A new method to study the transient feasibility of IVR-ERVC strategy

Progress in Nuclear Energy 87 (2016) 47e53

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Progress in Nuclear Energy
journal homepage: www.elsevier.com/locate/pnucene

A new method to study the transient feasibility of IVR-ERVC strategy
Rui Guo, Wei Xu, Zhen Cao, Xiaojing Liu*, Xu Cheng
School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Dong chuan Road 800, Shanghai, 200240, China

a r t i c l e i n f o

a b s t r a c t

Article history:
Received 16 April 2015
Received in revised form
13 November 2015
Accepted 14 November 2015
Available online 28 November 2015

The traditional method to evaluate the feasibility of IVR-ERVC strategy is based on the steady state of the
molten pool. But in the early stage, the transient behavior of the molten corium may impose a greater
threat to the integrity of the reactor pressure vessel. A new method to study the transient feasibility is
proposed in this paper. In order to calculate the critical heat flux in transient severe accident, a theoretical CHF model is developed suitable for the outer surface of the lower head. The effect of orientation
on bubble movement is taken into consideration, and the method to deal with the non-uniform heat flux
is also proposed. By comparing the prediction with the ULPU experimental data, the new model shows
satisfying accuracy. Parametric analysis of the new model shows that an increased reactor pressure
vessel diameter will lead to a decrease in critical heat flux at the lower head outer surface when the
structure of the external flow channel keeps unchanged. A transient severe accident analysis of the large

scale PWR shows that the transient behavior of the molten corium imposes a greater threat to the
integrity of the reactor pressure vessel.
© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND
license ( />
Keywords:
IVR
ERVC
CHF
Theoretical model
Transient analysis

1. Introduction
In-vessel retention of molten core corium by external reactor
vessel cooling (IVR-ERVC) is an important severe accident management strategy. The criterion of the IVR-ERVC is to assure the
thermal load from the melt is lower than the coolability limit,
everywhere on the lower head of the reactor pressure vessel. In that
case, the decay heat will be removed by the reactor cavity flooding,
to prevent the escape of radioactive material from the reactor
vessel.
It's generally accepted that the IVR-ERVC strategy will succeed
in AP600 and AP1000. But there is controversy that currently
proposed strategy without additional measures could provide
sufficient heat removal in higher power reactors. China is now
developing higher power passive PWR with an operating power of
1400 MW and 1700 MW, in order to obtain the independent intellectual property rights which is very important for nuclear exports. In the design, the feasibility of applying the IVR-ERVC
strategy to keep the integrity of the pressure vessel is one of the key
problems. So it is necessary to investigate it carefully.
The traditional method to evaluate the feasibility of IVR-ERVC

* Corresponding author.

E-mail address: (X. Liu).

strategy is based on the steady heat flux distribution in late stage
of severe accident (Theofanous et al., 1997a). The researchers
believe that the thermal load to the lower head is maximized when
the debris pool has reached a steady thermal state. Heat transfer
correlations available for steady molten pool are provided to
calculate the thermal energy on the lower head. Critical heat flux as
function of position on the lower head is also obtained based on the
steady state, which will not change with inlet water temperature,
mass velocity or heat flux distribution.
Although at steady state the total thermal load to lower head is
maximized, it is not guaranteed everywhere because the heat flux
is not distributed uniformly. So in the early stage, the transient
behavior of the molten corium may impose a greater threat to the
integrity of the reactor pressure vessel. Considering that the
boundary condition at the outer surface of RPV lower head varies in
the transient melting process, the existing critical heat flux
expression is not enough. In order to evaluate the feasibility of IVRERVC strategy in a transient severe accident, we need to know the
critical heat flux in different conditions. Experimental work is
effective, but as we know, this kind of experimental work is very
expensive and takes a long time. So it's useful to develop a theoretical model to predict CHF under this situation, in which the
characteristics in ERVC condition such as inclined heating wall and
non-uniform heat flux must be considered.
There are various mechanistic CHF models proposed so far.

