Condensation

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Department of Mechanical EngineeringDepartment of Mechanical EngineeringIndian Institute of Technology KanpurIndian Institute of Technology KanpurKanpur 208016Kanpur 208016IndiaIndia


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Film condensation modelFilm condensation model in the presence of in the presence of

non-condensable gasesnon-condensable gases

byby

Mahesh Kumar YadavMahesh Kumar Yadav

11205064Department of Mechanical Engineering Indian Institute of Technology Kanpur

Kanpur (UP) 208 016

Film condensation model in the presence of non-condensable

gases

Film condensation model in the presence of non-condensable

gases

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Motivation• The probability of LOCA DBA, DBA or BDBA so called ‘severe accidents’ are very low.

• However, it occurs (at Fukushima-2011, Three Mile Island (TMI)-1979,US, Santa Susana Field Laboratory-1959, US) and releases high amount of hydrogen. (eg.460 Kg of H2 in TMI-2 accident)

• Most of H2 burns when averaged concentration is 7.9 vol% leads to high pressure rise and significantly damages the containment (Henrie and Postma, 1983, 1987).

• One approach of condensation modeling is using empirical average HTC developed using volume averaged called ‘lumped-parameter’.

•Other approach is CFD based codes like MAAP, CONTAIN, GASFLOW (Travis et al., 1998), SPECTRA (Stempniewicz, 1999), MELCOR (Gauntt et al., 2000), CAST3M (Paillere et al., 2003).

• CFD codes provides detailed information in such scenario but inclusion of averaged quantities and averaged condensation rates based correlations question marked these.

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Year Incident INES level Country IAEA description

2011 Fukushima 5 Japan Reactor shutdown after the 2011 Sendai earthquake and tsunami; failure of emergency cooling caused an explosion

2011 Onagawa Japan Reactor shutdown after the 2011 Sendai earthquake and tsunami caused a fire

2006 Fleurus 4 Belgium Severe health effects for worker at commercial irradiation facility as a result of high doses of radiation

2006 Forsmark 2 Sweden Degraded safety functions for common cause failure in the emergency power supply system at nuclear power plant

2006 Erwin US Thirty-five litres of a highly enriched uranium solution leaked during transfer

2005 Sellafield 3 UK Release of large quantity of radioactive material, contained within the installation

2005 Atucha 2 Argentina Overexposure of a worker at a power reactor exceeding the annual limit

2005 Braidwood US Nuclear material leak

2003 Paks 3 Hungary Partially spent fuel rods undergoing cleaning in a tank of heavy water ruptured and spilled fuel pellets

1999 Tokaimura 4 Japan Fatal overexposures of workers following a criticality event at a nuclear facility

1999 Yanangio 3 Peru Incident with radiography source resulting in severe radiation burns

1999 Ikitelli 3 Turkey Loss of a highly radioactive Co-60 source

1999 Ishikawa 2 Japan Control rod malfunction

1993 Tomsk 4 Russia Pressure buildup led to an explosive mechanical failure

1993 Cadarache 2 France Spread of contamination to an area not expected by design

1989 Vandellos 3 Spain Near accident caused by fire resulting in loss of safety systems at the nuclear power station

1989 Greifswald Germany Excessive heating which damaged ten fuel rods

1986 Chernobyl 7 Ukraine Widespread health and environmental effects. External release of a significant fraction of reactor core inventory

1986 Hamm-Uentrop Germany Spherical fuel pebble became lodged in the pipe used to deliver fuel elements to the reactor

1981 Tsuraga 2 Japan More than 100 workers were exposed to doses of up to 155 millirem per day radiation

1980 Saint Laurent des Eaux 4 France Melting of one channel of fuel in the reactor with no release outside the site

1979 Three Mile Island 5 US Severe damage to the reactor core

1977 Jaslovské Bohunice 4 Czechoslovakia Damaged fuel integrity, extensive corrosion damage of fuel cladding and release of radioactivity

