Thermal Energy Storage in Copper Foams filled with Paraffin Wax

Transcription

1 Thermal Energy Storage in Copper Foams filled with Paraffin Wax by Pathik Himanshu Vadwala A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Mechanical & Industrial Engineering University of Toronto Copyright by Pathik Vadwala 2011

2 Thermal Energy Storage in Copper Foams filled with Paraffin Wax Pathik Vadwala Master of Applied Science Mechanical & Industrial Engineering University of Toronto 2011 Abstract Phase change materials (PCM) such as paraffin wax are known to exhibit slow thermal response due to their relatively low thermal conductivity. In this study, experiments were carried out to investigate a method of enhancing thermal conductivity of paraffin wax by making use of high porosity open cell metal foams. By adding metal foam, thermal conductivity of PCM s was shown to increase by times that of pure paraffin wax. The use of open cell metal foam material for thermal energy storage application was also investigated by designing and testing different thermal energy storage systems (TESS) - with and without metal foam. The effect of copper metal foam on heat transfer during melting and solidification was analysed by determining the convective heat transfer coefficient. Lastly, a numerical code was developed to predict the temperature field within PCM while melting. ii

3 Acknowledgments This research project conducted at the Heat Transfer and Combustion Laboratory in collaboration with the Center for Advanced Coating Technologies (CACT) at the University of Toronto was made possible by the help and support of many individuals and through the financial support by Natural Sciences and Engineering Research Council (NSERC) of Canada. First of all I would like to express my sincere thanks to my advisor, Professor Sanjeev Chandra for his guidance during the course of this project and for giving me the opportunity to prove my potential in the last two years. This project would not have been a reality without his enormous support and co-operation. I am also grateful to Professor Javad Mostaghimi, for providing valuable guidance in every aspect of this project. I would like to express my thanks to Ryan Mendell and the entire MIE machine shop, for fabricating various experimental parts needed for this study. Lastly, I would like to extend a special acknowledgment to my parents and brother Himanshu, Paragi and Jay Vadwala. Their sacrifices and motivation have been the primary reason for my position today. A heartfelt thank you goes out to all my friends in the department, laboratory and at home. iii

4 Table of Contents Abstract... ii Acknowledgments... iii Table of Contents... iv List of Tables... vi List of Figures... viii Nomenclature... xi Chapter Introduction Introduction Literature Review Research Objectives Organization of Thesis... 8 Chapter Thermal Conductivity Enhancement of Phase Change Materials Using Metal Foams Introduction Experimental Test Apparatus Results and Discussion Comparison with Theoretical Model Photographic observation of melting front Chapter Thermal Energy Storage System with Metal Foam Introduction Experimental Test Apparatus and Procedure Results and Discussion Thermal Resistance Three Stage Thermal Energy Storage System Chapter Numerical Simulation of Temperature Profile using Enthalpy Method Introduction Mathematical Model Numerical Solution iv

5 4.4 Verification of the Computational Model Chapter Conclusions References Appendix A Schematics Appendix B Thermal Conductivity Measurement Data Appendix C Thermal Energy Storage System Data Appendix D Results from Enthalpy Code v

6 List of Tables Table 2.1: Thermal diffusivity values at different temperatures Table 2.2: Effective Density and Specific Heat values for the foam-wax system Table 4.1 Various physical properties used in the numerical code Table B1: Temperature results for Table B2: Temperature results for Table B3: Temperature results for Table B4: Temperature results for Table B5: Temperature results for Table C1: Temperature variation while melting (without metal foam) at constant temperature of 105 at the top copper plate Table C2: Temperature results for solidification at 20.0 L/min (no metal foam) Table C3: Temperature results for solidification at 30.0 L/min (no metal foam) Table C4: Temperature results for solidification at 40.0 L/min (no metal foam) Table C5: Temperature results for solidification at 50.0 L/min (no metal foam) Table C6: Temperature results for solidification at 60.0 L/min (no metal foam) Table C7: Temperature variation while melting (with metal foam on wax side) at constant heat flux of 50 V (2800 W/m 2 ) Table C8: Temperature results for solidification at 20.0 L/min (foam on wax side) Table C9: Temperature results for solidification at 30.0 L/min (foam on wax side) Table C10: Temperature results for solidification at 40.0 L/min (foam on wax side) Table C11: Temperature results for solidification at 50.0 L/min (foam on wax side) Table C12: Temperature results for solidification at 60.0 L/min (foam on wax side) Table C13: Temperature variation while melting (with metal foam on both- air and wax side) at constant heat flux of 50 V (2800 W/m 2 ) Table C14: Temperature results for solidification at 20.0 L/min (foam on both sides) Table C15: Temperature results for solidification at 30.0 L/min (foam on both sides) Table C16: Temperature results for solidification at 40.0 L/min (foam on both sides) Table C17: Temperature results for solidification at 50.0 L/min (foam on both sides) Table C18: Temperature results for solidification at 60.0 L/min (foam on both sides) Table C19: Thermal resistance analysis data (without metal foam) Table C20: Thermal resistance analysis data (metal foam on wax side) Table C21: Thermal resistance analysis data (metal foam on both sides) vi

7 Table C22: Temperature results for solidification at 20.0 L/min (three stage TESS) Table C23: Temperature results for solidification at 30.0 L/min (three stage TESS) Table C24: Temperature results for solidification at 40.0 L/min (three stage TESS) Table C25: Temperature results for solidification at 50.0 L/min (three stage TESS) Table C26: Temperature results for solidification at 60.0 L/min (three stage TESS) Table D1: Experimental temperature results for melting (with metal foam) at a depth of 1 cm at constant heat flux of 50 V (2800W/m 2 ) Table D2: Temperature results from numerical code (phase change at a single temperature) for melting (with metal foam) at a depth of 1 cm at constant heat flux of 50 V (2800W/m 2 ) Table D3: Temperature results from numerical code (phase change over a temperature range) for melting (with metal foam) at a depth of 1 cm at constant heat flux of 50 V (2800W/m 2 ) vii

8 List of Figures Figure 2.1 : Schematic of the experimental apparatus showing the test sample and instrumentation. 11 Figure 2.2 : Photograph of the experimental apparatus showing test sample and instrumentation Figure 2.3 : Detailed view of Test sample showing the placement of thermocouples Figure 2.4 : Experimentally obtained temperature results for 85 plotted as a function of time at different axial distance along the length of the test sample. The experimental uncertainty is 2.6 in the temperature measurement Figure 2.5 : Experimentally computed thermal diffusivity values from Equation (2.1) for different surface temperatures and different distance along the length of the test sample. The thermal diffusivity values falling between two bounds are only taken into consideration Figure 2.6 : A unit cell structure of tetrakaidecahedron with six squares and eight hexagons [5] Figure 2.7 : Experimental pictures showing propagation of melting front of wax without metal foam Figure 2.8 : Experimental pictures showing propagation of melting front of wax with metal foam.. 26 Figure 3.1: Schematic of the TESS apparatus showing the instrumentation and air supply configuration Figure 3.2: TESS apparatus with instrumentation Figure 3.3: Detailed view of TESS showing the placement of thermocouples used for measuring inlet and outlet temperature of air Figure 3.4: TESS with no Metal Foam Figure 3.5: TESS with Metal Foam on wax side Figure 3.6: Experimentally obtained temperature results plotted as a function of time while melting at a distance of 1 & 2 cm along the length of wax compartment for both with foam and without foam case. The experimental uncertainty is 2.6 in the temperature measurement Figure 3.7: Experimentally obtained temperature results plotted as a function of time during melting at a distance of 1 & 2 cm along the length of wax compartment with metal foam. The experimental uncertainty is 2.6 in the temperature measurement Figure 3.8: Experimentally obtained temperature results plotted as a function of time while solidifying at a distance of 1 & 2 cm along the length of wax compartment for both with foam and without foam case when the mass flow rate of air is 40.0 L/min. The experimental uncertainty is 2.6 in the temperature measurement Figure 3.9: Experimentally obtained results for inlet and outlet temperature of air plotted as a function of time for both-with foam and without foam case when the mass flow rate of air is 40.0 L/min. The experimental uncertainty is 2.6 in the temperature measurement Figure 3.10: Photograph showing metal foam on both sides along with copper plates and thermocouples viii

