Condensation
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Transcript of Condensation
Condensation
CONDENSERS
Power plant – water is boiled in boiler and condensed in condenser
Oil refinery - oil is evaporated in distillation column and condensed into liquid fuels like gasoline and kerosene
Desalination plant – water vapor is produced by evaporation from brine and condensed as pure water
Condensation – enthalpy of phase change to be removed by a coolant
Enthalpy of phase change is relatively large, for water (2.5 106 J/kg) and associated heat transfer rates are also large
Heat transfer to phase interface – convective process – complicated by an irregular surface – bubbles and drops
CONDENSATION HEAT TRANSFER
• Film condensation
• Dropwise condensation
FILM CONDENSATIONCondensate wets the surface and forms a liquid film on the surface that slides down under the influence of gravity.
Surface is blanketed by a liquid film of increasing thickness, and this “liquid wall” between the solid surface and the vapor serves as a resistance to heat transfer
Liquid film
80° C
• Condensate film thickness are thin – heat transfer coefficients are large
• Example - steam at a saturation temperature of 305 K condenses on a 2 cm – O.D tube with a wall temperature of 300 K
• Average film thickness - 50m (0.05 mm) and the average heat transfer coefficient – 11,700 W/m2.K
• If the condensate flow rate is small, the surface of the film will be smooth and the flow laminar because
• Temperature difference is small
• Wall is short
• If the condensate flow rate is high, waves will form on the surface to give wavy laminar flow
• If the condensate flow rate is yet higher, the flow becomes turbulent
DROPWISE CONDENSATION
If the condensate does not wet the wall, because either it is dirty or it has been treated with a non-wetting agent, droplets of condensate nucleate at small pits and other imperfections on the surface, and they grow rapidly by direct vapor condensation upon them and by coalescence
When the droplets become sufficiently large, they flow down the surface under the action of gravity and expose bare metal in their tracks, where further droplet nucleation is initiated
THIS IS CALLED DROPWISE CONDENSATION
Droplets
80°C
Droplets slide down when they reach a certain size, clearing the surface and exposing it to vapor.
There is no liquid film in this case to resist heat transfer.
Heat transfer rates that are more than 10 times larger than those associated with film condensation can be achieved with dropwise condensation
Most of the heat transfer is through drops of less than 100m diameter
Thermal resistance of such drops is small; hence, heat transfer coefficients for dropwise condensation are large; values of upto 30000 W/m2.K have been measured.
Hence, dropwise condensation is preferred over filmwise condensation
Considerable efforts are put for non-wetting heat exchanger surfaces
If the surface is treated with non-wetting agent (stearic acid) to promote dropwise condensation, the effect lasts only few days, until the promoter is washed off or oxidised.
Continuous adding of the promoter to the vapour is expensive and contaminates the condensate.
Bonding a polymer such as teflon to the surface is expensive and adds additional thermal resistance
Gold plating is also expensive
Because of lack of sustainability of dropwise condensation, present day condensers are designed based on filmwise condensation
Filmwise condensation – conservative estimate
LAMINAR FLOW CONDENSATION ON A VERTICAL WALL
Temperature of the liquid-vapour interface is the saturation temperature that corresponds to Tsat
Vapour in the descending jet is colder than the vapour reservoir and warmer than the liquid in the film attached to the wall
Tsat
xx
Liquid Vapor
Velocity
0
Liquid
Vapor
Laminar
Turbulent
Wavy
Tw
T
Vapor reservoirCold wall
TsatTw
g
T
Tw
LAMINAR FLOW CONDENSATION ON A VERTICAL WALL
Consider a vertical wall exposed to a saturated vapour at pressure p and saturation temperature Tsat = Tsat(P).
