Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Pressure Drop and Heat Transfer to Turbulent Flow of Supercritical Pressure Water in a
VerticalUpward HelicallyCoiled Tube
YuFei Mao, LieJin Guo and BoFeng Bai
State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University
Xi'an, Shaanxi 710049, China
yfmao @stu.xjtu.edu.cn
Keywords: pressure drop, heat transfer, supercritical pressure, helical tube
Abstract
The frictional pressure drop and convective heat transfer characteristics of water at supercritical pressures were experimentally
studied in a verticalupward helical coiled tube, which was constructed of a 10mm ID stainless steel tube with 300mm coil
diameter and 50mm pitch. The experiments were performed in a range of system pressure 23.526.5 MPa, mass velocity
8001600 kgm2s1 and wall heat flux 100400 kWm2. The effects of various control variables on the frictional pressure drop
and convective heat transfer were systematically investigated. It was found that heat transfer in the helical tube resembles the
way heat transfer in the straight tube for supercritical fluid flows in present experimental parameter ranges. Based on the
experimental data, a correlation for the calculation of the forced convection heat transfer coefficient of water at supercritical
pressures in helical coils was proposed.
Nomenclature
cp isobaric specific heat capacity, Jkg K1
D coil diameter of the test section, m
d inner diameter of the test section, m
f Darcy friction factor
G mass velocity, kgm2s1
H specific enthalpy, Jkg1
h heat transfer coefficient, Wm2K1
L length of tube, m
Nu Nusselt number
P pressure, Pa
Pr Prandtl number
q heat flux, Wm2
Re Reynolds number
T temperature, K
Greek letters
AP total pressure drop, Pa
APf frictional pressure drop, Pa
APg pressure drop due to gravity, Pa
A thermal conductivity, Wm'1 K1
p dynamic viscosity, Nsm2
p density, kgm3
Subscripts
b bulk condition
c coil condition
w wall condition
Introduction
fluids flowing in channels has been a topic of important
fundamental engineering interests during the past decades.
For example, the development of the supercritical pressure
boiler requires a good knowledge of flow and heat transfer
of supercritical water over a wide range of operating
conditions. The recent developments in supercritical fluid
technologies, e.g., the supercritical watercooled reactor
(SCWR), the supercritical water oxidation (SCWO) for
organic waste disposal, and the supercritical water
gasification (SCWG) of biomass for hydrogen production,
necessitates revisiting the problem.
The peculiarity of the heat transfer to the supercritical fluid
flow is primarily attributed to the great variation of the fluid
physical properties in the critical and pseudocritical region.
There is considerable amount of work reported in the open
literature on fluid flow and heat transfer at supercritical
pressures. Recent surveys on experiments for supercritical
fluid flow and heat transfer by Pioro & Duffey (21 1'4, 2005)
show that most of the former experimental studies were
performed in straight pipes, while the research on flow and
heat transfer to supercritical fluids in curved or helical pipes,
which is of wide applications in power generation systems
and reactor facilities, is relatively sparse.
In the present study, experiments were carried out to
investigate the frictional pressure drop and heat transfer
characteristics to turbulent flow of water flowing upward in
a vertical helically coiled tube at supercritical pressures. The
main focus of the work is on enhanced heat transfer, which
is the most dominant mode of heat transfer in the pseudo
critical region and usually occurs at low or moderate heat
fluxes with relatively high mass flow rates.
Turbulent flow and heat transfer to supercritical pressure
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Plunger pump L mJ
Orifice flowmeters
Figure 1: Schematic diagram of the test loop.
No. I No. I
Inner sid c
Helix axis
No.12~No.l3
 Outerside
Pressure Iransducer
Differential pressure transducer
Armored thermocouple
V Welded Ihermocouple
Helix axis
S 3600 mm L1 3600 mm 1 2500 mmr
12000 mm
Figure 2: Schematic diagram of the test section.
Experimental System and Method
A supercritical pressure water test loop for present study is
schematically illustrated in Figure 1. Its maximum test
pressure is 42 MPa and the maximum circulating flow rate is
4000 kgh'. It mainly consists of a water tank to provide
water for heating, a highpressure plunger pump to supply
power for the fluid flow, a series of orifice flowmeters to
measure water mass flow rate, a regenerative heat exchanger
and three preheaters together to raise the water temperature
before water enters the test section, a test section to
investigate the pressure drop and heat transfer, and a
watercooled condenser to cool the hightemperature
working fluid. The preheaters are all electrically heated by
running AC current through the tube walls. The total
electrical power delivered to the preheaters is 460 kW.
