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Heat of fusion heat exchangers
Samuel J. Crawford1
University of New South Wales at the Australian Defence Force Academy
Phase Change materials provide an excellent means of storing heat energy by
employing their latent heat properties. Domestic hot water systems could benefit greatly
from the addition of a Latent Heat Storage System as this would allow heat stored
during the day to be used at night. Alan Fien and Dr Murat Tahtali have developed a
new technique for encapsulating Rochelle’s salt that provides a high capacity and cheap
method of creating a Latent heat Storage System. This projects aims at optimizing the
geometry of the capsule and exploring the capabilities of this new Latent Heat Storage
System.
Contents
I.
II.
Introduction
Background
A. Preceding research
B. Phase change material candidates
C. Rochelle‟s salt
D. Computer simulation methods
E. Solar power
F. Parcel geometry
G. Expected operating conditions
III. Methodology
A. Simulating the parcel
B. Internal heat flow model
C. Rigid body simulator
D. Heat exchanger flow model
IV. Results
A. Internal heat flow model
B. Rigid Body Simulator
C. Heat exchanger model
D. Combined analysis
V. Recommendations
VI. Conclusion
Acknowledgements
References
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APPENDICES
Appendix A. Project Gantt Chart
Appendix B. Work Breakdown Structure
Appendix C. Results of Rigid Body Simulator
Appendix D. Results of Heat Exchanger Analysis
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SBLT, School of Aerospace, Civil & Mechanical Engineering. ZACM4050.
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Final Thesis Report 2009, UNSW@ADFA
A1
B1
C1
D1
Nomenclature
Terms:
PCM
LHSS
CFD
DHW
FEM
VOF
RBS
2D
3D
=
=
=
=
=
=
=
=
=
Parameters:
Q
=
q
=
q”
=
V
=
Vp
=
Vw
=
cp
=
cv
=
L
=
g
=
k
=
ρ
=
Tout
=
Tin
=
Ts
=
T∞
=
Tf
=
A
=
xw
=
v
=
β
=
l
=
Ra
=
Np
=
Phase Change Material
Latent Heat Storage System
Computational Fluid Dynamics
Domestic Hot Water
Finite Element Modeling
Volume of Fluid method
Rigid Body Simulator
Two dimensional
Three dimensional
total heat energy within system [J]
the rate of change of heat energy within the system [W]
the heat flux through the surface [W·m-2]
total volume [m3]
parcel volume [m3]
water volume [m3]
specific heat [J·kg ·K-1]
volumetric specific heat [J·m-3·K-1]
heat of fusion latent heat [J·kg-1]
acceleration due to gravity [m·s-2]
thermal conductivity [W·m-1·K-1]
density [kg·m-3]
temperature of the flow exiting the system [K]
temperature of the flow entering the system [K]
temperature of the surface [K]
ambient temperature of the surrounding fluid [K]
film temperature, the average between the surface and ambient temperatures [K]
surface area [m2]
length of wall [m]
dynamic viscosity [m2·s-1]
Boussinesq coefficient [K-1]
fraction of liquid
Rayleigh’s number
number of parcels
I. Introduction
he modern household expects a constant source of domestic hot water twenty four hours a day. To
maintain this supply a typical, commercially available hot water system will use two basic methods
to heat the water to the required temperature; electrical or gas powered elements. On average, these
hot water systems consume 26.6% [1, 2] of a standard household‟s annual energy usage. In order to offset the
associated power costs, many Australian households have been outfitted with solar hot water systems, which
utilize solar radiation to supplement the electric or gas elements. Such systems have the potential to reduce the
energy of a hot water system by up to 75%. However, in general their contribution is to only slightly reduce
household heating costs [3], due to the limited ability of a hot water system to store heat energy. Current
domestic hot water systems utilize the specific heat of the supply water to store the heat energy. This creates a
restriction on the amount of heat that can be stored in DHW system, as the volume of water is limited by the
size of the containment tank and current law requires the system to maintain a safe temperature at or below
80°C to avoid scalding and greater than 60°C to halt Legionella growth [3], thus greatly limiting the amount of
specific heat it can store in the water. Another method for storing heat energy is through the latent heat of a
material. The latent heat of a material is the energy stored and released during a phase change. Traditionally,
latent heat has a much greater storage density than specific heat, for example it takes 8 times more energy to
raise the temperature of an ice cube at 0°C, than the same mass of water at 1°C [4]. Another benefit of utilizing
latent heat is that during the phase change, the materials temperature remains theoretically constant whilst
releasing heat energy [5]. This may be used in a domestic hot water system to store significant heat energy
without exceeding safe temperatures. Systems that incorporate the use of the latent heat properties of specific
materials are defined as Latent Heat Storage Systems (LHSS).
T
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Final Thesis Report 2009, UNSW@ADFA
Alan Fien and Dr Murat Tahtali have developed a new type of LHSS and manufacturing process which
involves small pillow shaped parcels made of an aluminium skin containing a Phase Change Material (PCM).
The PCM used will be Rochelle‟s salt; a dry salt with a melting point of 75°C. These parcels are poured into a
water heater container where the water flow interacts directly with the aluminium skin to transfer the heat
energy to and from the PCM. This system is intended to supplement current domestic hot water designs, by
simply pouring the parcels into the water heater storage units of these systems, with no thought given to the
arrangement of the parcels. This system may also be used in a large storage tank with a looped water system.
The looped water system supplies a flow to heat exchangers which transfer the heat energy into a separate DHW
flow indirectly, reducing the consequences of leaking or split parcels and allowing the use of a thermo-syphon.
Using a randomly packed arrangement means the parcels can be mass produced and implemented in the
marketplace quickly and cheaply, thereby greatly increasing the chance the system will be economically viable.
This LHSS would be most useful when used in conjunction with a solar hot water system. With a greater heat
energy storage density, a solar hot water system could store, during its daily charge cycle, the necessary energy
to be released when no sunlight is available, effectively removing the need to supplement the system with an
external power source. This system may also be utilised in an apartment block hot water system, where a
centralised storage tank can be supplemented with this LHSS as readily as can a DHW system, with little or no
alterations.
The aim of this project is to determine the heat transfer properties of the capsule form developed by Alan
Fien and Dr Murat Tahtali and to optimize the capsule shape. This involves analysing the basic shape and
adjusting the shape based on a set of geometric variables; the basis for adjustment is the heat transfer properties
and manufacturability. A Gandtt chart outlining the project‟s timeline and its Work Breakdown Structure is
provided in Appendix. A. The ultimate goal of the project is to prove the feasibility of this LHSS and to explore
the benefits or detriments that can be gained through its use.
II. Background
A. Preceding research
The first encapsulation method to receive widespread attention was the finned tubing heat exchanger
apparatus [6, 7]. A first notable attempt was that of Sparrow, Larsen and Ramsay [6]. They demonstrated the
benefits of using a finned tube against a finless, simple tube. The PCM used was a Paraffin wax, chosen for its
thermal stability. Their experiment has shown that the use of a finned tube rather than a simple one greatly
increases the heat transfer rates of the PCM material. The cost of the finned tubing limited further applications
and development. These were some of the earliest experiments to demonstrate the problems associated with the
drop in conduction due to the lack of convection when the PCM is freezing. This problem is due to the layers of
PCM close to the cooling source freezing first. Once frozen, the system relies on the conduction of the solid
PCM to transport the heat to the flow, which is persistently as poor as the liquid PCM.
In an attempt to remove the heat conduction problem most researchers have adopted a method of adding a
highly conductive material to the PCM. The result is usually a composite material with less storage density but
much greater heat flux. One such example created by Mehling, H., S. Hiebler, and F. Ziegler [8] consists of
around 80% PCM and 20% porous graphite, resulting in a material with a reported solid thermal conductivity of
approximately 25W·m-2∙K-1, which is a vast improvement over the standard commercial paraffin waxes
(~0.56W·m-2∙K) [9].
Agyenim, Eames and Smyth [10] investigated the comparison between using single and multi-tube systems
to increase the conductivity. Their results show there is a significant increase in thermal conductivity and
useable heat capacity due to the inclusion of extra internal piping. Their experiment also demonstrated the
presence of super-cooling within the paraffin based PCM.
There have been many experiments conducted with regards to various methods of encapsulating a PCM.
Depending on the PCM used and the method of encapsulation, most experiments reveal certain problems when
dealing with a LHSS so, as a result few have proved economically feasible. Lane [11] attempted to find a
diverse range of materials that could be encapsulated and used in a PCM module. Primarily they were trying to
create a Microencapsulated PCM using a polyester resin. Over 200 potential PCM‟s were used. The best
results were achieved by using CaCl2 · 6H2O; a hydrated salt. Stark [12] created a composite material using the
mircopores of a polymer film to hold the PCM. The volume of the PCM accounted for roughly 40% of the
composite. This system promoted mechanical stability during the melting/freezing phase transition.
