7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
A Simulation on Heat Transfer Characteristics of Solar Cavity Receiver for Hydrogen
Production by Gasification of Biomass and Supercritical Water Multiphase Flow
P. Xiao, L.J. Guo* and YJ. Lu
Xi'an Jiaotong University, State Key Laboratory of Multiphase Flow in Power Engineering
Xianning West 28#, Xi'an, 710049, China
Email: liguo@mail.xitu.edu.cn, Tel:++86 29 8266 3895, Fax: ++86 29 8266 9033
Keywords: solar cavity receiver, radiation heat transfer, convection heat transfer, wind effect
Abstract
In this work a cavity receiver for hydrogen production by biomass gasification in supercritical water using concentrated
solar energy is modeled by meanings of multifield coupling numerical simulation that couples radiation and convection
heat transfer to the multiphase flow gasification reaction. A uniform solar flux distribution on the inner surfaces of the
cavity receiver is assumed to simulate the solar input heat flux. The heat transfer characteristics of the cavity receiver
with various input heat flux are estimated by varying the inner surface temperature. As working fluid composed of
biomass particle and supercritical water flows in the coil tube and absorbs heat in the cavity, the heat flux according to
the experimental data is assumed on the coil tube. Temperature and velocity distribution of the cavity receiver with
different inclination angles and aperture diameter is analyzed. The results show that, the inclination angle has significant
effects on both the convective heat loss and the temperature distribution in cavity. Then, the effect of external wind at
different velocities and in different direction is studied numerically. It is found that wind with higher speed may enlarge
the convection and produces greater heat loss.
1. Introduction
Comparing with the fossil fuels, hydrogen is a type of
clean and renewable energy. Biomass has the potential to
accelerate the realization of hydrogen as a major fuel of the
future. For utilizing high moisture content biomass,
hydrogen production by gasification in supercritical water is
a feasible technology. The endothermic gasification reaction
for hydrogen production from biomass requires a great
quantity of energy sources. As is well known, the amount of
energy which can be obtained from the sun is abundant and
enough to meet the reaction energy needs.
Solar chemical reactors for highly concentrated solar
systems usually feature the use of a cavityreceiver type
configuration, i.e. a wellinsulated enclosure with a small
open aperture, to let in concentrated solar radiation. The
crucial question in order to estimate the thermal
performance of the thermochemical reactor is therefore how
to determine the heat transfer characteristics related to the
endothermic reaction. Usually, it is rather difficult to
calculate the exact heat transfer flow in the cavity by
experimental means. Therefore, numerical simulation is a
superior tool for this problem.
Researchers have done a lot of work regard to solar
thermochemical cavityreceiver reactors. Experimental and
simulation studies[][2][3] on cavity of various shapes have
been carried out. Clausing[41 and StineE51 firstly researched
on the cavity heat transfer model coupling radiation and
convection, and separately proposed the Nusselt number
correlations.
Convective losses in cubical and rectangular open
cavities have been extensively studied [6][7][8], the contours
of temperature and Nusselt correlations have been proposed
under different height and opening diameter.
K.S. Reddy[9] et have built a 2D simulation model of
hemispherical cavity and studied the influence of operating
temperature, emissivity of the surface, orientation and the
geometry on the total heat loss from the receiver. It was
observed that natural convection and radiation heat loss
were significantly influenced by the orientation and
geometry of the receiver.
J.K.Nayaki101 et have done the experimental and
numerical studies of the convective losses occurring from a
cylindrical cavity receiver at different velocities in two
different direction(head on and side on). It was found that
the wind induced convective heat losses are generally
higher than the nowind convective loss at all receiver
inclination angles.
The literature survey shows that the types of receivers
investigated both experimentally and numerically are either
with empty hollow or in simple shapes like cubical,
rectangular, cylindrical and hemispherical cavity.
Unfortunately, the results cannot be directly used for solar
cavity receivers for hydrogen production in supercritical
water, which contains endothermic coil tube inside the
cavity and complex geometry insulation.
According to the characteristic of solar cavity receiver for
hydrogen production by biomass gasification in
supercritical water, a threedimensional numerical analysis
has been carried out using Flunet 6.3 CFD software to
predict the heat transfer in the system. This simulation of
heat transfer is at two cases "with and without external wind
in the surround", and the result has been compared with the
previous works [9].
