J. of Supercritical Fluids 70 (2012) 75–89
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The Journal of Supercritical Fluids
journal homepage: www.elsevier.com/locate/supflu
Flow and heat transfer characteristics of r22 and ethanol at supercritical
pressures
Pei-Xue Jiang a,∗ , Chen-Ru Zhao a,b , Bo Liu a
a
Beijing Key Laboratory of CO2 Utilization and Reduction Technology/Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal
Engineering, Tsinghua University, Beijing 100084, China
b
Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history:
Received 21 December 2011
Received in revised form 20 June 2012
Accepted 20 June 2012
Keywords:
Supercritical pressures
R22
Ethanol
Frictional pressure drop
Convection heat transfer
a b s t r a c t
This paper presents an experimental investigation of the flow and convection heat transfer characteristics
of R22 and ethanol at supercritical pressures in a vertical small tube with an inner diameter of 1.004 mm.
The heat flux ranges from 1.1 × 105 W m−2 to 1.8 × 106 W m−2 , the fluid inlet Reynolds number ranges
from 3.5 × 103 to 2.4 × 104 , and the pressure ranges from 5.5 MPa to 10 MPa. The results show that for
supercritical R22, the frictional pressure drop increases significantly with the heat flux. At p = 5.5 MPa,
Rein = 12,000 and a heat flux of 106 W m−2 , the local heat transfer is greatly reduced due to the low density
fluid near the high temperature wall. Both buoyancy and flow acceleration have little effect on the heat
transfer. For supercritical ethanol, the frictional pressure drop variation with the heat flux is insignificant,
while the local heat transfer coefficient increases as the enthalpy increases. Ethanol gives better flow and
heat transfer performance than R22 at supercritical pressures from 7.3 MPa to 10 MPa for heat fluxes of
1.1 × 105 –1.8 × 106 W m−2 .
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
The third fluid cooling technology is developed to protect the
high heat flux surface in combustion chamber in liquid rocket
engines. In the third fluid cooling system, the third fluid besides the
oxidizer and the fuel, which are referred as propellant, is introduced
as the coolant and circulated to cool the nozzle and combustor
assembly. The third fluid is contained in a closed-loop cycle with
the high temperature combustor wall as the heat source and the
low temperature fuel as the cold sink [1]. The coolant is circulated
by a turbine-driven coolant pump through the passage formed by a
jacket enclosing the nozzle and combustor assembly with high heat
flux from the combustor absorbed by the coolant, and then fed into
the turbine to produce work by expansion for driving the oxidizer
pump, coolant pump and fuel pump. Afterwards the coolant vapor
condenses in a heat exchanger to heat the fuel or oxidizer or both;
thereby returning the heat from the combustor to the propellant
fed into the combustion chamber. In the third fluid cooled liquid
rocket engine, since the coolant is circulated outside the chamber,
the turbine outlet pressure is reduced and much higher turbine
expansion ratios can be obtained. Moreover, all of the propellant is
∗ Corresponding author. Tel.: +86 10 62772661; fax: +86 10 62770209.
E-mail address: [email protected] (P.-X. Jiang).
0896-8446/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.supflu.2012.06.011
fed to the combustor which can operate at higher pressures; thus,
the output thrust is increased.
During the heat absorbing process in the jacket enclosing the
nozzle and combustor assembly, the coolant (the third fluid) is
usually above its critical pressure, while during the heat rejection process the coolant (the third fluid) heats the propellant at
sub-critical pressures and condenses. R22 and ethanol have been
suggested as working fluids for third fluid cooling cycles in view of
their thermophysical properties, heat transfer and flow resistance
properties, critical parameters and safety. When the fluids are at
supercritical pressures such as when absorbing heat from the nozzle and combustor assembly, small fluid temperature and pressure
variations can result in drastic changes in the thermophysical properties as shown in Fig. 1 [2]. The specific heat, cp , reaches a peak at a
certain temperature defined as the pseudo critical temperature, Tpc .
Other properties including the density, thermal conductivity and
viscosity also vary significantly within a small temperature range
near Tpc . The flow resistance and heat transfer are then expected to
exhibit many special features due to the significant property variations and the consequent buoyancy and flow acceleration effects
[3].
In addition to the third fluid cooling systems, flow and convection heat transfer of supercritical fluids also occur in many other
industrial applications including aerospace engineering, power
engineering, chemical engineering, enhanced geothermal systems,
CO2 storage and cryogenic and refrigeration engineering. For
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P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
210
T pc
Subscripts
ad
adiabatic section
f
fluid
inner surface
i
in
inlet
o
outer surface
out
outlet
pseudo critical
pc
p
induced by pressure variation
T
induced by temperature variation
w
wall
instance, platelet transpiration cooling uses hydrogen or methane
at supercritical pressures flowing through chemically etched
coolant micron scale channels in the platelet formed by bonding
together thin metal sheets to protect high heat flux surfaces such
as rocket thruster walls [4]. In power engineering applications,
supercritical pressure water is widely used as the working fluid in
thermal power stations. In the supercritical pressure water-cooled
reactor (SPWR), the supercritical pressure water absorbs fission
heat from the fuel assembly in the reactor core and enters the
turbine at high temperature and high pressure, which enhances
the thermal power cycle efficiency. Supercritical pressure water
is also being actively considered as the coolant for the breeder
blanket in fusion power plants [5].
Comprehensive researches on the in-tube flow and convection
heat transfer of supercritical fluids have been conducted in the
past several decades by Petukhov [3], Domin [6], Protopopov [7],
Polyakov [8], Shitsman [9], Bourke et al. [10], Hall [11], Jackson
and Hall [12,13], Bringer and Smith [14], Schnurr [15], Tanaka et al.
[16], Shiralkar and Griffith [17] for applications of supercritical fluids in various industrial fields. The working fluids have mostly been
150
ρ
120
90
ρ/10, c
p
×
6
p = 7 MPa
p =10 MPa
cp
60
λ
30
0
μ
0
30
60
90
120
150
180
210
240
270
o
T/ C
(a) R22 (pc=4.99 MPa, Tc=96.2 ºC )
180
6
5, μ/20× 10 , λ× 10
3
λ
150
p = 7 MPa
p =10 MPa
120
ρ
90
60
×
Greek symbols
˛p
thermal expansion coefficient [K−1 ]
isothermal compression coefficient [Pa−1 ]
ˇT
ı
tube wall thickness [m]
thermal conductivity [W m−1 K−1 ]
molecular viscosity [Pa s]
fluid density [kg m−3 ] or electrical resistivity [ m]
T pc
180
p
non-dimensional buoyancy parameter
specific heat at constant pressure [kJ kg−1 K−1 ]
tube diameter [m]
gravitational acceleration [m s−2 ]
mass flux [kg m−2 s−1 ]
Grashof number
local heat transfer coefficient [W m−2 K−1 ]
turbulence kinetic energy [m2 s−2 ]
heating current [A]
bulk specific enthalpy [J kg−1 ]
non-dimensional flow acceleration parameter
pressure [MPa]
Prandtl number
heat quantity [W]
heat flux [W m−2 ]
inner radius of small tube [m]
distance from the axis [m]
Reynolds number
temperature [◦ C]
velocity [m s−1 ]
axial coordinate [m]
ρ/5, c
Bo*
cp
d
g
G
Gr*
hx
k
I
i
Kv
p
Pr
Q
q
R
r
Re
T
u
x
50, μ/2× 10 , λ× 10
3
Nomenclature
30
0
cp
μ
0
40
80
120
160
200
Tpc
Tpc
240
280
320
o
T/ C
(b) Ethanol (pc=6.15 MPa, Tc=240.8 ºC )
Fig. 1. Thermophysical property variations with temperature.
water and carbon dioxide. These results have provided significant
insight into the special features of the in-tube flow and convection heat transfer of supercritical fluids. Several correlations have
been developed for the pressure drop and heat transfer coefficient
of supercritical pressure fluids during heating based on the experimental and theoretical results.
Tarasova and Leont’ev [18] measured the flow resistance of
supercritical water flowing through 3.34 mm and 8.03 mm smooth
vertical tubes during heating and found that the measured results
were lower than the values of those without heating near the critical point due to the viscosity decrease. Razumovskiy [19] claimed
that the pressure drop resulting from the density variation could
not be ignored for large ratios of the heat flux to the mass flux based
on their studies of supercritical water flowing through a 6.28 mm
smooth vertical tube during heating.