Considering the cost involved with manufacturing and the low volume of PCM, this approach was largely
inadequate for use as a LHSS. Royon [13] developed a new material that contains the PCM within a
polyacrylamide in a 3D structure rather than the previously used 2D plate type arrangement. The product
remained well shaped, thermally stable and well suited for high cost applications but regrettably, it has little
relevance to the commercial DHW market. Hong and Xin-Shi [14] developed a compound that uses dispersed
paraffin and a high density polyethylene supporting material. The procedure created a relatively cheap, high
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Final Thesis Report 2009, UNSW@ADFA
heat storage capacity material that has many applications for lower temperature heat storage. However, as the
paraffins that are employed are limited to 55°C, it only has a limited applicability to DHW systems. Further
research into microencapsulation techniques has been carried out by a number of researchers [15]. However
their relevance appears limited to heating applications in space due to their high cost. Nonetheless, they are
reported to be effective forms of a LHSS.
B. Phase change material candidates
As described in [5, 9] the requirements of a domestic thermal energy storage system limit the PCM options
available to be used safely and economically. The basic requirement for a PCM is that it must have a
melting/freezing transition temperature within a useful range. For example, to provide an adequate heat storage
in a DHW system, the PCM must melt and freeze around 60-75°C [9]. Ideal PCM candidates are those that fill
the criteria of having a high heat of fusion, high thermal conductivity, high specific heat capacity, small volume
change during phase transition, non-corrosive, non-toxic properties and limited decomposition through heat
cycles with limited sub-cooling.
There has been significant research carried out towards the various substances that can be used as a PCM.
Several researchers have documented and updated lists of possible PCM‟s as more research is channeled
towards finding a commercially viable substance. Some of the more comprehensive lists have been created in
Abhat, Lorsch and Farid [5, 16, 17]. These lists may prove useful if Rochelle‟s salt is found to be inadequate
for the application.
The first PCM‟s to be used were based around inorganic salts. Initially it was thought that hydrated salts
would provide the best combination of low cost, high volumetric storage density and good conductivity.
However the problems due to phase segregation and super-cooling necessitated a nucleation agent to ensure that
the hydrated salt would melt congruently [5, 9]. These nucleation agents lower the volumetric heat storage
capacity of the PCM, therefore reducing their effectiveness.
Later, experimentation attempted to improve the performance of paraffin based waxes to levels appropriate
to a DHW LHSS, and closer to hydrated salts. Paraffin waxes have been found to have excellent thermal
stability over a large number of cycles [18]. However on average, by comparison, they only have half the
volumetric storage density of hydrated salts.
Hendra, Hamdani, Mahlia and Masjuki [19] evaluated the use of a material commonly found in Indonesia
known as Mikro which is composed of 60% Paraffin, 8% Damar (wood spices), 32% Kendal (animal fat) and
Vaseline with latent heat of 1.14 × 105 J/kg. Though the material appears no better or worse than any other
paraffin based PCM, the results illuminate the relationship between the performance parameters and the heat
flux. They also demonstrate the necessity to maximise the heat flux, to ensure the LHSS is capable of a high
heat energy output.
Interestingly, no experimentation into the thermo-physical properties of Rochelle‟s salt above 33°C has been
performed. This is unusual as dry Rochelle‟s salt has a melting temperature of approximately 75°C [20] which
is almost ideal for DHW use. It is also possible that a dry solution of Rochelle‟s salt will not exhibit the same
phase segregation problems associated with hydrated salts. Unless the experimentation surmises that Rochelle‟s
salt is not suitable as the PCM, it will remain the prime candidate. The phase volume change of Rochelle‟s salt
is expected to be similar to that of most PCMs, in the order of 10%; however due to large variations between
PCM‟s, it is unreasonable to assume this value is accurate [5, 9].
It should be noted that Kenisarin and Mahkamov [21] contended that the methods of differential thermal
analysis and differential scanning calorimetry are insufficient for developing a clear indication of the thermophysical properties of a PCM. This raises the question as to why almost every method used to experiment on
PCMs has been either of these two. They also cited the possible need for an international standard of testing
and a need for an international scientific centre to adopt the responsibility.
Eutectic compounds are the newest form of PCM to the field of LHSS research. Only a handful of useful
Eutectic compounds have been discovered and fewer still have undergone significant research into their
properties. Baran and Sagi [22] have investigated a Eutectic PCM containing palmitic and stearic acids. The
properties are found to be similar to that of paraffin waxes with a melting temperature of 52.3°C, a latent heat of
181.7 kJ/kg and high thermal stability. Jotshi, Hsieh, Goswami, Klausner and Srinivasan [23] experimented
with a Ammonium alum and ammonium nitrate that together form a eutectic that melts at 53°C and solidifies at
48°C, again with excellent thermal stability properties.
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Final Thesis Report 2009, UNSW@ADFA
C. Rochelle’s salt
Due to project time constraints and inaccessibility to lab equipment and personnel, an experiment to
determine the thermal properties of Rochelle‟s salt was not completed for this project. Therefore in order to
create a baseline feasibility study, an educated estimation into the expected properties of Rochelle‟s salt was
used as a substitute PCM. This was executed with a focus towards ensuring that a replacement PCM would
provide similar results should Rochelle‟s salt prove ineffective as a DHW PCM. Given the focus on creating a
cheap economically viable LHSS, it is expected that a paraffin based wax or hydrated salt will provide an
alternative to Rochelle‟s salt. Table 1 has been formulated by combining data from Abhat and Mohammed [5,
9] charting the most potential replacement paraffin waxes and hydrated salts.
In order to properly simulate the performance of the parcels, specific information is needed about the
TABLE 1: C ANDIDATE PHASE CHANGE MATERIALS
PCM
Melting
point (°C)
Latent Heat of Fusion per
-3
volume (kJ·m )
Latent Heat of Fusion per
-1
mass (J·kg )
Thermal Conductivity solid phase
-1 -1
(W·m ·K )
Parrafin 5913
22
145
190
0.21
Parrafin 6106
42
145
190
0.21
Parrafin 5838
48
145
190
0.21
Parrafin 6035
58
150
190
0.21
Parrafin 6403
62
150
190
0.21
Parrafin 6499
67
155
190
0.21
Octadecane
28
190
245
0.15
N/A
KF.4H2O
18.5
336
231
CaCl2.6H2O
29.7
256
171
N/A
Na2SO4.10H2O
32.4
377
254
0.544
NaHPO4.12H2O
35
405
281
0.514
Zn(NO3)2.6H2O
36.4
304
147
N/A
Na2S2O3.5H2O
48
322
201
N/A
Ba(OH)2.8H2O
78
581
267
N/A
MgCl2.6H2O
116
239
165
N/A
material they contain. Without certified knowledge of the characteristics of Rochelle‟s Salt, the properties of
the generally named „PCM‟ within the parcel are modeled using established features of previously tested PCMs.
Rochelle‟s salt is likely to exhibit behaviors similar to that of aqueous salts. Similarly, it is also more likely to
exhibit the same problems; therefore a replacement to Rochelle‟s salt will most likely be a paraffin based wax,
in order to avoid the problems associated with aqueous based salts. Because the properties of most aqueous
salts demonstrate performance that typically matches or betters that of paraffin based waxes, a simulation safety
margin was chosen which meant that the parcel PCM is modeled more acutely to the attributes of paraffin
waxes. A more comprehensive list of PCMs and their properties can be found in [5]. This list has been
shortened further into an index of the most relevant PCMs in [24]. From Table. 1 it can be established that
inorganic salts have a heat of fusion averaging from 200J·m-3, slightly higher than that of paraffin waxes from
180J·m-3. However as these substances are aqueous they do not fully represent a dry Rochelle‟s salt; a value
closer to the paraffin wax is used here. Therefore a heat of fusion of 200J·m-3 is used to represent Rochelle‟s
Salt. The Melting Temperature of dry Rochelle‟s Salt is reported by Newnham and Cross [20] as being 75°C,
which has been used in any simulations. The average thermal conductivity of the inorganic salts is 0.56W/m·K
(liquid) and 0.9W/m·K (solid) [24], which will be used to estimate Rochelle‟s salt. The PCM is modeled with a
density of 1600kg·m-3 and a specific heat capacity the same as water at 4182J·kg-1·K-1.
D. Computer simulation methods
There are many CFD methods that overcome the problems associated with the unusual discontinuity caused
by the phase boundary of the PCM as it freezes and melts during the heating cycles. Generally the more
complex the method, the more computationally expensive it becomes. A standard FEM analysis doesn‟t
provide a clear indication as to the location of the phase boundary. Since the phase boundary is continually
changing and the properties of the material either side of the boundary are significantly different, its position
needs to be accurately tracked during each iterative step. For that reason, standard FEM analysis is inadequate
and a different approach is required.