The test section is made of a 12 m long seamless stainless
steel tube with the inner diameter d of 10 mm, the outer
diameter of 14 mm, the coil diameter D of 300 mm, and the
pitch of 50 mm. As is shown in Figure 2, this test section is
mainly divided into two parts: one is an electrically heated
section for heat transfer experiments with the length of 7.2 m,
the electrical power delivered to which is 100 kW; the other
is a unheated section for pressure drop experiments with the
length of 2.5 m. The heated section is preceded by another
unheated section to eliminate the effect of the entry
conditions. The test section is well insulated thermally from
the atmosphere to minimize heat loss to the environment.
The boundary condition of uniform heat flux is assumed to
the heated section, and the unheated parts of the test section
are assumed isothermal.
Four armored Ktype thermocouples of 3 mm diameter were
installed into the core of tube to measure the bulk
temperature of the fluid at inlet, middle and outlet of test
section. A total of 60 Ktype thermocouples of 0.5 mm
diameter was welded to the outside surface of the test section
at 13 thermocouple stations to measure the wall temperature.
There were four thermocouples at the stations of No.1No. 11
and eight thermocouples at the stations of No.12No.13. The
first station was located at 600 mm from inlet of heated
section, the seventh station was located at 600 mm from
middle of heated section, and the last station was located at
100 mm from outlet of heat section. The distance between
the adjacent stations of No.lNo.6 and No.7No.12 is 500
mm. The location of thermocouples around the tube
crosssection is shown in Figure 2. The uncertainty in bulk
and wall temperatures measured by thermocouples was about
+0.5%.
The absolute pressures in the test section were measured by
Paper No
Paper No
three ST3000 Series pressure transducers with the range of
040 MPa. The pressure drop of the pressuredrop test
section was measured using two calibrated differential
pressure transducer of ST3000 Series with the range of
099.6 kPa and the range of 0686 kPa. The estimated
accuracy of the pressure and the pressure drop measurements
was about +0.5% and 1%, respectively. The mass flow of
the working fluid through the test section was measured by
three orifice flowmeters in different ranges attached to three
ST3000 Series differential pressure transducers with the
range of 099.6 kPa. These orifice flow meters were
calibrated with the weighting method and the uncertainty was
estimated to be less than 3%. The total electrical power
supplied to the test section and the preheaters was calculated
from the measured voltage and current through the section
respectively, and the estimated uncertainty was 3.25%.
All of the signals of the system pressure, mass flow,
temperature of the tube wall and the bulk fluid, and the input
heating powers of test section and preheaters were monitored
and recorded via an IMP (isolated measurement pod) data
acquisition system for future processing.
The bulk fluid temperature at each thermocouple station was
determined according to the fluid enthalpy at that station,
which was calculated from the known inlet, middle or outlet
bulk enthalpy (whichever was further away from the
pseudocritical point), the electrical heat input to that station
and the mass velocity. The inside wall temperature was
estimated from the measured outside wall temperature by
applying the space marching method for inverse heat
conduction problems (Taler & Zima 1999). The thermo
physical properties of supercritical pressure water were
obtained from the source code of the IAPWS95 formulation
(Wagner & PruB 2002).
The pressure drop test section is unheated and assumed to be
isothermal. Hence, the pressure drop due to flow acceleration
could be neglected, and the experimental frictional pressure
drop APf is calculated according to the following expression:
AP, = AP AP (1)
where, APf is the total pressure drop and APg is the pressure
drop due to gravity.
In present study, only the circumferential average heat
transfer coefficients were considered. The circumferential
average heat transfer coefficient at the position z along the
tube is defined as
h= q/ Tb) (2)
where w is the crosssectional average inner wall
temperature of tube at the position z.
The present experiments were carried out in a range of
system pressure P=23.526.5 MPa, mass velocity G=800
1600 kgm2s1', wall heat flux qw=100400 kWm2, and bulk
fluid enthalpy Hb=8002900 kJkg'.
Results and Discussion
To check the suitability and reliability of present
experimental system and method, experiments were firstly
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
carried out for the singlephase incompressible pipe flows in
a range of pressure from 8 to 15 MPa and Reynolds number
from 4x104 to 105. The experimental data were compared
with the prediction of the recommended correlations
respectively for frictional pressure drop by White (1932) and
convective heat transfer by Rogers (1964) which are as
follows:
the White correlation
f, =0.32Re 25 +0.048d/D, Re = 1.5 x104 105 (3)
the Rogers correlation
Nub = 0.023 Re 85Pr 04 (d/D) 1, Re = 104 105 (4)
OU .
0.05
0.04
0.03
0.02
0.01 L
20000
40000 60000 80000 100000 120000
Re
(a) frictional pressure drop
200 
1(1(1 I 1 I
30000 50000 70000 90000 110000
Re
(b) convective heat transfer
Figure 3: Experimental results of the check test for
incompressible pipe flow.
