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POLITECNICO DI MILANO
Facoltà di ingegneria industriale
Corso di laurea specialistica in ingegneria energetica
Transient Simulation of Phase Change
Material (PCM) Storage integrated in a
Domestic Hot Water (DHW) Heat Pump
System
Supervisor: Prof. Ing. Marcello Aprile
MSc thesis by:
Luca Erminio MANSUETI 841380
Riccardo GIANOLI 850102
Academic year 2016/2017
1
Table of figures
Figure 1.1: Classification of PCMs ………………………………………….. 15
Figure 1.2: Classes of materials that can be used as PCM and their typical
range of melting temperature and melting enthalpy ………...…... 16
Figure 1.3: Chemical structure of linear alkanes ……………………...……... 17
Figure 1.4: Chemical structure of fatty acids ………………………………... 18
Figure 1.5: Chemical structure of sugar alcohols ……………………………. 18
Figure 1.6: Chemical structure of polyethylene glycols …………………….. 18
Figure 1.7: Hysteresis model ………………………………………………… 21
Figure 1.8: Subcooling Model ……………………………………………….. 21
Figure 1.9: Combination of subcooling and hysteresis ……………………… 22
Figure 1.10: Phase diagram in which a second component (salt) is added to
water …………………………………………………………… 23
Figure 1.11: PCM (grey) embedded in a matrix material with pores or
channels ………………………………………………………... 25
Figure 1.12: Macroencapsulation in plastic containers ……………………… 25
Figure 1.13: Electron microscope image of many capsules …………………. 26
Figure 1.14: Schematic view of test section of finned-tube heat exchanger … 28
Figure 1.15: Comparison of melting time for the two heat exchangers studied
with variation of 𝑇𝐻 (flow rate = 0.6 L/min) …………………... 28
Figure 1.16: The physical configuration of the TTHX ……………………… 29
Figure 1.17: Physical configurations of all cases ……………………………. 29
Figure 1.18: Number of fin effect to the melting time, comparison between
case B, case C and case D with respect to the reference case A .. 30
Figure 1.19: Fin length effect to the melting time …………………………… 30
Figure 1.20: Illustrative moving boundary problem for solidification on a
plane wall ……………………………………………………… 32
Figure 1.21: The categories of thermal energy storage models ……………... 33
Figure 1.22: Brief schematic of PCM storage model for TRNSYS Type 840. 34
Figure 1.23: Brief schematic of PCM storage model for packed bed latent
heat thermal energy storage using PCM capsules ……………... 34
Figure 1.24: Left: water-to-air heat exchanger consisting of tubes and fins.
Right: tube arrangement: aligned (left) and staggered (right); the
upper part of the figure shows the connections between the pipes
in series, the lower part shows a cross section of the heat
exchanger ………………………………………………………. 35
Figure 1.25: Left: longitudinal section of a finned tube and its dimensions.
Right: cross section of four aligned tubes with its dimensions ... 35
2
Figure 1.26: Detailed structure of the nodal network ………………………... 36
Figure 1.27: Schematic diagram of the integrated heat pump system with
triple-sleeve energy storage exchanger ………………………... 39
Figure 1.28: Schematic of experimental setup: (1) solar flat plate collector
(varying heat source); (2) constant temperature bath; (3) electric
heater; (4) stirrer; (5) pump; (6 and 7) flow control valves; 8. flow
meter; (9) TES tank; (10) PCM capsules; (11) temperature
indicator; TP and Tf—temperature sensors (RTDs) ……….... 40
Figure 2.1: Heat exchanger scheme …………………………………………. 42
Figure 2.2: finned tube heat exchanger with 3 levels and 3 rows …………… 43
Figure 2.3: Storage node …………………………………………………….. 43
Figure 2.4: Fins geometry …………………………………………………… 49
Figure 2.5: Fin efficiency trend ……………………………………………… 50
Figure 2.6: Enthalpy-temperature curve ……………………………………... 51
Figure 2.7: Temperature-enthalpy function …………………………………. 53
Figure 2.8: Charging process results ………………………………………… 55
Figure 2.9: Discharging process results ……………………………………... 56
Figure 3.1: Plant layout ……………………………………………………… 60
Figure 3.2: Simulated transient behaviour of an ASHP…………… …………62
Figure 3.3: ASHP behaviour during the simulations ……………………… 63
Figure 3.4: Plate heat exchanger working principle …………………………. 65
Figure 3.5: Heat exchanger scheme …………………………………………. 67
Figure 3.6: Typical SOC trend ..…………………………………………….. 69
Figure 3.7: Typical trend of 𝑖𝑑𝑥_𝐻𝑋 and 𝑖𝑑𝑥_𝑃𝐶𝑀 ………………………... 71
Figure 3.8: Energy trend during the initial 2 hours .........……………………. 73
Figure 3.9: End of the charging process and beginning of the discharging
process…….……………………………………………………... 74
Figure 3.10: SOC trend during the night period …………………....………... 75
Figure 3.11: Overall dimensions of PK 80 …………………………………... 78
Figure 3.12: Technical dimensions of PK 80 ………………………………... 78
Figure 3.13: Plate parameters ………………………………………………... 81
Figure 3.14: Characteristic curve of P1 ……………………………………… 84
Figure 3.15: Characteristic curve of P2………………………………………. 84
Figure 3.16: COP parametrical trend ………...……………………………… 86
Figure 3.17: DHW trend……………………………………………………... 88
Figure 3.18: SOC trend in the first configuration ……………………………89
Figure 3.19: SOC trend in the second configuration…………………………. 90
Figure 3.20: Domestic Hot Water trend vs. system Coefficient Of Performance
(𝑇𝑎𝑖𝑟 = 7 °𝐶) ………………………………………………...… 92
Figure 3.21: Domestic Hot Water trend vs. system Coefficient Of Performance
(𝑇𝑎𝑖𝑟 = 10 °𝐶)..………………………………………………… 93
3
Figure 3.22: Domestic Hot Water trend vs. system Coefficient Of Performance
(𝑇𝑎𝑖𝑟 = 10 °𝐶)..………………………………………………… 93
Figure 3.23: 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 degradation….……………………………………… 94
Figure 3.24: 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 trend…………….……………………………………95
Tables
Table 1.1: Relevant properties of the most common PCMs …………………. 27
Table 2.1: Heat exchanger specifications ……………………………………. 54
Table 3.1: Tapping cycle L …………………………………………………... 66
Table 3.2: Initial conditions at time 0 ………………………………………... 72
Table 3.3: Nominal capacity table …………………………………………… 76
Table 3.4: ASPH mass flow rate table ……………………………………….. 77
Table 3.5: Concentrated pressure losses coefficient …………………………. 83
Table 3.6: Sizing results ………………………………………………...…… 98
Table 3.7: System energy consumption ……………………………………… 98
Table of contents
Acknowledgements 5
Abstract 6
Nomenclature 8
1 State of the art 13
1.1 Latent heat storage material requirements …………….…………… 13
1.1.1 Thermal properties ……….………………………………….… 13
1.1.2 Physical properties …………….….....…………………………14
1.1.3 Kinetic properties …….………………………….……………… 14
1.1.4 Chemical properties …………….………….……….…………… 14
1.1.5 Economics ……….……………………….…………………… 15
1.2 Classes of PCMs …….………………………….……………………… 15
1.2.1 Organic PCMs ….………………….……………………………. 16
1.2.2 Inorganic PCMs ……….……………….………………………... 19
1.3 Typical materials drawbacks and methods to reduce them ……….….... 20
1.3.1 Hysteresis and subcooling …………………….………………… 20
4
1.3.2 Phase separation ………………………………………………… 23
1.3.3 Mechanical stability and thermal conductivity improved
by composite materials …………………………………………. 24
1.3.4 Encapsulation to prevent leakage and improve heat transfer ….... 25
1.4 Heat exchanger design to enhance the heat transfer of a Latent Heat
Thermal Energy Storage (LHTES) system ..……………………..……. 26
1.5 Modelling …………….………………………………………………... 31
1.5.1 Temperature and enthalpy methods …………………………….. 31
1.5.2 Thermal energy storage models ………………………………… 33
1.6 Systems ………….…………………………………………………….. 38
1.6.1 Sunamp batteries …………….………….………………………. 40
2 Description of the PCM storage unit physical model 41
2.1 Introduction ……..……………………………………………………... 41
2.2 Model geometry ……….…………………….………………………… 42
2.2.1 Nodal network ….………………………….……………………. 42
2.2.2 Storage node ………………………….…………………………. 43
2.2.3 Pipe connections and model flexibility ………….……………… 44
2.3 Governing equations ……………..…………………………………….. 44
2.3.1 Overall heat transfer coefficient ….……………………………... 48
2.3.2 PCM temperature function and thermal properties .…………….. 50
2.4 Validation of the model …….………………………………………..… 54
2.4.1 Charging process ………….…………………………………….. 55
2.4.2 Discharging process ……………….……………………………. 56
3 PCM storage application: Domestic Hot Water (DHW) system 59
3.1 Introduction …………….…...…………………………………………. 59
3.2 Plant description ………………....…………………………………….. 60
3.3 Simulation control strategy ……………………...…....……………….. 65
3.3.1 State Of Charge (SOC) ………………………….………………. 68
3.3.2 System configurations …………………………………….…….. 69
3.3.3 Daily control logic ………………………………….………….... 71
3.3.4 Night control logic ……………………………….……………… 74
3.4 Components sizing ………………………………….…………………. 75
3.5 Parametric analysis ……………………………….……………………. 85
3.6 Results and discussions ………………………….…………………… 87
4 Conclusions 97
Bibliography 100
5
Acknowledgements
The authors would like to thank:
Prof. Ing. Marcello Aprile, who gave us a huge help and assistance in working
on this thesis and who spent with us a lot of time, showing an outstanding
availability.
Co-author Riccardo Gianoli would like to thank:
My parents Alfio and Paola, my sister and housemate Giulia, my girlfriend
Martina and all my friends and classmates for supporting me in reaching this
achievement.
Co-author Luca Mansueti would like to thank:
All my family for supporting me in good and bad times during this long and
hard path towards such a valuable goal.
My girlfriend Valentina, who has been making me very happy during all my
work, helping me to keep calm and concentrated.
Finally, all my lifelong friends, “qc” guys, “i ragazzi”, my fellow study
Giacomo and all the others who shared lots of their time with me for having
spent unforgettable moments together.
6
Abstract
Nowadays, thermal energy storage is becoming a topic of general interest.
The main goal of this thesis has been the creation of a model for a thermal
battery and for the study of a Domestic Hot Water system, which comprises an
energy storage system, an air-to-water heat pump and a plate heat exchanger.
As concerns the thermal battery, it has been reproduced and then validated a
transient model of a PCM (Phase Change Material) storage called Type 841
taken from a report of IEA Solar Heating and Cooling program (Task 32).
Moreover, some specific aspects of Type 841 have been improved.
A high temperature heat pump has been taken as a reference, simulating a
transient behavior within the first ten minutes after a switching on and a steady
state behavior for the remaining time.
A plate heat exchanger has been chosen, since it is the most common type for
this kind of application.
Parametric analyses have been performed in the final section, trying to minimize
either the size of the thermal battery or the heat pump and also trying to
maximize the ratio between the thermal energy provided to the user and the
incoming electric energy of the system. Finally, an optimal configuration has
been selected.
All the simulations have been performed with Matlab.
7
Sommario
Oggigiorno, lo storage di energia termica sta diventando un argomento di
interesse generale.
L'obiettivo principale di questa tesi è stata la creazione di un modello di una
batteria termica e lo studio di un sistema di acqua calda sanitaria, che
comprendesse un sistema di accumulo di energia, una pompa di calore aria-
acqua e uno scambiatore di calore a piastre.
Per quanto riguarda la batteria termica, è stato riprodotto e quindi validato un
modello in transitorio di un accumulo PCM (Phase Change Material)
denominato Type 841 e tratto da un report di IEA Solar Heating and Cooling
program (Task 32). Inoltre, alcuni aspetti specifici del modello Type 841 sono
stati approfonditi e migliorati.
Una pompa di calore ad alta temperatura è stata presa come riferimento,
simulando un comportamento in transitorio nei primi dieci minuti dopo
l'accensione e un comportamento a regime per il tempo rimanente.
È stato inoltre scelto uno scambiatore di calore a piastre, in quanto è il tipo più
comune per questo tipo di applicazione.
Analisi parametriche sono state condotte nella sezione finale, cercando di
minimizzare le dimensioni della batteria termica e della pompa di calore e
inoltre cercando di massimizzare il rapporto tra l'energia termica fornita
all'utente e l'energia elettrica in entrata nel sistema. Infine, è stata selezionata
una configurazione ottimale.
Tutte le simulazioni sono state eseguite con Matlab.
8
Nomenclature
Roman symbols
A surface 𝑚2
m mass 𝑘𝑔
�̇� mass flow rate 𝑘𝑔/𝑠
𝑉 Volume 𝑚3
𝑣 velocity 𝑚/𝑠
𝑐𝑃 specific heat 𝐽/𝑘𝑔𝐾
𝑎 heat transfer coefficient 𝑊/(𝑚^2𝐾)
𝑎𝑖𝑛 convective heat transfer coefficient on the inside surface of
the tube
𝑊/(𝑚^2 𝐾)
𝑎𝑓 heat transfer coefficient on the fin and pipe surface 𝑊/(𝑚^2 𝐾)
𝑎𝑒𝑙,𝑒𝑓𝑓 effective heat transfer coefficient 𝑊/(𝑚^2 𝐾)
𝑈 overall heat transfer coefficient 𝑊/(𝑚^2 𝐾)
d heat exchanger tube external diameter 𝑚
𝑑𝑤 heat exchanger tube thickness
𝑚
𝑙 heat exchanger tube length 𝑚
𝑠𝑐 Casing thickness 𝑚
𝑠𝑓 fin thickness 𝑚
𝑡𝑓 distance between two fins 𝑚
𝑡𝑙 fin height 𝑚
𝑡𝑞 fin width 𝑚
ℎ𝑓 fin efficiency -
𝑛𝑒𝑙 number of elements inside a node -
𝐻𝐿 PCM lowest enthalpy in liquid phase region per unit of
mass
𝐽/𝑘𝑔
𝐻𝑆 PCM highest enthalpy in solid phase region per unit of
mass
𝐽/𝑘𝑔
ℎ enthalpy 𝐽/𝑘𝑔
9
𝑡 time-step 𝑠
𝑡𝑚𝑎𝑥 maximum time-span 𝑠
𝑇 temperature 𝐾
P pressure Pa
𝐶 thermal capacity 𝑊/𝐾
𝑠𝑝 plate thickness 𝑚
𝑁𝑝 number of plates -
�̇� power W
Greek symbols
𝜆 thermal conductivity 𝑊/𝑚𝐾
𝜌 density 𝑘𝑔/𝑚^3
β concentrated pressure losses coefficient -
ξ distributed pressure losses coefficient
-
ε effectiveness -
𝜇 water dynamic viscosity 𝑃𝑎 ⋅ 𝑠
𝜓 Darcy friction factor -
𝛥𝐻 latent heat per unit of mass 𝐽/𝑘𝑔
𝛥𝑇ℎ𝑦𝑠𝑡 temperature difference due to hysteresis 𝐾
𝛥𝑇𝑆𝐶 temperature difference due to subcooling 𝐾
Dimensionless numbers
𝑁𝑢 Nusselt number -
𝑃𝑟 Prandtl number -
𝑅𝑒 Reynolds number -
10
Operands
𝑗 used in equation (3.10)
𝑗‘ used in equation (3.9)
Index
PCM Phase Change Material
f fin
t tube
in inner part of the heat exchanger
el element, fin
liq PCM liquid phase
sol PCM solid phase
pc PCM phase change, transition region
𝑤 water
eff Effective
0 inlet
air air
c casing
m m direction
n n direction
ST storage
max maximum
min minimum
primary primary flux of the plate heat exchanger
secondary secondary flux of the plate heat exchanger
p plate
h hydraulic
wet wet
pl partial load
11
conc concentrated
distr distributed
12
13
Chapter 1
State of the art
This paragraph starts with the description of the basic requirements on a
material to use it as a Phase Change Material. Then different drawbacks are
discussed in order to understand the reason why we need to avoid some kinds of
phenomena. Different classes of materials are then discussed with respect to
their most important properties, advantages and disadvantages. Since a material
is not usually able to fulfill all the requirements we need, solutions to improve
its behaviour are provided.
1.1 Latent heat storage material requirements
In a solid-liquid PCM the heat transfer occurs when it changes from solid to
liquid or from liquid to solid; this is called a change in state, or in “phase”. One
of the greatest ability of the PCM is to store 5-14 times more heat per unit of
volume than the common sensible storage materials, such as masonry, water or
rocks. However, for their employment as latent heat storage material they must
exhibit certain specific thermodynamic, kinetic and chemical properties.
Moreover, economic and availability considerations must be done.
1.1.1 Thermal properties
• Suitable phase change temperature 𝑇𝑝𝑐
• Large phase change enthalpy 𝛥ℎ𝑝𝑐
• Good thermal conductivity
In order to design a specific latent heat storage system, it’s necessary to fix the
operating temperature of the heating or cooling, so that it’s important to choose
a PCM with a particular phase change temperature, which has also to be
matched with the operating one. Moreover, the phase change enthalpy should be
as high as possible, especially on a volumetric basis, to achieve very high
storage density with respect to a sensible heat storage. Finally, a good thermal
conductivity is required to release or store heat, in a very short time; it would
assist the charging and discharging process, however the needing of a good
thermal conductivity strongly depends on the design and on the size of the
storage.
