Early-time jet formation in liquid-liquid impact problems: theory and simulations
File(s)
Accepted version
Author(s)
Cimpeanu, R
Moore, MR
Type
Journal Article
Abstract
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.
Date Issued
2018-12-10
Date Acceptance
2018-08-22
Citation
Journal of Fluid Mechanics, 2018, 856, pp.764-796
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Start Page
764
End Page
796
Journal / Book Title
Journal of Fluid Mechanics
Volume
856
Copyright Statement
© 2018 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000447209900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/K041134/1
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
drops and bubbles
gas/liquid flow
interfacial flows (free surface)
2ND-ORDER WAGNER THEORY
SMALL DEADRISE ANGLES
WATER-ENTRY PROBLEMS
DROP IMPACT
SOLID-SURFACE
3-DIMENSIONAL THEORY
ADAPTIVE SOLVER
EJECTA SHEET
FLUID LAYER
DEEP POOL
Publication Status
Published
Date Publish Online
2018-10-11