/>0149-1970/© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( />

48

R. Guo et al. / Progress in Nuclear Energy 87 (2016) 47e53

Among them, boundary layer separation model (Tong, 1975), bubble crowding model (Weisman and Pei, 1983), sublayer dryout
model (Lee and Mudawwar, 1988) and interfacial lift-off model
(Galloway and Mudawar, 1993) are receiving attention in the flow
conditions. Guo et al. (2014) proposed a theoretical CHF model for
subcooled flow boiling in a curved channel based on bubble
crowding model. The model was verified in uniform heat flux
condition, but it is unknown whether it is effective in non-uniform
heat flux condition.
In this paper, a theoretical CHF model is developed suitable for
the outer surface of the lower head, and the effect of various parameters on CHF are investigated. In order to evaluate the feasibility of IVR-ERVC strategy in a transient severe accident, the
1700 MW-class plant is simulated by the code MELCOR, to provide
heat flux distribution on the lower head at different time, and the
corresponding critical heat flux is calculated by the proposed CHF
model.

2. The proposed CHF model
2.1. CHF mechanism
The CHF mechanism of bubble crowding model was proposed
by Weisman and Pei (1983). They thought that under low quality
condition the flow region could be divided into bubbly layer and
bulk flow layer, and the limited turbulent interchange between
them leads to the onset of CHF. The max value of void fraction in
bubbly layer was postulated to be 0.82, which was determined by a
balance between the outward flow of vapor and the inward flow of
liquid at the bubbly layer and bulk flow interface. Guo et al. (2014)
established an experiment apparatus to study the CHF phenomenon in the IVR-ERVC condition, with the width of 150 mm and
depth of 156 mm. Fig. 1 presented the visual observation while the
boiling crisis occurred. The red line showed the approximate

location of heater surface. Bubble crowding and vapor blanketing
appeared near the wall, and small bubbles were dispersed in the
bulk flow region. It's rational to apply the bubble crowding model
to the IVR-ERVC.
The equation of critical heat flux is expressed as:

q ẳ G0 x2 x1 ịhfg

hf hld
hl hld

(1)

0

where G is the mass flux due to turbulent interchange at the edge
of the bubbly layer, x2 is the vapor quality of the bubbly layer, x1 is
the vapor quality in the bulk flow, and hld is the liquid enthalpy at
the point of bubble detachment, which is calculated from the Levy
(1967) model. From the above equation, we know that the turbulent interchange at the interface and the vapor qualities of the
bubbly layer and the bulk flow are precondition to calculate the
critical heat flux.
It is assumed that only those velocity fluctuations which are
larger than the vapor generation velocity could penetrate to the
interface, the turbulent interchange was determined by:

G0 ¼ Gji

(2)

where G is the mass flux, j is the velocity fluctuations that are
effective in reaching the wall, and i is the turbulent intensity at the
bubbly layer and bulk flow interface.
In the model of Weisman and Pei, vapor quality was calculated
using homogeneous flow model. Guo et al. (2014) considered that
the slip model was more suitable in IVR-ERVC condition, in which
the slip ratio varied with the inclination of the heater surface. The
vapor quality in bubbly layer is written as:

x2 ẳ

1
1ỵ

(3)

1a2 rl 1
a2 rg S

a2 is the void fraction in bubbly layer, which is assumed to be
0.82 at the CHF point. The slip ratio S is defined as the ratio of vapor
velocity to liquid velocity, and can be expressed as:
Sẳ1ỵ

ut
u2 ut x2

(4)

u2 is the average velocity in the bubbly layer. It is assumed to be one

half of the velocity at the interface, which can be calculated by the
Karman velocity profile. ut is the bubble rise velocity, and will
change with the inclination of the flow channel, given as:

"
ut ¼ 1:41

À
Á#1=4
sg sin q rl À rg
r2l

(5)

From Eq. (4) and Eq. (5), we can calculate the vapor quality and
slip ratio of the bubbly layer.
The vapor quality in the bulk flow can be got by energy balance
equation.

hg rg u2g 1 hịa2 ỵ hl rl u2l 1 hị1 a2 ị ỵ h1 r1 u1 h ẳ Gh

(6)

where hl is the liquid enthalpy, h1 is the average enthalpy of bulk
flow, h is the area fraction occupied by the bulk flow, u2l is the liquid
velocity in bubbly layer and u2g is the vapor velocity in bubbly layer.
From Eq. (6), the enthalpy of bulk flow is received. Then the vapor
quality of the bulk flow is given as:

x1 ¼

h1 À hl
hg À hl

(7)

