NTNU Norwegian University of Science and Technology Faculty of Engineering Department of Energy and Process Engineering
Chris-André Bastin LarsenLatent heat thermal energy storage from wood stoves with high-density polyethylene as phase change material
Chris-André Bastin Larsen
Latent heat thermal energy storage from wood stoves with high-density polyethylene as phase change
material
A numerical and experimental study
Master’s thesis in Energy and Environmental Engineering Supervisor: Erling Næss
Co-supervisor: Alexis Sevault June 2021
Master ’s thesis
Chris-André Bastin Larsen
Latent heat thermal energy storage from wood stoves with high-density polyethylene as phase change material
A numerical and experimental study
Master’s thesis in Energy and Environmental Engineering Supervisor: Erling Næss
Co-supervisor: Alexis Sevault June 2021
Norwegian University of Science and Technology Faculty of Engineering
Department of Energy and Process Engineering
Preface
This thesis presents my Master´s thesis for the Department of Energy and Process Engineering at the Norwegian University of Science and Technology (NTNU). Within my thesis I have studied heat transfer within and from a latent heat storage system, and taken a novel concept from numerical analysis and built a physical model for experimental validation.
I would like to express my sincerest gratitude to my supervisors; Professor Erling Næss at NTNU and Reasearch Scientist Alexis Sevault with SINTEF, for thorough guidance and support during my thesis work. Furthermore, thank you to researcher Ragnhild Sæterli with SINTEF for taking the time to help me with DSC measurements. In addition, a huge thanks to Department Engineer Martin Bustadmo for all the helpful advise and ideas, and outstanding craftsmanship in welding the physical model.
This study was supported by the research project IPN PCM-STOVE (321581/E20), supported by the Research Council of Norway and industry partner. IPN PCM-STOVE investigates innovative PCM-based heat storage integrated in wood stoves.
Chris-André Bastin Larsen, Trondheim 2021
Sammendrag
Vedovner har i lang tid vært en viktig kilde til oppvarmning i Norden, men den typiske husstand blir bedre og bedre isolert for å redusere behovet for oppvarming. En vedovn vil vanligvis levere mer varme enn det som er nødvendig for nyere og bedre isolerte hjem. For å effektivt utnytte vedovn som oppvarmingskilde trenger vi dermed løsninger for å redusere den høye varmeavgivelsen fra en vedovn, samt spre den utover et lengre tidsrom.
Latent termisk energilagring er et spennende konsept for midlertidig lagring av termisk energi.
Tradisjonelt sett har varme fra vedovner blitt lagret ved hjelp av kleberstein. Ved å benytte et latent termisk energilager i stedet er det mulig å lagre 5-14 ganger så mye energi per volum.
Hjørnesteinen i et hvert latent termisk energilager er faseendringsmaterialet. Når man skal velge riktig faseendringsmateriale er det flere faktorer å ta hensyn til. En ønsker å lagre så mye energi som mulig. Videre er det viktig at faseendringstemperaturen passer med den termiske prosessen som lageret er tilknyttet slik at en får utnyttet den latente delen best mulig. For et termisk lager tilknyttet en vedovn er det også viktig å vurdere mulige helsefarer ved materialet, ettersom at det skal plasseres innendørs.
Formålet med denne masteroppgaven er å undersøke et nytt konsept for latent varmelagring fra vedovner. Hovedfokuset er rettet mot varmeavgivelsen fra lageret etter endt fyring. Først er det gjennomført et søk etter mulige faseendringsmaterialer. Faseendringsmaterialene ble i hovedsak vurdert etter faseendringstemperatur, latent varmekapasitet og mulige helsefarer. Basert på søket ble polyetylen med høy tetthet (HDPE) valgt som faseendringsmateriale. Videre ble det forsøkt å estimere den latente varmekapasiteten, den spesifikke varmekapasiteten og
faseendringstemperaturen ved hjelp av “Differential Scanning Calorimetry (DSC)”. Og ved hjelp av en “Hot Disk Transient Plane Source (TPS)” analyse ble det forsøkt å bestemme den termiske konduktiviteten til HDPE. En CFD model basert på et latent varmelager ble utviklet, og med realistiske grense- og initialbetingelser ble den testet for ladning og utladning. I modellen ble vertikalt orienterte platefinner i stål benyttet for å forbedre varmeledningen inn og ut. Basert på resultatene fra denne numeriske undersøkelsen ble en fysisk enhet designet og testet i laboratoriet.
Konklusjonene fra denne studien indikerer at HDPE fremstår som et godt faseendringsmateriale for latent varmelagring fra vedovner. De numeriske undersøkelsene indikerte at 3 mm tykke, vertikalt orienterte platefinner i svartstål kunne sikre en tilfredsstillende varmeavgivelse ved utladning av lageret. Fra de eksperimentelle undersøkelsene ble det observert at lokal ekspansjon av HDPE kunne medføre utfordringer der deler av HDPE-en blir presset opp og ut av lageret. Ved bruk av vertikale platefinner er det foreslått at disse må strekke seg fra inner- til yttervegg og dermed dele opp totalvolumet i mindre deler. Videre undersøkelser av utfordringer og løsninger ved lokal ekspansjon er foreslått.
Abstract
Wood stoves have a long history of providing thermal comfort in the Nordic climate. Households are steadily becoming more insulated to reduce their heating demand, while wood stoves typically have a high heat release. The results is that utilizing wood stoves for heating in modern homes gives a mismatch in the heat required and delivered. Therefore new solutions are required to reduce potential overheating.
Latent heat thermal energy storage (LHTES) is an exciting concept for intermediate thermal energy storage. Traditionally, energy from wood-firing has been stored in soapstone or other types of rock. An LHTES can hold 5-14 times the energy per volume compared to a sensible storage.
The cornerstone in an LHTES is the Phase Change Material (PCM). Several important
considerations are needed regarding the choice of PCM, like the ability to store as much energy as possible. Furthermore, a phase change temperature in connection with the thermal process is essential to utilize the latent part of the energy storage. For an application placed in a household, potential health hazards also need to be considered.
The purpose of this thesis was thus to investigate a novel concept of LHTES in wood stoves. The main focus was directed at the heat release period post-combustion. First, a search for a suitable PCM was conducted. Important considerations were melting temperature, latent heat of fusion, and health hazards. High-density polyethylene(HDPE) was the PCM of choice. Attempts at characterizing thermo-physical properties of HDPE were carried out through a Differential Scanning Calorimetry (DSC) analysis and Hot Disk Transient Plane Source (TPS) analysis. These properties were latent heat of fusion, phase change temperature, specific heat capacity, and thermal conductivity. A Computational Fluid Dynamics (CFD) model of the LHTES concept with vertical plate fins as heat transfer enhancement was developed and tested for charging and discharging, with realistic initial and boundary conditions. Based on the numerical model, an experimental test container was designed, and tests were conducted with different degrees of insulation.
