Instability of a moving liquid sheet in the presence of acoustic forcing
TL;DR: In this paper, the excitation of thin planar liquid sheets formed by impinging two collinear water jets to acoustic waves was studied at varying frequencies and sound pressure levels (SPLs).
Abstract: The excitation of thin planar liquid sheets formed by impinging two collinear water jets to acoustic waves was studied at varying frequencies and sound pressure levels (SPLs). Experiments were conducted over a range of liquid velocities that encompassed the stable and flapping regimes of the sheet. For a given frequency, there was a threshold value of SPL below which the sheet was unaffected. The threshold SPL increased with frequency. Further, the sheet was observed to respond to a set of specific frequencies lying in the range of 100–300 Hz, the frequency set varying with the Weber number of the liquid sheet. The magnitude of the response for a fixed pressure level, characterized by the reduction in the extent of the sheet, was larger at lower frequencies. The droplet sizes formed by the disintegration of the sheet reduced with an increase in the measured response and the drop-shedding frequency was near the imposed frequency. Model equations for inviscid flow and accounting for the varying pressure field across the moving liquid sheet of constant thickness was solved to determine the linear stability of the system. Numerical solution shows that the most unstable wavelengths in the presence of the forcing to be smaller than in the absence, which is in line with observations. Both the dilatational and sinuous modes are coupled at the lowest order and become significant for the range of acoustic forcing studied. The model calculation suggests that the parametric resonance involving the dilatational mode may be responsible for the observed instability although the model was unable to predict the observed variation of threshold SPL with frequency.
Citations
More filters
TL;DR: In this article, the linear temporal stability of a viscous liquid sheet is studied in the presence of acoustic oscillations and the viscous potential flow theory is applied to account for liquid viscosity.
Abstract: The linear temporal stability of a viscous liquid sheet is studied in the presence of acoustic oscillations. The viscous potential flow theory is applied to account for liquid viscosity. Acoustic oscillations are provided by imposing a sinusoidal oscillation of the gas velocity or density. Results suggest that the viscosity has a stabilizing effect with a zero mean velocity, and dual effects with a non-zero mean velocity. The effect of oscillations at low velocity is more significant than effects realized at high velocity. Oscillations are a destabilizing factor, although they have a weaker effect at a larger frequency than that at a lower frequency due to the liquid viscosity. Acoustic oscillations promote the instability of the liquid sheet; however, the effects of mean velocity, the gas-to-liquid density ratio, liquid sheet thickness and surface tension are analogous, whether acoustic oscillations exist or not.
18 citations
TL;DR: In this article, the authors present a comprehensive modeling of spray formation in liquid fuel injectors, including internal hydrodynamics of fuel injector, break up of liquid sheet leading to primary and secondary atomization and prediction of size and velocity distributions of droplets in the spray.
Abstract: Comprehensive modeling of spray formation in liquid fuel injectors involves modeling of (i) internal hydrodynamics of fuel injector (ii) break up of liquid sheet leading to primary and secondary atomization and (iii) prediction of size and velocity distributions of droplets in the spray. Comprehensive models addressing all the three aspects are rare though some work has been reported that incorporate two of the three aspects. However, significant volume of literature exists on the individual modules. In the present work, progress and current trends in the individual modules have been extensively reviewed and their implications on development of comprehensive models have been discussed. The unresolved issues and future research directions are also indicated.
17 citations
Cites background from "Instability of a moving liquid shee..."
...The effects of acoustic excitation on the break up of liquid sheets [248, 249] are to be determined....
[...]
TL;DR: In this paper, the authors used 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.
Abstract: 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 . Here, and are the density and surface tension of the liquid, respectively, is the speed of the liquid jet, and 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.
12 citations
Cites background from "Instability of a moving liquid shee..."
...These images appear similar to those of Mulmule et al. (2010), where the entire liquid sheet is subjected to external acoustic waves, and those of Bremond et al. (2007), where undulations were produced by a head-on impingement of a single laminar jet on a vibrating impactor....
[...]
TL;DR: In this article, the stability of a radial liquid sheet produced by head-on impingement of two equal laminar liquid jets is analyzed and 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.
Abstract: 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 ...
11 citations
10 citations
References
More filters
TL;DR: In this article, the stability of the plane free surface is investigated theoretically when the vessel is a vertical cylinder with a horizontal base, and the liquid is an ideal frictionless fluid making a constant angle of contact of 90° with the walls of the vessel.