2.2. Non-uniform heat flux method
Fig. 1. Boiling photograph at CHF.

Currently, there are three approaches to account for the effect of


R. Guo et al. / Progress in Nuclear Energy 87 (2016) 47e53

49

non-uniform power shape (Yang et al., 2006): overall power, local
conditions, F-factor. The overall power approach assumes that the
critical power for non-uniform heated tube is the same as that for
uniform heated tube at the same cross-sectional geometry and
heated length at given inlet conditions. The local conditions
approach assumes that the CHF is independent of upstream history.
The F-factor approach derived by Tong assumes that there is a superheated liquid layer between the bubbly layer and the heated
wall. The enthalpy of the liquid layer at CHF is the same under
uniform and non-uniform power shape. In the subcooled region or
at low qualities, the upstream memory effect is small, and the local
heat flux determines the CHF. At high qualities, however, the
memory effect becomes strong, and the average heat flux determines the CHF.
In the IVR-ERVC conditions, given the water at the upper tank
being saturated at atmospheric pressure, water subcooling at the

heater inlet is about 10 K. Even at the CHF point, subcooled boiling
is the dominant regime. So the local heat flux determines the CHF
here.
The present method is to calculate CHF values at different
angular degrees first. Then we get the ratio of CHF value to the local
heat flux at different locations. If we gradually increase the local
heat flux, boiling crisis will take place at the point with minimal
ratio value as shown in Fig. 2.
2.3. Comparison of predictions with experimental data
ULPU experiments (Theofanous et al., 1997a,b; 2002a,b,c and
Dinh et al., 2003) have been conducted to identify the coolability
limit for AP600 and AP1000. The test facility was an effective fullscale simulation of the reactor axisymmetric geometry. Configuration I was focused on the bottom of the lower head in a saturated
pool boiling condition. In configurations II and III, the CHF experiments of the overall inclination angle were conducted under natural convection conditions. The configurations IV and V studied the
effect of the streamlined flow path. In the present study, ULPU IV
with a streamlined flow path is selected to verify the proposed CHF
model. The experimental facility was constructed as shown in
Fig. 3. The height of the facility was about 6 m. The radius of the
heater blocks was 1.76 m, as that of AP600 lower head. The heater
blocks were made of 7.6 cm thick copper, with a width of 15 cm, and
they were heated by imbedded cartridge heaters that were individually controlled to create any heat flux shape as will. Power
shaping was used to simulate the axisymmetric geometry in the

Fig. 3. Schematic of ULPU IV (Theofanous et al., 2002c).

reactor.
The comparison of predictions with experimental data is as
Fig. 4. It can be seen that with the increase of orientation, the
critical heat flux on the heated wall first increases then decreases,
which can be explained by our developed model. Bubble rise velocity increases with the orientation, so the slip ratio and steam
quality in the bubbly layer tend to become bigger. Meanwhile, the

thickness of the bubbly layer also increases. These factors result in
increase of CHF. But at high orientation, the upstream heat length is
longer, and the upstream overall power is bigger, which makes the
vapor quality of the CHF point bigger and easier to reach boiling
crisis. This results in decrease of CHF. At low orientation, the positive factor is dominant, but at high orientation, the negative factor
is dominant.

2000

1800

ULPU IV
model

2

qCHF(kW/m )

1600

1400

1200

1000

800

600
0

10

20

30

40

50

60

70

80

90

Angle(deg)
Fig. 2. Schematic of calculation in non-uniform power shape.

Fig. 4. Comparison of prediction and experimental data in ULPU IV.

100


50

R. Guo et al. / Progress in Nuclear Energy 87 (2016) 47e53

The critical heat fluxes predicted by the present model are
compared with the experimental CHF data. The results are quantitatively evaluated by the quantity K, defined as:

2200
2000

CHFp
CHFm

(8)
2

where subscripts p and m mean predicted and measured values
respectively.
The max error is less than 25%, and the standard deviation of K is
9.3%. This shows a relatively good agreement of this developed
model under IVR-ERVC condition.

1800

qCHF(kW/m )

K¼

2400

1600
1400
1200

2

200kg/m s
2
400kg/m s
2
600kg/m s

1000

2.4. Parametric effect

800

Fig. 5 shows the effect of inlet subcooling on CHF. The parameters in the calculation are the same as those in ULPU IV except the
inlet subcooling. The CHF value increases with inlet subcooling,
about 30% at 90 position of the lower head when the inlet temperature varies from 100  C to 60  C, which shows the potential of
cooling ability at severe accident if enough cooling water is provided when accident happens.
Fig. 6 shows the effect of mass velocity on CHF. The parameters
in the calculation are the same as those in ULPU IV except the mass
velocity. The CHF value increases with mass velocity, about 41% at
90 position of the lower head when the mass velocity varies from
200 kg/m2s to 600 kg/m2s. If circulation mass flow rate is raised by
reducing the resistance at the entrance and exit, the cooling limit of
the IVR-ERVC strategy will be improved significantly.
Fig. 7 shows the effect of channel gap on CHF. The parameters in
the calculation are the same as those in ULPU IV except the channel
gap. The CHF value decreases with gap at low orientation, while
increases with gap at high orientation, about 9% at 90 position of
the lower head when the gap varies from 15 cm to 25 cm. The

