and the slope of the forcing disturbance.

Numerical Study on Primary Breakup of Disturbed Liquid Jet Sprays Using a VOF Model and LES Method

In this study, the primary breakup of a high-speed diesel jet is investigated using a CFD methodology that combines an LES model with a VOF technique for free surface capture. Inner-nozzle turbulence and cavitation are simplified as the sinusoidal radial velocity with a given amplitude and frequency. The ligament and droplet formation process are captured, the liquid jet is disturbed by the radial velocity, and umbrella-shaped crests are created. Meanwhile, ligaments are formed from the edges of crests because of shear stress and surface tension. We investigate the effect on the characteristics of the surface wave and the liquid structure of different disturbance frequencies and amplitudes. The variation in the disturbance amplitude and frequency facilitates the formation of a variety of liquid structures, such as waves, upstream/downstream-directed bells, and droplet chains. Increasing the disturbance frequency reduces the growth rate of the surface waves of the liquid jet. With an increase in disturbance amplitude, the amplitude of surface waves evidently increases. Furthermore, as the disturbance frequency and amplitude increase, the thickness and Weber number of the radial liquid sheet decrease, and this causes the ligament diameter of the primary breakup to become small. Finally, the primary breakup time is investigated, and the time scale of the liquid jet primary breakup decreases as the disturbance amplitude increases, which indicates that an increase in the disturbance amplitude promotes the atomization of a disturbed liquid jet.

Growth of sinuous waves on thin liquid sheets: Comparison of predictions with experiments

A recent theory [M. S. Tirumkudulu and M. Paramati, “Stability of a moving radial liquid sheet: Time dependent equations,” Phys. Fluids 25(10), 102–107 (2013)] has shown that a radially expanding liquid sheet is unstable to sinuous wave disturbances due to the thinning of the liquid sheet while ignoring the presence of a surrounding gas phase. In this work, we compare the predictions of the aforementioned theory with the measurements of Crapper et al. [“Large amplitude Kelvin-Helmholtz waves on thin liquid sheets,” Proc. R. Soc. London, Ser. A 342(1629), 209–224 (1975)] who measured the amplitude and spatial growth rates of sinuous waves induced in radially expanding liquid sheets produced by fan spray nozzles. The predicted growth rates are remarkably close to the measurements over a range of forcing frequencies and amplitudes even though the experiments were performed in the presence of a surrounding gas phase. This is in contrast to large discrepancies observed by Crapper et al. when the same measurements were compared with the predictions of a spatial stability analysis for a moving liquid sheet that accounts for the inertia of the surrounding gas phase but ignores the thickness variation of the sheet.

Stability of a moving radial liquid sheet: experiments

A recent theory (Tirumkudulu & Paramati, Phys. Fluids, vol. 25, 2013, 102107) for a radially expanding liquid sheet, that accounts for liquid inertia, interfacial tension and thinning of the liquid sheet while ignoring the inertia of the surrounding gas and viscous effects, shows that such a sheet is convectively unstable to small sinuous disturbances at all frequencies and Weber numbers $(We\equiv {\it\rho}_{l}U^{2}h/{\it\sigma})$. Here, ${\it\rho}_{l}$ and ${\it\sigma}$ are the density and surface tension of the liquid, respectively, $U$ is the speed of the liquid jet, and $h$ is the local sheet thickness. In this study we use a simple non-contact optical technique based on laser-induced fluorescence (LIF) to measure the instantaneous local sheet thickness and displacement of a circular sheet produced by head-on impingement of two laminar jets. When the impingement point is disturbed via acoustic forcing, sinuous waves produced close to the impingement point travel radially outwards. The phase speed of the sinuous wave decreases while the amplitude grows as they propagate radially outwards. Our experimental technique was unable to detect thickness modulations in the presence of forcing, suggesting that the modulations could be smaller than the resolution of our experimental technique. The measured phase speed of the sinuous wave envelope matches with theoretical predictions while there is a qualitative agreement in the case of spatial growth. We show that there is a range of frequencies over which the sheet is unstable due to both aerodynamic interaction and thinning effects, while outside this range, thinning effects dominate. These results imply that a full theory that describes the dynamics of a radially expanding liquid sheet should account for both effects.

Stability of a moving radial liquid sheet: Time-dependent equations

We study the stability of a radial liquid sheet produced by head-on impingement of two equal laminar liquid jets. Linear stability equations are derived from the inviscid flow equations for a radially expanding sheet that govern the time-dependent evolution of the two liquid interfaces. The analysis accounts for the varying liquid sheet thickness while the inertial effects due to the surrounding gas phase are ignored. The analysis results in stability equations for the sinuous and the varicose modes of sheet deformation that are decoupled at the lowest order of approximation. When the sheet is excited at a fixed frequency, a small sinuous displacement introduced at the point of impingement grows as it is convected downstream suggesting that the sheet is unstable at all Weber numbers (We ≡ ρlU2h/σ) in the absence of the gas phase. Here, ρl is the density of the liquid, U is the speed of the liquid jet, h is the local sheet thickness, and σ is the surface tension. The sinuous disturbance diverges at We = 2 which sets the size of the sheet, in agreement with the results of Taylor [“The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets,” Proc. R. Soc. London, Ser. A 253, 313 (1959)]. Asymptotic analysis of the sinuous mode for all frequencies shows that the disturbance amplitude diverges inversely with the distance from the edge of the sheet. The varicose waves, on the other hand, are neutrally stable at all frequencies and are convected at the speed of the liquid jet.

