Reflux Condensation Heat Transfer of
Steam-Air Mixture under Gas-Liquid
Countercurrent Flow in a Vertical Tube
Oct 7, 2004
Institute of Nuclear Safety System, Inc.
Institute of Nuclear Technology
Technical Support Project
Takashi Nagae
1
Purpose
SG
Reactor
Vessel
原子炉容器
Pressurizer
Shutdown PSA evaluation in Japan found
that the mid-loop operation showed a high
core damage probability.
Mid-loop Operation・・・
The RCS inventory is so low that it may
decrease to the center line of the reactor
coolant piping.
加
圧
器
Core decay heat is cooled by RHR
Loss of RHR function
Boiling away of the core at an early stage
One of possible alternative cooling method is
Reflux condensation by SG
RHRポンプ
RHR
Pump
Fig 1 Mid-loop operation
Main Steam
Relief Valve
ＳＧ
Aux. Feed Water
Pressurizer
Reactor
Vessel
Steam
Condesate
Water
Fig 2 Reflux cooing
SG U-Tube
Reflux condensation ・・・
Core heat is removed by boiling
Steam flows to the SG and condenses inside
tubes
Condensate on the up-flow side flows back to
the core
2
To estimate realistic availability of reflux condensation
heat transfer we must consider following realistic
conditions
(1)Existence of noncondensable gases
← degrade heat transfer
(2)Gas-liquid countercurrent flow
← flow regime effect to heat transfer
z
Condensate
Film
ｄi
 Default model in RELAP5
→is not confirmed whether they are applicable for
condition (1)(2). （It is reported that the model
underestimates heat transfer in NUREG report.）
 Suggested models in other researchers
→are applicable only for narrow condition
ｄo
Condensate Steam&Air Condensate
Water
Water
Fig 3 Condensation with noncondensable
gases in U-tube
To investigate the reflux condensation heat transfer,
we had experiments of reflux condensation and
developed the new heat transfer models
Experiment
Table 2 Test conditions
Condenser tube inner
diameter
19.3mm
Condenser tube wall
thickness
3.04mm
Pressure※
0.1, 0.2, 0.4[MPa]
Inlet steam flow rate※
0.45～1.9[g/s]
Inlet air mass flow rate
0.03～0.18[g/s]
※Condition during reflux condensation
Measured temperatures are
(1) Mixture of steam and air : Tg
(2) Condenser tube outer wall : Tw,o
(3) Coolant water: Tc
at 9 distances from the condenser tube by
thermocouples
Local heat flux q’’ and interface
condensation heat transfer coefficient hi are
calculated and evaluated Nusselt numbers
Nui.
Fig 4 Test section
(Double-pipe, concentric-tube heat exchanger)
New heat transfer models
3
Calculations
Inner
tube
内管
Outer
外管tube
－ Calculation of local heat flux q’’ －
(1) Inlet side of test section
(2)
 cc p dTc
q"( z)dA  m
 c c p dTc ( z )
dT ( z ) m
 cc p c
q" ( z )  m

dA
d w,o dz
T w,o
h fg dm
 steam ( z)
d w,i
dz
msteam ( z ) M steam Psteam ( z ) M steam
Psteam ( z )


mair
M air Pair ( z )
M air Ptotal  Psteam ( z )
ｄo
ｄi
Liquid film
凝縮液膜
Δz
z
Outlet side of test section
4
Tg
Tc
q" ( z) 
Coolant
冷却水
蒸気・空気
Steam & air
－Calculation of interface condensation heat transfer coefficient －
1/K (z) = rw,i ln(rw,o /rw,i )/λw(z) + 1/hf (z) + 1/hi (z)
Overall heat resistance
tube wall
liquid film
interface
q’’ (z) = K(z) (Tg(z) - Tw,o (z))
Nui (z) = hi(z)dw,i /λs(z)
Nusselt number for the condensate film is obtained by applying the modified
McAdams correlation to the Nusselt analysis for falling laminar film on a cold plate

hc L  f L
 4
Nu f 

 1.28
 f  f ,0  f

 3 Re f
1/ 3
  f   g 
2


, L  (v f /

 