Abstract: A vessel containing a heavy liquid vibrates vertically with constant frequency and amplitude. It has been observed that for some combinations of frequency and amplitude standing waves are formed at the free surface of the liquid, while for other combinations the free surface remains plane. In this paper the stability of the plane free surface is investigated theoretically when the vessel is a vertical cylinder with a horizontal base, and the liquid is an ideal frictionless fluid making a constant angle of contact of 90° with the walls of the vessel. When the cross-section of the cylinder and the frequency and amplitude of vibration of the vessel are prescribed, the theory predicts that the m th mode will be excited when the corresponding pair of parameters (p m , q m ) lies in an unstable region of the stability chart; the surface is stable if none of the modes is excited. (The corresponding frequencies are also shown on the chart.) The theory explains the disagreement between the experiments of Faraday and Rayleigh on the one hand, and of Matthiessen on the other. An experiment was made to check the application of the theory to a real fluid (water). The agreement was satisfactory; the small discrepancy is ascribed to wetting effects for which no theoretical estimate could be given.
773 citations
TL;DR: In this paper, the stability of a thin layer of liquid moving in still air is studied theoretically with the object of throwing light on the break-up of films during atomization, and it is found that instability occurs if W = T/ρ 1U2h < 1 and that the wavelength for maximum growth factor, for W « 1, is λ = (4πT/ρ 2U2U2).
Abstract: The stability of a thin layer of liquid moving in still air is studied theoretically with the object of throwing light on the break-up of films during atomization. It is found that instability occurs if W = T/ρ1U2h < 1 and that the wavelength for maximum growth factor, for W « 1, is λ = (4πT/ρ2U2) where ρ1 is the liquid density, ρ2 is the air density, U is the film velocity, 2h is the film thickness and T is the surface tension of the liquid. Comparison with experimental data shows fair agreement with the observed wavelengths.
500 citations
TL;DR: In this paper, it was shown that the free edge of a sheet of uniform thickness moves into an expanding sheet at the same speed as antisymmetrical waves, sweeping the fluid into roughly cylindrical borders.
Abstract: The free edge of a sheet of uniform thickness moves into it at the same speed, (2 T /ρ t ) ½ , as antisymmetrical waves, sweeping the fluid into roughly cylindrical borders. Here T , ρ and t are surface tension, density and thickness of the sheet. In a radially expanding sheet t decreases with increasing radius and beyond a radius R where (2 T /ρ t ) ½ is greater than u the radial velocity of the sheet, the edge moves inwards faster than it is convected outwards. Photographs show that the edge of an expanding sheet establishes itself near but inside the radius R . The sheet produced by a swirl atomizer expands as a cone but photographs show that its thickness fluctuates very greatly at the point where it emerges from the orifice. The edge of a conical sheet of varying thickness establishes itself at a point well inside the radius at which (2 T /ρ t ) ½ = u , t being the mean thickness. A moving sheet of uniform thickness can be bounded by a stationary free edge at angle sin -1 ( W ½ ) to the direction of motion. Here W , the Weber number, is 2 T /ρ tu 2 . Photographs show free edges at this angle and therefore parallel to antisymmetrical waves. If this remained true in an expanding sheet the edges would coincide with the cardioids discussed in part II, but reasons are given to show that this is not the case. A small obstacle can divide an expanding sheet forming two edges which lie at the same angle to one another as the two cardioids, namely, 2 sin -1 ( W ½ ) but photographs show that these edges do not subsequently lie on cardioids.
473 citations
TL;DR: In this article, it was shown that a finite change in direction of flow can occur at a cardioid which therefore assumes the form of a sharp edge, and the predicted wave patterns agree with those revealed by the schlieren photographs.
Abstract: It is shown that capillary waves are of two kinds, symmetrical waves in which the displacements of opposite surfaces are in opposite directions, and antisymmetrical waves in which the displacements are in the same direction. Any disturbance can be regarded as composed of these two types of wave. The antisymmetrical waves are non-dispersive. In a sheet of uniform thickness a moving point disturbance produces two narrow line-like waves. In a radially expanding sheet a fixed disturbance point produces two narrow disturbances in the form of cardioids. It is shown theoretically that a finite change in direction of flow can occur at a cardioid which therefore assumes the form of a sharp edge. A method was found for producing and photographing a sheet with a sharp edge in the form of a cardioid. The symmetric waves are very different, they are highly dispersive and are propagated much more slowly than the antisymmetrical waves. Experimentally a point disturbance produces both kinds of wave simultaneously. Reflexion photographs show the antisymmetrical waves, while the schlieren method is needed to reveal the symmetrical waves. The symmetrical waves produced in a moving sheet by a point disturbance are parabolas when the sheet is uniform in thickness, and of a more complicated form when the sheet is expanding. The predicted wave patterns agree with those revealed by the schlieren photographs.
276 citations
TL;DR: Linear and nonlinear analyses of the instabilities and distortion of liquid streams injected into a gaseous media are discussed in this paper, where various fundamental mechanisms and the predictive capabilities for the distortions are emphasized.
237 citations