Download Performance of a new packed bed using stratified

Performance of a new packed bed
using stratified phase change capsules
..............................................................................................................................................................
Lei Yang and Xiao-song Zhang *
School of Energy and Environment, Southeast University, Nanjing, China
.............................................................................................................................................
Abstract
This article presents a numerical study of a new packed bed using a stratified phase change material
(PCM). The PCM is injected into polycarbonate spheres as phase change capsules. Water is used as
heat transfer fluid (HTF) for charging or discharging thermal energy to the PCM. Three kinds of
paraffin that have different melting points are used as the PCM and placed in the packed bed at
different heights. The PCM at the higher melting temperature is placed nearer to the hot water inlet.
The numerical calculation of HTF is based on the one-dimensional Schumann’s model, while the
temperature of the PCM is simulated using the apparent heat capacity method. Both charge and
discharge processes of this new stratified packed bed have been studied. The effects of HTF average
velocity and inlet temperature have also been investigated. Both the energy and exergy performance are
compared with those of the packed bed using only one kind of PCM. The comparison results indicate
that this new stratified packed bed has an advantage over traditional packed bed in terms of energy and
exergy.
Keywords: packed bed; stratified PCM capsules; numerical study; energy; exergy
*Corresponding author:
[email protected]
Received 25 November 2011; revised 23 February 2012; accepted 27 February 2012
................................................................................................................................................................................
1 INTRODUCTION
The latent heat storage has attracted a large number of applications in recent years due to much higher energy storage
density with a smaller temperature swing when compared with
the sensible heat storage method [1– 4]. Because of the poor
thermal conductivity of most phase change materials (PCMs),
heat transfer enhancement should be considered. A large improvement in the energy transfer rate can be obtained by encapsulating the PCM in small plastic spheres [5, 6] to form a
packed bed storage unit.
Farid [2] had suggested the use of more than one PCM
with different melting temperatures in a thin flat container to
improve the storage performance. Farid et al. [7, 8] developed a
unit consisting of vertical tubes filled with three types of waxes
having different melting temperatures. Both theoretical and
experimental measurements showed an improvement in performance. Watanabe et al. [9] developed a second law analysis
of a latent heat storage system with the PCM having different
melting points, and the distribution of optimum melting
points was estimated.
Gang and Mujumdar [10] presented a thermodynamic analysis of the thermal energy charge/discharge processes in a
latent heat thermal storage system using multiple PCMs.
Analytical results show that the exergy efficiency can be
enhanced dramatically using multiple PCMs compared with
single PCM. Fang and Chen [11] presented a theoretical model
for a shell and tube latent thermal energy storage unit using
multiple PCMs. Numerical results indicated that both the
PCM’s fractions and melting points play an important role in
the performance.
The charging and discharging rates are strongly dependent
on the difference between fluid temperature and melting
points of PCMs. Because the temperature of heat transfer fluid
(HTF) changes in its flow direction, this temperature difference
between the fluid and the PCMs also decreases in a single-type
PCM heat storage system, which causes a decreased charging
and discharging rates as fluid flows across PCMs. However, the
latent heat storage system with PCMs having different melting
points provides nearly constant temperature difference. So the
heat fluxes from fluid to the PCMs are nearly constant too.
The exergy loss of the system is also reduced, and enhancement
of energy charge – discharge can be achieved.
Although there is much research on the multiple PCM
storage system, its utilization in packed bed units is rare. In
this article, a stratified packed bed thermal storage unit using
three kinds of PCM having different melting points was
numerically studied. The system is designed to store redundant
solar energy in summer, and the storage energy is used for producing domestic hot water on rainy days. The utilization of
International Journal of Low-Carbon Technologies 2012, 7, 208– 214
# The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
doi:10.1093/ijlct/cts027 Advance Access Publication 2 April 2012
208
Performance of a new packed bed
multiple PCMs can greatly increase the energy storage or
release rate, accordingly improving the system performance. So
the energy and exergy performances were analyzed and compared with a single packed bed using only one kind of PCM.
The effects of HTF velocity and inlet temperature for this new
packed bed have also been investigated.
obtained from the literature [12]. The chosen PCMs do satisfy
domestic hot water usage and the differences of their melting
temperature are approximately the same. The paraffin of
melting point at 468C (C22H46) is used for comparison.
