7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Numerical Investigation on the Mixed Convection and Heat Transfer of
Supercritical Water in Tube in the Large Specific Heat Region
Xianliang LEI and Huixiong LI
State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University
NO.28 West XianNing Road, Xi'an, 710049, China
xianliang.lei@stu.xjtu.edu.cn and huixiong@mail.xjtu.edu.cn
Keywords: Mixed convection, Secondary Flow, Large Specific Heat Region
Abstract
Numerical simulation is performed to get further insight into water heat transfer phenomena in a 032 X 3mm horizontal
smooth tube under supercritical pressures. The heat transfer enhancement and heat transfer deterioration (HTD) in the
socalled Large Specific Heat Region (LSHR) of supercritical fluids is analyzed. The governing equations of the fluid are
solved on fixed threedimensional (3D) grid systems, and the RNGks model with enhanced wall treatment method is
employed to handle the coupled walltofluid heat transfer. The numerical results are compared with the corresponding
experimental data, and a good agreement is achieved. The variation in the tube inner wall surface temperature and the local
heat transfer coefficient with parameters, such as the water enthalpy, the water mass flow rate and the heat flux, are obtained. It
is showed that in the large specific region, there exists strong nonuniformity of the circumferential distribution of the tube
inner wall temperature, and as well, the heat flux on the inner tube wall are distinctly nonuniform along the tube wall
circumference. Further analysis of the numerical data shows that the abovementioned nonuniformity is due to the rapid
change in fluid properties, which results complex second flows and convection in the supercritical fluid. Based on the
numerical results, a critical value is applied for the parameter Gr/Re2 which is believed to be a key parameter to control the
secondary flow in LSHR. Only if the value is higher than 10 ', the phenomenon of HTD can be observed.
Introduction
Huge demand for electricity has been driving the
development of technologies in power and energy production
in the world. As one of the advanced coalconsumption
technologies, supercritical (ultra supercritical) pressure
boilers have been worldwidely used, especially in China,
due to it's a good deal of advantages such as the large
capacity, relatively low energy cost, low pollutant emission
and high efficiency. Furthermore, supercritical watercooled
reactors (SCWR) have been accepted as one of the six most
promising reactor concepts considered in the Generation IV
International Forum (GIF). In this case, flow and heat
transfer characteristics of supercritical pressure water in
channels becomes important for the design and operation of
related systems operating at supercritical pressures.
Early studies on the flow and heat transfer of supercritical
fluid (Lin and Chen, 1990; Chen et al., 1995) have shown
that there exists a socalled large specific heat region
(LSHR) for water, which is usually defined as a region with
the specific heat of water at constant pressure larger than 8.4
kJ/(kg K). Although the supercritical pressure water does not
experience phase change, the thermophysical properties
however exhibit drastic and fast variation with temperatures
in the large specific heat region (LSHR), which may result in
new features in the flow and heat transfer of the supercritical
water in channels and may cause troubles in the operation of
the related facilities.
It is worthy nothing that in the slidingpressure operation of
the supercritical pressure boilers, the working fluid may
frequently work in the larger specific heat region and
experience complex phase changes again and again in the
watercooledwall tubes of the boiler, and the change in
properties of the supercritical fluid in the pseudocritical
region (i.e., the large specific heat region (LSHR)) may
result in complex crossmixing of the fluid, and lead to the
uneven circumferential distribution of wall temperature and
thermal stress in the tube wall. Accordingly, understanding of
the complicated heat transfer phenomena of supercritical
water in the large specific heat region is very important for
the supercritical pressure boiler.
Nomenclature
P pressure/ MPa
T temperature/ K
G Mass flux/ kgm2s1
q Heat flux/ kWm2
H Bulk enthalpy/ kJkg
Cp Specific heat at constant pressure/ kJkg1
h Heat transfer coefficient/ kWm 2K1
D tube diameter/m
g gravity/ms2
Greek letters
2 Thermal conductivity/ Wm1 K1
P viscosity/ kgms1
p density/ kgm3
Nondimensional numbers
Re Reynold number (Re = UD)
Pr Prantal number (pr. c )
GrgPATD3
r Grashof number ( g )
Gr Grashof number (Gr = (p P)gD*
It is well known that the DittusBoelter equation (Dittus F.W
and Boelter L.M.K., 1930), i.e,
Nu = 0.023Reo8Pr/3 (1)
can be used to evaluate the performance of turbulent forced
convection heat transfer in pipes.
