Impact of liquids with different densities

Semënov, Yu. A.; Wu, G.X.; Korobkin, A.A.

doi:10.1017/jfm.2015.8

Cited by 13 publications

(10 citation statements)

References 18 publications

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“…Its main effect is to pull the jet further down. As Fr further drops, the jet tip will touch the plate and a closed cavity would therefore form, similar to what has been observed in the work of Semenov, Wu, and Korobkin, 16 which is beyond the scope of the current work. It should be pointed out that the effect of the gravity is considered in the particular case a = b = 2 with which the flow may be approximated as self-similar.…”

Section: Results With Finite Weber Reynolds or Froude Numberssupporting

confidence: 74%

Local flow at plate edge during water entry

Sun

2020

Physics of Fluids

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Section: Results With Finite Weber Reynolds or Froude Numberssupporting

confidence: 74%

Local flow at plate edge during water entry

Sun

2020

Physics of Fluids

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“…In addition, further validation of the numerical code will support any future results for more complex scenarios that are not so readily tackled using Wagner theory, for example the impact of two fluids with different densities, which has applications to aerosol formation in the dispersion of oil slicks or biological matter, see for example Murphy et al (2015). Note that Semenov et al (2015) exploit the similarity solution admitted by the geometry to investigate the impact of two fluid wedges of different densities numerically.…”

Section: Introductionmentioning

confidence: 88%

Early-time jet formation in liquid–liquid impact problems: theory and simulations

Cimpeanu

Moore²

2018

J. Fluid Mech.

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We perform a thorough qualitative and quantitative comparison of theoretical predictions and direct numerical simulations for the two-dimensional, vertical impact of two droplets of the same fluid. In particular, we show that the theoretical predictions for the location and velocity of the jet root are excellent in the early stages of the impact, while the predicted jet velocity and thickness profiles are also in good agreement with the computations before the jet begins to bend. By neglecting the role of the surrounding gas both before and after impact, we are able to use Wagner theory to describe the early-time structure of the impact. We derive the model for general droplet velocities and radii, which encompasses a wide range of impact scenarios from the symmetric impact of identical drops to liquid drops impacting a deep pool. The leading-order solution is sufficient to predict the curve along which the root of the high-speed jet travels. After moving into a frame fixed in this curve, we are able to derive the zero-gravity shallow-water equations governing the leading-order thickness and velocity of the jet. Our numerical simulations are performed in the open-source software Gerris, which allows for the level of local grid refinement necessary for a problem with such a wide variety of length scales. The numerical simulations incorporate more of the physics of the problem, in particular the surrounding gas, the fluid viscosities, gravity and surface tension. We compare the computed and predicted solutions for a range of droplet radii and velocities, finding excellent agreement in the early stage. In light of these successful comparisons, we discuss the tangible benefits of using Wagner theory to confidently track properties such as the jet-root location, jet thickness and jet velocity in future studies of splash jet/ejecta evolution.

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“…The solution procedure of the system of integral equations is similar to that in Semenov, Wu & Korobkin (2015), and it is based on the method of successive approximations. There is a flexibility in the choice of initial solution for the contact angle µ and the functions v(η), θ(η), βξ and γ(ξ).…”

Section: An Expanding Circular Cylinder With Detached Flowmentioning

confidence: 99%

Water entry of an expanding body with and without splash

Semënov

2019

J. Fluid Mech.

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A self-similar flow generated by water entry of an expanding two-dimensional smooth and curved body is studied based on the incompressible velocity potential theory, with gravity and surface tension effects being ignored. At each expansion speed, mathematical solutions for detached flow with a splash jet and attached flow with jet leaning on the body surface are obtained, both of which have been found possible in experiment, corresponding to hydrophobic and hydrophilic bodies, respectively. The problem is solved using the integral hodograph method, which converts the governing Laplace equations into two integral equations along the half real and imaginary axes of a parameter plane. For the detached flow, the conditions for continuity and finite spatial derivative of the velocity at the point of flow departing form the body surface are imposed. It is found that the Brillouin–Villat criterion for flow detachment of steady flow is also met in this self-similar flow, which requires the curvatures of the free surface and the body surface to be the same at the detachment point. Solutions for the detached flow have been obtained in the whole range of the expansion speeds, from zero to infinity, relative to the water entry speed. For the attached flow there is a minimal expansion speed below which no solution cannot be obtained. Detailed results in terms of pressure distribution, free surface shape and streamlines and tip angle of the jet are presented. It is revealed that when solutions for both detached and attached flows exist, the pressure distributions on the cylinder surface are almost the same up to the point near the jet root. Beyond that point, the pressure relative to the ambient one drops to zero at the detachment point in the former, while it drops below zero in the jet attached on the body and then returns to zero at the contact point in the latter.

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Impact of liquids with different densities

Cited by 13 publications

References 18 publications

Local flow at plate edge during water entry

Local flow at plate edge during water entry

Early-time jet formation in liquid–liquid impact problems: theory and simulations

Water entry of an expanding body with and without splash

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