The comparison results are shown in Figure 3. A total of 96
pressure drop experimental data was compared with the
White correlation, and the average relative deviation was
6.45%. A total of 88 heat transfer experimental data was
compared with the Rogers correlation, and the average
relative deviation was 4.12%. The good agreement between
the experimental data and the classical correlations
confirmed the reliability and validity of the measurements
and data reduction method in present study.
The Darcy equation is a theoretical equation which predicts
the frictional pressure drop of singlephase pipe flows and
can be expressed as
L G2
APf = f (5)
d 2p,b
o Present experimental data
 Prediction by White correlation
(a)
0 (
(a)
C Present experimental data
 Prediction b' Rogers correlation
l0
Paper No
It can be seen from Eq. (5) that the frictional pressure drop is
some function of the friction factor and the bulk density
when the tube length, tube diameter and mass velocity are
constant. For a helical coiled tube, the friction factor is
determined by the Reynolds number (Re=Gd/p), the coil
curvature and the relative roughness of the inside wall of
tube. The effect of the relative roughness is growing with the
increasing Reynolds number. When the Reynolds number is
large enough, the variation in friction factor will be very
small.
The experimental results of frictional pressure drop at
supercritical pressures are shown in Figure 4. It is found that
the pressure drop increases as the bulk enthalpy increases
especially in the high enthalpy region (where the bulk
Reynolds numbers are very high), which is due to that the
fluid density decreases with the increasing enthalpy (or
temperature) at supercritical pressures. The pressure drop
also increases as the mass velocity is increased, which is
similar to that of the constantproperty pipe flows. The effect
of the system pressure on pressure drop is opposite to that of
the mass velocity. With increasing pressure, the fluid density
increases, and hence the pressure drop decreases.
100
80
60
40
20
0
5
60
50
40
o
". 30
20
10
00 100( 1500 2000
H,/ kJkg'
(a) effect of mass velocity
1000 1500 2000
H / kJkg'
2500 3000
2500 3000
(b) effect of system pressure
Figure 4: Frictional pressure drop vs. bulk enthalpy.
The effects of various control variables, including system
pressure, mass velocity and wall heat flux, on forced
convection heat transfer of supercritical pressure water in the
helical tube were systematically investigated. The
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
experimental heat transfer coefficients are shown against
bulk enthalpy in Figure 5, Figure 6 and Figure 7, respectively.
As can be seen from these figures, the heat transfer
coefficient is remarkably increased in the pseudocritical
region and has a maximum value in the vicinity of the
pseudocritical point (at which the isobaric specific heat
attains a maximum value).
Figure 5 shows the effect of system pressure on heat transfer.
The heat transfer coefficient in the pseudocritical region
(especially near the pseudocritical point) is increasing as the
pressure is getting closer to the critical pressure. The
variation of heat transfer coefficient with pressure and bulk
temperature (or enthalpy) resembles the way that isobaric
specific heat varies with pressure and temperature (or
enthalpy).
90
80
70
t 60
E 50
40
4
30
20
10
600
G=1200 kgmis"' p
q =200 kWin 
SP =24 MPa
* P=26 MPa
S I I I I A
SA 4 2
900 1200 1500 1800 2100 2400 2700 3000
H,./kJ'kg'
Figure 5: Effect of system pressure on heat transfer.
According to Figure 6, the effect of mass velocity on heat
transfer for variableproperty flows at supercritical pressures
is similar to that which occurs for constantproperty flows.
The higher the mass velocity, the stronger the convection,
and hence the higher the heat transfer coefficient.
Figure 7 shows the effect of heat flux on heat transfer. With
increasing heat flux, the temperature difference between wall
and bulk increases. However, for supercritical fluid flows, it
was observed that the growth of the temperature difference is
greater than the increase of heat flux. Therefore, the heat
transfer coefficient decreases as the heat flux is increased.
The present experimental data performed in the helical tube
(P=24 MPa, G=1200 kgm2.s, q,=400 kWm2, d=10 mm)
were compared with the former experimental data performed
in the straight tube by Yamagata (1972) (P=24.5 MPa,
G=1200 kgm2.s1, q,=465 kWm2, d=10 mm) and by Xu
t1""41) (P=23 and 25 MPa, G=1200 kgm2s 1, q,=400
kWm 2, d=12 mm). The comparison results are shown in
Figure 8. It is found that, for supercritical fluid flows with
low or moderate heat fluxes and with relatively high mass
velocities, in the pseudocritical region, the heat transfer
coefficients of the helical tube are quite close to those of the
straight tube at the same flow conditions, which means the
contribution of the secondary flow in helical coils to heat
transfer is suppressed compared to that of the property
variation.