14
1.1.2 Physical properties
• Favourable phase equilibrium
• High density
• Small volume variation
• Low vapor pressure
• Reproducible phase change, also called cycling stability
All these properties are related to the design of the storage size, indeed a small
volume variation on the phase transformation and a low vapor pressure at the
operating temperature are useful to reduce the containment problems. Moreover,
a phase stability during freezing or melting is necessary to set up the heat
storage as best as possible, whereas a high density allows to reduce the size of
the system. Cycling stability is the capability of the material to repeat the
freezing and melting cycle as much as required by an application. In a latent
heat storage, it’s possible to deal with thousands cycle so sometimes a phase
separation occurs. When a PCM consists of several components, phases with
different compositions can form upon cycling. Phase separation is the effect
that phases with different composition are separated from each other
macroscopically. The phases with a different composition from the optimized
ones show a significantly lower capacity to store heat.
1.1.3 Kinetic properties
● No subcooling
● Sufficient crystallization rate
Subcooling occurs when a temperature significantly below the melting
temperature is reached, and then a material begins to solidify and so to release
heat. It’s necessary to limit this phenomenon as much as possible in order to
assure that melting and solidification can proceed in a narrow temperature
range.
1.1.4 Chemical properties
● Long-term chemical stability
● Compatibility with the material of construction
● No toxicity
● No fire hazard
PCM should be non-toxic, non-flammable and non-explosive for safety reason.
They can also suffer from degradation due to loss of water, chemical
15
decomposition or incompatibility with materials of construction. Chemical
stability is a very useful property because it assures long lifetime of the PCM if
it is exposed to high temperatures, radiation and gases.
1.1.5 Economics:
● Abundant
● Available
● Low price
● Good recyclability
An affordable price of the PCM is necessary to be competitive with other
options for heat and cold storage, and to be competitive with methods of heat
and cold supply without storage at all. Either for economical or environmental
reason a good PCM has to be recyclable in an easily way and it has also to be
available and abundant in the market.
1.2 Classes of PCMs
Nowadays a large number of Phase Change Materials are available on the
market, with very different temperature ranges. The most widespread
classification is the one developed by Atul Sharma in [1] and it’s represented in
fig. 1.1
Figure 1.1: Classification of PCMs [1]
16
In the field of the solar and thermal processes there are several classes of
materials, covering the temperature range 0°-130°. Since the two most important
criteria, the melting temperature and the melting enthalpy, depend on molecular
effects, it is not surprising that materials within a material class behave
similarly.
Figure 1.2: Classes of materials that can be used as PCM and their typical range
of melting temperature and melting enthalpy [2]
1.2.1 Organic PCMs
These material classes cover the temperature range between 0 ºC and about 200
ºC. Due to the covalent bonds in organic materials, most of them are not stable
to higher temperatures. The most important organic PCMs are paraffins, fatty
acids and sugar alcohols. They are able to melt and freeze repeatedly without
phase segregation and consequent degradation of their latent heat of fusion.
Moreover, they crystallize with little or no supercooling and usually without
showing signs of corrosiveness, so they are defined as congruent melting and
self-nucleating materials.
Organic materials can be divided in:
● Paraffin compounds
● Non-Paraffin compounds
17
Paraffin wax consists of a mixture of mostly straight chain n-alkanes 𝐶𝐻3–𝐶𝐻2–
𝐶𝐻3, however the general formula used is 𝐶𝑛𝐻2𝑛+2.
Figure 1.3: Chemical structure of linear alkanes [2]
The crystallization of the 𝐶𝐻3 chain releases a large amount of latent heat.
Paraffins exhibit very different melting point and latent heat of fusion indeed
they increase with the chain length. They show several PCMs’ requirements
such as:
❏ chemical stability below 500°
❏ low vapor pressure
❏ low volume variations
❏ little subcooling
❏ cycling stability and no phase segregation
❏ non-corrosive
❏ cheap
For these properties, systems using paraffins usually have very long freeze–melt
cycles. Besides some several favourable characteristics, they show some
undesirable properties such as
❏ low thermal conductivity
❏ moderately flammable
Non-paraffin compounds represent a great part of the PCMs and have highly
varied properties, indeed each of these materials have its own properties unlike
the paraffin’s, which have very similar properties. They could be further divided
in:
❖ fatty acids
❖ sugar alcohols
❖ polyethylene glycol
18
A fatty acid is characterized by the formula 𝐶𝐻3(𝐶𝐻2)2𝑛𝐶𝑂𝑂𝐻. In contrast to a
paraffin, the right part of the molecule ends with a – 𝐶𝑂𝑂𝐻 instead of a –𝐶𝐻3
group.
Figure 1.4: Chemical structure of fatty acids [2]
This is the non-paraffin compound more similar to a paraffin one, indeed it
shows a very little subcooling, no phase separation (it consists of only one
component) and a very low thermal conductivity. A difference to paraffins can
be expected in the compatibility of fatty acids to metals due to the acid
character.
Sugar alcohols are a hydrogenated form of a carbohydrate. The general
chemical structure is 𝐻𝑂𝐶𝐻2[𝐶𝐻(𝑂𝐻)]𝑛𝐶𝐻2𝑂𝐻.
Figure 1.5: Chemical structure of sugar alcohols [2]
They represent a new class of materials, they have a 90-200 °C operating
temperature range, a high density and also very high volume specific melting
enthalpies. However, they show more subcooling than the fatty acids.
Polyethylen glycol (PEG) is a polymer with the general formula 𝐶2𝑛𝐻4𝑛+2𝑂𝑛+1.
Figure 1.6: Chemical structure of polyethylene glycols [2]
19
They show a higher density than the fatty acids but lower than the sugar
alcohols. The melting temperature of all PEGs with a molecular weight
exceeding 4000 𝑔𝑚𝑜𝑙⁄ is around 58 – 65 °C so they suit very well to solar and
thermal applications.
1.2.2 Inorganic PCMs
Inorganic materials are further divided in:
❖ salt hydrates
❖ metallic
Compared to organic materials they show similar melting enthalpies per mass,
however due to their higher density they have a larger one per unit of volume.
Salt hydrates consist of a salt and water in a discrete mixing ratio which can be
considered as the alloys of inorganic salt and water: 𝐴𝐵 ⋅ 𝑛𝐻2𝑂 (𝐴𝐵 represents
some inorganic salt). The phase change process of this hydrated salt is
essentially the process of hydration and anhydration, as represented in the (1.1)
system of equations.
{𝐻𝑦𝑑𝑟𝑎𝑡𝑖𝑜𝑛: 𝐴𝐵 + 𝑛𝐻2𝑂 → 𝐴𝐵 ⋅ 𝑛𝐻2𝑂 + �̇�
𝐴𝑛ℎ𝑦𝑑𝑟𝑎𝑡𝑖𝑜𝑛: 𝐴𝐵 ⋅ 𝑛𝐻2𝑂 + �̇� → 𝐴𝐵 + 𝑛𝐻2𝑂
(1.1)
Even though they cannot be denoted by a general formula, the most common
attractive properties of the salt hydrates are:
❏ relatively high thermal conductivity; generally speaking, it could be two
times than the one of the paraffins
❏ small volume changes on melting
❏ high latent heat of fusion per unit volume during phase change process
❏ slightly toxic
❏ cheap and cost effective for thermal storage applications
Besides these good properties, the major problem in using salt hydrates as a
PCM is the incongruent melting during the phase change process. The reason of
this process is that during the hydration process, 𝑛 moles of water are not able to
dissolve 1 mole of salt, so the solid salt settles down at the bottom of the
container, not being able to recombinate with water during the reverse process
20
of freezing. Moreover, another big issue is the subcooling, indeed most salt
hydrates subcool and some of them by as much as 80 K, due to an insufficient
crystallization rate.
Metallics have not been seriously considered yet for PCM storage applications
due to weight penalties, however they have several good requirements such as:
❏ high thermal conductivity
❏ high heat of fusion per unit of volume (low with respect to the mass)
❏ low vapor pressure
They cover a low melting temperature range, indeed the most common metallics
PCMs have a melting point in between 30°-70°
Eutectics show lower melting point than the metallics, however they are able to
melt and freeze congruently forming a mixture of the component crystals during
crystallization. Since they freeze to an intimate mixture of crystals, phase
segregation is very unlikely. Either the heat of fusion per unit of volume or per
unit of mass is comparable with the metallics.
1.3 Typical materials drawbacks and methods to reduce them
In paragraph 1.1 the most important requirements of a PCM for thermal storage
applications have been listed, however it’s unlikely that a PCM fulfils all of
them. For this reason, in this paragraph, the most important drawbacks are
discussedin order to understand whether it’s possible to improve their
performances by applying developed strategies.
1.3.1 Hysteresis and subcooling
The hysteresis phenomenon appears during cooling of materials. It results in a
delay of the phase change, indeed in the enthalpy-temperature curve, shown in
fig. 1.7, it’s clearly visible how there’s a shift between the heating and cooling
phase. Even though the slope of the transition is the same, the phase change
temperatures can differ by more than 10 K.
21
Figure 1.7: Hysteresis model [7]
Contrary to the hysteresis phenomenon, the subcooling depends strictly on the
solid phase presence in the phase change process. It consists in a delay of the
crystallization process with respect to the melting temperature so that it makes
necessary to reduce the temperature, during the cooling process, well below the
phase change temperature in order to release the heat stored in the material. Fig.
1.8 shows the subcooling phenomenon in an enthalpy-temperature curve. In
technical applications of PCM, subcooling can be a serious problem. For
example, when water is subcooled to -8 °C, crystallization starts and so the heat
of crystallization of about 333 kJ/kg is released, however due to subcooling, 32
kJ/kg of sensible heat have been lost (4kJ/(kgK) ⋅ 8K), since the melting point of
water is 0 °C. If the heat released upon crystallization is much larger than the
heat lost due to subcooling, as in this case, the temperature rises to the melting
temperature, and stays there until the phase change process has been completed.
Figure 1.8: Subcooling Model [7]
22
What is the reason for subcooling, or better why does a material do not solidify
right away when cooled below the melting temperature? In order to understand
this point, the nucleation process has to be described in detail. At the very
beginning of the solidification process there are no solid particles or at most,
there are only very small ones called nucleus. For the nucleus to grow by
solidifying liquid phase on its surface, the system has to release heat to get to its
energetic minimum. The nucleus radius is called 𝑟. Since the heat released by
crystallization is proportional to the nucleus volume, and then to 𝑟3, whereas the
surface energy gained is proportional to 𝑟2,it’s possible that for small 𝑟 values
the heat released by the system is lower than the surface energy gained and then
the solidification process cannot proceed until further decrease of the
temperature with respect to the melting point. Based on this nucleation can be
divided in:
● Homogeneous nucleation: the solidification process solely starts by the
PCM itself
● Heterogeneous nucleation: the solidification is originated by special
additives intentionally added to the PCM, but also impurities contained
by the PCM.
Since the surface energy is relatively low with respect to the heat released at the
beginning of the process, in order to get rid of the subcooling it’s useful to find a
way to make the solid phase of the PCM grow on its own surface, causing then a
heterogeneous nucleation. These special additives are called nucleator i.e.
materials with a similar crystal structure as the solid PCM which are able to
reduce the subcooling up to 10 °C. One of the main problem of using the
nucleators is their instability at temperatures larger than 10-20 K with respect to
the melting point due to a similar crystal structure of the PCM.
In the end, hysteresis and subcooling can be combined in fig 1.9.
Figure 1.9: Combination of subcooling and hysteresis [7]
23
1.3.2 Phase separation
Whenever a pure substance with only one component is heated above the
melting temperature, the phase change process occurs, but it keeps the same
homogeneous composition as in the previous phase. Even in the opposite phase
change process, when then it’s cooled down below the melting point, after the
phase change it will always keep the identical homogeneous composition.
Moreover, the same phase change enthalpy and melting temperature is observed
at any place. Such phenomenon is called congruent melting. On the other hand,
when a substance consists of two components, the solution behaviour changes,
depending upon the weight fraction of each component. For example, a salt-
water solution with a water weight fraction of 90% is a homogeneous liquid
above -4°C. When the temperature falls below -4°C water freezes out of the
solution so that the substance is separated into two different phases, one with
only water, and a second one with a higher salt concentration than initially.
Since the original composition is changed, this phenomenon is called phase
separation.
Figure 1.10: Phase diagram in which a second component (salt) is added to
water [2]
Salt hydrates are extremely affected by this problem because it results in an
irreversible melting-freezing cycle due to the fact that the salt, which has a
higher density than water, settles down at the bottom of the heat exchanger,
being unavailable for recombination with water during the reverse process of
freezing. As shown in fig 1.10, the temperature at which the water starts to
freeze out the solution strictly depends on the weight fraction of the salt, indeed
24
the larger the presence of salt in solution, the lower will be the temperature at
which the phase separation occurs.
A well-known method to get rid of this phenomenon in a PCM, is the artificial
mixing, in which instead of waiting for diffusion to homogenize the PCM, the
faster process of mixing is used. In salt hydrates storage application this method
has been widely used by adding water in the solution, improving the cycling
stability but decreasing the storage density of the material.
Another way to reduce the phase separation problem is the so-called thickening,
which consists in adding a particular material to the PCM to increase its
viscosity. Due to the high viscosity, different phases cannot separate far until the
whole PCM is solid.
1.3.3 Mechanical stability and thermal conductivity improved by composite
materials
A large number of PCM is affected by the issue of having a low thermal
conductivity and since they store heat in a small volume and they have to
transfer it to the outside of the storage, it could represent a big problem. When
the PCM is in a liquid state the convection enhances the heat transfer process,
however in the solid-state convection is not present so, in order to achieve a fast
heat transfer rate, the thermal conductivity of the PCM has to be increased. How
the thermal conductivity could be increased? One solution is adding metallic
pieces with very high thermal conductivity in a macroscopic scale, but adding
anything to the PCM will reduce or eliminate convection in the liquid phase;
therefore, it is necessary to find out a better option. The best solution nowadays
under investigation is to put the PCM into metallic foams of different structure
and porosity.
It’s also important that during the phase change the PCM exhibits a good
mechanical stability and a low volume variation so that to keep the system
compact. In order to assure this skill, the PCM can be combined with other
materials to form a composite material with additional or modified properties. A
composite material is created by incorporating the PCM on a microscopic level
into a supporting structure such as
● graphite matrix
● metallic matrix/foam
● polymer foam
25
Figure 1.11: PCM (grey) embedded in a matrix material with pores or channels
[2]
1.3.4 Encapsulation to prevent leakage and improve heat transfer
To achieve a good mechanical stability, also the encapsulation of the material is
one of the solution actually used. This is, however, not the only reason of
adopting encapsulation, indeed it’s also applied to hold the liquid phase of the
PCM, and to avoid the contact of the PCM with the surrounding, which might
harm the environment or change its composition. Moreover, this method helps
in enhancing the heat transfer surface between the material and the surrounding
due to a large surface to volume ratio. This technology strictly depends on the
size so it’s possible to make the following classification:
● Macroencapsulation means filling the PCM in a macroscopic
containment that fits amounts from several millilitres up to several litres.
The most common material used to macroencapsulate the PCM is plastic
because it’s not corroded by salt hydrates. Plastic containers are
produced in an easy way and with very different shapes so there is no
restriction on the geometry of the encapsulation but if good heat transfer
is important, the low thermal conductivity of container walls made of
plastic can be a problem, so an option is to choose container with metal
walls. Fig 1.12 shows few examples of macroencapsulation in plastic
container
Figure 1.12 Macroencapsulation in plastic containers. From left to right: bar
double panels from Dörken (picture Dörken), panel from PCP (picture: PCP),
flat container from Kissmann, and balls from Cristopia, also called nodules [2]
26
● Microencapsulation is the encapsulation of solid or liquid particles of 1
µm to 1000 µm diameter with a solid shell. This technology is applied
only to the materials that are not soluble in water, indeed
microencapsulation of PCM is today technically feasible only for organic
materials. The two main technologies used to microencapsulate the PCM
are coacervation and polymerization, whereas fig 1.13 shows
commercial microencapsulated paraffin, with a typical capsule diameter
in the 2-20 µm range, produced by the company BASF.
Figure 1.13 Electron microscope image of many capsules [2]
One of the main advantages of using encapsulation is the possibility to integrate
the PCM with other materials with specific properties. On the other hand, one
possible drawback is that the likelihood of having subcooling increases.
1.4 Heat exchanger design to enhance the heat transfer of a
Latent Heat Thermal Energy Storage (LHTES) system
For the design, evaluation and optimization of a LHTES system, it’s important
to understand the heat transfer characteristics of the phase change process.
Melting occurs when a solid PCM receives and absorbs thermal energy to store
it in the system, whereas freezing occurs whenever it’s necessary to retrieve the
energy stored, accomplished through the solidification of the liquid PCM. In
between the solid and liquid state, a transition phase called mushy state has been
defined.
27
The heat transfer mechanism in a LHTES system is usually conduction
controlled and it could be described by equation (1.2) [5]:
𝜆𝜌 (𝑑𝑆(𝑡)
𝑑𝑡) = 𝑘𝑠 (
𝛿𝑇𝑠
𝛿𝑡) − 𝑘𝑙 (
𝛿𝑇𝑙
𝛿𝑡)
(1.2)
where 𝑆(𝑡) describes the position with respect to the time of the solid-liquid
interface, λ is the latent heat of fusion of the PCM, 𝑇𝑠 and 𝑇𝑙 are the solid and
liquid phase temperatures, 𝑘𝑠 and 𝑘𝑙 are the thermal conductivities of the solid
and liquid PCM, and ρ is the density of the PCM.
