Evaporation (Chapter 14)

Zan Wu zan.wu@energy.lth.se Room: 5123

Evaporation, Boiling

q

vätska, liquid1) Local boiling or subcooled boiling2) Boiling with net evaporation

Pool boiling

Forced convective boiling

Evaporation – Nukiyama’s experiment – boiling curve

IE

ts

qmin qmax q

t tråd-

wire

- t s

värmande tråd,heating wire

Heat flux increases/decreases

Evaporation – Boiling Curve

1.0 10 100 10000

2

4

6

8

10

12

14nucleate boiling transition

regime film boiling

naturalconvection

singlebubbles

jets &colonns

1

2a

2b

3

4

5

qmin

qmax

Hea

t flu

x, [1

05 W/m

2 ]

t = twall - ts

Saturated wateron a plane sur-face at p = 1 bar

Wall temperature increases/decreases

Evaporation

(a)

(b)

(c)

Principal sketch of nucleate boiling ((a) and (b)),and film boiling (c).

Bubble nucleation, growth and departure

Nucleate boiling heat transfer mechanisms

Micro-convection Transient conduction

Microlayer evaporation

Microlayer

Nucleate Boiling; theory, empiricism

Nu = function(Re, Pr)

fgf

wf h

qu

2/1

gfk )(

g

L

f

kffRe

Lu

f

kNu

L m

fn1

sf

PrRe1Nu C

Lk is related to bubble departure diameter

Nucleate Boiling – Rohsenow’s formula

0.332/1

gffgf

wsls

ffg

swp

)(Pr)(

f

gh

qCh

ttc

n = 1/3, 1+m = s

Eq. (14-9)

σ is the surface tension, σ = c1 + c2t

Evaporation; Nucleate Boiling Regime

.001 .01 0.1 1.00.1

1.0

10

100

Eq. (2-9)1 atm26 atm52.4 atm82 atm109 atm167.7 atm

ffg

swp

Pr)(

f

httc

)( gffgf

ghq

Evaporation- Csl and s in Rohsenow’s equation

Surface – liquid Csl s

Nickel – water 0.006 1.0

Platinum – water 0.013 1.0

Copper – water 0.013 1.0

Brass – water 0.006 1.0

Chrome – benzene 0.010 1.7

Chrome ethanol 0.0027 1.7

Evaporation, nucleate boiling: Cooper’s formula

0.67w

5.055.0R

)ln4343.012.0(R M)ln4343.0(P qPPA R

M is the molecular weight

R critical/P p p

PR

is the reduced pressure

is the surface roughness in m

A = 55

Physical properties could be expressed as functions of the reduced pressure

Evaporation, nucleate boiling; Gorenflo’s method

133.0

p0

p

w0

wPF0

RR

qqF

b

R

RR

27.0RPF 1

5.22.1P

PPPF

3.0R3.09.0 Pb

(14-12)

0 valid a certain reference state, namely

1.0R0 P 4.0P0 R m, 4 2w0 2 10 W/mq

Reference values for 0 in Table 14-III.

Evaporation, nucleate boiling; Gorenflo’s method – for water

2R

R

27.0RPF 1

68.01.673.1 PP

PF

15.0R3.09.0 Pb

Evaporation-temperature distribution in liquid phase for pool boiling

0 1 2 3 4 5 6 7 8100

101

102

103

104

105

106

107

108

109

Distance from the heating surface, [cm]

Tem

pera

ture

, o C

Water

Liquid surface100.4 oC

Vapor 100 oC

Bubble departure diameter in mm scaleLarge temperature drop and high heat transfer coefficient near the wall

Evaporation: equilibrium-force balance

p

r

2bubble liquid( ) 2r p p r

bubble liquid

2( )

rp p

Surface tensionA metal paperclip floating on water Lotus effect

Evaporation – effects on the boiling curve

SubcoolingA liquid enclosed in a heated container will not stay a temperature below the saturationtemperature very long. Before the liquid reaches the saturation temperature or if thewarm liquid is continuously replaced by cold liquid (e.g., by forced flow) the subcoolingwill, affect the boiling curve. It has been found that the nucleate boiling regime is notvery much affected but the values of qmax and qmin increase linearly with thesubcooling. The influence on the transition regime is less known.