increased gap will bring decreased vapor quality and decreased
turbulent interchange. The former will lead to increase of CHF and
the latter just the opposite. At low orientation, the former factor is
dominant, but at high orientation, the latter dominant.
In the ULPU IV experiment, the mass flow rate keeps nearly
unchanged with the channel gap. So it is necessary to study the
effect of channel gap on CHF with the same mass flow rate. Fig. 8
shows the results. The CHF value decreases with gap, about 10%
at 90 position of the lower head when the gap varies from 15 cm to
25 cm. With the same mass flow rate, the mass velocity will

600
0

10

20

30

40

50

60

70

80

90

100

90

100

90

100

Angle(deg)
Fig. 6. Mass flux effect on CHF.

2000

1800

2

qCHF(kW/m )

1600

1400

15cm
20cm
25cm

1200

1000

800

600
0

10

20

30

40

50

60

70

80

Angle(deg)
Fig. 7. Channel gap effect on CHF with the same mass flux.

2400

2000

2200

1800

2000

1600

2

qCHF(kW/m )

2

qCHF(kW/m )

1800
1600
1400
o

60 C
o
80 C
o
100 C

1200
1000

1400

1200

15cm
20cm
25cm

1000

800

800

600

600
0

10

20

30

40

50

60

70

Angle(deg)
Fig. 5. Inlet water temperature effect on CHF.

80

90

100

0

10

20

30

40

50

60

70

80

Angle(deg)
Fig. 8. Channel gap effect on CHF with the same mass flow.


R. Guo et al. / Progress in Nuclear Energy 87 (2016) 47e53

1400

means a quasi-steady state achieves. Eventually, metallic molten
pool of FeeZr is on the top, oxide molten pool of UO2eZrO2 in the
middle, and particulate debris at the bottom. It is worthwhile to
note that not all the lower plenum volume is taken by the molten
core material because the lower plenum volume is bigger than that
of the previous designed PWR.
Fig. 13 shows the water temperature change at the inlet of the
reactor cavity. At 2000 s, the water from the IRWST is 57  C, which
is subcooled. With increasingly absorbing decay heat, the water
temperature reaches to 101  C, which is slightly higher than the
saturation temperature at atmospheric pressure.
Fig. 14 shows the mass flow rate change of the reactor cavity.
Natural circulation is established in the cavity by the lower head
surface heating. Initially, the fluid is single phase and the mass flow
increases to 600 kg/s at 20,000 s. Later two phase flow is dominant
in the cavity, and the mass flow rate increases greatly. At 24,000 s,
the mass flow rate is 1217 kg/s, which is about twice of the single
phase flow rate.
Fig. 15 shows the heat load on the lower head at different accident times. As indicated, at 12,000 s the peak heat flux locates at

37, which is completely different from that of the steady molten
pool. At the early stage of the molten pool formation, solid debris
occupies most parts of the lower head, and some small oxide
molten pools are scattered among them. Since there is an oxide
molten pool close to the lower head wall at low angle, and the oxide
molten pool imposes higher heat load than the solid debris, the
heat flux there is high.
After knowing the detailed condition of the reactor cavity at
different times, the corresponding critical heat flux can be calculated by the present critical heat flux model. Fig. 16 shows the
critical heat flux distribution on the lower head at different times.
Different from the fixed width in the ULPU experiments, the
heating surface in the following calculation is hemispherical. So the
mass flux changes along the flow direction, which leads to a
different CHF distribution. At most of the angular positions, the
critical heat flux at 24,000 s is greater than that at 20,000 s while
their heat flux distribution is similar, which means that the thermal
threat to the lower head at 20000 s is greater than that at 24,000 s.
Comparing the parameters at the two moments, mass flow is the
main difference. In the previous parametric effect study, we know
that the critical heat flux increases while the mass flux increases. So
the critical heat flux at 24,000 s is higher.
Fig. 17 shows the ratio of heat flux to CHF values at different
times. At 24,000 s, when the steady molten pool is formed, the ratio
everywhere on the lower head is less than one, which means the
heat load is lower than the critical heat flux on the lower head, and
the IVR-ERVC strategy is effective at this time. But at 20000 s,
before the steady molten pool formed, situation is worse. At 68 and
72 position, the heat flux and CHF ratio is greater than one, which
means the heat load is higher than the critical heat flux, and the
IVR-ERVC strategy fails. The result indicates clearly that the traditional method to evaluate IVR feasibility based on the steady

molten pool is not conservative always.