Usually, once the measured heat transfer coefficient in a
channel is higher than that predicted by the DittusBoelter
equation, it is considered that heat transfer enhancement
occurs, while the measured heat transfer coefficient is lower
than that computed by the DittusBoelter equation, the heat
transfer deterioration is considered to occur.(Pioro et al.
2004).
A number of experimental investigations on the forced
convection and free convection have been fulfilled in
supercritical water flowing inside channels. Yamagata et al.
(1972) performed the experimental investigation on the
forced convective heat transfer for the vertically upward flow
of water in a 10 mm i.d. tube and clarified the characteristics
of the heat transfer deterioration at high heat fluxes, and
proposed the following equation for predicting the heat
transfer deterioration.
q =0.20.G12 (2)
Shitsman (1963) conducted experiments with supercritical
water flowing in circular tubes with the parameter q/G in the
range from 0.72 to 0.86, and found the following criteria for
deteriorated heat transfer, i.e. when
q/G >0.4 (3)
heat transfer deterioration appeared but in only some part of
a heated length.
Kirillov et al. (1990) had taken into account the role of free
convection in heat transfer at the nearcritical point (the point
where the specific heat has a peak value is considered the
pseudocritical point, included in the LHSR region) the
region around the critical point where all thermophysical
properties exhibit large gradients. They thought that the
deteriorated heat transfer was affected by both the
acceleration and the variation in physical properties of the
fluid in the cross section in the turbulent transport.
Moreover, heat transfer enhancement has ever been observed
of the supercritical fluid in heating ducts by researchers
(Yamagata, 1972; Krasyakova et al, 1977). However,
sometimes, heat transfer deterioration has also been observed
under similar conditions. Styrikovich et al, 1967, Krasyakova
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
et al. 1967, Ornatsky et al, 1970, Kruzhilin, (1974)
respectively observed the phenomenon of supercritical water
heat transfer deterioration at low mass fluxes or at high heat
fluxes. Igor L. et al (2005) presented a review of
experimental investigations on heat transfer of supercritical
water flowing inside different channels, they Summarized
the past research work.
In spite of much research, however, heat transfer mechanism
of supercritical water in channel inside at high heat fluxes is
not clearly at supercritical pressure, especially in the large
specific region. Kafengaus (1975) had been used a
mechanism for "pseudoboiling" to explain heat transfer
deterioration, but it is only a guess.
In recent decades, more and more numerical simulations
were carried out by commercial CFD codes to study the heat
transfer characteristics of supercritical water. Kim et al
(2"" 4) compared number of turbulence models for upward
flows in circular tubes at supercritical pressure by FLUENT
and analyzed the reason why a big difference between
simulation results and experimental data. Cheng et al. (2005)
studied heat transfer in triangular and square lattice bundles
using CFX software. Yang et al. (2007) investigated heat
transfer in supercritical water for upward flow in circular
tube using STARCD and qualitatively analyzed the
nonuniformity in subchannel of square tight lattice bundle.
Unfortunately, all the previous studies focused on the feature
of heat transfer, the mechanism behind the heat transfer
enhancement or the heat transfer deterioration and the reason
for nonuniformity have not clarified yet up to now, and the
strategy that can be used to avoid or prevent heat transfer
crisis has not been clearly figured out. Therefore, it is
necessary to carry out further studies on the flow and heat
transfer characteristics of supercritical water in the large
specific region in different ducts.
In the present paper, the commercial CFD code Fluent 6.3 is
utilized to investigate heat transfer in supercritical water for
horizontal flows in circular tubes. The RNGke model with
Enhanced Wall Treatment method is employed to handle the
coupled walltofluid heat transfer. Compared with the
numerical results and experimental data, the model is very
suitable to predict heat transfer in supercritical water. Then
investigated the heat transfer features under different
secondary flow is used to explain the phenomenon of HTD
through and an appropriate parameters can reflect the ratio of
natural convection and forced convection is applied to
illustrate mixed convection quantitatively.
Computational methods
Physical model
L=8000mm
'.
Uin,
Ti T ou,, t
T t7 t t t t t t 7A toTuut
q _ 0, .
AA
Figure 1: Sketch map of a horizontal smoothed tube
The geometry and size of the tube used in the present paper
is widely utilized in supercritical pressure boilers. Figure. 1
I a *_1q
 
1 1
shows a sketch map of a horizontal smoothed tube of 032 X
3mm and length of the tube is 8000mm, the circumferential
angle at top generatrix is defined 0 degree and the bottom is
180degree.
