Boiling Heat Transfer

Dr Vishwas Wadekar

Technology Director HTFS Research Aspen Technology

Definitions/Terminology�Saturation temperature (Tsat ) - boiling point temperature at prevailing pressure. For a mixture this will be bubble point temp.

� Superheat-excess temperature over the saturation value (T - Tsat)•Wall superheat = (Twall - Tsat)

�Subcooling- opposite of superheat given by (Tsat - T )

�Quality- Vapour phase mass fraction, ratio of vapour flowrate to total flowrate

�Subcooled and saturated boiling

Pool Boiling

Pool Boiling Curve - I

Single

Phase

Nucleate

Boiling

Transition

Boiling

Film

Boiling

LOG Wall Superheat ( Tw - Tsat )

LO

G (

q)

Critical

heat flux

(Wall temperature controlled case)

Single Phase - No

bubbles, wall superheat too low

Nucleate Boiling -Bubbles grow and

break away from wall. Coefficient

increases with ∆Tsat

Transition Boiling -Localised dry

patches on the wall

Film Boiling - Vapour film at wall

Pool Boiling Curve - II

Single

Phase

Nucleate

Boiling

Transition

Boiling

Film

Boiling

LOG Wall Superheat ( Tw - Tsat )

LO

G (

q)

Critical

heat flux

(Heat flux controlled case)

Single Phase - No

bubbles, wall superheat too low

Nucleate Boiling -

Bubbles grow and break away from

wall. Coefficient

increases with ∆Tsat

Transition Boiling -Localised dry

patches on the wall

Film Boiling - Vapour film at wall

Pool Boiling Curve for water

Equilibrium Bubble- Force Balance

r

π r2 ∆p = 2π r σ

∆p = 2 σ/ r

σ

∆p

∆p - Excess pressure; σ - surface tension

p pb

Bubble Growth-I

� Bubble will be at equilibrium if (pb - p) = ∆p

� Bubble will grow if (pb - p) > ∆p

ρ gv

sat

h

T =

dp

dT

∆∆p

∆∆∆∆T

Tsat

p

∆p = 2 σ/ r

� Bubble will grow if (Tb - Tsat ) > ∆Τs where,∆Ts = (2 σ/ r)(dT/dp)

� dT/dp can be obtained from Claussius-Clapeyron

equation; assuming ρl >> ρg

Bubble Growth-IIFinal equation

For water @ 373 K with r = 5x10-6, superheat required is -

ρ∆

σ∆

gv

sats

h r

T 2 T =

K2

T s 5.6)6.0)(102260)(105(

373059.036

=××

××=∆

−

Bubble Nucleation

� Bubble starts with r = 0, therefore ∆Ts = α !!

� Equation is based on continuum theory; we should look at behaviour of molecules as r → 0

� However, even statistical thermodynamics gives very high ∆Ts ( in hundreds of K )

� How to reconcile this with practical experience??

ρ∆

σ∆

gv

sats

h r

T 2 T =

Heterogeneous Nucleation

• Microscopic cavities in heating wall surface

• Initially gas/vapour is trapped in them as liquid is filled

• This provides for initial nucleation

• What about subsequent continued nucleation?

Heterogeneous Nucleation

• Each departing bubble leaves small amount vapour at the cavity bottom

• This provides nucleation for subsequent bubble

• Thus the cycle of nucleation, bubble growth and departure continues

Bubble Departure� Surface tension holds the bubble to the surface� Buoyancy force, g(ρL– ρV)detach bubble from heating surface � Bubble departs when it has become large enough so that buoyancy forces > surface tension

forces� What will happen if buoyancy forces are decreased? How?