1200

4. Conclusion

decrease when the channel gap increases, which leads to the
decrease of the CHF value.
Fig. 9 shows the effect of reactor vessel radius on CHF. The parameters in the calculation are the same as those in ULPU IV except
the vessel radius. The CHF decreases with radius, about 8% at 90
position of the lower head when the radius varies from 1.76 m to
2.35 m. It means that the increased reactor pressure vessel volume
caused by the increased power in the advanced plant will lead to
decreased critical heat flux at the lower head outer surface when
the structure of the external flow channel keeps unchanged. At the
same time, heat load on the vessel wall increases with the power.
So the thermal margin to keep the integrity of the lower head decreases, which will lead to failure of the lower head.
3. Transient feasibility of IVR-ERVC strategy
In this paper, the transient severe accident process is studied in
a large scale passive PWR. Its nominal electric power is 1700 MW.
The coolant system is composed by three loops, and each loop
consists of one hot leg, two cold legs, one steam generator and two
pumps. The passive safety systems are designed to avoid the loss of
a heat sink and a core meltdown. When the core exit temperature is
higher than 922.05 K, the reactor cavity will be flooded by water
from in-containment refueling water storage tank (IRWST). The
MELCOR nodalizationl of the 1700 MW passive PWR is shown in
Fig. 10.
In the MELCOR simulation, the initial event is taken as a large
break on cold leg together with station black-out (SBO) transients

that lead to loss of coolant of the primary system, and both IRWST
gravity injection and recirculation are assumed fail. At the onset of
the accident, substantial amount of coolant is ejected to the
containment, which will actuate the operation of the passive safety
systems. After the accumulator (ACC) inventory is depleted, the
liquid level in core keeps reducing, and the core begins to melt. The
core materials fall into the lower plenum region and molten pools
form. The configuration of MELCOR molten pool model is given in
Fig. 11. MP2 represents the metallic molten pool, MP1 the oxide
molten pool, and PD the solid particulate debris. Contiguous volumes containing molten pool components constitute coherent
molten pools that are assumed to be uniformly mixed by convection so as to have uniform material composition and temperature.
Fig. 12 shows the oxide molten pool formation process in the
lower plenum. Oxide molten pool appears at 8000 s, and grows to
12.6 m3 at 24,000 s. After that its volume keeps unchanged, which
2000

1800

1600

2

qCHF(kW/m )

51

1.76m
2.13m
2.35m

1000

A new method to study the transient feasibility of IVR-ERVC
strategy is proposed. Results are summarized as follows:

800

600
0

10

20

30

40

50

60

70

Angle(deg)
Fig. 9. Lower head radius effect on CHF.

80

90

100

(1) A theoretical model based on bubble crowding has been
developed to predict the CHF on the outer surface of the RPV
lower head.
(2) The max error between the predicted and measured CHF in
ULPU IV experiment is less than 25%, which shows the
availability of the proposed model.


52

R. Guo et al. / Progress in Nuclear Energy 87 (2016) 47e53

Fig. 10. MELCOR nodalizationl of the 1700 MW passive PWR.

110

100

o

Temperature( C)

90

80

70

60

50
0.0

Fig. 11. Molten pools in lower plenum (Gauntt et al., 2005).

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

2.8

3.2

4

Time(10 s)
Fig. 13. Inlet water temperature of the reactor cavity.

14
1400

12
1200

10
1000

Mass flow(kg/s)

3

Volume(m )

8
6
4

800

600

2

400

0

200

-2
0.0

0.4

0.8

1.2

1.6

2.0
4

Time(10 s)
Fig. 12. Oxide molten pool volume.

2.4

2.8

3.2

0
0.0

0.4

0.8

1.2

1.6

2.0

2.4

4

Time(10 s)
Fig. 14. Mass flow rate of the reactor cavity.


R. Guo et al. / Progress in Nuclear Energy 87 (2016) 47e53

(3) CHF decreases with reactor vessel radius, which means IVRERVC method may lose effectiveness in high power reactor
plant.
(4) The traditional method to evaluate IVR feasibility based on
the steady molten pool is not conservative always.