1969 Lucens Switzerland Total loss of coolant led to a power excursion and explosion of experimental reactor

1967 Chapelcross UK Graphite debris partially blocked a fuel channel causing a fuel element to melt and catch fire

1966 Monroe US Sodium cooling system malfunction

1964 Charlestown US Error by a worker at a United Nuclear Corporation fuel facility led to an accidental criticality

1959 Santa Susana Field Lab. US Partial core meltdown

1958 Chalk River Canada Due to inadequate cooling a damaged uranium fuel rod caught fire and was torn in two

1958 Vinča Yugoslavia During a subcritical counting experiment a power buildup went undetected - six scientists received high doses

1957 Kyshtym 6 RussiaSignificant release of radioactive material

to the environment from explosion of a high activity waste tank

1957 Windscale Pile 5 UK Release of radioactive material to the environment following a fire in a reactor core

1952 Chalk River 5 Canada Reactor shutoff rod failure with several operator errors lead to major excursion of more than double the reactor output

• Nuclear Accidents:

Source: IAEA

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Level Definition People and environment Radiological barriers & control Example

7 Major accident Major release of radio active material with widespread health and environmental effects Chernobyl, Ukraine, 1986

6 Serious accident Significant release of radioactive material require implementation of planned countermeasures. Kyshtym, Russia, 1957

5 Accident with wider consequences Limited release of radioactive material Severe damage to reactor core

Three Mile Island, 1979

4 Accident with local consequences Minor release of radioactive material Fuel melt or damage to fuel resulting in more than 0.1%

release of core inventoryFUKUSHIMA 1, 2011

3 Serious incident Exposure in excess of ten times the statutory annual limit for workers Exposure rates of more than 1 Sv/h in an operating area Sellafield, UK, 2005

2 IncidentExposure of a worker in excess of the

statutory annual limits

Radiation levels in an operating area

of more than 50 mSv/hAtucha, Argentina, 2005

1 Anomaly

• International Nuclear Events Scale (INES):

Source: IAEA

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Objective

• To analyze the condensation process in the presence of non-condensable gas with the process parameter like mass flow rate, mixture composition, velocity, pressure etc.

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In this presentation...

Introduction to condensation

Literature review

Parameters affecting condensation

Modeling approach

Experimental setup

General adopted correlations

Property calculation for the NCG/vapor mixture

Parametric study

Measuring devices

Summary and Conclusions

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Introduction to Condensation

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Introduction to condensation

(a) Dropwise condensation

(b) Film wise condensation

Applications:

Distillation of water

Cooling of water vapor in condenser (in power plants and thermal power management systems)

Types of condensation

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Fig. Schematic model of film condensation

(a) Condensation in a vertical tube (b) BL without the presence of NCG (c) BL with the presence of NCG

Introduction to condensation continue…

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2( )( )

2l v

l

g yu y

3. ( )

3l l v

l

gm

.2( )l l v

l

gd m d

dx dx

14

4

( )l l

l l v fg

k Tx

gh

( )( ) sat w

x sat w l

T Th T T k

13 4

( ) 1

4l l v fg l

xl

ghh

T xk

Fig. Laminar film condensation without the presence of NCG

Classical Nusselt analysisIntroduction to condensation continue…

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Literature Review

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Literature reviewOutline:

Parameters affecting condensation

Modeling approach

Experimental setup

General adopted correlations


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Primary NCG mass fraction, subcooling, superheating, operating pressure, flow

direction

SecondarySuction effect, mist formation, film

waviness or roughness

TertiaryEffect of NCG used like argon, helium and

the condensing surface orientation.

Based on how frequently a parameter considered in the literature, they can be classified as:

Parameters affecting condensationLiterature review continue…

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Types of approach

Boundary layer solution

Based on solving boundary layer (NCG/vapor BL and condensate film BL) equations with appropriate interfacial jump and boundary conditions (Similarity variable, computational and mechanistic approach)

Heat and mass transfer analogy

Based on heat balance at the liquid-gas interface where interface temperature is determined iteratively (Empirical and mechanistic approach)

Diffusion theoryConductivity of condensation (kcond) is calculated using either Clausius-Clapeyron equation or HMTA. Then condensation HTC is calculated on the basis of that kcond .