Nucleate Boiling Correlations

From pool boiling curveq = B(∆T)m

Define q = αnb∆T

so αnb = Aqn

Note: A and n depend on fluid, pressure,

and surfaceTypical value of n is 2/3, hence αnb is dependent on heat flux (or ∆T)

Nucleate Boiling Correlations

• Correlations - Two types– Based on reduced pressure

– Based on physically based dimensionless groups

• Reduced Pressure correlation– Example: Cooper correlation

667.0Xqnb =α

where pc is critical pressure (N/m2), pr = p/pc, , M = molecular weight, A =dimensional

constant, ε = surface roughness (µm)

( )( ) 5.055.0

10

log21.012.0log10 −−−

−= MpApX rr

ε

Two-phase Flow Patterns and ∆p Prediction

Definitions/Terminologylg MMM &&& +=

( )lg

g

gMM

Mx

&&

&

+=

( )S

Mm;

S

Mm;

S

MM

S

Mm l

l

g

g

lg&

&

&

&

&&&

& ==+

==

( )

l

g

l

g

g

g

xmU;

xmU

ρρ

−==

1&&

– Mass flow rate

– Vapour quality

– Mass flux

– Superficial velocity

Definitions: Void Fraction

– Void fraction is a volume fraction for gas phase

– For one dimensional model this becomes the area fraction for gas phaseAg

S - total area Ag - gas phase

flow area

S

Ag

g =ε

Flow Patterns – Vertical Upflow

Bubble Slug Churn Annular Wispy annular

Flow Patterns – Horizontal Flow - I

Bubble Flow

Stratified Flow

Wavy Flow

Flow Patterns – Horizontal Flow - II

Annular Flow

Slug Flow

Plug Flow

Semi-slug Flow

Example of Flow Pattern Map - I

–Flow pattern map of Hewitt and Roberts (1969) for vertical upflow in tubes

2

llUρ

2

ggUρ

AnnularWispy

annular

Churn

Slug

Bubble

Example of Flow Pattern Map - IIComposite graph of Taitel and Dukler (1976) based on models for flow pattern transitions (horizontal tubes)

ρ∆

ρ=

gDUFr

g

g

( )

ρ∆=

gD

dz/dpT

l

lReFrK =00

.1

Flow Pattern Transition

Slug flow

Annular flow

Flow Patterns: Upflow Boiling

Annular

Churn

Slug

Bubble

Dispersed

–Single phase liquid inlet

–Amount of vapour fraction increases along the length

–Hence different flow patterns

Frictional Pressure Drop

L

2

LL

L D

mf2

dz

dp

ρ=

&

TP

2

TPTP

TP D

mf2

dz

dp

ρ=

&

For single phase flow

then for two phase flow

What are fTP, mTP, ρTP?

Frictional Pressure Drop

LTP

L

2

L

2

TP

L

TP

TP dz

dp

m

m

f

f

dz

dp

ρ

ρ

=

&

&

Dividing two phase ∆p by single phase ∆p

Thus ΦL contains all unknowns

L

2

Ldz

dp

φ=

Lockhart-Martinelli Correlation2

L

LTP dz

dp

dz

dpφ

=

L

LL

L D

mf2

dz

dp

ρ=

&

= function of (X2)2

lφ

g

l

dz

dp

dz

dp

X

=2

φl φg

100

X

100

Lockhart-Martinelli Parameter• Martinelli parameter is square root of ratio of liquid to gas frictional pressure gradient

• For turbulent-turbulent flow it can be shown that

Xtt Martinelli parameter

=

1.05.09.01

η

η

ρ

ρ

−

g

l

l

g

x

x

Flow Boiling

• Convective heat transfer component

αc = F αLwhere αL is coefficient for liquid phase; F an enhancement factor

•• Nucleate boiling component

Treated similar to nucleate pool boiling heat transfer, accounting for the interaction with flow

Flow

Components of Flow Boiling

Typical variation of

α for fixed mass

flux

Quality

Heat Tra

nsfe

r C

oeff

icie

nt (W

/m2K

)

Nucleate boiling region

Decreasing q&

Convective Component

Two-phase convective heat transfer componentHere the heat transfer is through faster moving liquid

film being dragged by higher velocity vapour Favourable conditions

- Low pressure and low heat flux- High flow rate and high vapour quality- Plain surface

Flow

Nucleate Boiling Component

Nucleate boiling componentHere the heat transfer is driven by vapour bubble dynamics