GravityThe influence of the gravity or other body forces is of interest as the boiling process alsoappears in rotating or accelerated systems. Reduction of the gravity is important forboiling processes in space applications. Because the gravity acceleration g is includedin most expressions its role is evident.

Surface roughnessA heating surface might be treated in various ways to find out the importance of thesurface roughness. The effect of qmax on surface roughness is very complicated. Thefilm boiling regime is not affected significantly by surface properties which isunderstandable as the liquid phase is not in direct contact with the solid surface. Thenucleate boiling regime is however affected by the surface roughness.

Evaporation – transition regime

Evaporation – Taylor instability

Honey

Honey

g

cold water

humid air

(a) (b)

f gfunction ( , ( ))g Tλ

An instability of an interface between two fluids of different densities and with the denser fluid at the top.

Evaporation – Taylor instability, dimensional analysis

a b cf gconst ( )g Tλ

c3b2a1 ]m[kg]s[m]m[N[m]

1/2cb1/2,a

Tf g

constant( )

λg

2 3 for one-dimensional wavesconstant

2 6 for two-dimensional waves

Evaporation - arrangement of vapor jets at qmax

T 1T /41

T2

T

1

Evaporation – Kelvin-Helmholtz instability

U

high pressurelow pressure

Flag movement

Evaporation – Helmholtz instabilityT1

ug

g

Hf

vapo

r jet

vapo

r jetsurrounding

liquidsurroundingliquid

heating surface vapo

r jet

T /41

Details of instability in the jet surface

Hgg

2λ

u

Evaporation- estimation of qmax for a horizontal surface

h

jgfggmax A

Auhq

16)4/(

/ 2T

2T

hj

1

1

λλ

AA

4/1gffg

1/2gmax )(149.0 ghq

4/1gffg

1/2gmax )(131.0

z ghq

Hλ 1Tλ (14-25)

(14-26)

Evaporation-other geometries, pool boiling

max g f g fgfunction( , , , , , )q g L h

zmax

max1 q

qY )( gf

2

g

LY

see Table 14-IV

Forced convective boiling forimmersed bodies

maxf g

g fg

function(We , / )Lqh U

LUL

2gWe

3/1

fgg

max )We/4(11DUh

q

Low velocities

High velocities

3/1

2/1gf

4/3gf

fgg

max

We2.19)/(

169)/(

DUhq

(14-34)

(14-35)

Forced convective boiling forimmersed bodies

Circular cylinder in cross flow

1/ 2f g

max

g fg1/ 2

f g

0.275 ( / ) 1 high velocity

0.275 ( / ) 1 low velocity

qh U

Forced convective boiling forimmersed bodies

Boiling in tubes, flow regimes-horizontal tubes

Bubbly

Plug

Stratified

Wavy

Annular

Annular with liquid spray

Slug

Boiling in tubes, flow regimes-vertical tubes

(a) (b) (c) (d) (e) (f) (g)

(a) homogeneous bubbles(b) inhomogeneous bubbles(c) slugs of the gas phase(d), (e) partial annular flow(f) annular flow(g) annular flow with liquid droplets in the gas phase

Boiling in tubes, flow pattern map-horizontal tubes – Baker plot

10 100 1000 10000

0.1

1.0

10

100

Gfkg/(m2s)

Gg/

k

g/(m

2 s)

Stratifiedflow

Plug flow

Slug flow

AnnularflowWavy

flow

Bubbly flow

2

1/ 2

g f

air H O

3/12

f

OH

OH

fOH 2

2

2

Gg = mg/Across,Gf = mf/Across

Boiling in tubes, flow pattern map-vertical tubes – Hewitt and Roberts

Gg = mg/Across,Gf = mf/Across

1.0 10 100 1000 10000 1.E+5 1.E+60.1

1.0

10

100

1000

10000

Gf2f kg/(ms2)

Gg2

g k

g/(s

2 m)

Annularflow

Annular flow withliquid droplets

Bubbly flow

Slug flow

Partial annularflow

Two-phase flow, definitions and relations

VV

VVV g

fg

g

g

fg

gF m

mmm

mX

AmG / Fg GAXm )1( Ff XGAm

fgR /uuu

Void fraction

flowing mass quality

mass velocity

phase velocity ratio

Two-phase flow, definitions and relations

f

F

f

fSf

)1(

XG

Amu

g

F

g

gSg

GX

Am

u

))1(

F

F

g

f

f

g

XεXε

uu

f

g

F

FSgSf

)1(

X

Xuu

Superficial velocities

(14-45) (14-47)