Since one of the main disadvantage of using PCMs is their low thermal
conductivities, another way to improve the heat transfer rate is to modify the
heat exchanger structure by adding several fins. Fins are generally employed to
increase the heat transfer surface between PCM and the Heat Transfer Fluid
(HTF) and consequently to improve the thermal performance of a LHTES
system. Different parameters and properties are taken into account in the
selection of the fin material, such as density, thermal conductivity, safety,
corrosion potential and cost. In Table 1.1 some of the most common material
properties are summed up.
Table 1.1: Relevant properties of the most common PCMs [5]
Regarding the necessity to increase the heat transfer area, several ideas and
innovations have been proposed in literature. M. Rahimi in [4] has conducted an
experimental study in order to investigate melting and solidification processes of
a PCM in a finned tube heat exchanger, comparing it with a finless heat
exchanger. As shown in fig 1.14, the heat exchanger is made of the typical
aluminium fins and copper tubes and it includes a transparent plexiglass box
which is filled with PCM in a way that the material is in the spaces between
tubes and fin.
28
Figure 1.14: Schematic view of test section of finned-tube heat exchanger [4]
The experiment results show that the average temperature of the PCM increases
more rapidly when enhanced tubes are employed and that the melting time in a
finned tube heat exchanger is reduced of more than 50%, despite the decrease of
the melting time with the increase of the HTF inlet temperature is less effective
in a finned tube heat exchanger with respect to a bare one. Fig 1.15 shows the
comparison of melting time for the two heat exchangers studied with a variation
of 𝑇𝐻 (HTF inlet temperature).
Figure 1.15: Comparison of melting time for the two heat exchangers studied
with variation of 𝑇𝐻 (flow rate = 0.6 L/min)
29
Abduljalil A. Al-Abidi in [6] has investigated the effect of the number of fins
and the fins length on the melting rate of a PCM in a Triplex Tube Heat
Exchanger (TTHX). These type of heat exchangers are built up with three
concentric tubes and are recently applied in energy storage applications. In
latent heat applications, one HTF flows through the inner tube while another
HTF flows through the outer annulus of the tubes and a PCM in between the
HTFs. Fig 1.16 shows the TTHX section, consisting of three horizontally
mounted concentric tubes with length of 500 mm and four longitudinal fins (fin
pitch of 42 mm, length of 480 mm, and thickness of 1 mm) welded to each of the
inner and middle tubes.
Figure 1.16: The physical configuration of the TTHX [6]
The experiment has been made by considering as reference case a TTHX
without fins (case a); the melting rate of a 4,6 and 8 fins TTHX has been
respectively measured with respect to the one of the reference case. Case B, C
and D have respectively 4,6 and 8 fins, as shown in fig 1.17.
Figure 1.17: Physical configurations of all cases [6]
30
Fig 1.18 points out that there has been a big influence of the number of fins on
the melting fraction, indeed the melting time of PCM was decreased by
increasing the number of fins. The complete melting time for Cases B, C, and D
were 69.5%, 56.5%, and 43.4% of that of the TTHX without fin (Case A).
Figure 1.18: Number of fin effect to the melting time, comparison between case
B, case C and case D with respect to the reference case A [6]
The main reason of this clear result is that the fins increase the heat transfer area
and then the heat transfer coefficient between the HTF and the PCM, moreover
they are able to conduct the heat directly to the PCM surfaces and so even the
heat losses are reduced.
Besides the number of fins in a TTXH, also the fin length is a very important
parameter, since it’s able to decrease the melting time of a PCM. In the
experimental results has been shown that the time required to complete melting
for fin length of 10 mm, 20 mm, 30 mm, 42 mm were 73.9%, 60.8%,47.8%, and
43.4% respectively of the case A. Fig 1.19 shows the improvement of the
melting rate by using longer fins.
Figure 1.19: Fin length effect to the melting time [6]
31
1.5 Modelling
Different studies about thermal latent heat energy storage in phase change
materials have been performed in literature. The main objective is the
development of mathematical models in order to understand the heat transfer
problems related to latent heat storage. Most of these models are validated
through the comparison between numerical results and experimental data
obtained in laboratory. These studies allow to predict the performance of a
thermal battery studying some fundamental parameters such as the
melt/solidified fraction or the time spent during charging/discharging process
and to obtain some parametric simulations in order to understand the effect of
certain parameters on storage performance. In this section, a brief description of
the different models and the associated analysis are reported.
1.5.1 Temperature and enthalpy methods
Transient heat transfer problem including phase change process are generally
described as “moving-boundary problems”. In 1989, J.Stefan in his work about
the ice formation on the ground in the polar sea [7] introduced the so-called
“Stefan-condition”, that describes the growth rate of the solid/liquid boundary
layer. This condition is still the base for many approaches that deal with moving
boundary problems.
In this kind of problem, the hardest obstacle is the treatment of the interface
between solid and liquid phase. In that region thermophysical properties change
continuously as the latent heat is absorbed or released depending on the heat
transfer fluid conditions. So, it’s very important to localize its position during
melting and solidification process, where heat and mass balance conditions have
to be met.
In literature, it’s possible to find two different approaches employed to solve the
Stefan problem: the temperature method and the enthalpy method. Both are
explained by S.Maranda in his master’s thesis [8]. The first method considers
the temperature as the sole dependent variable and temperature equations are
defined both for solid and liquid region and an energy balance at the interface is
applied to describe the growth rate of the solid part. This approach needs some
assumptions to derive the differential equations that characterize the problem:
heat transfer is driven only by conduction and convection is neglected, latent
heat is constant and it’s released or absorbed at the phase change temperature,
nucleation difficulties and supercooling effects are not present, thermophysical
material properties are considered as constant within each phase and in the end,
density variations of material from solid to liquid are neglected. Hence, the first
32
approach presents three differential non-linear equations that could be solved
only reducing it to a 1-dimensional and semi-finite problem, where the wall
temperature is kept constant and the temperature of the heat transfer fluid is the
same of the phase change temperature. An additional simplification is done
considering the sensible heat of the material as negligible compared to its latent
heat and consequently the temperature distributions in the solid and liquid phase
are assumed to be linear. This behaviour is illustrated in fig. 1.20, where
temperature distribution is drawn as red line.
Figure 1.20: Illustrative moving boundary problem for solidification on a plane
wall [8]
In this way, the non-linearity of Stefan condition collapses. This latter
simplification is the so called quasi-stationary approximation and it’s studied by
many authors, trying to estimate the error in terms of percentage.
The enthalpy method is the most popular fixed-domain method for solving
Stefan problem. The idea is to divide the entire volume occupied by the PCM
material into a finite number of control volumes and to apply the energy
conservation equation for each control volume. Moreover, it’s introduced a
phase indicator which defines the liquid fraction of each control volume. Since
the energy equation is applicable both for liquid and solid, it’s not necessary to
know a priori where the interface is sited, and then its position is calculated
retrospectively through the phase indicator, which depends on the temperature
value computed at the previous time step. In this method, the only variable is the
temperature of the phase change material and the phase change is considered an
isothermal process. The enthalpy is a temperature dependent variable and the
heat flows are computed through the volume integration of the enthalpy of the
system. The use of enthalpy method is very convenient due to the following
reasons: the governing equation are similar to the single-phase equation, there is
no conditions to satisfy at the solid-liquid interface and it allows a “mushy” zone
33
between the two phases. Finally, there is no need to deal with a moving
boundary layer and this makes this method the most widespread in literature.
The only drawback is that the accuracy of this method strongly depends on the
spatial discretization of the considered domain. Increasing the number of
“mesh” density, the accuracy increases but also the number of equations to solve
and consequently it requires a higher computational power of the processor.
1.5.2 Thermal energy storage models
These are the main methods that have been used to implement different kind of
numerical models according to the several possible configurations of the thermal
batteries. One of the most diffuse software is TRNSYS and in 2013 Sunliang
Cao et al. [9] have reviewed and listed the models for thermal energy storage
implemented in that software. Fig. 1.21 shows a summary table.
Figure 1.21: The categories of thermal energy storage models [9]
34
In this paragraph, some of these models are briefly described and a specific
attention is paid for bulk PCM tank with fin-tube heat exchanger since it could
be such the model studied in the following chapter.
Type 840 is a model capable to simulate a simple water tank (several double
port connections and internal heat exchangers) with integrated PCM modules of
different geometries (spherical, rectangular and plates). PCM are located into
the tank in a vertical position and different zones with different melting
temperatures can be identified. Finally, instead of water, PCM slurries can be
used as storage medium. A brief schematic of the model is reported in fig 1.22.
Figure 1.22: Brief schematic of PCM storage model for TRNSYS Type 840 [9]
The following numerical model is for capsulated PCM storage: “Packed bed
latent heat thermal energy storage system using PCM capsules”. The packed bed
storage is filled with PCM spherical capsules. The heat transfer fluid passes
through the packed bed system allowing the charging and discharging processes
of PCM materials. A brief schematic of the model is represented in fig. 1.23.
Figure 1.23: Brief schematic of PCM storage model for packed bed latent heat
thermal energy storage using PCM capsules [9]
35
These are examples of Types used in TRNSYS to describe different kind of
latent heat storage and as it can be seen in the summary table, some other
models can be used, but in this report a particular focus has been made on the
Type 841 since it’s the only one in TRNSYS that deals with bulk PCM tank
integrated with fin-tube heat exchanger. Jacques Bony et al in [10] provides a
detailed explanation of this model.
Type 841 is capable of simulating a rectangular bulk PCM tank that is
charged/discharged through an integrated water to air finned heat exchanger.
Fig. 1.24 represents the heat exchanger with two possible tube arrangements.
Figure 1.24: Left: water-to-air heat exchanger consisting of tubes and fins.
Right: tube arrangement: aligned (left) and staggered (right); the upper part of
the figure shows the connections between the pipes in series, the lower part
shows a cross section of the heat exchanger [10]
The spacing between the fins is filled with the PCM materials, the HTF flows
within the tube and a rectangular casing is built around the entire heat
exchanger. This configuration corresponds to the PCM storage tank.
Fig. 1.25 shows respectively the longitudinal and cross section.
Figure 1.25: Left: longitudinal section of a finned tube and its dimensions.
Right: cross section of four aligned tubes with its dimensions [10]
36
In the model, the heat exchanger and the storage volume are subdivided in nodes
and they do not coincide. It is used the enthalpy method and so an energy
conservation equation is applied for each node so that the enthalpy evolution in
time is described.
In fig. 1.26 a detailed structure of the nodal network is shown.
Figure 1.26: Detailed structure of the nodal network [10]
Heat transfer in the PCM is calculated considering only conduction and
convection, when the PCM is in liquid state, is neglected. This assumption is
true for heat exchangers that have a small space between the fins.
As previously mentioned, numerical stability of the enthalpy method is a
problem and according to a demonstration in the report of IEA, a steady state
approach for heat exchanger nodes is chosen. The time step used during the
simulation with TRNSYS is established according to the characteristics of the
storage nodes. Finally, this model has been validated with an experimental tank
that was built in the Institute of Thermal Engineering in Austria.
The last example of interesting model is the Type 185 of TRNSYS that is
capable to treat the supercooling effect for bulk PCM storage. Supercooling
effect allows to lower substantially the heat losses from the storage since the
temperature of the PCM material is closer to the ambient temperature. For this
reason, this model is ideal for seasonal storage purposes.
All these models are useful to conduct some analysis about the performance of
the thermal latent heat storage. Sharma et Al in [11] and Chen and Sharma [12]
have developed a two-dimensional model based on enthalpy formulation to
predict the interface profile of the PCMs. They have also studied the effect of
37
thermophysical properties of different PCMs with different types of heat
exchanger container materials, on the performance of the latent heat storage
system. The results are briefly reported below:
● The selection of the thermal conductivity of the heat exchanger container
material and effective thermal conductivity of the PCM also very
important as these parameters have effect on the melt fraction.
● As the thermal conductivity of container material increases, time
required for complete melting of the PCM decreases.
● Effect of thickness of heat exchanger container material on melt fraction
is in-significant.
● The initial PCM temperature does not have very important effect on the
melt fraction, while the boundary wall temperature plays an important
role during the melting process and has a strong effect on the melt
fraction.
An interesting study has been conducted by Kamal A. et al [13] in which a
model for solidification of a PCM material around a tube with radial fins is
performed and the validation against experimental measurements is made. In
particular, the PCM studied is a material used for cold thermal energy storage
and it’s a different application (temperature around 0°C) from this thesis’ one,
however the technology employed (tube heat exchanger with fins) is of great
interest. The results show that, increasing the fin diameter, increases the
interface velocity and the time for complete solidification reduces. Moreover,
reducing the temperature of the cooling fluid, the interface velocity is enhanced
and the time for complete solidification decreases. Finally, the fin thickness
appears to have little influence on the interface velocity and on the time for the
complete solidification.
Ismail et al [14] presented the results of a numerical and experimental
investigation on finned tubes. The model is based on the pure conduction, the
enthalpy formulation approach and the control volume method. Their results are
validated against available results and their own experimental measurements.
The number of fins, fin length, fin thickness, the degree of superheat of the
initial temperature of PCM and the aspect ratio of the annular spacing (the
volume of the annular space between the inner tube carrying the refrigerant fluid
and the external symmetry surface) are found to influence the time for the
complete solidification, solidified mass fraction and the total stored energy. In
particular, fin thickness has a relatively small influence on the solidification
time while the fin length and the number of fins strongly affect either this last
parameter or the solidification rate. The aspect ratio of the annular space has a
strong effect on the time required for the complete solidification. In the end, the
temperature difference between the phase change temperature and the tube wall
38
temperature has an opposite effect on the solidification of PCM. Indeed, the
time for a complete solidification seems to decrease with the increasing of this
parameter.
The majority of these model considers conduction as the only way to transfer
heat in the PCM material in the melted phase, however Ismail and Silva
presented the results of a numerical study on the melting of a PCM around a
horizontal circular cylinder in the presence of natural convection in the melted
phase [15].
Many other models of finned tube heat exchanger have been performed and
most of them have studied the same parameters in different configurations of the
heat exchangers: M. J. Hosseini et al in [16] have been performed a thermal
analysis for a double tube heat exchanger, focusing on the fin’s height and
Stefan number.
Abduljalil A et al in [6] have investigated heat transfer enhancement to
accelerate the melting rate of the PCM for a triplex tube heat exchanger (TTHX)
with internal and external fins, studying some parameters, among which the fin
length, the number of fins and the Stefan number.
The last work mentioned in this review is an experimental study conducted by
Rahimi et al in [17] to investigate melting and solidification processes of
paraffin RT35 as phase change materials in a finned-tube. In particular, the
effect of changing the hot inlet temperature of the HTF and the flow rate either
on the solidification process or on the melting process.
Other studies could be reported, nevertheless these reports are sufficiently
exhaustive to get a clear idea of the problems and the analysis already performed
on the modelling of a thermal latent energy storage with the use of PCM
materials.
1.6 Systems
Applications of thermal storage systems cover a wide range of modern industry
and innovative applications. Industry, agriculture, cold storage, transportation,
textiles and vehicles are just some examples. But one of the most interesting
application, on which researchers have been investigating, is the utilization of
PCM materials in the building sector to decrease the energy consumptions. As
concerns these latter investigations, solar thermal collectors, heat pumps and
PV/PVT are the technologies studied in association with thermal latent energy
39
storage. Long and Zhu used paraffin for thermal storage in an air source heat
pump water heater to take advantage of the off-peak electrical energy [18]. In
this way, the energy is more effective. Later, Agyenim and Hewitt researched
the same concept with RT58 [19] and recently improved it [20].
Real et al in [21] used two storage tanks with different PCM melting
temperatures. A cold tank has been used to take advantage of the low outside
temperatures at night to cool the PCM with a high COP and it’s then been used
later to cool the building when the outside temperature rises. The second tank
operated as an alternative hot reservoir which provides to the system the
flexibility to dissipate the heat to the tank at a constant temperature, assuring to
never reduce the COP below a minimum value. COP operation is independent
of external conditions and electricity savings in the warm mode are obtained.
Fuxin Niu et al in [22] designed an Air Source Heat Pump (ASHP) system with
a parallel triple-sleeve energy storage exchanger, in which the PCM is used to
ensure the reliable operation under various weather conditions and to enhance
the system performance at low ambient temperatures. The innovative device
also includes a solar thermal collector loop for exploiting free solar energy.
Thermal heat can be transferred into the system and stored by the PCM using
water as a heat transfer medium.
In fig. 1.27 it is reported a plant scheme.
Figure 1.27: Schematic diagram of the integrated heat pump system with triple-
sleeve energy storage exchanger [22]
N. Nallusamy et al in [23] developed a TES system able to produce hot water at
an average temperature of 45°C and used as domestic applications, by
40
combining sensible and LHS concept. The TES unit contains paraffin as Phase
Change Material (PCM) filled in spherical capsules, which are packed in an
insulated cylindrical storage tank. The water, used as HTF to transfer heat from
the constant temperature bath/solar collector to the TES tank, also acts as
sensible heat storage (SHS) material.
In fig 1.28 a plant scheme is reported.
Figure 1.28: Schematic of experimental setup: (1) solar flat plate collector
(varying heat source); (2) constant temperature bath; (3) electric heater; (4)
stirrer; (5) pump; (6 and 7) flow control valves; 8. flow meter; (9) TES tank;
(10) PCM capsules; (11) temperature indicator; TP and Tf—temperature sensors
(RTDs). [24]
1.6.1 Sunamp batteries
The last important applications are the products sold by Sunamp, a Scottish
company embedded in renewable energy sector, a world leader in high power-,
high energy-density thermal energy storage. Sunamp aims to facilitate
renewable and low-carbon heat and cool providing an efficient, scalable, cost
saving solution. In Scotland, the electric energy produced in excess by isolated
PV panels is not paid when exported to the national grid.