Grid meshes
The structured bodyfitted mesh is used in the present
study to fit the complex tube geometries, and a turbulence
model using Enhanced Wall Treatment require the Y+
values (the distance of the first point to the wall) less than
1. The face mesh contained 1853 quadrilaterals; and the
volume is generated by cooper type with source of head
face grid along the length of the tube, which is composed
of 5548800 hexahedral elements in the total computation
domain. Figure 2 shows the cross section grid and the
local amplification in the near wall region.
Figure 2: Crosssection grid and local amplification in the
near wall region
Physical property
Figure 3 typically shows the physical properties of water
at pressures of 26MPa and 34MPa.
600 650 700 750 800
T/K
Figure 3: shows the physical properties of water at a
pressure of 26MPa and 34MPa
Heat transfer at supercritical pressures is largely affected
by the thermal physical properties, and especially, the
properties abrupt variation of water in the vicinity of the
pseudocritical temperature. Based on the IAPWS95 (the
International Association for the Properties of Water and
Steam), the thermal properties of water at pressures of
26MPa and 34MPa are applied in this study, and the effect
of temperature on the water physical properties is mainly
considered, because the lateral and axial variation in
pressure are small.
Numerical Method
The mass, momentum and energy conservation equation
are solved by Fluent 6.3.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Conservation of mass, i.e., the socalled continuity equation,
can be derived by applying Reynolds' transport Theorem
(RTT) to any material volume and can be written in many
ways, for instance
S+V.(p) =0 (4)
Where, p is the density, v is the velocity vector, and
8 denotes the partial derivative operator.
For the case of a Newtonian fluid, where the stress tensor is
at most a linear function of the rate of strain tensor, the
standard incompressible NavierStokes equations can be
presented as follows (Schlichting H, 1979),
a (5)
t(pu)+V(puu) =Vp+V.[(Vu+u )]+pg+F (5)
In order to translate this coupled, partial differential
equation into algebraic expressions, a finitevolume
method is employed and the equations of motion and
continuity are integrated over each computational cell. A
secondorder upwind scheme is used for the discretization
of the equations in the current work, and the discretized
equations are then linearized and solved in a segregated,
first order implicit manner (Tao, 2001).
The accuracy of numerical simulations of heat transfer in
supercritical water may depend on turbulence models. A
number of investigations about the application of turbulence
models in the numerical simulation of flow and heat transfer
for supercritical water have been carried out. From the 1950s
to the 1970s, eddy diffusivity models were mainly used by
researchers, such as Deissler (1954), Goldman (1954), Hsu
(1961), Schnurr (1976). Later, other turbulence models, such
as ks model, Jones &Launder ks model, mixinglength
model and RNG ks model, et al. was used. Yang et al (2007)
found that the twolayer model (Hassid and Poreh, 1978) can
give a better prediction to the heat transfer than other models,
and the standard ks high Re model with the standard wall
function also shows an acceptable prediction capability. Kim
et al (2"'i4) compared number of turbulence models for
upward flows in circular tubes at supercritical pressure and
concluded that RNG ks with the enhanced nearwall
treatment can obtained most understanding predictions. The
reason why some selected turbulence models predict higher
wall temperature or lower heat transfer coefficients was
analyzed and they found that these models give distorted
density distributions especially in the nearwall region which
caused the turbulence structure of the flow acceleration and
the buoyancy near the wall were not well predicted. The
turbulence kinetic energy increases slower than the main
velocity and the buoyancy also has an effect to the
turbulence kinetic energy in an accelerating flow. The
different estimated level of turbulence kinetic energy makes
the different prediction results. These may also be the reason
why all models cannot agree with the experimental data very
accurate.
Therefore, the RNGks model with Enhanced Wall
Treatment method is used to simulate the unique and
complicated turbulent heat transfer characteristics at
supercritical pressure. The governing equation of turbulent
kinetic energy and dissipation equations are given as follows.
Turbulent kinetic energy :
(pk)+ (pku,)= (agp O)+G,+G p Y +S, (6)
8t 8x a 8x
Dissipation:
a ) a a (7)
(pE)+(pu,)= p(ak j )+C, _(QG, CG,)C +s,
at ax x x k
Where G =pu,'u qo= pg T' Y, =2p
ar Pr, ax
C1,=0.0845, C2=1.42,C3,=1.68. ak and a, are turbulent
Prantal number.
The RNG ks model was derived using a rigorous statistical
technique (called renormalization group theory). It is similar
in form to the standard ke model, but includes some
refinements, such as the RNG model has an additional term
in its E equation that significantly improves the accuracy for
rapidly strained flows. The feature make the RNG ke model
more accurate and reliable for a wider class of flows than the
standard ks model (FLUENT, 2006).