9 Figure 3.11: TESS with metal foam on both sides Figure 3.12: Experimentally obtained temperature results plotted as a function of time while solidifying at a distance of 1 cm along the length of wax compartment for all the three cases when the mass flow rate of air is 40.0 L/min. The experimental uncertainty in temperature measurement is Figure 3.13: Experimentally obtained results for inlet and outlet temperature of air plotted as a function of time for all the three cases when the mass flow rate of air is 40.0 L/min. The experimental uncertainty is 2.6 in the temperature measurement Figure 3.14: Experimentally computed Nusselt number with respect to Reynolds number for all the three cases Figure 3.15: Experimentally computed power extracted with respect to flow rate of air for all the three cases of TESS Figure 3.16: Experimentally computed convective heat transfer coefficient with respect to flow rate of air for all the three cases of TESS Figure 3.17: Computed value of solid wax resistance with respect to non-dimensional solidification time for all three cases of TESS Figure 3.18: Computed value of Overall Thermal Resistance R with respect to non-dimensional solidification time for all three cases of TESS Figure 3.19: A cross section view of 3 stage TESS showing the 3 layers of foam separated by copper plates Figure 3.20: Top view of the TESS showing the hole for thermocouple fitting Figure 3.21: Photograph showing the flexible silicon rubber heaters that were used for melting wax56 Figure 3.22: Three stage TESS apparatus with instrumentation Figure 3.23: Experimentally obtained results for outlet temperature of air plotted as a function of time. The mass flow rate of air in L/min is indicated in the parenthesis. The experimental uncertainty is 2.6 in the temperature measurement Figure 3.24 : Experimentally computed Nusselt number with respect to Reynolds number for all the three stage TESS Figure 3.25: Experimentally computed average power extracted Q (W) with respect to flow rate of air Figure 3.26: Experimentally computed average convective heat transfer coefficient (W/m 2 K) with respect to flow rate of air Figure 4.1: Discretization domain for one-dimensional phase change problem with boundary conditions Figure 4.2 Flowchart Figure 4.3 : Experimentally obtained temperature results plotted as a function of time, during melting at a distance of 1 cm along the length of wax compartment with metal foam, along with the computed ix

10 temperature values from C++ code, for phase change at a single fixed temperature. The experimental uncertainty is 2.6 in the temperature measurement Figure 4.4 : Experimentally obtained temperature results plotted as a function of time, during melting at a distance of 1 cm along the length of wax compartment with metal foam, along with the computed temperature values from C++ code, for phase change at a single fixed temperature and phase change over a temperature range. The experimental uncertainty is 2.6 in the temperature measurement. 75 Figure A1: Two stage TESS drawing Figure A2: Three stage TESS drawing x

11 Nomenclature E = Energy (J) m = Mass flow rate of fluid (L/min) = Specific Heat (J/kg.K) L = Latent heat of fusion (KJ/kg) e = Error associated with given instrument = Uncertainty in a measurement erfc = Complimentary error function k = Thermal conductivity (W/mK) = Thermal diffusivity (m 2 /sec) = Porosity = Density (kg/m 3 ) = Convective heat transfer coefficient of air (W/m 2 K) = Cross-sectional area of TESS (m 2 ) Q = Power (W) Re = Reynolds number Nu = Nusselt number = Hydraulic diameter (m) = Characteristics length (m) u = Mean velocity of air (m/sec) = Dynamic viscosity (Nsec/m 2 ) xi

12 = Temperature of the fluid ( ) = Melting temperature of the PCM ( ) = Temperature of fluid at the center of TESS ( ) = Convective resistance on air-side (K/W) = Solid wax resistance (K/W) R = Overall thermal resistance (K/W) = Width of the copper plate (m) = Thermal conductivity of copper plate (W/mK) = Thermal conductivity of wax (W/mK) = Thickness of solidified layer of wax that varies with time (m) = Time required for solidification front to reach the distance (sec) = Time required for total solidification (sec) H = Total volumetric enthalpy (J/kg) h = Sensible enthalpy (J/kg) = Liquid fraction Fo = Finite difference Fourier number = Space increment (m) = Time increment (sec) = Non-dimensional solidification time - xii

13 CHAPTER 1. INTRODUCTION Chapter 1 Introduction 1.1 Introduction Thermal energy storage is of critical importance in many engineering applications. As solar energy is available only during daytime, its application requires an efficient storage system so that the energy gathered during daytime can be utilised later at night. Similar problems arise in waste heat recovery systems where heat availability and utilisation periods are often different, requiring thermal energy storage [1,4]. The most commonly used method of thermal energy storage is the sensible heat method. The sensible heat storage refers to energy systems that store thermal energy without changing phase. Sensible heat devices store energy by raising the temperature of the storage medium. The amount of energy stored depends on the temperature change and specific heat of the material and can be expressed as: where m is the mass and is the specific heat. As specific heat of a material is generally two orders of magnitude smaller than its latent heat, sensible heat storage requires a much larger volume of material to store the same amount of energy as compared to latent heat storage [6]. Hence, sensible heat storage devices are very heavy and bulky in size. Heating of a material that undergoes phase change (usually melting) is called latent heat storage. The 1

14 CHAPTER 1. INTRODUCTION amount of energy stored depends on the mass and latent heat of fusion of the material and can be expressed as: where L is the latent heat of fusion. Materials used for latent heat storage are referred to as phase change materials (PCMs). Latent heat storage is more attractive as it provides a high energy storage density and can absorb or release energy at a constant temperature [3]. Hence the use of PCMs for thermal energy storage has been of great interest in recent years in fields such as waste heat recovery, solar energy utilization and passive cooling of electronic devices [1-4]. PCM s are generally divided into three main categories: organic, inorganic and eutectic compounds. Low temperature PCM s (< 200 ) (organic, inorganic or eutectic) are mainly used in waste heat recovery systems and buildings, while high temperature PCM s (> 200 ) (inorganic or eutectic) are used in solar power plants and other high temperature applications [35]. Materials to be used for phase change thermal energy storage must have high latent heat of fusion and high thermal conductivity. They should also have a melting temperature lying in a practical range of operation, melt uniformly, be chemically inert, low cost, non toxic and non corrosive [1,4]. As paraffin wax possesses most of these properties it attracts considerable attention as a PCM. However, paraffin waxes have inherently low thermal conductivity and so it takes considerable time to melt and solidify, which reduces the overall power of the thermal storage device and thereby restrict their application [2]. Several methods have been proposed to increase the thermal conductivity of paraffin wax including addition of 2

15 CHAPTER 1. INTRODUCTION enhancers such as metallic fillers, finned tubes and aluminum shavings [4]. However, these enhancers add significant weight and cost to the storage system and some of them are incompatible with PCM s [2]. High porosity open cell metal foams can also serve as thermal conductivity enhancers as they are available in copper, graphite, aluminum or nickel foam whose thermal conductivity is very high (>80 W/mK) and have low bulk density and are chemically inert [3]. The purpose of the present study was to determine the feasibility of using metal foams to enhance the heat transfer capability of phase change materials. In the present work, 10 pores per inch (PPI) copper foam (95% porous) was impregnated with paraffin wax that melts in the temperature range of Literature Review Extensive research has been carried out to improve the thermal response of PCM by adding different high thermal conductivity enhancers. In this section a summary of the relevant research regarding PCM s is presented. The use of finned tubes with different configurations has been proposed by various researchers. Lacroix and Benmadda [53] studied the behaviour of a vertical rectangular cavity filled with PCM. They found that both solidification and melting rates were improved by long fins. Velraj et al [54] studied the impact of internal longitudinal fins on a cylindrical vertical tube filled with paraffin wax. They concluded that adding fins reduces the solidification time by a factor of 1/n, where n is the number of fins. They also pointed out 3

