hydrodynamics and acoustics of a drop impact on a … · droplet falling onto a liquid surface //...

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»


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.


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


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


Pinch off of the drop from a nozzle: levitation of the satellite droplets


Part 1. Drop detach

Bridge breakup


H=80 см

U=3.7 м/с

We=925

Fr=280

Re=18500

3 мин 10 с

fps=20000 к/с


ЭКСПЕРИМЕНТАЛЬНАЯ УСТАНОВКА


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


( )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=


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


-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


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


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


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



Detachment of castor oil from a round nozzle

Variability of Droplet Shape

18


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 .


H=80 см

U=3.7 м/с

We=925

Fr=280

Re=18500

3 мин 10 с

fps=20000 к/с


Primary contact of the drop with targeted fluid


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


Излучение звука при дефргагментации-2


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


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


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


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


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


Regime 1:Two contrasting Bubbles

33

H=80 см

U=3.7 м/с

We=925

Fr=280

Re=18500


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


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


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


Deformation and splitting of round homogeneous dye spot

into spiral arm and separated fibers


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 .


39


0 0

0

, ,

M M M

0r

0

00

, 0,

M M

0r


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


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


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. .


Благодарю за вниманиеЮ.Д.Чашечкин, ИПМех РАН


hydrodynamics and acoustics of a drop impact on a … · droplet falling onto a liquid surface //...

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