Boundary Condition
Table 2 shows the boundary conditions used for the
circular tube case in the present study.
Table 2 Boundary conditions for the circular tube
Inlet temperature 564 K700K
Inlet mass flux 300, 600 kg/m2s
Heat flux 200,250,300, 400,600 kW/m2
Outlet 26MPa, 34MPa
Model validation
In order to verify the reliability of the present method,
numerical simulation was performed to study the flow and
heat transfer of supercritical water at various heat fluxes at a
pressure of 24.5MPa, under conditions corresponding to the
experiments performed by Yamagata et al (1972). Figure 4
shows the numerical predictions for the wall temperature
plotted against the bulk enthalpy.
o
5 400
a 380
E
a)
i
1600 1800 2000 2200 2400
Bulk Enthalpy (kJ.kg')
(Vertically upward flow)
(Point: experimental data  Line: numerical results)
Figure 4: Comparison of experimental and computed wall
temperature as a function of bulk enthalpy
It is seen that difference between the predicted wall
temperature and the measured wall temperatures is generally
within 16% for every considered heat flux.
Results and discussions
Heat transfer c etric ient (HTC) and wall temperature
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure 5 and Figure 6 show the HTC and innerwall
temperature versus bulk enthalpy at different heat fluxes at a
pressure of 26MPa.
50' '
P=26MPa
G=300kg.m2.s
q=100kW.m2
q=100kW.m2
q=200kW.m2
I ; ,
A
, P=26MPa
G=600kg.m2.s
$ q=200kW.m
Sq=200kW.m2.
S q=300kWm2
S q=300kWm'
Sq=400kWmr2
S q=400kW.m2
,* q=600kW.m2
q=600kWm2
.". ,.. . .... . ,
* ,,' ', ',... z .. ,
, ..... *............ ... ..r:: .,....
1200 1600 2000 2400 2800 3200
Bulk Enthalpy (kJ.kg 1)
(Solid: top generatrix I Hollow: bottom generatrix)
Figure 5: HTCs as functions as water enthalpy at different
heat fluxes (p=26MPa)
1200
1100
1000
2
900
C
S800
700
600
P=26MPa
G=300kgm2.s l.
o cq=l=kW.m
q=Q0kWm
q 00kWm
q 200kWr
k
P=26MPa
G=600kgm 2*s
q=200kW.m
q 200kWm 2
........ q=300kW.m
q300kW.m
q400kW.m
q400kWm
.* q600kWm 2
...."" **q=600kWm2
4
I I. ....I I I
 t .' 2 2: : ;.r^ ,:, ,
1200 1600 2000 2400 2800
Bulk Enthalpy (kJ.kg 1)
3200
(Solid: top generatrix 1 Hollow: bottom generatrix)
Figure 6: Temperatures as functions as water enthalpy at
different heat fluxes (p=26MPa)
As shown in Figure 5 and Figure 6, the HTC and the inside
wall temperature exhibit different characteristics at various
wall heat fluxes. At low heat fluxes, the HTC and the inside
wall temperature increase slowly with the bulk enthalpy of
water. When the bulk temperature enter into the large
specific heat region, variation of temperature become smaller
than before, the heat transfer coefficient increase abruptly
and the heat transfer coefficient gets a peak at a bulk
temperature near the pseudocritical temperature, and then
the heat transfer coefficient decreases and the inner wall
temperature increases owning to the specificheat become
smaller.
At moderate and high heat fluxes, the wall temperature in the
top generatrix region increases faster than that in the bottom
generatrix region, Before the water bulk enthalpy enters into
the large specific heat region (from 1726kJ/kg to 2720kJ/kg),
the heat transfer coefficient of the top generatrix in
R
./
.. .,....
horizontal tube begin to decreases, and heat transfer
deterioration occurs. The rate of temperature variation at
high heat flux is significant. The HTC of the top generatrix
takes a maximum at a low bulk enthalpy and then decreases
with the bulk enthalpy. The HTC gets highest value and
lowest value at the bottom and at the top of the tube
respectively. Obviously, the deteriorated heat transfer in the
top generatrix region usually appears at the higher heat
fluxes and the lower mass fluxes.
Figure 7 and Figure 8 show the HTC and innerwall
temperature plotted against bulk enthalpy at different heat
fluxes and mass fluxes.