16 CHAPTER 1. INTRODUCTION that for lower Biot numbers, addition of fins makes the surface heat flux more uniform, whereas for higher Biot numbers the addition of fins improves the magnitude of surface heat flux and appreciably reduces the solidification time. Stritih et al [11] studied the heat transfer characteristics of a latent-heat storage unit with and without a finned surface. They developed a correlation giving the dimensionless Nusselt number as a function of Rayleigh number. A comparison of the equations for melting and freezing shows that natural convection is present during melting and increases heat transfer, whereas during solidification conduction is the dominant form of heat transfer. They concluded that heat transfer during solidification is greater if fins are included and a 40% reduction in solidification time is observed with fins. Mettawee and Assassa [15] placed aluminum powder in the PCM for a compact PCM solar collector. Solar energy was stored in the PCM and was discharged to cold water flowing in pipes located inside the PCM. The propagation of melting and freezing fronts was studied during the charging and discharging process. It was found that the addition of aluminum powder in wax reduced the charging time by 60%. In the discharging process, it was found that the useful heat gained was increased by adding aluminum powder in the wax. Bugaje et al. [14] found that the thermal response of paraffin wax was enhanced by the use of metal matrices embedded within the body of wax. Significant reductions in melting and freezing times were obtained by the use of aluminum sheet metal. Melting times were reduced by factors of up to 2.2 and freezing times reduced by factors of up to 4.2. It was also found that thermal response enhancement is greater during freezing than melting as conduction plays a greater role in freezing while natural convection becomes significant during melting. 4

17 CHAPTER 1. INTRODUCTION Py et al [8] did some research on a new supported PCM made of paraffin impregnated in a compressed expanded natural graphite (CENG) matrix and found thermal conductivities in the range of 4 to 70 W/mK while that of paraffin wax is 0.24 W/mK. It was also found that CENG induced a decrease in overall melting and solidification time. Zhong et al [13] used CENG matrices with different densities to see the increase in thermal response of paraffin wax. To predict the performance of paraffin wax/ceng composites as a thermal energy storage system, their structure, thermal conductivity and latent heat were characterized. Results indicated that the thermal conductivity of the composites can be times that of pure paraffin wax. Mesalhy et al [49] studied numerically and experimentally the effect of porosity and thermal properties of a porous medium filled with PCM. In their model, the governing partial differential equations describing the melting of phase-change material inside porous matrix were obtained from volume averaging of the main conservation equation of mass, momentum and energy. From their model it was found that the best technique to enhance the response of PCM is to use a solid matrix with high porosity and high thermal conductivity. Model results indicate that estimated value of the average output power using carbon foam of porosity 97% is about five times greater than that for using pure PCM s. One intrinsic problem of a graphite matrix is its anisotropy in which the thermal conductivity depends on direction [35]. To solve this problem, some metal materials with high thermal conductivities were used by several researchers to enhance the heat transfer performance of the PCM s. Zhao et al. [35] did experimental investigation on the solid/liquid phase change in which paraffin wax was embedded in high porosity (> 85%) open cell copper metal foams. The test samples were electrically heated on the bottom surface with a constant heat 5

18 CHAPTER 1. INTRODUCTION flux. They found that the addition of metal foam increases the overall heat transfer by 3-10 times during the melting process. They also found that the temperature gradient in metal foam sample is significantly reduced compared to pure PCM. 6

19 CHAPTER 1. INTRODUCTION 1.3 Research Objectives The objectives of this research are: To measure the enhancement in thermal conductivity of paraffin wax when used with 10 pores per inch (PPI) copper metal foam with porosity ( ) = To evaluate the use of high porosity copper metal foam material in thermal energy storage application To design and test different thermal energy storage systems (TESS), with and without copper metal foam, and to analyze the effect of copper metal foam on heat transfer, during charging and discharging process, by determining the convective heat transfer coefficient Develop a Nusselt number correlation based on geometric parameters to describe the experimental results To build an actual TESS device and test its performance Develop a numerical code to determine the temperature field within PCM during charging i.e. melting process 7

20 CHAPTER 1. INTRODUCTION 1.4 Organization of Thesis The present chapter gives a general background, literature review and objectives of this research thesis. Chapter 2 explains the experimental apparatus and methodology used to determine the enhancement in thermal conductivity of paraffin wax when used with copper metal foam. The thermal conductivity value determined from the experiments is then compared with a theoretical model developed by Boomsma and Poulikakos [5]. A photographic study of propagation of the melting front of wax with and without metal foam - is carried out to determine the enhancement in rate of heat transfer. Chapter 3 describes the design and analysis of a TESS and compares the performance of TESS (with and without metal foam). The effect of addition of metal foam on thermal resistance is analysed. The final part of the chapter describes the design and performance analysis of a TESS device. Chapter 4 describes the numerical model developed to determine the temperature field in PCM while melting. It is concluded that the assumption of single temperature phase change is not valid and so the code is modified such that it considers phase change over a temperature range. Chapter 5 lists the conclusions drawn from the present research. At the end, references, and the appendices containing schematics and raw data obtained during experimental runs are included. 8

21 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS Chapter 2 Thermal Conductivity Enhancement of Phase Change Materials Using Metal Foams 2.1 Introduction Phase change materials such as paraffin wax are known to exhibit slow thermal response due to their relatively low thermal conductivity [1,4]. In this study, experiments were carried out to investigate a method of enhancing thermal conductivity of paraffin wax by making use of high porosity open cell metal foams. In the present work, 10 pores per inch (PPI) copper foam (95% porous) was impregnated with paraffin wax that melts in the temperature range of The copper foam was heated at one end with a constant temperature boundary condition and time varying temperatures were measured along its length. Thermal conductivity was measured by modeling the test sample as a semi-infinite medium. The experimental results were then compared with a theoretical model proposed by Boomsma and Poulikakos [5]. In addition, photographic observation of propagation of melting front of wax was done, for both pure wax and foam-wax system, to determine the enhancement in melting rate of wax for the same time and surface temperature conditions when used with copper metal foam. 9

22 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS 2.2 Experimental Test Apparatus The experimental apparatus used to test the foam-wax composite system is shown schematically in Figure 2.1. A rectangular copper foam with a thickness of 20 mm and a pore density of 10 PPI (Dalian Thrive Mining Co. Ltd, Dalian, China) was cut using an electric-discharge machine (AD325L CNC Wire EDM, Sodnick, Japan) to the dimensions of 260 mm x 20 mm x 20 mm (L x W x H). In order to provide a heating surface to the foam, and to ensure maximum attainable heat transfer to the foam, a T-shaped copper plug was soldered to the flat face of the foam by using a Sn-alloy soldering paste (Loctite RP15, Henkel AG and Company, Dusseldorf, Germany). The foam and plug were inserted into a 300 x 25 x 25 mm square polycarbonate tube (McMaster-Carr, OH, US). Before inserting the foam, 2 mm diameter holes were drilled on one face of the tube at distances of 1, 2, 3, 5, 7, 9, 11 and 28 mm from one end of the polycarbonate tube. Eight Type-K thermocouples with a 0.25 mm diameter junction were inserted through the holes drilled in the polycarbonate tube to measure the temperature variation along the length of the foam. The holes were then covered with high temperature cement (CC High Temperature, Omega, Stamford, CT) to prevent leakage of wax. The thermocouple voltages were recorded by a National Instruments Data Acquisition (DAQ) unit and transmitted directly to a personal computer. The output voltages of the thermocouples were recorded in real-time using a personal computer equipped with LabVIEW Signal Express v

23 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS Figure 2.1 : Schematic of the experimental apparatus showing the test sample and instrumentation 11

