Heat and mass transfer experiments in the Heat and mass transfer experiments in the Center for Energy ResearchCenter for Energy ResearchNational University MexicoNational University Mexico

Eduardo RamosHeat and Mass Transfer GroupCenter for Energy Research

National University of Mexico

Institute of Fundamental Technological ResearchPolish Academy of Sciences

23 June 2006

ContentsContents

1. Periodicity and bifurcation in capillary boiling

2. Quasi 2D-vortices generated by the Lorentz force in an electrolyte

3. Natural convection in a centrifuge

1. Periodicity and bifurcation in capillary boiling1. Periodicity and bifurcation in capillary boiling

1. Motivation.Nucleate boiling transfers large amounts of heat per unit mass.

S.G. Bankoff AIChE J. (1958): Grooves may function as vapor traps.V. K. Dhir, Ann. Rev. Fluid Mech. (1998) Review.

Principles of Heat Transfer , Kreith 1993

In nucleate boiling, phase change occurs at fractures or small cavities on the walls.

Artificial nucleation sites: Commercially available surface geometries that promote high performance nucleate boiling.

Omegapiezo

Omegapiezo High performance boiling surface, sintered porous surface.

Sintered material copper mesh: 100um-150um

SDK Technik GmbH

Two models considered for studying artificial nucleation sites.

Model 1. Heating wire at the bottom of the capillary.Capillary diameter= 0.5 mm , length=4 mm

Model 2. Concentric heating wire

Capillary diameter= 0.7 mm, length = 60 mm

Capillary model 1

Diameter 0.85 mm

Diameter 1.4 mm

4 mm

Observations with Model 1: Bubble transit at the tip of the capillary

Long interval between bubbles

Absence of bubble

Presence of bubble

Short interval between bubbles

…LLLSLLLLLSLLL…

time (s)

sign

al o

utpu

t (V

)

Observations with Model 1

Average long interval ~ 0.18 sAverage short interval ~0.075 s

Large interval between bubbles

Small interval between bubbles

Time between bubbles (s)

Cou

nts

Event

Tim

e be

twee

n bu

bble

s (s

)

Visualization

Gra

y le

vel

Gray level monitor

time (s)

Origin of the double frequency…

liquid packet

monitor 1

monitor 2

monitor 1

monitor 2

Gra

y le

vel

time (s)

…but liquid packet and natural bubble departure sometimes coincide

liquid package

Velocity of the liquid packet inside the capillary

~32 mm/s

Observations indicate that the liquid packets can be formed by two mechanisms:

liquid accumulation at the bottom of the capillary.

waves on the descending liquid films.

Power spectrum

* 1000 bubbles, 160 packages.

Single bubbles (~5.5 Hz) Short period events (~12 Hz)

|M|

f (Hz)

Return map for the time interval T between subsequent bubbles.

1

2

3

1 Long Long2 Short Long3 Long Short

n

t

t

n

n+1

Model for the time interval T between subsequent bubbles.

)(16

)()()( 2

1

nnn

nnnnnn

dT

dTbTcaT

13.0

)cos(9.28.36)(

0205.0

5.19

)cos(2.131)(

nn

nn

d

c

b

a

nmmnn

n

,0

noise white:

n

Experiment Model

t

t

t

t

n+1

Model with =0

n n

n+1

n

0 5 10

100

50

0

counts

Number of bubbles per package

Experiment Model

Capillary model 2

Wire diameter 0.254 mm

CapillaryInternal diameter 1.4 mm

60 mm

Upper and lower ends move

Observations with Model 2: Bubble transit at the tip of the capillary

Period doubling a) 15 W/m, b) 18 W/m, c) 22 W/m, d) 24 W/m

a) b)

c) d)

LLLLL

SLSLS LSSSL

The

rmoc

oupl

e ou

tput

(m

V)

time (s)

Observations with Model 2: Return maps

Period doubling a) 15 W/m, b) 18 W/m, c) 22 W/m, d) 23 W/m

a) b)

c) d)

LL

SL

LS

SL

LSSS

SL

LS

t

tn

n+1

Observations with Model 2: Bifurcation diagram

Heat flux (W/m)

Tim

e pe

riod

(s)

Summary *We studied capillary boiling as a model of artificial nucleation.

* Bubble emission (and heat transfer) depend strongly on the geometry and on the dynamical interaction of liquid and vapor inside the capillary.

* Period doubling of bubble emissions has been observed for long capillaries.

2. Quasi 2D-vortices generated by the Lorentz force 2. Quasi 2D-vortices generated by the Lorentz force in an electrolytein an electrolyte

Electrolyte container

Working fluid: Sodium bicarbonate solutionFluid layer depth: 4 mm

Maximum magnetic field: 0.33 TMagnet diameter: 19 mm

Electrical current : Jo = 5-100 mA

Experimental setup

Particle Image Velocimetry

Scaling

Distance: magnet diameter D fluid layer depth hTime: D /Velocity (1): U = /D Electrical current: JoMagnetic field: BoLorentz force: JoBoVelocity (2): U/D ~JoBo U= JoBoD / Electrical conductivity

22

2

Nondimensional parameters

• Reynolds number

Re = UD/ =JoBoD / = U/U• Hartmann number

Ha =Bo D (/)1/2

• Depth of the fluid layerh = h/D

3

Re

0 15 304

Experimental observations.