P=34MPa
G=300kg.m .s 1
*q100kW.m2
o q100kWm.
q=200kW.m2
cq :"111 .,,,
P=34MPa
G=600kg.m 2.s
q250kW.m
 q 250kW.m2
q400kW.mr2
q 400kW.m
q600kW.m2
q 600kWm.2
ts...s. *. .. .
0 LARGE SPECIFIC HEAT REGION
1200 1600 2000 2400 2800 3200
Bulk Enthalpy (kJkg 1)
(Solid: top generatrix II Hollow: bottom generatrix)
Figure 7: HTCs as functions as water enthalpy at different
heat fluxes (p=34MPa)
Compared with the innerwall temperature distribution at a
pressure of 26MPa, the temperature and heat transfer
coefficient at a pressure of 34MPa show a similar tendency,
but variation of HTC at 26MPa is different from that at
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
34Mpa. The HTC gets a peak value higher than the peak at a
pressure of 34MPa. The maximum value appeared at lower
enthalpy compared with the value at 34PMa. The HTC is
lower than that in 26MPa due to thermalphysical properties
change gently.
1100
1000
0900
0800
E
700
600
P=34MPa
G=300kg.m2.s
q=lOOkWMm2
 q100kWn2
q=200kW.m2
q=200kW.m2
P=34MPa
G=600kg.m2.s1
q=250kWm2
q=250kW.m2
S q=400kWm2
.. Vlq 400kW.*m'
I "2
A.
1200 1600 2000 2400
Bulk Enthalpy (kJkg1)
2800 3200
(Solid: top generatrix I Hollow: bottom generatrix)
Figure 8: Temperatures as functions as water enthalpy at
different heat fluxes (p=34MPa)
Temperature, HTC and Heat Flux Circumference
distribution
In order to better understand the mechanism in heat transfer
deterioration supercritical pressure water, the variation of the
temperature, heat transfer coefficient and heat flux of the
innerwall surface along the circumference of the tube at
different crosssections are shown in Figure 911.
1272 1584 P=34MPa
.. ,"
,
...........
180 150 120 90 60 30 0
Circumference Angle ()
S 2437
P=26MPa
2543
G=600kgm s 2656

','............. ...: ." .. ..
..... :.....'..,. .
S.. ..... ....
180 150 120 90 60 30 0
Circumference Angle ()
Bulk Enthalpy
1287 P=26MPa
1705 G 600kg m2 S
1934
2250 q=00kWm2 / ..'
*2421
./ /
.......... ......."  ,,....
180 150 120 90 60 30 0
Circumference Angle ()
Figure 9: Inner wall temperatures as functions of circumference angle at different bulk enthalpy
S1272 1584
S1308 * 624
6 ...".. 1663
1703
*** .. ... 17403
4 1742
.. *' 1821
2 .. .. , 1861
1892
0.
'*'
180 150 120 90 60 30 0
Circumference Angle ()
P=26MPa Bulk Enthalpy
1891
. =600kgm s 1954
/' 400kWmI2 2026
1279 2204
1 400 2437
1529 2543
S1653 2774
% 1772 2893
% 3014
'31
."". ... .. ..33
. .... '
180 150 120 90 60 30 0
Circumference Angle ()
P=26MPa Bulk Enthalpy
600kgm2S1 1287
G 600kWm 1705
1705
Sq600kW 2 1934
2250
2421
.". ... .2535
2672
S,  2811
180 150 120 90 60 30 0
Circumference Angle ()
Figure 10: HTCs as functions of circumference angle at different bulk enthalpy
760 
700 
680
I I I I
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
P=34MPa
315 G=600kg 2 s 1
310
305
300
295 ..
290 ..
285
180 150 120 90 60 30 0
Circumference Angle ()
P=26MPa
G=600kg m.2 s1
q=400kWm2
B . ...,
1653 2204 3014
1772 3131 '..
3233
180 150 120 90 60 30 0
Circumference Angle ()
Bulk Enthalpy P=26MPa
1287 G=600kgm'2
1705 q=600kWml2
1934 .
2250 \
2811 1
2535 1 /
*"..% .....
180 150 120 90 60 30 0
Circumference Angle ()
Figure 11: Heat fluxes as functions of circumference angle at different bulk enthalpy
From low enthalpy to high enthalpy region (1200 kJ.kg
2800 kJkg '), the circumferential temperature distribution
is nonuniform due to the effect of buoyancy. Figure 9
shows that Fluid temperature close to the top generatrix is
always higher than that in the bottom region and there is
very large temperature gradient along the circumference
inside wall surface at different heat fluxes. At low heat flux,
temperature slightly increases with bulk enthalpy. Once the
bulk enthalpy enters into LSHR, the temperature difference
between top generatrix and bottom region is decreasing. At
high heat flux, temperature raise fast at 0 degree before the
temperature reaches to pseudocritical point at low enthalpy,
then the temperature difference disappear at high enthalpy.