Favourable conditions- High pressure and high heat flux

- Low flow rate and low vapour quality- Enhanced boiling surfaces

Two-phase Forced Convection

Heat transfer is through a thin liquid filmTemperature at vapour-liquid interface is Tsat

No bubble generationEvaporation occurs at vapour-liquid interface

Tsat

Tw

Flow

Liquid

VapourLiquid

Flow Boiling

• Convective heat transfer component

αc = F αLwhere αL is coefficient for liquid phase; F an enhancement factor

•• Nucleate boiling component

Treated similar to nucleate pool boiling heat transfer, accounting for the interaction with flow

Flow

Increasing vapour mass fraction

1/Xtt

Chen F factor

>

+

≤

=

1.01

if 213.01

35.2

1.01

if 1

tt

736.0

tt

tt

XX

X

F

Chen Nucleate Boiling Component� αnb= Sαp where S is a suppression factor; αp , pool boiling coefficient is obtained from Forster-Zuber correlation

� Suppression factor, S, is related to a two-phase Reynolds number, ReTP

� ReTP = F1.25 Rel

∆Te, pool

∆Te, flow

Chen Suppression factor

• Suppesion factor for nucleate boiling

• Effect of flow on nucleate boiling

1.17

TF

6Re1053.21

1−

⋅+=S

• Overall correlation

α = FαL+Sαnb

Heterogeneous Nucleation

• Each departing bubble leaves small amount vapour at the cavity bottom

• This provides nucleation for subsequent bubble

• Thus the cycle of nucleation, bubble growth and departure continues

More Complex Shapes

• Vapour in these can sustain a degree of subcoolingwithout condensing

• Liquid flows down partially inside the cavities giving high coefficients associated with evaporation from very thin liquid film

Re-entrant

cavity

Doubly re-entrant

cavity

Enhancing Nucleate Boiling

• Large number of artificially made re-entrant /doubly re-entrant cavities

• These initiate and sustain nucleate boiling at low wall superheat

• These cavities need to be interconnected so that vapour can pass from one cavity to another

Tubes with Porous Metallic CoatingHigh flux tube - Porous coating of thin metallic matrix from fine metal particles

Random interconnected passages provide numerousnucleation sites

0.2 - 0.3

mm

� Different metal coatings are available on inside or outside tubes

� Dry-out could occur at lower vapour quality

Results with Composite Test-section

Composite test-section for in-tube boiling

Three parts of the test-sectionElectrical resistance heatingDetailed thermal measurements

Results with and without enhancement device can be directly compared for single phase and flow boiling heat transfer

Same mass fluxSame heat fluxNearly same pressure

0

10000

20000

30000

40000

50000

60000

70000

0 1 2 3

Length (m)

Heat

tran

sfer c

oeff

icie

nt

(W/m

2K

) Pressure = 1.66 bar

Mass flux = 285 kg/m2s

Heat flux = 41 kW/m2

coated section plain section

Flow

coated section

High Flux Coating-Flow Boiling

Wire Loop Inserts- Single phase

0

10 00

20 00

30 00

0 1 2 3

Length (m)

Hea

t tr

an

sfer

coef

fici

ent

(W/m

2K

)

Pressure = 1.44 bar

M ass flux = 287 kg/m2s

Heat flux = 2.59 kW/m2

section with

wire insertssection with

wire insertsplain section

F low

Wire Loop Inserts- Single phase

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1 2 3

Length (m)

Hea

t tr

an

sfer

coef

fici

ent

(W/m

2K

)

Pressure = 1.66 bar

Mass flux = 285 kg/m2s

Heat flux = 41 kW/m2

section with

wire inserts

section with

wire insertsplain section

Flow

• For in-tube boiling critical heat flux is related to dryout phenomenon in the annular flow region

• Dryout is influenced by entrained liquid

droplets in the vapour core

Flow Boiling and Critical Heat Flux Limit

Critical vapour quality associated with CHF

• Critical quality can be increased if entrained droplets are deposited on heating surface

• Entrained droplets can be deposited on heating surface if swirling motion is imparted to them

Flow Boiling and Critical Heat Flux Limit

• Swirl flow devices such as helical microfins, twisted tape inserts, etc can be used for this purpose