International Journal of Multiphase Flow 37 (2011) 769–776
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International Journal of Multiphase Flow
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Comparison of the heat transfer characteristics of supercritical pressure water
to that of subcritical pressure water in vertically-upward tubes
Jianguo Wang a,b, Huixiong Li a,⇑, Shuiqing Yu a, Tingkuan Chen a
a
b
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
College of Energy, Xi’an University of Science and Technology, Xi’an 710054, PR China
a r t i c l e
i n f o
Article history:
Received 3 June 2010
Received in revised form 26 January 2011
Accepted 29 January 2011
Available online 5 February 2011
Keywords:
Supercritical pressure water
Large specific heat region
Subcritical pressure water
Two-phase region
Heat transfer deterioration
Heat transfer enhancement
a b s t r a c t
A systematic comparison was made between the forced convection heat transfer characteristics of the
supercritical pressure water and that of the subcritical pressure water in vertically-upward tubes. It
was found that, severe heat transfer deterioration did not occur in the vertically-upward internallyribbed tube at supercritical pressures, and the variations in the inside wall temperature with the bulk
fluid enthalpy experienced three stages, namely, the continuously increasing stage, the smoothly changing stage and another continuously increasing stage at the supercritical pressures; however, at subcritical
pressures, there existed at least four stages for the variation of the inside tube wall temperature, i.e., the
continuously increasing stage, the basically unchanging stage, the sharply rising stage and another continuously increasing stage. The heat transfer coefficients in the subcritical two-phase region, in which the
heat transfer deterioration did not occur, were much greater than those in the heat transfer enhancement
region of supercritical pressure water. In the large specific heat region of supercritical pressure water, the
enhanced heat transfer was impaired by increasing the heat flux; however, in the subcritical two-phase
region, the higher the heat flux, the greater the heat transfer coefficient would be. It was also found that
the heat transfer deterioration of supercritical pressure water was similar in mechanism to the DNB
(departure from nucleate boiling) at subcritical pressures.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Supercritical fluids have been used in various industries such as
power engineering, aerospace engineering, chemical engineering,
and refrigeration engineering (Jiang et al., 2008). At present, using
supercritical pressure water in fossil-fired power plants is the largest industrial application of fluids at supercritical pressures (Pioro
et al., 2004). Furthermore, mainly in order to increase the thermal
efficiency of modern nuclear power plants, the supercritical pressure water-cooled reactor (SCWR) has been accepted as one of
the six most promising reactor concepts recommended by Generation IV International Forum (GIF). Wide uses of supercritical pressure water, especially in power engineering, have made heat
transfer of water at supercritical pressures a very important and
attractive issue, because a thorough understanding of the heat
transfer characteristics of supercritical pressure water is crucial
to the optimal design and safe operation of such systems operating
at supercritical pressures. Although the supercritical pressure
water does not experience phase change, the thermophysical properties exhibit drastic changes with temperatures in the neighbor⇑ Corresponding author. Tel.: +86 13201529683.
E-mail address: [email protected] (H. Li).
0301-9322/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijmultiphaseflow.2011.01.013
hood of the pseudocritical temperature, making the heat transfer
of supercritical pressure water flowing inside tubes quite peculiar.
The existing investigations (Goldmann, 1961; Shitsman, 1963;
Swenson et al., 1965; Ackerman, 1970; Yamagata et al., 1972; Jackson and Hall, 1979; Kitoh et al., 1999; Kirillov, 2000; Jackson, 2002;
Pioro and Duffey, 2005, 2007) have showed that, near the pseudocritical temperature (i.e., in the pseudocritical region), the heat
transfer enhancement might occur at low heat fluxes, and this enhanced heat transfer is impaired by increasing the heat flux; however, some time, as the heat flux is increased to a certain value, a
remarkable deterioration of heat transfer might take place. In China, with the development of supercritical pressure boilers, many
investigations on the heat transfer of supercritical pressure water
have also been made (Wang et al., 2009). From these investigations, it has been shown that there exists a so-called large specific
heat region for supercritical pressure water, which is defined as a
region where the specific heat of water at constant pressure is
greater than 8.4 kJ/kg K (Chen et al., 1995), as shown in Fig. 1. It
can be seen from Fig. 1 that the range of fluid enthalpy in the large
specific heat region of the supercritical pressure water is about
from 1750 to 2700 kJ/kg. Generally, such large specific heat region
is just in the neighborhood of the pseudocritical temperature, tpc. In
our opinion, in the design of supercritical pressure boilers, the
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J. Wang et al. / International Journal of Multiphase Flow 37 (2011) 769–776
80
70
p=25MPa
cp, kJ/kg⋅K
60
26MPa
50
27MPa
40
28MPa
29MPa
30
20
30MPa
cp=8.4 kJ/kg⋅K
10
large specific heat region
0
1200
1600
2000
2400
2800
3200
Bulk enthalpy, kJ/kg
Fig. 1. Large specific heat region of supercritical pressure water.
1: Water tank; 2: Filter; 3: Water pump; 4: Valve; 5: Orifice;
large specific heat region is more specific and easily determined
than the pseudocritical region.