Conclusions from this thesis indicate that HDPE appears to be a viable choice as PCM for the LHTES concept on top of a wood stove. Numerical investigations revealed that a vertical arrangement of 3 mm thick steel plates as heat transfer enhancement could ensure satisfactory discharging. From experimental testing, it was observed that local expansion of HDPE could cause issues with overflow, and it is suggested that with a vertical plate fin arrangement, they should extend through the entire volume and thereby separate the volume into smaller parts. It is also recommended to explore other solutions to the issue of local expansion.
Contents
Sammendrag i
Abstract ii
List of Figures vi
List of Tables vii
Nomenclature x
1 Introduction 1
1.1 Objectives . . . 2
1.2 Thesis structure . . . 2
2 Phase change materials 3 2.1 Classification of PCM . . . 3
2.2 Selection criteria . . . 4
2.3 PCMs found in literature . . . 6
2.4 Commercially available PCMs . . . 9
3 Material characterization 10 3.1 HDPE - HD6070EA . . . 10
3.2 Differential Scanning Calorimetry . . . 11
3.2.1 Results from the DSC analysis for the HD6070EA blend of HDPE . . . 13
3.3 Transient Plane Source (TPS) Method . . . 16
3.3.1 Testing at higher temperatures . . . 19
3.3.2 Results from TPS-analysis of HD6070EA . . . 20
3.4 Preliminary melting test of HD6070EA PCM . . . 22
4 Metal foams 23 5 CFD model of LHTES concept 24 5.1 Geometry . . . 25
5.2 Meshing . . . 26
5.3 Auxiliary data . . . 26
5.4 Estimating external heat transfer coefficient . . . 27
5.5 Boundary- and initial conditions for discharging . . . 31
5.6 Boundary- and initial conditions for charging . . . 31
5.7 Results . . . 31
5.7.1 External heat transfer coefficient . . . 31
5.7.2 Simulated heating - semi-insulated . . . 33
5.7.3 Simulated cooling - semi-insualted . . . 34
6 Experimental model of LHTES concept 36
6.1 Development of experimental test unit . . . 36
6.2 Instrumentation of experimental test unit . . . 37
6.3 Laboratory setup . . . 38
6.4 Filling unit with HDPE . . . 39
6.5 Experimental test conditions . . . 41
6.6 Experimental results . . . 43
6.6.1 Experimental heating . . . 43
6.6.2 Experimental cooling . . . 45
6.6.3 Energy stored . . . 46
6.6.4 Determination of the external heat transfer coefficient from experiment . . 48
6.6.5 Comparison between simulation and experiment . . . 49
7 Discussion 50 7.1 Differential Scanning Calorimetry . . . 50
7.1.1 Sample weight, heating rate and crucible . . . 50
7.1.2 Latent heat and melting temperature . . . 51
7.1.3 Specific heat capacity . . . 51
7.2 Hot Disk TPS . . . 52
7.2.1 Test conditions . . . 52
7.2.2 Sample size and homogeneity . . . 53
7.3 CFD results . . . 53
7.3.1 Limitations and assumptions . . . 53
7.3.2 Results . . . 54
7.3.3 Mushy zone constant . . . 55
7.4 Experimental tests . . . 56
7.4.1 Weight and porosity . . . 56
7.4.2 Local expansion during melting of HDPE . . . 56
7.4.3 Oxidation of the HDPE . . . 57
7.4.4 Fin thickness . . . 57
7.4.5 Thermocouples . . . 57
7.4.6 Comparison with previous experiments . . . 58
7.4.7 External heat transfer coefficient . . . 59
7.4.8 Comparison between simulation and experiment . . . 60
8 Conclusion 61
9 Further work 63
Bibliography 64
Appendix A Uncertainty analysis A-1
Appendix B Poster presented at ENERSTOCK2021 B-1
Appendix C Data tables and additional figures C-1 Appendix C.1 Suppliers of phase change materials . . . C-1 Appendix C.2 Datasheet - HD6070EA . . . C-1 Appendix C.3 Hot disk data . . . C-3 Appendix C.4 Preliminary melting test of HD6070EA . . . C-5 Appendix C.5 Specific heat capacity of sapphire . . . C-7 Appendix C.6 Dimensions of test unit . . . C-9 Appendix C.7 Experimental campaign . . . C-11 Appendix C.8 Temperature data . . . C-12
Appendix D MATLAB Code D-2
Appendix D.1 Heat stored . . . D-2 Appendix D.2 Heat transfer coefficient . . . D-4
Appendix E Risk assessment E-1
List of Figures
1 Thermal energy storage methods. . . 4
2 Subdivisions of solid–liquid PCMs. . . 5
3 Thermogram of a typical melting process of a pure substance . . . 11
4 Heat flow measured during the three different steps of the classical three-step method for determining specific heat capacity. . . 14
5 Heat flow to HDPE sample with fitted straight line between the two sensible zones before and after the peak, with fitted tangent on the left foot. Tonset is found as the crossing between the two fitted lines, and is here found to be 124.2◦C. . . 15
6 Calculated specific heat capacity for HDPE based on Equation 3.4 and specific heat capacity for the reference material sapphire, based upon literature values that can be found tabulated in the appendix. . . 15
7 Samples prepared for testing with the Hot Disk TPS 2500s. . . 17
8 Setup of samples with Hot Disk sensor. . . 19
9 Sample and sensor arrangement for testing at elevated temperatures in silicone bath. 20 10 Thermal conductivity measurements with standard deviation. . . 21
11 Volumetric heat capacity with standard deviation. . . 21
12 Test unit developed by SINTEF. . . 24
13 Geometry used in ANSYS simulation and surface mesh of given geometry. . . 25
14 Volume meshing from ANSYS Fluent 2020 R2, with a more detailed view on the boundary layers growing on the solid surfaces. . . 26
15 Heat transfer coefficient for the boundary surfaces. The heat transfer coefficient associated with radiation is assumed to be equal for both the cylinder wall and top plate. Calculated based on the correlation given in Section 5.4. . . 32
16 Based upon the convective and radiative heat transfer coefficients for the cylinder wall, a linear relationship for the range 313–413 K was developed and fed into the boundary conditions in ANSYS. . . 33
17 Average temperatures and liquid fraction during six hours of heating from the bottom. 34 18 Heat transfer into geometry at the bottom surface, and convection away from the front wall. . . 34
19 Average temperatures and liquid fraction during the 11 hours of cooling. . . 35
20 Heat transfer at the front wall during cooling. . . 35
21 Pictures of the PCM storage unit for experimental testing. . . 37
22 Placement of the measurement points inside the test unit. . . 38
23 Unit after being filled with 2.65 kg of HDPE. . . 39
24 Problems with air pockets and local expansion of HDPE. . . 40
25 Experimental setup for the four different cases. . . 42
26 Mean HDPE temperatures and power inputs during charging. . . 44
27 Mean wall temperatures during charging. . . 44
28 Mean HDPE temperatures during discharging. . . 45
29 Mean wall temperatures during discharging. . . 46
30 Energy balance of the experimental setup. . . 48
31 Experimental and numerical results for the mean HDPE temperature, outer wall temperature, and bottom temperature for the first 6 hours. . . 49 C.32 Inquiry of HDPE properties. . . C-1
C.33 Preliminary test-setup. . . C-5 C.34 The evolution of HDPE pellets as it was melted in a casserole at a constant tempera-
ture of 200 C. . . C-6 C.35 Dimension of the different parts making up the test unit. . . C-9 C.36 Dimensions of the two different plate fins. . . C-10 C.37 Complete experimental test rig, developed by Henning Hvål Mathisen as part of his
master thesis. . . C-11 C.38 Air cavity between two fins. . . C-12
List of Tables
1 Potential phase change materials and their most important properties. Sorted according to melting temperature, from lowest to highest. . . 7 2 Commercially available phase change materials and their most important properties.