For the heat transfer, Shitsman [9] found that, for relatively large
tubes (din = 8 mm for example), the local wall temperatures varied non-linearly and local heat transfer deterioration was observed
in buoyancy-aided flow cases (upward flow in a heated passage)
resulting from the buoyancy effect whereas in buoyancy-opposed
flow cases (downward flow in a heated passage) the local wall
temperature varied smoothly. Jackson and Hall [12] explained the
in-tube buoyancy affected convection heat transfer behavior for
supercritical fluids using a semi-empirical theory and proposed a
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
77
Fig. 2. Schematic of experimental system.
non-dimensional buoyancy parameter, Bo*, to evaluate the significance of the buoyancy effect [13]. This semi-empirical theory had
agreed fairly well with most of the buoyancy affected experimental
results in the literature [20].
When the tube size is reduced and the heat flux is increased
further, flow acceleration is expected to occur due to the extreme
axial temperature and pressure variations. Jackson [5] discussed
the effects of the heat flux on forced convection heat transfer of fluids at supercritical pressures. With the fluid temperature increases
or the pressure decreases along the tube, the density decreases and
the fluid accelerates, which reduces the turbulence production and
the heat transfer. When the heat flux is low, the effect is small, but at
very high heat fluxes, the turbulence could be significantly reduced
and the flow may even re-laminarise. This effect dominates in high
heat flux flows and results in overall heat transfer deterioration.
McEligot et al. [21] proposed the non-dimensional heating acceleration parameter, Kv, to assess the flow acceleration effect due to
thermal expansion.
Kurganov et al. [22] pointed out that unlike the buoyancy effect,
the flow acceleration effect is important only in small diameter
tubes. For large diameter tubes the buoyancy effect is the main
factor, for moderate diameter tubes the flow acceleration effect can
also be ignored if the buoyancy effect can be ignored, while for small
diameter tubes, the flow acceleration effect can be very important.
Li et al. [23] investigated the convection heat transfer of CO2
at supercritical pressures in a 2 mm diameter vertical small tube
and showed that for Rein = 9 × 103 , when the heat flux was higher
than 3 × 104 W m−2 , local heat transfer deterioration was observed
in the upward flows, whereas no such behavior appeared in the
downward flows, which indicated that the buoyancy effect strongly
influenced the heat transfer. The flow acceleration due to heating was insignificant. Jiang et al. [24,25] studied the heat transfer
of supercritical CO2 in a 0.27 mm diameter vertical mini tube and
showed that when the inlet Reynolds numbers exceeded 4 × 103 ,
the buoyancy and flow acceleration had little influence on the
local wall temperature, with no heat transfer reduction observed in
either flow direction. However for relatively low Reynolds numbers
(<2.9 × 103 ) and high heat fluxes (1.13 × 105 W m−2 for example),
the local wall temperatures varied non-linearly along the tube in
both upward and downward flows, with the convection heat transfer coefficients in downward flows higher than those in upward
flows. The experimental results indicated that for 0.27 mm tubes,
the flow acceleration due to heating strongly influenced the turbulence and reduced the heat transfer for high heat fluxes. The
buoyancy effect still could not be neglected although relatively
small even with strong heating.
For supercritical fluids flowing through 1 mm channels at heat
fluxes up to 106 W m−2 , such as when R22 or ethanol are used to
cool the high heat flux surface in the liquid rocket engine combustion chamber, the radial and axial temperature gradients are
extremely large. The flow and heat transfer are expected to be more
significantly affected by the severe temperature variations, with
strong buoyancy and flow acceleration effect possibly be induced
by the radial and axial density variations.
This paper presents an experimental investigation of the flow
and convection heat transfer of R22 and ethanol at supercritical
pressures in a vertical tube with an inner diameter of 1.004 mm
for various pressures, heat fluxes, and mass fluxes. The effects of
the thermophysical property variations, buoyancy and flow acceleration are evaluated and discussed. The flow and heat transfer
characteristics of R22 and ethanol are compared. The results are
helpful to obtaining a better understanding of the heat transfer
characteristics of supercritical fluids in small tubes at high heat
fluxes with large temperature differences between the fluid and the
wall. The results are also of great help when developing empirical
correlations for the flow and heat transfer with severe radial thermophysical property variations in the cooling passage for designing
and optimizing the third fluid cooling systems.
2. Experimental system and data reduction
2.1. Experimental apparatus
The experimental system is illustrated in Fig. 2. The working
fluid (R22 or ethanol) flows from the container to an accumulator and then through a filter before it is pressurized by the
supercritical fluid pump (Thar P-350) and heated in the pre-heater
to the required inlet temperature. A manostat is installed after
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P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
2.2. Data reduction method
2.2.1. Frictional pressure drop
The pressure drop measured in the experiments, p, includes
the pressure drop in the inlet and outlet adiabatic sections, pad,in
and pad,out , the frictional pressure drop in the heating section, pf ,
and the pressure drop resulting from the fluid expansion along the
test section during heating, pa [26].
p = pf + pad,in + pad,out + pa
(2)
The pressure drops in the inlet and outlet adiabatic sections are
calculated as:
pad,in = f0,in
pout = f0,out
Fig. 3. SEM photograph of the test section.
the pump to stabilize the system pressure and mass flow rate.
The mass flow rate is measured by the mass flowmeter (Model
MASS2100/MASS6000, MASSFLO, Danfoss). The fluid is heated in
the test section by Joule heating from a current stabilized power
source, and cooled by the sub-cooler after leaving the test section.
A decompression valve is installed to adjust and stabilize the system pressures. Then the fluid flows back to the supercritical pump.
The pump head of the supercritical pump is cooled by a cooling
bath.
The test section is a vertical smooth stainless steel 1Cr18Ni9Ti
tube. The length of the heating section is 152 mm, and the length
of the adiabatic section before and after the heating section is both
52 mm. An SEM photograph of the tube cross section is shown in
Fig. 3. The test section is connected to the test loop by flanges and
high-pressure fittings. The inner tube diameter is 1.004 mm and the
outer diameter is 2.011 mm. The test section is insulated thermally
and electrically from the test loop by a layer of polytetrafluoethylene (PTFE) placed between the flanges and between the screws
and the flanges. The flow direction (upward or downward) of the
fluid flowing through the test section is switched by a set of valves.
Mixers are installed before the points where the inlet and outlet
fluid temperatures are measured by accurate RTDs (Pt-100). The
inlet pressure is measured by a pressure transducer (EJA430A) and
the pressure drop between the inlet and outlet is measured by a
differential pressure transducer (Model EJA130A). The local outer
wall temperatures of the heating section are measured using 15
equally spaced K-type thermocouples welded onto the outer tube
surface. The local heat flux is calculated from the heating current
and the electrical resistance of the tube. The electrical resistivity
variation with temperature is experimentally measured. The test
section is first evacuated by vacuum-pumping, and then heated by a
constant current until the wall temperature and the heating voltage
across the test section are steady. Then the electrical resistance, ,
at the measured wall temperature is calculated as:
=
(U/I) × ((do2 − di2 )/4)
L
(1)
The system is assumed to be steady when the wall temperature
and the inlet and outlet fluid temperature variations are all within
±0.2 ◦ C and the flow rate and inlet pressure variations are within
±0.2% for at least 10 min. A correlation is then established to correlate the electrical resistivity to temperatures for temperatures of
20–300 ◦ C.
G2 Lin
2in d
(3)
G2 Lout
2out d
where Lin and Lout are the lengths of the adiabatic inlet and outlet
sections, in and out are the densities based on the inlet and outlet
bulk temperatures, G is the mass flux, and the friction factors for
the inlet and outlet adiabatic sections, f0,in and f0,out , are calculated
using Finolenko equation [27]:
f0,in = (1.82log Rein − 1.64)−2
(4)
f0,out = (1.82log Reout − 1.64)−2
where Rein and Reout are based on the fluid inlet and outlet average
velocities and properties respectively. The inlet and outlet average
velocities are calculated from the mass flux and the local densities;
the local properties are determined by the local bulk temperatures.
The pressure drop resulting from the fluid expansion along the
test section during heating is calculated as [26]:
pa = G2
1
out
−
1
in
(5)
Thus, the frictional pressure drop through the heating section is
calculated as:
pf = p − pad,in − pad,out − pa
(6)
2.2.2. Heat transfer coefficient
The local heat transfer coefficient, hx , at each axial location is
calculated as
hx =
qw (x)
Tw,i (x) − Tf (x)
(7)
The local heat flux on the inner surface, qw (x), is calculated as:
I 2 (t)x/ (do2 − di2 )/4 − Qloss,x
I 2 Rx (t) − Qloss,x
=
qw (x) =
di x
di x
(8)
The test section heat loss, Qloss,x , is determined from the temperature difference between the tube wall and the surroundings
by a correlation, which is obtained by polynomial fitting the experimentally measured heat loss (which is assumed to be equal to
the electrical power input to the tube when evacuated by vacuumpumping) and the temperature difference between the tube wall
and the surroundings.