From an engineering point of view, heat transfer deterioration
should be avoided all the time in power plants, including both
the supercritical pressure water reactors and the supercritical
pressure boilers. To obtain a better understanding of the heat
transfer mechanism, a large number of experimental and numerical studies on heat transfer to fluids at supercritical pressures were
carried out by various researchers (Jackson and Hall, 1979; Cheng
and Schulenberg, 2001; Pioro and Duffey, 2005; He et al., 2008;
Sharabi and Ambrosini, 2009). Unfortunately, the mechanism of
the heat transfer deterioration or enhancement of supercritical
pressure water has not been understood thoroughly due to the
complexity of heat transfer of supercritical pressure water in the
large specific heat region (Chen et al., 1995; Koshizuka et al.,
1995; Sharabi and Ambrosini, 2009; Wang et al., 2009).
It has been well known that two types of heat transfer deterioration exist in subcritical pressure power system, one of which is
the DNB (departure from nucleate boiling) occurring in the subcooled or low steam quality region, and another one is the dryout
occurring in the high steam quality region (Collier and Thome,
1994; Mosyak and Hetsroni, 1999; Kim and Ghajar, 2006). The
mechanism of these two types of heat transfer deterioration is
clear. In order to get a deep insight of the heat transfer characteristics of supercritical pressure water, it may be necessary to make a
systematic comparison between the heat transfer characteristics of
supercritical pressure water and that of subcritical pressure water.
In the present paper, a systematic comparison is made based on
the experimental data obtained at Xi’an Jiaotong University, Xi’an,
China, between the heat transfer characteristics of the supercritical
pressure water and that of the subcritical pressure water. The present investigation may be helpful for the development of SCWR.
2. Test loop and experimental conditions
The experiments were carried out in the high-pressure steamwater two-phase flow test loop built at Xi’an Jiaotong University.
The schematic diagram of the loop is shown in Fig. 2. Deionized
water was used as the flowing media and was pumped by a
high-pressure plunge-type pump, which can provide a maximum
pressure of 40 MPa. Part of the water was returned to the water
tank through a bypass, and the rest part of the water flowed
through measuring orifices and adjusting valves into a heat exchanger to absorb the heat of the hot fluid coming from the test
section, and then was heated to a specific state in a pre-heater installed just upstream the test section. The test section was electrically heated by alternating currents of 10,000 A with low voltage.
6: Heat exchanger; 7: Pre-heater; 8: Test section; 9: Condenser;
10: Cooling water inlet; 11: Cooling water outlet; 12: Rotor flow meter
Fig. 2. Schematic diagram of the test loop.
The fluid flowing out from the test section was cooled first by
the above-mentioned heat exchanger and then by a condenser,
and finally flowed into the water tank. The mass flow rate was
measured with the orifice meters calibrated by weighing method.
Three kinds of tubes were used in the present experiments. The
first kind of tubes was a six-head internally-ribbed tube with an
outer diameter of 31.8 mm and a wall thickness of 6.0 mm and
the second kind of tubes was a smooth tube with a diameter of
Ø31.8 6.0 mm, both of which were made of SA-213T12 steel.
The third kind of tubes was a four-head internally-ribbed tube with
an outer diameter of 28.6 mm and a wall thickness of 5.8 mm,
which was made of SA-213T2 steel. The mean inner diameter of
the six-head internally-ribbed tube was measured to be
17.63 mm and that of the four-head internally-ribbed tube was
15.24 mm. The test sections were all installed vertically with upward flow. The electrically-heated length of all the test sections
was 2000 mm.
Fig. 3 shows the test section schematic and thermocouple layout. The fluid temperatures were measured by 10 pairs of
Ø3 mm NiCr–NiSi sheathed thermocouples installed in the preheater and the test section. The fluid pressure at the inlet of the
test section was measured by Rosemount 3051 capacitance-type
pressure transmitter. A 3051 capacitance-type differential pressure
transducer was used to measure the pressure drop of the test section. Total 26 thermocouples were welded on the tube outer surface to measure the outside wall temperatures. The electrical
power was defined as a product of the effective value of the voltage
and current. All the data were monitored and collected by a computer equipped with an IMP3595 distributed data acquisition
board connected with all the sensors used in the experiments.
Water and steam properties were calculated using IFC-67 equations. The heat transfer coefficient was calculated from the inside
wall heat flux and the temperature difference between the inside
wall of the tube and the bulk fluid. Estimated uncertainties in measured and calculated parameters were listed in Table 1.
It should be mentioned that the existence of internal ribs results in non-uniform distributions of the inside wall heat fluxes
and wall temperatures along the circumferential direction of the
internally-ribbed tube. However, because the internally-ribbed
tube made of steel is opaque, it is very difficult to determine
the location of the internal rib and make the thermocouple
welded to the tube outer surface correspond to that. For the sake
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J. Wang et al. / International Journal of Multiphase Flow 37 (2011) 769–776
current
copper
terminal
pressure
measurement
ring
four-head
ribbed tube
six-head
ribbed tube
1-6 section 7 8 section 9 10 section
Fig. 3. Test section schematic and thermocouple layout.