Sorted according to melting temperature, from lowest to highest. . . 9 3 Thermophysical properties of HDPE based on values found in the literature. . . 10 4 Measured weight of reference and sample used during DSC testing. . . 12 5 Companies contacted about delivery of metal foams. Companies that responded,
but still have blanks in the last three columns were not able to deliver metal foam, either due to them never having produced such a structure before, only delivering closed-cell foams or they had stopped production of metal foams. . . 23 6 Properties of HDPE in CFD model. . . 27 7 Steel properties. . . 27 8 Estimated heat stored in the separate parts making up the experiment control volume
at the end of charge. . . 47 9 Estimated heat stored in the separate parts making up the experiment control volume
after 10 hours of cooling. . . 47 10 Values used to calculate stored heat. 1: Split into separate parts, see code in
Appendix D.1. . . 47 11 Calculated total heat transfer coefficient for the front wall. . . 49 A.12 Uncertainties. . . A-2 A.13 Specific heat capacity and uncertainties at different temperatures. . . A-4 C.14 Suppliers of PCMs. . . C-1 C.15 Results from testing of the HDPE blend HD6070EA with the hot disk TPS at room
temperature. . . C-3 C.16 Results from testing of the HDPE blend HD6070EA with the hot disk TPS, in liquid
bath holding 50◦C. A total of five tests were done, however for some unknown reason the first test showed significant noise and was therefore removed. . . C-3 C.17 Results from testing of the HDPE blend HD6070EA with the hot disk TPS, in liquid
bath holding 60◦C . . . C-3 C.18 Results from testing of the HDPE blend HD6070EA with the hot disk TPS, in liquid
bath holding 70◦C . . . C-3 C.19 Results from testing of the HDPE blend HD6070EA with the hot disk TPS, in liquid
bath holding 80◦C . . . C-4
C.20 Results from testing of the HDPE blend HD6070EA with the hot disk TPS, in liquid bath holding 90◦C . . . C-4 C.21 Results from testing of the HDPE blend HD6070EA with the hot disk TPS, in liquid
bath holding 100◦C . . . C-4 C.22 Temperature data at charge end. . . C-12 C.23 Temperature data 10 hours after charge end. . . D-1
Nomenclature
A Area [m2]
Cr Performance factor latent heat [−]
D Diameter [m]
H Height [m]
KΦ(T) Calibration factor, DSC [−]
L Length [m]
Ls Latent heat of fusion [J/kg]
P Probing depth [m]
Q Energy stored [kW h]
R Resistance [Ω]
T Temperature [K / ◦ C]
X Measured variable Y Calculated result
a Temperature coefficient of resistance [K−1]
cp Specific heat capacity [J/kg K]
g Gravitational constant [m·s−2]
h Heat transfer coefficient [W·m−2·K−1] m Mass [kg,g,mg]
p Pressure [P a]
q Heat transfer [W] r Radius [m]
t Time [s]
u x-component of velocity [m/s]
v y-component of velocity [m/s]
Abbreviations
CFD Computational Fluid Dynamics DSC Differential Scanning Polyethylene HDPE High-Density Polyethylene
LHTES Latent Heat Thermal Energy Storage PCM Phase Change Material
TC Thermocouple
TPS Transient Plane Source Greek letters
α Thermal diffusivity, TPS [mm2/s]
β1 Heating rate, DSC [K/min]
β2 Thermal expansion coefficient [K−1] β3 Liquid fraction [-]
∆ Change
Emissivity in Stefan-Boltzmann law [-]
λ Thermal conductivity [W ·m−1·K−1] µ Dynamic Viscosity [mPa ·s]
ν Kinematic Viscosity [ m2/s]
∂ Partial derivative Φ Heatflow, DSC [mW]
ρ Density [kg·m−3]
σ Stefan-Boltzmann constant [W ·m−2·K−4]
τ Dimensionless time [-]
θ Time constant [s−1] Subscripts
∞ Property related to surroundings 0 DSC, empty crucible
0 TPS, probe quality
c Corrected conv Convective m Melting property rad Radiation
ref Reference reg Regression
s Surface
w Wall
Superscripts
∗ Dimensionless
− Average
1. Introduction
During 2019, the total energy consumption in Norway was 213.5 TWh, where 48.7 TWh was consumed by private households. Although electricity is the main source for household heating, it is estimated that 5.4 TWh of the energy consumption in Norwegian households came from wood-fired stoves [1]. In addition to providing thermal comfort in the Nordic climate, wood firing is associated with social gatherings and provides a desired atmosphere.
Because the world is facing the dangers of climate change and has come together in the Paris agreement to reduce emissions of CO2 and thereby limit global warming to 1.5 ◦C, great steps have been taken to build better-insulated homes to reduce the need for energy [2]. A modern passive house for a single family typically requires a total power of 2 kW, whereas wood stoves produce a minimum of 6–8 kW [3]. Hence, there is an obvious mismatch that will need a solution if
wood-fired stoves are going to be utilized efficiently.
Latent heat thermal energy storage (LHTES) is an interesting concept for intermediate storage of energy. By utilizing the energy required to transform a material between two phases, typically solid to liquid, LHTES units can store 5–14 times the energy per volume compared with sensible storage [4]. Traditionally, energy from wood firing has been stored in soapstone or other types of rock, but LHTES can provide a higher energy density and thereby reduce the required volume and weight.
The cornerstone in LHTES is the phase change material (PCM) which, true to its name, is the product between the two phases. Several important considerations need to be made regarding the choice of PCM. First and foremost, it needs to be able to store an acceptable amount of energy.
Second, the phase change temperature needs to be within the temperature range of the connected thermal process, to fully utilize the latent part of the energy storage. Third, with an application that is placed indoors, its important that the PCM does not pose any health hazards.
Although the concept is still in an early phase of exploration, and a great deal regarding
integration and efficiency still needs to be investigated, some research has already been done on the concept [5–13]. More specifically, Sevault et al. [9] numerically investigated a passive LHTES system in the shape of a coaxial cylinder acting as a stovepipe using erythritol as PCM. There were concerns regarding the degradation temperature of erythritol because it is only 160◦C. Further numerical investigation was carried out by Sevault et al. [10] but this time with high-density polyethylene (HDPE) as PCM, and it was concluded that while the energy stored during charging would increase the thermal comfort in the room, the heat released after combustion would be insufficient to use the potential of LHTES fully.