The local bulk fluid temperature, Tf (x), is obtained using the NIST
software REFPROP 8.0 [2] and the local bulk fluid enthalpy, ib (x),
calculated as:
ib (x) = ib,in +
qw (x)di x
G
(9)
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
The Reynolds number based on the mean bulk temperature is
defined as:
udi
(10)
The inner wall temperature, Tw,i (x), is calculated using the measured outer wall temperature, Tw,o (x), and the internal heat source,
qv , as:
Tw,i (x) = Tw,o (x) +
qv (x) 2 di
qv (x) 2
d ln
do − di2 +
16
8 o
do
I 2 Rx (t) − Qs,x
(do2 − di2 )/4 x
Working fluids
R22, ethanol
Inner tube diameter (mm)
Inlet pressures (MPa)
Heat fluxes (W m−2 )
Fluid temperatures (◦ C)
Fluid inlet Reynolds numbers
1.004
5.5–10
1.1 × 105 –1.8 × 106
25–200
3.5 × 103 –2.4 × 104
3. Experimental results and discussion
(11)
where qv is calculated as:
qv (x) =
Table 1
Test conditions.
(12)
2.3. Experimental uncertainty analysis
The experimental uncertainty in the local heat transfer coefficient mainly results from the heat flux and the temperature
measurement uncertainties. The thermocouples and the RTDs are
calibrated by the National Institute of Metrology, PR China before
installation. The accuracy of the RTDs used to measure the inlet and
outlet bulk temperatures is ±0.1 ◦ C; the maximum uncertainty of
the K-type thermocouples used to measure the outer wall temperature is ±1.2 ◦ C within the temperature range used in the present
study. The average temperature difference between the wall and
the fluid is greater than 10 ◦ C. The uncertainty of the temperature
difference is evaluated to be 12.1%.
The overall uncertainty of the heat flux is mainly related to the
accuracy of the heat input to the fluid, which is determined by the
heating electric current and the voltage, the heating area, and the
heat loss. The accuracy of the heating electric current and voltage
are 1.1% and 0.28% respectively; the accuracy of the heating area
is 0.3%, which is mainly determined by the heating section length
measured by vernier caliper with accuracy of ±0.02 mm (the tube
diameter is measured by SEM, and the uncertainty is negligible)
and the uncertainty induced when welding the heating electrodes,
which is about ±0.5 mm; the heat loss is less than 4%, which is
assumed to be the heat loss uncertainty. Therefore, the overall
uncertainty of the heat flux is estimated to be 4.2%. The overall
uncertainty of the heat transfer coefficient 12.8% is then calculated
from the uncertainty of the temperature difference, 12.1%, and the
heat flux, 4.2%.
The pressure transducer (Model EJA430A) accuracy is 0.075%
of the full range of 25 MPa, thus, the measurement uncertainty
is 18.8 kPa. The minimum inlet pressure in the present cases is
5.5 MPa, therefore, the uncertainty in the inlet pressure is estimated
to be 0.3%. The accuracy of the differential pressure transducer
(Model EJA130A) is 0.075% of the full range of 125 kPa, thus, the
measurement uncertainty is 0.094 kPa. The minimum pressure
drop in the present cases is 5 kPa, therefore, the uncertainty in the
pressure drop is estimated to be 1.9%. According to the instruction of the mass flowmeter, the mass flow rate uncertainty is 0.1%
within 5–100% of the mass flowmeter full range of 25 kg h−1 , which
is 1.25–25 kg h−1 . Since the mass flow rate ranges from 5.5 kg h−1 to
11.7 kg h−1 , the mass flow rate uncertainty is estimated to be 0.1%
in the present cases.
The uncertainty of the frictional factor calculated from the frictional pressure drop mainly results from the uncertainties of the
measured pressure drop, the mass flow rate and the heating section length, which are 1.9%, 0.1% and 0.3% respectively. Therefore,
the uncertainty of the frictional factor is 1.9%.
The frictional pressure drop and the convection heat transfer characteristics of the supercritical pressure R22 and ethanol
flowing through a 1.004 mm inner diameter vertical tube are experimentally investigated for the conditions summarized in Table 1.
The frictional pressure drop through the test section, the local
wall temperature, the local heat transfer coefficient, the buoyancy
parameter Bo*, the flow acceleration parameter, Kv, and its two
components, KvT and Kvp , are evaluated for various inlet Reynolds
numbers, pressures and wall heat fluxes to examine the effects
of thermophysical property variations, buoyancy and flow acceleration due to thermal expansion and pressure drop on the heat
transfer.
3.1. Frictional pressure drop
The influence of property variations, especially the effect of density and viscosity variations with the temperature on the frictional
pressure drop is evaluated by comparing the frictional pressure
drops through the heat section for various heat fluxes in Fig. 4
with those predicted using Filonenko equation [27], which is based
on constant property flow data and neglects density and viscosity
variations with temperature. The friction factor, f0 , is calculated as
f0 = (1.82log Re − 1.64)−2
(13)
where Re is based on the average of the inlet and outlet fluid temperature.
The predicted frictional pressure drops using Petukhov correlation [3] and Itaya correlation accounting for the influence of
viscosity [28] based on the wall temperature are also presented
in Fig. 4. Petukhov correlation includes a viscosity correction term,
(b /w ), to correct the influence of the fluid viscosity near the wall,
100
80
Δpf / kPa
Re =
79
60
40
20
0
200
400
600
800
1000
1200
1400
qw/ kW⋅m -2
Fig. 4. Frictional pressure drops for various heat fluxes.
R22, p = 5.5 MPa, G = 4000 kg m−2 s−1 , upward flow.
Solid dot: measured results; solid line: predictions by Filonenko equation.
Dash line: predictions by Petukhov correlation; dot line: predictions by Itaya correlation.
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P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
20
30
25
16
Δpf / kPa
Δpf / kPa
20
15
12
8
10
4
5
0
100
200
300
400
500
600
700
0
120
800
qw/ kW⋅m -2
and the frictional factor with the property variation correction, fvp ,
is then:
fvp
=
6
f0
7−
b
w
(14)
where f0 is calculated using Eq. (13).
In Itaya correlation fvp is calculated as:
fvp
=
f0
0.72
w
(15)
b
where,
f0 =
0.314
0.7 − 1.65log Reb + (log Reb )2
(16)
Since the heat flux is relatively high in the present study, the
local fluid temperature varies significantly along the tube and the
local frictional resistance is significantly affected by the local properties; thus, the local frictional pressure drops in each subsection
are calculated as:
pf,x = fvp,x
x G2
d 2b,x
240
300
360
420
480
540
qw/ kW⋅m-2
Fig. 5. Frictional pressure drops for various heat fluxes.
R22, p = 5.5 MPa, G = 2000 kg m−2 s−1 , upward flow.
Solid dot: measured results; solid line: predictions by Filonenko equation.
Dash line: predictions by Petukhov correlation; dot line: predictions by Itaya correlation.
1
180
(17)
where fvp is the local frictional factor calculated using the correlations, x is the length of each subsection and the thermophysical
properties are based on the local wall and fluid temperatures in
each subsection. The predicted frictional pressure drop along the
entire heating section, pf , is then obtained by summing up the
local pressure drops in each subsection.
The measured and predicted frictional pressure drops of R22
for various heat fluxes at p = 5.5 MPa for upward flow are shown in
Fig. 4 for G = 4000 kg m−2 s−1 and in Fig. 5 for G = 2000 kg m−2 s−1 .
pf increases with increasing heat flux, and increases significantly
when the heat flux exceeds a certain value. This is mainly due to
that the fluid temperature increases with increasing heat flux, so
the fluid density decreases and the velocity increases to maintain
flow continuity. The frictional pressure drop then increases as a
result. When the fluid temperature approaches Tpc , the density
decreases and the velocity severely increases, the frictional pressure drop sharply increases. Although the fluid viscosity decreases
as the temperature increases, which reduces the friction between
the fluid and the wall to some extent, the effect of density decreasing overwhelms the viscosity decrease which results in increasing
frictional pressure drop as shown in Figs. 4 and 5.
Fig. 6. Frictional pressure drops for various heat fluxes.
R22, p = 7.3 MPa, G = 2000 kg m−2 s−1 , upward flow.
Solid dot: measured results; solid line: predictions by Filonenko equation.
Dash line: predictions by Petukhov correlation; dot line: predictions by Itaya correlation.