Table 1
Uncertainties in measured and calculated parameters.
3. Comparison of the wall temperature characteristics
Value
Uncertainty
Pressure (MPa)
Differential pressure (kPa)
Electrically-heated power (kW)
Mass flow rate (kg/s)
Fluid temperature (°C)
Wall temperature (°C)
Heat flux (kW/m2)
Heat transfer coefficient (kW/m2 K)
1.1%
2.0%
3.3%
2.8%
0.4
10.08%
5.4%
9.7%
of simplicity, the internally-ribbed tube was taken as a smooth
tube with a diameter equal to the mean internal diameter of
the internally-ribbed tube, and thus the distributions of the inside
wall heat fluxes and wall temperatures along the circumferential
direction of the internally-ribbed tube were considered to be uniform. In this study, at a certain location in the test section, the
average temperature of several temperature measurement points
along the circumferential direction of the tube represents the outside wall temperature at that location. For a smooth tube, if the
heat transfer along the axial direction of the tube is neglected,
then the heat conduction of the smooth tube under the condition
of fully-circumferential uniform heating can be taken as onedimensional heat conduction with internal heat source. So the inside wall temperature of the smooth tube can be calculated from
the one-dimensional heat-conduction equation. The fluid enthalpy at any location in the smooth tube can be calculated from
the known inlet and outlet bulk enthalpies, because the bulk enthalpy increases uniformly from inlet to outlet of the tube under
the condition of fully-circumferential uniform heating.
The experimental parameters were as follows. For experiments
with the six-head internally-ribbed tube and the smooth tube, the
pressures p at the inlet of the test section were 12.6, 15.4, 25.0 and
29.0 MPa, respectively and the mass flux G was from 600 to
1200 kg/m2 s, and the inside wall heat flux q varied from 150 to
650 kW/m2. For experiments with the four-head internally-ribbed
tube, the pressures p at the inlet of the test section were 14.2, 17.0,
25.0 and 29.0 MPa, respectively and the mass flux G was from 600
to 1250 kg/m2 s, and the inside wall heat flux q varied from 150 to
600 kW/m2.
In each of the tests, the mass flux and pressure were firstly adjusted to given values, and then, kept the heat flux to test section
constant, but raised the electrical power of the pre-heater to increase the fluid enthalpy at the inlet of the heat transfer test section. Once the wall temperature of the heat transfer test section
was over 700 °C due to heat transfer deterioration or the heating
power reached the maximum, the test was over.
Fig. 4 gives a comparison of the inside wall temperature distributions at supercritical pressures to those at subcritical pressures
in the vertically-upward internally-ribbed tubes. It can be seen
from Fig. 4a and b that the variations in the inside wall temperature with the bulk fluid enthalpy at supercritical pressures are different from those at subcritical pressures, though the two
experimental conditions are the same except pressure. As seen
from Fig. 4a, when the bulk fluid enthalpy is lower than 1669 kJ/
kg, the inside wall temperatures of the four-head internally-ribbed
tube increase continuously with the increase in the bulk fluid enthalpy at 29.0 MPa. In this region, the temperature differences between the inside wall of the tube and the bulk fluid are basically
unchanged and are about 40 °C, and as a result, the heat transfer
coefficients are also generally unchanged at a fixed heat flux. This
is the so-called normal heat transfer mode for supercritical pressure water.
It is seen in Fig. 4a that when the bulk fluid enthalpy is greater
than 1669 kJ/kg but lower than the pseudocritical enthalpy Hpc
2153.8 kJ/kg, the fluid is in the large specific heat region of the
supercritical pressure water. In this area, the inside wall temperatures change smoothly, and the temperature differences between
the inside tube wall and the bulk fluid became smaller and smaller
gradually and reach a minimum value of about 22 °C with the increase in the bulk fluid enthalpy. That is to say, the heat transfer
coefficients become higher gradually with the increasing bulk fluid
enthalpy and approaches a peak value, which means that the heat
transfer enhancement occurs in this area. With the further increase
in the bulk fluid enthalpy, i.e., in an area where the bulk fluid enthalpy is greater than the pseudocritical enthalpy 2153.8 kJ/kg,
the inside wall temperatures of the tube continuously increase
again with the increasing bulk fluid enthalpy, as shown in Fig. 4a.
Thus, it is seen from Fig. 4a that at the supercritical pressure, the
variations in the inside wall temperature with the bulk fluid enthalpy generally experienced three stages, namely, the first continuously increasing stage, the smoothly changing stage and the
second continuously increasing stage.
