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

1
4th RCM on the IAEA CRP on Natural Circulation
Phenomena, Modelling and Reliability of Passive
Safety Systems that Utilize Natural Circulation
Experimental and theoretical Studies on
Condensation in a stagnant Steam-Gas Mixture

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

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Presentation in previous RCMs

• In the last two RCMs the presentations were made
  on the
• Effect of noncondensable gas on steam
  condensation inside a vertical tube
• Effect of non-condensable gases on condensation
  heat transfer in stagnant environment

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Condensation in stagnant environment

• The presentation deals with the following
• Experimental studies on condensation in presence
  of air on a horizontal tube
• Development of a theoretical model to investigate
  condensation in presence of noncondensable gas
  when steam/air mixture is non-flowing
• 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

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Condensation in stagnant environment
Experimental and theoretical studies on
condensation of steam in presence of
noncondensable gas in stagnant environment on the
outer surface of tubes/plates are performed.

• 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.

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Passive Containment Cooling System (PCCS)
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Condensation in stagnant environment
Schematic Illustration of the Model
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The model
Heat balance at interface
The heat transfer through the condensate film is
equal to the heat transfer through the gas/vapor
interface which is sum of latent heat and
sensible heat.
Condensation heat transfer is defined as
Total heat flux,
hcond Condensation heat transfer coefficient ,
hf Film heat transfer coefficient hg -
Convective heat transfer coefficient
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Film heat transfer
Condensate film model The film heat transfer
coefficient on vertical surface is calculated by
Nusselt equation
for Ref lt 30
Kutateladze (1963) has proposed the following
expression for the film heat transfer coefficient
to account for the rippling effect.
for 30ltReflt1600
For condensation on horizontal tube the 0.943 is
replaced by 0.725 in Nusselt equation
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Mass transfer
A mass balance at the interface is done to yield
the following equation
where, L is the characteristic length which is
outer diameter for horizontal tube and length of
the tube for vertical tube
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Heat and mass transfer analogy
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
hg can be obtained from above expression
By heat and mass transfer analogy
mcond and hcond can be estimated from equations
defined above
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Heat transfer enhancement
Suction effect To consider this effect, a
correction factor, is introduced in the
definition of the Sherwood number
where ? is often referred to as a suction factor
Herranz et al. have proposed a simple equation
and is given as
Tave is logarithmic average temperature of bulk
and liquid/gas interface
Using the corrected Sherwood number, mass
transfer flux is modified as
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Condensation conductivity
The condensation heat transfer coefficient, is
rewritten as
Peterson et al. defined the condensation heat
transfer coefficient in terms of condensation
conductivity, as
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Condensation conductivity
They provided an expression for thermal
conductivity using the thermodynamic
Clausius-Clapeyron equation and it is given as
The condensation conductivity can be defined from
model proposed. Following expression for
condensation conductivity is found using the
using the fundamentals of mass transfer and heat
and mass transfer analogy
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Correlations
Some of the correlations available in
literature There are number of correlations are
available in the literature. Some of the
correlations developed are given below. Dehbi
correlation
0.3 m lt L lt 3.5 m 1.5 atm. lt Ptot lt 4.5 atm. 10
oC lt (Tb-Tw) lt 50 oC
The correlation developed by Uchida
The correlation developed by Liu et al. is given
as
2.533 X 105 Pa lt Pt lt 4.559 X 105 Pa 4 oC lt dT lt
25 oC and 0.395 lt Xs lt 0.873
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Experimental set-up
Photograph
Schematic of the steam condensation experimental
set up
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Geometry and parameters

• 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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Measurements

• For outside heat transfer coefficients
• Temperature of air/steam mixture in the vicinity
  of the tube was measured and the corresponding
  saturation pressure of steam at that location was
  estimated.
• The average outside wall temperature was
  estimated from the thermocouples brazed on the
  tubes.
• The coolant temperature at the inlet and outlet
  of the condensing tube.

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Analysis
From a steady state energy balance on the coolant
we get,
The outside heat transfer coefficient
where, Tb is bulk steam/air temperature and Tw is
average outside wall temperature.
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BARC data Horizontal tube
Heat transfer coefficient decreases due to the
higher resistance for steam to diffuse from the
bulk to the condensate film
Variation of heat transfer coefficient with air
mass fraction
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BARC data Horizontal tube
The heat transfer coefficient increases as the
driving force ratio for mass transfer increases
but decreases due to the wall subcooling.
Variation of heat transfer coefficient with wall
cooling
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BARC data Horizontal tube
The increase in pressure increases the density
and the Grashof number is proportional to the
square of the density (?2). So the heat transfer
coefficient which depends on Grashof number will
increase due to the increase in pressure.
Variation of heat transfer coefficient as
function of pressure
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BARC data Horizontal tube
Comparison between experimental and theoretical
heat transfer coefficients
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BARC data Horizontal tube
Comparison between theoretical heat transfer
coefficients obtained by assuming (i) Ti Tw
,

(ii) Ti ? Tw
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Horizontal Vs vertical orientation
Comparison of heat transfer coefficients for
horizontal and vertical orientations of the tube
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Other data
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Condensation conductivity
Comparison of condensation conductivity estimated
in the model and by Herranz modified formula
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Dehbis data Vertical tube
Comparison of heat transfer coefficients
estimated by present model with Dehbi's data and
corrlations
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Dehbis data Vertical tube
Comparison of the heat transfer coefficients
estimated by present model With Dehbis
experimental data
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Dehbis data Vertical tube
Comparison between theoretical heat transfer
coefficients
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Anderson data Vertical plate
Comparison of present model and various
correlations with Andersons experimental data
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Conclusions

• The heat transfer coefficient decreases due to
  the increase in air mass fraction for constant
  wall subcooling and pressure due to the higher
  resistance to diffuse air from the boundary layer
  to the bulk.
• The heat transfer coefficient decreases
  marginally due to increase in wall subcooling
  when the pressure and air mass fraction are kept
  constant.
• The heat transfer coefficient increases due to
  increase in the pressure for constant air mass
  fraction and wall subcooling.

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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
• 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.