Experimental Finding out correlations based on the experimental data’s (Empirical approach)

Modeling approachLiterature review continue…

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Equations Liquid film region Vapor /gas region

Conservation of mass

Diffusion equation

Conservation of momentum

Conservation of energy

( ) ( ) ( )m m m m

uu u v u g

x y y y

( ) ( ) 0l lu vx y

( ) ( )l l l l

uu u v u g

x y y y

( ) ( ) 0m mu vx y

"

( ) ( ) ( )pm m m pg pv g

T qc u T v T c c j

x y y y

( ) ( )pl l l l

Tc u T v T k

x y y y

2" * ( ) m

g D m gg v

MHere q k T R T j

y M M

* (1 ) Here ( ) ( ) jD g g

g m g m g v

W Wj D W D T and j

y T y

( ) ( ) gm m

ju W v W

x y y

(i) Governing equations

Boundary layer solutionModeling approach continue…

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Condition Equation

Mass flux

Stream wise velocity

Temperature

Interfacial shear

Energy flux

(ii) Interface conditions

Boundary layer solution continue…

. . . .

g vlm M M M

, ,l mu u

, ,l mT T

0m

y

u

y

."

l fg

Tk M h q

y

(iii) Interface constraint

Constraint Equation

Impermeable interface to NCG

Saturation state @ interface Ti =Tsat,v

.

0gM

(iv) Boundary conditions

Condn Equation

At y=0 u=v=0; T=Tw

At

At

y .

; li m

dT T m u v

dx

y ,; g gu u W W

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Heat and mass transfer analogy

• Heat balance at the interface

• Total heat transfer coefficient

• Condensate film thickness

Since, we know that

1

1 1tot

f c s

hh h h

( ) ( )( )f i w c s ih T T h h T T

4* 3

12 2 3 3

1 2 3 1 2 3 4 1 2

1.259

( ) ( ) ( )

Nu

p i i pa a x a x l b b x b x b x m c c x

.

; h ; h( )

fgl mf s m c

i b i

mhk kh Nu

d T T

hm is calculated using Shm relation as given below.

,

, .

nc im

nc i nc b

WmdSh

D W W

Modeling approach continue…

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Diffusion theory

The condensation conductivity is given as

or

, , ,

,

using HMTAfg i nc i nc bavg

condb i nc i

W WDHk

T T W

Then the condensation HTC is calculated as

Peterson et al (1993)cond

cond

Sh kh

L

2 2 2 2

2 3 2 2

1 1 et al (1993); et al (1998)tot v fg tot v fg

cond condavg i b

P M h D P M h Dk Peterson k Herranz

R T R TT

Modeling approach continue…

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• Interface shear stress consideration

(i) McAdams modifier (1951)

where 1.28 for Re 30; =1.0 for Re 30( )

lfh x

k

(ii) Blangetti et al model (1982)

14 4 4, ,

fx x la x tu

l

h LNu Nu Nu

k

* *2*3*

, *

Re1 where comes from equation

3 21

f gx la

g

l

Nu

Where Nux,la is Local laminar Nusselt number given by

and Nux,tu is Local turbulent film Nusselt number given by

*, Re Pr (1 ) wh values of a, b, c, d, e, f is given in above table. b c f

x tu f gNu a e ere

Special considerationsLiterature review continue…

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• Film roughness consideration

Special considerations continue…

0.215, ,

0.215 0.25, ,

where n=0.68Pr

where n=0.68Sc ; f 0.0791Re

n

ror x os x

s

n

ror x os x s

s

fNu Nu

f

fSh Sh

f

Correction suggested by Norris (1970)

Three popular models for estimating the roughness of the condensate are

(i)Moody correlation (1944)

(ii)Wallis correlation (1969)

(iii)Haaland correlation (1990)

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3 2 1001.375 10 1 21.544

Rerf d

1 300r sf fd

• Suction effect consideration Kays and Moffat correlation (1975)

1 1.