3 MATHEMATICAL MODEL
2 SYSTEM DESCRIPTION
The new packed bed thermal storage unit using stratified PCM
capsules is shown in Figure 1. The storage tank is of 0.60 m
height and 0.36 m diameter, which is insulated with glass
wool. The PCM capsules are made of polycarbonate spheres
filled with paraffin, and placed in series in the tank. PCMs
with higher melting points are placed in higher positions
where they are closer to the HTF inlet.
Hot water is used as HTF and flows from the top down to
melt the PCM in the charge process, while in the discharge
process, cold water flows from down to the top. The hot water
can be produced from solar energy or other renewable heat
resources. In off-peak hours, electrical energy can also be used
to make hot water.
Three kinds of paraffin are used as PCMs. Their thermophysical properties are presented in Table 1, which can be
For a simplified model, the following assumptions are made:
(i) the fluid flow is laminar and incompressible; (ii) the flow
field is steady state and the velocity is fully developed; (iii)
radial heat transfer and heat losses to the surroundings are
neglected; (iv) the effect of natural convection in the melting
of the PCM is neglected, and the thermal resistance of the
capsule wall is zero; and (v) the thermo-physical properties of
the PCM and HTF are temperature-independent.
Under the above assumptions, the one-dimensional
Schumann’s model [13] is adopted to describe the heat transfer
of HTF through the storage tank:
@Tf
@Tf
@ 2 Tf
þu
¼ kf
þ
ha
ðT
T
Þ
ð1Þ
1rf cf
p p
f
@t
@x
@x2
where Tf is the water temperature, rf and cf are the density and
heat capacity, respectively, kf the thermal conductivity, Tp the
temperature of the PCM, ap the superficial particle area per
unit volume, 1 the void fraction of the storage tank, h the heat
transfer coefficient between water and PCM capsules, which
can be estimated from an empirical correlation proposed by
Beek [14]:
Nu ¼ 3:22Re1=3 Pr1=3 þ 0:117Re0:8 Pr 0:4
ð2Þ
where Nu is the Nusselt number, Pr the Prandtl number and
Re the Reynolds number.
For the solution of PCMs, the apparent heat capacity
method is used. This method regards the phase change process
occurring in a small temperature range and takes the latent
heat as a large apparent heat capacity in the temperature range.
So, the equation of PCM heat transfer in the storage tank is:
ð1 1Þ Cp
Figure 1. Schematic diagram of the stratified packed bed.
Table 1. Thermo-physical properties of paraffin.
Paraffin
C21H44
C22H46
C24H50
Melting point
(K)
311.35
317.15
323.75
Latent
heat
(kJ/kg)
Density
(kg/m3)
213
252
255
788
791
796
Specific heat
(J/mol K)
Solid
Liquid
570.7
598.1
651.4
698
739
805
@Tp
¼ hap ðTf Tp Þ
@t
ð3Þ
where Cp is the apparent heat capacity of the PCM which can
be determined as follows:
8
r cs
ðTp , Tm DTÞ
>
>
< s
rs cs þ rl cl
rL
Cp ¼
þ
ðTm DT Tp Tm þ DTÞ
>
2
2DT
>
:
rl cl
ðTp . Tm þ DTÞ
where Tm is the melting temperature of the PCM and L the
melting latent heat. r and c are the density and heat capacity,
respectively, and the subscripts s and l mean the solid and
International Journal of Low-Carbon Technologies 2012, 7, 208– 214 209
L. Yang and X. Zhang
liquid state. DT is the semi-phase change temperature range,
which is set as 0.18C here.
In the charge process, the initial temperature of both PCM
and HTF is set as 308C, while 608C is used in the discharge
process. The inlet and outlet boundaries are both isothermal
conditions.
Equations (1) and (3) are approximated by the control
volume method [15]. The simplicity of Equation (3) allows
an explicit statement for the temperature of PCM, while
Equation (1) is solved using an implicit manner. In every
time step, convergence was considered to be reached
when temperature residuals of both HTF and PCM fell
below 1024.
In order to validate the model and assumptions, numerical simulation is conducted for the condition of the experimental measurement in the literature [16]. The experimental
setup consists of an insulated cylindrical storage tank with
0.36 m diameter and 0.46 m height. The packing (storage
medium) is formed by 55-mm diameter plastic spheres filled
with paraffin wax having a melting temperature of 608C.