For his Master’s research, Mathisen [11] built an experimental concept LHTES unit and conducted experimental testing. Much of his work laid the foundation for the experimental investigation contained in this thesis. To improve the heat transfer into LHTES and thereby reduce the charging time, Lindegård [12] used a numerical approach and looked at cylindrical fins and metal foams to
mitigate the poor thermal conductivity of HDPE. As a summer student with SINTEF energy, Bathen [13] built an experimental test container based upon Lindegård’s numerical results and tested it in the laboratory developed by Mathisen. Her results indicated a significant increase in charging compared with the results of Mathisen.
The project work conducted prior to this thesis focused on the heat release from LHTES. Results indicated that a sufficient amount of heat release was possible if the container walls were kept at sufficient temperatures. Similar to Lindegård [12], a numerical approach was taken with the emphasis on enhancing the heat transfer from within the storage toward the outside walls. The project focused on cylindrical fins and metal foams as heat transfer enhancers and HDPE as PCM.
In this Master’s thesis, the numerical model from the project work was further developed and a geometry with vertical fins made from steel was investigated. A literature review on different PCMs with melting temperatures between 100 and 160 ◦C was conducted. The PCM of choice for this thesis was HDPE and it was attempted to determine some of its properties using differential scanning calorimetry (DSC) and Hot Disk transient plane source (TPS). Based on the numerical results, a concept LHTES unit for wood stoves was designed and experimentally tested.
1.1. Objectives
The objectives of this thesis were to:
1. Search through the literature for potential PCMs and give an evaluation of their applicability based upon qualities such as latent heat of fusion, melting temperature and health hazard.
2. Investigate possibilities of acquiring a metal foam volume. And an analysis of optimum metal foam parameters, if this becomes relevant.
3. Determine thermophysical properties of HDPE, over a certain temperature range. The methods used included DSC to determine latent heat, melting temperature and specific heat capacity, and TPS to determine thermal conductivity and volumetric heat capacity.
4. Further develop a numerical model of an LHTES unit with different types of heat transfer enhancements on the inside, including shape and material, and test it under certain
conditions. Included in this is an estimation of the heat transfer coefficient for free convection and radiation on vertical and horizontal plates.
5. Based on the results from the numerical model, develop a physical model and conduct experimental tests on it, including an experiment uncertainty analysis.
1.2. Thesis structure
An overview of the thesis is presented in the following, with a brief explanation of the content in each section. In the first section, the objectives of this thesis are introduced, provided with background and previous research on the subject. In the second section, a review of phase change materials together with potential candidates for the LHTES in connection with wood stoves is
presented. The third section comprises the theory, methodology, and results of categorizing an HDPE using Differential Scanning Calorimetry (DSC) and Hot Disk Transient Plane Source (TPS).
Documentation of the attempts towards acquiring a metal foam structure for laboratory testing is presented in the fourth section, with a discussion on why this had to be disregarded.
Further, in the fifth section, the theory, setup, and results for a numerical investigation of a proposed LHTES geometry are presented. The sixth section presents the experimental design and setup together with results from the experiments with different boundary conditions. In the discussion in section seven, the results are compared to similar activities found in the literature as well as a comparison of the numerical and experimental results. Lastly, the conclusion is presented and suggestions for further work are presented.
2. Phase change materials
In every thermal storage application, one could argue that the most important element for success is an appropriate medium for storing thermal energy. Different applications will put different restrictions on the properties of the storage material[14]. This thesis is directed at latent heat storage for batch combustion in a wood stove, and therefore a literature review was conducted for potential PCM candidates. The focus has been on the thermophysical properties of the PCMs, as well as on other important aspects such as toxicity, thermal stability, commercial availability and economy.
2.1. Classification of PCM
A PCM undergoes a transition from one phase to another as it is heated or cooled. This transition can be between gas and liquid, liquid and solid, gas and solid or solid to solid. As the material undergoes the transition between two phases, energy is stored or released through a change in the vibrational state of the atoms and molecules [14]. For a relatively small thermal storage unit, intended to be placed on top of a wood stove, a solid–liquid PCM was considered the best choice.
The argument for this is that the gas phase will either require high pressure or high volume, both of which are undesirable as the whole purpose of latent versus sensible storage is to reduce volume, and high pressure in a home application is not desirable. A solid–solid PCM could be argued for but the temperature control in the formation phase is important, and with wood firing, it is hard to implement any type of temperature control. Therefore, the focus of the literature review will be on PCMs of the solid–liquid type.
As can be seen from Figure 1, the solid–liquid PCMs are subdivided into three categories: (1) eutectic, (2) organic and (3) inorganic. Eutectics are mixtures of a set of substances that can dissolve in one another as liquids [16]. The resulting melting/solidification temperature is usually lower than that of its constituents. The eutectics can again be subdivided into three categories based upon the constituents: organic–organic, inorganic–organic and inorganic–inorganic. Organic and inorganic PCMs follow the definition in chemistry, where an organic compound is one
Figure 1: Thermal energy storage methods. [15, p. 2]
containing carbon and an inorganic one does not. For the organic PCMs, a further separation into paraffin compounds and nonparaffin compounds is normal. The nonparaffin compounds are again split into either fatty acid or other nonparaffin compounds. Meanwhile, inorganic PCMs are typically either salt hydrates or metallics. This categorization of solid–liquid PCMs is illustrated in Figure 2 [15, 17].
2.2. Selection criteria
In the process of designing a latent heat storage unit, it is important to find a PCM suitable for this application. There are several aspects that should be considered [15, 17–20]:
• The PCM should have a melting temperature within the temperature range of the connected process, preferably at a temperature slightly lower than the process temperature, allowing for faster melting because the difference in temperature is the driving force. The PCM should also not exhibit too much supercooling, where the PCM is still liquid below the fusion temperature.
• The PCM needs a degradation temperature that is higher than the maximum temperature expected from the thermal process. For example, in the case of batch combustion, the degradation temperature should be above 250–300 degrees.
Figure 2: Subdivisions of solid–liquid PCMs.[17, p. 6]
• The PCM need to have a large latent heat of fusion, allowing for storage of more energy. For a process where the PCM will be heated over a large temperature range, the specific heat capacity also becomes important.
• To provide fast charging and discharging of the storage, the thermal conductivity of the PCM plays a very important role according to previously conducted project work. (ref)
• A small volume change, i.e., a small density difference between the liquid and solid phase.
• With the need for many melting/solidification cycles, the PCM should also be thermally stable. The properties such as melting temperature and latent heat of fusion should not change too much with increasing cycles.
• Depending on the application, factors such as corrosion and toxicity also become important.