However, in contrast, at a pressure of 14.2 MPa, when the bulk
fluid enthalpy is lower than 1426 kJ/kg, the inside wall temperature increases continuously with the increasing bulk fluid enthalpy, which is similar, or, to some extent, identical to that at
supercritical pressure. When the bulk fluid enthalpy is greater than
1426 kJ/kg but lower than 2309 kJ/kg, the fluid enters into the
two-phase region of subcritical pressure water, and the inside wall
temperature of the four-head internally-ribbed tube is basically
unchanged with the increase in the bulk fluid enthalpy. When
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J. Wang et al. / International Journal of Multiphase Flow 37 (2011) 769–776
600
φ28.6 5.8 mm
Hpc=2153.8 kJ/kg
internally-ribbed tube
2
2
29.0 MPa,1000 kg/m s,450 kW/m
2
2
500
14.2 MPa,1000 kg/m s,450 kW/m
tb1-when 29.0 MPa
450
tb2-when 14.2 MPa
Inside wall temperature
550
400
tb2
o
Dryout
tpc=396.9 C
xcr=0.73
350
300
250
tb1
0
1
x 14.2 MPa
the large specific heat region
HT-heat transfer
200
900
1200
the enhanced
HT region
1500
1800
2100
2400
2700
3000
3300
Bulk enthalpy, kJ/kg
(a) Four-head internally-ribbed tube
600
Hpc=2136.2 kJ/kg
φ31.8 6.0 mm
internally-ribbed tube
2
2
25.0 MPa,800 kg/m s,450 kW/m
2
2
12.6 MPa,800 kg/m s,450 kW/m
Inside wall temperature
550
500
tb1-when 25.0 MPa
450
tb1
tb2-when 12.6 MPa
tb2
400
o
350
Dryout
tpc=384.5 C
xcr=0.68
x 12.6 MPa
300
the large specific heat region
250
HT-heat transfer
200
600
900
the enhanced
HT region
1200 1500 1800 2100 2400 2700 3000 3300
Bulk enthalpy, kJ/kg
(b) Six-head internally-ribbed tube
Fig. 4. Comparison between the inside wall temperatures at supercritical pressures
and those at subcritical pressures.
the steam quality exceeds a certain critical value, which is 0.73 in
Fig. 4a, corresponding to an enthalpy of 2350 kJ/kg for the subcritical pressure water, the inside wall temperature increases sharply
due to the occurrence of heat transfer deterioration. In the superheated steam region, the inside wall temperature increases continuously with the increasing bulk fluid enthalpy, but still keeps at a
level much lower than that of the corresponding supercritical fluid
case. Therefore, it can be seen from Fig. 4a that, at the subcritical
pressure, the variations in the inside wall temperature with the
bulk fluid enthalpy experienced at least four stages, namely, the
continuously increasing stage, the basically unchanging stage, the
sharply rising stage and another continuously increasing stage.
From the above analysis, it can be seen in Fig. 4 that for the
supercritical pressure water, there are two different heat transfer
modes in the experimental conditions, one of which is the normal
heat transfer mode, and another is the enhanced heat transfer
mode. The normal heat transfer of supercritical pressure water
can be defined here as a process in which the inside wall temperatures increase continuously with the increasing bulk fluid enthalpy, while the enhanced heat transfer of supercritical pressure
water can be defined as a process in which the inside wall temperatures change smoothly with the increase in the bulk fluid enthalpy. However, for the subcritical pressure water, there are three
different heat transfer modes at the experimental conditions as
shown in Fig. 4, namely, the normal heat transfer (i.e., forced convection heat transfer of single-phase water and superheated
steam), forced convection boiling heat transfer and the heat
transfer deterioration. Considering the fact that the heat transfer
coefficients of the convection boiling (two-phase) is much greater
than those of the single-phase forced convection heat transfer, the
forced two-phase convection boiling heat transfer can be considered as the enhanced heat transfer mode. Therefore, it can be said
that there are three different heat transfer modes at subcritical
pressures as shown in Fig. 4, i.e., the normal heat transfer, the enhanced heat transfer and the deteriorated heat transfer.
It should be mentioned that the mechanism of heat transfer
enhancement of supercritical pressure water is completely different from that of subcritical pressure water. Some researchers
(Swenson et al., 1965; Renz and Bellinghausen, 1986; Sharabi
and Ambrosini, 2009; Wang et al., 2009) suggested that the drastic
change in thermophysical properties near the pseudocritical point
resulted in the heat transfer enhancement in the large specific heat
region of supercritical pressure water. In this paper, it is suggested
that the drastic changes in thermophysical properties in the large
specific heat region, especially the sudden rise in specific heat at
constant pressure, resulted in the occurrence of heat transfer
enhancement. The reason why sudden rise in specific heat at constant pressure can promote heat transfer is as follows. The sudden
increase in the specific heat of water in the large specific heat region will make the heat taken away by water increase, which is
similar to the latent heat of nucleate boiling at subcritical pressures, and thus, the inside wall of tube can be cooled timely and
enhance the heat transfer of water. However, as well known, it is
the nucleate boiling phenomenon that results in the big increase
in the heat transfer coefficients at subcritical pressures.