However, HTCs display exactly the opposite variation at
low heat flux compared with temperature. It can be found
from Figure 10 that the HTCS exhibit dramatic change at
moderate and high heat fluxes. At a heat flux of 400kW/m2,
a maximum local HTC appear at the middle of tube. The
peak value become larger and the maximum HTC
transferred to the bottom generatrix slowly.
Heat flux distribution is totally different from wall
temperature distribution; the heat flux gets minimum value
at 0 degree. With the increasing in circumferential angles,
the inner wall heat flux continues to increase until it reaches
a peak value within a range of 1090 degrees. It could be
easily recognize that the heat flux value at 0 degree is lower
than other nearwall regions from Figure 11. In other word,
heat has been mainly transferred from the top region to this
position due to a large temperature difference exist.
It may also found that when enthalpy equal to 1653 kJ.kg'1,
HTC at top generatrix start to reduce, local HTD occurs.
And it is very strange that heat transfer deterioration does
not appear in the maximum wall temperature at 1954
kJ.kg' .Maybe at this point, force convection greatly
enhanced weakened the effects of the free convection.
HTD mechanism
Figure 12 show variation of the thermalproperties, flow
velocity and temperature distribution on the cross section at
the enthalpy of 2150 kJ.kg' in smooth tube.
yveloc
enth temperate
221923E+
K
21 668E+0
60040
Figure 12: Water properties, temperature, velocity contour
and vector on a cross section at P=26MPa, h=2150 kJ/kg in
smooth tube
Under the action of the outer wall heated at low heat flux, a
thin fluid layer in the vicinity of inner wall absorbs a large
amount of heat, the temperature increase sharply. At the
same time, thermophysical properties of the thin fluid layer
drop suddenly and greatly near the pseudocritical
temperature; water can carry away more heat due to specific
heat increase to a high value. The local temperature
difference between fluid and topgeneratrix innerwall
decreased. On the one hand, with the temperature increasing,
the density of the flow close to the innerwall drop
dramatically make the density difference large, the variation
will lead to the buoyancy force increasing, which will speed
up fluid in the crosssection of tubes. On the other hand, the
tube crosssection axial velocity fast increasing, the
acceleration effect obvious.
Secondary flow is caused by buoyancy and by the
acceleration effect as abovementioned; the intensity of
secondary flow will enhance or deteriorate heat transfer.
As show in Figure 12, the bulk temperature of the flow in
the top generatrix innerwall reaches to the pseudocritical
temperature earlier than the bottom generatrix. Then the
density of the flow in the top generatrix innerwall drop
rapidly and dramatically. So the volume of the water in the
topgeneratrix will increase much more and the pressure
will increase much sooner compared with the
bottomgeneratrix. The pressure balance will force the water
in the top of horizontal tube flows into the bottom. Because
of the density decrease and mass loss, the mass flux will
decrease in vicinity of the bottom. By the reason of the
lower mass flux, and also because the thermal conductivity
of the water in the topgeneratrix section drop rapidly, the
heat transfer here becomes much worse.
The bulk temperature will increase more quickly than in low
enthalpy region and it is an unfavorable feedback to the heat
transfer. Therefore, when the mass flux is small enough, the
local heat transfer deterioration (local HTD) may occur at
the top of the horizontal tube.
Secondary. ,,,
Secondary flow is very useful to understanding the
occurrence of the heat transfer deterioration. Figure 13 and
Figure 14 shows variation of secondary flow on
crosssection at different bulk enthalpy at a pressure of
26MPa, mass flux 600 kgm2.1, heat flux 400kWm2 and
600kWm2, respectively. (Range of enthalpy about Local
HTD included in red Frame)
H1629S
Ic~
W2204
Figure 13: variation of secondary flow on crosssection at
different bulk enthalpy
(P=26MPa, G=600 kg.m2.s1, q=400 kWm2)
At moderate heat flux, the vortex center of secondary flow
is almost located in the middle of tube. When the
temperature of the fluid layer near top generatrix is slightly
higher than the pseudocritical temperature but water bulk
enthalpy is lower than the enthalpy corresponding to the
pseudocritical temperature, secondary flow is enhanced at
this point, a small new vortex emerge at the top of
horizontal tube within the range of 15911890 kJ/kg, the
heat transfer deterioration occur in this enthalpy region.