For relatively low heat fluxes, such as qw = 341 kW m−2 in Fig. 4
and qw = 136 kW m−2 in Fig. 5, the temperature difference between
the fluid and the wall is small, and the property variations are
insignificant in the tube. Filonenko equation predicts the measured frictional pressure drop fairly well. In addition, there is no
significant difference among the Petokhov correlation predictions,
Itaya correlation predictions and the measured results. As the heat
flux increases, both the fluid temperature and the wall temperature rise, and the temperature difference between the fluid and
the wall increases resulting in sharp property variations across
the tube and a remarkable effect of the fluid layer near the wall
(the temperature of which is similar to the wall temperature)
on the frictional resistance. Since in the present cases, the wall
temperature is much higher than the fluid temperature in the
center (which is close to the bulk temperature), the fluid density
near the wall decreases, which increases the fluid velocity near
the wall more than in the center and intensifies the fluid mixing
near the wall; thus, the friction between the fluid and the wall
increases as a result. The fluid viscosity decreases near the wall,
which reduces the friction between the fluid and the wall to some
extent. The effect of neither the density nor viscosity variations
near the wall on the frictional pressure drop can be neglected
since the tradeoff between the density and viscosity variations
determines the frictional pressure drop. For qw = 551 kW m−2 in
Fig. 4 and qw = 242 kW m−2 and 327 kW m−2 in Fig. 5, the two
effects almost balance; thus, Petukhov and Itaya correlations which
only consider the viscosity variation effect underestimate the frictional pressure drop. Filonenko equation, which evaluates the
properties based only on the bulk temperature, produces better
results.
As the heat flux increases further, the bulk temperature
approaches Tpc and the wall temperature exceeds Tpc , so the fluid
density near the wall decreases and the fluid stays in a gas-like state.
The flow resistance increases drastically, which overwhelms the
viscosity decrease; thus, Filonenko equation underpredicts the frictional pressure drop and the other two correlations produce much
lower results as shown in Figs. 4 and 5. When both the bulk and wall
temperatures exceed Tpc for higher heat fluxes, qw = 1250 kW m−2
and 1335 kW m−2 in Fig. 4 and qw = 728 kW m−2 and 777 kW m−2
in Fig. 5, the density and viscosity variations effects on the flow
resistance decrease; thus, the predictions of all three correlations
approach the measured results.
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
81
60
120
7.3 MPa
10 MPa
100
50
Δpf / kPa
Δpf / kPa
80
40
60
40
30
20
0
0
300
600
900
qw/ kW⋅m
1200
1500
20
1800
0
150
300
600
750
(a) R22
Fig. 7. Frictional pressure drops for various heat fluxes.
Ethanol, p = 10 MPa, G = 4000 kg m−2 s−1 , upward flow.
Solid dot: measured results; solid line: predictions by Filonenko equation.
Dash line: predictions by Petukhov correlation; dot line: predictions by Itaya correlation.
50
7.3 MPa
10 MPa
45
Δpf / kPa
Fig. 6 presents the measured and predicted frictional pressure drops of R22 for various heat fluxes at p = 7.3 MPa,
G = 2000 kg m−2 s−1 , and upward flow. As in Figs. 4 and 5, the
predicted values using Filonenko equation without the property
variation correction terms based on the wall temperature agree
fairly well with the measured results for relatively low heat fluxes,
while the other correlations with only viscosity correction terms
underpredict pf . As the heat fluxes increase, the thermophysical properties differences between the fluid center and the wall
increase, so the predicted values deviate from the measured results.
The ethanol density and viscosity variations differ from those of
R22, which produces different results when comparing the measured and predicted pf , as shown in Fig. 7. The frictional pressure
drop variations with the heat flux for ethanol are relatively insignificant. The ethanol density variation with temperature is less severe
than that of R22 for the temperature range in the present study
(since the critical temperature for ethanol, 248 ◦ C, is relatively high,
the fluid and wall temperatures are below Tpc in most cases), while
the viscosity decreases drastically with the temperature; thus, the
flow resistance reduction due to the viscosity decrease overwhelms
the density variation effect for ethanol. Even for low heat fluxes, the
fluid viscosity near the wall based on the wall temperature, is much
smaller than that based on the bulk temperature, which reduces the
flow resistance. Thus, the measured frictional pressure drops are
generally lower than the predictions of Filonenko equation using
properties based on the bulk temperature. Itaya correlation with
the viscosity correction based on the wall temperature produces
better results than the other two correlations as shown in Fig. 7.
The influences of pressure on the frictional pressure drops of
R22 and ethanol are shown in Fig. 8(a) and (b). For p = 7.3 MPa,
which is close to the critical pressure, pc = 4.99 MPa, the frictional
pressure drop varies more significantly with the heat flux mainly
due to the thermophysical property variations, especially the sharp
density decrease with temperature as the pressure approaches pc .
However, for p = 10 MPa, the thermophysical property variations
are relatively small; thus, the increase in the frictional pressure
drop with the heat flux is smaller. As the pressure increases to
10 MPa, the frictional pressure drop decreases by 20–30% as shown
in Fig. 8(a) and (b).
The frictional pressure drops for R22 and ethanol are compared
for p = 7.3 MPa and 10 MPa in Fig. 9(a) and (b). The flow resistance
is closely related to the thermophysical properties of the fluid near
the wall evaluated at the wall temperatures, especially for the cases
450
-2
qw/ kW . m
-2
40
35
30
25
20
0
300
600
900
1200
1500
1800
-2
qw/ kW . m
(b) Ethanol
Fig. 8. Frictional pressure drops for various pressures.
G = 4000 kg m−2 s−1 , upward flow.
with relatively large heat fluxes where the wall temperature is high
and the temperature difference between the bulk fluid and the
wall is quite large (greater than 20 ◦ C in most cases). The R22 density variation is sharper than the ethanol density variation while
the ethanol viscosity variation is sharper than the R22 viscosity
variation, as shown in Fig. 10(a) and (b). For R22, the flow resistance increases resulting from the large density decrease, while for
ethanol, the viscosity decreasing with the temperature significantly
reduces the flow resistance and the frictional pressure drop for
ethanol is smaller than for R22 when the pressure and the mass flux
are the same. For p = 10 MPa, the ethanol frictional pressure drop is
10–20% lower than for R22, and for p = 7.3 MPa, where the property
variations are more significant, the ethanol frictional pressure drop
is 20–30% lower than for R22.
3.2. Heat transfer
3.2.1. Heat transfer of R22
The local wall temperature and heat transfer coefficient variations with the local enthalpy are shown in Fig. 11(a) and (b) for
various heat fluxes at p = 5.5 MPa, G = 2000 kg m−2 s−1 and upward
flow. The local wall temperature increases with the enthalpy when
the heat flux is relatively low, qw = 136 kW m−2 , 242 kW m−2 and
327 kW m−2 . As the bulk temperature increases and approaches
Tpc , the specific heat, cp , increases greatly, which enhances the
82
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
60
1500
R22
Ethanol
1200
Δpf / kPa
ρ/ kg . m-3
50
40
30
20
R22
Ethanol
900
600
300
0
0
300
600
900
1200
-2
qw/ kW . m
1500
1800
(a) p=7.3 MPa
0
40
80
120
160
200
T/ oC
(a) Density
R22
Ethanol
6
μ× 10 / Pa . s
Δpf / kPa
320
R22
Ethanol
2000
40
1600
1200
800
400
30
0
20
280
2400
60
50
240
0
300
600
900
1200
1500
1800
-2
qw/ kW . m
(b) p=10 MPa
Fig. 9. Frictional pressure drops for R22 and ethanol.
G = 4000 kg m−2 s−1 , upward flow.
heat transfer between the fluid and the wall, and the heat transfer coefficient increases as a result, as shown in Fig. 11(b). As the
heat flux increases to qw = 521 kW m−2 and 631 kW m−2 , the fluid
temperatures pass through Tpc , the wall temperatures are above
Tpc and the local enthalpy increases along the test section. The
local wall temperature firstly increases to a local maximum, then
decreases, and increases again. This creates minimum local heat
transfer coefficient where the maximum wall temperature occurs.
The heat transfer coefficient then increases when the bulk temperature passes through Tpc and then decreases. This is mainly
due to that as the bulk temperature approaches Tpc , the bulk specific heat increases greatly, which enhances the heat transfer as
a result. However, when the heat flux is relatively high, the wall
temperatures are usually fairly high as well, so the fluid density,
thermal conductivity and specific heat near the wall are quite low,
which impairs the heat transfer between the fluid and the wall,
and the heat transfer coefficient decreases. As the fluid temperature increases and approaches Tpc , the bulk averaged specific heat
across the tube increases, which overcomes the negative effect of
the low density, low thermal conductivity and low specific heat
near the wall; thus, the heat transfer recovers, the wall temperature decreases and the heat transfer coefficient increases. As the
fluid and wall temperatures increase to much higher than Tpc , the
fluid density, thermal conductivity and specific heat decrease so the
0
40
80
120
160
200
240
280
320
T/ oC
(b) Viscosity
Fig. 10. Density and viscosity variations for R22 and ethanol at p = 10 MPa.
heat transfer is reduced and the heat transfer coefficient decreases
again as shown in Fig. 11(b).