Fig. 4b shows another comparison of the wall temperature distributions at a different supercritical pressure to that at a subcritical pressure in the six-head internally-ribbed tube. It can be seen
from Fig. 4b that, in the region where the bulk fluid enthalpy is less
than 1300 kJ/kg, the inside wall temperatures of the tube at
25.0 MPa are about equal to that at 12.6 MPa, with the two experimental conditions are the same except pressure. However, with
the continuous increase in the bulk fluid enthalpy, the inside wall
temperature of the tube at 25.0 MPa is higher than that at
12.6 MPa, as seen clearly from Fig. 4b. As well known, there is no
constant-temperature evaporation region for supercritical pressure
water, and it is understandable that the temperatures of supercritical pressure water increase continuously with continuous heat
absorption, and the inside wall temperatures, which are higher
than the temperatures of supercritical pressure water, also increase continuously. However, the nucleate-boiling heat transfer
at subcritical pressures is very drastic due to phase change, and
there exist small temperature differences between the inside tube
wall and the bulk fluid, and moreover, the inside-tube-wall temperatures will more or less stay the same, and as a result, with
the continuous increase in the bulk fluid enthalpy, the increasing
inside-tube-wall temperatures at supercritical pressures will be
higher than those at subcritical pressures.
It also can be seen from Fig. 4 that the variations in temperature
differences between the inside tube wall and the bulk fluid with
the bulk fluid enthalpy at supercritical pressures are different from
those at subcritical pressures.
As shown in Fig. 4a, in the low enthalpy region where the bulk
fluid enthalpy is less than 1426 kJ/kg and in the high enthalpy region where the bulk fluid enthalpy is greater than 2700 kJ/kg, the
temperature differences between the inside tube wall and the bulk
fluid at supercritical pressures are nearly equal to those at subcritical pressures, and remain unchanged with the increase in the bulk
fluid enthalpy. In the heat transfer enhancement region of supercritical pressure water, with the increase in the bulk fluid enthalpy,
the temperature differences between supercritical pressure fluid
and the inside tube wall become smaller and smaller and reach a
minimum value; however, in the two-phase region of the subcritical pressure water even with the bulk fluid enthalpy the same as
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J. Wang et al. / International Journal of Multiphase Flow 37 (2011) 769–776
p=25.0 MPa G=1200 kg/m2s q=660 kW/m2
Inside wall temperature, oC
550
500
φ31.8×6.0mm smooth tube
φ31.8×6.0mm
internally-ribbed tube
450
400
tpc=384.05 oC
350
the large specific heat region
300
250
900
40
Heat transfer coefficient, kW/m2K
(a)
600
Hpc=2136.2 kJ/kg
1200
1500
1800
2100
2400
2700
3000
36
32
28
φ 28.6
5.8 mm
internally-ribbed tube
2
2
G=800 kg/m s, q=300 kW/m
p=14.2 MPa
p=25.0 MPa
24
20
16
12
8
14.2 MPa
4
0
900
3300
1200
1500
4. Comparison of heat transfer coefficients
Fig. 6 shows a comparison of heat transfer coefficients (abbreviated as HTC, hereafter) of water at supercritical pressures to those
at subcritical pressures in the vertically-upward internally-ribbed
tubes. As seen clearly from Fig. 6a, in the region where the bulk
fluid enthalpy is less than 1300 kJ/kg and in the region where the
bulk fluid enthalpy is greater than 2700 kJ/kg, the variations in
heat transfer coefficients with the bulk fluid enthalpy at supercritical pressures are nearly the same as those at subcritical pressures,
and the values of heat transfer coefficients of water at supercritical
pressures are, basically, equal to those at subcritical pressures.
However, the variations in heat transfer coefficients with the bulk
fluid enthalpy in the large specific heat region of water at supercritical pressures are totally different from those in the two-phase
region of water at subcritical pressures. One of the characteristics
of heat transfer enhancement in the large specific heat region of
supercritical pressure water is that a peak value exists for the heat
transfer coefficients in this region, and for example, the maximum
value of the HTC is about 15 kW/m2 K at 25.0 MPa, which is however much lower than the HTC value of water at a subcritical pressure of 14.2 MPa. In the present study, the heat transfer
enhancement is considered to have occurred in the large specific
(b)
44
Heat transfer coefficient, kW/m2K
that of the supercritical pressure water, the temperature differences between the fluid and the inside tube wall remain unchanged at roughly 13 °C. Therefore, it can be said that from the
viewpoint of temperature differences between the bulk fluid and
the inside tube wall, the normal heat transfer of supercritical
pressure water is characterized by the basically unchanged temperature differences, while the enhanced heat transfer is characterized by a low temperature difference in comparison to the normal
heat transfer.
Fig. 5 gives a comparison between the inside wall temperatures
of the internally-ribbed tube and those of the smooth tube with a
diameter of Ø31.8 6.0 mm. It can be seen from Fig. 5, in the low
enthalpy region where the bulk fluid enthalpy is less than 1750 kJ/
kg, the inside wall temperatures of the internally-ribbed tube are
about equal to those of the smooth tube, with the two experimental conditions are the same. In this area, the effect of enhanced heat
transfer of the internally-ribbed tube does not appear. However, as
seen clearly in Fig. 5, when the bulk fluid enthalpy is close to the
pseudocritical enthalpy, the inside wall temperatures of the internally-ribbed tube are significantly lower than those of the smooth
tube, which indicates that the heat transfer is enhanced by the
internally-ribbed tube.
x
the large specific heat region
1800
2100
2400
2700
3000
Bulk enthalpy, kJ/kg
Bulk enthalpy, kJ/kg
Fig. 5. Comparison between the wall temperatures of the internally-ribbed tube
and those of the smooth tube.