Nomenclature
g gravitational constant (ms1)
P pressure (Nm2)
T temperature(K)
Q heat transfer flux (W)
G mass flow rate (kg s)
U velocity vector (m s')
A area of surface (m2)
L characteristic length (m)
h enthalpy (kJ kg1)
q wall heat flux (W m2)
f body force per unit volume
k conductivity coefficient
a thermal diffusivity (m2 S1)
Cp specific Heat Capacity (kJ kg1 K 1)
Ra Rayleigh number
Ri Richardson number
Re Reynold number
Gr Grashof number
Pr Prandtl number
X distance from the surface (m)
Greek letters
a inclination angle (0)
p density (kg m3)
tp diffusion coefficient
X thermal conductivity (W m1 K1)
P3 volume coefficient of expansion (K 1)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
reaction in supercritical water can easily happen.
Insulation
SSecondary Concentrator
,: I,
Coil Tube
58
0 60 (cm)
Figure. 1 Schematic of solar cavity receiver
The working fluid is circulated through the tubular
reactor using a plunger pump. A flowmeter measures the
mass flow rate of mixed flow entering the coil tube. The hot
flow is circulated at constant inlet temperature and pressure
through the receiver. The temperature of working fluid in
the tube, the inner wall and outer wall of receiver are
measured with Ktype thermocouples.
In the present study, the temperature of inlet, cavity wall
and coil outer surface, and the pressure of inlet and outlet
were obtained. Thus, the heat flux in cavity can be estimated
as below[11.
S= G.(ho h,) (1)
3. Numerical Scheme
Subsripts
o outside
i inward
r Reactor
in inside
ct coil tube
p constant pressure
R related
cv convection
cd conduction
ra radiation
atm atmosphere
2. Experimental Facility
The schematic of the solar cavity receiver for hydrogen
production from biomass gasification is shown in Fig.l,
which consists of a approximate cubic cavity with insulation
encased, a cone secondary concentrator on the aperture
plane used to enhance the solar concentrating ratio, as well
as a snake like coil tube inside the cavity. The working fluid
composed of biomass particle and supercritical water flows
in the coil tube and be heated to temperature up to 927K and
pressure above 30MPa. The coil tube was designed to 10mm
outside diameter and length of 18m. At this size and
temperature, the biomass particles and supercritical water
can be adequately heated and the biomass gasification
Figure.2 Computational grid of the solar cavity receiver
A 3D numerical investigation of the cavity receiver as
fig. 2 is carried out and the convection and radiation heat
loss from the aperture of the cavity receiver is numerical
studied. To prevent the case that flow field near the cavity
aperture is influenced by the outer enclosure, the diameter
of the outer domain is about thirty times the diameter of the
receiver. In this model, a cubic outer domain (length of 30m)
was established to simulate infinite atmosphere surrounding
the cavity.
Unstructured tetrahedral meshes were applied in the
simulation domain to improve simulation accuracy. To show
the temperature and pressure detail changes near the
receiver, meshes close to the cavity wall and tubular reactor
were refined. The boundary layer grid thickness near tubular
reactor is was set to 2mm (0.5mm X 4), and the average grid
size close to cavity wall was lmm.
The grid independence study was carried out, and inner
wall heat transfer rate was the characteristic parameter. The
outer domain grid size was double changed from 10 X 10
nodes to 20 X 20 nodes, 40 X 40 nodes, and so on. We
believed the result was not influenced by grid size when the
condition, ratio of former value and latter value (inner wall
heat transfer rate) less than + 10% was achieved.
Consequently, the total grid number is 939711 with
nonesecondaryconcentrator cavity receiver, and 1050241
with secondaryconcentrator cavity receiver.
3.1 Governing equations
In this paper, control volume method was used to make a
solution to the temperature and velocity field. The gas fluid
in the model was defined incompressible Newton flow.
Boussinesq approximation was considered while solving the
momentum equation. The properties of the working flow
were taken based on the average temperature of the receiver
surface and the ambient air. In pressure velocity coupling,
SIMPLEC algorithm was used with second upwind scheme
for the discretizaiton of governing equations.
Continuity equation:
V *(pU) = 0 (2)
Momentum equation:
(pU V)U= Vp + AU + pf (3)
Energy equation:
V(kVT) = 0 (4)
Since flow velocity inside the cavity was low, the RNG k
a viscous model was used to the mixed convective flow
simulation, which was applicable at low Reynolds number
condition. The Prantl number of working gas flow was set
0.7, and the effect of viscous dissipation was neglected.