H=1705 H=1933 H224& 242 H=2S 35 H=2672
Figure 14: variation of secondary flow on crosssection at
different bulk enthalpy
(P=26Mpa, G=600 kg.m2.s1, q=600 kWm2)
At high heat flux, the significant variation of physical
properties on the tube cross section in the process of
turbulent transport lead to secondary flow enhanced and
heat transfer deterioration, the intensity of the secondary
flow have greatly increased due to a sharp reduction of
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
density, the vortex position is pulled to the top by the
intensified buoyancy and acceleration effect. Then the
vortex shift back to the bottom of tube, owning to the axial
momentum quickly increase weakened the secondary flow.
The relationship between Mixed convection and HTD
In Generally, Gr usually can be used to determine the extent
of the effects of natural convection and Re always used to
decide the force convection. Figure 15 shows variation of
the buoyancy and force convection ratio against bulk
enthalpy.
'12
P=34MPa P=26MPa
G=600kg.m2.s G=600kg.m2.s
10 250kW.m2 200kWm
400kWm 2 300kWm
8 600kWm 2 400kW.m
600kWm
N G=300kg.m 2.s G=300kg.m 2s
S6 100kW.m 2 100kW.m
E / :,,,,i  ..,
0 4
2 .."..
1200 1600 2000 2400 2800 3200
Bulk Enthalpy (kJ.kg1)
Figure 15: Buoyancy force variation with bulk enthalpy
The ratio of the Gashoft and Reynold number reflects the
affection of natural convection and force convection. Gr/Re2
is usually used to decide the intensity of mixed convection.
Jackson and Hall (1979) analysis changes of shear stress
along the boundary layer and developed a useful criterion.
The criterion is given below.
Gr/Re27<105 (8)
Compared the value of the two parameters, it is found that
the criterion of Gr/Re27 can be well explained the heat
transfer deterioration phenomenon of this article.
As shown in Figure 15, Gr/Re27 value slowly increases to a
peak at low enthalpy. The buoyancy becomes greatly large
caused by the sharp thermal properties variation when the
Gr/Re27 reaches to the maximum value. The local heat
transfer deterioration phenomenon may appear in the
enthalpy region corresponding of the peak. In addition, as
heat flux increase, the ratio of free convection and force
convection increase.
More importantly, it can be found that only when the
Gr/Re27reaches to critical value by comparing the result
mentioned earlier, which must be higher than 10'5, the
phenomenon of HTD can be observed.
Conclusions
In the present paper, Numerical analysis has been performed
to investigate the phenomenon of nonuniform heat transfer
and discussed the affection of mixed convection to HTD in
horizontal smooth tube. Some observations and conclusions
are given below:
1591 H1653 H*1772 *H109
1. Numerical results are compared with the corresponding
experimental data, a good agreement is achieved,
indicating that RNGke model with enhanced wall
treatment method is quite reliable to simulate the unique
and complicated turbulent heat transfer characteristics at
supercritical pressure.
2. The strong nonuniform circumferential temperature
distribution in crosssection is caused by the effect of
natural convection, which leads to innerwall heat
transfer coefficients and heat flux varied greatly along
circumference angle, especially at higher heat flux. The
phenomenon of HTD is found at moderate heat flux and
at low mass flux (For example, G=600kg*m2*s1,
q=400kWm2 or G=300kg.m2*s1, q=200kWm2).
3. According to the secondary flow evolution, it can be
observed that the vortex center transfer at different
enthalpy due to severe variations of the thermal
properties. When the vortex center was pulled to the top
region or a new vortex is formed, which is caused by free
convection enhanced or acceleration effect intensified at
high heat fluxes or low mass fluxes, the HTD appear.
4. The criterion of Gr/Re27 can be well explained the heat
transfer deterioration phenomenon, the peak of Gr/Re27
emerge in low enthalpy. With the heat flux increases, the
value increase and shift to the lower enthalpy region.
Moreover, local heat transfer deterioration phenomenon
appears only if Gr/Re27 reaches to the maximum and is
higher than 105. At this moment, free convection is
achieved to the strongest.
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).