The “moving boundary-moving mesh” approach described by Albert and O‟Neill [25] constantly updates the
mesh so that it‟s boundary aligned with that of the phase boundary. This approach ensures that the properties of
the two phases remain distinct and allows the computation of the inner elements to be handled separately,
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Final Thesis Report 2009, UNSW@ADFA
subsequently maintaining a high level of computational efficiency. Overall this is a relatively simple method
that has been proven as effective and accurate. FLUENT adopts a similar approach to deal with interfaces
between phases. It uses a fixed grid combined with an algorithm to track and update the exact position of the
phase interface independent of the grid. FLUENT describes this method as the “Volume of Fluid” (VOF)
method. The “Constant Interpolation Profile” method as described in Yabe, Xiao and Utsumi [26] typically
deals with multiphase systems that include gas and plasma. Moreover the method can still be adopted for use
here. It exploits the semi-langarian scheme with transforming grids to extend the usability of the method to
compressible flow. Even so, the method is overly complex for a relatively simple phase change system such as
this. A fixed grid, sharp interface method has been developed by Ye, Shyy and Chung [27] that instead uses a
fixed grid similar to that of a standard FEM analysis. However the grid includes a sharp detail algorithm at the
interface between the changing phases. The mass, momentum and energy conditions are explicitly calculated
along the boundary to provide an accurate representation of the moving boundary. This method is better suited
to gas based phase changes than to solid-liquid interfaces. A continuous interface method which deals with a
slow transition between liquid and solid phases may be used. However this process is computationally
expensive [25] and has the potential to create inaccuracies in the system as described by Ye, Shyy, Tai and
Chung [28]. Since the interface within the parcel is far more likely to be fairly distinct, a continuous interface
would create needless complications.
Creating a program to simulate the random packing arrangement of the parcels is a difficult task.
Nandakumar [29] has developed a search algorithm that arranges particles of arbitrary shape within a container.
The algorithm does not simulate the dynamics of the packing process; instead it attempts to find an adequate end
state through collision detection and search algorithms. Nandakumar‟s simulation also reveals the porosity and
is capable of finding the expected pressure loss for a given arrangement. Stroeven [30] has developed a
software package that deals with the random packing of particles in cement. The principal is the same as the
requirements of this project. Jia [31] has developed a packing algorithm that deals only with arbitrary shapes as
opposed to most algorithms that deal with spheres alone. The algorithm is reported to be much faster than
others as it digitises both the shape and container for simpler calculations, reducing the required computations.
Despite these techniques no commercially available software package accessible to support this project‟s
simulation.
E. Solar power
There has been very little research performed regarding the performance improvements gained by using a
LHSS in conjunction with a DHW system [32]. There are two reports that attempt to find the advantages of
coupling the two systems. Ibáñez, Cabeza, Solé, Roca and Nogués [33] experimented with the long term effects
of utilising a simple LHSS in arrangement with a solar powered water heater in Spain. The model was created
with TRNSYS and used a simple example of a PCM module to simulate the heating/cooling cycle. The results
demonstrate a decrease in energy required from the local power grid of approximately 4-8% over an annual
cycle. However the results are vague and there is insufficient boundary conditions given to recreate the
experiment. It should be noted that these results were also derived from European weather conditions, which
are vastly different to Australian conditions.
Talmatsky and Kribus [32] investigated the gain to be had to the end user by implementing a basic LHSS
with a solar powered DHS system. They experimented with changes in load profiles, different PCM volume
fractions, different kinds of PCM and the site at which the system is tested. Contradictory to belief, the results
have shown that the addition of the PCM system yielded no significant advantages over current specific heat
storage systems. It was found that there was unexpected additional heat losses occuring during the freezing of
the PCM throughout the night cycle. El-Sebaii, Al-Ghamdi, Al-Hazmi and Faidah [34] implemented a simple
setup using solar radiation to heat a thin layer of stearic acid within a basin containing water during daylight
hours to determine the effects of the PCM during the night. Results, though vague, demonstrated a significant
improvement had been sustained within the night cycle as the temperature of the water would remain relatively
constant through the entire phase thus requiring less energy from external sources, in some tests none. The
variations between experiments mean that no significant conclusion can be made concerning the benefits of a
LHSS without continued research.
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Final Thesis Report 2009, UNSW@ADFA
F. Parcel Geometry
The shape of the parcel is defined by
the manufacturing technique that will be
used in its creation. The extent to which
the shape can be altered is limited by
how the manufacturing plant can be
manipulated. The process begins with a
flat plate of a specified width and an
assumed infinite length. The plate is fed
into the plant which then bends it into a
long cylinder and laser welds the seam.
This means the circumference of the
cylinder is defined by the width of the
plate.
The long cylinder is then
vertically lowered into the next stage. A
set of gears have the dual action of
pulling the cylinder through the plant
Figure 1-Geometry of the parcel, including important features
and kinking both ends of the parcels at
the required lengths. The gear teeth close the first end and a PCM is poured into the open end of the parcel from
above until it is overflowing. By that time the gears have pulled the parcel up, until the next set of kinking teeth
which seal the remaining open end of the parcel. Following the gear teeth is a welding tool that permanently
seals the kinked ends of the parcel. The teeth on the gears set the other variable within the manufacturing plant,
the length of each parcel. Subsequently the parcels have been set up virtually to allow alterations in both length
and diameter for each experiment. Note that this process allows no air within the parcel, which is important for
volume change induced stress analysis. The result of the manufacturing process is shown in Fig. 1. The width
of the parcel is defined by the diameter, approximately equal to half the circumference of the cylinder used to
create the parcel. This project aims to create a desired length and diameter of the parcel, allowing the
manufacturing plant to be setup as follows:
𝑊𝑖𝑑𝑡𝑕𝑝𝑙𝑎𝑡𝑒 = 𝑊𝑖𝑑𝑡𝑕𝑙𝑎𝑠𝑒𝑟 𝑠𝑒𝑎𝑚 + 𝜋 ∙ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑝𝑎𝑟𝑐𝑒𝑙
(1)
𝐴𝑛𝑔𝑙𝑒𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑒𝑒𝑡 𝑕 = 360 ∙ 𝐿𝑒𝑛𝑔𝑡𝑕𝑝𝑎𝑟𝑐𝑒𝑙 𝜋 ∙ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑔𝑒𝑎𝑟
(2)
G. Expected Operating Conditions
DHW systems operate over varying
loads during their daily cycle. This is
due to the cycle of day and night and the
influence this has on human behavior.
This means that a hot water system
typically experiences higher loads during
the early night and early morning, and
low to no loads during the peak daylight
hours in the middle of the day. As a
consequence, this LHSS will be
expected to work with two distinct
cycles; a charge cycle during the day and
Figure 2 – Diagram of thermo-syphon and storage tank arrangement
a discharge cycle over the peak usage
time. For this project, the LHSS is expected to store all the energy it will require in its charge cycle and release
energy the same amount in the discharge cycle. An average Australian individual will use approximately 50L of
domestic hot water per day2, which in a typical domestic hot water system is requisite to a temperature of 6570°C. Accordingly the LHSS will be required to store enough heat energy to supply 50L of hot water per
person. As this LHSS is expected to cycle daily with a charge cycle (heating cycle) occurring during the day
and a discharge cycle (cooling cycle) occurring during the night, the total required heat capacity is given by Eq.
(3), assuming a water density of 1000kg·m-3 and that the charge cycle is capable of both keeping the temperature
of the water constant and charging at the same time.
𝑄 = 𝑉𝑐𝑣𝑤𝑎𝑡𝑒𝑟 𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛
(3)
= 50 ∙ 4181.3 ∙ 65 − 15 = 10.45𝑀𝐽 𝑝𝑒𝑟 𝑑𝑎𝑦 𝑝𝑒𝑟 𝑝𝑒𝑟𝑠𝑜𝑛
The average instantaneous flow rate required by a family of five is approximately 25L per minute, which is
the common flow rate of non-water saving showerheads2. This roughly equates to 0.42L·s-1, which is the
2
http://www.sedo.wa.gov.au/pages/hot_water.asp
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Final Thesis Report 2009, UNSW@ADFA
expected maximum flow rate required by a household with 2.5 bathrooms3. A reasonable mixture rate is two to
one cold water to hot water in Australia3. Therefore the maximum heat rate required by a household is given by
Eq. (4) [35].
(4)
𝑞 = (0.42 ∙ 0.33) ∙ 4181.3 ∙ 65 − 15 = 28.9𝑘𝑊
With a daily limit of 50L of hot water equates to an absolute maximum of 6 minutes of shower time per
person per day. Note that neither of these quantities are exact values for the requirements of a domestic hot
water system but are estimations only. The requirements of hot water systems vary widely between different
areas and assorted households. These values are considered by the researcher to be the plausible target
requirements for an average Australian domestic hot water system, based on research performed into currently
available systems and household usage. This system may also be used in large apartment blocks. This is the
reason heat capacity is given on a per person basis, with the intention that it can be easily scaled to expected
requirements. Large apartment blocks can use systems that employ a thermo-syphon arrangement to stimulate
flow within the system, thereby eliminating the need for an externally powered pump. Figure 2 provides a
demonstration of the setup of such a system.