24 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS To ensure a leak-proof joint between copper plug and the tube, ultra blue RTV silicon gasket (Permatex) was applied on the mating surfaces of plug and the tube. The silicon gasket was allowed to dry for 24 hours and after that paraffin wax (melting temperature 50 C, thermal conductivity 0.21 W/mK) was poured into the polycarbonate tube in liquid state and allowed to solidify. A 7 mm diameter and 40 mm long blind hole was drilled in the center of the copper plug to insert the cartridge heater (Model CSH /120V, Omega, Stamford, CT). The heater was 6.35 mm (1/4 in.) in diameter and is 38.1 mm (1.5 in.) long. It had an electrical resistance of 130 and produced a maximum power output of W at 120 V. Power to the heater was provided by a variable transformer which in turn was connected to a temperature controller. To prevent any heat loss to the surroundings the entire test sample was covered using 38.1 mm (1.5 in.) thick fibreglass insulation with a aluminized outer surface, having an average thermal conductivity of W/mK (Micro-Flex, Johns Manville Corporation, Denver, CO). A 3 mm diameter and 78 mm long blind hole was drilled at one edge of the plug to insert the thermocouple probe to maintain a constant surface temperature of the plug. A Type-K (chromel-alumel) thermocouple probe with a 304SS sheath of mm diameter (Model TJ36-CASS-032-G-6, Omega, Stamford, CT) was inserted in the plug. The other end of the thermocouple was connected to a temperature controller (Model CN2110, Omega, Stamford, CT) which helped to maintain a constant surface temperature by controlling the power output to the heater. 12

25 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS Test Sample S Temperature Controller Data Acquisition Figure 2.2 : Photograph of the experimental apparatus showing test sample and instrumentation Thermocouple wires Figure 2.3 : Detailed view of Test sample showing the placement of thermocouples 13

26 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS The uncertainty in the temperature measurement is measured using the root sum squares (RSS) method. In RSS, the bias and precision elemental errors within the instrumentation are combined to determine the realistic value for uncertainty. The uncertainty associated with data acquisition system is: The type K thermocouples used in these experiments have a standard limit of error of. The resolution of LabView was set at, thus the zero order uncertainty associated with it was. Hence, the uncertainty associated with thermocouples is: 14

27 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS Hence the overall uncertainty associated with temperature measurement is the combined error of thermocouple and data acquisition system: 15

28 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS 2.3 Results and Discussion The analysis of metal foam impregnated with paraffin wax uses the standard solutions used in analysis of heat conduction in semi-infinite medium described by Cengel [37]. Several assumptions regarding the heat transfer that were made in the analysis are as follows: The porosity is constant throughout the length of the foam Natural convection and radiation heat transfer effects inside the porous medium are neglected and the heat transfer is one dimensional: heat transfer occurs only in the direction normal to the surface The physical properties of the solid and fluid phases are assumed to be the same and constant over the entire temperature range; i.e. volume change is neglected The solid and fluid phases are in local thermal equilibrium The length of the test sample is long enough to assume it is a semi-infinite medium A medium is said to be semi-infinite if a step change in temperature at one end (x = 0) does not change the temperature at the other end (x = l ) during the time of observation. To demonstrate that this was a reasonable assumption in these experiments, time varying temperatures at different points along the length of the column are plotted in Figure 2.4 for the case T s =

29 Temperature (c) CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS x = 1cm x = 2 cm x = 3 cm x = 5 cm x = 7 cm x = 9 cm x = 11 cm x = 26 cm Time (sec) Figure 2.4 : Experimentally obtained temperature results for 85 plotted as a function of time at different axial distance along the length of the test sample. The experimental uncertainty is 2.6 in the temperature measurement. It can be seen from Figure 2.4 that even after 1500 seconds the temperature at a distance of x = 26 cm does not change at all. Thus, the assumption that the test sample is a semi infinite is valid during this time interval. Based on the assumptions listed above the temperature variation along the length of foam for a specified surface temperature, T s = constant is given by Cengel [37] as ( ) 17

30 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS where is the transient temperature measured by a thermocouple at distance x and time t from the face of the test sample using the data acquisition unit. is the initial temperature of the test sample i.e. ambient temperature and is the surface temperature which is kept constant with the help of a temperature controller. So the only unknown in Equation (2.1) is the thermal diffusivity which can therefore be directly calculated. Equation (2.1) is valid only when there is a step change in surface temperature. In the present case the copper plug takes at least 4 to 5 minutes to reach the constant-surface temperature condition and because of that, the temperature recorded by the thermocouples is lower than the true temperature at which the foam-wax system would have been if its surface temperature was increased instantaneously. As the measured value of temperature is always lower than the true value, the numerator on the left hand side of Equation (2.1) is always smaller than in reality. As thermal diffusivity is inversely proportional to the temperature difference, the value we calculate from Equation (2.1) is expected to be smaller than the true value. The values of thermal diffusivity are measured at = 65, 70, 75, 80 and 85 C. The values of thermal diffusivity at different temperatures and location are shown in Figure 2.5. Thermal diffusivity is plotted on a log scale whereas time is plotted on a normal scale. It can be seen from the graph that the thermal diffusivity value is initially higher and after about 200 seconds it reaches a constant value. Thermal diffusivity value starts dropping once steady state is reached because at steady state is a constant value and so the temperature terms on left hand side of Equation (2.1) are all constant. Thus, at steady state, thermal 18

31 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS diffusivity is inversely proportional to time and as time is always increasing thermal diffusivity value starts dropping once steady state is reached. Hence, to ignore the initial and end effects and for simplicity, only the values that are within the two bounds shown in Figure 2.5 are taken into consideration. Figure 2.5 : Experimentally computed thermal diffusivity values from Equation (2.1) for different surface temperatures and different distance along the length of the test sample. The thermal diffusivity values falling between two bounds are only taken into consideration. The thermal diffusivity values that are within the bounds were averaged for each temperature. After that, they were averaged over different temperatures to find the overall average thermal diffusivity value for the foam-wax composite system. This overall average value was used to find the effective thermal conductivity of the foam-wax system. 19

32 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS Effective thermal conductivity is calculated by using the relation: where = thermal diffusivity, = density and = specific heat. The effective value of density and specific heat that will be used in Equation (2.2) was computed by accounting for the volume fraction of each substance, giving the resulting relation for density and specific heat based on porosity as: where = porosity of metal foam. The subscripts and s are used for fluid and solid phases respectively. The subscript denotes the effective value of a property. The value of for 10 PPI copper foam is 0.95 [52]. 20

33 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS Table 2.1 shows the computed values of thermal diffusivity whereas table 2.2 shows the computed values of effective density and specific heat using Equation (2.3) and (2.4) Temperature ( C) Average value of thermal diffusivity - (m 2 /sec) x x x x x 10-6 Overall average value of thermal diffusivity 1.02 x 10-6 Table 2.1: Thermal diffusivity values at different temperatures Material Density (kg/m 3) Effective Density (kg/m 3 ) Material Specific Heat (J/kg.K) Effective Specific Heat (J/kg.K) Copper 8933 [37] Copper 385 [37] Wax 930 [1] Wax 2900 [1] 2755 Total Effective Density Total Effective Specific Heat Table 2.2: Effective Density and Specific Heat values for the foam-wax system The effective thermal conductivity is then calculated by substituting the values, computed in Table 2.1 and 2.2 into Equation (2.2). The effective thermal conductivity computed by using Equation (2.2) is 3.8 W/mK 21

34 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS 2.4 Comparison with Theoretical Model The calculated thermal conductivity can be compared with a theoretical model developed by Boomsma and Poulikakos [5] who developed a model to estimate effective thermal conductivity of a porous metal foam, based on the idealizing its structure as being a series of cells with the shape of a tetrakaidecahedron. The complete cell of tetrakaidecahedron consists of six squares and eight hexagons. It is the idealized shape that most of the foam cells would attain because of the nature of foam manufacturing process. [5,56] Figure 2.6 : A unit cell structure of tetrakaidecahedron with six squares and eight hexagons [5] 22