When the heat flux increases further to 728 kW m−2 and
777 kW m−2 , the local wall temperature increases dramatically to a
maximum and then decreases, with a much sharper peak observed.
The temperature difference between the fluid and the wall can be
as high as hundreds of degrees at the peak, as shown in Fig. 11(a),
the density, thermal conductivity and specific heat near the wall are
much lower, which significantly reduces the heat transfer. As the
bulk fluid temperature approaches Tpc , the heat transfer recovers
due to the increased bulk specific heat. The local wall temperature
decreases and the local heat transfer coefficient increases. As the
fluid temperature increases further to far above Tpc , the fluid stays
in a gas-like state and the heat transfer between the fluid and the
wall is again reduced so the local wall temperature increases as
shown in Fig. 11(a).
The local temperature and heat transfer coefficient variations
with the local enthalpy for various heat fluxes for R22 with
G = 4000 kg m−2 s−1 are shown in Fig. 12(a) and (b). For heat fluxes
of 341–843 kW m−2 , the local wall temperature increases with the
enthalpy. When the fluid temperature is less than Tpc , and the wall
temperature is less than or near Tpc , the heat transfer coefficient
variation with the enthalpy is relatively small. As the fluid and
wall temperature increase, the wall temperature is much higher
than Tpc , so the density, thermal conductivity and specific heat
of the high temperature fluid near the wall are very low, which
reduces the heat transfer. The heat transfer coefficient between
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
540
136 kW . m
242 kW . m
327 kW . m
521 kW . m
631 kW . m
728 kW . m
-2
450
-2
-2
540
-2
-2
341 kW . m
-2
450
-2
777 kW . m
-2
843 kW . m
1250 kW . m
-2
-2
270
180
90
0
683 kW . m
-2
1001 kW . m
-2
1141 kW . m
-2
-2
1335 kW . m
-2
270
180
90
240
300
360
420
480
ib/ kJ . kg
0
540
240
300
(a) Temperature
24000
242 kW . m
327 kW . m
20000
521 kW . m
631 kW . m
728 kW . m
-2
-2
-2
540
341 kW . m
552 kW . m
683 kW . m
843 kW . m
-2
1001 kW . m
-2
1141 kW . m
1250 kW . m
1335 kW . m
-2
-2
20000
-2
-1
-2
hx/ W . m . K
-2
16000
12000
-2
-2
-2
-2
12000
8000
4000
0
480
24000
-2
777 kW . m
16000
420
(a) Temperature
136 kW . m
-2
360
ib/ kJ . kg
-1
-1
-2
-1
hx/ W . m . K
552 kW . m
o
Tw , Tf / C
360
o
Tw , Tf / C
360
83
8000
4000
240
300
360
ib/ kJ . kg
420
480
540
-1
(b) Heat transfer coefficient
0
240
300
360
ib/ kJ . kg
420
480
540
-1
(b) Heat transfer coefficient
Fig. 11. Local wall temperatures and heat transfer coefficients for various heat
fluxes.
R22, p = 5.5 MPa, G = 2000 kg m−2 s−1 , upward flow.
Symbols in (a): wall temperature; solid line: fluid temperature; dash dot line: pseudo
critical temperature.
the fluid and the wall is further reduced as the heat flux and wall
temperature increase as shown in Fig. 12(b). When the heat flux
increases to 1001–1335 kW m−2 , a local maximum wall temperature is observed with higher maximums at higher heat flux, as
shown in Fig. 12(a), but not as high as in the cases in Fig. 11(a).
The local heat transfer deterioration resulting from the low density fluid layer near the wall is reduced with increasing mass flux
as shown by comparing the local wall temperature variations in
Figs. 11 and 12.
When the pressure increases to 10 MPa, the thermophysical property variations with temperature are smaller than for
p = 5.5 MPa, so the heat transfer characteristics are quite different
as shown in Fig. 13(a) and (b), which present the local wall temperature and heat transfer coefficient variations with the enthalpy
for p = 10 MPa, G = 4000 kg m−2 s−1 , and upward flow. The local wall
temperature increases with the enthalpy without a local maximum
and with no increase in the coefficient downstream for the heat
fluxes used in the present study. The local heat transfer coefficient
decreases with the enthalpy as shown in Fig. 13(b) mainly due to
the increase at the local wall temperature and the wall to fluid
temperature difference. The temperature difference increases further when the heat flux increases since the high temperature fluid
near the wall has a low density, low thermal conductivity and low
Fig. 12. Local wall temperatures and heat transfer coefficients for various heat
fluxes.
R22, p = 5.5 MPa, G = 4000 kg m−2 s−1 , upward flow.
Symbols in (a): wall temperature; solid line: fluid temperature; dash dot line: pseudo
critical temperature.
specific heat which causes the local heat transfer coefficient to
decrease as the enthalpy increases.
The heat transfer coefficients at various pressures for R22 are
compared in Fig. 14. When the pressure is far above pc , which is
4.99 MPa for R22, such as p = 7.3 MPa and 10 MPa, the heat transfer
coefficient is relatively low and the variation with the enthalpy is
relatively small. As the pressure approaches pc , 5.5 MPa for example, the heat transfer coefficients are 100–200% higher those at
7.3 MPa and 10 MPa at the same enthalpy as shown in Fig. 14.
3.2.2. Heat transfer of ethanol
The local wall temperature and heat transfer coefficient variations with the local enthalpy for various heat fluxes at p = 7.3 MPa,
G = 4000 kg m−2 s−1 and upward flow for ethanol are shown in
Fig. 15(a) and (b). The local wall temperature variation is small
while the enthalpy is small. However, as the enthalpy becomes
relatively large near the test section outlet, the wall temperature increases significantly and the heat transfer coefficient first
increases and then decreases. For ethanol, the viscosity decreases
sharply with temperatures as shown in Fig. 10(b); thus, as the
temperature and the enthalpy increase, the viscosity decreases
which intensifies the fluid turbulence, especially for fluid near the
wall which is most influenced by the high wall temperature. The
84
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
196 kW . m
-2
282 kW . m
-2
348 kW . m
433 kW . m
513 kW . m
360
581 kW . m
643 kW . m
300
-2
400
-2
o
-2
213 kW . m
384 kW . m
-2
731 kW . m
-2
901 kW . m
-2
420
-2
-2
o
Tw , Tf / C
-2
300
480
111 kW . m
Tw , Tf / C
500
200
595 kW . m
-2
1250 kW . m
1380 kW . m
-2
-2
-2
-2
1070 kW . m
1490 kW . m
-2
240
180
120
100
60
0
220
240
260
280
300
ib/ kJ . kg
0
240
320
280
320
360
-1
28000
12000
-2
111 kW . m
-2
196 kW . m
282 kW . m
348 kW . m
433 kW . m
513 kW . m
581 kW . m
643 kW . m
-2
-1
hx/ W . m . K
560
-2
595 kW . m
731 kW . m
901 kW . m
1070 kW . m
1250 kW . m
1380 kW . m
1490 kW . m
-2
-2
-2
-2
6000
4000
-2
-2
-2
-2
-2
-2
20000
16000
12000
8000
2000
0
220
240
260
280
300
ib/ kJ . kg
-1
320
Fig. 13. Local wall temperatures and heat transfer coefficients for various heat
fluxes.
R22, p = 10 MPa, G = 4000 kg m−2 s−1 , upward flow.
Symbols in (a): wall temperature; solid line: fluid temperature; dash dot line: pseudo
critical temperature.
18000
15000
12000
9000
6000
3000
240
280
320
360
400
ib/ kJ . kg
-1
Fig. 14. Heat transfer coefficients for various pressures.
R22, G = 4000 kg m−2 s−1 , upward flow.
Solid: 10 MPa; hollow: 7.3 MPa; center-crossed: 5.5 MPa.
440
4000
240
280
320
360
400
440
ib/ kJ . kg
480
520
560
-1
(b) Heat transfer coefficient
(b) Heat transfer coefficient
-1
-2
hx/ W . m . K
520
384 kW . m
24000
-2
-2
0
200
480
213 kW . m
-2
-1
-2
hx/ W . m . K
-2
8000
440
-1
ib/ kJ . kg
(a) Temperature
(a) Temperature
10000
400
480
520
Fig. 15. Local wall temperatures and heat transfer coefficients for various heat
fluxes.
Ethanol, p = 7.3 MPa, G = 4000 kg m−2 s−1 , upward flow.