1600
1400

8000s
12000s

16000s
20000s
24000s

2

Heat Flux(kW/m )

1200
1000

References

800
600
400
200
0
0

10

20

30

40

50

60

70

80

90

100

Angle(deg)
Fig. 15. Heat flux distribution on the lower head.

1800
1600

2

Critical heat Flux(kW/m )

1400
1200
1000
800

8000s
12000s
16000s
20000s
24000s

600
400
200

Dinh, T.N., Tu, J.P., Salmassi, T., Theofanous, T.G., 2003. Limits of coolability in the
AP1000-related ULPU-2400 configuration V facility. In: The 10th International
Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-10). Korean
Nuclear Society, Seoul, Korea. October 5e9 (paper G00407).
Galloway, J.E., Mudawar, I., 1993. CHF mechanism in flow boiling from a short
heated walldII. Theoretical CHF model. Int. J. Heat Mass Transf. 36 (10),
2527e2540.
Gauntt, R.O., Cole, R.K., Erichson, C.M., et al., 2005. MELCOR Computer Code Manuals. In: Reference Manuals, vol. 2. Sandia National Laboratories, Albuquerque.
NM 87185e073.
Guo, R., Kuang, B., Cheng, X., 2014. A theoretical CHF model for subcooled flow
boiling in curved a channel at low pressure. Ann. Nucl. Energy 69, 196e202.
Lee, C.H., Mudawwar, I., 1988. A mechanistic critical heat flux model for subcooled
flow boiling based on local bulk flow conditions. Int. J. Multiph. Flow 14 (6),
711e728.
Levy, S., 1967. Forced convection subcooled boilingdprediction of vapor volumetric
fraction. Int. J. Heat Mass Transf. 10 (7), 951e965.
Theofanous, T.G., Liu, C., Additon, S., Angelini, S., Kymalainen, O., Salmassi, T., 1997a.
In-vessel coolability and retention of a core melt. Nucl. Eng. Des. 169, 1e48.
Theofanous, T.G., Maguire, M., Angelini, S., Salmassi, T., 1997b. The first results from
the ACOPO experiment. Nucl. Eng. Des. 169, 49e57.
Theofanous, T.G., Tu, J.P., Dinh, A.T., Dinh, T.N., 2002a. The boiling crisis phenomenon:Part I. Nucleation and nucleate boiling heat transfer. Exp. Therm. Fluid Sci.
26, 775e792.
Theofanous, T.G., Tu, J.P., Dinh, A.T., Dinh, T.N., 2002b. The boiling crisis phenomenon:Part II. Dryout dynamics and burnout. Exp. Therm. Fluid Sci. 26, 793e810.
Theofanous, T.G., Tu, J.P., Salmassi, T., et al., 2002c. Quantification of Limits to
Coolability in ULPU-2000 Configuration IV. CRSS-02.05, 3.

Tong, L.S., 1975. A Phenomenological Study of Critical Heat Flux. ASME Paper, 1975.
Weisman, J., Pei, B.S., 1983. Prediction of critical heat flux in flow boiling at low
qualities. Int. J. Heat Mass Transf. 26 (10), 1463e1477.
Yang, J., Groeneveld, D., Leung, L., 2006. An experimental and analytical study of the
effect of axial power profile on CHF. Nucl. Eng. Des. 236 (13), 1384e1395.

Appendix nomenclature

0
0

10

20

30

40

50

60

70

80

90

100

Angle(deg)

1.2

8000s
12000s
16000s
20000s
24000s

1.0

0.8

General symbols
G: mass flux (kg/m2s)
G0 : lateral mass flux (kg/m2s)
h: enthalpy (J/kg)
hfg: latent heat (J/kg)
i: turbulent intensity
K: ratio of predicted to measured CHF
q: heat flux (W/m2)
S: slip ratio
u: velocity (m/s)
ut: bubble rise velocity (m/s)
x: steam quality

Fig. 16. Critical heat flux distribution on the lower head.

q/CHF

53

Greek symbols

a: void fraction
h: portion of bulk flow region
q: angular position
r: density (kg/m3)
J: effective portion of velocity fluctuation

0.6

0.4

Subscripts
0.2

0.0
0

10

20

30

40

50

60

Angle(deg)
Fig. 17. Heat flux and CHF ratio.

70

80

90

100

1: bulk flow
2: bubble layer
d: bubble departure
f: saturated liquid
g: vapor
l: liquid
m: measured
p: predicted