35 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS They developed the following equations to calculate the effective thermal conductivity : ( ) ( ) ( ) ( ) ( ) ( ) ( ( )) where = porosity of the metal foam (i.e. 0.95), e = dimensionless cubic node length, = thermal conductivity of solid phase (i.e. Copper foam, 400W/mK), thermal conductivity of fluid phase (i.e. paraffin wax, 0.21 W/mK), = effective thermal conductivity of the composite system. A detailed derivation of these equations is given in reference [5]. The value of e is determined by the authors to be a constant equal to

36 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS The theoretical value of effective thermal conductivity is then computed by making use of Equations (2.4) to (2.9) and the value comes out to be 5.02 W/mK, which is within 25% of the value calculated in the previous section. Besides the reason stated in the previous section, about the time required for heater to reach the constant surface temperature condition, the difference between experimental and theoretical value of thermal diffusivity can be due to the following factors : The porous medium is considered to be uniform but in reality the porosity varies along the length. Also the model is highly dependent on porosity. A small increase in porosity causes a large decrease in thermal conductivity. The theoretical model does not take into account the thermal resistance between the foam and copper plug. 24

37 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS 2.5 Photographic observation of melting front The objective of this chapter is to investigate the propagation of melting front of wax with and without the use of metal foam. The photographs are taken at various values of for both cases to compare the amount of wax melted. The photographs are taken 45 minutes after the heater was turned on, by which time the melting front was stationary Figure 2.7 : Experimental pictures showing propagation of melting front of wax without metal foam 25

38 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS The photographs shown in Figure 2.7 are taken at various temperatures, for melting front of wax, without the use of metal foam. It can be seen clearly from the photographs that the maximum amount of wax that can be melted without the use of metal foam at 85 C is around 1.2 cm. Temperature is not increased beyond 85 C as it results in softening of the polycarbonate tube Figure 2.8 : Experimental pictures showing propagation of melting front of wax with metal foam 26

39 CHAPTER 2. THERMAL CONDUCTIVITY ENHANCEMENT OF PHASE CHANGE MATERIALS USING METAL FOAMS The photographs shown in Figure 2.8 are taken at various temperatures with the use of metal foam. It can be seen from the pictures that the maximum amount of wax that can be melted at 85 C is around 3 cm which is 2.5 times more than that can be melted without the use of metal foam. The thermal conductivity of paraffin wax is very low (0.21 W/mK) and because of that the amount of wax that can be melted is also very low (for a given time and temperature boundary condition). However, when wax is used with metal foam it increases the overall thermal conductivity of the foam-wax composite system and so a greater amount of wax can be melted with the same temperature boundary condition with the use of metal foam. Also, as metal foam is 95% porous, only 5% reduction in storage volume of wax is observed in foam-wax composite system. 27

40 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Chapter 3 Thermal Energy Storage System with Metal Foam 3.1 Introduction The purpose of a thermal energy storage device is to overcome the time difference between the availability of and demand for thermal energy. These systems are used in order to store thermal energy during a period when the supply is sufficient or cheaper, to be discharged when the supply becomes insufficient or expensive [6]. A latent heat storage system is a practical device that promises high thermal storage density because the phase change material (PCM) can absorb or release a large amount of heat during melting or solidification process [17]. One of the major drawbacks of current PCM s is their low thermal conductivity and so it takes considerable time to melt and solidify, which in turn reduces the rate at which thermal energy can be stored and extracted and so it restricts their application. One way of improving the thermal conductivity is to make use of high porosity (> 85%) open cell metal foams which enhances heat transfer due to their high thermal conductivity and high surface area density. The aim of this section is to evaluate the use of high porosity metal foam in thermal energy storage application. 28

41 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM 3.2 Experimental Test Apparatus and Procedure One of the objectives of this research is to demonstrate the use of metal foam material for thermal energy storage. The objective is to fabricate a small scale thermal energy storage device, both with and without metal foam, and to carry out necessary experimentation to determine the effect of metal foam. The experimental apparatus consists of the air facility, thermal energy storage system (TESS) and instrumentation. A schematic representation of the experimental setup is shown in Figure 3.1. Compressed air provided by the laboratory was connected to a pressure regulator attached to a globe valve, which when adjusted, can control the amount of air released to the test section. Measurement of mass flow rate was done by an electronic gas mass flow-meter (Model FMA1842, Omega Company, Stamford, CT) for a flow rate range of 20.0 L/min to 60.0 L/min. The air enters the test section via ductwork mated to a 9.5 mm (0.375 in.) tee-junction. The direction of air flow was from left to right in Figure 3.1 and progresses downstream where it exits to the surrounding. Both inlet and outlet tee-junctions were fitted with 13 mm (0.5 in.) Type K thermocouple pipe plug probes to measure the inlet and outlet temperature of air respectively. The TESS was made out of 6.35mm thick polycarbonate sheet (McMaster Carr, OH, USA). The dimensions of the TESS were 212 mm x 62.5 mm x 62.5 mm (L x W x H). Two rectangular slots were milled on the inside of the TESS box to accommodate the copper plates. The purpose of the copper plate was to form two separate compartments, the top compartment to store wax and the bottom one to pass air through it, as well as to provide a heating surface to melt wax. The height of wax compartment was 20 mm whereas that of air compartment was 25 mm. 29

42 Figure 3.1: Schematic of the TESS apparatus showing the instrumentation and air supply configuration CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM 30

43 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM A flexible silicon rubber heater (Model SRFG 208/10-P, Omega Company, Stamford, CT) with dimensions of mm x 50.8 mm (2 in. X 8in.) approximately the same size as the test sample was used for melting the wax during the charging process. It had an electrical resistance of 82.0 Ω and produces a maximum power output of 160 W at 115 V. Power to the heater was provided by a variable transformer that was used to supply 50 V to the heater to ensure that the TESS was not heated rapidly. Three Type-K (chromel-alumel) thermocouples, two at the copper plates and one in the middle of the wax section were used to measure the transient variation in temperature during charging as well as discharging process. In order to ensure good contact between thermocouple and the copper plate, thermocouple wires were welded to the copper plate using a Hotspot TC welder. The thermocouple welded to the top copper plate, which had heater attached to it, was used as an input to the temperature controller (Model CN2110, Omega, Stamford, CT) to maintain a constant temperature boundary condition on the top surface. A small hole was drilled in the middle of the wax compartment to attach a mm (0.032 in.) compression fitting. A Type-K thermocouple probe with a 304 SS sheath of mm diameter (Model TJ36- CASS-032-G-6, Omega Company, Stamford, CT) was inserted until the probe tip was approximately at the mid-point of the sample width. In order to ensure minimum heat loss to the surroundings the entire test sample was covered using 38.1 mm (1.5 in.) thick fibreglass insulation with an aluminized outer surface, having an average thermal conductivity of k = W/mK (Micro-Flex, Johns Manville Corporation, Denver, CO). The pipe plug thermocouples along with the thermocouple at the middle and bottom of wax compartment were connected to a National Instruments Data Acquisition (DAQ) unit that transmits the temperature readings of the thermocouple in real- 31

44 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM time to a personal computer equipped with a graphical programming environment to record the temperature readings (LabVIEW Signal Express V 3.0, National Instruments Corporation, Austin, TX). In order to ensure maximum attainable heat transfer from the copper plate to the foam struts, a Sn-alloy soldering paste (Loctite RP 15, Henkel AG and Company, Dusseldorf, GER) was applied to bond the two components (copper foam and copper plate) together. The solder paste was applied on both copper plates (with thermocouples welded) and then metal foam was sandwiched between them. To ensure good contact between the foam and copper plates, the entire sample was clamped using two C- clamps. After that, the entire sample along with C-clamps was placed in the oven and heated till the oven reached a temperature of 225. The sample was left to cool overnight in the oven. Molten wax was poured into the TESS device and allowed to solidify. Due to the difference in solid and liquid densities of wax, the volume of wax decreased upon solidification leaving an air gap at the top. When the wax was melted again, it expanded in volume and filled the air gap. A typical experimental run started off by turning on the heater to melt the wax. Temperatures at the center and bottom of the wax were recorded with the data acquisition device. Once the wax had completely melted the heater was switched off and the compressed air supply turned on. Mass flow rate of air was controlled by adjusting the globe valve. The inlet and outlet temperature of air were measured by the pipe plug thermocouple probes and were recorded by the data acquisition device. The compressed air supply was kept on for an hour. This experimental procedure was repeated for different flow rates of air ranging from 20.0 L/min to 60.0 L/min. 32