Sunamp have designed a system for domestic hot water to exploit this energy
that otherwise would be lost. SunampPV is a thermal battery in which the PCM
materials is directly heated by the electric energy generated by PV panels.
Sunampstack is a more complex configuration with a heat pump feeded by
electric energy and a thermal battery with PCM that takes the heat coming from
the heat pump as useful effect. This last configuration fits for larger buildings. In
[24] it’s possible to get an idea of this technology.
41
Chapter 2
Description of the PCM storage unit physical
model
2.1 Introduction
The PCM storage model has been built to simulate the transient behaviour of the
thermal battery as a function of different configurations and external conditions.
After a detailed study on previous models, Type 841 has been taken as a starting
point to develop a new model that could improve it. As a matter of fact, in the
final section of the chapter 2 it has been reported a comparison among the new
model, Type 841 and the experimental data against which, previously, Type 841
has been validated. The modelling of the phase change phenomenon is based on
the enthalpy method. However, instead of using a method of finite differences in
the explicit formulation as in Type 841, a system of differential equations has
been built. The detailed explanation of the governing equations of the system
has been done in the section 2.3.
Since the thermal battery has to work in a domestic environment, its
compactness is one of the most important physical requirements. For this reason,
a finned tube heat exchanger has been chosen. In order to exploit, as better as
possible, the heat transfer surface, and promote the heat transfer rate between the
heat carrier fluid and PCM, a large number of fin plates has been attached to the
tubes. In this application, the spacing between fins and tubes has been filled with
PCM so that the presence of the fins enhances the heat transfer from the PCM to
the heat carrier fluid and vice versa.
The dimensions of the heat exchanger could be set as an input of the model,
moreover very different configurations could be adopted. An important feature
is its physical flexibility, indeed it’s possible to decide the path of the water flow
in the tube, the kind of connection between pipes in series and also the mass
flow rate value for each level of the heat exchanger.
The model has been implemented in Matlab.
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2.2 Model geometry
2.2.1 Nodal network
The finned tube heat exchanger has been subdivided into nodes of equal size,
each one comprises a finned tube section and the surrounding area filled by the
PCM. Each node represents a certain region in which the PCM temperature and
the water temperature has been assumed to be constant in the whole region. Fig.
2.1 represents a schematic longitudinal section of the heat exchanger and the
nodes subdivision, in which a possible tube connection configuration has been
applied.
Figure 2.1: heat exchanger scheme
A structure of the nodal mesh has been created by defining a number of
columns, a number of rows and a number of levels. The number of columns
represents the number of nodes in which each tube has been subdivided, the
number of rows represents the number of tubes connected in series whereas the
number of levels represents the number of tubes in parallel, as it’s possible to
see in fig. 2.2.
43
Figure 2.2: finned tube heat exchanger with 3 levels and 3 rows
2.2.2 Storage node
In order to achieve a sufficient numerical accuracy, each storage node has been
subdivided in a defined number of elements. One element comprises a pipe
section of length equal to the distance between two fins 𝑡𝑓 , one fin and the
surrounding PCM region. The fin height 𝑡𝑙 has been set equal to the sum of the
distance between two tubes in series and the tube diameter 𝑑.
Figure 2.3: Storage node
44
Either the tube length or the number of columns are two of the model inputs,
therefore the node length and the number of elements contained in each node
can be respectively computed by equation (3.1) and (3.2).
𝑁𝑜𝑑𝑒 𝐿𝑒𝑛𝑔𝑡ℎ =𝑙
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐶𝑜𝑙𝑢𝑚𝑛𝑠
(2.1)
𝑛𝑒𝑙 =𝑁𝑜𝑑𝑒 𝐿𝑒𝑛𝑔𝑡ℎ
𝑡𝑓
(2.2)
2.2.3 Pipe connections and model flexibility
As depicted in fig 2.1 the tube in series are connected by pipe bends. The path of
the water flow inside the heat exchanger is directly dependent on the way each
tube is connected to the others. Since the PCM mass covers a wide region of the
heat exchanger, it’s possible that, during the charging or the discharging process
of the storage, the PCM temperatures of different nodes differ consistently. In
order to exploit as better as possible all the PCM regions and all the energy
stored, an index able to identify which is the following storage node in the water
path has been created. In this way the model is able to simulate different heat
exchanger configurations and to suit them to the state of charge of the storage.
Whenever a heat exchanger with different levels has to be modelled, it’s
possible either to change the configuration or to vary the water mass flow rate
level by level. If the PCM temperature value is not sufficiently high in some
regions, it’s possible to avoid the heat transfer by excluding the tubes nearby
that regions upon the pathway of the water flux within the heat exchanger.
Either the first node or the last node of the pathway have to be either in the first
or in the last column of the nodal mesh, otherwise a hypothetical inlet or outlet
node in the middle of a tube wouldn’t have physically sense.
2.3 Governing equations
The entire section 2.3 is devoted to the description of the governing equations of
the heat transfer phenomenon inside the thermal battery.
As mentioned in the section 2.1, the equations employed in this model describe
the transient behaviour of the system. Since the battery contains two different
elements, which change their thermal behaviour in time, it’s crucial to define a
precise structure of the nodal network in order to depict the governing equations.
45
As represented in figure 2.1 the entire battery has been divided in several nodes
of same size, whom represent a certain region of the battery. Each node includes
three different elements: a piece of tube which inwardly faces the heat carrier
fluid, the surrounding fins and a fixed amount of PCM material located in the
empty space between the fins and the external casing.
For each node a system of two differential equations, derived from the energy
conservation law, has been formulated, as illustrated below:
{𝑚𝑤𝑐𝑝,𝑤
𝛿𝑇𝑤,𝑖
𝛿𝑡= �̇�ℎ𝑥 + �̇�𝑤𝑐𝑝,𝑤(𝑇𝑤,𝑖−1 − 𝑇𝑤,𝑖)
𝑚𝑆𝑇
𝛿ℎ𝑆𝑇,𝑖
𝛿𝑡= �̇�ℎ𝑥 + �̇�𝑙𝑜𝑠𝑠 + �̇�𝑐𝑜𝑛𝑑,𝑚 + �̇�𝑐𝑜𝑛𝑑,𝑛
(2.3)
(2.4)
The variables of the system are the heat carrier fluid temperature and the storage
enthalpy, and both represent the average value of that region.
As “storage” it’s meant the incorporation of the PCM with the fin, tube and
additional material such as the external casing as it would be the same “body”.
Index 𝑖 refers to the position of the considered node.
The first equation represents the energy conservation of the water flowing inside
the tubes:
• 𝑚𝑤𝑐𝑝,𝑤𝛿𝑇𝑤,𝑖
𝛿𝑡 shows the variation in time of the water thermal energy in
that node.
• �̇�ℎ𝑥 is the heat transfer between the water and the storage in the same
node and it could be explicited with equation (2.5).
�̇�ℎ𝑥 = 𝑈𝐴𝑡𝑜𝑡𝑛𝑒𝑙(𝑇𝑆𝑇,𝑖 − 𝑇𝑤,𝑖) (2.5)
Looking at this equation, it’s possible to identify a third variable 𝑇𝑆𝑇,𝑖 not
mentioned yet, which has been deeply discussed in section 2.3.2.
46
𝐴𝑡𝑜𝑡 is the total contact surface between storage and water. It’s obtained by
summing the fins area and tube area, according to equation (2.6).
𝐴𝑡𝑜𝑡 = 𝐴𝑓 + 𝐴𝑡 = 2 (𝑡𝑞𝑡𝑙 −𝜋𝑑2
4) + 𝜋𝑑(𝑡𝑓 − 𝑠𝑓)
(2.6)
The detailed explanation of the overall heat transfer coefficient computation is
shown in the following chapter 2.3.1.
• �̇�𝑤𝑐𝑝,𝑤(𝑇𝑤,𝑖−1 − 𝑇𝑤,𝑖) is the heat transfer due to the movement of water
mass from a node to another in that precise instant of time. The index
(𝑖 − 1) refers to the previous node, following the water pathway
direction.
The second equation represents the energy conservation of the storage “body”:
• 𝑚𝑆𝑇𝛿ℎ𝑆𝑇,𝑖
𝛿𝑡 shows the variation in time of the storage energy in that
node.
• �̇�ℎ𝑥 is the heat transfer between the water and the storage in the same
node. It is equal to the �̇�ℎ𝑥 computed in the water side but with opposite
sign, according to equation (2.7).
�̇�ℎ𝑥 = 𝑈𝐴𝑡𝑜𝑡𝑛𝑒𝑙(𝑇𝑤,𝑖 − 𝑇𝑆𝑇,𝑖) (2.7)
• �̇�𝑙𝑜𝑠𝑠 is the heat loss to the ambient due to not a perfect isolation of the
external casing, according to equation (2.8).
�̇�𝑙𝑜𝑠𝑠 = (𝑈𝐴)𝑙𝑜𝑠𝑠 ⋅ (𝑇𝑎𝑚𝑏 − 𝑇𝑆𝑇) (2.8)
Depending on the position of the node inside the thermal battery, the term
(𝑈𝐴)𝑙𝑜𝑠𝑠 changes according to the dimension of the contact layer between the
PCM and the casing.
Here it is illustrated how it has been computed 𝑈𝑙𝑜𝑠𝑠:
𝑈𝑙𝑜𝑠𝑠 = (1
𝑎𝑎𝑖𝑟+
𝑠𝑐
𝜆𝑐)
−1
(2.9)
𝑎𝑎𝑖𝑟 has been fixed to a typical value of 0.005 𝑘𝑊
𝑚2𝐾 in natural convection.
47
• �̇�𝑐𝑜𝑛𝑑,𝑚 is the heat transfer by conduction between storage nodes in the
horizontal direction, as it’s possible to see in figure 2.3 and it’s
computed according to equation (2.10).
�̇�𝑐𝑜𝑛𝑑,𝑚 = 𝜆𝑚𝐴𝑓
𝑛𝑒𝑙𝑡𝑓2(𝑇𝑆𝑇𝑚+1,𝑛
+ 𝑇𝑆𝑇𝑚−1,𝑛− 2𝑇𝑆𝑇𝑚,𝑛
) (2.10)
𝑇𝑆𝑇𝑚+1,𝑛 and 𝑇𝑆𝑇𝑚−1,𝑛
are respectively the temperature of the previous and the
following adjoining nodes of the considered one, on the same row n.
𝜆𝑚 is the average thermal conductivity in the m directions and it is computed
according to the following equation:
𝜆𝑚 =𝑡𝑓
(𝑡𝑓 − 𝑠𝑓
𝜆𝑃𝐶𝑀+
𝑠𝑓
𝜆𝑓)
(2.11)
• �̇�𝑐𝑜𝑛𝑑,𝑛 is the heat transfer by conduction between storage nodes in the
vertical direction, as it’s possible to see in figure 2.3 and it’s computed
with the following equation.
�̇�𝑐𝑜𝑛𝑑,𝑛 = 𝜆𝑛
𝑡𝑙𝑡𝑞𝑛𝑒𝑙𝑡𝑓(𝑇𝑆𝑇𝑚,𝑛+1
+ 𝑇𝑆𝑇𝑚,𝑛−1− 2𝑇𝑆𝑇𝑚,𝑛
) (2.12)
𝑇𝑆𝑇𝑚,𝑛+1 and 𝑇𝑆𝑇𝑚,𝑛−1
are respectively the temperature of the lower and upper
adjoining nodes of the considered one on the same column m.
𝜆𝑛 is the average thermal conductivity in the m directions and it is computed
according to the following equation:
𝜆𝑛 =(𝜆𝑃𝐶𝑀(𝑡𝑓 − 𝑠𝑓) + 𝜆𝑓𝑠𝑓)
𝑡𝑓
(2.13)
The heat transfer by conduction is negligible with respect to the heat transfer
between the water and the storage when the battery is working. In case of
switching off the battery, these last two terms have to be taken into account and
they are no more negligible. So, it’s important to highlight also these terms.
In this model they have been included in the simulation.
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2.3.1 Overall heat transfer coefficient
The computation of the overall heat transfer coefficient 𝑈 has been performed
according to “VDI heat atlas”, section “Heat transfer to finned tubes” [25].
During this procedure one single storage node has been considered. The overall
heat transfer coefficient between the heat carrier fluid and the PCM has been
computed by using equation (2.14).
1
𝑈=
1
𝑎𝑒𝑙,𝑒𝑓𝑓+
𝐴𝑒𝑙
𝐴𝑡,𝑖𝑛⋅ (
1
𝑎𝑖𝑛+
𝑑𝑤
𝜆𝑡)
(2.14)
Where 𝑎𝑖𝑛 has been computed by using the equation (2.15), which is the
Gnielinski equation [25], so that to get the Nusselt number.
𝑁𝑢 =
𝜓8
⋅ 𝑅𝑒 ⋅ 𝑃𝑟
1 + 12.7 ⋅ √𝜓8
⋅ (𝑃𝑟23 − 1)
⋅ [1 + ((𝑑 − 𝑑𝑤)
𝑙)
23
]
(2.15)
Where 𝜓 is the Darcy friction factor and it has been computed according to
equation (2.16)
𝜓 = (1.8 ⋅ log 𝑅𝑒 − 1.5)−2 (2.16)
where the Reynolds number and the Prandtl number have been computed as
follows:
𝑅𝑒 =𝜌 ⋅ 𝑣 ⋅ (𝑑 − 2 ⋅ 𝑑𝑤)
𝜇
(2.17)
𝑃𝑟 =𝜇 ⋅ 𝑐𝑝,𝑤
𝜆𝑤
(2.18)
Once the Nusselt has been computed, 𝑎𝑖𝑛 has been easily calculated by using the
equation (2.19).
𝑎𝑖𝑛 =𝑁𝑢 ⋅ 𝜆𝑤
(𝑑 − 2 ⋅ 𝑑𝑤)
(2.19)
49
Usually a finned tube heat exchanger, like the one used in this model, deals with
a moving medium such as air. In that case the convection effects have to be
considered, however in this case, since the heat exchanger deals with a
stationary medium (PCM) and since the cavities between the fins are quite
narrow, convection effects are neglected. The heat transfer coefficient on the fin
and pipe surface 𝑎𝑓 is then calculated according to the equation (2.20), by using
half of the distance between two fins and the PCM thermal conductivity 𝜆𝑃𝐶𝑀.
𝑎𝑓 =2 ⋅ 𝜆𝑃𝐶𝑀
(𝑡𝑓 − 𝑠𝑓)
(2.20)
In order to calculate the effective heat transfer coefficient 𝑎𝑒𝑙,𝑒𝑓𝑓 the fin
efficiency has been considered.
Figure 2.4: Fins geometry [25]
According to [25], for a rectangular fin the coefficient 𝑗 and 𝑗′ has been
computed as follows:
𝑗′ = 1.28 ⋅𝑡𝑙
𝑑⋅ (
𝑡𝑞
𝑡𝑙− 0.2)
0.5
(2.21)
𝑗 = (𝑗′ − 1) ⋅ (1 + 0.35 ⋅ ln 𝑗′) (2.22)
The fin efficiency is then calculated according to equation (2.23)
ℎ𝑓 =tanh 𝑋
𝑋
(2.23)
50
where
𝑋 = 𝑗 ⋅𝑑
2⋅ √
2 ⋅ 𝑎𝑓
𝜆𝑓 ⋅ 𝑠𝑓
(2.24)
In fig 2.5 it’s possible to see how the fin efficiency decreases with the increase
of 𝑋.
Figure 2.5: Fin efficiency trend [25]
The effective heat transfer coefficient has then been calculated according to
equation (2.25).
𝑎𝑒𝑙,𝑒𝑓𝑓 = 𝑎𝑓 ⋅ [1 −𝐴𝑓
𝐴𝑒𝑙⋅ (1 − ℎ𝑓)]
(2.25)
2.3.2 PCM temperature function and thermal properties
As revealed above, this chapter is dedicated to the third variable 𝑇𝑆𝑇,𝑖 and how
it’s possible to bypass the problem of having an undefined system of two
equation with three unknowns.
51
It has been created a function that relates the storage temperature and the storage
enthalpy on the basis of the thermal properties of the material taken from the
dataset of Type 841.
In this way it has been possible to explicit 𝑇𝑆𝑇,𝑖 as a function of the main
variable ℎ𝑆𝑇,𝑖, making the system well defined.
Figure 2.6: Enthalpy-temperature curve [10]
Fig. 2.6 shows the enthalpy-temperature curve of the PCM material that has
been reproduced in the model. Three linear functions for solid, phase change
region and liquid have been used with different slope due to different specific
heats, assumed constant in that specific region. The phase change region is
defined within the temperature interval between 𝑇𝑚1 and 𝑇𝑚2, however, as it has
been illustrated in the “State of the art” section, sometimes particular
phenomenon could appear. As a matter of fact, in addition to the red lines which
describes the behaviour of PCM during the heating phase, a blue line has been
illustrated in order to represent the behaviour of the PCM during the cooling
phase. Subcooling phenomenon is described by the upper part of the blue line,
indeed instead of starting the transition phase at temperature 𝑇𝑚2, the material
cools down remaining in liquid phase up to a certain temperature defined as
𝑇𝑚2 − 𝛥𝑇𝑆𝐶 . Once having reached this temperature, the material starts the
transition phase, increasing its temperature of few degrees. At this point, it’ s
possible to notice the hysteresis phenomenon: the blue line doesn’t coincide
52
perfectly with the red line, but it completes the transition phase reaching a lower
temperature with respect to 𝑇𝑚1. Indeed, during the transition phase the red and
blue line are parallel and moreover, they maintain a fixed distance, which is
exactly equal to 𝛥𝑇ℎ𝑦𝑠𝑡.