Pressure drop for two-phase flows: Lockhart-Martinelli method

f

F

f

Sff

)1(Re

DXGDu

g

F

g

SggRe

DGXDu2f f S

f f0

12

L up f dz

D

2

g gSg g

0

12

L up f dz

D

.01 0.1 1.0 10 1001.0

10

100

1000

v-v

t-v

v-t

t-t

Index Liquid Gas t-t Turbulent Turbulent v-t Laminar Turbulent t-v Turbulent Laminar v-v Laminar Laminar

f

gf

0.1

1.0

(dp/dx)f / (dp/dx)g

(dp/

dx) T

F / (

dp/d

x)f

Pressure drop for two-phase flows: Lockhart-Martinelli method

g

f2

)/()/(

dxdpdxdpX

f

TF2f )/(

)/(dxdpdxdp

22f

1C1XX

Martinelli parameter

two-phase multiplier

C = 20 if turbulent flow prevails in the liquid as well as in the gas (tt)C = 12 if the liquid flow is viscous (laminar) and the gas flow

is turbulent (vt)C = 10 if the liquid flow is turbulent and the gas flow is laminar (tv)C = 5 if laminar flow prevails in the liquid as well as in the gas (vv)

Pressure drop for two-phase flows: Friedel’s method

LO

2LO

TF

dxdp

dxdp

LO means liquid only

Formulas for 2LO see book.

Oil recovery from deep sea: presure drop

Gas-oil or gas-oil-water multiphase flow

Temperature along the oil pipes from deep sea affects thermophysical properties, e.g., oil viscosity varies a lot with temperature

Low flow velocity, gravitational loss dominated

High flow velocity, frictional loss dominated

Forced convective boiling –heat transfer and temperature distribution

Single phase liquid

Bubble flow

Slug flow

Annular flow

Annular flowliquid drops in the vapor

Liquid drops in the vapor

Single phase vapor

Convection to liquid

Subcooled boiling

Saturated nucleate boiling

Forced convectionacross a liquid film

Dry out

Convection to vapor

FLOW TYPE HEAT TRANSFER REGIMES

x = 1

x = 0

Fluidtemperature

Saturationtemperature

Walltemperature

TEMPERATURE PROFILE

Dryout

Inlet

Outlet

A

B,C

D

E

F

G

H

Chen’s method for estimating the heat transfer during forced convective boiling

CKKTF FS

1.0

g

f

5.0

f

g9.0

F

Ftt

1

XXX

g

ftt )/(

)/(dxdpdxdp

X

0.1 1.0 10 1001.0

5.0

10

50

100

Approximative range ofdata points

1/Xtt

F =

(Re T

F/Re f

)0.8

Chen’s method for estimating the heat transfer during forced convective boiling, continued

8.0

f

TF

ReRe

F

tt

0.736

tt tt

11 if 0.1

1 12.35 0.213 if 0.1

XF

X X

Df0.4

f0.8fC PrRe023.0

fFf /)1(Re DXG

Chen’s method for estimating the heat transfer during forced convective boiling, continued

1.E+5 1.E+60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.E+4

ReTF = RefF1.25

S

Aproximative area for alldata points

1.17TF

6 Re1053.211

S

0.75s

0.24s0.24

g0.24fg

0.29f

0.5

0.49f

0.45p

0.79f

KKf00122.0 pth

c

)()( sswss tptpp

sws ttt

Chen’s method for estimating the heat transfer during forced convective boiling, continued

CKKTF FS

Calculate αTF for a number of tm according to

Then create a graph q = αTF tm vs tm

At q = qw find the true tm

Alternative method for estimating the heat transfer during forced convective boiling-Gungor & Winterton

TF KK CS E

86.0tt

16.14 )/1(37.1Bo104.21 XE

)/(Bo fgw hGq

1.17f

26 Re1015.111

ES

Here αKK is taken from Cooper’s formula,αC from Dittus-Boelter’s equation

Alternative method for estimating the heat transfer during forced convective boiling-Steiner & Taborek

n/1nC

nKKTF

Here αKK is taken from Gorenflo’s method,αC from Gnielinski’s formulan = 3

Thank you very much!!