45 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Temperature Controller Air Mass Flow meter Data Acquisition Figure 3.2: TESS apparatus with instrumentation TC for measuring air temperature Heater Figure 3.3: Detailed view of TESS showing the placement of thermocouples used for measuring inlet and outlet temperature of air 33

46 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Figure 3.4: TESS with no Metal Foam Figure 3.5: TESS with Metal Foam on wax side 34

47 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM 3.3 Results and Discussion The heat transfer characteristics of the TESS can be analyzed using standard heat exchanger correlations described by Cengel [37]. Several assumptions were made in the following analysis: Natural convection and radiation heat transfer effects inside the porous medium are neglected i.e. heat transfer is considered to be only through conduction Physical properties of the fluid and solid phases remain constant throughout the temperature range Conduction resistance from the soldering paste and copper plate are neglected Physical properties of the fluid are evaluated at bulk mean temperature and 1 atm pressure The heat transfer coefficient is considered to be constant along the length of foam Convection is defined as the heat transfer from a solid surface to a fluid in the presence of bulk fluid motion. Despite the complexity of convection, the rate of convection heat transfer is observed to be proportional to the temperature difference and is conveniently expressed by Newton s law of cooling as [37] ( ) 35

48 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM From an energy balance the heat transfer to the fluid (air) flowing through the channel is equal to the increase in energy of the fluid ( ) ( ) The value of convective heat transfer coefficient - h is computed by using equation (3.3) in which is the temperature of copper plate that is measured experimentally with the thermocouple. The concept of similitude allows one to define dimensionless numbers that provides a means to compare systems with varying dimensions and flow parameters. In laminar flow, the hydrodynamic entry length as described by Kays and Crawford [55] is approximately: The hydrodynamic entry length for TESS from Equation (3.4) is found to be 2.85 m at the maximum flow rate of 60.0 L/min. In the present study as the length of TESS is only 200 mm the flow is still developing and so the fluid does not feel the effect of presence of polycarbonate wall on the other side. Hence, the fluid motion can be considered as flow over a flat plate and the characteristic length is taken to be length of the copper plate i.e. Lc = 200 mm. The factors controlling forced convection are defined as: Nusselt number 36

49 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Reynolds number where the mean velocity is determined from When metal foam was used, TESS was able to store approximately 180 ml of wax. As density of wax is 930 kg/m 3, the total mass of wax used was approximately kg. The latent heat of wax is 190 KJ/kg and so the TESS was able to store 31.8 KJ of energy. The volume occupied by wax was around 1.9 x 10-4 m 3 and the remaining volume i.e. 1 x 10-5 m 3 was occupied by metal foam. As density of copper is 8933 kg/m 3 the mass of metal foam used was approximately kg. Using the same ideology, if it is required to store 1 MJ of energy then the TESS should be designed such that it can hold 5.3 kg wax and that would require a total storage volume of 6.3 x 10-3 m 3. The mass of metal foam used will be approximately 2.8 kg. 37

50 Temperature (c) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Time (sec) 1cm (no foam) 2cm (no foam) 1cm (foam) 2cm (foam) Figure 3.6: Experimentally obtained temperature results plotted as a function of time while melting at a distance of 1 & 2 cm along the length of wax compartment for both with foam and without foam case. The experimental uncertainty is 2.6 in the temperature measurement. As paraffin wax melts in the temperature range of 42-50, it is considered to have melted completely when the temperature at depth of 2 cm reaches 55. As seen from the figure, without the use of metal foam, paraffin wax takes around 5000 seconds to melt completely whereas with the use of metal foam it takes around 1800 seconds. The time required to melt approximately the same amount of wax when using metal foams is reduced to 36% of that necessary without metal foam. Also, the temperature gradient in wax without metal foam is significantly higher than with metal foam. This reduction of temperature gradient can be attributed to the significant increase in effective thermal conductivity due to addition of 38

51 Temperature (c) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM metal foam so that, the temperature distribution in the foam-wax system is more uniform than it is in pure wax Beginning of Phase change End of Phase change Time (sec) 1cm 2cm Figure 3.7: Experimentally obtained temperature results plotted as a function of time during melting at a distance of 1 & 2 cm along the length of wax compartment with metal foam. The experimental uncertainty is 2.6 in the temperature measurement. As discussed earlier, the temperature gradient while melting is significantly lower than that in a pure wax system. Also, from the graph it can be seen that the phase change starts when the slope of the temperature profile starts decreasing and phase change is complete when the slope starts increasing again. From the graph, with the help of tangents drawn to the curve, it can be seen that phase change starts around 42 and it ends around

52 Temperature (c) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Time (sec) 1cm (no foam) 2cm (no foam) 1cm (foam on wax side) 2cm (foam on wax side) Figure 3.8: Experimentally obtained temperature results plotted as a function of time while solidifying at a distance of 1 & 2 cm along the length of wax compartment for both with foam and without foam case when the mass flow rate of air is 40.0 L/min. The experimental uncertainty is 2.6 in the temperature measurement. It can be seen that the foam-wax system solidifies more uniformly than the pure wax system. As discussed earlier, the effective thermal conductivity of foam-wax system is significantly higher than that of pure wax, which in turn reduces the thermal resistance to heat transfer and so the temperature gradient is very small (<5 ). The temperature of wax at a depth of 1 cm reaches 60 when used with metal foam, whereas without it the temperature reaches 70. As wax, with and without metal foam, is at different initial temperature at the beginning of solidification, it is difficult to say whether metal foam helps to increase heat transfer during solidification or not. 40

53 Temperature (c) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM T outlet (no foam) T inlet T outlet (foam-wax side) Time (sec) Figure 3.9: Experimentally obtained results for inlet and outlet temperature of air plotted as a function of time for both-with foam and without foam case when the mass flow rate of air is 40.0 L/min. The experimental uncertainty is 2.6 in the temperature measurement. It can be seen that the outlet temperature of air with metal foam is slightly higher than that of a pure wax system. This small increase in outlet temperature of air shows that addition of metal foam on wax side does not help much in terms of heat transfer to air. Addition of metal foam on wax side only helped to increase heat transfer during melting, but not during solidification. Hence, in order to increase the heat transfer to air, it becomes necessary to add metal foam on the air side as well. The addition of high porosity metal foam provides a large solid-to-fluid surface area, combined with a high thermal conducting metallic phase, such as copper, would allow for enhanced heat transfer by conducting heat from the metallic struts to the air flowing through them. 41

54 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Copper plates Thermocouples Figure 3.10: Photograph showing metal foam on both sides along with copper plates and thermocouples Figure 3.11: TESS with metal foam on both sides 42

55 Temperature (c) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Time (sec) 1cm (no foam) 1cm (foam-wax side) 1cm (foam-wax & air side) Figure 3.12: Experimentally obtained temperature results plotted as a function of time while solidifying at a distance of 1 cm along the length of wax compartment for all the three cases when the mass flow rate of air is 40.0 L/min. The experimental uncertainty in temperature measurement is 2.6. As discussed earlier, addition of foam on wax side does not significantly affect heat transfer to air, so foam was added on the air side, to determine its impact on heat transfer. As wax, at the beginning of solidification, is at uniform initial temperature, at least for foam on wax and for foam on wax as well as air side, it would be easier to conclude if addition of foam on air side helps to increase heat transfer to air or not. It can be seen from Figure 3.12 that, after an hour, wax is at a temperature of 24 when metal foam is used on both wax and air side, whereas at the same time wax is at a temperature of 34 when metal foam is used only on the wax side. Thus, wax solidifies much faster with foam on both wax and air side. Addition of metal foam on air side reduces the thermal resistance of heat transfer to air and so wax 43