Fig. 2.6 represents the enthalpy-temperature curve of a PCM, but in the model,
as mentioned above, fins, tube and additional material have to be incorporated
with it, creating the storage node. Therefore, all the thermal properties used to
realize this curve have been modified, considering average values among those
three elements. The specific heats have been calculated according to equation
(2.26) for the solid phase and (2.27) for the liquid phase:
𝑐𝑝𝑠,𝑆𝑇=
𝑚𝑡𝑐𝑝𝑡+ 𝑚𝑓𝑐𝑝𝑓
+ 𝑚𝑃𝐶𝑀𝑐𝑝𝑠,𝑃𝐶𝑀+ 𝑚𝑎𝑑𝑑𝑐𝑝𝑎𝑑𝑑
𝑚𝑆𝑇
(2.26)
𝑐𝑝𝑙,𝑆𝑇=
𝑚𝑡𝑐𝑝𝑡+ 𝑚𝑓𝑐𝑝𝑓
+ 𝑚𝑃𝐶𝑀𝑐𝑝𝑙,𝑃𝐶𝑀+ 𝑚𝑎𝑑𝑑𝑐𝑝𝑎𝑑𝑑
𝑚𝑆𝑇
(2.27)
The specific heats correspond to the slope of the linear function, respectively for
the solid and for the liquid phase.
The other important thermal property which has been modified, is the latent heat
of PCM. Since the transition phase takes place in a temperature range, the
sensible heat corresponding to this region has been added considering the entire
mass of the storage node:
𝛥𝐻𝑆𝑇 =
[𝑚𝑃𝐶𝑀𝛥𝐻𝑃𝐶𝑀 + 𝑚𝑆𝑇
(𝑐𝑝𝑠,𝑆𝑇+ 𝑐𝑝𝑙,𝑆𝑇
)
2(𝑇𝑚1 − 𝑇𝑚2)]
𝑚𝑆𝑇
(2.28)
As it’s possible to notice in the last part of the equation, the sensible heat has
been computed considering an average of the solid and liquid specific heat of
the storage node.
Using this “new” thermal properties of the storage and on the basis of other data
such as 𝛥𝑇ℎ𝑦𝑠𝑡 and 𝛥𝑇𝑆𝐶 , it has been possible to create two different enthalpy-
53
temperature functions: the first one for the cooling phase and the second one for
the heating phase.
Here below, it’s reported the temperature-enthalpy function created in Matlab:
Figure 2.7: Temperature-enthalpy function
The last important clarification concerns the subcooling. In a real situation the
PCM material inside the thermal battery ends the subcooling phase and starts the
transition phase approximately in few seconds. Due to this reason, it’s possible
that a certain number of storage nodes has reached the fixed temperature (𝑇𝑚2 −𝛥𝑇𝑆𝐶), after which the transition phase can start, nevertheless other nodes can be
still in a liquid state having a higher temperature. In this situation, after a short
period of time all the PCM starts the transition phase even if a part of it has not
reached the temperature (𝑇𝑚2 − 𝛥𝑇𝑆𝐶) yet.
Modelling this type of behavior is not a simple challenge and in this thesis, it
has been decided to introduce a simplification in doing it: it has been created an
indicator that counts how many storage nodes have reached the temperature
(𝑇𝑚2 − 𝛥𝑇𝑆𝐶) at that precise instant of time. When the indicator signals a
number equal or greater than a fixed threshold (10 nodes), then from the next
timestep on all the storage nodes start the transition phase, independently on
their temperature, given that it’s smaller or equal to 𝑇𝑚2.
54
2.4 Validation of the model
At the Institute of Thermal Engineering, Graz University of Technology,
Austria, an experiment on a heat exchanger filled with PCM, as the one
represented in the model has been made. All the results are available from [10]
and the validation of the model has been made against these data. The
specifications of the finned tube heat exchanger used in the experiment are listed
in table 2.1.
Table 2.1: Heat exchanger specifications [10]
The PCM used in the experiment is Sodium Acetate Trihydrate (SAT), chemical
formula (𝑁𝑎𝐻𝐶𝑂𝑂 · 3𝐻2𝑂). SAT is one of the most important PCMs for
thermal application due to its high energy storage density and high thermal
conductivity. It has a phase change temperature of 58 °C, and it’s therefore
suitable for hot water supplying, by storing low temperature thermal energy. The
only problem related to this kind of PCM are the phenomena of subcooling and
phase segregation during the solidification process, for this reason its application
requires the use of effective nucleating and thickening agents [26].
The experiment has consisted in two processes: the storage charging process and
the storage discharging process.
55
2.4.1 Charging process
During the charging process it has been supposed that either the PCM
temperature or the water temperature within the tube, at the initial time of the
experiment were at 30 °C.
An inlet mass flow rate of 0.103 kg/s, at a temperature of 71 °C has been
applied. The model validation consists in replicate either the PCM or the water
flux temperature evolution in time, in the last node of the heat exchanger. The
model simulations have been compared either with the results achieved by
running the Type841 model or with the experimental results taken from [10].
The final comparison is represented in fig 2.8.
Figure 2.8: Charging process results
As shown in fig. 2.8 the water temperature results in the last node of the heat
exchanger, agree with either the experimental results or with the Type841
results. This can be considered an important achievement because the outlet
temperature of the storage is crucial for a correct interaction with the other
components of the system.
The PCM temperature evolution in time is very similar to the one of the
Type841, however it differs considerably to the experimental results. In reality
the PCM phase transition process ends before the prediction of the simulation
and the beginning of this process is not as sharp. The temperature agreement on
56
this side leaves room for improvement, however the most important result is the
correct evolution in time of the outlet water temperature.
2.4.2 Discharging process
During the discharging process it has been supposed that either the PCM
temperature, or the water temperature within the tube, at the initial time of the
experiment were at 72 °C. An inlet mass flow rate of 0.111 kg/s, at a
temperature of 30 °C has been applied. In this simulation is clearly visible the
main potential of PCM, indeed it’s able to maintain a constant temperature for a
considerable period of time. The outlet water temperature takes a great
advantage from this skill because, as far as the battery has a good state of
charge, it receives a latent heat flux from the PCM, until the phase change
process is over. For this reason, the outlet water flux maintains a good level of
temperature and this skill makes the thermal battery very suitable to a domestic
use.
In fig 2.9 the results of the discharging process are shown.
Figure 2.9: Discharging process results
Also in this process the PCM temperature agrees very well with the results of
the Type841 and it differs from the experimental results, especially in the
sharpness of the curve, although it’s clearly visible that the experimental trend is
similar to the simulated one.
57
The water outlet temperatures differ slightly from the Type 841 results,
however, during the phase change process, the model developed agree with the
experimental data in a better way than the Type841.
Either during the charging or the discharging process, the water temperatures fit
to the experimental results better than PCM temperatures. This could be an
outcome of how the PCM storage node has been simulated, incorporating fins,
tubes and additional material with PCM material: actually, these three elements
don’t have the same behaviour of a PCM, since none of them deal with a
transition phase phenomenon. The PCM material incorporation in the same node
of fins, tube and additional material it’s been a strong approximation and it has
caused the distance among the PCM curves. Anyway, looking at the
experimental PCM curve during the charging process, it’s clear that its shape is
very similar to the simulated ones. The main difference is only related to a
shorter transition phase. On the other hand, looking at the experimental PCM
curve during the discharging process, the general shape is really different from
the simulated ones, showing a minimum after around 600s and a maximum after
around 1300s. This fact can be explained by considering the subcooling
phenomenon that it has been simulated very schematically, as described at the
end of chapter 2.3.2.
In conclusion, the model developed during this work can be considered very
similar to Type 841, even if some aspects could be studied more thoroughly,
such as the subcooling process, that how it has been illustrated above, it’s a very
complex phenomenon to be reproduced, or the heat transfer phenomenon among
PCM material, fins, tubes and external casing.
58
59
Chapter 3
PCM storage application: Domestic Hot
Water (DHW) system
3.1 Introduction
One of the most important characteristic of PCM storage is the possibility to
reduce drastically the size of the storage tank. Instead of using a standard hot
water tank with size big enough to be not easily installed in an apartment, a
configuration with a PCM storage tank has been investigated.
Since the main objective of this thesis is the testing of the PCM battery in a
domestic hot water system, an arrangement along with a high-temperature heat
pump, a plate heat exchanger, two pumps and two valves has been studied.
A tricky part of this work has been the choice of the control strategies of the
entire system. Despite the selected configuration is rather basic, lots of possible
layouts and, especially, control strategies have been considered. In the end, the
last choice which is presented in the following paragraphs, concerns a control
strategy based on the state of charge (SOC) of the PCM battery.
In the final section of chapter 3, a series of parameters have been selected in
order to perform a parametric analysis directed to minimize the dimensions of
the thermal battery and the power absorbed by the heat pump, given that the hot
water demand is guaranteed in terms of energy but also in terms of temperature.
A tapping cycle has been taken from the UNI EN 16147 so that to have
reference values of temperature and energies to provide at the user during the
entire day.
As it is possible to notice from this brief introduction, many cues have been left
to be taken by possible future works. Starting from the several possible
configurations with different control strategies going to the economic aspect,
lots of new studies could be carry out.
60
3.2 Plant description
The plant layout has been set up in order to exploit as better as possible the
ability of the PCM storage unit to provide instantaneously useful thermal
energy. Indeed, an Air Source Heat Pump (ASHP), has usually to deal with a
transient process that takes time to achieve sufficiently high water temperature.
The coupling of the two components allows the Domestic Hot Water (DHW)
production by exploiting the outside air temperature, without using any
conventional fossil fuel.
As shown in fig. 3.1 the DHW system mainly comprises an high temperature
ASHP, a PCM storage unit, a plate heat exchanger, two water pump P1 and P2,
and two check valves V1 and V2.
Figure 3.1: Plant layout
As discussed in the chapter 2, the Phase Change Material within the storage unit
has a phase transition temperature of 58°C, whereas the conventional ASHP are
not able to provide temperature higher than 55°C. In order to recharge the PCM
unit, a high temperature heat pump is needed in such a configuration. The
“Daikin Altherma” high temperature ASHP for example, is able to provide hot
water up to 80°C by exploiting the outside air temperature until a limiting
condition of -20°C. Due to this reason it couples very well with a PCM storage
unit and it has been adopted. The heat pump comprises an evaporator, which
transfers the air thermal energy to the refrigerant and make it evaporate; a
61
compressor, which increases the refrigerant vapor pressure; a condenser, in
which the refrigerant condensates and transfers thermal energy to the water side,
and an isenthalpic valve, which decreases the refrigerant pressure in an
isenthalpic process.
The maximum increase of temperature provided by the ASHP strictly depends
on its size and on the water mass flow rate elaborated. Before reaching the
nominal working conditions, in which it provides the ∆T𝑚𝑎𝑥, starting from the
time in which it has switched on, the ASHP faces a transient process in which
the heating capacity gradually increases until it reaches its maximum value. Due
to the complexity of the transient phenomena that affects the heat pumps, the
real behaviour at partial load is very difficult to be well-replicated in the system
simulations. For this reason, a fake water mass node has been placed
downstream of the ASHP so that, before flowing to the PCM unit, the ASHP
needs to heat up also the fake water mass contained in that node, and this
process takes an amount of time which could be compared to a real ASHP
transient duration. The water flux temperature at the outlet of this node
corresponds to the real outlet flux temperature of the ASHP.
The thermal transient analysis of the fake water mass has been performed by
following the lumped parameters model, according to equation (3.1)
𝜌𝑐𝑉𝜕𝑇
𝜕𝑡= −ℎ𝐴(𝑇 − 𝑇𝑓)
(3.1)
Where ℎ is the convective heat transfer coefficient, 𝐴 is the heat transfer surface
and 𝜌𝑐𝑉 is the thermal capacity of the fake water mass.
The water mass is supposed to be in contact with an external fluid, whom
temperature is defined by equation (3.2)
𝑇𝑓 = 𝑇𝑤𝑎𝑡𝑒𝑟,𝑖𝑛,𝐴𝑆𝐻𝑃 + ∆T𝑚𝑎𝑥 + 𝑘 (3.2)
Where 𝑘 is a constant introduced to allow the water mass to reach the
temperature 𝑇𝑓, otherwise it would approach the fluid temperature 𝑇𝑓 only in an
asymptotically way. By solving equation (3.1) it has been possible to define the
temperature of the water mass according to equation (3.3).
𝑇𝑚𝑎𝑠𝑠 = (𝑇𝑤𝑎𝑡𝑒𝑟,𝑖𝑛,𝐴𝑆𝐻𝑃 + ∆T𝑚𝑎𝑥 + 𝑘) − (∆T𝑚𝑎𝑥 + 𝑘) ⋅ 𝑒− (𝑡−𝑡𝑜𝑛)
𝜏 (3.3)
62
Where 𝑡 is the current time of the simulation in second, 𝑡𝑜𝑛 is the time at which
the ASHP has been switched on, and 𝜏 is defined by equation (3.4).
𝜏 =𝜌𝑐𝑉
ℎ𝐴
(3.4)
During the performed simulation 𝜏 has been fixed so that to complete the ASHP
transient process in 10 minutes, which is a good approximation of a real
behaviour of a heat pump.
In fig. 3.2 is shown an example of the phenomenon above discussed, in which
𝑇𝑤𝑎𝑡𝑒𝑟,𝑖𝑛,𝐴𝑆𝐻𝑃 has been fixed at 45 °C, ∆T𝑚𝑎𝑥 is equal to 15 °C and 𝑘 has been
set equal to 1.
𝑇𝑚𝑎𝑠𝑠 represents the water outlet temperature of the ASHP.
Figure 3.2: Simulated transient behaviour of an ASHP
Fig. 3.3 shows the behaviour of the ASHP during the simulation, where the blue
line represents the result of a heat pump activation supposing that it
instantaneously works in nominal conditions and then supposing that it provides
instantaneously the maximum ∆T, the green line represents the result of a heat
pump activation considering an initial transient behaviour, whereas the red line
represents the ASHP inlet water temperature. It’s possible to figure out how the
outlet water temperature affected by the transient (green line) is always lower
than the outlet temperature in nominal conditions (blue line). In the following
example 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 has been fixed at 67 °C.
63
Figure 3.3: ASHP behaviour during the simulations
The last important consideration about the ASHP concerns the operation in
partial load conditions. Since the purpose of the heat pump in the simulated
system is to recover the PCM storage, ASHP undergoes several ON-OFF cycles,
so that the most of the time it works at partial load conditions, guarantying the
same heating capacity as it would work at full load, but absorbing more power,
causing a reduction of the Coefficient Of Performance (COP).
In order to simulate this behaviour, report [28] has been taken as a reference.
The procedure consists in computing the COP at full load operating conditions
by consulting table 3.3, where
𝐶𝑂𝑃 =𝐻𝐶
𝑃𝐼
(3.5)
Then, a mean part load ratio (PLR) is computed as the ratio between the heating
capacity really supplied by the ASHP in that particular time step and the
maximum energy, which could be supplied in the same time interval in the case
of continuous working at full capacity, according to equation (3.6).
𝑃𝐿𝑅 =𝐻𝐶𝑝𝑙
𝐻𝐶
(3.6)
64
In this way it’s possible to compute the last coefficient called part load factor
PLF as a function of PLR according to equation (3.7).
𝑃𝐿𝐹 =𝑃𝐿𝑅
[𝑃𝐿𝑅 ⋅ 𝐶𝑐 + (1 − 𝐶𝑐)]
(3.7)
𝐶𝑐 is a coefficient that can be computed experimentally by the manufacturer. In
case of lack of it in the capacity tables, its value can be assumed equal to 0.9, as
it has been done in this thesis.
In the end, the new coefficient of performance at partial load condition 𝐶𝑂𝑃𝑝𝑙
can be computed with the following equation:
𝐶𝑂𝑃𝑝𝑙 = 𝑃𝐿𝐹 ⋅ 𝐶𝑂𝑃 (3.8)
The power absorbed by the ASHP at partial load conditions is then calculated
according to equation (3.9).
𝑃𝐼𝑝𝑙 =𝐻𝐶
𝐶𝑂𝑃𝑝𝑙
(3.9)
On the hot water supply side, a plate heat exchanger has been chosen due to its
compactness, its simplicity and its large availability in the market at a low price.
A plate exchanger consists of a series of parallel plates that are placed one above
the other so that to allow the formation of a series of channels for fluids to flow
between them. As shown in fig. 3.4 each plate of the heat exchanger is made by
4 holes placed on its corners: thanks to the correct placement of some seals
(black lines in the figure 3.4), hot and cold fluid flow through alternating
channels, so that a single plate is always in contact with the cold fluid on one
side and with the hot fluid on the other side. In order to increase the heat transfer
coefficient and facilitate the flux of the water, the plates are corrugated. Due to
the high conductive material of the plates, this component is able to transfer heat
coming from the PCM storage unit, to the water flux coming from the cold
water supply, achieving as a final result the production of Domestic Hot Water.
The sizing procedure and the overall heat transfer coefficient computation of
single pass plate heat exchanger has been discussed in the section 3.4.