Symbols in (a): wall temperature; solid line: fluid temperature; dash dot line: pseudo
critical temperature.
viscosity decreases significantly and the turbulence is intensified
as a result; therefore, the heat transfer between the fluid and the
wall is further enhanced. Compared with R22, the ethanol density
variation with temperature is relatively small, as shown in
Fig. 10(a), so the negative effect of the density decrease of the high
temperature fluid near the wall on the heat transfer is overwhelmed
by the positive effect of the viscosity decrease, which then prompts
an increase in the heat transfer coefficient with the enthalpy. However, as the fluid temperature and the enthalpy increase further
near the outlet, the fluid density, especially the fluid density near
the wall decreases; thus, the wall temperature increases and the
heat transfer coefficient decreases. Similar variations are observed
for the local wall temperature and heat transfer coefficient variations with the enthalpy for various heat fluxes at p = 10 MPa,
G = 4000 kg m−2 s−1 and upward flow in Fig. 16(a) and (b).
The heat transfer coefficients at p = 7.3 MPa and 10 MPa for
ethanol are compared in Fig. 17. Except for the data affected
by the high temperature fluid near the wall near the outlet, the
heat transfer coefficient generally increases with the enthalpy
for both p = 7.3 MPa and 10 MPa. The pressure effect on the heat
transfer coefficient is quite small with the heat transfer coefficients for 7.3 MPa only slightly higher that those for 10 MPa
since the former is closer to the critical pressure for ethanol,
6.15 MPa.
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
500
400
20000
219 kW . m
398 kW . m
601 kW . m
749 kW . m
899 kW . m
1070 kW . m
1240 kW . m
1390 kW . m
1480 kW . m
-2
-2
-2
-2
-2
-2
-2
-2
16000
-2
1610 kW . m
o
Tw , Tf / C
-2
-1
hx/ W . m . K
-2
300
200
280
320
360
400
440
ib/ kJ . kg
480
520
560
-1
219 kW . m
398 kW . m
601 kW . m
749 kW . m
899 kW . m
1070 kW . m
-2
24000
-2
-2
20000
-2
1480 kW . m
-2
-1
hx/ W . m . K
-2
16000
12000
8000
320
360
400
ib/ kJ . kg
440
-1
480
520
560
(b) Heat transfer coefficient
Fig. 16. Local wall temperatures and heat transfer coefficients for various heat
fluxes.
Ethanol, p = 10.0 MPa, G = 4000 kg m−2 s−1 , upward flow.
Symbols in (a): wall temperature; solid line: fluid temperature; dash dot line: pseudo
critical temperature.
24000
-2
-1
hx/ W . m . K
20000
16000
12000
8000
280
320
360
40
50
60
70
80
90
-2
-2
1390 kW . m
1610 kW . m
280
30
Fig. 18. Heat transfer coefficients for R22 and ethanol.
p = 10.0 MPa, G = 4000 kg m−2 s−1 , upward flow.
Solid: R22 (Tpc = 137.3 ◦ C for 10 MPa); hollow: ethanol (Tpc = 271.6 ◦ C for 10 MPa).
-2
-2
-2
1240 kW . m
0
20
Tf / C
28000
4000
240
8000
o
(a) Temperature
4000
240
12000
4000
100
0
240
85
400
-1
ib/ kJ . kg
Fig. 17. Heat transfer coefficients for various pressures.
Ethanol, G = 4000 kg m−2 s−1 , upward flow.
Solid: 10 MPa; hollow: 7.3 MPa.
440
480
520
3.2.3. Comparison of R22 and ethanol heat transfer coefficients at
supercritical pressures
The heat transfer characteristics of R22 and ethanol at supercritical pressures differ due to their thermophysical property variations
in these operating conditions. The heat transfer coefficient variations with bulk fluid temperature, Tf , are compared in Fig. 18. The
heat transfer coefficients for R22 decrease with the Tf whereas those
for ethanol increase with Tf . The higher Tf is, the larger the differences between the heat transfer coefficients for ethanol and those
for R22 are. Generally, the heat transfer coefficients for ethanol
are 50% to even several times higher than those for R22 for similar fluid temperature, pressures and mass fluxes. This is related to
the thermophysical property characteristics, especially the viscosity and density variations with temperature for R22 and ethanol.
For relatively higher heat fluxes as in the present study, the wall
temperature is quite high and the temperature difference between
the fluid and the wall is large, so the radial property variations in the
tube are usually significant and the influence of the thermophysical
properties evaluated at the wall temperature on the heat transfer
coefficients is expected to be more significant than the effect at the
bulk properties.
3.2.4. Influence of the buoyancy
During the supercritical heat transfer in a tube, the fluid thermophysical properties change drastically when the temperatures
are near the pseudo critical temperature. These strong fluid property variations in both the radial direction (from the fluid core to the
wall) and the axial direction are expected to affect the heat transfer
when the flow passes through the near critical region.
A density gradient is induced across the tube by the radial temperature gradient between the fluid core and the wall. With the
relatively high heat fluxes used in the present study, which are
105 –106 kW m−2 , the temperature difference between the bulk
fluid and the wall can be as high as 200 ◦ C. The radial density gradient resulting from such large temperature differences are quite
sharp, with the high temperature fluid adjacent to the wall in a
highly gas-like state with a fairly low density while the fluid in the
core is still in a liquid-like state. Therefore, the high temperature
fluid adjacent to the wall tends to flow upwards due to buoyancy.
For upward flow cases, the upwards buoyancy force near the
wall is in the flow direction and accelerates the flow near the wall
more than in the core, so the average velocity difference between
the wall region and the core region is reduced. The shear stresses
between the wall and the core and the turbulence production are
reduced, and the heat transfer is reduced as a result. For downward
86
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
1E-6
540
136 kW . m
242 kW . m
327 kW . m
521 kW . m
631 kW . m
728 kW . m
-2
136 kW . m
242 kW . m
327 kW . m
-2
521 kW . m
-2
631 kW . m
-2
728 kW . m
-2
450
-2
-2
-2
-2
-2
-2
500
1E-7
o
o
Bo*
300
1E-8
270
Tf / C
400
360
Tw , Tf / C
600
-2
200
180
1E-9
100
90
300
350
400
ib/ kJ . kg
450
500
550
Re3.425 Pr0.8
(18)
Re =
g˛p di4 qw
2
Gd
500
0
550
600
341 kW . m
552 kW . m
683 kW . m
843 kW . m
1001 kW . m
1141 kW . m
1250 kW . m
1335 kW . m
-2
-2
1E-7
-2
-2
-2
-2
-2
500
-2
400
300
1E-8
200
1E-9
100
1E-10
200
250
300
350
400
ib/ kJ . kg
-1
450
500
0
550
(b) G=4000 kg·m-2·s-1
Where,
Gr∗ =
ib/ kJ . kg
450
1E-6
Bo*
flow cases, the buoyancy force near the wall is opposite to the flow
direction; thus, the velocity gradient is increased, the shear stress
is intensified near the boundary, more turbulence is generated and
the turbulent kinetic energy increases, so the heat transfer between
the fluid and the wall is enhanced.
Jackson and Hall [13] introduced non-dimensional buoyancy
effect parameter, Bo*, to evaluate the buoyancy effect as:
Bo =
400
(a) G=2000 kg·m-2·s-1
Fig. 19. Local wall temperatures for upward and downward flows.
R22, p = 5.5 MPa, G = 2000 kg m−2 s−1 .
Symbols: wall temperature (solid: upwards; hollow: downwards).
Solid line: fluid temperature; dash dot line: pseudo critical temperature for 5.5 MPa.
Gr∗
350
-1
-1
∗
300
o
250
250
Tf / C
0
200
1E-10
200
(19)
Fig. 20. Local Bo* for various heat fluxes.
R22, p = 5.5 Mpa.
Solid line: fluid temperature; dash dot line: pseudo critical temperature for 5.5 MPa.
(20)
According to McEligot and Jackson [29], the buoyancy effect is
negligible for Bo* < 6 × 10−7 for both upward and downward flows.
For upward flows with 6 × 10−7 < Bo* < 1.2 × 10−6 , the buoyancy
reduces the heat transfer while for 1.2 × 10−6 < Bo* < 8 × 10−6 , the
heat transfer reduction gradually decreases as the Bo* increases,
but the buoyancy still negatively affects the heat transfer. For
Bo* > 8 × 10−6 the buoyancy enhances the heat transfer. For downward flow, the buoyancy will always enhance the heat transfer for
Bo* > 6 × 10−7 .
The buoyancy effect on the heat transfer for relatively high heat
fluxes and large temperature differences is of great importance in
developing third fluid cooling system using R22 or ethanol. Because
the buoyancy is mainly induced by the density variations with temperature, R22 is expected to be more influenced by the buoyancy
effects than ethanol since the R22 density variations are relatively
large within the parameter ranges considered here.