f


K : overall heat transfer coefficient
rw,i : tube inner radius
rw,o : tube outer radius
λw : thermal conductivity of tube
hf : heat transfer coefficient for
liquid film
Nu : Nusselt number
dw,i : tube inner diameter
g )1/ 3 λs : thermal conductivity of film
Test condition
Experimental result
5
Pressure = 0.1MPa
Inlet steam flow rate = 1.23g/s,
Inlet air flow rate = 0.06g/s
Tg ： Mixture of Steam and air
temperature
Tw,o ： Condenser tube outer wall
Tc
temperature
： Coolant temperature
Tg
Tw,o
Tc
Tg,c*
Tg,c**
Temperature (℃)
120
100
80
* RELAP5
**Moon
60
RELAP5 default heat transfer model
underestimate the heat transfer coefficients
Moon’s empirical correlation
F = htot/ hf
= 2.58x10-4 Reg0.200 Ref0.502 Ja-0.642 Wair0.244
（6119< Reg <66586, 0.140< Wair <0.972,
0.03<Ja<0.125）

40
20

0
0
0.5
1
1.5
Axial Location (m)
2
2.5
Fig 5 Temperature profile (at steady state)
No measurement in low temperature
region
Exploration of the correlation
overestimate the heat transfer coefficient
Ｆ ：非凝縮性ガスによる熱伝達の劣化係数
hfpt：非凝縮性ガスを含む場合の凝縮熱伝達率
hf ：純粋蒸気のNusseltによる凝縮熱伝達率の理論値
Reg ：蒸気・空気の混合ガスレイノルズ数、Reg ：液膜のレイノルズ数
Ja : ヤコブ数、Wrir ：局所の空気質量流量比
Development of Heat transfer models
1000000
Turbulent
flow
0.1MPa
0.2MPa
0.4MPa
Eq （１）
Eq.
(13)
100000
Nu i
10000
100
1
0.001 0.01
Correlation for the local heat transfer
coefficients
Correlation for local Nusselt number is obtained
as a function of the steam-to-air partial pressure
ratio and plotted in Fig 6.
Nui = 120 (Ps /Pa )0.75 ，(Nu <500)
(1)
Eq (1) is not valid for turbulent flow region and
we can’t neglect the influence of gas flow
1000
10
6
Laminar
flow
0.1
1
10
P steam /P air
100 1000
Fig 6 Nusselt numbers
100000
0.1MPa
0.2MPa
0.4MPa
10000
Turbulent
flow
Nui,cal
1000
100
Laminar
flow
10
 To develop the correlation in turbulent flow region,
steam Reynolds number is adopted to Eq (1).
Nui = 120 (Ps /Pa )0.75max(1.0， aRe,sb)
(Re,s≦5000，a=0.0012，b=1.0)
(2)
 Comparing between the measurement and
calculation from Eq (2) shows good agreement
not only in laminar flow region but also in
turbulent flow region.
1
1
10
100
1000
10000 100000
Nu i,meas
Fig 7 Comparison between measurements and calculation (Nusselt numbers)
7
Improvement of Heat transfer models
Additional experiment (increasing air mass flow to
0.2-1.0g/s) to improve the correlation in turbulent
flow region
10000
□0.2MPa
△0.4MPa
In low heat transfer area, Eq(2) underestimate the
Nusselt numbers
Nu,si,cal.
1000
100
+50%
Estimation only by the steam Reynolds number is
not enough when air mass flow rate increases
10
-50%
1
1
10
100
1000
10000
Nu,s i,meas.
Fig 8 Comparison between measurements and
Eq(2) (air mass flow: 0.2-1.0g/s）
In low heat transfer area, Eq(2) over estimate the
Nusselt numbers
Effect of Re,s ｂ (b=1) is too big
8
Improvement of Heat transfer models
10000
1000
Nu,gi,cal.
The steam Reynolds number Re,s in Eq(2) was changed
to steam-air mixture Reynolds number and Eq(3) was
derived
◇0.1MPa
□0.2MPa
△0.4MPa
h ( z )d w,i
 P ( z) 
Nui ( z )  i
 120 steam 
g ( z )
 Pair ( z ) 
(a = 0.0035，b = 0.8)
100
+50%
10
-50%
1
1
10
100
1000
10000
Nu,g i,meas.
Fig 9 Comparison between measurements and
Eq(3) (air mass flow: 0.03～1.0g/s）
0.75
b
max( 1.0, a Re g ) (3)
Comparing between the measurement and calculation
from Eq (3) shows good agreement not only in
laminar flow region but also in turbulent flow region
including the air mass flow increasing condition
Evaluation of Heat transfer models
9
Temperature measurements by thermocouples may contain errors, so
