hydrodynamics and acoustics of a drop impact on a … · droplet falling onto a liquid surface //...
TRANSCRIPT
HYDRODYNAMICS AND
ACOUSTICS OF A DROP
IMPACT ON A FLUID
Yuli D. Chashechkin
Федеральное государственное бюджетное учреждение науки
Институт проблем механики им. акад. А.Ю. Ишлинского Российской академии наук
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Introduction. Drops in life, science, technology and design
Phase of a drop dynamics: pinch off, falls, impact, transformation in a accepted fluid body;
General theory: concepts of “motion” and “fluid flow”
Fundamental set of governing equations
Fluid dynamics and physics: where is the boundary?
What we need from experiments and numerics?
Conclusion. Definition ad a “fluid flow” concept.
Институт проблем механики им. акад. А.Ю. Ишлинского РАН, УСУ «ГФК ИПМех РАН»
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
1. 1. Prokhorov, V. E. and Chashechkin, Yu. D. Dynamics of a single drop detachment in the air
// Fluid Dyn. 2014. 49(4), 109-118.
2. Chashechkin, Yu. D. and Prokhorov, V. E. Detachment of a single water drop // Dokl. Phys.
59(1), 10–15.
3. Chashechkin, Yu. D. The complex structure of wave fields in fluids // Procedia IUTAM. 2013.
8, 65–74.
4. Chashechkin, Yu. D. and Prokhorov, V. E. Drop-impact hydrodynamics: short waves on a
surface of the crown // Dokl. Phys. 2013. 58(7), 296–300.
5. Prokhorov, V. E. and Chashechkin, Yu. D. Emission of the sequence of sound packets during a
drop falling onto the surface of water // Dokl. Phys. 2012. 57(3), 114–118.
6. Prokhorov, V. E. and Chashechkin, Yu. D. Underwater and air sound signals in the case of a
droplet falling onto a liquid surface // Dokl. Phys. 2012. 57(4), 151–156.
7. Prokhorov, V. E. and Chashechkin, Yu. D. Dynamics of underwater sound emission for a
droplet falling onto a liquid surface // Dokl. Phys. 2012. 57(4), 183–188.
8. Chashechkin, Yu. D. and Prokhorov, V. E. The fine structure of a splash induced by a droplet
falling on a liquid free surface at rest // Dokl. Phys. 2011. 56(2), 134–139.
9. Prokhorov, V. E. and Chashechkin, Yu. D. Sound generation as a drop falls on a water surface
// Acoust. Phys. 2011. 57(6), 807–818.
10. Prokhorov, V. E. and Chashechkin, Yu. D. Two regimes of sound emission induced by the
impact of a freely falling droplet onto a water surface // Dokl. Phys. 2011. 56(3), 174–177.
11. Chashechkin, Yu. D. and Prokhorov, V. E. Aero- and hydroacoustics of the impact for a
droplet freely falling onto the water surface // Dokl. Phys. 2010. 55 (9), 460–464.
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Environment: transport atmosphere-hydrosphere, climatic factors,
microbes, spores, viruses, sound, erosion of soil, ….
Technology: jet propulsion, printing, drop cooling dropping, oil
recovery, transportation, food-, bio-and medicine industries;
Hydroacoustics and distant observation in the ocean;
Military technology (non-local blast)
Design,
Relax: Drop and rain sounds in Nature ,
Deep into the Earth – underground sounds
Subject of fundamental studies unifying classical mechanics and modern
physics
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
5
~ 1r
uR
0 r R
0 u n2
Ca
τ n n
,
,
,
Boundary Conditions:
Upstream:
Free Surface:
0 u
Example of the Problem Formulation
1 1 1( )
Fr We Rep
t
s
uu u k F τ
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Pinch off of the drop from a nozzle: levitation of the satellite droplets
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Part 1. Drop detach
Bridge breakup
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
H=80 см
U=3.7 м/с
We=925
Fr=280
Re=18500
3 мин 10 с
fps=20000 к/с
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
ЭКСПЕРИМЕНТАЛЬНАЯ УСТАНОВКА
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
10
TECHNICAL PERFORMANCE
Hydrophone ГИ51Б
bandpass 0.002÷125 kHz,
sensitivity 30 mV/Pa.