1057 THREE-DIMENSIONAL DEFORMATION AND MERGENCE OF WAVES CAUSED BY INFLECTIONAL INSTABILITY IN A RADIAL LIQUID SHEET

Three-dimensional deformation and merging of instability waves in a radial liquid sheet was clarified. A radial liquid sheet forms when a radially flowing liquid film on a disk emerges from the disk and destabilizes just outside the disk. Such instability is caused by the inflection point in the flow velocity profile, and is therefore referred to as "inflectional instability." The instability initially generates two-dimensional waves that grow and deform to cause turbulent transition. The three-dimensional deformation of instability waves is similar to that of of vortices formed by inflectional instability in a single-phase free shear flow. This suggests that the deformation of the waves is caused by the enhancement of perturbed vortex filaments. However, the waves scarcely merge, whereas vortices in the free shear flow merge frequently. This implies that merging of instability waves in liquid sheets is prevented by surface tension.

A Study on Perforation of a Liquid Sheet Caused by Thermocapillary Effect

The perforation of a thin liquid sheet by thermocapillary effect has been investigated. In a radial liquid sheet, which is produced by release of a liquid film spreading on a disk into the air, a laminar-turbulent transition occurs just outside the disk edge. The coherent turbulent structure after the transition forms the extremely thin liquid sheet locally and perforates it. In addition, the perforation is promoted by the impingement of a hot air flow on the thin liquid sheet. This perforation promotion requires specific condition of liquid flow velocity and airflow temperature. This study proposed the theoretical model of thermocapillary induced perforation of the thin liquid sheet and predicted the specific condition for the thermal perforation promotion in the radial liquid sheet. This model representing time diminishing sheet thickness is derived from a momentum balance between inertial force, Marangoni force and Laplace pressure. A simplified model gives the simple algebraic equation expressing the time required to the perforation. The validity of the theory is verified by comparing the theoretical perforation time with that calculated from a numerical simulation based on CIP method. The specific condition for the perforation promotion, which is estimated from the theoretical perforation time, agrees well with experimentally observed one. This agreement demonstrated that the perforation promotion is caused by thermocapillary effect.

Influence of the Physical Properties of a Liquid on Perforations in a Radial Liquid Sheet Jet

Perforations caused by the laminar-turbulent transition of a radial liquid sheet are described. A liquid film discharged from a small gap between a disk and a nozzle flows radially outward on the disk and forms a radial liquid sheet beyond the disk edge. The radial liquid sheet is unstable because of the internal velocity profile with an inflexion point. The instability causes a laminar-turbulent transition just beyond the disk edge and the transition leads to strong turbulence. Flow patterns depend completely on the frequency of perforations produced by this turbulence; that is, a large number of perforations leads to atomization of the liquid sheet, whereas no perforations results in a smooth liquid sheet. In this paper, we clarified the dependence of perforation on the physical properties of test liquids.

A Study on Nonlinear Growth of Disturbance Waves in a Radial Liquid Sheet

A Study on Nonlinear Growth of Disturbance Waves in a Radial Liquid Sheet

高温および低温気流による放射状自由液膜流の穿孔促進(流体工学,流体機械)

高温および低温気流による放射状自由液膜流の穿孔促進(流体工学,流体機械)

1010 高温および低温気流による放射状自由液膜流の穿孔促進(OS-5 界面が関わる複雑熱流体現象(3))

1010 高温および低温気流による放射状自由液膜流の穿孔促進(OS-5 界面が関わる複雑熱流体現象(3))

Perforation of a Radial Liquid Sheet Caused by Laminar-Turbulent Transition and Improvement/Suppression Factors of the Perforation

Perforations caused by a laminar-turbulent transition of a radial liquid sheet are described. A liquid film produced by an impingement of liquid to a disk center spreads out radially on the disk and forms a radial liquid sheet outside the disk edge. The radial liquid sheet is unstable because of an internal velocity profile with an inflexion point. The instability causes a laminar-turbulent transition just outside the disk edge and the transition leads to strong turbulence. Flow patterns completely depend on the frequency of perforations produced by the strong turbulence. The countless perforations lead to atomization of the liquid sheet and no perforation results in a smooth liquid sheet. The perforation frequency relies on the configurations of aggregations produced by fine waves after the transition. The wavy short aggregations induce the countless perforations and atomization immediately after the transition. The perforation frequency also relies on liquid properties and temperature of ambient air flow. Chemical properties of the liquid sustaining a very thin liquid sheet of a bubble suppress the perforation and hot ambient air flow promotes the perforation.