The heat flow through the parcel is caused by two methods; conduction and convection. As there is no air
gap within the parcel, there is no potential for significant radiative heat transfer to occur. Conduction occurs
due to the molecular interaction between the PCM, the parcel skin and the external water flow. The skin of the
parcel is intended to be aluminum with a thermal conductivity k of approximately 248.5W·m-1·K-1 [36] Copper,
with a higher thermal conductivity at approximately 405W·m-1·K-1 [36], may be used as an alternative. This
indicates that the conductivity of the skin is approximately three orders of magnitude greater than the
conductivity of the PCM. The skin thickness, which is expected to be no more than 0.5mm, is also much
smaller than the diameter of the parcel at 12mm. This signifies that the effect of the aluminum skin on the speed
of the heat flow in and out of the PCM is negligible as the heat flow through the PCM is significantly slower
than that of the skin. This assumption is made for each of the models where the aluminum skin is not modeled
to avoid adding unnecessary complexity to the mesh.
Conduction is defined by the following equation [36]:
𝑑𝑇
(5)
𝑞 = 𝐴𝑞 ′′ = −𝐴𝑘𝑐
= 𝑚𝑐𝑝 𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛
𝑑𝑥
Convection is based on the following equation [36]:
𝛿𝑇
𝑞 = 𝐴𝑞 ′′ = −𝐴𝑘𝑓
= 𝐴𝑕𝑓 (𝑇𝑠 − 𝑇∞ )
(6)
𝛿𝑦 𝑦=0
Convection in a system is predicted by the Rayleigh number of the system. The Rayleigh number relates the
buoyancy forces to the thermal diffusivity of the system. A low Rayleigh number indicates that the force due to
convection is insignificant. The critical Rayleigh number, as given by Incropera [36] is 103. To establish the
significance of the natural convection developed within the parcel, the Rayleigh number of the fluid within the
parcel must be compared to the critical Rayleigh number.
𝑔 1 𝑇𝑓 𝜌𝑃𝐶𝑀 𝐶𝑝
(7)
𝑅𝑎 =
𝑇𝑠 − 𝑇∞ 𝑥 3
𝑣𝑘
−9.81 ∙ 1 318 ∙ 1600 ∙ 4183.3
=
288 − 348 ∙ 0.0123 = 58.9 ≪ 103
0.404 ∙ 0.9
Therefore it can be concluded that the effect of convection within the parcel is negligible as there is
insufficient room and viscosity for any plausible natural convection. Note that since the dynamic viscosity of
the PCM is not known, the dynamic viscosity of water is used instead. This is expected to create a Rayleigh
number higher than the actual due to the low viscosity of water. Therefore the total heat energy contained
within the parcel is defined as the total specific heat contained by both phases of the PCM plus the latent stored
within the molten phase.
𝑞 = 𝑐𝑣𝑠𝑜𝑙𝑖𝑑 𝑃𝐶𝑀 𝑇𝑝 𝑉𝑝 ∙ 1 − 𝑙 + 𝑐𝑣𝑙𝑖𝑞𝑢𝑖𝑑 𝑃𝐶𝑀 𝑇𝑝 𝑉𝑝 ∙ 𝑙 + 𝐿𝑃𝐶𝑀 𝜌𝑉𝑝 ∙ 𝑙
If the volumetric specific heat cv is the same for either phase of the PCM then this reduces to:
𝑞 = 𝑐𝑣 𝑇𝑝 𝑉𝑝 + 𝐿𝑃𝐶𝑀 𝜌𝑉𝑝 ∙ 𝑙
(8)
The thermal conductivity is taken to be constant throughout this project, irrespective of whether a different
PCM is used in future as each PCM has a similar conductivity, as shown in Table. 1. This implies that the
conduction is mainly dependent on the temperature difference and the size of the parcel which defines the dx
(Eq. (5)) and the area (Eq. (5)). These equations demonstrate that the heat flow within is most influenced by the
thermal conductivity and temperature difference of the parcels. The significance of the thermal conductivity as
compared to the geometry of the parcel is explained later in the results chapter. These equations also
demonstrate the relationship between surface area and heat flux and volume and heat capacity. Increasing the
volume of parcels will increase the amount of PCM within the parcel and therefore the amount of heat energy
3
http://www.hotwaterexperts.com.au/Uploads/Images/rheen-instant.pdf
8
Final Thesis Report 2009, UNSW@ADFA
single parcels can store. Similarly, increasing the surface area of the parcels will increase the rate at which heat
can be released into the surrounding flow. However, increasing the size of the parcel also increases the
characteristics length, limiting the ability for heat at the centre of the parcel to reach the surface. These
properties and others are investigated in the following chapters.
III. Methodology
This chapter describes the methods used to develop each model and the reasoning behind certain parameter
selections. Note that the ANSYS supplied utilities GAMBIT and FLUENT are the meshing and CFD programs
chosen for use in this project. MATLAB is used as the primary programming language, except where otherwise
stated.
A. Simulating the parcel
Several simulations are conducted in this project and each has the following underlying characteristics. The
manufacturing process used to create these parcels is not available to the researcher at the time of writing this
document, therefore the true shape of the parcel can only be estimated based on the process that will be used to
create it. Therefore the estimated parcel shape, as defined in Fig. 1, is used as a basis for all simulations
conducted here. Only the diameter or length of the parcel is changed as all other features are defined by these
two parameters. The PCM contained within the parcel is modeled as described in the Chapter II part C and is
consistent within the project. Water is the only fluid that is modeled to interact with the parcels beside the
PCM. Where it is modeled, it is defined as having the parameters given in Callister [37]. As described in
Chapter II part G, the aluminium skin of the parcels is not modeled due to its insignificant affect on heat
conduction.
B. Internal heat flow model
This model is used to represent the internal heat flow through the PCM within the parcel by recreating the
expected geometry of the final parcel and simulating a flow of water over its surface. The parcel‟s geometry, as
seen in Fig. 1, is symmetrical about three planes. Accordingly, the model generated has been created as an
eighth of the whole parcel shape, with three simulated symmetry planes. This allows for an overall finer mesh as
less volume is required to be meshed. Several different models are used in this experiment; each varied slightly
in either the diameter or length parameters. This was done to examine the heat properties of the parcel with
respect to changes in diameter and length. There are also two separate groups of simulations performed as the
parcel will have two distinct cycles within its environment. These are the charging and discharging cycles as
described in Chapter II part G, identified as the heating and cooling cycles here respectively. The heating cycle
is set as having a PCM initially at 65°C upon having reached the temperature of the surrounding water after the
previous discharge cycle. At this temperature the PCM is solid. The parcels walls are set at a constant
temperature of 80°C, representing the water flowing over the parcel after being heated by an external source
such as solar power or a gas or electrical element. The cooling cycle uses a PCM initially set at 80°C, having
been heated from the previous charge cycle. The PCM is a liquid at this temperature. The surrounding water
flow is modeled at 65°C, requiring the fluid to be further heated to at least 70°C by the parcels. In a thermosyphon arrangement, the return water from the heat exchanger loop will have ideally equalised with the
incoming domestic cold water, raising its temperature to 65°C. This is not exactly the case as, realistically,
there will be a temperature gradient between the top and bottom of the thermo-syphon heat exchanger.
However this is viewed by the researcher as being the worst case scenario regarding heat flux where, if the
system is able to cope with the low heat flux here, it is assumed it will be able to do this under normal operating
conditions. Each FLUENT model is set with transient conditions using a pressure based solver and the solution
is found accurate to the first order with the interior fluid modeled as the PCM described in Chapter II part D. A
step size of one second is implemented as this adequately shows trends within the heat properties as
demonstrated by Fig. 7. The mesh for each model is generated in GAMBIT with a minimum of 150,000 cells to
ensure sufficient accuracy [38]. The model uses six different lengths and five different diameters, creating thirty
models in total. The variances caused by these altering models are investigated to in order to develop
relationships between the length, diameter and heat flux and energy storage capacity.
In order to gain a preliminary understanding of the mechanics driving the heat flow through the parcel, a
prototype model using a much finer grid of 342,136 cells and a smaller time step size of 0.25 seconds was
produced. This was implemented to create a basis from which to compare all the other models and to establish
the heat property trends of the parcel as there is no previously established research into the effects that the
unusual shape of the parcel may have on these properties.