Ha = 0.3h = 0.21

75

x

y

J Lorentz force o

x

y

4.5 cm

Velocity field, upper layer (z = 3.75 mm)

Jo =25 mA

Ha=0.3

Re=75

Stream lines Jo =25 mA, Re = 75, Ha =0.3

x

y

Velocity

vmax = 6.7 mm/s = 1.05 s-1

Vorticity

Jo =25 mA, Re = 75, Ha =0.3x

y

Composante vitesse v (I=25mA, h=3.5mm, y=y_yeux)

-0.008

-0.007

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0 5 10 15 20 25 30 35 40 45

x ( mm)

y-component of velocity

v(m/s)

x(mm)Jo = 25 mA, Re = 75

h = 3.5 mm, y = vortex center

Jo = 10 mA, Re=30, Ha=0.3 Jo =100 mA, Re= 304, Ha=0.3

Stream lines

Vitesse = f(I)

y = -8E-07x2 + 0.0002x + 0.0005

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 20 40 60 80 100 120

I (mA )

U (m/s)Polynomial (U (m/s))

Maximum velocity vs Jo

Jo (mA)

v(m/s)

15

304

Transversal section

x

y

Velocity profiles as functions of z

y

z

Bottom

Free surface

Laser beam

Camera

Beam splitterLayer of electrolyte

GlassMagnet

Free surface

Contours of velocity magnitude

Magnet

Maximum velocity

CC

D

Plan laser vertical

Bottom wall

MagnetMagnet

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.001 0.002 0.003 0.004 0.005 0.006U (m/s)

Centrey=10.1mmy=6.42mmy=3.67mm

Velocity profiles as functions of z

(Upstream of the center of the magnet)

Jo = 25 mA, Re = 75, h = 4mm

z (mm)

v (m/s)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007U (m/s)

Centrey=- 3.67mmy=- 7.43mmy=- 11.02mmy=- 16.52mm

Velocity profiles as functions of z

(Downstream of the center of the magnet)

Jo = 25 mA, Re = 75, h = 4mm

z (mm)

v (m/s)

jjijj iy

ix

ˆˆ)1(

,ˆ),( kyxBB ozo

kyxbb zˆ),(

Steady, two dimensional model(likely to be useful for the upper regions of the fluid layer)

)0),,(),,((),,( yxvyxuwvu

Jo

BoUM

x

bMj

y

bMj z

yz

x

020 zz Bub

002 2Re zz Byb

HaBvyp

yv

vxv

utu z

022z

z Bxb

Hauxp

yu

vxu

utu

0

yv

xu

Governing equations, two dimensional model

)()()(323

4 5

22

zyxmrmrmz

B ooo

z

Magnetic field for a point dipole

Evaluated at z=0

)()(321

4 3 yxmr

mB o

ooz

020 zz Bub

z 2

xB

yv

xu

tz

zzzz

02 Re

Vorticity equation

Stream function

Magnetic induction

...ReRe )2(2)1()(zz

ozz

For small Re

...ReRe )2(2)1()( uuuu o

...ReRe )2(2)1()( vvvv o

A linearized solution may be attempted with

0)()()( oooz vu

)1()1(2z

xBz

z

02 )1(

Vorticity equation order Re

Stream function

The solution diverges for r=0 and r:

cosln)1( rr

similar to the Stokes paradox

The solution is not altogether usless...

GK Batchelor

Salas, Cuevas & Ramos, Magnetohydrodynamics, 37 (2001)

Numerical solution is required

* Solution to the full system of equations, including induced and nonlinear terms

* Two dimensional physical model like the one

described before, but considering a finite size magnet

* Finite volume discretization method

Re=60, Ha=0.2 Re=300, Ha=0.2

Numerical resultsStream lines dipolar magnetic filed

Re= 30 (60), Ha=0.2

Comparison with experiments

Re=300, Ha=0.2

Comparison with experiments

Summary

*A class of electromagnetically driven flows in shallow fluid layers has been observed.

*For the experimental conditions examined, the influence of the bottom wall extends up to approximately 3 mm.

*A two dimensional model that includes nonlinear effects captures some features of the experimental observations.

3. Natural convection in a centrifuge3. Natural convection in a centrifuge

g

TF

TC

No rotationNo rotation

A A’

B

B’

Plane AA’ Plane BB’Pr=6, Ra=7.5x10 , A=0.25

4

TCT

TF

Teórico, Ra~5x10

AA’

5Experimento, Ra=2.5x10

6

Teoría, Ra ~5x10 Experimento, Ra = 2.5 x 10

BB’

5 6

g

TF

TC

With rotationWith rotation

A A’

B

B’

Centrifuge

Pr=6, A=0.28, Ra = 2.5 x 10, Ta = 1.7 x 10 764

Centrifuge inertia

flu

id in

erti

a

Summary

* No Rotation* No Rotation: One single, no axisymmetric cell (AA’), four vortices (BB’)

* Rotation* Rotation: Time dependent flow, characteristic time 55 s.

The End