1063-7842/00/4512- $20.00 © 2000 MAIK “Nauka/Interperiodica” 1529
Technical Physics, Vol. 45, No. 12, 2000, pp. 1529–1537. Translated from Zhurnal Tekhnicheskoœ Fiziki, Vol. 70, No. 12, 2000, pp. 18–27.
Original Russian Text Copyright © 2000 by Chizhov, Schmidt.
INTRODUCTION
An impact of a liquid drop on an obstacle at a veloc-
ity comparable to the sound speed in the liquid gener-
ates shock and expansion waves interacting with each
other and with free surfaces, the evolution of a cumula-
tive jet, and the formation and collapse of cavitation
bubbles. Therefore, the phenomenon of high-velocity
drop impact is closely related to many fundamental
problems in mechanics of continua and physics of
strength. This phenomenon is also of interest in applied
problems, such as the erosion action of liquid–gas
streams, coating application, mining art, working of
hard materials, cleaning of surfaces, production of new
materials, astrophysics problems, etc. [1–6].
Comprehensive reviews on impacts of drops on
obstacles can be found in [1, 5, 7–9]. However, phe-
nomenon of high velocity has not been adequately stud-
ied even qualitatively. The objective of this paper is to
describe the detailed pattern of a drop impact on an
absolutely rigid surface and on a thin liquid layer under
conditions at which liquid compressibility shows up
most vividly, that is, at impact velocities comparable to
the sound speed in the liquid. Emphasis will be to the
effect of liquid viscosity and surface tension, interac-
tion between impact products and ambient gas, mecha-
nism of initiation and disruption of the cumulative jet,
jet velocity evaluation, formation mechanism of cavita-
tion cavities, loads experienced by the obstacle, differ-
ences between plane and axisymmetric impacts,
change in the flow structure upon striking the liquid
layer, and reasons for experimental spread and discrep-
ancy between analytical and experimental estimates.
DROP IMPACT PATTERN
Generally, drop–obstacle interaction produces a liq-
uid flow with the well-developed wave structure and
heavily deformable free surface (Fig. 1).
One interesting feature of a convex-drop impact is
that, at the initial impact stage, the free surface, which
does not contact the rigid one, does not deform. The
compression region of the drop is bounded by a shock
wave adjacent to the contact domain boundary (see
Fig. 1a). This is because the velocity of motion of the
contact boundary V
E
= V
0
(t) (where V
0
is the ini-
tial velocity of the drop and β(t) is the angle between
the free surface and the rigid wall), being infinitely
large at the contact instant t = 0, decreases, remaining
greater than the shock wave velocity up to a certain
instant t
c
. Therefore, disturbances propagating from the
wall have no time to interact with the free surface. The
compression of the liquid is maximal at the contact
periphery and continues to grow with time.
At the critical instant t
c
, the shock wave leaves the
contact boundary and interacts with the free surface to
form a shock wave in the ambient gas and an expansion
wave propagating inside the drop. The free surface
starts to deform and a near-wall high-velocity cumula-
tive jet is formed (Fig. 1b). The time of jet formation
depends on viscous and surface effects in the liquid
near the wall, and the jet velocity far exceeds the impact
one.
When the shock wave in the drop approaches its top,
the expansion wave, following the shock wave, causes
the formation of a toroidal cavitation area whose cross
section is shown in Fig. 1c. At the final stage of interac-
tion, the expansion wave collapses at the symmetry
axis, and a vast cavitation area with the greatest rarefac-
tion near the axis is formed (Fig. 1d). As the expansion
wave propagates toward the rigid surface, the cavitation
area occupies nearly the whole drop excepting a thin
layer near the free surface and the near-wall jet region.
The instabilities develop, the liquid coating breaks
down, and the drop takes a shape of a crown and disin-
tegrates into small fragments [10].
β cot
GASES AND LIQUIDS
Impact of a High-Velocity Drop on an Obstacle
V. Chizhov and A. A. Schmidt
Ioffe Physicotechnical Institute, Russian Academy of Sciences,
Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia
E-mail: Anton.Chizhov@pop.ioffe.rssi.ru
Received March 1, 2000
Abstract—Processes arising when a high-velocity liquid drop strikes a rigid obstacle or a liquid layer were
investigated using numerical simulation. The flow pattern being formed features a complicated interaction of
compression shock and expansion waves between each other and with free surfaces, the initiation of a cumula-
tive jet flow, and the formation of cavitation areas. Factors governing the interaction process are analyzed.
Obtained results are compared with experimental data. © 2000 MAIK “Nauka/Interperiodica”.