Hpc=2136.2 kJ/kg
40
φ 28.6 5.8mm
φ 31.8 6.0 mm
36
internally-ribbed tube
p=25.0 MPa
32
G=1000 kg/m s
internally-ribbed tube
p=17.0 MPa
2
G=800 kg/m s
2
28
24
20
2
q=300 kW/m
2
q=400 kW/m
2
q=450 kW/m
2
q=260 kW/m
2
q=460 kW/m
2
q=660 kW/m
16
12
8
4
17.0 MPa
0
-4
900
1200
1500
x
the large specific heat region
Hpc=2136.2 kJ/kg
1800
2100
2400
2700
3000
Bulk enthalpy, kJ/kg
Fig. 6. Comparison between the heat transfer coefficients at supercritical pressures
and those at subcritical pressures in vertically-upward internally-ribbed tubes.
heat region of supercritical pressure water, as the HTC value in
the most part of this region is greater than 12 kW/m2 K, and is
much higher than that of the supercritical water in its normal heat
transfer region, which is in the range from 8 to 12 kW/m2 K, as
seen clearly from Fig. 6a.
However, it is clearly seen in Fig. 6a that the HTC remains unchanged in the two-phase region at 14.2 MPa and the value of
the HTC is about 29.5 kW/m2 K, which is much larger than that
at supercritical pressures.
In the two-phase flow boiling region of water at subcritical
pressures, the bulk fluid temperature is generally kept at a constant, which is equal to the local water saturation temperature ts,
and the inside wall temperature of the tube, twi, is also nearly a
constant, and thus the temperature difference, twi ts, is a constant, and consequently, the heat transfer coefficient in this region
is a constant under conditions with a fixed heat flux. The possible
reason for the heat transfer coefficients in subcritical two-phase
flow boiling region being much larger than those in the heat transfer enhancement region at supercritical pressures is as follows. In
the two-phase boiling region at subcritical pressures, the macroconvection of bulk fluid and the micro-convection caused by the
boiling near the tube wall together make the heat transfer coefficients very large. As well known, the formation, growth and departure of bubbles not only take away latent heat but also push the
superheated liquid near the tube wall into the bulk fluid, and at
the same time, the cold bulk liquid supplements the vacancy generated by the departure of bubbles. However, for the supercritical
pressure water, even in the enhanced heat transfer region, heat
transfer is carried out only by the variable-property single-phase
convection, and the contributions from micro-convection near
the tube wall in this case might be much smaller than the liquid
J. Wang et al. / International Journal of Multiphase Flow 37 (2011) 769–776
5. Comparison of heat transfer deterioration
Usually, the heat transfer deterioration is defined as phenomena with sudden decrease in the heat transfer coefficient on the
wall for a constant-wall-temperature system or a sharp increase
in the wall temperature for a constant-heat-flux system. As mentioned before, there are two kinds of heat transfer deterioration
at subcritical pressures, one of which is the DNB, and another
one is the dryout. According to the literature (Belyakov et al.,
1971; Chen et al., 1995; Pioro and Duffey, 2005), there are also
two kinds of heat transfer deterioration at supercritical pressures
in vertically-upward tubes. The first type of deteriorated heat
transfer observed in supercritical pressure liquid was due to the
change in flow structure in the entrance region of the tube, and
can occur at any bulk fluid enthalpy up to the pseudocritical enthalpy (Belyakov et al., 1971). The second type of deteriorated heat
transfer may occur in supercritical pressure fluids when the wall
temperature exceeds the pseudocritical temperature tpc but the
bulk fluid temperature is still less than tpc (Pioro and Duffey,
2005). According to Belyakov et al. (1971), the first type of deteriorated heat transfer at supercritical pressures was related to the
formation of boundary layer within the entrance region of the tube.
Belyakov believed that, when the flow direction of the natural convection was same as that of the forced convection, the boundary
layer of fluid would be in a state of laminar flow, which eventually
resulted in the occurrence of heat transfer deterioration, and the
first type of deteriorated heat transfer may not occur at all in the
supercritical pressure boilers. In the present study, no such socalled first type of deteriorated heat transfer was observed.