4226 放射状自由液膜流れの微粒化に及ぼす液体物性と周囲気体温度の影響(G05-13 気泡・液滴(2),G05 流体工学)

This paper describes flow patterns of a radial liquid sheet. A liquid film produced by a impingement of liquid to a disk center spreads out radially on the disk and forms a radial liquid sheet after the disk edge. The radial liquid sheet is unstable because of a internal velocity profile with a inflexional point. The instability cause strong tubulence through a laminar-turbulent transition immediately after the disk edge. Flow patterns of the radial liquid sheet depend completely on the frequency of perforations produced by the strong turbulence. The perforation frequency rely on flow conditions, liquid properties and temperture of ambient gas. Countless perforations lead to atomization of the liquid sheet and no perforation results in a smooth liquid sheet. This study reveals that the flow conditions each flow pattern emerges in and hot ambient gas promotes the atomization.

Growth of Disturbance Wave Induced by Radial Liquid Sheet Instability

The growth and three-dimensional deformation of a disturbance wave in the laminar-turbulent transition of a radial liquid sheet flow are studied. The radial liquid sheet is formed by the release of a radial liquid film flowing on a disk from the edge of the disk to still air. When the Reynolds number is large, a concentric disturbance wave appears and grows downstream on the free surfaces of the liquid sheet. The disturbance wave is induced by an unstable disturbance attributed to an inflectional velocity profile inside the liquid sheet. The detailed observation of a disturbance wave excited by a supersonic wave reveals the growth and three-dimensional deformation of the disturbance wave.

1007 放射状自由液膜流の乱流遷移による液膜穿孔現象の詳細観察(GS-2,5 連成問題・界面,研究発表講演)

1007 放射状自由液膜流の乱流遷移による液膜穿孔現象の詳細観察(GS-2,5 連成問題・界面,研究発表講演)

Growth Process of Disturbance Wave Induced by Instability of a Radial Liquid Sheet(Liquid Flow)

Growth Process of Disturbance Wave Induced by Instability of a Radial Liquid Sheet(Liquid Flow)

308 放射状自由液膜流の乱流遷移による液膜穿孔過程の微視的観察(S42-1 流れの可視化実験解析(1),S42 流れの可視化実験解析)

308 放射状自由液膜流の乱流遷移による液膜穿孔過程の微視的観察(S42-1 流れの可視化実験解析(1),S42 流れの可視化実験解析)

Growth of Disturbance Wave Induced by Instability of a Radial Liquid Sheet

Growth process and three-dimensional deformation process of the disturbance wave, which appears in the laminar-turbulent transition process of a radial liquid sheet flow, are clarified. The radial liquid sheet is formed by the release of a radial liquid-film flowing on a disk from the edge of the disk to still air. When the Reynolds number is large, a concentric disturbance wave ('D wave') appears and grows downstream on free surfaces of the liquid sheet. 'D wave' is caused by the unstable disturbance, which is attributable to the inflectional velocity distribution of the liquid sheet. After the growth and the three-dimensional deformation of 'D wave', a laminar-turbulent transition occurs. The detail observation and amplitude measurement of 'D wave', which is excited by supersonic wave, reveal growth process and three-dimensional deformation process of the 'D wave'.

Instability of Radial Liquid Sheet Flow

In this paper, the stability of a radial liquid sheet is described experimentally and theoretically. The liquid sheet was formed by the release of a radial liquid film flowing on a disk from the edge of the disk to still air. When the Reynolds number was large, a concentric disturbance wave (D wave) appeared and grew downstream on both free surfaces of the liquid sheet. To clarify the cause of the D wave, its frequency was measured by a laser beam reflection method and the cross section of the wavy liquid sheet was observed by the laser-induced fluorescence (LIF) method. Temporal and spatial linear stabilities of the liquid sheet were also investigated. The frequency and wavelength of the D wave and the phase difference between the D waves on the two liquid surfaces agreed well with those of the disturbance predicted using the stability theory. This means that the D wave on the liquid surface is caused by unstable disturbance, which is attributable to the inflectional velocity distribution of the liquid sheet. It was also found that Gaster's simplified equation, which transforms the temporal growth rate to a spatial one in the stability theory, is inadequate for a disturbance with a high growth rate.

914 放射状自由液膜流の乱流遷移過程に現れる筋状液塊に関する研究

The formation process of the slender liquid lump, which is produced in the laminar-turbulent transition process of a radial liquid sheet flow, is clarified. The radial liquid sheet is formed by the release of a radial liquid-film flowing on a disk from the edge of the disk to still air. When the Reynolds number is large, a concentric disturbance wave ('D wave') appeares and grows downstream on free surfaces of the liquid sheet. 'D wave' is caused by the unstable disturbance, which is attributable to the inflectional velocity distribution of the liquid sheet. After the growth of 'D wave', laminar-turbulent transition occurs and slender liquid lumps are formed. Slender liquid lumps disintegrate into drops downstream. The detail observation of the laminar-turbulent transition process reveals that the formation of the slender liquid lumps takes root in three-dimensional deformation of 'D wave'.