• As with all commercial products, the economic aspect becomes important as well. The PCM should not be too expensive and should be readily available on the market.
• For some applications it has also been seen that the viscosity of the PCM is important. With high viscosity, there could potentially arise problems from air bubbles inside the PCM in the liquid phase. The viscosity will also limit the heat transfer to only conduction because the PCM is too viscous for gravity to induce any movement within the fluid and therefore, any free convection.
Even though all of these criteria are somewhat important for the successful implementation of a PCM as a thermal storage medium, some applications will put stricter restrictions on certain properties. For example, in our case of a thermal storage unit placed on top of a batch-fired wood stove, where the storage will be semi-open, i.e., not vacuum sealed, and placed indoors, the PCM cannot be toxic or produce toxic exhaust as it is heated. Another very important aspect that will
naturally differ considerably depending on the process that the storage unit is connected to, is the melting temperature as well as the degradation temperature. If the melting temperature is too high compared with the temperature of the connected process, the entire purpose of latent heat storage is lost, as one will only be able to utilize the sensible part of the storage. A too low melting temperature will give other challenges. For the purpose of illustration, assuming the PCM does not exhibit supercooling, the melting temperature and solidification temperature are the same.
Thereby, the melting temperature will also be the discharging temperature of the storage unit.
Then, if this temperature is too low, meaning that it is too close to the room temperature, the heat discharging rate of the storage unit will be low because the temperature difference between the storage unit and room is the driving potential for heat exchange. With this, the problem of supercooling is also introduced because the melting temperature can be in the desired discharge range, but due to supercooling the solidification temperature can be significantly lower and thereby inhibit the heat discharge.
Because of this, the melting/solidification temperature needs to be chosen with care, so that it fits with the connected process and serves the purpose that is intended. For our purpose of a thermal storage unit connected to a wood-fired stove, the department/SINTEF has specified that the melting/solidification temperature should be in the range 100−160◦C. This should allow for reasonable charging and discharging.
2.3. PCMs found in literature
Throughout the literature, a considerable number of different PCMs are proposed and tested for their physical properties, with melting temperatures ranging from several degrees below zero to metals melting above 1000◦C. Naturally, many of these will be of no interest for our proposed thermal storage unit. As mentioned under the section on selection criteria, the PCM for our purpose needs to have a phase change temperature in the range 100−160◦C. Table 2 provides a summary of PCMs found in the literature, with some of the most important thermophysical properties and health hazard.
From the literature on PCMs, it became apparent that reporting viscosity was not standard practice, and most sources only provided values for latent heat and melting temperature. The viscosity values that were found came mainly from the material databases, MatWeb.com [21] and PubChem.com [22]. Values for thermal conductivity and specific heat capacity also proved hard to find for some materials. However, most of the materials lacking this information were not pursued due to their health hazard rating, and therefore further efforts were side-stepped for other activities in this thesis. In the following the main groups of materials are presented.
Arabinitol,erythritol and D-mannitolare all compounds categorized as polyols. These organic compounds contain multiple hydroxyl groups, and as can be seen from Table 2, they all
Thermophysicalproperties MaterialTypeTmLatentHeatCpλµDensityHealth1 Reference [◦ C][kJ/kg][kJ/kgK][W/mK][mPa·s][kg/m3 ]hazard ArabinitolOrganic106256----0[23] HectaneOrganic115285---846-[24] ErythritolOrganic117320–3401.1–2.70.33–0.7318400014501[17,23–26] AcetanilideOrganic119222---12201[23] HDPEOrganic120-140150–2551.9–3.20.2–0.5532000–2000009000[17,25,27,28] BenzoicacidOrganic121–123114–147-0.140.8–1.410802[25,27] BenzamideOrganic124–127169---13402[25,27] SebacicacidOrganic130–134228---12701[25,27] PhthalicanhydrideOrganic131159---15303[25,27] MaleicacidOrganic131–141235–3851.2–2.1--15903[17,25,27] UreaOrganic133–135170–2581.8–2.10.6–0.8-13402[17,25,27] Dimenthyl terephethalateOrganic142170--1.0712901[25,27,29] D-mannitolOrganic150–165224–3001.3–2.40.1–0.2--1[17,23,24,27,30] AdipicacidOrganic150–155213–260--4.5413601[25,27,30,31] SalicylicacidOrganic157–159199---14402[27,30] Potassium thiocyanateInorganic157–177112–114---18863[27,30] Magnesium chloride hexahydrate
Inorganic1171502.0–2.40.58–0.7-1570-[17] Table1:Potentialphasechangematerialsandtheirmostimportantproperties.Sortedaccordingtomeltingtemperature,fromlowestto highest.1:NumberingbasedontheblueindicatorinthecoloreddiamondofNFPA704:StandardSystemfortheIdentificationoftheHazards ofMaterialsforEmergencyResponse[27].
have high latent heats of fusion [23]. However, they all pose different challenges. Firstly, erythritol exhibits severe supercooling, where the phase change from liquid to solid occurs at a much lower temperature than the melting temperature [24]. Haillot et al. have also indicated that the price of erythritol is very high, based on laboratory supply prices [25]. Secondly, D-mannitol is slightly hazardous when in contact with skin or eyes, or through inhalation. It is also suggested by Gasia et al. that D-mannitol exhibits a significant decrease in melting temperature and latent heat after 100 melting cycles [27]. Lastly, arabinitol appears to be not as well documented in the literature for PCMs intended for energy storage. With a melting temperature in the lower end of the desired range and the indication in Jankowski and McCluskey that many sugar alcohols exhibit
supercooling, it is not advisable to proceed further with this material.
The next group is the aromatic hydrocarbons, which include benzoic acid,benzamideand dimenthyl terephthalate. Of these three, both benzoic acid and benzamide pose a health hazard. Benzoic acid causes skin, eye and respiratory irritation, as well as damage to organs and serious eye damage after prolonged exposure. Both benzoic acid and benzamide are harmful if swallowed, with benzamide suspected of causing genetic defects. Naturally, these two cannot be considered for a unit that could be a home appliance. The latter, dimenthyl terephthalate, is less hazardous but can still cause an allergic skin irritation [27].
Sebacic acid, phthalic anhydride, maleic acidand adipic acidare dicarboxylic acids, which at room temperature are colorless and odorless. As for the previously presented materials, these acids also present health hazards. Sebacic and adipic acids both cause serious eye irritation, with sebacic acid also causing skin and respiratory irritation. Phthalic anhydride and maleic acid also cause serious eye irritation and even eye damage. In addition, they may also cause an allergic skin reaction and respiratory irritation, and are harmful if swallowed [27]. Therefore, these four acids are also not appropriate for the application in question.
Acetanilide is described as an odorless solid with a leaf- or flake-like appearance. It is also known as N-phenylacetamide. It is considered to have a health hazard of 1 under the NFTA 704 health hazard classification, with irritation to skin and eyes, as well as emitting toxic fumes when heated to decomposition.