Microphone: RFT MV-101
bandpass 0.02÷40 kHz
sensitivity 1580 mV/Pa
Video Camera: Optronis CR 3000x2
CCD matrix 13.57х13.68 мм
max rate 100000 fps
internal memory 8 Gb
max image size 3 Mpx
Lighting:
two floodlight RayLab Xenos RH 1000
Data acquisition:
four ADC channel s– 12 bit, 0.1 µs
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
( )ζ ,z x y=
( ) ( )( )0
0 ζσ σ α Δ ζ 0i ik ik k s i z
p p n n n ^ =¢ ¢- - - + =
2 2
2 2ζ
ζw , Δ
zt x y^=
¶ ¶ ¶= = +
¶ ¶ ¶
Boundary conditions on a free surface:
kinematic and dynamic
Three different objects:
DROP
AIR
TARGET FLUID
σa
D σt
Dσa
t
Governing equations
ρdivρ 0
t
¶+ =
¶v
( )ρ
ρ ρ μΔpt
¶+ Ñ = - Ñ + +
¶
vv v g v
( ) ( )ρ
ρ κ ρT i
TT T Q
t
¶+ Ñ = Ñ Ñ +
¶v
( ) ( )ρ
ρ κ ρii S i S
SS S Q
t
¶+ Ñ = Ñ Ñ +
¶v
( )ρ ρ( , , )ip T S=
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
12
Liquid Density
, g/cm-3
Surface
Tension
,
dyne/cm
Viscosity
, cm2s-1
Bridge
size
D, mm
Breakup
upward
velocity of
the Rest,
mm/s
Bo Oh-1
Water 1 73 0.01 0.4 1400 0.02 200
Alkohol 0.80 23 0.012 0.5 400 0.08 90
Sunflower
Oil
0.93 33 0.6 0.25 50 0.02 1.6
Glycerin 1.26 62 12 0.2 0 0.008 0.08
Castor Oil 0.96 36 10 0.05 0 0.0006 0.04
Properties and Dimensionless Quantities, 20ºС
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
-3g cm
/ 3 -2cm s
2 -1cm s
42.2 10 56.7 1038.4 10
65.24 10 61.35 10
92.3 10 101.8 10 41.7 10
U
33.2 10 31.6 10
Fluid
parameter
Etanol water glicerol 0il
0.80 1.00 1.26 0.93
27.5 74 49.2 35.5
0.012 0.01 12 0.6
, s 0.07 0.04 0.05 0.06
, s 0.12
, cm 0.17 0.27 0.22 0.19
,cm 2.93 0.01
, s 0.013 0.017 0.015 0.014
, s 0.7
, m/s 23 74 0.04 0.6
Bo 8.9 3.3 5.0 6.9
Oh 2.4 0.14
/g g 2 /
1/4
3/g g 3 /d
1/4
3/g g
3 2/
2
WeDU
Dimensional and dimensionless parameters of the flow
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Weber
Reynolds
Froude2
WeFr
Bo
dU
gD
ReUD
Ohnesorge
2
OhD
Bond
2
BogD
3 2/
Pinch off of the drop from a nozzle: waves and oscillations drops
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
15
Detachment Geometry vs Time
0.75
1
4
6мм
1.5
2.5
10 20 30
4.5
5
5.5
t, мс
hf
B
A
hc
a
b
Satellite dimensions
SI Satellite distance
Rest of the fluid on the nozzle
Main droplet dimensions
T=20 ms
T=35ms
f=560 Hz
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
16
5 10 15 20
0.3
0.35
0.4
t, мс
hc
см
10 20
1
2
t, мс
a/g
10 20
-10
0
10
t, мс
v, см/с
3
1
2
ба
Water: Detailed Trajectory of Satellite
Velocity
Normalized
acceleration
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Detachment of castor oil from a round nozzle
Variability of Droplet Shape
18
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Райзер В. Ю., Черный И. В. Микроволновая диагностика поверхностного слоя океана.
СПб: Гидрометеоиздат. 1994. 231 с.
Работы лаборатории механики жидкостей начались в 2002 г. в рамках работ по
оптимизации инструментов дистанционного зондирования .
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
H=80 см
U=3.7 м/с
We=925
Fr=280
Re=18500
3 мин 10 с
fps=20000 к/с
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Primary contact of the drop with targeted fluid
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
30.1210
16
см1 2
30.1210
24
см1 2
30.1210
32
см
см
1 2
1
2
30.1210
48
см1 2
30.1210
68
см1 2
30.1210
102
см1 2
30.1210
0
см
см
1 2
1
2
30.1210
8
см1 2
Evolution of the crown: droplets, streamers, shevron, capillary waves
XVIII Зимняя школа по механике сплошных сред, Пермь, ИМСС УрО РАН, 19 марта 2013 г.
5 10
0.4
1.2
2
t, мс
f, кГц
2 6 10 14
0.8
0.9
t, мс
I
0.4 0.8 1.2 1.6
0.05
0.1
0.15
0.2
f, кГц
, см
5 10
0.1
0.14
0.18
t, мс
, см
0 5 10 15
0
10
28-12-04-1 -я полуволна=разрежение f500
t, мс
P, Па
0 50 100
-5
0
5
10
P, Па
2 4 6
1.2
1.6
t, мс
f, кГц60 100
0.1
0.3
f, кГц
S б
t, мкс
в
а
Dispersion of the surface waves length
Contact acoustic impulse
Variations of the surface waves frequency
Капиллярные волны на поверхности венца
XVIII Зимняя школа по механике сплошных сред, Пермь, 19 марта 2013 г.