56 Temperature (c) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM was able to lose heat and hence cool much faster than in case of pure wax or with metal foam on wax side T outlet (no foam) T inlet T outlet (foam-wax side) T outlet (foam-wax & air side) Time (sec) Figure 3.13: Experimentally obtained results for inlet and outlet temperature of air plotted as a function of time for all the three cases when the mass flow rate of air is 40.0 L/min. The experimental uncertainty is 2.6 in the temperature measurement. A significant increase in outlet temperature of air is seen for the case of metal foam on both sides as compared to the previous two cases pure wax and metal foam on wax side. This significant increase in outlet temperature of air is mainly due to: 1. Increase in the convective heat transfer coefficient h due to the tortuous path provided by metal foam to incoming air that causes the flow to be more turbulent 44

57 Nusselt Number CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM 2. Metal foams provide a large solid-to-fluid surface area and the presence of high thermal conducting metallic phase enhances heat transfer by conducting heat from metallic struts to the passing air R² = R² = Nu(no foam) Nu(foam-wax side) Nu(foam-wax & air side) Reynolds Number Figure 3.14: Experimentally computed Nusselt number with respect to Reynolds number for all the three cases. The experiments were performed at different flow rates of air for all the three cases and so it was necessary to combine the data from these different experimental runs and transfer them onto one graph to show the net effect of addition of metal foam. Hence, a graph of Nusselt as a function of Reynolds number is plotted for all the three cases in which Nusselt number and 45

58 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Reynolds number are calculated using Equation (3.5) and (3.6) respectively. It can be seen that Nusselt numbers for pure wax and foam on wax side are almost identical for all Reynolds number. The reason being that addition of metal foam on wax side only helped to reduce the melting time of wax and not much gain was obtained in terms of heat transfer to air. But, by adding foam on the air side a significant increase in outlet temperature of air was seen and that resulted in much higher Nusselt number for the same Reynolds number. The Nusselt number varies linearly with Reynolds number for all the three cases with an R 2 value of at least 99%. Figures 3.15 & 3.16 show the average power extracted Q (W) and average convective heat transfer coefficient (W/m 2 K) for different flow rates of air for all three cases of TESS. These values are averaged over the entire time range for which the air supply is on i.e seconds. 46

59 Convective heat transfer coefficient - h (W/m 2 K) Power extracted (W) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM No foam Foam-wax side Foam-wax & air side Flow-rate of air (L/min) Figure 3.15: Experimentally computed power extracted with respect to flow rate of air for all the three cases of TESS Flow rate of air (L/min) No Foam Foam-wax side Foam-wax & air side Figure 3.16: Experimentally computed convective heat transfer coefficient with respect to flow rate of air for all the three cases of TESS 47

60 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM 3.4 Thermal Resistance During the solidification process, the solidification front of wax is moving towards the top copper plate i.e. solidification front is moving towards the outer surface whereas heat transfer is in the opposite direction i.e. inwards through the already solidified PCM. Therefore, during solidification, the thermal resistance of solid wax increases [8]. Hence, it is essential to determine this thermal resistance and see how it varies with time. The power extracted from the TESS P varies inversely as the sum of the thermal resistance due to copper plate ( ), convective resistance on air side ( ) and resistance due to solidified layer of wax ( ) so that: The resistance due to the copper plate, per unit area, is given by: The convective resistance on the air side, per unit area, is given by: and the solid wax resistance, per unit area, that varies with time as: 48

61 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM where is the thickness of the solidification front in m. = 0 corresponds to the beginning of solidification and corresponds to end of solidification. Though varies with time, for comparison purposes, is considered to be 10 i.e. constant for all the three cases. The value of h used in Equation (3.10) is determined experimentally by making use of Equation (3.3). Also, as the copper plate is very thin (3 mm) would be very small and hence for further analysis it is neglected. These resistances being in series, the overall thermal resistance is expressed by The equation used for calculation of the front position with respect to time is the heat energy balance assuming that all the heat produced by the solidification at is withdrawn towards the external fluid i.e. air [10,12]. Thus: Substituting the expression for P from Equation (5.7) one gets, Integrating both sides we get, 49

62 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM ( ) Upon integration and substituting the limits we get an expression for solidification time required to reach length as: * + The time required for complete solidification of wax is calculated by substituting the value of as l and is labelled as. The value of l for all the three cases is the length of wax i.e m. Thus, * + As the time required for solidification would be different for all three cases of TESS, it becomes essential to non-dimensionalise it so that they can be compared against each other. The dimensionless solidification time = 50

63 Solid wax resistance - Rw (K/W) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM The effect of increase in wax resistance during the solidification process is illustrated by plotting the solid wax resistance against the non-dimensional solidification time. is calculated by making use of Equation (3.11) and substituting different values of from 0 to 0.02 m Non-dimensional solidification time ( ) No foam Foam-wax side Foam-wax & air side Figure 3.17: Computed value of solid wax resistance solidification time for all three cases of TESS with respect to non-dimensional Without foam, the solid wax contribution to the overall thermal resistance increases sharply during the first 20% of the solidification time. Without foam, after total solidification, solid wax resistance was approximately (K/W). Adding metal foam on the wax side, after total solidification, solid wax resistance was approximately (K/W). As shown earlier, adding metal foam on both wax and air side did not help to reduce the melting time of wax 51

64 Overall Thermal Resistance - R (K/W) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM and so the solid wax resistance at total solidification is same as that for the case of metal foam on wax side. However, adding metal foam on air side helped to decrease the overall thermal resistance R and this decrease can be seen when overall thermal resistance R is plotted against non-dimensional solidification time as shown in Figure The overall thermal resistance is calculated by making use of Equation (3.12) Non-dimensional solidification time ( ) No Foam Foam-wax side Foam-wax & air side Figure 3.18: Computed value of Overall Thermal Resistance R with respect to nondimensional solidification time for all three cases of TESS 52

65 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM 3.5 Three Stage Thermal Energy Storage System The aim of the study described in this section was to build an actual TESS device and test its performance. The TESS fabricated before were made out of polycarbonate and had only two stages i.e. it contained wax on one side and air on the other. The main drawback of two stage TESS was that the metal foam section through which air is passed had only its top surface in contact with wax whereas the bottom surface was in contact with the polycarbonate wall and so not all the available surface area of metal foam was used for heat transfer. The TESS described here had three channels of metal foam stacked on each other separated by copper plates. The top and the bottom channel of foam were filled with paraffin wax whereas air was passed through the middle channel of foam. Also, in order to prevent the formation of hot spots along the corners of TESS, compressed air was admitted through three separate inlets instead of just one. The three stage TESS was made out of 4.5 mm thick, hollow Aluminum box (McMaster Carr, OH,USA). The dimensions of the TESS were 200 mm x 76.2 mm (3 in.) x 76.2 mm (3 in.) (L x W x H). Two rectangular slots were milled on the inside of the Aluminum box to accommodate the copper plates. The copper plates helped to form three separate compartments as shown in Figure Two small holes were drilled, one on top and the other on bottom surface, in the middle of the Aluminum box, to attach a mm (0.032 in.) compression fitting as shown in Figure A Type-K thermocouple probe with a 304 SS sheath of mm diameter (Model TJ36-CASS-032-G-6, Omega Company, Stamford, CT) was inserted until the probe touched the copper plate. 53

66 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Figure 3.19: A cross section view of 3 stage TESS showing the 3 layers of foam separated by copper plates Figure 3.20: Top view of the TESS showing the hole for thermocouple fitting 54