Urea is an organic compound also known as carbamide. As a latent storage material, its thermophysical properties indicate that it could be well suited for our application. However, according to Haillot et al. [25], it suffers from low cycling stability and is therefore not a good choice. Although Haillot et al. claim that urea is nontoxic, Gasia et al. [27] indicated that it can irritate skin, eyes and the respiratory system, and is also suspected of causing cancer. It has a
rating of 2 under the NFTA 704 classification.
Salicylic acidis a phenolic acid that is widely used in skin care products to help against certain rashes and acne. In its solid form, it is colorless and crystalline. The melting temperature is at the higher end of our range, and the latent heat appears to be desirable. Its NFTA 704 rating is 2, with serious irritation to eyes and it is toxic if swallowed [27].
Potassium thiocyanateis an inorganic salt and has a low melting point compared with other inorganic salts. Its melting temperature is reported to be within a wide range in the literature, and only the lower end of the reported range is within our desired range. The latent heat is rather low, and with an NFTA 704 rating of 3, it does not appear to be a good option. It is harmful if swallowed, if it comes into contact with skin and if inhaled, and causes serious eye irritation [27].
HDPE is best known for its use in plastic bottles. This polymeric hydrocarbon is probably the most promising candidate due to it having a melting temperature well within the desired range, potentially a latent heat of 200 kJ/kg or above, and is not toxic or harmful in any way. Because of these properties, a blend of this material, supplied by INEOS, will be further investigated in this thesis. Attempts at determining the melting temperature, latent heat, specific heat capacity and thermal conductivity will be carried out.
2.4. Commercially available PCMs
Thermophysical properties
Material Type Tm Latent Heat Density λ Tmax Comments Supplier
[◦C] [kJ/kg] [kg/m3] [W/m·K] [◦C]
RT100 Organic 100 120 880 0.2 120 - Rubitherm [32]
RT100HC Organic 100 180 1000 0.2 150 - Rubitherm [32]
A118 Organic 118 285 1450 0.7 200 - PCMproducts [33]
A133 Organic 133 125 880 0.23 250 - PCMproducts [33]
A144 Organic 144 115 880 0.23 250 - PCMproducts [33]
ATS 115 Inorganic 115 158 1500 0.6 150 Corrosive Axiotherm [34]
H105 Molten salt 104 125 1700 0.5 390 - PCMproducts [33]
PureTemp 108 - 108 180 870 0.15 - - PureTemp [35]
H115 Molten salt 114 100 2200 0.5 390 - PCMproducts [33]
S117 Hydrated salt 117 125 1450 0.7 140 - PCMproducts [33]
H120 Molten salt 120 120 2220 0.5 390 - PCMproducts [33]
PureTemp 151 - 151 217 1360 0.15 - - PureTemp [36]
Table 2: Commercially available phase change materials and their most important properties. Sorted according to melting temperature, from lowest to highest.
Several companies specialize in supplying PCMs and solutions for most temperatures and applications. A list of suppliers found is given in the Appendix C.1. Although these companies provide a wide variety of PCMs, there appeared to be a shortage of PCMs with a melting
temperature in the desired range. However, 11 were within our range and can be seen in Table 2.
Most of them have quite a low maximum operating temperature compared with the melting temperature, and for our application, it is recommended that the material can withstand at least 300◦C. The three molten salts from PCMproducts appear to be the only ones with a high enough maximum operating temperature, and although their specific latent heat might appear low, their high density should make up for this. With them being salts, there might be an issue of corrosion, but this has not been further investigated. In conclusion, these three molten salts could potentially be used, but as mentioned earlier it was decided to pursue HDPE as the PCM for our application.
3. Material characterization
In the following section, the theory behind, and experimental methodology used to quantify, some of the thermal properties of HDPE will be presented. After presenting the theory and methodology, the results from these experiments are presented. Two different methods are used. First, DSC is used to determine the melting temperature, latent heat of fusion and specific heat capacity.
Secondly, TPS is used to determine thermal conductivity and volumetric heat capacity.
3.1. HDPE - HD6070EA
Based on the literature review, the PCM that was categorized was HDPE. However, this material is supplied by several different companies and with different properties. In this thesis, an HDPE blend supplied by INEOS, identified as HD6070EA, was tested. The datasheet for this HDPE blend can be found in Appendix C.2.
Tm[◦C] Latent heat [kJ/kg] Specific heat capacity [kJ/kgK] Thermal conductivity Density
HDPE 120–140 150–255 1.8–3.2 0.55–0.20 700-1000
Table 3: Thermophysical properties of HDPE based on values found in the literature [17, 25, 27]. The ranges presented for specific heat capacity, thermal conductivity and density are related to a wide temperature range from 25–200◦C.
As described by Sevault et al. [8], an important parameter for a latent heat storage unit is the ratio between the latent heat capacity and the sensible heat capacity:
Cr = Ls
Ls+cp(T−T∞). (3.1)
For a pure sensible storage unit, this ratio will be 0, while for melting temperatures equal to the ambient temperature it will be 1. If one assumes an average specific heat capacity of 2.5 kJ/kg for HDPE, a material temperatureT = 180◦C, an ambient temperatureT∞= 22◦C, and employ the range of latent heats given in Table 3, we can find a range forCr. This gives a Cr value of
0.275–0.368. With a storage applications that operate over a large temperature interval, above 150
◦C in the present case, this value will be at the lower end for most materials.
3.2. Differential Scanning Calorimetry
DSC consists of measuring a heat flow rate to a sample and a reference at a prescribed temperature. The sample and reference are contained within separate cells and heated in a differential way to maintain temperature equality. The difference in heating to the two cells is required to eliminate the influence of the container they are held in. The DSC apparatus then records the evolution of heat flow with time, as the temperatures of the two cells are changing with time. The temperature change is defined in K per time unit, usually per minute. In Figure 3, a typical thermogram for melting of a pure substance can be seen [37].
Figure 3: Thermogram of a typical melting process of a pure substance [37].
Based on the thermogram for a given sample, one can determine the latent heat, specific heat capacity and melting temperature of the sample in question. Firstly, the temperature at which melting occurs is determined by the intersection between the straight line connecting the sensible zone in the two phases and the tangent of the left curve foot. The intersection is indicated in Figure 3 and markedTonset [37, 38].
Determining the specific heat capacity was done through what Hoehne calls the “classical”
Three-Step procedure [38]. In the first step, the heat flow of the zero line is determined using empty crucibles as both sample and reference. This step removes the contribution to specific heat capacity by the crucible holding our sample. In this step, as well as in the preceding steps, 40µl aluminum crucibles were used. In the second step, a reference sample with known specific heat capacity was placed in the sample crucible and run over the same temperature program as the empty crucible in step 1. In this step, a prepared sapphire sample of 22.39 mg was tested. For sapphire, the specific heat capacity is known from tabulated values given by TA instruments (Appendix C.4). The last step was then to replace the reference substance from the sample holder with the HD6070EA blend of HDPE. For all of the measurements above the temperature was programmed to an iso-thermal phase at 25◦C for 5 minutes, before heating to 150◦C with a heating rate ofβ1 = 10 K/min. The sample of HD6070EA was heated and cooled according to this temperature program twice before the actual test was conducted in order to get proper thermal contact between HDPE and crucible.