At present, there are mainly two types of explanations on the
mechanism of heat transfer deterioration of supercritical pressure
fluids. One is the pseudo-film boiling theory (Ackerman, 1970), and
another one suggests that the variations in thermophysical properties near the pseudocritical points make heat transfer deterioration
occur (Pioro and Duffey, 2005), which is based on single-phase
fluid dynamics (Koshizuka et al., 1995). However, the generally accepted conclusion has not been obtained yet. In the pseudo-film
boiling theory based on two-phase fluid dynamics, deterioration
of heat transfer at supercritical pressures is explained by transition
from pseudo-nucleate to pseudo-film boiling (Koshizuka et al.,
1995). Unfortunately, due to the complexity of variable-property
heat transfer and the lack of direct convincing evidence of various
theoretical explanations on the heat transfer deterioration of
supercritical pressure water, there remains a debate on how the
variations in thermophysical properties to make heat transfer
deterioration occur. Some researchers (He et al., 2008; Sharabi
and Ambrosini, 2009) suggested that the heat transfer deterioration of supercritical fluid was caused by the effect of buoyancy,
which stem from the changes in thermophysical properties, others
(Petukhov and Polyakov, 1988; Polyakov, 1991) thought the effects
of buoyancy and fluid acceleration caused by large drops of density
with temperature lead to heat transfer deterioration together.
According to the open literature, Ackerman (1970) was the first
researcher who has compared the heat transfer deterioration of
supercritical pressure water with film boiling at subcritical pressures. Ackerman suggested that a pseudo-film boiling phenomenon could occur at supercritical pressures, and the pseudo-film
boiling phenomenon at supercritical pressures was analogous to
the film boiling at subcritical pressures in mechanism. Ackerman
pointed out the thin fluid layer covering the heat transfer surface
of tube at supercritical pressures was a film of vapor-like bubble.
Fig. 7 gives a comparison of the heat transfer deterioration of water
at supercritical pressures and the DNB at subcritical pressures. As
demonstrated in Fig. 7, the heat transfer deterioration at supercritical pressures and the DNB at subcritical pressures both occurs in a
region with low fluid enthalpy, and the wall temperature curve at
26.0 MPa closely resembles the DNB curve at 15.4 MPa, suggesting
that the heat transfer deterioration at supercritical pressures may
be similar to the DNB at subcritical pressures. Another similarity
of the heat transfer deterioration at supercritical pressures to the
DNB at subcritical pressures is that both the heat transfer deterioration at supercritical pressures and the DNB at subcritical pressures are caused by the covering of the heat transfer surface by
low-density fluids. However, the fluids covering the heat transfer
surface in the DNB case at subcritical pressures are vapor films produced from the violent water boiling, while the fluids covering the
surface with deteriorated heat transfer at supercritical pressures
are single-phase fluids.
In the present paper, the heat transfer deterioration is considered to be a result of combined effect caused by the rapid variations
700
650
o
boiling at subcritical pressures. The drastic changes in thermophysical properties near the pseudocritical points, especially the
sudden rise in the specific heat of water at supercritical pressures,
contributes, but within a limited content, to the local heat transfer
promotion.
It can be seen from Fig. 6b that in the large specific heat region
of supercritical pressure water, both the magnitude of the HTC
peak, and the range covered by heat transfer enhancement in
terms of fluid enthalpy, and, as well, the value of the bulk fluid enthalpy corresponding to the HTC peaks decrease with the increasing heat flux, indicating the impairment of the heat transfer
enhancement with increasing heat fluxes, and even, the occurrence
of heat transfer deterioration at high heat fluxes.
As shown in Fig. 6b, obvious heat transfer deterioration occurs
in the low enthalpy region when the heat flux is 660 kW/m2 at a
pressure of 25.0 MPa in the vertically-upward internally-ribbed
tube, and heat transfer deterioration also occurs in the high enthalpy region when the heat flux is 460 kW/m2 in this tube at the same
pressure of 25.0 MPa. One of the characteristics of heat transfer
deterioration is that there is a sudden decrease in HTC and in the
present study, the heat transfer deterioration is considered to occur when the HTC is less than 8 kW/m2 K.
From the viewpoint of heat transfer coefficients, the normal
heat transfer of supercritical pressure water is characterized with
the basically unchanged heat transfer coefficients. The enhanced
heat transfer is characterized with the high heat transfer coefficients in comparison to the normal heat transfer, and the deteriorated heat transfer is characterized with a sudden decrease in, and
the low value of heat transfer coefficients in comparison to the normal heat transfer.
Inside wall temperature, C
774
600
550
500
450
φ31.8× 6.0 mm ribbed tube
25.0 MPa,800 kg/m2s,660 kW/m2
15.4 MPa,800 kg/m2s,450 kW/m2
φ32.0× 3.0 mm smooth tube
26.0 MPa, 600 kg/m2s,
350 kW/m2
φ31.8× 6.0 mm smooth tube
15.4 MPa, 600 kg/m2s,
350 kW/m2
400 t -when 25.0 MPa
b1
350 tb2-when 15.4 MPa
heat transfer deterioration
at supercritical pressures
DNB
tb1 tb2
Dryout
1
0
300
x 15.4 MPa
the large specific heat region
250
200
600
Hpc=2136.2 kJ/kg
900
1200 1500 1800 2100 2400 2700 3000 3300
Bulk enthalpy, kJ/kg
Fig. 7. Comparison between the heat transfer deterioration at supercritical
pressures and the DNB at subcritical pressures.