C. Rigid Body Simulator
The rigid body simulator was tasked with creating a packed bed of randomly arranged parcels within a unit
volume in order to gain an understanding of the performance of the parcels within a heat exchanger
9
Final Thesis Report 2009, UNSW@ADFA
environment. As the parcels are intended to be poured into a cylinder, with no thought given to their placement,
a method for randomly packing the parcels into an area needs to be created to simulate the parcels falling into a
heat exchanger. Although several methods exist, after many attempts, the researcher found that the only method
that would produce significantly accurate results involved modeling the trajectory and motion of the parcels
falling into a container. This necessitated the creation of a simplified rigid body simulator that uses an ODE and
the equations of motion, coupled with a collision detection and resolution system to properly model the path of
the parcels as they fall and bounce off the container and each other. As described in Chapter II parts D there
were no commercially available products found that could meet these requirements, and the simulator had to be
created from scratch. In order to reduce the significant development time, the simulator was restricted to
dealing only with gravity, collisions and a simplified form of friction. After research into the guides provided
by Baraff, Guendelman and Dingle [39-41], the algorithm shown in Fig. 3 was created for the simulator:
RIGID B ODY SIMULATOR ALGORITHM
Figure 3 - Flowchart describing Rigid Body Simulator algorithm
The algorithm in Fig. 3 returns the safe position and orientation of the parcel after it has come to rest, by
calculating the remaining kinetic energy within the parcel and checking to see if any more motion is possible.
The code to run this simulation was created in MATLAB with some minor code written in C++ to increase
computational speed. The safe position of the parcel that is returned is the last position found where no contact
is occurring, at a distance threshold smaller than 0.001mm. The translation of the parcel is returned in (x, y, z)
coordinates about the origin which is also the centroid of the container. The orientation of the parcel is returned
as a vector and an angle. The vector describes the axis as a direction from the origin about which to rotate. The
angle is the amount of rotation required using the right hand rule4. A demonstration of the aforementioned
rotation method is given in Fig. 4. The results were created in this way for ease of exportation to GAMBIT.
EXAMPLE OF RIGID B ODY SIMULATOR TRANSLATION AND ROTATION
Figure 4 - Example of vector axis rotation
After extracting the results from the rigid body simulator, an intermittent step is used where another MATLAB
program takes the simulator results and creates a journal file to be read into GAMBIT which creates, translates
and rotates the parcels within a unit volume essentially automatically resulting in a model ready for meshing.
This was undertaken because of the excessive number of attempts to ensure that the simulator was producing
accurate results and so inspection of these attempts became a time consuming priority. The code that was used
4
http://www.magnet.fsu.edu/education/tutorials/java/handrules/index.html
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Final Thesis Report 2009, UNSW@ADFA
for this simulation is entirely too large and complex to be included with report but can be obtained by contacting
the author.
D. Heat exchanger flow model
The aim of this model is to investigate the
performance of the parcels within a unit
volume of heat exchanger. This is performed
using the position and orientation results
given by rigid body simulator to place the
parcels within a randomly packed bed and
modeling the water surrounding the parcels.
The parcels are alleged to keep a constant
temperature throughout the simulation,
assuming it to remain at 75°C whilst
discharging their heat energy into the flow
through their surface. The water within the
model is assumed to be incoming at 60°C.
This value was chosen over the previously
used 65°C to create a more pronounced flow
which is easier to visualize. The model
created by GAMBIT and used in this
experiment appears as shown in Fig. 5. Each
Figure 5 - Model of unit volume of water excluding parcel volumes
model is based on a unit volume of
125,000mm3, equal to 125mL and in the shape
of a symmetrical cube of side length of 50mm. The parcels used in this model have a diameter of 12mm and a
length of 32mm. This was chosen by plant manufacturer Alan Fien and the most likely final shape of the parcel.
Therefore each parcel has an approximate volume of 2.5mL as reported by FLUENT.
This model represents the volume of water contained within a unit volume of heat exchanger. The holes in
the figure are the volumes where the parcels were placed and subtracted. Unfortunately, due to the random
nature of the parcel arrangement, meshing this volume in three dimensions is very difficult and no workable
solution was found within the project‟s timeline. As a compromise, a section taken through the middle of the
volume was created and meshed in two dimensions then provided there was no mesh skewing, this would
provide a model from which probable conclusions could be made.
In order to determine whether a thermo-syphon arrangement is possible, the convective heat properties of the
water flow needs to be determined. This is obtained by modeling the natural convection of the water within the
parcel environment. To do this in FLUENT, two methods were attempted. The basic method used by this model
is to simply define a density of the water based on temperature. This causes a buoyancy force on the parcels due
to the pressure created from the difference in temperature between regions and their corresponding densities.
The density is defined by linear interpolating between a value of 983.2kg·m-3 at 60°C and 971.8kg·m-3 at 80°C5.
Although the relationship between density and temperature is not linear, a linear model is accurate enough for
the purpose of this experiment [38]. However it was found that FLUENT would not converge to a solution with
this model, therefore the Boussinesq model was used for all experiments. The Boussinesq equation simplifies
the FLUENT solver by replacing the buoyancy term with the following approximation:
∴ 𝜌 − 𝜌0 𝑔 ≈ −𝜌0 𝛽 𝑇 − 𝑇0 𝑔
(9)
This is done by using the Boussinesq approximation:
𝜌 = 𝜌0 1 − 𝛽∆𝑇 𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 𝛽 𝑇 − 𝑇0 ≪ 1
𝜌 − 𝜌0
∴𝛽=
−𝜌0 𝑇 − 𝑇0
983.2 − 971.8
=
= −5.8654 ∙ 10−4
−971.8 ∙ 353 − 333
This method typically results in a faster convergence, as described in [38]. Also as natural convection
models have greater difficulty converging, a low Rayleigh number, given in Eq. (7), is used initially, and is
steadily increased until the model is accurate. This allows the model to stabilize quicker as there is less chance
of a vortex developing. The Rayleigh number is allowed to converge in step increments increasing until a
gravity force of 9.81ms-2 is attained. Besides the water flow properties, other geometric properties such as the
volume ratios and the average cross sectional area are determined to provide information about the performance
required by the parcels.
5
http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html
11
Final Thesis Report 2009, UNSW@ADFA
The volume is discovered using a CATIA based analysis of the model exported from GAMBIT. The cross
sectional area is also examined by CATIA by taking six cross sections of the model and reporting the area
ratios.
IV. Results
Each contrasting model has created a separate differing result that necessitates their own separate analysis to
understand the principals and relationships driving each property. At the end of this section the results are
combined in order to gain insight on whether this project has revealed if this LHSS is feasible.
A. Internal heat flow model
The internal heat flow model demonstrates the link between the solid profile and the temperature
distribution. The shape of the parcel is the primary factor affecting the temperature profile of the parcel,
followed closely by the difference in thermal conductivity between the two phases. The outer edges of the parcel
act like fins, creating a short characteristic length. This creates a large area for the heat to flow through,
meaning that the outer edges cool the quickest. The centre of the parcel resembles an oblong sphere. A sphere
has the shortest characteristic length of any object, inferring that it has minimal surface area per volume. This
means that the PCM within the centre of the parcel takes much longer to cool. This can be seen in Fig. 6,
where, although the initial solid profile has the same shape of the parcel, it quickly forms an oblong sphere
similar in shape to the centre of the body.
Figure 6 – Temperature and Solidity profile taken through the centre plane of the parcel
Figure 6 describes the temperature distribution of the parcel compared to the solid profile of the PCM. It can be
seen that the solid purple region closely matches that of the liquid phase of the material. This is because of the
transient heat loss properties of the parcel. The parcel does not release its heat in a steady fashion. Instead, it
initially releases its heat very easily into the surrounding flow, benefitting from the high heat flux caused by the
large temperature difference between the parcel and the flow. As heat is released from the parcel, this
difference drops quickly as a solid layer forms from the inner surface of the parcel skin. The PCM around the
outter edges rapidly solidifies, having the greatest access to the water flow. As this layer grows it creates an
increasing gap between the water flow and the hotter molten centre of the parcel. The growing temperature gap
exponentially decreases the ability for the parcel to transfer heat out of its surface. This effect is also seen in
Fig. 6 through monitoring the way this layer increases with time. This exponential decrease in heat flux is
demonstrated in Fig. 7b, which depicts the heat flux and subsequent stored heat energy in the system over time.
Note that the simulation is run until 99% of the stored heat has been released.
12
Final Thesis Report 2009, UNSW@ADFA
4
Stored heat Vs Time
120
0
-1
Surface heat flux (W/m2)
100
Stored heat (J)
80
60
40
20
0
Surface heat flux Vs Time
x 10
-2
-3
-4
-5
-6
0
50
100
-7
150
0
50
Time (s)
a)
100
150
Time (s)
b)
Figure 7 – a) The stored heat energy within the volume of a parcel. b) The heat flux through the surface of the parcel.
As can be seen in Fig. 7a, the stored heat within the parcel has an exponential relationship with the heat flux
of the parcel surface over time. In fact the derivative of the stored heat is directly proportional to the heat flux.
This is expected as there is no other method by which the parcel may lose energy. As a result, it is expected this
LHSS will store the heat very efficiently given that there cannot be any losses due to friction because there are
no required motion of particles but, if an occurrence eventuates, it will only aid the system.