To determine the flow pattern of working gas in the cavity,
nondimensional Rayleigh number was estimated as below.
It is shown that the maximum Rayleigh is 3.17 X 108 in the
cavity. Generally, laminar flow has the Rayleigh number
less than 1010, while turbulence flow has greater Rayleigh
number than that. Therefore, we can confirm that the flow
pattern in the cavity is laminar flow.
Ram =Gr.Pr='
3.17 x 107 <10
ap/
pCp
p PT), T
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
input flux. The inner surface temperature would be:
T = T,, (8)
Cavity outer surfaces boundary condition
Considering the effect of insulation, the outer surfaces of
the cavity and the secondary concentrator were taken as the
adiabatic boundary condition. The heat flux through cavity
outer surfaces would be:
q = 0 (9)
Coil tube outer surfaces boundary condition
The tubular reactor absorbs heat to supply energy source
for biomass gasification reaction. So, adiabatic boundary
condition was taken for these surfaces, the heat flux through
coil tube outer surfaces would be:
q = (10)
A,
Outer domain boundary condition
The outer domain is assumed to be a pressure inlet
boundary condition. Thus, boundary condition would be:
P = P (11)
4. Results and Discussion
To find the factors influencing the heat transfer of cavity
receiver in reality, the numerical simulation study was
divided into following steps. First of all, the cavity without
secondary concentrator and coil tubular reactor with various
inclination angles under different heat load was researched.
Then, secondary concentrator was added in the model, and
the influence of secondary concentrator on convection heat
transfer was studied. In addition, the effect of external wind
at different velocities and in different direction was
analyzed. Finally, coil tubular reactor took part in the
system. The heat transfer characteristics of cavity receiver
were obtained.
A comparison of temperature contours under different
inclination angles with previous works was carried out to
verify model accuracy of this work.
4.1 Model accuracy verification
3.2 Boundary condition
Cavity inner surfaces boundary condition
The inner surfaces of the cavity were taken as the
isothermal boundary condition. The temperature of which
was varied from 400K to 1000K to estimate the various heat
a =00 0=30 0=60'
K.S.Reddy's work
Figure.3 Temperature contours comparison with Reddy's work
20 40 60 80
Inclination of the receiver(degree)
100
Figure.4 comparison of convection heat loss at 400 C with other
heat transfer models (Tm=400 C)
The convection heat loss model for cavity receiver is
compared with other well known models, such as Clausing[41
and Stine[5, McDonald[12 and Reddy[9]. Similar size with
previous works and numerical simulation method in present
work was taken.
As the result shown (fig. 3), the temperature contour near
the cavity has good agreement with Reddy's work, which
has been proved to be most accurate[91. The little
disagreement was due to that the diameter of outer domain
in present work (L,, /L =30/1) was even larger than
Reddy's work (L,, / L = 5/1).
Fig. 4 presents the difference of convective heat loss from
cavity aperture with other models. It is observed that the
most great related deviation is less than + 10%. It is
because that the mesh refinement method and outer domain
length is not same to those models.
In conclusion, it is evident that the numerical model and
results in present work is accuracy and authentic.
4.2 The effect of thermal load on total heat loss
 Convection heat loss
3500 * Radiation heat loss
400 500 600 700 800 900 1000
Tin(K)
Figure.5 Natural convective heat loss at different inner
temperature (inclination angle U=22)
The inner wall temperature of the cavity represented the
heat transfer characteristic of convection heat transfer under
different thermal loads. With the assumption, i) the cavity is
empty inside, ii) the energy inflow equals to energy outflow,
iii) conduction heat loss equals to zero, the total thermal
load is sum of convection heat loss and radiation heat loss.
For example, to heat the cavity inner surface up to 700K,
heating power of 2092W (1486W for convection plus 607W
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
for radiation) is needed.
Qo = c +Qra (12)
As the inner temperature increases from 400K to 1000K,
convection heat loss and radiation heat loss under the
inclination angle of 220 (practical applied angle) both raises
sharply, which is represented in figure 5. That is for the
energy balance reason. Otherwise, radiation heat loss grew
even faster than convection heat loss. This is because
radiation heat loss from the cavity approximately
proportional to four power of temperature, according to
StefanBoltzmann law [13]
4.3 The effect of inclination angles on natural
convection heat loss
It is reported that natural convection heat loss of solar
cavity receiver, without external wind effect, occupies 60%
of the total heat loss through the aperture opening 14]. In
order to investigate the magnitude of natural convection
heat loss, the inclination angle of the cavity was varied from
00 to 900.