The wall could be flat or could be the outside surface of a vertical tube
If the surface is maintained at a temperature Tw < Tsat, vapour will continuously condense on the wall, and if the liquid phase wets the surface well, will flow down the wall in a thin film
Provided the condensation rate is not too large, there will be no discernable waves on the film surface, and the flow in the film will be laminar
• Fluid dynamics of the flow of a thin liquid film
• Heat transfer during the flow of a thin liquid film
y + dy
d
gh d
satT T H + dH
Hy
u
v
Laminar film of condensate
Tsat
x
T
= Tsat
x
T
Tw
Tsat
x
v
0
Tw
0
x = δ(y)Interface
From reservoir of saturated vapor
0u
Zero shear ,y
ASSUMPTIONS
• Laminar flow and constant properties are assumed for the liquid film
• Gas is assumed to be pure vapour and at a uniform temperature equal to Tsat. The merit of this simplification is that it allows us to focus exclusively on the flow of the liquid film and to neglect the movement of the nearest layers
of vapour
• Shear stress at the liquid-vapour interface is assumed to be negligible
• With no temperature gradient in the vapour, heat transfer to the liquid-vapour interface can occur only by condensation at the interface and not by
conduction from the vapour
2
2
2
2
y
u
x
u
x
P
y
uv
x
uu LL
Steady state two dimensional incompressible flow
gy
v
x
v
y
P
y
vv
x
vu LLL
2
2
2
2
vanishesequationmomentumx,Hence,vu
L~y;~x
gy
v
x
v
dy
dP
y
vv
x
vu LLL
2
2
2
2
2
2
x
vg
y
vv
x
vu LvLL
pressurecHydrostatigpotioninviscidthefromimposedpressuredy
dPv
Neglected, y<<x
FRICTION
L
EFFECTSINKING
vL
INERTIA
L x
vg
y
vv
x
vu 2
2
Assuming inertia is negligible
02
2
gx
vvLL
Boundary conditions
0
00
x
vx
vx
1Cxgx
vvLL
Integrating
21
2
2CxC
xgv vLL
000 2 Cvx
110 CgCxgx
v
x
vx vLvLL
21
2
2CxC
xgv vLL
02 C
vLgC 1
2
2xx
gv
L
vL
xgx
gv vLvLL 2
2
2
2
2
1
xxg
y,xvL
vL
Film thickness is unknown function of (y)
Local mass flow rate per unit width (y)
0
dxvy L
0
2
2
2
1dx
xxgy
L
vLL
y
0
3
322
6
1
2
xxgy
L
vLL
622
L
vLL gy
3
3
L
vLL gy
3
2
L
vLL gy
3
3
L
vLL gy
3
3
L
vLL gbybm
B – width of the plate perpendicular to the plane of paper Flow rate is proportional to the sinking effect - g(L-v)Flow rate is inversely proportional to the liquid viscosity (Friction)
HEAT TRANSFER PROBLEMFilm velocity is low Temperature gradients in the y-direction are negligible since both wall and film surface are isothermal
02
2
dx
Td
211 CxCT;Cdx
dT
wsatwsatw
ww
sat
TTCTCTTxCT
TCTTx
TTx
CxCT
111
2
21
0
wwsat Tx
TTT
This is a linear temperature profile similar to the conduction in a plane wall
Heat flux into the wall = Heat flux across the film
wsatlwsat
wl
TTk
A
QTTh
dx
dTk
l
wsat
wsatl
wsat
wl
k
TT
TTk
TT
dxdT
k
h
lk
h
Determination of film thickness
;
gy
L
vLL
3
3
3
3
L
vLL gbybm
dy
dgbyb
dy
md
L
vLL
3
3 2
Rate of condensation of vapour over a vertical distance dy
Rate of heat transfer from the vapour = Heat releasead as vapour is condensed to the plate through the liquid film
wsatlfg
TTdybkhmdQd
wsat
fg
l TT
h
bk
dy
md
wsat
fg
l
L
vLL TT
h
bk
dy
dgbyb
dy
md
3
3 2
Cyhg
TTk
dyhg
TTkd
TT
h
k
dy
dg
fgvLL
wsatlL
fgvLL
wsatlL
wsat
fg
l
L
vLL
4
3
3
4
3
2
000 C,y
y
hg
TTk
fgvLL
wsatlL
4
4
4
144
yhg
TTky
fgvLL
wsatlL
4
14
4
yTTk
khgkh
wsatlL
lfgvLLl
L
wsatL
lfgvLLL
wsatL
lfgvLLL dyy
LTT
khgdy
yTT
khg
Lh
0
4
14
13
0
4
13
1
44
1
4
13
49430
LTT
khg.h
wsatL
lfgvLLL
3
3
L
vLL gbybm
4
144
yhg
TTky
fgvLL
wsatlL
4
344
3
yhg
TTkgbm
fgvLL
wsatlL
L
vLL
All liquid properties evaluated at
2wsat
fTT
T