The local wall temperature variations with enthalpy for various heat fluxes for upward and downward flows at p = 5.5 MPa and
G = 2000 kg m−2 s−1 for R22 are compared in Fig. 19. When the heat
flux is relatively low, the local wall temperature increases with the
enthalpy, whereas for high heat fluxes, local maximum wall temperatures are observed for both the upward and downward flow
cases. The wall temperature variations in the upward and downward flows are consistent with each other and the differences are
quite small, which indicates that the buoyancy effect on the heat
transfer is insignificant. Although the radial density variation in the
tube is significant due to the large temperature difference between
the fluid and the wall, especially when the fluid changes from the
liquid-like state in the core to the highly gas-like state adjacent to
the wall in the radial direction, the local heat transfer decreases
due to the high temperature fluid near the wall. Nevertheless, the
Reynolds number is high due to the large mass flux despite the small
channel size, which reduces the inhibitory effect of the buoyancy
on the turbulence near the wall; thus, the differences due to the
buoyancy for the upward and downward flows are insignificant.
The corresponding non-dimensional buoyancy parameter, Bo*,
variations with the enthalpy for various heat fluxes at p = 5.5 MPa
and G = 2000 kg m−2 s−1 for R22 are shown in Fig. 20(a). When
the fluid temperature is below Tpc (the corresponding enthalpy
ipc = 373.5 kJ kg−1 ), Bo* increases with the heat flux, reaches a maximum near Tpc and decreases drastically with the enthalpy when the
fluid temperature exceeds Tpc . Bo* decreases when the mass flux
is increased to G = 4000 kg m−2 s−1 as shown in Fig. 20(b). Bo* is
below 10−7 for all the experimental conditions used in the present
study. The experimental results are consistent with the McEligot
and Jackson criteria [29] that the buoyancy is insignificant when
Bo* < 6 × 10−7 .
3.2.5. Influence of flow acceleration
The fluid expands as the temperature increases and pressure
decreases along the tube during heating and accelerates to maintain
continuity; thus, the axial pressure gradient increases as a result.
The shear stress in the vicinity of the wall will be reduced to balance the increased pressure gradient, so the turbulence near the
wall is suppressed. The flow may even be “laminarized” when the
flow acceleration is strong, which means that although the flow
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
327 kW . m
521 kW . m
631 kW . m
728 kW . m
1E-7
600
-2
-2
500
242 kW . m
327 kW . m
521 kW . m
631 kW . m
728 kW . m
-2
-2
200
250
300
350
400
ib/ kJ . kg
450
500
Kvp
o
300
1E-10
200
1E-11
1E-12
200
0
550
100
250
300
600
341 kW . m
552 kW . m
683 kW . m
843 kW . m
1001 kW . m
1141 kW . m
1E-7
-2
-2
-2
1335 kW . m
500
1E-8
200
300
350
400
-1
ib/ kJ . kg
450
500
0
550
4qw d˛p
(21)
(22)
Kvp is the non-dimensional compressible flow acceleration
parameter describing the effect of flow acceleration due to the
pressure drop through the tube:
Kvp = −
dp
d
· ˇT
Re
dx
1250 kW . m -2
1335 kW . m -2
600
500
300
1E-10
100
250
300
350
400
ib/ kJ . kg
450
500
0
550
(b) G=4000 kg·m-2·s-1
where KvT is in accord with the non-dimensional thermal expansion acceleration parameter, Kv, proposed by McEligot et al. [21],
which describes the effect of flow acceleration due to the thermal
expansion defined as:
Re2 b cp
1141 kW. m -2
-1
Reynolds number is in the turbulent region, the heat transfer is
similar to laminar flow.
A non-dimensional flow acceleration parameter, Kv, can be
defined based on continuity as:
KvT =
683 kW . m -2
1001 kW. m -2
1E-9
1E-12
200
Fig. 21. Local KvT for various heat fluxes.
R22, p = 5.5 MPa.
Solid line: fluid temperature; dash dot line: pseudo critical temperature for 5.5 MPa.
4qw d˛p
b dub
d
dp
=−
+
= Kvp + KvT
· ˇT
2
Re
dx
dx
ub
Re2 b cp
552 kW . m -2
843 kW . m -2
1E-11
(b) G=4000 kg·m-2·s-1
Kv =
341 kW . m -2
200
100
250
Kvp
300
1E-7
200
0
550
400
o
KvT
400
Tf / C
-2
500
(a) G=2000 kg·m ·s
1E-6
-2
450
-2 -1
(a) G=2000 kg·m ·s
-2
1250 kW . m
400
-1
-2 -1
-2
350
ib/ kJ . kg
-1
-2
500
400
200
100
600
-2
1E-9
Tf / C
300
1E-7
-2
-2
1E-8
400
KvT
136 kW . m
-2
-2
o
-2
-2
o
242 kW . m
-2
Tf / C
136 kW . m
Tf / C
1E-6
87
(23)
When the pressure gradient, dp/dx, is relatively small, such as for
the fluid flow through a regular size tube as in McEligot et al. [21],
Kvp is usually negligible compared with KvT , which indicates that
the influence of the flow acceleration due to the pressure drop is
much less than that of the thermal expansion acceleration, and the
flow acceleration is mainly induced by the temperature increasing
along the tube. However, when the tube size is reduced and the
pressure drop increases, the influence of flow acceleration due to
pressure drop needs to be re-evaluated carefully.
Fig. 22. Local Kvp for various heat fluxes.
R22, p = 5.5 MPa.
Solid line: fluid temperature; dash dot line: pseudo critical temperature for 5.5 MPa.
The variation of the non-dimensional thermal expansion acceleration parameter, KvT , with the enthalpy for various heat fluxes at
p = 5.5 MPa, G = 2000 kg m−2 s−1 for R22 are shown in Fig. 21(a). KvT
increases as the heat flux increases, reaching a maximum near Tpc
and then drastically decreases. When the R22 mass flux increases to
G = 4000 kg m−2 s−1 , KvT decreases for the same heat flux as shown
in Fig. 21(b), which indicates that the thermal expansion acceleration effect decreases when increasing the mass flux. The local
maximum KvT is below 4 × 10−7 and the average is below 2 × 10−7
in the present study. The peak position of the maximum KvT is not
exactly consistent with Tpc , where the maximum ˛p occurs, this
is mainly due to that besides ˛p , other parameters including the
Reynolds number, viscosity and specific heat also affect the KvT
variation as shown in Eq. (22), especially Re, with the square of
which KvT is inversely proportional to, increases significantly with
the enthalpy near Tpc as the density decreases and the flow accelerates, which tends to reduce KvT ; thus, the maximum KvT appears
just a little before Tpc . The variations of the non-dimensional compressible flow acceleration parameter, Kvp , with the enthalpy for
various heat fluxes at p = 5.5 MPa and G = 2000 kg m−2 s−1 for R22
are shown in Fig. 22(a). In the same way, Kvp increases as the
heat flux increases, reaching a maximum at Tpc and then drastically decreases. Compared with KvT , the position where maximum
Kvp appears is much closer to Tpc , where the maximum ˇT occurs.
This is mainly because that the Kvp is inversely proportional to Re,
as shown in Eq. (22); thus, the Reynolds number effect on Kvp is
not as significant as on KvT , and the local Kvp variations is mainly
affected by ˇT . The mass flux effect on Kvp is insignificant as shown
88
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
in Fig. 22(b), which differs from the conclusions for Bo* and KvT ,
since although the Reynolds number increases as the mass flux
increases which tends to reduce Kvp , the pressure drop and the
pressure gradient also increases, which tends to increase Kvp . The
local maximum Kvp is below 10−8 and generally about 10 fold
smaller than the corresponding KvT , which indicates that the influence of flow acceleration due to pressure drop is still insignificant
compared with that of the thermal expansion flow acceleration
even when the tube inner diameter is reduced to 1 mm as in the
present study.
McEligot et al. [21] suggested for turbulent flow, that the turbulence may be significantly reduced for KvT ≥ 3 × 10−6 while Murphy
et al. [30] found that for KvT ≤ 9.5 × 10−7 the fluid flow remains turbulent. In the present study Kv is far less than these two threshold
values, which indicates that the flow acceleration has little effect
on the turbulence and the heat transfer.
that of R22, so the ethanol frictional pressure drop is smaller than
for R22. The ethanol heat transfer coefficient increases as the fluid
temperature increasing and is much higher than that of R22; thus,
ethanol is more suitable as a coolant for third fluid cooling to protect high heat flux surfaces in combustion chambers of liquid rocket
engines.
Acknowledgments
The project was supported by the Key Project Fund from the
National Natural Science Foundation of China (No. 50736003). We
thank Professor J.D. Jackson of the School of Mechanical, Aerospace
and Civil Engineering, the University of Manchester, UK, for many
suggestions for this research. We also thank Prof. David Christopher
for editing the English.
