Evaporation (Chapter 14) - Värmeöverföring | … · 2015-05-14 · Evaporation (Chapter 14) ......
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Transcript of Evaporation (Chapter 14) - Värmeöverföring | … · 2015-05-14 · Evaporation (Chapter 14) ......
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
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 – 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 – 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 – 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
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