67 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM These two thermocouples were used to measure the transient temperature variation as well as to ensure the complete melting of wax. Two square end plates (76.2 mm x 76.2 mm) were made out of 5 mm thick aluminum to seal the two faces of TESS. To introduce air supply, three holes were drilled along the center line of the aluminum end plates to attach three 13.0 mm compression fittings. In order to attach the end plates to the aluminum box, sixteen 3.0 mm diameter holes were drilled on both, the end plates as well as the mating surfaces of the aluminum box, so that the end plates can be bolted firmly to the aluminum box and thereby forming a rigid structure. A flexible silicon rubber heater (Model SRFG 304/10-P, Omega Company, Stamford, CT) with dimensions of 7.62 mm x mm (3 in. x 4 in.) is used to melt wax during the heating process. Four such heaters are used, two on each side as shown in Figure 3.21, with a gap between them to provide an opening for the thermocouple. All four heaters were connected in parallel. The heater has an electrical resistance of Ω and produces a maximum power output of 120 W at 115 V. Power to the heater is provided by a variable transformer that is used to supply 50 V to the heater to ensure that the TESS is not heated rapidly The remaining instrumentation (i.e. thermocouple probes for measuring inlet and outlet temperature of air, air Mass Flow meter and the air circulation loop) was the same as used for testing the two-stage TESS described in the previous section. The three stage TESS was able to contain approximately 250 ml of wax in each compartment. As there were two such wax compartments, the total volume of wax used was approximately 500 ml. 55

68 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM End caps Heater Figure 3.21: Photograph showing the flexible silicon rubber heaters that were used for melting wax Figure 3.22: Three stage TESS apparatus with instrumentation 56

69 Temperature (c) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Time (sec) T inlet T outlet(20) T outlet(30) T outlet(40) T outlet(50) T outlet(60) Figure 3.23: Experimentally obtained results for outlet temperature of air plotted as a function of time. The mass flow rate of air in L/min is indicated in parentheses. The experimental uncertainty is 2.6 in the temperature measurement. It can be seen from Figure 3.23 that even after 5400 seconds, the outlet air is at a higher temperature as compared to two stage TESS for the same mass flow rate condition. The difference in temperature is approximately 7-9 as seen from Figure The three stage TESS is broader and has wax compartments on both sides as compared to the two stage TESS. Hence, the three stage TESS will be able to store more than twice the amount of wax and thereby latent energy, as compared to the previous case. Thus, as the available energy for extraction is higher, the outlet air is at a higher temperature for the three stage TESS. However, it should be noted that the air still reaches a maximum temperature of around 46 for both two stage and three stage TESS. 57

70 CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM This shows that addition of one more wax compartment does not help to increase the maximum attainable temperature of the TESS. However, it does help to supply air at a high temperature for a longer duration of time. Hence, it can be concluded that the number of wax or air compartments depends on the application. If an application requires fast energy extraction or high temperature supply of air for a short period of time (< 1 hour) then it is economical to have only one wax compartment and the number of air compartments depend on how fast the energy needs to be extracted. On the other hand, if an application requires high temperature supply of air for a long period of time (> 1 hour) then it is economical to have more than one wax compartment and the total number of wax compartments depend on the duration for which the high temperature air needs to be supplied. As the experiments were performed for different flow rates of air ranging from 20.0 L/min to 60.0 L/min, a graph of Nusselt vs. Reynolds number is plotted similar to the one for two stage TESS. Nusselt number and Reynolds number are calculated using Equation (3.5) and (3.6) respectively. It can be seen that Nusselt number varies linearly with Reynolds number with an R 2 value of at least 99% 58

71 Nusselt Number CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM R² = Reynolds Number Figure 3.24 : Experimentally computed Nusselt number with respect to Reynolds number for all the three stage TESS Figures 3.25 & 3.26 show the average power extracted Q (W) and average convective heat transfer coefficient (W/m 2 K) for different flow rates of air. These values are averaged over the entire time range for which the air supply is on i.e seconds. 59

72 Average convective heat transfer coefficient (W/m 2 K) Average Power extracted (W) CHAPTER 3. THERMAL ENERGY STORAGE WITH METAL FOAM Flow-rate of air (L/min) Figure 3.25: Experimentally computed average power extracted Q (W) with respect to flow rate of air Flow rate of air (L/min) Figure 3.26: Experimentally computed average convective heat transfer coefficient (W/m 2 K) with respect to flow rate of air 60

73 CHAPTER 4. NUMERICAL SIMULATION OF TEMPERATURE PROFILE USING ENTHALPY METHOD Chapter 4 Numerical Simulation of Temperature Profile using Enthalpy Method 4.1 Introduction Phase change of materials is an example of a boundary value problem, named after the physicist Jozef Stefan, who introduced the general class of such problems in Very few analytical solutions are available in closed form and the ones that are available are for onedimensional heat transfer in an infinite or a semi-infinite region [17]. When the PCM changes state, both liquid and solid phases are present and they are separated by a moving interface between them. There have been several numerical methods developed to deal with the problem of phase change but the most attractive and common ones are the enthalpy methods. The enthalpy method simplifies the phase-change problem since the governing equations are same for the two phases and the method does not require explicit treatment of conditions on the phase change boundary. The fact that the temperature and liquid fraction fields are decoupled and thus can be calculated separately, makes it relatively easy to implement [9]. 61

74 CHAPTER 4. NUMERICAL SIMULATION OF TEMPERATURE PROFILE USING ENTHALPY METHOD 4.2 Mathematical Model The two-stage TESS (with metal foam) problem as described in the previous section is solved numerically during melting. In order to check the validity of the code, temperature profile that is obtained from the numerical code would be compared with the experimental temperature results obtained at a depth of 1 cm shown in Figure 3.7. In the present analysis the problem for phase change is solved numerically under the following assumptions: The effects of natural convection within the melt are neglected and heat transfer is considered to be one dimensional i.e. heat transfer occurs only in the direction normal to the surface The PCM (paraffin wax) is assumed to have a definite melting point ( = 50 ) i.e. phase change is isothermal The physical properties of the solid and fluid phases of PCM are assumed to be same and constant over the entire temperature range i.e. volume change is neglected Thermal resistance across the copper plate is neglected Lateral sides of the TESS are well insulated The problem is solved without considering the presence of metal foam and the physical properties such as density and specific heat are calculated by accounting for the volume fraction of each substance as described in Equations (2.3) and (2.4). Thermal conductivity value derived from Boomsma s model [5] is used in the code 62

75 CHAPTER 4. NUMERICAL SIMULATION OF TEMPERATURE PROFILE USING ENTHALPY METHOD As a result of the above assumptions, the enthalpy formulation for the conduction-controlled phase change can be written as [9] ( ) where H is the total volumetric enthalpy, which is the sum of sensible and latent heat: and where In the case of isothermal phase change, the liquid fraction is given by [9]: { Substituting Equation (4.2) into Equation (4.1) we get: ( ) 63

76 CHAPTER 4. NUMERICAL SIMULATION OF TEMPERATURE PROFILE USING ENTHALPY METHOD Equation (4.5) together with equations (4.3) and (4.4) and the appropriate initial and boundary conditions represents the mathematical model of conduction controlled isothermal phase change. 4.3 Numerical Solution For the problem of one-dimensional phase change, Equation (6.5) reduces to: ( ) Thus, ( ) The fully implicit discretization equation for an internal node i can be written as 64

77 CHAPTER 4. NUMERICAL SIMULATION OF TEMPERATURE PROFILE USING ENTHALPY METHOD Figure 4.1: Discretization domain for one-dimensional phase change problem with boundary conditions Consider first the case when control volume i is fully solid or fully liquid. In that case, from the definition of sensible enthalpy Equation (4.3) and the liquid fraction Equation (4.4), we have [9]: and After introducing Equations (4.9) and (4.10), Equation (4.8) reduces to a heat diffusion equation: 65