Sample Mass [mg] mcruicible [mg] mtotal [mg]
Reference, sapphire 22.39 ±0.10 48.92 ±0.10 71.31 ±0.14 HDPE 11.61 ±0.10 48.86 ±0.10 60.47 ±0.14 Table 4: Measured weight of reference and sample used during DSC testing.
Because the reference sample was run over the same temperature program as the empty crucible, the following is valid:
cp, ref ·mref·β1=KΦ(T)·(Φref −Φ0) (3.2) whereKΦ(T) is a temperature calibration factor, Φ represents the heat flows, andβ1 the heating rate in K/time. Similarly, for the run with our HDPE sample, we get:
cp, hdpe·mhdpe·β1 =KΦ(T)·(Φhdpe−Φ0) (3.3) With the specific heat capacity of our reference known, the specific heat capacity of the HDPE sample can then be calculated from:
cp, hdpe = Φhdpe−Φ0
Φref −Φ0 · mref mhdpe
·cp, ref (3.4)
By adding step 2, the need for knowing the calibration factorKΦ(T) is therefore eliminated.
According to Hoehne, the condition Chdpe·mhdpe=Cref ·mref ensures that the experimental conditions for steps 2 and 3 are very similar, and many of the possible sources of error in DSC measurements thus have some partial compensation [38]. Because of this, the HDPE sample was prepared so that its weight was roughly half the sapphire reference weight because it was expected that the HDPE would have approximately twice the specific heat capacity.
Determination of the latent heat is done here by finding the area under the peak, limited by the straight line connecting the sensible regime before and after the peak. To determine this area, a linear regression between the points before and after the peak was carried out. Subsequently, an integration between the sample heat flow and the regression heat flow was done, ultimately giving the latent heat of melting for HDPE. The latent heat of fusion was found from:
Ls = Rtend
tstartΦs−Φregdt
ms . (3.5)
The DSC measurements were carried out on an HP DSC827 by Mettler Toledo. This DSC type allows for testing with pressures up to 10 MPa, and temperatures up to 700◦C. Before conducting the measurements, the test chamber was purged using nitrogen gas and it was ensured that the outlet was open such that all measurements were carried out at atmospheric pressure. Weight measurements were perfomed on a KERN ABT 100-5 NM scale, with a given uncertainty of 0.1 mg.
Because of limited access to the laboratory facilities, provided through SINTEF, only this one three-step test was carried out. Optimally, several tests, with different masses of the HDPE sample as well as different heating rates, should have been conducted to validate the results.
3.2.1. Results from the DSC analysis for the HD6070EA blend of HDPE
After performing the three-step method for determining the specific heat capacity of our HDPE, the resulting heating rates versus temperature were plotted and can be seen in Figure 4. The figure shows that no particular irregularities are present. However, both the sapphire reference and HDPE sample present a build-up toward a more stable heat flow in the first 1.5 minutes, or in terms of temperature, to 15 ◦C. For later calculations, this build-up phase was neglected, and as can be seen from the two following figures, Figures 5 & 6, they are plotted from 40◦C.
Figure 4: Heat flow measured during the three different steps of the classical three-step method for determining specific heat capacity.
In addition to determining the specific heat capacity of HDPE, these DSC measurements should allow for the determination of the melting temperature and latent heat of fusion. Following the procedure outlined in Section 3.2, a straight regression line connecting the two sensible zones was found using MATLAB, and can be seen as the red dotted line in Figure 5. With this regression line, it was then possible to find the latent heat of fusion as the area between this line and the curve for the heat flow to the sample, divided by the sample mass. This area is often referred to as the peak area and is indicated by the gray area in Figure 5. In conclusion, the latent heat of fusion for HDPE was found to be220.11 kJ/kg.
To find the melting temperature of HDPE, the tangent to the left foot of the peak area was found.
Then, by finding the crossing of this tangent and the straight line connecting the two sensible zones, one obtains the melting temperature of the sample. The melting temperature of HDPE was found to be124.2 ◦C.
Figure 5: Heat flow to HDPE sample with fitted straight line between the two sensible zones before and after the peak, with fitted tangent on the left foot. Tonset is found as the crossing between the two fitted lines, and is here found to be 124.2◦C.
With the three-step method described in Section 3.2, the specific heat capacity of HDPE was found and is plotted in Figure 6.
Figure 6: Calculated specific heat capacity for HDPE based on Equation 3.4 and specific heat capacity for the reference material sapphire, based upon literature values that can be found tabulated in the appendix.
It is important to point out that it was assumed that the DSC instrument used for this test was properly calibrated. However, this might not be the case and variations in temperature and heat flow recordings may be present. In addition, one of the most important factors in determining the total uncertainty is the measurement repeatability [39]. In summary, with only having done one
test and assuming the DSC to be calibrated, there is certainly a high degree of uncertainty associated with these results. A further evaluation can be found in the discussion.
3.3. Transient Plane Source (TPS) Method
To determine the thermal conductivity of the HD6070EA blend of HDPE, measurements on a Hot Disk TPS 2500S were carried out. The Hot Disk TPS 2500s is based upon the TPS method, where a double-spiral sensor element of negligible heat capacity is utilized. Usually, the sensor spiral is made of nickel with Kapton insulation film covering it. This sensor acts as both a heat source and resistor thermometer. A stepwise heat pulse is produced from an electrical current through the sensor element, and this generates a dynamic temperature field within the sample. The
temperature increase is measured by the sensor as a function of time, and the response in the sample is analyzed based on the model described in ISO22007-2 [40].
The resistance of the probe, for small increases in the temperature during the transient recording, can be expressed as:
R(t) =R0[1 +a·∆T(t)]. (3.6) Here,R0 is the initial resistance of the probe at temperature T0, the temperature coefficient of resistance of the probe isaand ∆T(t) is the mean temperature increase of the probe. The mean temperature increase will be dependent on two conditions, the first being the temperature
difference across the insulating layer of the probe and the other being the temperature increase of the sample surface during the measurement.
∆T(t) = ∆Ti(t) + ∆Ts(t) (3.7)
Here, the subscripts i and s, represent the temperature increase of the insulating layer and sample, respectively. To solve for the thermal conductivity, the probe is approximated using several concentric, equally spaced circular ring sources. The solution to the thermal conductivity equation becomes:
∆Ts(τ) =P0(π3/2rλ)D(τ), (3.8) where P0 is the power output from the probe, r is the radius of the outermost ring source andλis the thermal conductivity of the sample material. The dimensionless specific time functionD(τ) is defined as:
D(τ) = [m(m+ 1)]−2 Z τ
0
σ−2h
m
X
l=1
l
m
X
k=1
k exp−(l2+k2) 4m2σ2
I0
lk 2m2σ2
i
, (3.9)
where τ = (t/θ)1/2 and θ=r2/α. With unavoidable delays between hardware and software, a time correction is introduced,tc. Hence, the correctedτc= ((t−tc)/θ)1/2 should be introduced in equation 3.8.