4000 
300
2500
I 2000 \
) \\
1000 \
500 \
/"i
o)
0 20 40 60 80 1 0
Inclination angle(degree)
Figure. 6 Natural heat loss at different inclination (Tm=800K)
m0
15
300
45
460
>750
90
X Position(m)
Figure. 7 longitudinal section average temperature at different
inclination angles
As in fig. 6, upon increasing the inclination angle of the
receiver, the maximum convection heat loss occurs at 00,
and the convection heat loss reduces to minimum at 900,
there it gives 77.2% in total heat loss at 00, and only 28.7%
at 900.
The longitudinal section average temperature at different
inclination angles is shown in fig. 7. With inclination
increasing, the working flow in the cavity can be maintained
in high uniform temperature. Especially, with inclination
angle less than 450, the temperature distribution in the
cavity is obviously improved. Greater inclination angle can
form narrower related longitudinal exist at the opening
plane (X=0.745), thereby reduces the natural convection
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
heat loss and improves the temperature distribution of inner
flow. Furthermore, as the inclination of the receiver
increases from 00 to 900, the stagnant air zone increases
within the receiver (fig. 8). Due to increase in the stagnant
air zone, the convection heat loss decreases from 00 to 900.
Therefore, we should enlarge the inclination angle to
reduce the convection heat loss from the cavity and increase
the proportion of heat transfer flow absorbed by tubular
hydrogen production reactor.
4.2 The influence of secondary concentrator on total
heat loss
with secondary concentrator
 without secondary concentrator
I 2500
s2000
1500oo
0 500
0 10 A 40 50 60 70 8' 0 9'0
Figure.9 Comparation of natural convective heat loss
with/without secondary concentrator
800 g3 .50
2 750 45
600
0 go50
The radiation heat loss is influenced by i) inner surface
temperature, ii) view factor of inner surface and aperture
opening, which are independent with the secondary
concentrator. Thus, radiation heat loss will not change after
secondary concentrator's addition. Total heat loss is studied
only considering the convection factor.
It is observed from fig. 8 that the approaching flow from
the far field is sucked into the open cavity and heated by the
inner surface, then escapes from the top surface by the
buoyant effect. The heat transfer from the top surface is
mainly by conduction in the thermal stagnant region. The
heat transfer from the low surface is mainly by convection,
which is the weakest mode of heat transfer. The secondary
concentrator addition will enlarge the stagnant region and
reduce the temperature gradient in cavity, thus achieve
higher longitudinal average temperature inside the cavity,
and then weaken the convection heat loss.
Upon the comparison of fig.7 and fig.10, secondary
concentrator can significantly enhance the temperature of
working flow near the exit of cavity. The most obvious
improvement is at a=750, with temperature increase of
404 C. For the reason that the secondary concentrator can
reduce total heat loss and maintain high flow temperature in
cavity, this component should be applied to improve heat
transfer efficiency.
4.3 The natural convection heat loss correlation
In this paper, the characteristic of natural convection heat
loss in cavity with secondary concentrator has been
analyzed. The Nusselt number correlation which is function
of inclination angle and inner surface temperature is given
below.
Nuc = 3.07 x 104 (1 + cosa)1694 *T072362 (13)
hv = Nu A/L
X position(m)
Figure. 10 longitudinal section average temperature at different
inclination angles with secondary concentrator
To compare the heat transfer characteristic of cavity
receiver with and without secondary concentrator, two
similar models was built to study its effect. The results of
first model without secondary concentrator are presented in
fig. 6 and fig. 7, while the results of second model with
secondary concentrator are shown in fig. 9 and fig. 10.
Q, = h, A (T, T,1.)
T, = 7
Tn
Range of parameters
400K < T < 1000K
0 < a < 900
+10%
Convection Nusselt number(data)
Figure. 11 Compared plot for Nusselt number of the cavity
receiver
A compare for Nusselt number of numerical study result
and correlation result is worked out. As it is shown in figure
11, the correlation degree is 0.9928, and standard deviation
is 0.02457, which represents that the natural convection heat
loss correlation is accuracy and acceptable.