References
Ackerman, J.W. Pseudoboiling heat transfer to supercritical
pressure water in smooth and ribbed tubes. J. Heat Trans.,
Vol. 92, 490498 (1970)
Cheng, X. & Kuang, B. Numerical analysis of heat transfer
in supercritical water cooled flow channels. Nucl. Eng. Des.,
Vol. 237, 240252 (2007)
Deissler, R.G. & Cleveland, O. Heat transfer and fluid
friction for fully developed turbulent flow of Air and
superCritical water with variable fluid properties. Trans
ASME, Vol. 76(1), 7385 (1954)
Dittus, F.W. & Boelter, L.M.K. Heat transfer in automobile
radiators of the tubular type. University of California
Pubilications in English, Berkeley, 2,443461 (1930)
Fluent Inc., Lebanon (2006)
Goldmann, K. Heat transfer to supercritical water at 5000
psi flowing at high mass flow rates through round tubes. Int.
Devel. Heat Trans., Part III, ASME, 561568 (1961)
Hsu, Y.Y & Smith, J.M. The effects to density variation on
heat transfer in the critical region. ASME, J. Heat Trans.,
Vol. 83(2), 176182 (1961)
Jackson, J.D. & Hall, W.B. Turbulent forced convection in
channels and bundles, Hemisphere, New York, Vol. 2, 563
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
(1979)
Yang, J. Oka, Y. Ishiwatari, Y. et al., Numerical
investigation of heat transfer in upward flows of
supercritical water in circular tubes and tight fuel rod
bundles, Nucl. Eng. Des., Vol. 237,420430 (2007)
Kamenetsky, B. & Shitsman, M., Experimental
investigation of turbulent heat transfer to supercritical water
in a tube with circumferentially varying heat flux. In:
Proceeding of the 4th international Heat Transfer conference,
Vol. VI, Paris, Versailles, France. Elsevier publ. Company,
Paper B 8.10(1970)
Kim, S.H. Kim, Y.I. Bae, Y.Y Cho, B.H. Numerical
simulation of the vertical upward flow of water in a heated
tube at supercritical pressure. In: Proc. Of ICAPP04,
Pittsburgh, PA, USA, June 1317 (paper 4047) (2 1 14)
Roelof, F. & Komen, E. CFD analysis of heat transfer to
supercritical water flowing vertically upward in a tube,
Jahrestagung Kerntechnik. May 1012, Murnberg, Germany
(2005)
Schlichting, H. Boundary layer theory. 8th ed., New York:
McGrawHill, 6469 (1979)
Schnurr, N.M. Sastry, VS. Shapiro, A.B. Numerical analysis
of heat transfer to fluids near the thermodynamic critical
point including the thermal entrance region. AMSE, J. Heat
Trans., Vol. 98(4), 609615 (1976)
Shitsman, M.E. Impairment of the heat transmission at
supercritical pressure. Teplofizika Vysokikh Temp., Vol.
1(3), 267275 (1963)
Shitman, M.E. The effect of natural convection on
temperature conditions in horizontal tubes at supercritical
pressures. Therm. Eng., Vol.13 (7), 6975 (1966)
Shitman, M.E. Temperature conditions of evaporative
surfaces at supercritical pressures. Electric. Stations, Vol.
38(2), 2730 (1967)
Tao, W.Q., Numerical Heat Transfer. Xi'an: Xi'an Jiaotong
University Press (2001)
Pioro, I.L. & Dumouchel, T. Hydraulic resistance of fluids
flowing in channels at supercritical pressures (survey). Nucl.
Eng. Des., Vol. 231(2), 197197 (2"114)
Pioro, I.L. & Duffey, R.B. Experimental heat transfer in
supercritical water flowing inside channels (survey), Nucl.
Eng. Des., Vol.235, 240724 t'1 12 i5)
Vikhrev, Y.V Kon'kov, A.S. Solomonov, VM. Sinisyn, I.T.,
Heat transfer in horizontal and inclined steamgenerating
tubes at supercritical pressures. High Temp., Vol. 11(6),
11831185 (1973)
Waston, GB. Lee, R.A. Wiener, M. Critical heat flux in
inclined and vertical smooth and ribbed tubes, Proc. of the
5th Int. Heat Transfer Conference, Vol. 4, 275279 (1974)
Wong, Y.L. Groeneveld, D.C. Cheng, S.C., CHF prediction
for horizontal tubes, Int. J. Multiphase Flow, Vol. 16,
123138 (1990)
Yamagata, K. Nishikawa, K. Hasegawa, S. et al., Forced
convection heat transfer to supercritical water flowing in
tubes. Int. J. Heat Mass Transfer, Vol. 15(12), 25752593
(1972)