P =24 MPa v7
*( = KOO ,kgm's'.s
.
7 Av
:.(12(H a kg
*V .
*A A
, o : ;
; =1200 kgms' a
c P=24 MPa a0 9
A P=26 MPa o ,
S 0
O ? ,"" ," "
 0
.." A W
.. (b)
Paper No
80(
70
60
li 5(1
SE
40
S 30
20
10
 G = 800 kgm' s'' (a)
A G =1200 kgm s
v G =1600kgm s v
1' =24 MPa
q,=200 kWm A
at
l l l
)0 900 1200 1500 1800 2100 2400 2700 3000
H,,/ kJkg
SG(=1200 kgms' (b)
SA G =1600 kgm s A
A A
A A,&,
P=24MPa A A
q =400 kWm' AA
A tCW t
1200 1500 18K00 2100 2400 2700 3000
H,/ kJ kg'
Figure 6: Effect of mass velocity on heat transfer.
90
80 0 q (=200 kWm qp (a)
70 A q =400 kWm
o 60 =24 MPa
S50 (G =1200 kgm s'' 0
40 0 4
40
30 A^t L
20 
10
1) 'I 12
600 900 1200 1500 1800 2100 2400 2700 3000
H / kJ.kg'
140
0 q =200 kWm" O (b)
120 6
A q =400 kWm s
100 o
P =24 MPa
E 80 G =1600 kgm "s aL 0 A
" 60
It E
40
20 t o b 1A
0
800 1200 1600 2000 2400 2800
H ,/kJ'kg'
Figure 7: Effect of wall heat flux on heat transfer.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
60
0 Helical tube (a)
P=24 MPa
50 
G =1200kgms'
q =400( kW m'n i
40 A !
&, Straight tube ** A'
P=24.5 MPa
30 =1200 kgmnts 's
20 =465 kWm"' '" N
10
900 1200 1500 1800 2100 2400 2700 3000
H,/ kJ kg'
(a) with the experimental data by Yamagata (1972)
60 r
50
40
30
'4
20
10
900 1200 1500 1800 2100 2400 2700 3000
H, / kJkg"
(b) with the experimental data by Xu (2i" '11
Figure 8: Comparison of present experimental data with
former experimental data performed in straight tubes.
Based on a total of 615 experimental data points, a
correlation for the calculation of the convective heat transfer
coefficients of supercritical pressure water flowing in the
helical coiled tube was obtained as follows:
0480632 (p /pb ) 0 851
Nub = 0.0161Re 848 Prb p1 (6)
where
Prb = / = b Z =(H Hb )/(T T,) (7)
The comparison between the prediction by Eq. (6) and the
present experiment data is shown in Figure 9. Most of the
predicted results are within a deviation of +20% and the
average relative deviation is 9.78%.
3000 1 ..
0 500 1000 1500 2000 2500 3000
Nit
Figure 9: Comparison of the prediction by Equation (6)
with the experimental data.
Paper No
Conclusions
Pressure drop and heat transfer experiments have been
performed on supercritical pressure water flowing in a helical
coiled tube. The results are basically consistent with those of
previous work carried out in straight tubes. Differences in
pressure drop and heat transfer between supercritical pipe
flow and incompressible pipe flow are related to the
significant variations in thermophysical properties of fluid
in the pseudocritical region.
Frictional pressure drop of the supercritical fluid flow
increases with the increasing bulk enthalpy and with the
decreasing system pressure. Heat transfer in the
pseudocritical region is greatly enhanced due to the property
variation. The heat transfer coefficient has a maximum in the
vicinity of the pseudocritical point, and the maximum
progressively decreases as system pressure or wall heat flux
is increased. The effect of mass velocity on pressure drop and
heat transfer for variableproperty pipe flows at supercritical
pressures is similar to that which occurs for incompressible
pipe flows. With increasing mass velocity, the frictional
pressure drop and heat transfer coefficient are all increased.
For supercritical fluid flows with low or moderate heat fluxes
and with relatively high mass velocities, in the pseudocritical
region, the contribution of the secondary flow in helical coils
to heat transfer is suppressed compared to that of the
property variation.
A turbulent forced convection heat transfer correlation of
supercritical pressure water flowing in the helical tube is
obtained without considering the effect of the coil curvature.
More experiments in a wider parameter ranges are needed for
developing better correlations for estimating the pressure
drop and heat transfer of supercritical fluids flowing in
helical coils.
Acknowledgements
This work was financially supported by the National Natural
Science Foundation of China for Creative Research Groups
(Grant No. 50821604).
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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