There are two separate cycles for the parcel to undergo on a daily basis. The second cycle, as described in
Chapter II part G, is the charge cycle, where the LHSS is assumed to have no stored energy and a flow of
externally heated water passes over the parcels to charge them by increasing their temperature. The surface heat
flux and stored heat for an individual parcel over time for the charge cycle is given in Fig. 8.
4
Stored heat Vs Time
120
7
6
Surface heat flux (W/m2)
100
Stored heat (J)
80
60
40
20
0
a)
Surface heat flux Vs Time
x 10
5
4
3
2
1
0
50
100
Time (s)
150
200
0
0
50
100
Time (s)
150
200
b)
Figure 8 – a) The stored energy within the volume of a parcel. b) The heat flux through the surface of the parcel
The charging cycle of the parcels takes significantly more time to reach an asymptote as compared to the
discharge cycle. This can be contributed to the differenent thermal conductivity arrangement between the two
cycles. The discharge cycle begins with a liquid centre forming a solid layer which increases over time. The
charge cycle is the exact opposite, beginning with a solid centre generating into an increasing liquid layer over
time. The higher conductivity of the solid layer causes a decreasing thermal conductivity in the charge cycle
which is initially high. Despite this however, the profile between the two figures remains the same, indicating
that the speed by which the heat is transferred is governed by the conductivity but the gradient of heat transfer
remains a function of the parcel geometry. Despite this the two systems are almost completely symmetrical. By
comparing figure blah and figure blah, it can be seen that the charge cycle takes 48% more time to complete. A
comparison between the average temperature between the two cycles is given in Fig. 9.
13
Final Thesis Report 2009, UNSW@ADFA
Average parcel temperature through Discharge cycle
Average parcel temperature through Charge cycle
80
80
Average temperature of parcel (oC)
Average temperature of parcel (oC)
78
75
70
76
74
72
70
68
65
0
50
100
66
0
150
50
100
Time (s)
Time (s)
a)
150
200
b)
Figure 9 - Temperature profile of both cycles over time a) Discharge cycle. b) Charge cycle
The initial quick temperature change seen in Fig. 9 can be contributed to the change in specific heat of the
PCM. This change occurs rapidly until the freezing or melting point of the PCM is reached, at which point the
change in temperature decreases with time until it asymptotes around the maximum or minimum temperature.
The second component of the internal heat flow model is to develop relationships between the shape of the
parcel as defined by its length and diameter and its heat properties. Figure 10 displays the results of this
experiment by comparing the average heat flux and stored heat over a period of one minute when the length or
diameter of the parcels is held constant. Note that error bars are included in the figure to give an indication as to
inaccuracies caused by the slight variations between the numbers of cells between meshes.
Heat transferred through surface Vs Diameter
Length:50mm
400
Average Total Heat Energy over 1min (J)
Average heat transferred through surface over 1min (J)
Total heat energy Vs Diameter
350
300
Length:44mm
250
200
Length:38mm
150
Length:32mm
100
Length:26mm
50
Length:20mm
6
8
10
12
a)
14
16
Diameter (mm)
18
20
1.4
Length:50mm
1.2
1
Length:44mm
0.8
Length:38mm
0.6
Length:32mm
0.4
Length:26mm
0.2
Length:20mm
6
22
8
300
250
Diameter:17mm
200
Diameter:14mm
100
Diameter:11mm
50
Diameter:8mm
20
c)
25
30
35
Length (mm)
40
45
50
Average heat transferred through surface over 1min (J)
Average Total Heat Energy over 1min (J)
Diameter:20mm
150
12
14
16
Diameter (mm)
18
20
22
Heat transferred through surface Vs Length
Total heat energy Vs Length
400
350
10
b)
1.4
1.2
Diameter:20mm
1
Diameter:17mm
0.8
0.6
Diameter:14mm
0.4
Diameter:11mm
0.2
Diameter:8mm
20
25
30
35
Length (mm)
40
45
50
d)
Figure 10 - a) Average heat store for constant length. b) Average heat flux for constant length. c) Average heat store for constant
diameter d) Average heat flux for constant diameter
There are several important characteristics that can be derived from Fig. 10. The first is the importance of
changes in diameter against changes in length. From Fig. 10a and c it can be seen immediately that diameter
has a much greater effect on the heat storage capacity of the system. Also, the heat flux is affected by diameter
greater than length although lesser so than the heat storage capacity. Given that the heat storage capacity of the
parcel increases more rapidly than the heat transfer rate, there may be some implications to increasing the
diameter to meet heat flux requirements. This is owing to the fact that, as the heat storage capacity increases,
there may be wasted amounts of PCM that do little to assist the performance of the system and may add
14
Final Thesis Report 2009, UNSW@ADFA
unnecessary costs to the manufacturer. Increasing the length of the parcel provides an almost linear increase in
both heat storage capacity and heat transfer rate. This may allow the manufacturer to meet heat flux
requirements whilst minimising wasted heat storage capacity. Moreover it is likely that, compared to diameter,
increasing length will have a greater effect on reducing the density of the packed. This conclusion is based on
the fact that increasing the diameter will make the parcel more similar to a sphere, which has a higher packing
density, than an elongated cylinder in shape; similar to the parcel in a random arrangement. It will likely be a
fine balance between the two parameters that will determine the optimum shape of the parcel.
Frequency of result
B. Rigid Body Simulator
The Rigid Body Simulator works via the
algorithm described in Chapter III part C and
Histogram of RBS results
results recorded are in the form of a table
4
containing the position and rotation of each
parcel after the simulation has been run for a
3
set number of parcels or, until the container is
full. In this study there were five separate
2
experiments run, each beginning with a
1
different starting point in order to ensure that
they all remain distinct from one another. This
0
was accomplished since it is believed by the
14 15 16 16 17 18 19 20
researcher that a single experiment cannot
adequately define the conditions of a randomly
Number of parcels per unit volume
packed bed of parcels. The comprehensive list
of simulation results is given in Appendix. B.
Figure 11 - Histogram of RBS results
Given the variability of the results achieved, a
statistical study to indicate the level of accuracy from the results is performed. The outcome is given in Fig. 11.
Although there were only a small number of tests performed, this data demonstrates a number of significant
discrepancies within the results. This is not unexpected, since this simulation is of a randomly arranged packed
bed. However this information does indicate that the approximate value of parcels per volume is not the
average value, but instead, it‟s more likely to be approximately 18.5, the value that will be used in further tests.
C. Heat Exchanger model
Several results were derived from the heat exchanger model. Firstly, the volume and cross sectional area
ratios are given in Table. 2. These ratios describe the volume of water per volume of parcels. Each model
resulted in a different ratio which can be contributed to the random packing nature of the parcels. It is assumed,
although not proven in this project, that over an infinitely large volume, this ratio would eventually reach an
asymptotic value. The variances in results between several tests performed are given in Fig. 11. The results
given in Table. 2 are an extract from the complete results attached in Appendix. C.
TABLE 2: P ARTIAL RESULTS OF RBS
Test 1
Test 2
Test 3
Test 4
Test 5
Average
Water percentage of volume
Parcel percentage of cross sectional area
63.27
36.53
70.53
26.40
62.79
37.97
64.14
33.95
63.01
34.96
64.75
33.96
Number of parcels per unit volume
18.31
14.69
18.55
17.87
18.44
17.57
20,378.48
15,990.06
20,619.42
20,020.72
20,093.82
19,420.50
Parcel surface area per unit volume
(mm2)
Figure blah – table of partial results of RBS
As described in Chapter II part G, the water volume required by an individual is 50L per day. This Chapter
also describes the amount of heat energy required by the parcels. The water surrounding the parcels is assumed
to sustain a temperature of 75°C, having equalised with the surrounding parcels. Therefore the required volume
of parcels, total volume and subsequent number of parcels are given by the following equations:
𝑄 = 10.5𝑘𝐽 𝑝𝑒𝑟 𝑝𝑒𝑟𝑠𝑜𝑛 𝑝𝑒𝑟 𝑑𝑎𝑦 = 𝐿𝑃𝐶𝑀 𝜌𝑝 𝑉𝑝 + 𝑐𝑣𝑤𝑎𝑡𝑒𝑟 ∆𝑇𝑤𝑎𝑡𝑒𝑟 𝑉𝑤𝑎𝑡𝑒𝑟
(10)
𝑉𝑝 = 0.3525𝑉
(11)
(12)
𝑉𝑤𝑎𝑡𝑒𝑟 = 0.6475𝑉
𝑄
∴ 𝑉𝑡𝑜𝑡𝑎𝑙 =
0.3525𝐿𝑃𝐶𝑀 𝜌𝑝 + 0.6475𝑐𝑣𝑤𝑎𝑡𝑒𝑟 ∆𝑇𝑤𝑎𝑡𝑒𝑟
10450000
=
= 37.96𝐿
0.3525 ∙ 180 ∙ 1600 + 0.6475 ∙ 4181.3 ∙ (75 − 15)
37.96
∴ 𝑁𝑝 =
∙ 18.5
0.125
15
Final Thesis Report 2009, UNSW@ADFA
= 5619 𝑝𝑒𝑟 𝑝𝑒𝑟𝑠𝑜𝑛 𝑓𝑜𝑟 𝑡𝑕𝑒 𝑝𝑎𝑟𝑐𝑒𝑙 𝑜𝑓 𝑙𝑒𝑛𝑔𝑡𝑕 32𝑚𝑚 𝑎𝑛𝑑 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 12𝑚𝑚
Note that these equations assume that the specific heat storage in the parcels is negligible. This is calculated
for two reasons. Firstly it would have a very small effect as the parcels remain fixed and only their temperature
difference would count towards the stored energy, which would only be in the range of 5-10°C. Secondly, this
information is not yet established at the time of writing and thirdly the specific heat of the PCM is also expected
to be much lower than that of water. The number of parcels represents the minimum required to supply 50L of
hot water per cycle per person. In this simplified form, this shows that this LHSS has the potential to reduce the
size of the typical domestic hot water system by up to 24%, at least in heat energy capacity terms.