, ,. 12 2, 3

.

,

(Re 1000) Pr2Re Prexp 1 where Nu Nu 3.66

Re Pr 1 12.7 Pr 12

Reexp

s

x x mx o x o x

m o x x sx

x xx

m o

fm G

NuG Nu fm

m ScSh

G Sh

1 1

6, ,. 1

2 23

(Re 1000)21 where Sh for 2300 Re 5 10 ; Sh 3.66 for Re 2300

Re 1 12.7 12

s

mo x o x

x x sx

f ScG

fm Sc Sc

1.11

1012

1 6.91.8log

Re 3.7r

d

f

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• Developing flow consideration

Reynolds et al (1969): It is assumed that the temperature and concentration profile develop simultaneously. 34 2

,

34 2

,

0.8(1 7 10 Re )1

0.8(1 7 10 Re )1

xot o x

xot o x

Nu Nuxd

Sh Shxd

• Turbulent model

Turbulent viscosity is given as:

Prandtl mixing length theory

Kato et al (1968)

2t m

uL

y

20.4 1 exp 0.0017( )

sing assumption: at y= ; u 0 (Chen C. K., 2009)

t

L m

y y

u

Special considerations continue…

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• Vierow, K. et al, Horizontal Heat Exchanger Design and Analysis for Passive Containment Heat Removal System, U. S. Department of Energy, Nuclear Engineering Education Research, Final Technical Report, 2002 through 2005

Experimental setup

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• Oh, S., and Revankar, S.T., Effect of noncondensable gas in a vertical tube condenser, International Journal of Nuclear Engineering and Design, vol. 235, pp. 1699–1712, 2005

Experimental setup continue…

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• Lee, K.Y., and Kim, M.H., Effect of an interfacial shear stress on steam condensation in the presence of a noncondensable gas in a vertical tube, , International Journal of Heat and Mass Transfer, vol. 51, pp. 5333–5343, 2008

Experimental setup continue…

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• Wilke and Lee (1955)

• Rao et al (2008)

• Bucci et al (2008)

• Holman (1992)

• Kays et al (2005)

• Herranz et al (1998)

10 2.072

8.2

1.87 10

7235exp 77.3450 0.0057v

TD

P

T TPT

"., ,

m,

ln(1 ) where B =1v i v b

v mv i

w wm K B

w

10.75 3

10.75 3

1.04 0.0395Re Pr

1.04 0.0395Re

o

o

Nu

Sh Sc

21

3

1

0.046 where Ra=GrPr= ( )

Nu with n=3 (Churchill, 1977)

pbuo w cw

n n ncombined force natural

g C bNu Ra T T

k

and Nu Nu

where is suction factorinc avg

o avgnc

X TSh Sh

X T

32

4, 2

, ,

1 1

1 110 1.084 0.249

( ) ( / )a b

a ba b a b a b

TM M

DM M P r f kT

General adopted correlationsLiterature review continue…

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Property Binary mixture Multi-component mixture

Diffusion coefficient

Grashof number

Viscosity

Specific heat

Thermal conductivity

Mass fraction of NCG

Mole fraction of NCG

2.07253.4439 10 (Cenzel, 2002)avg

tot

TD

P ,

,1/

g avgeff n

j avg jvj

xD

x D

3gb gi gb

2

g ( - )L (Herranz et al, 1998)Gr

x nc nc v v x = W +W (T ) '

11

( ) = (Reid et al, 1987)

1 ( / )

ni avg

m ni

ij j ij

T

D x x

11

( ) = (Reid et al, 1987)

1 ( / )

ni avg

m ni

ij j ij

k Tk

A x x

x nc nc v v = W +W (T )vk k k

px nc pnc v pv = W +W (T )vC C C

,

( ) / ( ) ( / )