The total number of capsules in the storage tank is 264,
and the spherical capsules are uniformly packed in eight
layers. Water is used as HTF and the inlet temperature is
708C. The flow rate of HTF is 2 l/min and the initial temperature is 328C.
Figure 2 presents the numerical and experimental temperature of the PCM at the half height and outlet of the tank. As
can be seen in Figure 2, the numerical result agrees well with
the experimental measurement.
The grid independence inspection is also made in the preliminary calculations to examine the effects of time step and
grid size on the solution. Two time steps, viz. 0.005 and 0.01 s,
and three different grid sizes, viz. 0.0025, 0.005 and 0.0075 m,
were tested. As a compromise between the calculating time and
the accuracy, 0.01 s and 0.005 m were adopted as the time step
and grid size, respectively.
Figure 2. Comparisons of numerical results with experimental results.
210 International Journal of Low-Carbon Technologies 2012, 7, 208– 214
4 RESULTS AND ANALYSIS
The energy and exergy analysis of this stratified packed bed
are made and compared with the traditional packed bed using
a single PCM. Both charge and discharge processes are
researched.
The instantaneous energy transfer rate is:
qðtÞ ¼ mf cf jTf;in Tf;out j
ð4Þ
Taking the storage tank as a heat exchanger, the energy efficiency can be expressed as follows:
Tf;in Tf;out hðtÞ ¼ ð5Þ
Tf;in Tf;ini where mf is the mass flow rate of water and subscripts in,
out and ini, respectively, indicate inlet, outlet and initial
conditions.
4.1 Charge process
In the charge process, hot water flows from the top down
through the packed bed and transfers energy to the PCM. The
average flow velocity is 0.0001 m/s, and the inlet temperature is
constant at 608C.
Figure 3 shows the outlet water temperatures of this stratified packed bed and single PCM packed bed. The stratified
packed bed took 180 min to completely melt the PCM. But
for the single PCM packed bed, nearly 240 min was needed.
So, the charge period can be observably reduced by using more
than one kind of PCM. This advantage is very important and
beneficial to latent energy storage.
Figure 4 displays the variations of energy transfer rate versus
charge time. The transient energy rate of the stratified packed
bed is higher than that of the single PCM bed after 60 min. In
this figure, where the energy transfer rate changes little it
Figure 3. Outlet water temperature during the charge process.
Performance of a new packed bed
Figure 4. Energy transfer rate during the charge process.
Figure 5. Exergy storage during the charge process.
means the melting is in progress. For the stratified packed bed,
the melting started earlier than the single bed, and the phase
change duration is shorter. When the outlet temperature of
water is equal to the inlet temperature, the charge process is
completed, which leads the energy transfer rate to be zero.
In the charge process, the total exergy supplied by HTF can
be expressed as follows:
Exsup ¼
Tf;in
mf cf Tf;in Tf;out T0 ln
dt
Tf;out
0
ðt
ð6Þ
where T0 is the reference temperature as 308C.
Neglecting exergy stored by plastic capsules and exergy gain
due to heat leakage, the total exergy charged is the sum of
charged exergy of HTF and the PCM.
The charged exergy at the PCM is:
ExPCM ¼
Tp;i
MPCM;i cp;l Tp;i Tl;i T0 ln
Tl;i
i
X
Ts;i
MPCM;i cp;s Ts;i Tp;ini T0 ln
þ
Tp;ini
i
X
Tl;i
MPCM;i cp Tl;i Ts;i T0 ln
þ
Ts;i
i
X
Figure 6. Exergy supply during the charge process.
supplied exergy and charged exergy as follows:
ð7Þ
The first term, second term and last term of Equation (7)
denote charged exergy during liquid state, solid state and twophase state, respectively.
The charged exergy at the HTF is:
ExHTF ¼
X
i
Tf;i
MHTF;i cf Tf;i Tf;ini T0 ln
Tf;ini
ð8Þ
In the charge process, the exergy efficiency is the ratio of
hex;char ¼
ExHTF þ ExPCM
Exsup
ð9Þ
The variation of exergy storage versus charge time was shown
above. Because the average melting temperature of the stratified
packed bed is approximately the same as that of the single bed,
when the charge is completed, the difference in the exergy
storage is not significant according to Equations (7) and (8).
From Figure 5, it can also be seen that the charge period
needed is reduced by using the stratified bed.