However the LHSS also has a requirement to be capable of producing a large amount of heat for fixtures for
short periods of time as described in Chapter II part G. The LHSS is required to have the capacity to deliver
28.9kW (Eq. (4)) of energy into the flow for a short period of time. As shown by Fig. 7b, the heat flux through
the surface of the parcel is not constant. To equal the performance of modern hot water systems, the LHSS must
be capable of delivering this energy, even at the end of the cycle when heat flux is minimal. In order to
maintain a shower at constant temperature, each parcel in the LHSS must be able to deliver the following heat
energy into the flow.
−28900
(13)
𝑞=
= −5.14𝑊
5619
𝑞
−5.14
(14)
𝑞 ′′ = =
= −4.36𝑘𝑊 · 𝑚−2
𝐴 1.18 ∙ 10−3
By interpolating the data given in Fig. 7b, it is shown that the modeled parcel is able to supply this heat flux
for almost 9 seconds if the temperature difference between the surface of the parcel and the flow remains
constant. This is obviously an inadequately short time to have a shower. However, this does not properly
define the true reaction of the
parcel as the temperature will not
remain constant and the parcel
will not need a heat flux greater
than the requirement specified
here. Any heat flux that is not
required will not cause a transfer
of heat into the flow.
To determine whether the
heat exchanger can be used in
conjunction with a thermosyphon, the water flow driven by
convection within the heat
exchanger must be found. As
stated previously, a 3D mesh
could not be generated without
error and therefore a 2D mesh
representing the cross section of
the volume was created. This 2D
mesh represents the system with
Figure 12 – Pathlines of fluid, with coloured temperature gradient (K), taken as a cross
section through unit volume of parcels, which are represented as white areas.
reasonable accuracy; however,
note that this is not the ideal
model as 2D flow has a limited capacity to avoid obstacles when compared with a 3D flow. Figure 12 and 13
represents the flow as streamlines through the cross section. These pictures demonstrate the complexity of the
flow within the system due to the random packing arrangement.
16
Final Thesis Report 2009, UNSW@ADFA
Figure 13 – Close to converged results of natural convection simulation, pathlines with coloured temperature gradient (K)
There were five tests using different cross sections performed here to find the convective driven mass
transfer through each side of the meshes. Of these five tests only one returned a significantly converged
solution, revealed in Fig. 12. Two other tests shown here in Fig. 13, though reaching low residual values (less
than 10-3), would not converge any further and therefore cannot be considered completely accurate solutions.
The remaining two models would not converge to an average residual value less than one. In summing up, it is
concluded that this model will not supply sufficiently accurate data to determine whether a thermo-syphon
arrangement can be used with this LHSS. The results here do demonstrate the complexity of the flow due to
natural convection, which includes a significant number of vortexes and unusual flow patterns. The temperature
gradient demonstrates that the flow is far more sensitive to the surrounding geometry than its density gradient
due to temperature and the consequent buoyancy forces. Given this, it is unlikely that a CFD model will be able
to accurately model the natural convection of this system and in turn report the necessary information required
to determine the feasibility of including a thermo-syphon in the LHSS design.
D. Combined analysis
The results given by the heat exchanger model and the internal heat flow model are combined here to create
a more thorough analysis of the performance of this system. Equation (14) indicates the necessary heat flux
required by the parcels in order to maintain the high flow of the shower. Since the heat flux is only required at
the value given in this equation, there is a delay before the outgoing heat flux will begin to decline. This result
is shown in Fig. 14.
Stored energy Vs Time
Heat flux Vs Time
140
0
Constant surface temperature
Constant q" to transition
120
-1000
58% solid, transition point
-2000
Surface heat flux (W/m2)
Stored Heat energy (J)
100
80
60
40
-3000
-4000
-5000
58% solid, transition point
-6000
-7000
-8000
20
Constant surface temperature
Constant q" to transition
-9000
0
a)
0
20
40
60
80
100
120
Time (s)
140
160
180
200
-10000
0
20
40
60
80
100
120
Time (s)
140
160
180
200
b)
Figure 14 - Comparison between constant heat flux and constant temperature difference. a) Stored heat energy with the parcel’s
volume. b) The heat flux through the surface of the parcel.
The red line shown in figure blah indicates the time when the system is unable to maintain the heat flux
necessary to raise the incoming flow to the necessary temperature which is now after approximately 22.6
seconds, an increase of 13.6 seconds, but still grossly under the necessary level. This development demonstrates
that the limiting factor of this LHSS is its ability to transfer heat through its surface into the water flow. This
can be contributed to the relatively low thermal conductivity of the PCM and the geometry of the parcels. The
aim of the remainder of this section is to explore methods to maximise the time the system is able to provide the
minimum heat flux requirement. The conclusion reached previously was shaped by using a worst case scenario.
Standard water saving type shower heads typically uses around 9L per minute2, 64% less than a high flow
17
Final Thesis Report 2009, UNSW@ADFA
shower head. The previous model also assumes that the incoming water temperature is at 15°C and contained
within a separate loop as established in Chapter II part G but may be higher, depending on the local
environment. This result also does not include the initial volume of water, found by Eq. (12) to be
approximately 26.68L, which is already at or above the required temperature and can be used immediately. In
the following sections the ability of the LHSS, when applied to a 50L system, is explored to demonstrate an
increase in capability that can be contributed to this system. Firstly, the number of parcels is determined.
50
𝑁𝑝 =
× 18.5 = 7400 𝑝𝑒𝑟 𝑝𝑒𝑟𝑠𝑜𝑛
0.125
With this number of parcels, the heat capacity of the system then becomes:
𝑄 = 200 ∙ 1600 ∙ 0.3525 ∙ 50 + 0.6475 ∙ 50 ∙ 4181.3 ∙ 75 − 15 = 13.76𝑀𝐽
This demonstrates the LHSS has the potential to store up to 24% more heat than a typical system that uses
only specific heat energy storage for the same size volume. Using a water saving showerhead reduces the
maximum required heat flux of the LHSS as given in Eq. (13).
( 9/60 ∙ 0.33) ∙ 4181.3 ∙ 65 − 15
𝑞=
= 1.4𝑊
7400
𝑞
−3
𝑞 ′′ = =
= −1.19𝑘𝑊 ∙ 𝑚−2
𝐴 1.18 ∙ 10−3
This results in a reduction of the heat flux requirement of approximately 73%. There is also the pre-heated
water within the storage tank to consider.
𝑉𝑤𝑎𝑡𝑒𝑟 = 0.6475 ∙ 𝑉𝑡𝑜𝑡𝑎𝑙 = 32.375𝐿
Therefore, at a flow rate of 9L per minute, the system will drain this reserve supply in the time given by Eq.
(15).
32.372
= 215.8𝑠 = 10.9𝑚𝑖𝑛𝑢𝑡𝑒𝑠
(15)
(9/60) · 0.33
The corresponding increase in the time that the system is able to maintain the heat flux is given by the new
performance curves shown in Fig. 15. Note that this system is now under what is considered by the researcher
to be the lowest possible heat flux requirement.
Stored energy Vs Time
Heat flux Vs Time
140
0
96% solid, transition point
-1000
120
Stored Heat energy (J)
80
60
q" = -4360W m-2
40
q" = -1190W m-2
Surface heat flux (W/m2)
-2000
100
-3000
-4000
-5000
96% solid, transition point
-6000
-7000
-8000
q" = -4360W m-2
20
-9000
0
0
50
100
150
200
-10000
q" = -1190W m-2
0
50
Time (s)
100
150
200
Time (s)
a)
b)
Figure 15 - Comparison between maximum heat flux requirement of -4.36kW/m2 and minimum requirement of -1.19kW/m2. a) Stored
energy with the volume of the parcel. b) The heat flux through the surface of the parcel.