Effect of subcoolingRohsenow refined• avoided linear temperature profile• Integral analysis of temperature distribution across the film Temperature profile whose curvature increases with the degree of subcooling Cp,L(Tsat-Tw)
Replace in previous equations
All liquid properties evaluated at
hfg and v are evaluated at the saturation temperature Tsat
wsatL,pfg'fg TTC.hh 680
'fgfg hbyh
2wsat
fTT
T
JAKOB NUMBERIs a measure of degree of subcooling experienced by the liquid film
fg
wsatL,p
h
TTCJa
wsatL,pfgfg TTC.hh 680
Ja.hh fgfg 6801
Reynolds Number
4
44
b
b
P
AD;u;
DuRe c
hL
mL
hmL
LLLLRe
44
LRe
4
3
3
L
vLLgy
LL
vLL
L
gRe
3
3
44
2
3
2
32
3
4
3
4
LL
LvL
ggRe
2
32
3
4
L
LvL
gRe
Lx
ll
h
kLx
h
k
avgLx h4
3h
3
avg
L2L
2L
3
Lx
L2L
2L
h43
k
3
g4
h
k
3
g4Re
3
1
23
1
471
llavg
gRek.h
Hydraulic diameter
44
c
c
P L
A L
ADh
P
δ
L
2
2
44
c
c
P L
A L
ADh
P
4
4
c
c
P D
A D
ADh
P
δ
D
D
δ
L
Wavy Laminar flow over vertical platesAt Reynolds number greater than about 30, it is observed that waves form at the liquid vapour interface although the flow in liquid film remains laminar. The flow in this case is Wavy Laminar Kutateladze (1963) recommended the following relation for wavy laminar condensation over vertical plates
3
1
2221 25081
l.
lwavy,vert
g
.Re.
kReh
lv,Re 180030
820
3
1
2
703814
.
lfgl
wsatlwavy,vert
g
h
TTLk..Re
Turbulent flow over vertical plates (Re > 1800)Labuntsov proposed the following relation
3
1
275050 253588750
l
..l
turbulent,vertg
RePr
kReh
Film condensation on an inclined Plates
Condensatecoshh vertinclined
2
1
3
18806440
3
12
10825
L
.L
.L
l
l
L PrRe.Regk
h
Non-dimensionalised heat transfer coefficients for the wave-free laminar and turbulent flow of condensate on vertical plates
Wave-free laminar
Wavy laminar
Turbulent
l
l
h( v g )
k
2 1 3
Pr = 10
5
3
2
1
10,0001800100010030100.1
1
Re
Problem: Saturated steam at atmospheric pressure condenses on a 2 m high and 3 m wide vertical plate that is maintained at 80C by circulating cooling water through the other side. Determine (a) the rate of heat transfer by condensation to the plate (b) the rate at which the condensate drips off the plate at the bottomSolution: saturated steam at 1 atm condenses on a vertical plate. The rats of heat transfer and condensation are to be determinedAssumptions: 1. steady operating conditions exist 2. The plate is isothermal. 3. The condensate flow is wavy laminar over the entire plate (will be verified). 4. The density of vapour is much smaller than the density of the liquid v<<l
Properties: The properties of water at the saturation temperature of 100C are hfg = 2257 × 103 J/g and v = 0.6 kg/m3. The properties of liquid water at the film temperature 90C are
96281
6750
4206
103260
103150
3965
902
80100
2
26
3
3
.Pr
K.m/W.k
K.kg/JC
s/m.
s.Pa.
m/kg.
TTT
l
pl
l
ll
l
l
wsatf
wsatL,pfgfg TTC.hh 680
801004206680102257 3 .h fg
kg/Jh fg3102314
4
1
3
34
13
4801001031504
675010002314396539658199430
49430
.
.....
LTT
khg.h
wsatL
lfgvLLL
Km
W.hL 222656
s/kg.mmhmQ
W.TTAhQ
sf
wsatsL
13290102314307464
307464801003222562
3
55623
13290
103150
4443
..
.b
mRe
LL
2
1
3
18806440
3
12
10825
L
.L
.L
l
l
L PrRe.Regk
h
2
1
3
18806440
3
126
962815562108255562819
103260
6750
.....
.
.
h ..L
Km
W.hL 247691
3
7691 4 2 3 100 80 2307420
2307420 2314 10 0 9972
L s sat w
sf
Q h A T T . W
Q mh m m . kg / s
3
4 4 4 0 99724221
0 315 10 3L L
m .Re
b .
This confirms that condensation is in turbulent region
Comments: This Reynolds number confirms that condensation is in Wavy laminar domain