65
Figure 3.4: Plate heat exchanger working principle
The PCM storage charging process starts by switching on the water pump P1,
which receives the hot water from the high temperature ASHP and feeds the
PCM unit. V1 is a check valve, able to avoid the inversion of the flow in the
circuit, which would give rise to an overall system malfunctioning.
Whenever Domestic Hot Water (DHW) is required, the discharging process of
the PCM storage unit takes place and the water pump P2 is switched on. It’s
important to underline that only one between the charging and the discharging
process can take place, so that if P2 is on, P1 is off and vice versa. V2 is a check
valve too and it’s been placed for the same reason, previously discussed, of V1.
The PCM unit structure implies the constraint of, respectively, receiving the
water inlet flux and providing the water outlet flux, always on the same sides.
The kind of layout discussed above has a very simple design and it’s also able to
respect this constraint, for this reason it suits very well for a DHW system.
3.3 Simulation control strategy
The main goal of the system simulations is to satisfy the load required by the
user in each moment of the day. In the European regulations UNI EN 16147,
depending on the size of the building, several tapping cycles are defined [27]. In
each of them, at every time of the day, it’s been defined a required amount of
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DHW energy in 𝑘𝑊ℎ, the kind of load required, the ∆𝑇𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 during the
tapping cycle and the ∆𝑇𝑚𝑖𝑛 from which it’s possible to start counting useful
DHW energy.
Table 3.1 shows the Tapping Cycle L, chosen as a reference for the simulations
performed.
Table 3.1: Tapping cycle L
67
As represented in table 3.1 the tapping cycle lasts 15 hours, it starts at 7 AM and
it ends at 10 PM. The system has been built in order to start providing useful
thermal energy at the beginning of each interval. An energy counter has been
placed on the DHW side of the heat exchanger so that it’s possible to evaluate,
second per second, the amount of energy provided in that time interval. This
component computes the instantaneous thermal energy according to equation
(3.10)
�̇�𝑇 = �̇�𝐷𝐻𝑊 ⋅ 𝑐𝑝,𝑤 ⋅ (𝑇𝑜𝑢𝑡,𝐻𝑋 − 𝑇𝑖𝑛,𝐻𝑋) (3.10)
Where, as depicted in fig. 3.5 𝑇𝑖𝑛,𝐻𝑋, is the temperature of the water flux
corresponding to the cold supply, whereas 𝑇𝑜𝑢𝑡,𝐻𝑋 is the Domestic Hot Water
temperature.
Figure 3.5: Heat exchanger scheme
The energy counter performs then the summation, on each second, of the energy
provided and only if at the end of the interval this summation is larger than the
energy required by the tapping cycle, the load can be considered satisfied. It’s
important to underline that the energy counter starts counting energy only if
equation (3.11) is satisfied, otherwise the thermal energy, in every second in
which this condition is not valid, has been put equal to zero.
(𝑇𝑜𝑢𝑡,𝐻𝑋 − 𝑇𝑖𝑛,𝐻𝑋) ≥ ∆𝑇𝑚𝑖𝑛 (3.11)
68
3.3.1 State Of Charge (SOC)
Before describing the system control strategy adopted to achieve this goal, it’s
useful to introduce the concept of PCM storage unit State Of Charge (SOC).
SOC is very important within the system control logic because it describes
instantaneously the storage conditions: it’s possible to evaluate whether it’s
convenient or not to actuate a discharging process or, on the other hand, if a
charging process is needed. The SOC is computed at the end of each time step of
the simulation and it implies the consideration of the whole number of nodes
contained in the nodal mesh. For each one, the node enthalpy ℎ𝑆𝑇,𝑖 has been
evaluated and then a summation of all the enthalpies values has been performed;
the result of this summation has then been divided for the nodes number so that
to obtain the average PCM unit enthalpy. The average PCM enthalpy ℎ̅𝑆𝑇 is then
compared with two particular enthalpies: ℎ𝑠𝑜𝑙 and ℎ𝑙𝑖𝑞; ℎ𝑠𝑜𝑙 represents the
enthalpy of the PCM, where the phase change phenomenon begins. In this
condition all the material within the node considered, is in solid state. On the
other hand, ℎ𝑙𝑖𝑞 represents the enthalpy of the PCM where the phase change
phenomenon is definitely over. In this condition all the material contained in the
node is in liquid state. The difference between these two enthalpies represents
the latent heat of melting.
The SOC has the defined according to equation (3.12)
𝑆𝑂𝐶 =ℎ̅𝑆𝑇 − ℎ𝑠𝑜𝑙
ℎ𝑙𝑖𝑞 − ℎ𝑠𝑜𝑙⋅ 100 [%]
(3.12)
In this way the SOC assumes negative values whenever the average PCM
temperature is lower than the phase change temperature and all the PCM unit is
in solid state. On the other hand, it assumes values larger than 100% whenever
the average PCM temperature is larger than the phase change temperature and
all the PCM unit is in liquid state.
The SOC is a theoretical tool used during the simulation, able to provide very
useful information about the storage conditions.
Fig 3.6 shows a typical SOC trend during the first two hours of the simulation,
where it’s possible to notice how, during the PCM unit discharging process,
which begins approximately at 8:05 AM, the SOC drastically decreases until
reaching negative values.
69
Figure 3.6: Typical SOC trend
3.3.2 System configurations
As briefly introduced in the section 3.2, depending on the load required by the
user, and depending on the SOC of the storage unit, the system could face
different configurations. In order to simplify the control strategy, there has been
the needing to introduce two indexes able to describe the current system
configuration.
The first index introduced is 𝑖𝑑𝑥_𝐻𝑋, which indicates whether the heat
exchanger is open or closed. If this component has to provide the thermal energy
needed to satisfy the load required by the user, it has to be open and 𝑖𝑑𝑥_𝐻𝑋 has
to be set equal to 1. In this case the water flux flows from the PCM unit to the
heat exchanger through the activation of the water pump P2. On the other hand,
whether the load has already been satisfied or whether is not required by the
user, the heat exchanger has to be closed and consequently 𝑖𝑑𝑥_𝐻𝑋 has to be set
equal to 0. In this other case the heat exchanger is not facing any water flux.
The second index introduced is 𝑖𝑑𝑥_𝑃𝐶𝑀, which indicates whether the storage
unit is facing a charging process, a discharging process or is simply closed.
When a charging process is occurring 𝑖𝑑𝑥_𝑃𝐶𝑀 is set equal to 1, when a
discharging process is occurring 𝑖𝑑𝑥_𝑃𝐶𝑀 is set equal to -1 and in the end when
the PCM unit is only undergoing thermal losses with the environment and
conduction heat transfer between adjoining nodes, 𝑖𝑑𝑥_𝑃𝐶𝑀 is set equal to 0.
As described in the section 3.2, each of the three configurations makes the PCM
unit face a different inlet water flux. Due to this reason, for each of the three
70
configurations, three different ODE functions have been implemented in the
Matlab code, so that to let the PCM unit face the right water flux inlet
temperature at each second of the simulation.
Corresponding to the PCM unit charging condition (𝑖𝑑𝑥𝑃𝐶𝑀 = 1), the dedicated
ODE function implemented has been called “derivate_charging”. In this
function, as described in the section 2.3, it’s been built a system of differential
equations for each node of the storage, in which the inlet water flux temperature
at the first node corresponds to the outlet water flux temperature of the ASHP.
On the other hand, the outlet water flux temperature of the PCM unit
corresponds to the inlet water flux temperature of the ASHP.
Whenever the PCM unit is facing a discharging process (𝑖𝑑𝑥𝑃𝐶𝑀 = −1), the
dedicated ODE function implemented has been called “derivate_discharging”.
In this function the same differential equations system has been built, however,
in this case, the inlet water flux temperature at the first node of the PCM unit
corresponds to the outlet water flux temperature of the heat exchanger and the
outlet water flux temperature of the PCM unit corresponds to the inlet water flux
temperature of the heat exchanger.
The last possible configuration regarding the PCM unit refers to the situation in
which there’s no needing to further recharge the storage, due to a sufficient
SOC, and there’s also no needing to provide thermal energy to the user. In this
case the PCM unit is closed (𝑖𝑑𝑥𝑃𝐶𝑀 = 0). The dedicated ODE function for this
configuration has been called “derivate_STOP_PCM” in which the overall heat
transfer coefficient between the heat carrier fluid and the PCM has been set
equal to zero, so that the only temperature variation regarding the PCM storage
nodes is due to the thermal losses with the environment and the heat transferred
by conduction between adjoining storage nodes. These last two phenomena
depend respectively on the heat fluxes �̇�𝑙𝑜𝑠𝑠 and �̇�𝑐𝑜𝑛𝑑 , previously described in
detail in the section 2.3.
Fig 3.7 shows a typical trend of the two indexes discussed above during the first
3 hours of the simulations, from 7 AM to 10 AM.
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Figure 3.7: Typical trend of 𝑖𝑑𝑥_𝐻𝑋 and 𝑖𝑑𝑥_𝑃𝐶𝑀
3.3.3 Daily control logic
The overall system simulation lasts 24 hours starting from 7 AM, however in
this section it’s described the strategy adopted to achieve the simulation goal,
during the first 15 hours of the simulation (from 7 AM to 10 PM), which is the
time interval described in detail by the European regulations UNI EN 16147
[27].
The daily simulation is further divided in 𝑁 time-step, where the time-step
length is defined according to equations (3.13)
𝑡𝑆𝑇𝐸𝑃_𝑙𝑒𝑛𝑔𝑡ℎ =𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛_ℎ𝑜𝑢𝑟𝑠 ⋅ 3600
𝑁
(3.13)
Where 𝑡𝑆𝑇𝐸𝑃_𝑙𝑒𝑛𝑔𝑡ℎ is expressed in second and 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛_ℎ𝑜𝑢𝑟𝑠, as discussed
above, is set equal to 24.
Usually 𝑁 is set equal to 14400, so that 𝑡𝑆𝑇𝐸𝑃_𝑙𝑒𝑛𝑔𝑡ℎ = 6 𝑠.
𝑡𝑆𝑇𝐸𝑃_𝑙𝑒𝑛𝑔𝑡ℎ is very important because, during the time described by this
quantity, the system control logic doesn’t change, and moreover at the end of
this time, a control on the overall system condition is performed so that to
decide whether it’s appropriate to change configuration or to let it unchanged. If
for example, assuming 𝑡𝑆𝑇𝐸𝑃_𝑙𝑒𝑛𝑔𝑡ℎ = 6 𝑠 , the first control occurs after 6 𝑠 from
the beginning of the simulation, the second control occurs after 12 𝑠 from the
beginning of the simulation, and so on.
72
At the initial time of the simulation (7:00 AM), the PCM unit is supposed to
hold a SOC slightly above 100 %, obtained by activating a charging process
during the night, as better explained in the section 3.3.3. Moreover, it’s been
supposed that, at the beginning of each daily time interval defined by the
European regulations UNI EN 16147 [27], the user requires DHW thermal
energy, so that the heat exchanger has to be open and consequently (𝑖𝑑𝑥𝐻𝑋 = 1).
During the whole simulation time it’s been adopted the condition in which, if
the heat exchanger is open, the only way to provide useful thermal energy, is to
activate the discharging process of the PCM storage unit, by switching on the
water pump P2 (𝑖𝑑𝑥𝑃𝐶𝑀 = −1). The only missing initial condition, regarding
the system initial configuration, to define is actually the PCM inlet water flux
temperature, which is guessed at 35 °C.
All the other parameters to define, such as the outside air temperature 𝑇𝑎𝑖𝑟, or
the physical structure of the PCM unit (number of columns, number of rows,
number of levels, tube length), and so on, are further treated in the parametric
analysis, in the section 3.5.
The following table 3.2 sums up the system initial conditions at the initial time
of the simulation.
Table 3.2: Initial conditions at time 0
𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 0
𝑖𝑑𝑥_𝐻𝑋 1
𝑖𝑑𝑥_𝑃𝐶𝑀 -1
𝑆𝑂𝐶 111 %
𝑇𝑤,𝑖𝑛𝑙𝑒𝑡,𝑃𝐶𝑀 35 °C
At the end of each time-step, in order to assess the proper system configuration
to adopt for the next time-step, different quantities are evaluated. The first
quantity to be evaluated is the cumulated thermal energy provided in the time-
step taken into account. This quantity comes directly from the energy counter, as
described at the beginning of the section 3.3. The most important decision to
take, at this point of the simulation, is the value assigned to 𝑖𝑑𝑥𝐻𝑋 . Indeed, the
only possibility that allows the heat exchanger to be closed in the next time-step
(𝑖𝑑𝑥𝐻𝑋 = 0), is that, as discussed above, the load required by the user has
already been satisfied, otherwise the heat exchanger remains open (𝑖𝑑𝑥𝐻𝑋 = 1).
Fig 3.8 shows how the cumulative energy always overcomes the energy required
by the European regulations UNI EN 16147, before the end of each time
73
interval. The red line simply represents the energy value which has to be
achieved until the end of each time interval, so that to assume the load satisfied.
Figure 3.8: Energy trend during the initial 2 hours
Once the value to be assigned to 𝑖𝑑𝑥𝐻𝑋 has been decided, a value must be
assigned to 𝑖𝑑𝑥_𝑃𝐶𝑀 too.
Whether the heat exchanger of the next time-step is open (𝑖𝑑𝑥𝐻𝑋 = 1), the PCM
unit has to provide as much energy as possible in order to satisfy the load. In this
condition the SOC hasn’t been taken into account because, whatever will be the
SOC, the energy stored in the system must be transferred to the heat exchanger,
so 𝑖𝑑𝑥_𝑃𝐶𝑀 is set equal to -1.
On the other hand, whether the heat exchanger of the next time-step is closed
(𝑖𝑑𝑥𝐻𝑋 = 0), two configurations are possible. If the SOC at the end of the time-
step is larger or equal than 100%, there’s no needing to further recharge the
PCM unit, so that 𝑖𝑑𝑥_𝑃𝐶𝑀 is set equal to 0. If the PCM unit has consistently
discharged until it reaches a SOC lower than 𝑆𝑂𝐶_𝑚𝑖𝑛, there’s the urgent
needing to recharge it, otherwise it cannot be ready to provide the thermal
energy required, whenever 𝑖𝑑𝑥𝐻𝑋 will turn to 1. 𝑆𝑂𝐶_𝑚𝑖𝑛 is a value prefixed at
the beginning of the simulation, as discussed in section 3.5. It’s clear that in this
particular condition 𝑖𝑑𝑥_𝑃𝐶𝑀 is set equal to 1.
The choice of 𝑆𝑂𝐶_𝑚𝑖𝑛 is crucial to guarantee that the ASHP is switched on
only when strictly needed and that the PCM unit has achieved a sufficient level
of charge to face the loads of the next time-steps.
74
In fig 3.9 is shown how, when the heat exchanger is closed, the PCM unit ends
up the charging process, only when the SOC reach the 100 %. Moreover, it’s
possible to figure out how, at 8:05 AM, the heat exchanger has been switched on
and consequently the PCM unit has been started the discharging process. This
procedure occurs because at that time, a new interval, defined by the European
regulations UNI EN 16147, begins. Starting from 8:05 AM it’s possible to
appreciate how the SOC drastically decrease due to a consistent load required by
the user.
Figure 3.9: End of the charging process and beginning of the discharging
process
3.3.4 Night control logic
The night control logic is the control strategy which cover the timespan between
10 PM and the beginning of the new simulation (7 AM). The main goal of this
kind of strategy is to guarantee that, the initial system conditions are sufficiently
good to meet all the loads required during the day. In particular, the night
control logic, focus its attention to recharge the PCM unit in order to assure that
at the beginning of the new simulation, the SOC is around 110 %. This value has
been chosen as a convention during all the simulation and it represents a
condition in which all the PCM unit is in liquid state and its average temperature
settles around 65 °C.
The most important antagonist factor in reaching this achievement is, as
previously discussed, the heat transfer between the PCM unit and the
environment, where the environment temperature 𝑇𝑎𝑚𝑏 has always been set
equal to 25 °C. Indeed, during the night, no load is required by the user and then
75
𝑖𝑑𝑥𝐻𝑋 = 0 for the whole night period. For this reason, the PCM unit is supposed
to be switched OFF (𝑖𝑑𝑥𝑃𝐶𝑀 = 0) for the longest period of time. In order to
overcome the problem related to the thermal losses the following strategy has
been developed.
Immediately after the end of the daily period, the PCM unit is kept closed
(𝑖𝑑𝑥𝑃𝐶𝑀 = 0) until one hour before the beginning of a new daily simulation (6
AM). In this way, in the period between 22 PM and 6 AM, the PCM unit is
affected by the thermal losses with the environment and then the 𝑆𝑂𝐶 gradually
decreases. The charging process of the PCM unit begins exactly at 6 AM, so that
the 𝑆𝑂𝐶 starts to increase. This process is stopped only if the 𝑆𝑂𝐶 overcomes a
pre-fixed value called 𝑆𝑂𝐶𝑚𝑎𝑥,𝑛𝑖𝑔ℎ𝑡. In this way, either the ASHP consumption
or the water pump P1 consumption are limited and a sufficient 𝑆𝑂𝐶 value is
guaranteed at the beginning of a new daily simulation (7 AM).
Fig 3.10 shows how the SOC gradually decreases from the beginning of the
night period (10 PM) to 6 AM. Starting from 6 AM it sharply increases until it
reaches the value desired, slightly before the beginning of the new simulation.
Figure 3.10: SOC trend during the night
3.4 Components sizing
Section 3.4 is entirely dedicated to the sizing of each component of the system.
In chapter 2 the PCM battery model is described in detail and in this section, it is
possible to see how its flexibility has been exploited during the simulations.