0 1 2 3
0
0.5
1
1.5
2
2.5
3
0 1 2 3
0
0.5
1
1.5
2
2.5
3
0 1 2 3
0
0.5
1
1.5
2
2.5
3
0 1 2 3
0
0.5
1
1.5
2
2.5
3
0 1 2 3
0
0.5
1
1.5
2
2.5
3
0 1 2 3
0
0.5
1
1.5
2
2.5
3
0 1 2 3
0
0.5
1
1.5
2
2.5
3
0 1 2 3
0
0.5
1
1.5
2
2.5
3
0 1 2 3
0
0.5
1
1.5
2
2.5
3
Диаметр капли 0.5 см, время в секундах, размеры – см.
0 1 2 3
0
0.5
1
1.5
2
2.5
3
Излучение звука при дефргагментации капли-1
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Излучение звука при дефргагментации-2
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
a
Splash-down Angle a & Sound Emission
0 0.1 0.2 0.3 0.4-20
0
20
40
0 0.1 0.2 0.3 0.4-20
0
20
40
t, с
0 0.1 0.2 0.3 0.4-20
0
20
40
t, с
0 0.1 0.2 0.3 0.4-50
0
50
0 0.1 0.2 0.3 0.4-50
0
50
0 0.1 0.2 0.3 0.4-50
0
50
t, с
0 0.1 0.2 0.3 0.4-20
0
20
40
a=13.9
a=16
a=22.9
a=39.7
a=12.4
a=10.9
H=100 cm
a=0.6
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
0 0.05 0.1 0.15 0.2
-15
-10
-5
0
5
10
15
20 40 60 80
1
2
p, Па
0.198 0.2 0.202 0.204
-10
-5
0
5
10
p, Па
0.2238 0.224
-2
-1
0
1
2
3
p, Па
0.1979 0.1981 0.1983
1418
20 40 60
80100
79 кГцf, кГц
p, Па
t, c
x10-5
x10-5
f, кГц
IIIIIt, сt, с
t, мкс
t, мкс
t, с
III
II
It, мкс
t, мкс
t, с
f, кГц
f, кГц
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
3030
Sound packets and splash hydrodynamics
2.4 кгц
0 0.05 0.1 0.15 0.2 0.25
-15
-10
-5
0
5
10
t, с
P, Па
0 100 200 300
-5
0
5
10
100 200
50
80
0.19 0.195
-10
-5
0
5
225.4 225.8
-10
0
10
15 30 450
0.5
1
f, кГц
162 168
1
2.4 кГц t, мс
f, кГцP, Па P, Паt, мс
2.4 кГц
IIIII
t, мсt, мс
2.5 кГц
I III
IV
P, Па
t, мс
t, мс
P, Па
P, ПаP, Па
t, мкс
II
S
t, мкс
f, кГц
t, мс
а
б
в
д
г
е
32 kHz
27 kHz
2.6 kHz
2.4 kHz
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
высота z, скорость vz, ускорение a, акустическое давление P vs time t
Hd = 50 см U = 2.9 m/s We = 570 Bo = 3.3 Re = 14500
0.00 0.05 0.15 0.20
0.0
0.5
1.0
-2
0
2
f, kHz
t, s0 50 100 150
0.5
1.5
2.5
10 30 5075
95
t, мкс
f, кГц
t, мкс
P, Па
0.169 0.17 0.171
-1.5
0
1.5
3
4 8 12
0.2
0.6
f, кГц
S
t, с
p, Па
0.197 0.198 0.199
-1
0
1
5 10 15
0.2
0.6S
f, кГц
P, Па
t, с
IIIII
I
t, s
p, Pap, Pa p, Pa
t, s
t, s
t, sf, kHz f, kHz
f, kHz
-2
0
2
2
z, cm a, km/s2
P, Pa
1
21km/Sacceleration jumps
6P= / 10 Pa/m
50 S period of emitteds
V a
F
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
32
2 3
0 0
410
6d dE U R эрг
2 24
0
2 10a
P rE dt эрг
c
Drop kinetic energy
ch
cd
/ 2 1.5p c cE d h эрг
Emitted energy in a sound
Surface energy of the bridge
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Regime 1:Two contrasting Bubbles
33
H=80 см
U=3.7 м/с
We=925
Fr=280
Re=18500
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
0.05 0.15 0.25 0.35 0.45
-30
-10
0
10
30
18-01-09-1 ГФ h=4.5см H=57см f500
50 100 150 200
0.2
0.6
1
f, kHz
S
0.035 0.04-5
0
5
10
0.233 0.237 0.241
-30
-10
010
30
3.9 kHz
t, s
P, Pa
SINGLE BEEP REGIME
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
35
0.1 0.2 0.3 0.4
-20
-10
0
10
20
30-12-05-1 ГФ h=3 см H=100см f500
t, s
P, Pa
0.23 0.235 0.24
-20
0
20
30-12-05-1 ГФ h=3 см H=100см f500
0.0785 0.0795 0.0805 0.0815
7
9
11
13
20 40 60 80 0
0.5
1
f, kHz
20 kHz
2.1 kHz
S
0
1 3656 / ,
Pf D Hz
a
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
36
0.15 0.25 0.35 0.45
-20
-10
0
10
20
21-01-09-1 ГФ h=5см H=55см f500
t, s
P, Pa
0.141 0.143 0.14501
3
5
0.1411 0.1413
0
3
0.323 0.3233
15
25
0.3265 0.32715
2511 kHz
65 kHz
83 kHz
DOUBLE BEEP REGIME
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Deformation and splitting of round homogeneous dye spot