Although the total charge exergy of the stratified packed bed
and the single packed bed are nearly the same, the supplied
exergy from HTF of the former is lower than the latter in
Figure 6, which means less exergy is destroyed. So from
International Journal of Low-Carbon Technologies 2012, 7, 208– 214 211
L. Yang and X. Zhang
Equation (9), the stratified packed bed will have higher exergy
efficiency.
4.2 Discharge process
In the discharge process, cold water flows from the down to
the top through the packed bed and absorbs energy from the
PCM. The average flow velocity in the charge process is
0.0001 m/s, and the inlet temperature is constant at 308C.
As aforementioned, the effect of natural convection in the
phase change process was neglected. So the discharge process
will show the converse results of the charge process. Its energy
transfer rate and efficiency can also be calculated from
Equations (4) and (5). The energy transfer rate and efficiency
variation versus time are the same as that of the charge process,
which is not shown here.
There are some differences in the exergy analysis. In the discharge process, the initial exergy was the charged exergy in the
charge process. With the discharge in progress, the remaining
exergy kept decreasing. When the remaining exergy reached
zero, the discharge process ended.
The net discharge exergy is:
ðt
Tf;out
dt
ð10Þ
Exdis ¼ mf cf Tf;out Tf;in T0 ln
Tf;in
0
In the discharge process, the exergy efficiency is expressed as
the ratio of the net discharge exergy and the initial exergy:
hex;dis ¼
Exdis
Exini
ð11Þ
Figure 7 shows the variation of the net exergy discharge versus
discharge time. The net exergy discharge of the stratified
packed bed is higher than that of the single bed, which means
that the exergy destroyed is lower. Namely in the discharge
Figure 7. Exergy discharge during the discharge process.
212 International Journal of Low-Carbon Technologies 2012, 7, 208– 214
process, the stratified packed bed has smaller irreversibility.
The result is similar to the charge process. This figure also
shows that the new packed bed can reduce the discharge
period.
The exergy efficiency of a complete cycle with the charge
and the discharge processes can be defined as the ratio of the
net discharged exergy during the discharge process to the net
charged exergy during the charge process [9]. So, the exergy efficiency can be expressed by the product of the exergy efficiencies of the charge and discharge processes as follows:
hex;cycle ¼ hex;char hex;dis
ð12Þ
For the charge, discharge and complete cycle, the exergy efficiency is shown in Figure 8. It can be clearly seen that, in the
charge, discharge or the complete cycle, the stratified packed
bed has a higher exergy efficiency than the single packed bed.
4.3 Influence of average velocity of HTF
From the comparison analysis, the stratified packed bed has
greater advantages over the single bed. In this section, the
influence of HTF velocity for this new packed bed was studied.
For the symmetrical characteristic of the charge and discharge
processes in the energy analysis, only the charge process was
mentioned here. Four different velocity values were compared
and the inlet temperature was set to be constant at 608C.
Figures 9 and 10 show the outlet temperature and energy
transfer rate for various values of average velocities. It can be
seen from Figure 9 that the time for complete charge decreases
when the velocity of HTF increases. The time for complete
charge decreases almost by half when the velocity increases
from 0.0001 to 0.0002 m/s. But the effect will not be so significant, when the velocity increases very highly.
In Figure 10, the higher the velocity of HTF is, the higher
the energy rate that can be reached, and hence less time
for complete charge is needed. This is due to an increasing heat
transfer coefficient between HTF and PCM capsules.
Furthermore, the increasing velocity enhances the axial convection heat transfer in the water existing in the void of the packed
Figure 8. Comparison of the exergy efficiency.
Performance of a new packed bed
Figure 9. Outlet temperature for different velocities.
Figure 11. Outlet temperature for different inlet temperatures.
Figure 10. Energy transfer rate for different velocities.
Figure 12. Energy transfer rate for different inlet temperatures.
bed, making the temperature of this part of the water to
increase faster. The increased temperature difference between
the water and the PCM also leads to an increased energy
transfer rate.
the higher inlet temperature results in a higher temperature
difference between HTF and the PCM, and the energy transfer
rate increases. From these two figures, it can be seen that when
the inlet temperature of HTF increases from 58 to 648C, the
time for complete charge can decrease by nearly 1 h. Higher
inlet temperature can also raise the quality of energy storage
and is good for latent energy storage.