The temperature increase over the sensor, introduced in equation 3.7, becomes constant after a short time, typically less than 100 ms. From here, the procedure of determining the thermal
conductivity and diffusivity starts with an iteration, where the diffusivity and the time correction are set as optimization parameters and a linear relationship between ∆Ts andD(τ) is developed.
The diffusivity and time correction are found from the last step of the iteration, and the thermal conductivity is found as the slope of the linear relationship. A least-squares fitting procedure is used to develop the linear relationship [40].
For further information on the calculation principle, please refer to the articleTransient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials by Gustafsson [41] and the bookConduction of Heat in Solids by Carslaw and Jaeger [42], more specifically, Chapter 10.
The HDPE used in the experiment was delivered as very small pellets with a radius of around 1 mm. Thus, to prepare a bulk sample that could be tested with the TPS 2500s, enough pellets to give a sample thickness of around 15 mm were placed in the kettle arrangement depicted in Figure C.33. This was done by simply holding a ruler in the middle of the kettle and filling it up until the 15 mm mark was reached. The HDPE was then heated at a constant 220 ◦C until it was apparent that all pellets had melted and the upper surface became smooth. After the sample had cooled, it was taken out of the kettle and the same procedure was repeated to produce two samples that the double-spiral sensor could be sandwiched between. The two samples were further prepared by sawing out a cylinder of 53 mm diameter with a hole saw. To avoid potential air gaps between the two samples, the surface on each of them was further smoothed out with very fine sandpaper. After preparation, the two samples had a height of 18 mm±1 mm and a diameter of 53 mm± 1 mm, and are shown below in Figure 7.
Figure 7: Samples prepared for testing with the Hot Disk TPS 2500s.
Before starting with the testing, choosing an appropriate sensor was necessary. Based on the instruction manual for the TPS 2500s [43], the largest possible sensor should be used. The sample height should be at least equal to the sensor radius, whereas the diameter of the sample should be at least equal to the diameter of the sensor. If one were to adjust the sample size based on the sensor choice, it is suggested that:
Sample thickness: r ≤H≤2·r Sample diameter: 4·r≤D≤6·r
This suggests that based on our sample size, a sensor of radius 9–13 mm should be used. Therefore, the 8563 sensor with Kapton insulation was used, which has a radius of 9.9 mm.
With the sample size and the sensor size now determined, the available probing depth could be found and the measurement time calculated. The probing depth is the measurement of how far a heat wave has traveled into the sample during the time of recording. It is given by:
∆P = 2√
α tmax, (3.10)
whereα is the thermal diffusivity and tmax is the time window used for calculating the thermal transport properties [40]. The probing depth must be shorter than the maximum distance from the sensor to any boundary of the sample because this could lead to erroneous readings due to the heat wave reaching the boundaries of the sample and thereby breaching the assumption of an infinite medium. With our chosen sensor and sample, the maximum available probing depth was calculated to be around 15 mm. Using this available probing depth with a thermal diffusivity, α= ρcλ
p, calculated based on values for thermal conductivity, density and specific heat capacity in
Lindegård’s Master’s thesis [12], and turning around Equation 3.10, the measurement time can be found.
tmax= (∆P)2
4α (3.11)
With an assumed thermal diffusivity of 0.26mm2s−1 and a probing depth of 15 mm, the maximum time was 216 s. For the Hot Disk TPS 2500s, the available measurement time closest to this value is 160 s and this value was therefore used in the measurements. When performing several
measurements one after the other, the sample needs time for the temperature to return to isothermal conditions. The instruction manual indicates that the relaxation time should be 36 times that of the transient recording time, which resulted in a time of 96 minutes between repeated measurements [43].
The last input that the Hot Disk needs to perform measurements is the power output of the sensor.
Here, the aim is to get a suitable total temperature increase during the transient measurement time. According to the instruction manual, one should aim for an increase of 2–5 K. Here, a simple trial and error approach was taken, starting at a 25 mW power output, and increasing the power until the temperature increase was above 2 K. This resulted in a power output of 150 mW, which in turn gave a temperature increase of about 2.4 K. A power output that is too high could result in irreversible sensor damage, and it was therefore considered important to start with a sufficiently
low power output.
To provide sufficient contact between sensor and sample, and ensuring that it was positioned in the middle during the entire test, the arrangement in Figure 8 was set up. The sensor was positioned in the center of the bottom sample, with the other sample put adjacently on top. A weight was placed on top, and a lid was placed over the arrangement. As can be seen from the Figure 8b, the PT100 temperature sensor was placed close to the sample. With this arrangement, tests at room temperature were carried out.
According to the instruction manual [43], the Hot Disk Thermal Analyzer has an accuracy of 5%
and a precision of 2%.
(a)Arrangement of sensor and weight to keep it in place.
(b) The arrangement was placed under lid to prevent draft.
Figure 8: Setup of samples with Hot Disk sensor.
3.3.1. Testing at higher temperatures
To carry out tests at temperatures above room temperature, the sample was placed in a silicone bath maintaining a programmed temperature before and during testing. For these tests, the Thermoscientific A40 refrigerated bath circulator was employed, with silicone oil 180. The bath is
connected to the Hot Disk software and allows for programming temperatures and time intervals.
Testing at bath temperatures from 50to100◦C with a 10◦C interval was carried out. To ensure that both the sample and the bath had reached the desired temperature, the bath was programmed to hold the desired temperature for two hours with a maximum variation of 0.5◦C. After the two hours, the sample temperature was then required to have a smaller fluctuation than 0.01◦C, with a timeout after four hours. For all the tests, the timeout after four hours was reached with a sample temperature fluctuation in the range 0.04−0.08◦C. The test procedure and settings were equal to those outlined for testing at room temperature.
Figure 9: Sample and sensor arrangement for testing at elevated temperatures in silicone bath.
3.3.2. Results from TPS-analysis of HD6070EA
With five tests at seven different temperatures, the average value at each temperature with standard deviation is plotted in Figure 10. Complete tables with results can be found in Appendix C.3.
Figure 10: Thermal conductivity measurements with standard deviation.
From the TPS analysis, one also obtains values for the volumetric heat capacity, as this is simply the thermal conductivity divided by the thermal diffusivity. If one then obtains the density of the material, determination of the specific heat capacity comes from dividing the volumetric heat capacity by the density.
Figure 11: Volumetric heat capacity with standard deviation.
At room temperature, 24.5◦C, the volumetric heat capacity is 1833 kJ m−3K−1, and the density of HDPE is 960kg m−3 according to the datasheet provided by the supplier. As a result, this indicates that the specific heat capacity is 1909.4kJ kg−1K−1, which is 20.8% lower than what was found with DSC.