Appendix A. Supplementary data
4. Conclusions
The flow and convection heat transfer of R22 and ethanol
at supercritical pressures in a 1.004 mm vertical small tube are
experimentally investigated for various heat fluxes, pressures and
mass fluxes against the background of third fluid cooling systems development. The fluid thermophysical property variations
at supercritical pressures, the buoyancy effect and the flow acceleration effect due to thermal expansion and pressure drop are
analyzed.
The frictional pressure drop in the heated tube is mainly
determined by the fluid density and viscosity variations with
the temperature. For supercritical R22, the density varies sharply
with the temperature for the conditions in the present study.
The correlations without considering the density variations effect
underestimate the measured frictional pressure drops. For supercritical ethanol, the density variations with the temperature are
relatively small, while the viscosity decreases sharply with the temperature; thus, the frictional pressure drops are lower than the
correlation predictions without property variation modifications,
such as the Filonenko equation. Predictions using Itaya correlation
with a viscosity modification agree fairly well with the measured
results. The frictional pressure drops for ethanol are slightly lower
than those for R22 for the conditions in the present study.
For the convection heat transfer for supercritical R22 when
the pressure is relatively high, such as p = 7.3–10 MPa, the local
wall temperature increases as the fluid temperature and enthalpy
increase, while the local heat transfer coefficient decreases with
the enthalpy, without a local heat transfer minimum. When the
pressure is reduced to 5.5 MPa, which is near the critical pressure,
4.99 MPa, and the mass flux is relatively small, the temperature
difference between the wall and the fluid is greater than 200 ◦ C for
high heat fluxes since the low density, low specific heat and low
thermal conductivity near the wall severely restrict the heat transfer between the fluid and the wall, and local heat transfer is severely
reduced. For supercritical ethanol, the density variation with temperature is relatively small, while the viscosity sharply decreases
as the temperature increases, which enhances the heat transfer.
The density variation then has little influence on the heat transfer
except near the outlet and the heat transfer coefficient increases
with the local bulk temperature and enthalpy.
For the present study conditions, the buoyancy and flow acceleration have little effect on the heat transfer. The flow acceleration
due to pressure drop is negligible compared with that due to the
thermal expansion.
Considering frictional flow resistance and heat transfer characteristics performance of supercritical R22 and ethanol for pressures
of 7.3–10 MPa, the ethanol viscosity decreases more rapidly than
Supplementary data associated with this article can be
found, in the online version, at http://dx.doi.org/10.1016/
j.supflu.2012.06.011.
References
[1] V. Balepin, Concept of the Third Fluid Cooled Liquid Rocket Engine, 2006, AIAA2006-4695.
[2] E.W. Lemmon, M.L. Huber, M.O. McLinden, Reference Fluid Thermodynamic
and Transport Properties, NIST Standard Reference Database 23 Version 8.0,
2007.
[3] B.S. Petukhov, Heat transfer and friction in turbulent pipe flow with variable
physical properties, Advances in Heat Transfer 6 (1970) 503–564.
[4] H.H. Mueggenburg, J.W. Hidahl, E.L. Kessler, Platelet Actively Cooled Thermal
Management Devices[R], 1992, AIAA-1992-3127.
[5] J.D. Jackson, Some striking features of heat transfer with fluids at pressures
and temperatures near the critical point, in: Proceedings of the International
Conference on Energy Conversion and Application (ICECA ‘2001), 2001, pp.
50–61.
[6] G. Domin, Heat transfer to water in pipes in the critical/supercritical region (in
German), Brennstoff-Wärme-Kraft 15 (1963) 527–532.
[7] V.S. Protopopov, Generalized correlations for the local heat transfer coefficient
in turbulent flow of water and carbon dioxide at supercritical pressures in
uniformly heated tubes, Teplofizika Vysokikh Temperatur 15 (1977) 815–821.
[8] A.F. Polyakov, Heat transfer under supercritical pressures, Advances in Heat
Transfer 21 (1991) 1–53.
[9] M.E. Shitsman, Impairment of the heat transmission at supercritical pressures,
(in Russian), Teplofizika Vysokikh Temperature 1 (1963) 267–275.
[10] P.J. Bourke, D.J. Pulling, L.E. Gill, Forced convective heat transfer to turbulent
CO2 in the supercritical region, International Journal of Heat Mass Transfer 13
(1970) 1339–1348.
[11] W.B. Hall, Heat transfer near the critical point, Advances in Heat Transfer 7
(1971) 1–86.
[12] J.D. Jackson, W.B. Hall, Forced convection heat transfer to fluids at supercritical pressure, in: S. Kakas, D.B. Spalding (Eds.), Turbulent Forced Convection in
Channels and Bundles, 1979, pp. 563–611.
[13] J.D. Jackson, W.B. Hall, Influences of buoyancy on heat transfer to fluids in
vertical tubes under turbulent conditions, in: Turbulent Forced Convection in
Channels and Bundles, Hemisphere, New York, 1979, pp. 613–640.
[14] R.P. Bringer, J.M. Smith, Heat transfer in the critical region, AIChE Journal 3
(1957) 49–55.
[15] N.M. Schnurr, Heat transfer to carbon dioxide in the immediate vicinity of the
critical point, Transaction of the ASME 91 (1969) 16–20.
[16] H. Tanaka, N. Nishiwaki, M. Hirata, A. Tsuge, Forced convection heat transfer to
fluid near critical point flowing in circular tube, International Journal of Heat
and Mass Transfer 14 (1971) 739–750.
[17] B.S. Shiralkar, P. Griffith, Deterioration in heat transfer to fluids at supercritical pressure and high heat fluxes, Journal of Heat Transfer-Transactions of the
ASME 91 (1969) 27–36.
[18] N.V. Tarasova, A.I. Leont’ev, Hydraulic resistance during flow of water in heated
pipes at supercritical pressures, High Temperature 6 (1968) 721–722.
[19] V.G. Razumovskiy, Heat transfer and hydraulic resistance of smooth channels
at turbulent flow of water of supercritical pressure, Ph.D. thesis, Institute of
Engineering Thermal Physics, Academy of Sciences, Kiev, Ukraine, 1984 (in
Russian).
[20] J.D. Jackson, Studies of buoyancy-influenced turbulent flow and heat transfer in vertical passages, in: Proceedings of 13th International Heat Transfer
Conference, August 13-18, 2006, Sydney, Australia: Begell House, 2006, paper
number: KN-24.
[21] D.M. McEligot, C.W. Coon, H.C. Perkins, Relaminarization in tubes, International
Journal of Heat and Mass Transfer 13 (1970) 431–433.
P.-X. Jiang et al. / J. of Supercritical Fluids 70 (2012) 75–89
[22] V.A. Kurganov, V.B. Ankundinov, A.G. Kaptil’ny, Experimental study of velocity
and temperature fields in an ascending flow of carbon dioxide at supercritical
pressure in a heated vertical tube, High Temperature 24 (1986) 811–818.
[23] Z.H. Li, P.X. Jiang, C.R. Zhao, Y. Zhang, Experimental investigation of convection heat transfer of CO2 at supercritical pressures in a vertical circular tube,
Experimental Thermal and Fluid Science 34 (2010) 1162–1171.
[24] P.X. Jiang, Y. Zhang, R.F. Shi, Experimental and numerical investigation of convection heat transfer of CO2 at super critical pressures in a vertical mini tube,
International Journal of Heat and Mass Transfer 51 (2008) 3052–3056.
[25] P.X. Jiang, Y. Zhang, Y.J. Xu, R.F. Shi, Experimental and numerical investigation
of convection heat transfer of CO2 at supercritical pressures in a vertical tube
at low Reynolds numbers, International Journal of Thermal Sciences 47 (2008)
998–1011.
89
[26] Y. Parlatan, N.E. Todreas, M.J. Driscoll, Buoyancy and property variation effected
in turbulent mixed convection of water in vertical tubes, Journal of Heat Transfer 118 (1996) 381–387.
[27] F.D. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, John
Wiley and Sons, New York, 1990.
[28] T. Yamashita, H. Mori, S. Yoshida, M. Ohno, Heat transfer and pressure drop of
a supercritical pressure fluid flowing in a tube of small diameter, Memoirs of
the Faculty of Engineering, Kyushu University 63(4) (2003) 227–244.
[29] D.M. McEligot, J.D. Jackson, Deterioration” criteria for convective heat transfer
in gas flow through non-circular ducts, Nuclear Engineering and Design 232
(2004) 327–333.
[30] H.D. Murphy, F.W. Chambers, D.M. McEligot, Laterally converging flow. Part I.
Mean flow, Journal of Fluid Mechanics 127 (1983) 379–401.