Indeed, as previously discussed, the number of columns, rows and levels of the
76
battery are some of input parameters of the model. Simulation can be performed
varying for example the number of total nodes or keeping fixed them but
varying the number of levels and rows and consequently dividing equally the
entire mass flow rate among each level in case of parallel configuration. Despite
it’s allowed to consider also the series configuration, making flow the entire
mass flow rate in each level, it’ s not been performed any simulations with this
arrangement due to problems related to the simulation time which are too long.
These are only some of the innumerable configurations that are possible to deal
with during the simulations and this is one of the main strengths of the PCM
battery model.
Turning to the heat pump, as explained in the chapter 3.2, it has been considered
a steady state model, except for the initial 10 minutes of operation whenever it’s
switched on, during which a transient behaviour has been simulated. In order to
get closer as much as possible to the reality, a real technical datasheet of a high
temperature ASHP has been taken from the website of “Daikin” [29]. In
particular the model “Daikin Altherma Split alta temperatura” has been chosen.
The table 3.3 represents the ASHP nominal capacity.
Table 3.3: Nominal capacity table [29]
77
This table represents the heating capacity (HC) and the power absorbed (PI) as a
function respectively, of the air temperature 𝑇𝑎 and the outlet water temperature
(LW), at nominal conditions.
EW represents the inlet water temperature and ΔT is the maximum increment of
temperature for each column. Obviously, these table fits only for specific air
temperatures. Due to this fact, in the model it has been implemented a function
which allows to extract the heating capacity and the power absorbed
proportionally to table values for a range of temperatures that goes from -20 °C
to 15 °C, so that to ensure a set of temperature large enough to perform different
simulations for various locations and seasons. This function has been built by
performing a linear interpolation of the data taken from table 3.3. As explained
before, in the first 10 minutes after each switching on, the maximum ΔT is not
reached and so the transient model comes in. In table 3.3 it’s been reported the
capacity for three distinct types of ASHP which differ for their maximum
heating capacity: from the top to the bottom 11 𝑘𝑊, 14 𝑘𝑊 and 16 𝑘𝑊. Since
the size of the modelled system is limited, only the 11 𝑘𝑊 and the 14 𝑘𝑊 ones
can be simulated, however ensuring a good flexibility also for the ASHP model.
The last consideration about the ASHP concerns the mass flow rate flowing in
the heat pump: in the model it is kept constant in each time interval of an entire
simulation, but it can vary depending on the size of the ASHP and on the
maximum ΔT chosen. Then, these last two parameters are set as inputs of the
model and depending on the value that they assume, the mass flow rate is
consequently fixed. As a matter of fact, the manufacturer provides an additional
table 3.4 that specifies the mass flow rate according to the value of maximum
ΔT and the size of the ASPH.
Table 3.4: ASPH mass flow rate table
Since the mass flow rate of the heat pump is the same of the PCM battery during
the charging process and the 𝛥𝑇 = 5°𝐶 case implies a mass flow rate too high
78
for the PCM storage, 𝛥𝑇 = 5°𝐶 has been discarded upon the possible
configurations and only the cases of 𝛥𝑇 = 10°𝐶 and 𝛥𝑇 = 15°𝐶 have been
implemented. Even this last choice contributes to increase the level of flexibility
of the model.
Another component described in this section is the plate heat exchanger that
allows the heat transfer between the heat mass flow rate coming from the PCM
battery and the water flux coming from the cold supply, on the user side. In
chapter 3.2 a brief explanation of the operating principle and physical structure
is reported and below the sizing procedure is illustrated.
In order to simulate a realistic heat exchanger, data from a real technical
datasheet have been consulted: in figure 3.11 and 3.12 is reported a scheme of
the overall and technical dimensions features of a plate heat exchanger,
engineered by “Pacetti” company. The specific model is called PK 80 [30].
Figure 3.11: Overall dimensions of PK 80
Figure 3.12: Technical dimensions of PK 80
79
As it possible to understand upon the upper part of fig. 3.12, PK 80 is a plate
heat exchanger with cross flows: it means that the primary fluid coming from
the PCM storage goes from top-left to down-right and vice versa the secondary
fluid coming from the water supply goes from down-left to top-right.
In order to compute the heat transfer between the fluids the ε-NTU method has
been chosen.
Introducing the theoretical maximum exchangeable heat, according to equation
(3.14), it’s possible to define the effectiveness of the heat exchanger as the ratio
between the real heat exchanged and the theoretical maximum exchangeable
heat (3.15).
�̇�𝑚𝑎𝑥 = 𝐶𝑚𝑖𝑛 ⋅ 𝛥𝑇𝑚𝑎𝑥 (3.14)
휀 =�̇�
�̇�𝑚𝑎𝑥
(3.15)
Where 𝐶𝑚𝑖𝑛 is the minimum thermal capacity between primary and secondary
fluid. The thermal capacity is computed according to equation (3.16).
𝐶 = �̇�𝑤 ⋅ 𝑐𝑝,𝑤 (3.16)
𝛥𝑇𝑚𝑎𝑥 is the maximum temperature difference inside the heat exchanger and it’s
computed as the difference between the inlet temperature of the primary fluid,
that can vary in time according to the thermal battery conditions, and the inlet
temperature of the water supply that is kept fixed at 10 °C, according to equation
(3.17).
𝛥𝑇𝑚𝑎𝑥 = 𝑇𝑖𝑛,𝑝𝑟𝑖𝑚𝑎𝑟𝑦 − 𝑇𝑖𝑛,𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 (3.17)
The effectiveness is a function of NTU (Number of Thermal Units) and the ratio
between the minimum and maximum thermal capacity is defined as 𝐶𝑟,
according to equation (3.19).
휀 = (𝑁𝑇𝑈, 𝐶𝑟) (3.18)
𝐶𝑟 =𝐶𝑚𝑖𝑛
𝐶𝑚𝑎𝑥
(3.19)
where NTU is defined according to equation (3.20).
𝑁𝑇𝑈 =𝑈ℎ𝑥𝐴
𝐶𝑚𝑖𝑛
(3.20)
80
Where 𝑈ℎ𝑥 is the overall heat transfer coefficient of the heat exchanger, whereas
𝐴 is the total exchange surface.
Equation (3.21) can be explicited for counter current fluxes, like the heat
exchanger simulated in the model, according to equation (3.21).
휀 =1 − exp [−𝑁𝑇𝑈 ⋅ (1 − 𝐶𝑟)]
1 − 𝐶𝑟 ⋅ exp [−𝑁𝑇𝑈 ⋅ (1 − 𝐶𝑟)]
(3.21)
In case of balanced flows, the equation used is the following one.
휀 =𝑁𝑇𝑈
1 + 𝑁𝑇𝑈
(3.22)
Looking at the previous equations, the only variables, that hasn’t been so far
defined, are the overall heat transfer coefficient 𝑈ℎ𝑥 and the total area A. In
order to understand the computation of these two elements, it’s useful to focus
on fig. 3.11. By definition, the overall heat transfer coefficient is the inverse of
the sum of the all heat transfer resistances.
In this work, two convective resistance and one conductive resistance have been
considered so that the final equation is illustrated in equation (3.23).
1
𝑈ℎ𝑥=
1
𝑎𝑝𝑟𝑖𝑚𝑎𝑟𝑦+
𝑠𝑝
𝜆𝑝+
1
𝑎𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦
(3.23)
𝑎𝑝𝑟𝑖𝑚𝑎𝑟𝑦 and 𝑎𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 are respectively the convective heat transfer coefficient
of primary and secondary fluxes. Both can be derived by the Nusselt number
which is defined by equation (3.24).
𝑁𝑢 =𝑎 ⋅ 𝑑ℎ
𝜆𝑤
(3.24)
𝑑ℎ is the hydraulic diameter and it is computed according to equation (3.25).
𝑑ℎ =4𝐴𝑤𝑒𝑡
𝑃𝑤𝑒𝑡
(3.25)
Looking at fig 3.13, it’ s possible to better understand the computation of 𝐴𝑤𝑒𝑡
and 𝑃𝑤𝑒𝑡.
81
Figure 3.13: Plate parameters
The channel flow area is computed according to equation (3.26).
𝐴𝑤𝑒𝑡 = 𝑏 ⋅ w (3.26)
The channel flow perimeter is computed according to equation (3.27).
𝑃𝑤𝑒𝑡 = 2 ⋅ (𝑏 + 𝛷 ⋅ 𝑤) (3.27)
Where Φ is the ratio of the developed length and the protracted length.
Nusselt number has been computed with a correlation taken from [31],
according to equation (3.28).
𝑁𝑢 = (𝑁𝑢𝑙3 + 𝑁𝑢𝑡
3)13 ⋅ 𝑃𝑟
13 ⋅ (
𝜇
𝜇𝑤)
0.17
(3.28)
Where μ is the dynamic viscosity of the considered fluid, whereas 𝜇𝑤 is the
dynamic viscosity of water. In this case, the ratio (𝜇
𝜇𝑤) is equal to 1.
82
In the following equations all the steps useful to compute 𝑁𝑢 are shown:
𝑁𝑢𝑙 = 3.65 ⋅ 𝛽−0.455 ⋅ 𝛷0.661 ⋅ 𝑅𝑒0.339
(3.29)
𝑁𝑢𝑡 = 12.6 ⋅ 𝛽−1.142 ⋅ 𝛷1−𝑚 ⋅ 𝑅𝑒𝑚
(3.30)
𝑚 = 0.646 + 0.0011 ⋅ β (3.31)
𝑓 = (𝑓𝑙3 + 𝑓𝑡
3)13
(3.32)
𝑓𝑙 = 1774 ⋅ 𝛽−1.026 ⋅ 𝛷2 ⋅ 𝑅𝑒−1 (3.33)
𝑓𝑡 = 46.6 ⋅ 𝛽−1.08 ⋅ 𝛷1+𝑝 ⋅ 𝑅𝑒−𝑝 (3.34)
𝑝 = 0.00423 ⋅ β + 0.0000223 ⋅ 𝛽2 (3.35)
Reynolds number is computed by using equation (3.35).
𝑅𝑒 =𝜌 ⋅ 𝑣 ⋅ 𝑑ℎ
𝜇
(3.36)
Prandtl number is computed with equation (3.36)
𝑃𝑟 =𝜇 ⋅ 𝑐𝑝,𝑤
𝜆𝑤
(3.37)
This procedure has been implemented in order to compute the real heat transfer
to the load side and consequently the temperature crossing the heat exchanger
for each time step of the simulation.
The final consideration concerns the total exchange area 𝐴: it depends strictly on
the area of a single plate, but also by the number of plates assembled together, as
it’s possible to see upon equation (3.38).
𝐴 = 𝐴𝑝 ⋅ 𝑁𝑝 (3.38)
Increasing the number of plates, the effectiveness of the heat exchanger and
consequently the heat transfer rate increases. Moreover, 𝑁𝑝 is the only
parameter of the plate heat exchanger that can vary on each simulation,
guarantying a bit of flexibility also for this element. On the other hand,
increasing too much this number does not make any sense since the
83
effectiveness reaches values close to 1 and it would mean to simulate an ideal
heat exchanger. For this reason, during simulations the maximum number of
plates considered has been equal to 10.
Finally, a brief discussion about the pressure drops inside the circuit and
consequently about the choice of the circulating water pumps P1 and P2 has
been reported.
Pressure drops have been computed as the sum of concentrated and distributed
losses, computed respectively according to equation (3.39) and (3.40).
𝛥𝑃𝑐𝑜𝑛𝑐 = 𝛽 ⋅ 𝜌𝑤 ⋅𝑣2
2
(3.39)
𝛥𝑃𝑑𝑖𝑠𝑡𝑟 = 𝜉 ⋅ 𝜌𝑤 ⋅ 𝑙 ⋅𝑣2
2 ⋅ (𝑑 − 2 ⋅ 𝑑𝑤)
(3.40)
where 𝛽 is the concentrated pressure losses coefficient, taken from table 3.5.
Table 3.5: Concentrated pressure losses coefficient
84
𝜉 represents the distributed pressure losses coefficient taken from the Moody
Chart.
Then, a pressure drop value within the plate heat exchanger has been taken from
[30] and consequently summed up to the P2 circuit overall pressure losses.
Once added up the pressure losses inside the both circuits, it has been possible to
choose the P1 and P2 from a catalogue of the “Biral” company [31].
In figure 3.14 and 3.15 the characteristic curves, respectively for the selected
pump P1 and P2, have been reported and the operating point have been
highlighted with a red circle.
Figure 3.14: Characteristic curve of P1
Figure 3.15: Characteristic curve of P2
85
As explained in chapter 3.5, the circulating pump P1 works with a fixed volume
flow rate given by the technical datasheet of the heat pump and for this reason
the red circle in figure 3.14 covers a very small working region.
In figure 3.16 the working region is more extended since the parametric analyses
have been conducted with different mass flow rate in the circulating pump P2
circuit.
The power absorbed by the circulating pumps has been calculated with equation
(3.41).
�̇�𝑝𝑢𝑚𝑝 =�̇� ⋅ 𝛥𝑃
𝜌𝑤 ⋅ 𝜂𝑝𝑢𝑚𝑝
(3.41)
3.5 Parametric analysis
So far, any particular feature of the components has been described, however
it’s not been studied yet the best way to combine them in order to satisfy the
load. As largely discussed above, the DHW system disposes of very different
parameters so that, by varying them, its behaviour during the 24 hours of
simulation gradually changes.
In this section, an analysis has been performed in order to find out the smallest
size of the PCM unit able to guarantee the load, depending on different
parameters such as the ASHP size, the ASHP circulating water mass flow rate
and the 𝑆𝑂𝐶𝑚𝑖𝑛. The PCM size corresponds to the number of the nodes forming
the nodal mesh and the first task of this analysis is to define a range of this
value, which allows the system to respect the load.
Once the minimum PCM size has been identified, the next two parameters to
choose, have been respectively the outside air temperature 𝑇𝑎𝑖𝑟 and the 𝑆𝑂𝐶𝑚𝑖𝑛.
The choice of this latter parameter has been deeply investigated because it
determines either the charging strategy of the PCM unit or the ASHP
consumption. In the performed analyses, a value of 𝑆𝑂𝐶𝑚𝑖𝑛 equal to 80 % have
been adopted because it allows to maintain a good SOC, without switching on
too many times the ASHP. On the other hand, for what concerns the outside air
temperature 𝑇𝑎𝑖𝑟 , three different values have been chosen, which are -7 °C, 7 °C
and 10 °C. As it’s possible to figure out from equation (3.40), a low outside air
temperature significantly deteriorates the COP. Due to this reason, in order to
contain the ASHP consumption when the outside air temperature is below 0 °C,
𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 has been further investigated. For all the other values of 𝑇𝑎𝑖𝑟, 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃
86
has always been set to 67 °C because it’s a good trade off in recharging easily
the PCM unit and in not deteriorating too much the COP.
Another crucial parameter to choose has been the circulating mass flow rate in
the ASHP, indeed, as it’s possible to appreciate in table 3.4, a lower mass flow
rate allows the ASHP to elaborate a larger ∆T, however the heat transfer
coefficient in the PCM unit decreases due to lower velocities and consequently
lower 𝑅𝑒 numbers. An ASHP water mass flow rate value equal to 15,8 𝑙𝑚𝑖𝑛⁄ has
been considered an excellent trade off and then it’s been adopted. Moreover, it’s
been verified that the 11 𝑘𝑊 ASHP can guarantee the load required by the
tapping cycle L, therefore the 14 𝑘𝑊 ASHP has not been taken in consideration.
In order to compute the performance results of the ASHP, a double interpolation
of the data in table 3.3 has been applied. The Coefficient Of Performance (COP)
has been computed, according to equation (3.39), for five different values of
𝑇𝑎𝑖𝑟 and for four ASHP outlet temperature provided by table 3.3.
𝐶𝑂𝑃 =𝐻𝐶
𝑃𝐼
(3.39)
Where HC represents the heating capacity, whereas PI represents the power
absorbed.
Fig. 3.16 shows the results obtained by applying the 11 𝑘𝑊 ASHP datasheet.
Figure 3.16: COP parametrical trend
y = -0.0226x + 3.7212
y = -0.0254x + 4.069
y = -0.0369x + 5.3762
y = -0.0332x + 4.7437
y = -0.0143x + 2.8196
y = -0.0435x + 6.0575
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 20 40 60 80
CO
P
ASHP outlet temperature [°C]
COP
Tair -2
Tair 2
Tair 7
Tair 3
Tair 5
Tair -15
Tair 12
Linear (Tair -2)
Linear (Tair 2)
Linear (Tair 2)
87
A linear interpolation has been performed for each curve and then another
interpolation has been made on the coefficients of these linear equations, so that
to get as a final result a COP function either of 𝑇𝑎𝑖𝑟 or of the ASHP outlet
temperature, according to equation (3.40), which represents the COP function
for the 11 𝑘𝑊 ASHP.
𝐶𝑂𝑃 = (−0,0011 ⋅ 𝑇𝑎𝑖𝑟 − 0,0277) ⋅ 𝑇𝑜𝑢𝑡,𝐴𝑆𝐻𝑃 + (0,0039 ⋅ 𝑇𝑎𝑖𝑟
2 + 0,136 ⋅ 𝑇𝑎𝑖𝑟 + 3,9657) (3.40)
Since 𝑇𝑎𝑖𝑟 has been fixed, the only parameters which affects the COP during
the simulation is actually 𝑇𝑜𝑢𝑡,𝐴𝑆𝐻𝑃.
The heating capacity provided by the ASHP has been computed according to
equation (3.41).