J. Wang et al. / International Journal of Multiphase Flow 37 (2011) 769–776
of thermophysical properties of the supercritical pressure water in
the large specific heat region. A possible reason for the occurrence
of heat transfer deterioration in the vertically-upward tubes at
supercritical pressures is that when heat flux increases to a certain
value, there exists a large radial gradient in fluid temperature, and
as a result, a thin layer of fluid directly contacting the inside tube
wall absorbs heat easily and becomes hot enough and firstly ‘‘enter’’
into the large specific heat region with its density and thermal conductivity dropping dramatically and rapidly, while the properties of
the bulk fluid in the center region of the tube remains unchanged.
The decrease of thermal conductivity will cause a decrease in heat
transfer. The buoyancy force due to a large and rapid decrease in
fluid density with temperature accelerates the flow velocity near
the wall, which causes a reduction in the velocity gradient. That is
to say, the flow velocity distribution becomes flat. As a result, turbulence production is reduced in the near-wall region, and the turbulent diffusivity is impaired when the low-density fluid layer
becomes thick enough to reduce the shear stress in the region
where energy is typically fed into the turbulence, i.e., the buoyancy
effects might make the low-density fluid layer be in a state of laminar flow. The above-mentioned factors eventually make the heat
transfer surface of the tube covered by light and hot fluids, and
the effect on heat transfer is similar to that of the vapor films on
subcooled boiling at subcritical pressures, and the heat transfer
deterioration may occur, resulting the sharply increasing in the wall
temperature. Indeed, similar ideas are given further attention in recent studies, also making use of advanced numerical techniques
(McEligot and Jackson, 2004; McEligot et al., 2008). Of course, because of the particularity and complexity of supercritical fluid heat
transfer, a further in-depth study on the mechanism in heat transfer
deterioration of supercritical pressure water is necessary.
Conventionally, the critical heat flux, qcr, was used to describe
the DNB, i.e., the first type of deteriorated heat transfer and the
critical steam quality, xcr, was used to describe the dryout, i.e.,
the second type of deteriorated heat transfer at subcritical pressures. According to the literature, there were two methods for
determining the starting point of deteriorated heat transfer at
supercritical pressures. One is to determine the critical heat flux,
at which deteriorated heat transfer occurs, for example, a correlation qcr = 0.2G1.2, proposed by Yamagata et al. (1972). Another
method is to determine the critical length of the tube, within
which deteriorated heat transfer did not occur (Glushchenlo
et al., 1972; Petukhov and Polyakov, 1974). However, the second
method used to determine the critical length of the tube was
complex.
Moreover, from the viewpoint of wall temperature, the deteriorated heat transfer is characterized with sharp increase in wall
temperature.
In short, it was found that the heat transfer characteristics of
supercritical pressure water was greatly different from not only
that of the vapor–water two-phase flow at subcritical pressures,
but also that of the single-phase subcritical pressure water. There
existed three different heat transfer modes for supercritical pressure water: (1) the normal heat transfer, (2) the deteriorated heat
transfer, with low HTC but high tube wall temperatures and large
temperature differences between the inside wall and the bulk fluid,
and (3) the enhanced heat transfer with high HTC and low wall
temperatures and small temperature differences between the inside wall and the bulk fluid. It should be pointed out here that such
categorization does not mean that the three heat transfer modes
for supercritical pressure water will be included in one experimental condition. In general, with increasing bulk fluid enthalpy, two
modes may appear: the normal heat transfer and the heat transfer
enhancement at low heat fluxes, e.g., in experimental conditions
shown in Fig. 4, and at conditions of high heat fluxes, the normal
775
heat transfer and the heat transfer deterioration may appear as
shown in Fig. 7.
6. Conclusions
(1) It was found that, severe heat transfer deterioration did not
occur in the vertically-upward internally-ribbed tube at
supercritical pressures, and the variations in the inside wall
temperature with the bulk fluid enthalpy experienced three
stages, namely, the continuously increasing stage, the
smoothly changing stage and another continuously increasing stage at the supercritical pressures; however, at subcritical pressures, there existed at least four stages for the
variation of the inside tube wall temperature, i.e., the continuously increasing stage, the basically unchanging stage, the
sharply rising stage and another continuously increasing
stage.
(2) The heat transfer coefficients in the subcritical two-phase
region, in which the heat transfer deterioration did not
occur, were much greater than those in the heat transfer
enhancement region of supercritical pressure water. In the
large specific heat region of supercritical pressure water,
the enhanced heat transfer was impaired by increasing the
heat flux; however, in the subcritical two-phase region, the
higher the heat flux is, the greater the heat transfer coefficient would be.
(3) There existed three different heat transfer modes for supercritical pressure water: (1) the normal heat transfer, (2) the
deteriorated heat transfer, and (3) the enhanced heat transfer. It was also found that the heat transfer deterioration of
supercritical pressure water was similar in mechanism to
the DNB at subcritical pressures.
Acknowledgements
The authors want to thank the anonymous reviewers for their
helpful comments and suggestions. The authors acknowledge the
support of the National Basic Research Program of China (973 Program) (Grant No. 2009CB219805) and the National Natural Science
Foundation of China (Grant No. 50876090) and the Special Funds of
the Education Department of Shaanxi Province (Grant No.
09JK585).
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