Boiling Heat Transfer Dr Vishwas Wadekar HTFS, Aspen Technology Definitions/Terminology Saturation temperature (T sat ) - boiling point temperature at prevailing pressure. For a mixture this will be bubble point temp. Superheat-excess temperature over the saturation value (T - T sat ) •Wall superheat = (T wall -T sat ) Subcooling- opposite of superheat given by (T sat - T ) Quality- Vapour phase mass fraction, ratio of vapour flowrate to total flowrate Subcooled and saturated boiling Pool Boiling
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Boiling Heat Transfer
Dr Vishwas Wadekar
HTFS, 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