𝐻𝐶 = �̇�𝑤,𝐴𝑆𝐻𝑃 ⋅ 𝑐𝑝,𝑤 ⋅ (𝑇𝑜𝑢𝑡,𝐴𝑆𝐻𝑃 − 𝑇𝑖𝑛,𝐴𝑆𝐻𝑃) (3.41)
And then the power absorbed is computed as follows:
𝑃𝐼 =𝐻𝐶
𝐶𝑂𝑃
(3.42)
In the end, in order to evaluate the energy provided and absorbed by the ASHP,
equation (3.41) and (3.42) have been integrated during the whole simulation
time to obtain respectively 𝑒𝑛𝑒𝑟𝑔𝑦ℎ𝑒𝑎𝑡𝑖𝑛𝑔 and 𝑒𝑛𝑒𝑟𝑔𝑦𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑.
3.6 Results and discussions
The first step of the parametric analyses, as discussed above, has been the sizing
of the storage unit. The PCM volume has indeed to be sized in order to respect
two important constraints given by the European regulations UNI EN 16147,
which are at first the supply of the thermal load, and then the achievement of a
DHW that is larger or equal the sum between the cold supply water temperature
and the minimum ∆T needed by the user. Moreover, the PCM unit has been
oversized in order to get an average ∆T during the peak of the load which is
2,5°C larger than the one required. Since the water inlet temperature, coming
from the user cold supply, is always equal to 10 °C, according to UNI EN
16147, and the ∆T minimum required during the peak is equal to 30 °C, the goal
of the simulation is to reach an average ∆T equal to 42,5 °C.
Due to compactness and economic constraints, the lowest size has been sought.
88
This analysis has been performed in the first two daily hours because, as it’s
possible to figure out from table 3.1, the most critical condition for the DWH
system falls in the period between 8:05 AM and 8:25 AM, where the energy
required by the user is equal to 3,605 𝑘𝑊ℎ. It’s been verified that if the load is
guaranteed in the initial period (7 AM – 9 AM), the system will be able to
provide the required amount of thermal energy in the whole simulation period.
The sizing analysis has started from a PCM volume equal to 44,2 𝑙, which
corresponds to a total PCM unit volume equal to 55,3 𝑙. This configuration has
been obtained by setting the nodal mesh with 6 rows, 10 columns and 11 levels
and it’s been chosen arbitrarily. Since with this kind of storage volume the load
required is supplied, but the ∆T desired is not reached, bigger sizes have been
investigated, because larger PCM thermal capacity are needed in order to
guarantee larger DHW temperature, always supposing to start the simulation at
7 AM with the same SOC.
Fig 3.17 shows how the DHW temperature increases with larger PCM sizes.
Figure 3.17: DHW trend
As it’s possible to figure out from fig. 3.17, the smallest storage size able to
reach the goal of the simulation is equal to 76 𝑙 , which corresponds to a PCM
volume of 64,28 𝑙 and a nodal mesh configuration of 8 rows, 10 columns and 12
levels.
42.5
39.5
40
40.5
41
41.5
42
42.5
43
43.5
44
50 55 60 65 70 75 80 85 90
Tem
per
atu
re [
°C]
Storage volume [l]
DHW
89
The first configuration analysed shows a higher average DHW temperature with
respect to the next one because its size is so small that the SOC decreases below
the 𝑆𝑂𝐶𝑚𝑖𝑛 , even before the occurrence of the biggest load, whereas in the
second configuration analysed, which has a larger volume than the first one, the
SOC remains above the 𝑆𝑂𝐶𝑚𝑖𝑛 until the worst condition is reached. In this way,
when the first configuration is adopted, the ASHP needs to be switched on even
in the first period of the day so that the SOC is restored to approximately 100 %.
Due to this reason the DHW temperature during the peak slightly increases.
Despite a small DHW increment, which can be considered a good result, the too
low size of the PCM unit doesn’t allow to reach the goal above discussed and
then larger sizes have to be investigated.
Fig. 3.18 and 3.19 show the behaviour just described, where the first figure
shows the SOC trend of the first configuration analysed, in which the too low
PCM size forces the ASHP to switch on before the beginning of the big load,
whereas the second figure shows the SOC trend of the second configuration
analysed, in which the SOC recover occurs entirely after the big load has
provided.
Figure 3.18: SOC trend in the first configuration
90
Figure 3.19: SOC trend in the second configuration
The first lot of simulation has been performed by fixing an outside 𝑇𝑎𝑖𝑟 equal to
7 °C, which is a common value adopted to test this kind of DHW heat pump
systems. While the water mass flow rate elaborated by the ASHP has been fixed
to 15,8 𝑙𝑚𝑖𝑛⁄ , the variation of the water mass flow rate elaborated by the
circulating water pump P2 and used to provide the energy to the user, has been
further investigated. The whole energy absorbed by the DHW system during the
simulations has been analysed, as the electric energy provided to the ASHP and
the one provided to the user.
The summation of the energy required by the user in the tapping cycle L,
according to table 3.1, is equal to 11,665 𝑘𝑊ℎ. During all the simulations
performed, a time-step equal to 6 𝑠 has been used and for this reason, due to a
discretization error, the energy provided to the user, slightly increases up to a
value around 12 𝑘𝑊ℎ. Moreover, since the SOC at the beginning of the
simulation (7AM) and the SOC at the end of the night period (24 hours later) are
almost the same (around 110 %), the 𝑒𝑛𝑒𝑟𝑔𝑦ℎ𝑒𝑎𝑡𝑖𝑛𝑔 provided by the ASHP
must agree with the energy provided to the user, in order to respect the overall
energy balance of the system. It’s been observed that, during all the simulations
performed, the difference between these two energies has never overcomes the
value of 0.3 𝑘𝑊ℎ, corresponding to a maximum error of around 2%. The entity
of this error is related to the fact that the difference between the initial and the
final SOC is not precisely equal to zero, but, since the final SOC is usually
slightly lower than the initial one, it assumes values of around 1%. For this
91
reason, the 𝑒𝑛𝑒𝑟𝑔𝑦ℎ𝑒𝑎𝑡𝑖𝑛𝑔 provided by the ASHP is a little bit lower with
respect to the one provided to the user and the ∆𝑒𝑛𝑒𝑟𝑔𝑦 is due to the slight
variation of the internal energy of the PCM unit, starting from the beginning
until the end of the simulation.
In order to evaluate in a precisely way the energy consumption, an effective
system coefficient of performance has been defined according to equation
(3.43).
𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 =𝐸𝑢𝑠𝑒𝑟
𝐸𝑃1 + 𝐸𝑃2 + 𝐸𝐴𝑆𝐻𝑃
(3.43)
where 𝐸𝑢𝑠𝑒𝑟 has been fixed to 11,665 𝑘𝑊ℎ, whereas 𝐸𝑃1 is the energy
consumption of the circulating water pump P1, 𝐸𝑃2 of the circulating water
pump P2 and 𝐸𝐴𝑆𝐻𝑃 of the Air Source Heat Pump.
Furthermore, an average DHW temperature has been obtained according to
equation (3.44).
�̅�𝐷𝐻𝑊 =∫ 𝑇𝐷𝐻𝑊 𝑑𝑡
𝑡𝑆𝐼𝑀
0
𝑡𝑆𝐼𝑀
(3.44)
where 𝑡𝑆𝐼𝑀 is the whole time of the simulations, equal to 86400 𝑠.
One of the simulations goal is to reach an as larger as possible value of �̅�𝐷𝐻𝑊, so
that the temperature regulation will be easier and more efficient.
Fig. 3.20 shows the opposite trends of the values introduced above with the
increase of the water mass flow rate elaborated by the water pump P2 and called 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 𝑚𝑎𝑠𝑠 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒.
92
Figure 3.20: Domestic Hot Water trend vs. system Coefficient Of Performance
(𝑇𝑎𝑖𝑟 = 7 °𝐶)
The �̅�𝐷𝐻𝑊 increasing trend is obtained due to an increasing water mass flow rate
circulating in the PCM unit during the discharging process, and consequently
higher 𝑅𝑒 numbers and higher heat transfer rates on the water side. Moreover,
the 휀 of the heat exchanger increases with larger discharging mass flow rate, so
that it allows to reach higher temperatures. On the other hand, the decreasing
trend of 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 is induced by an increasing energy consumption of the water
pump P2, due to higher pressure losses on this side of the water circuit.
Fixing the increase scale of the �̅�𝐷𝐻𝑊 at 0,5 °C and the decrease scale of the
𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 at 0,01, it’s possible to find a value of the discharging mass flow rate
which allows to balance these two opposite effects and provides a good trade-off
solution to maximize the two indexes. The optimal discharging mass flow rate
corresponds to the intersection of the two curves and in this case its value is
around 18 𝑙 𝑚𝑖𝑛⁄ .
The same lot of simulations have been performed even with 𝑇𝑎𝑖𝑟 equal to 10 °C
and -7 °C. Even in these two analyses the same trend can be appreciated,
however the most important difference in the three cases is the value of
𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 which drastically decreases when 𝑇𝑎𝑖𝑟 is equal to -7 °C.
47.95
48.45
48.95
49.45
49.95
50.45
50.95
51.45
51.95
52.45
52.95
2.47
2.48
2.49
2.50
2.51
2.52
2.53
2.54
2.55
2.56
2.57
10 13 15 18 20 25
Tem
per
atu
re [
°C]
𝐶𝑂𝑃
_𝑠𝑦𝑠𝑡𝑒𝑚
Discharging mass flow rate [l/min]
DHW vs. 𝐶𝑂𝑃_𝑠𝑦𝑠𝑡𝑒𝑚
COP_system T_DHW_avg
93
Fig. 3.21 shows the results obtained with 𝑇𝑎𝑖𝑟 equal to 10 °C, whereas fig. 3.22
shows the results obtained with 𝑇𝑎𝑖𝑟 equal to -7 °C.
Figure 3.21: Domestic Hot Water trend vs. system Coefficient Of Performance
(𝑇𝑎𝑖𝑟 = 10 °𝐶)
Figure 3.22: Domestic Hot Water trend vs. system Coefficient Of Performance
(𝑇𝑎𝑖𝑟 = −7 °𝐶)
47.95
48.95
49.95
50.95
51.95
52.95
53.95
54.95
2.782.792.802.812.822.832.842.852.862.872.882.892.902.912.922.93
10 13 15 18 20 25
Tem
per
atu
re [
°C]
𝐶𝑂𝑃
_𝑠𝑦𝑠𝑡𝑒𝑚
Discharging water mass flow rate [l/min]
DHW vs. 𝐶𝑂𝑃_𝑠𝑦𝑠𝑡𝑒𝑚
COP_system T_DHW_avg
47.95
48.45
48.95
49.45
49.95
50.45
50.95
51.45
51.95
52.45
52.95
1.68
1.69
1.70
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
10 13 15 18 20 25
Tem
per
atu
re [
°C]
𝐶𝑂𝑃
_𝑠𝑦𝑠𝑡𝑒𝑚
Discharging water mass flow rate [l/min]
DHW vs. 𝐶𝑂𝑃_𝑠𝑦𝑠𝑡𝑒𝑚
COP_system T_DHW_avg
94
Despite a good average 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚, the simulations performed with 𝑇𝑎𝑖𝑟 equal to
10 °C shows a severe deterioration trend with larger discharging mass flow rate.
For this reason, the optimal value of the mass flow rate shifts toward larger
value and it’s identified around 21 𝑙 𝑚𝑖𝑛⁄ .
For what concerns the simulations performed with 𝑇𝑎𝑖𝑟 equal to -7 °C, despite a
very low average value of 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚, it shows a less steep decreasing trend and
the optimal water mass flow rate has been identified around 20 𝑙𝑚𝑖𝑛⁄ .
Fig. 3.23 shows the 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 deterioration with decreasing 𝑇𝑎𝑖𝑟.
Figure 3.23: 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 degradation
Since the ASHP COP depends on its outlet water temperature, and since a bad
ASHP COP affects the 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚, an analysis on the 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 has been
performed, so that to limit the DHW system consumption, when critical outside
air temperature conditions occur.
A further lot of simulations has then been made by adopting 𝑇𝑎𝑖𝑟 equal to -7 °C,
a discharging mass flow rate equal to 15 𝑙 𝑚𝑖𝑛⁄ , and five different 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 ,
respectively equal to 61 °C, 63 °C, 65 °C, 67 °C and 69 °C.
1.50
1.70
1.90
2.10
2.30
2.50
2.70
2.90
9 14 19 24
𝐶𝑂𝑃
_𝑠𝑦𝑠𝑡𝑒𝑚
Discharging mass flow rate [l/min]
𝐶𝑂𝑃_𝑠𝑦𝑠𝑡𝑒𝑚
Tair -7°C Tair 7°C Tair 10°C
95
Fig. 3.24 shows the 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 trend with an increasing 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃.
Figure 3.24: 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 trend
As it’s possible to appreciate from fig. 3.24, a value of 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 which
maximize the 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 has been identified and it’s around 65 °C. The reason
why a further decrease of 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 induces a decrease of the 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 is due
to the fact that the ASHP COP is more affected by the partial load condition
degradation, as discussed in section 3.2. For this reason, the optimal 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃
guarantees a trade-off between the increase of the COP in nominal condition
and the decrease of the COP due to the partial load, with a decreasing 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 . Moreover, a decrease of 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 induces a light increase of the charging time
of the PCM unit and then larger consumption of the circulating water pump P1,
for this reason, when the outside air temperature maintains values larger than
0 °C, it’s preferable to keep 𝑇𝑠𝑒𝑡,𝐴𝑆𝐻𝑃 equal to 67 °C, since the 𝐶𝑂𝑃𝑠𝑦𝑠𝑡𝑒𝑚 does
not fall below critical values.
1.7
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.8
1.81
60 61 62 63 64 65 66 67 68 69 70
𝐶𝑂𝑃
_𝑠𝑦𝑠𝑡𝑒𝑚
ASHP set temperature [°C]
𝐶𝑂𝑃_𝑠𝑦𝑠𝑡𝑒𝑚
96
97
Chapter 4
Conclusions
The study of PCMs and its applications are topics deeply discussed in literature,
however its employment inside a finned tube heat exchanger as thermal storage
has been treated in very few papers.
The starting point of this thesis has been the construction of a thermal energy
storage transient model starting from the study of a previous model called Type
841, that is not actually available. A final validation of the model against it and
the experimental measures collected by the authors of Type 841 has been
presented.
After this step, it has been possible to establish the goodness of the thesis model,
even if some differences appear. For this reason, it could be a good starting
point for students interested in studying very detailed features of a latent thermal
storage, indeed as previously discussed the model leaves room for improvement,
such as the subcooling process modelling or the heat transfer phenomena among
external casing, PCM, fins and tube materials.
The second part of the thesis work has concerned the creation of a model which
could reproduce a DHW system, integrated with the PCM storage battery and
simulated in the previous part of this work. The DHW system comprises
different elements, including a plate heat exchanger, two circulating pumps and
finally a high temperature heat pump, that has been the most critical element to
model besides the PCM thermal battery. Its transient behaviour has been
simulated roughly, introducing a time interval after each switching on, in which
the heat pump is not able to work at nominal conditions but only at partial load.
As well, a degradation model due to issues related to ON-OFF cycles, has been
adopted so that to get closer to a real behaviour of a heat pump.
These are the most important aspects that could be improved in future works.
In table 3.6 are listed the most important results obtained upon the sizing of the
DHW system, and some of the installed equipment specifications.
98
Table 3.6: Sizing results
ASHP size 11 𝑘𝑊
PCM volume 64,28 𝑙 Storage volume 76 𝑙
nr. of tubes in series 8
nr. of parallel tube coils 12
P1 specifications Biral A 15 kW, 8-107 𝑊
P2 specifications Biral A 40-18 250 GREEN, 16-594 𝑊
In table 3.7 are listed the daily system energy consumption for three different
𝑇𝑎𝑖𝑟, by adopting the most efficient configuration.
Table 3.7: System energy consumption
𝑇𝑎𝑖𝑟 -7 °C
discharging mass flow rate [l/min]
10 13 15 18 20 25
system energy
consumption [kWh] 6,549 6,575 6,612 6,644 6,692 6,769
COP system 1,78 1,77 1,76 1,76 1,74 1,72
𝑇𝑎𝑖𝑟 7 °C
discharging mass flow rate [l/min]
10 13 15 18 20 25
system energy
consumption [kWh] 4,534 4,568 4,583 4,608 4,649 4,716
COP system 2,57 2,55 2,55 2,53 2,51 2,47
𝑇𝑎𝑖𝑟 10 °C
discharging mass flow rate [l/min]
10 13 15 18 20 25
system energy
consumption [kWh] 3,981 3,995 4,022 4,056 4,092 4,158
COP system 2,93 2,92 2,90 2,88 2,85 2,81
One of the main interesting application of the model presented, could be its
employment during experimental activities about PCM thermal energy storage.
Since in reality it’s not easy to understand the real State Of Charge of the
thermal battery due to the complications related to the installation of sensors
inside the storage casing, this model can be used as a reliable support in
calculating the SOC. It has to be used intelligently, updating the input values
whenever for example the thermal battery has been charged completely or
99
simply after a precise interval of time. This last operation is necessary to avoid
too much errors, related to the inaccuracies of the model that add up as
simulation time goes on, risking showing results very far from the real final
condition of the thermal battery.
Finally, new parametric analyses could be conducted, introducing for example
bigger tapping cycles and considering also a heat pump of 14 𝑘𝑊.
These are only some suggestions which could be applied to future works about
the topics discussed.
100
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