N.K. Maheshwari, P.K. Vijayan and D. Saha

1
3rd RCM on the IAEA CRP on Natural Circulation
Phenomena, Modelling and Reliability of Passive
Safety Systems
that Utilize Natural Circulation
TRACKING OF NON-CONDENSABLES

• N.K. Maheshwari, P.K. Vijayan and D. Saha
• Reactor Engineering Division,
• Bhabha Atomic Research Centre,
• Trombay, Mumbai, INDIA - 400 085

2

Presentation in 2nd RCM
In the last RCM a presentation was made on the
Effect of noncondensable gas on steam
condensation inside a vertical tube

• The presentation dealt with the following
• Development of a theoretical model for the
  calculation of the condensation heat transfer
  coefficient in presence of noncondensable gas
  flowing inside vertical tube.
• Comparison of various models for condensate film
  heat transfer.
  
• Comparison of the heat transfer coefficients
  obtained from theoretical studies and
  experiments.

3

Condensation in stagnant environment
The present talk deals with condensation of steam
in presence of noncondensable gas in stagnant
environment on the outer surface of tubes/plates

• The problem is relevant to containment cooling
  using Passive Containment Cooling System (PCCS).
  
  
• In the Advanced Heavy Water Reactor (AHWR), PCCS
  with passive external condensers (PECs) removes
  energy released into the containment through the
  PEC to a water pool above it. The containment
  steam condenses on the outer surfaces of the
  tubes and water from the pool circulates through
  these tubes by natural circulation.

4

Passive Containment Cooling System (PCCS)
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Condensation in stagnant environment

• Work done
• Experimental studies on condensation in presence
  of air over horizontal tube
  
• Development of a theoretical model to investigate
  condensation in presence of noncondensable gas
  when steam/air mixture is nonflowing
  
• Studies on the effects of various parameters on
  condensation in presence of noncondensable gas
  
• Comparison of theoretical results with BARC
  experimental data
  
• Comparison of theoretical results with
  experimental data available in literature

6

Condensation in stagnant environment
Schematic Illustration of the Model
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Heat balance at interface
Heat transfer in gas /vapor boundry layer
(1)
Heat transfer through condensate film
(2)
Heat balance at boundary layer
(3)
Condensation heat transfer is defined as
(4)
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Heat balance at interface
Substituting in (3)

(4)
Total heat flux,
(5)
(6)
hcond Condensation heat transfer coefficient ,
hf Film heat transfer coefficient
hg - Convective heat transfer coefficient
9

Condensate film heat transfer
Condensate film model The film heat transfer co
efficient on vertical surface is calculated by
Nusselt equation
for Ref
(7)
Kutateladze (1963) has proposed the following
expression for the film heat transfer coefficient
to account for the rippling effect.
Where,
(8)
for 30
For condensation on horizontal tube the 0.943 is
replaced by 0.725 in Nusselt equation
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Mass transfer at interface
A mass balance at the interface is done to yield
the following equation
(9)
As the condensate surface is impermeable to the
noncondensable gas, Eq. can be simplified as,
Where, D is diffusion coefficient and hm is mass
transfer coefficient
(10)

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Mass transfer at interface
The above equation can be recast, in terms of
Sherwood number (hmL/?D) , as
(11)
Where, L is the characteristic length which is
outer diameter for horizontal tube and length of
the tube for vertical tube
Modifications are carried out to account for the
effect of suction by multiplying Sherwood number
by a factor
12

Gas/vapor sensible heat transfer
Heat transfer at gas/vapor boundary layer
In case of stagnant gas environment, the natural
convection boundary layer approach provides the
expressions for sensible heat transfer through
the gas/vapor boundary layer formed during
condensation of vapor.
The Grashof number is defined as
(12)
hg can be obtained from above expression
By heat and mass transfer analogy
mcond and hcond can be estimated from equations
(11) and (4)
(13)
13

Correlations
Some of the correlations available in literature
There are number of correlations available in
the literature. Some of the correlations
developed are given below. The Dehbi correlatio
n
0.3 m
The correlation developed by Uchida
The correlation developed by Liu et al. is given
as
2.533 x 105 Pa 4 oC
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Experiment set up
Schematic of the steam condensation experimental
set up
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Experimental set up
Photograph of experimental set-up
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Tests on horizontal tube

• Experiments were performed on condensation in
  presence of air on outer surface of horizontal
  tube in BARC
  
• - Tube outer diameter 21.3 mm
• - Tube length 750 mm
• Range of parameters
• - Pressure
  1.6-4.0 atm
  
• - Air mass fraction 0.20-0.95
• - Wall subcooling 30-55 0C

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Comparison between Experimental and theoretical
results
Variation of heat transfer coefficient with air
mass fraction
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Comparison between experimental and theoretical
heat transfer coefficients

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Comparison of theoretical results
Comparison between theoretical heat transfer
coefficients obtained by assumin
g (i) Ti Tw ,

(ii) Ti ? Tw
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Vertical tube
Comparison of the heat transfer coefficient
estimated by present model With Dehbis experime
ntal data
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Vertical tube
Comparison between theoretical heat transfer
coefficients
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Vertical Plate
Comparison of present model and various
correlations
with Andersons experimental data
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Parametric study

• The analysis is performed to study for following
  parameter effects for vertical tube in stagnant
  atmosphere
  
• Air mass fraction
• Wall subcooling
• Pressure

• Results are compared with following correlations
• Dehbi correlation
• Uchida correlation
• Liu correlation

24

Noncondensable mass fraction effect
Variation of heat transfer coefficient with
noncondensable
mass fraction
25

Wall subcooling effect
Variation of heat transfer coefficient with wall
subcooling with constant bulk temperature
26

Wall subcooling effect
Variation of the heat transfer coefficient with
wall subcooling for constant wall temp.
27

Pressure effect
Variation of the heat transfer coefficients
with total pressure
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Conclusions

• The theoretical model developed can be used to
  study the heat transfer for various geometries.
  
• Theoretical analysis shows that the heat transfer
  coefficient for horizontal tube is more than that
  of vertical tube.
  
• The heat transfer coefficient decreases due to
  the increase in air mass fraction for constant
  wall subcooling and pressure due to the higher
  resistance for the steam to diffuse into the
  boundary layer from the bulk.
• The heat transfer coefficient decreases
  marginally due to increase in wall subcooling
  when the pressure and air mass fraction are kept
  constant.
• Heat transfer coefficient can be estimated
  assuming the interface temperature equal to wall
  temperature for the range of the various
  parameters discussed. The resistance offered by
  the condensate film in this case is small as
  compared to the resistance offered by the
  gas/vapour boundary layer due condensation of
  steam.