calculated local heat transfer coefficients may have errors
To evaluate the accuracy of calculation, we calculated the mixture of steam
and air temperature profile and compared with measurements
It was verified that Eq (3) effectively simulate the temperature profile.
We confirmed the validity of Eq (3) as heat transfer model
Wair=0.03g/s
Wair=0.06g/s
Wair=0.12g/s
Wair=0.18g/s
W steam(0)=1.24～1.26g/s, Wair=0.12g/s
160
P=0.1MPa
Eq (3)
P=0.1MPa,式(2)
P=0.2MPa
P=0.2MPa,式(2)
Eq (3)
120
100
P=0.4MPa
P=0.4MPa,式(2)
Eq (3)
80
60
40
20
0
120
P=0.1MPa, W steam(0)=1.22～1.37g/s
Tg ，Temperature( ℃)
Tg ，Temperature(℃)
140
Eq (3)
Wair=0.03g/s,式(2)
Wair=0.06g/s,式(2)
Eq (3)
Eq (3)
Wair=0.12g/s,式(2)
Wair=0.18g/s,式(2)
Eq (3)
100
80
60
40
20
0
0
0.5
1
1.5
Z ，Axial Location(m)
2
2.5
0
0.5
1
1.5
2
Z ，Axial Location(m)
Fig 10 Comparison between measurements and calculation (temperature profile)
2.5
10
Comparing local heat transfer coefficient
between measurements and Eq (3)
Evaluation of Heat transfer models
Moon’s experiment (test condition)
10000
◇
□
△
hc,cal
1000
0.1MPa
0.15MPa
0.25MPa
Condenser tube inner
diameter
16.56mm
Condenser tube wall
thickness
1.25mm
Pressure※
0.1, 0.15,
0.25[MPa]
Inlet steam flow rate※
0.37～0.91[g/s]
Inlet air mass flow rate
0.15～0.68[g/s]
+50%
100
-50%
10
10
100
Measurement
limitation
1000
10000
h c,meas
Fig 11 Comparison between measurements
and calculation (hc)
 Comparing local heat transfer coefficient
between measurements and Eq (3)
（1/hc = 1/hf + 1/hi）
 We confirmed the validity of Eq (3) as heat
transfer model in with Moon’s experiment
11
７．Summary
To estimate realistic availability of reflux condensation heat transfer we
must consider following realistic conditions
1. Existence of noncondensable gases
2. Gas-liquid countercurrent flow
 An experimental facility was constructed to study reflux condensation heat
transfer in the riser section of PWR U-tubes
 New heat transfer models were developed
① Correlation for local Nusselt number was obtained as a function of the
steam-to-air partial pressure in laminar flow region
②In turbulent flow region steam-air mixture Reynolds number was adopted
 It was verified that New heat transfer models effectively simulate the
temperature profile
12
８．Future plan
Incorporation of new models into RELAP5
Validation of new models in RELAP5
Reference
Comparison with RELAP5 heat transfer models
P=0.1MPa，Wsteam=1.22g/s，Wair=0.18g/s
界面熱伝達率：hi
(W/m2 K)
hi (W/m2K)
10000
Comparing local heat transfer coefficient with
measurements, Eq (2) and RELAP5 models
Turbulent
乱流域
flow
1000
Table 3 Calculation with RELAP5 heat transfer models
Laminar
層流域
flow
100
Eq (2)
式(2)
Relap5ﾓﾃﾞﾙ
measurement
測定値
10
0.1
界面熱伝達率：hi
hi (W/m2(W/m
K) 2 K)
10000
14
1
Psteam/Pair
分圧比：Ps/Pa
10
100
Laminar flow
Turbulent flow
0.1MPa
Underestimate
(20～50%)
Good agreement
0.4MPa
Underestimate
（10～25%）
Underestimate
（45～50%）
P=0.45MPa，Wsteam=1.24g/s，Wair=0.12g/s
Turbulent
乱流域
flow
RELAP5 condensation heat transfer models tend to
underestimate the heat transfer coefficient in all
region.
1000
100
Laminar
層流域
flow
Eq
(2)
式(2)
10
Relap5ﾓﾃﾞﾙ
measurement
測定値
1
0.01
0.1
1
P分圧比：Ps/Pa
steam/Pair
10
We will incorporate the new models into RELAP5 as a
option and we will be able to calculate SG reflux
condensation more accurate than default models.
100
Fig 9 Interface condensate heat transfer coefficient
（Comparison with RELAP5)
※Now we are under additional experiment because
data in turbulent flow region is not sufficient.

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