1 ( ) / ( ) ( / )T v x v x nc v

nc x

T v x v x nc v

P P T P T M Mw

P P T P T M M

,,

T s ncnc x

T

P Px

P

, (Peterson, 2000)

ln

jb jij ave

jb

ji

x xx

xx

Literature review continue…


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Parametric study

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Parametric study continue…

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Important findings

Steam and NCG flow side Cooling water flow side

Pressure range: 1-2.5 atm

Then Tsat:100-127 0C

Length of the plate: 70 cm

Film thickness: 0.18 mm

Condensate mass: 15.5 gm/s=55.8 kg/hr

Inlet temperature: 25 0C

Outlet temperature: 27 0C

Then temp. difference: 2 0C

Heat transfer required: 35 kW

Corresponding Mass flow rate required: 4.2 kg/s=15120 kg/hr

Steam and NCG flow side Cooling water flow side

Pressure range: 1-2.5 atm

Then Tsat:100-127 0C

Length of the plate: 50 cm

Film thickness: 0.17 mm

Condensate mass: 13 gm/s=46.8 kg/hr

Inlet temperature: 25 0C

Outlet temperature: 27 0C

Then temp. difference: 2 0C

Heat transfer required: 30 kW

Corresponding Mass flow rate required: 3.7 kg/s=13320 kg/hr


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Measuring Devices

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Measuring devices

• Mass flow rate measurement

• Film thickness measurement

• Gas concentration measurement

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• Can measure the mass flow rate of any gas or liquid, ideally suited for saturated and superheated steam.

• Measure five process parameters at the same time: mass flow rate, temperature, pressure,

volumetric flow rate, and fluid density.

Hydrogen flow meter

Steam flow meter

Mass flow rate measurementMeasuring devices continue…

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Model Thickness range Model Thickness range

F20 15nm - 100µm F50 20nm - 100µm

F20-UV 01nm - 40µm F50-UV 5nm - 40µm

F20-NIR 100nm - 250µm F50-NIR 100nm - 250µm

F20-EXR 15nm - 250µm F50-EXR 15nm - 250µm

F20-UVX 1nm - 250µm F50-UVX 5nm - 250µm

F20-XT 10nm – 1mm F50-XT 10nm – 1mm

F70 15nm – 13mm F50-CTM-NIR 0.1nm – 2mm

Film thickness measurementMeasuring devices continue…

Film thickness is measured as:

R={(n-1)2+k2}/{(n-1)2+k2}

Where R= Reflection

n=film refractive index

K=film extinction coefficient

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Gas concentration measurementMeasuring devices continue…

• Quadrupole Mass Spectrometers (QMS) is kind of ionisation gauge with separation system (according to mass to charge ratio) for the different species.

• QMS operates best at 10-6 mbar.

Fig. Gas concentration measurement system in

PANDA

Fig. Mass spectrometry in TOSQAN

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Gas concentration measurement continue…

Fig. PANDA calibration system

Difficulties in measurements:

• Steam get condensed and may adsorbed in the capillary section. To avoid this capillary tubes are heated upto 150 ºC.

• The pressure inside the test section is quite high. It needs to be reduced as low as 10-6 mbar for best working of QSM.

• As the pressure inside the chamber is not constant. So, the time required to feed the sample to the QSM is different. Due to this, calibration is required again.

• The increase in feeding time of sample leads to the possibility of leakage.

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Summary and conclusions

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Summary and Conclusions• It has been noted that no full mechanistic model available in the literature. Either they are based on

some correlations or giving some kind of input from the experiment.

• Condensate film thickness is of the order of 0.001-1 mm for the plate length of 50-70 cm.

• Condensate film thickness (order of 0.001-1 mm ) can be measured using optical technique. This technique can also be used for measuring the roughness of the film.

• The gas concentrations is measured using a device called Quadrupole Mass Spectrometers (QMS).

• Calculation of mixture composition for vapor and gas is a uphill task as not only the transfer of sample from test section to QMS involves many complexities but also QMS requires samples at nearly vacuum for best measurement.

• With all such difficulties, it’s great satisfaction that the setup is feasible in our laboratory.

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Quotation of the instruments

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End of Presentation

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Condensation