into spiral arm and separated fibers
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Deformation and splitting of homogeneous dye spot into spiral arm and separated fibrous
(40 см, 820 об/мин, 7,5 см): 1, 6, 12, 14 с .
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
39
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
0 0
0
, ,
M M M
0r
0
00
, 0,
M M
0r
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Cauchy-Helmholtz Decomposition of fluid
flows: translation, rotation and deformation
of a fluid particle
tdt dt r U r U
Motion is transformation of vector metric
space into itself saving distance:
decomposed on translation and rotation
v
v v ii r k i k ijk j k l
l
r r r U dt U dtx
33R
Parameters (Invariants) of motions
(velocity) (celerity)d
dt
p XV U c
Mp U2
E
p U
Deformable continuous media is submerged into configuration space:
M r p
p U2
E
p U
Flows of deformable Continuum medium
Shear operator connects
independent parts of
elementary operator of
motion and destroys
independence of operators of
shift and rotation.Bertrand J. 1868, S. Lie (1893)
0 0 0, , M M M0r
0 0 0, 0, M M0r
Four Definitions of Motion:Practical, Physical, Mathematical and Geometrical
Topical Problems of Fluid Mechanics - 2014, Prague, Czech Republic , February 19 - 21, 2014
M x F&&
D’Alembert – Navier – Stokes – Fourier – Fick – Mendeleev systemis fundamental set of governing fluid flow equations (complete and self consistent)
+ conventional boundary conditions (no-slip, no-flux, attenuation of disturbances at infinity distance from the source
Three types of sources
StationarySlowFast atomic-molecular
div 0t
v
j v
pt
vv v g v
( , , ), , , ,i ip T S e e p T S TTT j
SSS j
T i
TT T Q
t
v
T S
SS S Q
t
v Compatibility condition
for the fundamental set
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Fi
iSQ
TQ ~ /MT L U
m MT
( )
( )
T T
T M
T m
Q Q Stat
Q T
Q
A few Large scale and rich family of Fine Intrinsic Scales
characterizing set of singular disturbed equations and their solutions
Large (Regular) length scales
,/ln1
dzd
internal wave length bUT
Fine (Singular) length scales:
2 / ,
NN
U U
, d L
Dimensionless parameters – ratios of intrinsic scales: Re, Fr, C, Ar, St, (Pe, Sc)
0Re / / ,Ud U d
0Fr / 2 /d U Nd dC /
d
zexp0Density
Size of an obstacle
2 / ,S
N S N
3L g N
1 2 30
0
; ; ; T
S
T T T TC R R R
d S S S S
a a a
n n
n n
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Only invariants can be observed that are space and time intervals
(distance and duration), mass, momentum, energy, other material
quantities (index of refraction, dispersion coefficients, sound
velocity…thermodynamic parameters
and derivative quantities).Fluid particles as parts of continuous medium cannot be specified and identified.
Fluid velocity is non-observable parameter.
Momentum is observable parameter and can be defined as forcing
action of a flow on an obstacle or by flow rate.
Definition:
A fluid flow is momentum flux supplemented by self- consistent
change of thermodynamical physical quantities
Sense of physical quantities is defined by the set governing equations.
Non-identical transformations change the sense of physical quantities
noted by the same symbols. .
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic
Благодарю за вниманиеЮ.Д.Чашечкин, ИПМех РАН
“Particles in Flows”. Summer school and Workshop. August 30, 2014, Institute of mathematics, Prague, Czech Republic