As can be seen in Fig. 15, there is a significant increase in the amount of time the system is capable of
maintaining a high heat flux through the surface. This model is able to generate the required heat flux for
approximately 137 seconds; 114 seconds more than the maximum heat flux model.
Note that both the previous tests in this section were performed with the conditions expected within a
thermo-syphon arrangement where the temperature difference between the water flow and the parcels is small,
at approximately 10°C which, as described in Chapter II part G, is not an accurate representation of the
temperature difference but can be considered as the worst case scenario. In the case of a best case scenario, the
return loop of water will have reached the temperature of the domestic cold water flow, which is modeled here
at 15°C. This would also represent the temperature of the water flow over the parcels in a direct contact LHSS
where the supply domestic water interacts directly with the parcel surface without the intermittent water loop.
Directly passing the domestic water over the parcel surface results in a temperature difference of 50°C;
assuming that the incoming water begins at approximately 15°C. Two further experiments were conducted to
compare the previously outlined schemes to the same systems with a temperature difference of 50°C. The
results of these experiments are shown in Fig. 16.
18
Final Thesis Report 2009, UNSW@ADFA
Comparison between assumed systems
Comparison between assumed systems
450
0
q"= -1.19k W m ,  T: 50 C
-2
400
-500
q"= -4.36k W m-2,  T: 50oC
q"= -1.19k W m-2,  T: 10oC
350
-1000
Surface heat flux (W/mK)
q"= -4.36k W m-2,  T: 10oC
Transition point
300
Stored heat (J)
o
250
200
150
-1500
-2000
-2500
-3000
100
-3500
50
-4000
q"= -1.19k W m-2,  T: 50oC
q"= -4.36k W m-2,  T: 50oC
q"= -1.19k W m-2,  T: 10oC
0
0
100
200
300
400
Time (s)
500
600
700
800
-4500
q"= -4.36k W m-2,  T: 10oC
Transition point
0
100
200
300
400
Time (s)
500
600
700
800
a)
b)
Figure 16 – Comparison of the performance of parcels with each different set of requirements. a) Stored heat within the volume of
the parcel. b) The heat flux through the surface of the parcel.
It can be seen from Fig. 16 that enacting the flow directly over the parcel surface greatly increases the heat
flux of the system, as shown by the greater temperature difference. This is expected since the heat flux is driven
primarily by the temperature difference and conductivity of the parcel, hence increasing the temperature
difference five times, as shown here, has increased the time the system is able to remain at peak output by
approximately five times. This system is now able to maintain the minimum flow temperature for
approximately 137 and 595 seconds with a heat requirement of -9.29 and -2.54 kW·m-2 respectively. These
values almost match the output of a standard modern commercial heat system. Note that implementing a direct
contact version of this LHSS will require a much more comprehensive stress and safety study to ensure that the
parcels do not rupture during their use, threatening contamination of the domestic hot water supply. In a
separate loop setup this is not a problem as the two water flows are kept separate, only heat is transferred
between the two. These results demonstrate that the this LHSS is capable of meeting the minimum
requirements of a modern commerical hot water system, including matching the minimum heat transfer rate to
provide for fixtures whilst instigating the ability of the system to store greater quantities of heat energy. Further
research needs to be performed to confirm to the data gathered here, however this study has shown that this
LHSS has the potential to be a feasible and welcome addition to traditional DHW heat storage systems.
V. Recommendations
In order to further the researches reviewed in this paper and create a complete analysis of this LHSS there
are several recommendations for future projects. Most importantly, the actual properties of the PCM to be used,
Rochelle‟s salt, needs to be established to increase the accuracy of this project and for any further research. As
well as determining the basic requirements of thermal conductivity, latent and specific heat and melting point;
the thermal stability properties of the material should also be investigated to ensure that the system is capable of
producing the same results over a great number of cycles.
The research presented in this case alludes to the number of parcels that will fit into a unit volume which can
be expanded to include various lengths and diameters of them that the optimum shape can be established. With
the necessary program already established here, this would take far less time to complete. Also, a verification
experiment to determine the accuracy of the packing program should be completed to ensure that the results
given by the program are reasonably accurate.
The natural convection models developed here failed to provide any reasonable result. Unfortunately a
physically equivalent experiment was not able to be conducted here due to the lack of access to the parcels and
lack of project time available to complete such an experiment. Therefore it is recommended that a physical
experiment be conducted in future to explore the feasibility of a thermo-syphon based design as opposed to a
virtual study. This experiment could be partnered in conjunction with a single parcel verification experiment to
confirm the data found in this project, as the two experimental setups would be very similar and it would not be
difficult to perform the two in parallel.
Due to a lack of information regarding the thermal expansion of Rochelle‟s salt, no applicable stress analysis
could be completed here. It is recommended in future work that a detailed stress analysis of this system,
including the stresses within the parcels placed at the bottom of the storage tank, is carried out in order to further
expand the feasibility study.
As there was no concrete information regarding DHW system requirements apart from the approximate
figures supplied, a study into the different categories and their related requirements should be recorded in future
to provide clearer guidelines into the requirements of different market sectors, and the applicability of this
system to each.
19
Final Thesis Report 2009, UNSW@ADFA
VI. Conclusion
This thesis has created a baseline feasibility study which is used to ascertain whether this LHSS may be
capable of supplementing or replacing current DHW storage systems. This was done by exploring the heat
characteristics and packing properties of the parcel shape and comparing these properties to the requirements
given to current DHW systems.
The geometry of the parcel creates an unusual surface heat transfer rate. Initially the parcel has a very high
heat transfer rate due to a combination of the large temperature difference between the oncoming flow and the
parcel itself and the unusual shape of the parcel which creates fin like extensions at its corners. These fins have
a large surface area to volume ratio, allowing the heat to be released quickly despite the low conductivity of the
PCM. However, as the PCM around the fins changes state, the shape of the remaining PCM becomes similar to
an elongated sphere as shown in Fig. 6, thus creating a poor surface area to volume ratio. This means that the
heat flux of the parcel always begins very high, but exponentially asymptotes to zero. Most of the useable heat
flux is within the first fifth of the parcel‟s cycle as shown in Fig. 7b. Therefore, despite the availability of stored
heat energy towards the end of a cycle, the LHSS is unable to administer this energy to the surrounding flow.
This introduces the premise that the application of this LHSS will be limited by the rate at which it can deliver
energy into the flow, not by how much energy it can store. Increasing the length of the parcels results in an
approximately linear increase in both the heat energy storage capacity and the surface heat transfer rate of the
parcels on a per parcel basis. Increasing the diameter of the parcel culminates in a moderately exponential
increase in heat transfer rate and a faster exponential increase heat energy storage capacity on a per parcel basis.
This means increasing the diameter of the parcel will as likely create waste storage volume, thus adding
unnecessary costs. Increasing the length however, would result in less wasted heat storage capacity, although
this may cause problems due to the unusual geometry this creates and will likely result in a lower packing
density.
The heat exchanger model explored the capability to implement a thermo-syphon in conjunction with this
system. Though there was some success with 2D meshes, these results failed to provide reasonably accurate
results conducive to the expected mass flow rate through the system. Therefore it was concluded that due to the
complexity of the randomly packed bed arrangement, currently available CFD software is unable to cope with
this simulation.
The heat exchanger model found the estimated packing density and subsequent heat energy storage capacity
and heat flux of the system per unit volume. From these values the estimated total storage capacity was found
on a per person basis. It was established that this LHSS is capable of storing up to 24% per volume more heat
energy than a specific heat based DHW storage tank. A decision was formulated from the worst case scenario
given in Chapter IV part D that the system is able to supply the minimum heat transfer rate for approximately
22.6 seconds. The best case scenario described in the same section found a supply time of 594.7 seconds. It
was determined that maximising the temperature difference greatly increases the heat transfer rate of the LHSS.
Reducing the heat flux requirements, which is carried out by increasing the number of parcels within the flow,
also increases the time the system is able to maintain a high heat transfer rate though not as quickly as
increasing the temperature difference. In conclusion, raising the temperature difference by promoting good flow
should be the primary aim for tank designers, followed closely by maximising the number of parcels. This
project has developed an excellent base understanding into the complicated properties of this LHSS, and has
shown that this system, as represented here, is a feasible supplement or alternative to current heat storage
methods.
Acknowledgements
I would like to thank my supervisors Alan Fien and Dr Murat Tahtali, for their guidance throughout the
project. In particular I would like to thank Murat for the countless hours he spent delving into to the complexity
of the Rigid Body Simulator and bouncing back with answers; his banter was invaluable for furthering this
component of the project. I would also like to thank my family and friends for their support and enthusiasm
towards this project.
20
Final Thesis Report 2009, UNSW@ADFA
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