Nonlinear breakup of thin liquid sheets
TL;DR: In this paper, the authors derived conservation equations using a control volume method and solved using MacCormack's predictor-corrector scheme to determine the breakup of thin planar liquid sheets due to nonlinear growth of disturbances.
Abstract: The breakup of thin planar liquid sheets due to the nonlinear growth of disturbances is determined. Conservation equations are derived using a control volume method and solved using MacCormack's predictor-corrector scheme. It is found that the size and geometry of ligaments, formed during breakup, vary with the weber number. Antisymmetric waves, which spontaneously intensify at higher values of the Weber number, give rise to thin ligaments. At lower values of the Weber number antisymmetric waves formed initially get transformed into symmetric interfaces giving larger ligaments. The magnitude of the initial amplitude of the disturbances is shown to strongly influence the disintegration. The results are compared with experimental results obtained for thin water sheets and good agreement is demonstrated.
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TL;DR: In this article, the temporal evolution of three-dimensional instabilities on a planar liquid sheet segment is studied using direct numerical simulation, and the level-set and volume-of-fluid methods for the liquid-gas interface tracking.
Abstract: The temporal evolution of three-dimensional instabilities on a planar liquid sheet segment is studied using direct numerical simulation, and the level-set and volume-of-fluid methods for the liquid-gas interface tracking. Three atomization cascades are distinguished at early breakup, which are well categorized on a gas Weber number (Weg) versus liquid Reynolds number (Rel) map. These atomization processes include lobe stretching that occurs at low Rel and low Weg, hole and bridge formation that occurs at moderate Rel and high Weg, and lobe corrugation occurring at high Rel and low Weg. Qualitative comparison between the sizes of the ligaments and droplets that result from each process is presented. A transitional region between the prescribed atomization domains is found. At high Rel, the transitional boundary is a constant Ohnesorge line defined based on gas We and liquid Re ( O h m ≡ W e g ∕ R e l ). At low Rel, the transitional region follows a hyperbolic line on the Weg–Rel plot. These atomization pro...
56 citations
16 Dec 2009
TL;DR: In this paper, the effects of the nozzle shape and spray pressure on the liquid sheet characteristics were investigated for four nozzles with different exit widths (1.0, 1.5, 2.0 and 2.5 mm).
Abstract: The main objective of this research is to study analytically and experimentally the liquid sheet breakup of a flat fan jet nozzle resulting from pressure-swirling. In this study the effects of nozzle shape and spray pressure on the liquid sheet characteristics were investigated for four nozzles with different exit widths (1.0, 1.5, 2.0 and 2.5 mm). The length of liquid sheet breakup, liquid sheet velocity and the size of formed droplets were measured by a digital high speed camera. The breakup characteristics of plane liquid sheets in atmosphere are analytically investigated by means of linear and nonlinear hydrodynamic instability analyses. The liquid sheet breakup process was studied for initial sinuous and also varicose modes of disturbance. The results presented the effect of the nozzle width and the spray pressure on the breakup length and also on the size of the formed droplets. Comparing the experimental results with the theoretical ones for all the four types of nozzles, gives a good agreement with difference ranges from 4% to 12%. Also, the comparison between the obtained results and the results due to others shows a good agreement with difference ranged from 5% to 16%. Empirical correlations have been deduced describing the relation between the liquid sheet breakup characteristics and affecting parameters; liquid sheet Reynolds number, Weber number and the nozzle width.
56 citations
TL;DR: In this article, the effects of nozzle shape and spray pressure on the liquid sheet characteristics were investigated for four nozzles with different exit widths (10, 15, 20 and 25 mm) and the length of liquid sheet breakup, liquid sheet velocity and the size of formed droplets were measured by a digital high speed camera.
55 citations
TL;DR: In this article, a nonlinear model for the instability and breakup of an annular liquid sheet is proposed, where the liquid sheet was considered to move axially and is exposed to co-flowing inner and outer gas streams.
42 citations
TL;DR: A second-order instability analysis has been performed for sinuous disturbances on two-dimensional planar viscous sheets moving in a stationary gas medium using a perturbation technique in this paper.
Abstract: A second-order instability analysis has been performed for sinuous disturbances on two-dimensional planar viscous sheets moving in a stationary gas medium using a perturbation technique. The solutions of second-order interface disturbances have been derived for both temporal instability and spatial instability. It has been found that the second-order interface deformation of the fundamental sinuous wave is varicose or dilational, causing disintegration and resulting in ligaments which are interspaced by half a wavelength. The interface deformation has been presented; the breakup time for temporal instability and breakup length for spatial instability have been calculated. An increase in Weber number and gas-to-liquid density ratio extensively increases both the temporal or spatial growth rate and the second-order initial disturbance amplitude, resulting in a shorter breakup time or length, and a more distorted surface deformation. Under normal conditions, viscosity has a stabilizing effect on the first-order temporal or spatial growth rate, but it plays a dual role in the second-order disturbance amplitude. The overall effect of viscosity is minor and complicated. In the typical condition, in which the Weber number is 400 and the gas-to-liquid density ratio is 0.001, viscosity has a weak stabilizing effect when the Reynolds number is larger than 150 or smaller than 10; when the Reynolds number is between 150 and 10, viscosity has a weak destabilizing effect.
33 citations
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TL;DR: In this paper, the velocity and radius of a column of axisymmetric fluid with a free surface were derived from the Navier-Strokes equation, where the equations form singularities as the fluid neck is pinching off.
Abstract: We consider the viscous motion of a thin axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier–Strokes equation. We compare our results with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.
550 citations
"Nonlinear breakup of thin liquid sh..." refers background in this paper
...Earlier studies of Sellens [15] and Eggers and Dupont [ 20 ] show that the numerical instabilities can be reduced by incorporating viscous terms in the governing differential equations....
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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
01 Jan 1981
TL;DR: In this paper, a second-order accurate method for solving viscous flow equations has been proposed that preserves conservation form, requires no block or scalar tridiagonal inversions, is simple and straightforward to program (estimated 10% modification for the update of many existing programs), and should easily adapt to current and future computer architectures.
Abstract: Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.
427 citations
TL;DR: In this paper, a study of the stability and disintegration of flat sheets produced by single-hole spray nozzles at various densities of the surrounding air has been made, and it is shown that a flat laminar sheet injected in vacuo is stable, and that drops are formed only at its edges.
228 citations
"Nonlinear breakup of thin liquid sh..." refers methods in this paper
...The linear growth values have been used to determine the breakup lengths by Dombrowski and Hooper [ 4 ]....
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212 citations