4.4 Influence of the inlet temperature of HTF
In this section, the influence of HTF inlet temperature for this
new stratified packed bed was studied. Only the charge process
was researched. Four different inlet temperature values were
compared. The velocity of HTF was set to be 0.0001 m/s.
Figures 11 and 12 show the outlet temperature and energy
transfer rate for various values of inlet temperatures. Higher
inlet temperature of HTF leads to higher energy transfer rate,
which consequently reduces the charge time. This is because
5 CONCLUSIONS
A numerical investigation is performed for a new stratified
packed bed using a PCM having different melting points. The
following conclusions can be drawn:
International Journal of Low-Carbon Technologies 2012, 7, 208– 214 213
L. Yang and X. Zhang
(1) The stratified packed bed can reduce energy charge and discharge time compared with a single packed bed. This advantage is very beneficial for latent energy storage and usage.
(2) The stratified packed bed has less irreversibility than a
single packed bed. In the charge, discharge or the complete
cycle, the stratified packed bed has higher exergy efficiency
than a single packed bed.
(3) Increasing HTF velocity can increase the energy transfer
rate and reduce the charge (or discharge) time. But the
effect will not be so significant when the velocity increases
very highly.
(4) Higher inlet temperature of HTF can increase the energy
transfer rate and reduce the charge (or discharge) time,
and also raise the quality of storage energy.
ACKNOWLEDGEMENTS
This work is financially supported by the 12th Five Year
National Science and Technology Support Key Project of China
(No. 2011BAJ03B14).
REFERENCES
[1] Lane GA. Low temperature heat storage with phase change materials. Int J
Ambient Energy 1980;1:155– 68.
[2] Farid MM. Solar energy storage with phase change. J Solar Energy Res
1986;4:11– 29.
[3] Bedecarrats JP, Strub F, Falcon B, et al. Phase-change thermal energy
storage using spherical capsules: performance of a test plant. Int J Refrig
1996;19:187 –96.
214 International Journal of Low-Carbon Technologies 2012, 7, 208– 214
[4] Esen M, Durmus A, Durmus A. Geometric design of solar-aided latent
heat store depending on various parameters and phase change materials.
Sol Energy 1998;62:19– 28.
[5] Wood RJ, Gladwell SD, Callahar PWO, et al. Low temperature thermal
energy storage using packed beds of encapsulated phase-change materials.
In: Proceedings of the International Conference on Energy Storage, Brighton,
UK, 1981, pp. 145 – 58.
[6] Saitoh T, Hirose K. High-performance of phase change thermal
energy storage using spherical capsules. Chem Eng Commun
1986;41:39 –58.
[7] Farid MM, Kanzawa A. Thermal performance of a heat storage module
using PCMs with different melting temperatures: mathematical modeling.
Trans ASME J Sol Energy Eng 1989;111:152– 7.
[8] Farid MM, Kim Y, Kanzawa A. Thermal performance of heat storage
module using PCMs with different melting temperatures: experimental.
Trans ASME J Sol Energy Eng 1990;112:125– 31.
[9] Watanabe T, Kanzawa A. Second storage law optimization of a latent heat
system with PCMs having different melting points. Heat Recovery Syst
CHP 1995;15:641– 53.
[10] Gang ZX, Mujumdar AS. Thermodynamic optimization of the thermal
process in energy storage using multiple phase change materials. Appl
Therm Eng 1997;17:1067 –83.
[11] Fang M, Chen GM. Effects of different multiple PCMs on the performance of a latent thermal energy storage system. Appl Therm Eng
2007;27:994 –1000.
[12] Himran S, Suwono A. Characterization of alkanes and paraffin waxes for
application as phase change energy storage medium. Energy Sources
1994;16:117 –28.
[13] Schumann TEW. Heat-transfer: a liquid flowing through a porous prism.
J Franklin I 1929;208:405 –16.
[14] Beek J. Design of packed catalytic reactor. Adv Chem Eng 1962;3:203– 71.
[15] Patankar SV. Numerical Heat Transfer and Fluid Flow. Hemisphere
Publishing Corporation, 1980.
[16] Nallusamy N, Sampath S, Velraj R. Experimental investigation on a combined sensible and latent heat storage system integrated with constant/
varying (solar) heat sources. Renew Energy 2007;32:1206– 27.