4.4 The effect of external wind
1 m/s
*2m/s
3 3m/s
v4m/s
5mi/s
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
4.4 The entire system heat flux calculation
Based on above results, the parameters of biomass
gasification reactor in the cavity can be determined by these
steps. i) The exit temperature of reactor "To" is assumed by
a certain value. ii) The inclination angle "a", the pressure
"P" in reactor, the mass flow rate "G", the inner surface
temperature of cavity "Tm", the inlet temperature of reactor
"T," and the external wind vector U are decided by the
actual measured parameters. iii) The convection heat loss
"Qv," and radiation heat loss "Qra" can be identified
according to eq.1316 and fig.5. The reactionneeded heat
flux "Qr" is calculated by the literatures 5]. iv) The entire
processes are simulated by the model in this paper, and the
average temperature of coil tube outer surface "Tor" is
obtained. v) To compute the exit temperature of reactor
"T' using simulation results, and give the value of TO to
To for iterative computations, when they are not nearly equal.
vi) Finally obtain various kinds of the heat fluxes using the
calculated To.
The overall heat fluxes including convection heat loss,
radiation heat loss and reactionneeded heat flux are shown
in the table 1 below. The feedstock, case 1 for 0.lmol/kg
glucose in 4.8 kg/h supercritical water and case 2 for
0.2mol/kg glucose in 4.8 kg/h supercritical water are
applied616]
Table 1
Wind direction angle()
Figure. 12 Mixed convection heat loss with different external wind
direction and velocity
With various external wind direction and velocity, the
convection heat loss of the cavity has been worked out.
Three representative wind direction angles, i) 00 for headon;
ii) 900 and 2700 for sideon; iii) 1800 for backon have been
chosen to study the direction influence. The variation of
convection heat loss with wind velocity difference is shown
in Fig. 12. It can be seen that, for the velocity more than
3m/s, the trends of convection heat loss are similar. This is
due to the Richardson number above 1, which is the
determined number for mixed convection heat transfer. For
this condition forced convection is dominate, and the
maximum value exists at the same angles.
R Gr ApgL
Ri = 2 2(17)
Re2 pU2
It is observed that the convection heat loss for sideon
wind is greater than the headon and backon cases. The
sideon wind can generate swirling flow in cavity and
enhance the flow speed close to the inner surface. For this
reason, the maximum convection heat loss occurs at the
sideon case. Higher wind speed produces high heat loss
except the case of 2m/s at 1800 angle. This is due to the fact
that the backon wind acts as a barrier at the cavity aperture
preventing the hot air movement from the receiver.
Conclusions
In this communication, based on the assumption of the
uniform solar flux distribution in the inner surface of the
receiver, the effects of thermal loads, inclination angles,
secondary concentrator and external wind are studied
numerically for the biomass gasification hydrogen
production solar cavity receiver were investigated. The
following conclusions can be drawn from this study.
(1) The radiation heat loss and convection heat loss have
been achieved with various heat load of the cavity.
With heat flux increasing inward the cavity, an
increase of both radiation and convection heat loss
happens. Otherwise, radiation heat loss grows faster
than convection heat loss.
(2) The natural convection heat loss from the receiver for
various orientations has been predicted. The
maximum convection heat loss occurs at the 00
inclination, which is 77.2% of total heat loss. In
contrast, the minimum convection heat loss occurs at
900 inclination, 28.7% of total heat loss.
(3) The results of a 3D numerical analysis of solar cavity
without wind effect have been presented in terms of
Nusselt number correlations for inner surface
temperature and inclination angle. The correlation
degree and standard deviation have been given. The
comparison of present model with previous models
has done.
(4) The relationship of convection heat loss with external
wind direction and velocity has been investigated to
speed range of Im/s to 5m/s and direction of headon,
backon and sideon. The results shows that higher
speed external wind produces greater convection heat
loss and sideon direction causes maximum value.
(5) The overall heat transfer characteristic of solar cavity
receiver has been studied. The various heat fluxes are
calculated and presented.
(6) The accuracy of the combined natural convection and
surface radiation heat loss estimations of cavity
receiver may be improved by incorporating radiation
model using Monte Carlo Method for solar radiative
flux distribution in the cavity inner surface.
Acknowledgements
This research has been carried out sponsored by "National
Basic Research Program of China" (No. 2009CB220000)
and "The National High Technology Research and
Development Program of China" (No. 2007AA05Z147).
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