Finite element analysis on solar energy harvesting using ferroelectric polymer

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 115 (2015) 722–732 www.elsevier.com/locate/solener

Finite element analysis on solar energy harvesting using ferroelectric polymer Manish Sharma, Aditya Chauhan, Rahul Vaish ⇑, Vishal Singh Chauhan School of Engineering, Indian Institute of Technology Mandi, Mandi 175 001, India Received 26 September 2014; received in revised form 11 February 2015; accepted 15 March 2015 Available online 7 April 2015 Communicated by: Associate Editor Bibek Bandyopadhyay

Abstract Solar energy harvesting through pyroelectric effect has been under the scrutiny of researchers since the past few years. However, the low energy density coupled with requirement of rapid temperature fluctuations has hindered any successful commercial ventures in this field. This study is an attempt towards eliminating these drawbacks associated with pyroelectric energy generation using ferroelectric polymers. Langmuir–Blodgett Polyvinylidene difluoride copolymer–Trifluoroethylene–Chlorofluoroethylene P(VDF–TrFE–CFE) thin films were used in conjunction with pyroelectric effect and forced cooling to simultaneously increase energy and power density. In this regard, a two faceted approach of linear pyroelectric harvesting and harvesting through Ericsson cycle have been analyzed and compared. The models for the same have been developed and analyzed using finite-element method. Two separate cases of air cooling and water cooling were investigated. Peak values of power density for water cooling and air cooling processes (direct pyroelectric effect) are found to be 0.437 lW/cm3 and 0.2 lW/cm3, respectively. These values are obtained at optimized value of load resistance and load capacitance (RL = 7 MX and CL = 2 lF for water cooling while RL = 14 MX and CL = 2 lF for air cooling). The maximum values of power density that can be obtained from water and air cooling process are 19.65 mW/cm3 and 16.35 mW/cm3 (using Ericsson cycle) at 0.013 and 0.011 Hz frequency, respectively. It was also observed that water cooling is more efficient than air cooling for energy harvesting. This study can lead to growth in the field of solar energy harvesting using pyroelectric effect. Ó 2015 Elsevier Ltd. All rights reserved.

Keywords: Pyroelectric; Ferroelectric; Olsen cycle; Energy harvesting

1. Introduction Solar energy has been projected as a prominent source of renewable energy for future energy requirements. The solar radiation can be directly utilized as an energy source for powering many devices and systems. There are numerous ways to harvest solar energy including photovoltaic cells, solar thermal power plant and solar thermoelectric generators. Photovoltaic cells convert sunlight directly into ⇑ Corresponding author. Tel.: +91 1905 237921; fax: +91 1905 237945.

E-mail address: [email protected] (R. Vaish). http://dx.doi.org/10.1016/j.solener.2015.03.029 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.

electricity using suitable band-gap semiconductor materials such as Silicon and Gallium Arsenide (Gra¨tzel, 2005; Mickey, 1981). Solar thermoelectric generators produce electro-motive force using the Seebeck effect employing heterogeneous metallic junctions and fixed thermal gradients (Telkes, 1954; Chen, 1996). However, solar energy harvesting can also be achieved using pyroelectric materials. The change produced in the spontaneous polarization of a non-centrosymmetric dielectric material, as a consequence of the change in its temperature, is termed as pyroelectric effect. Pyroelectric materials form a subset of the piezoelectric materials and contain all ferroelectric

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Nomenclature Fss am ag qm qg ID Id eg em Tg hg kg Qs QR Hab Isolar In CL RL Tm hm km

angle factor between surface and sky absorption coefficient of pyroelectric material absorption coefficient of glass plate density of pyroelectric material density of glass plate direct solar radiation diffused solar radiation emissivity of glass plate emissivity of material surface glass temperature glass thickness glass thermal conductivity heat supplied to the material in heating heat released from the material in cooling heat absorption rate of material by solar radiation intensity of solar radiation intensity of solar radiation normal direction load capacitance load resistance material temperature material thickness material thermal conductivity

materials. The change in polarization stems from the shift in the degree of non-centrosymmetry owing to thermal lattice vibrations corresponding to different temperatures. This change in polarization can be used for generation of electric current and subsequently electric power by using suitable means. Direction of the pyroelectric current changes with changing nature of thermal gradient. As the materials temperature increases (dT/dt > 0) polarization decreases due to re-orientation of dipole moment. It results in the generation of an electrical current in external circuit. On the contrary, in case of material’s cooling (dT/dt < 0) polarization increases as dipoles gain their orientation, causing flow of current in reverse direction. Utilization of pyroelectric effect for energy generation from solar temporal variations offers to be a promising prospect. Literature reveals a number of studies discussing the pyroelectric effect and its possible applications for energy harvesting (Yang et al., 2012; Harb, 2011; Cuadras et al., 2010; Sebald et al., 2009; Fang et al., 2010). However, attempts at commercialization of linear pyroelectric harvesters have been limited owing to the low energy and power density associated with such methods of harvesting. However, this drawback can be easily offset by the sheer economics of operation associated with a pyroelectric generator. Pyroelectric harvesting technology employs solid state conversion mechanism through pyroelectric phenomenon involving little or no moving parts. Additionally, these systems are essentially autonomous and require little to no maintenance when generating heat from transient

Cm Rm IP p a b U cm cg Ag Am Tt To Tf t th tc ha hw Vm Vg

material capacitance electric resistance of material pyroelectric current pyroelectric coefficient solar azimuth angle solar altitude angle surface inclination to the vertical specific heat capacity of pyroelectric material specific heat capacity of pyroelectric material surface area of glass surface area of material time dependent temperature profile of pyroelectric material temperature of ambient air final time of cycle time period of cycle heating duration cooling duration thermal convective coefficient of air thermal convective coefficient of water volume of pyroelectric material volume of glass plate

temporal gradients. Lastly, when employing polymer thin films, the commercial benefits associated with installing and operation of a pyroelectric conversion system is expected to be high when compared to either semiconductor-based solar cells or hetero-junction based thermo-electric generators. In order to further reduce the cycle time and increase power output, cooling using various natural and artificial sources has been proposed. Studies have been reported where a fraction of the generated energy is redirected to pump a coolant for rapid heat exchange (Navid et al., 2010). Additionally, Olsen and co-workers have proposed an Ericsson-like cycle for enhanced thermal energy harvesting by successfully utilizing induced pyroelectricity (Fang et al., 2010). Olsen cycle involves high field energy harvesting and uses induced polarization by means of electric field. We have also investigated thermal energy harvesting through Olsen cycle in our previous studies (Chauhan et al., 2014; Vats et al., 2014; Patel et al., 2014). The present study is an attempt to harvest solar energy with use of ferroelectric polymers (direct pyroelectric effect and Ericsson/Olsen cycle). Two separate case studies have been discussed, one each for direct pyroelectric effect and for enhanced conversion using Ericsson cycle. A comparative analysis has been provided to compare the power and energy outputs obtained from both the techniques. The approach involves investigating energy harvesting while employing cooling through external means. A suitable system was designed and analyzed for each of the cases

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mentioned above. The assumptions and analytical details have been discussed in the subsequent sections. To the best of our knowledge, no similar attempt has been made till date. 2. Materials and methods In the present study, we have made use of polyvinylidene fluoride–trifluoroethylene–chlorofluoroethylene P(VDF–TrFE–CFE) ferroelectric co-polymer. PVDF and its co-polymers have been the subject of rigorous investigation owing to their excellent ferroelectric properties. PVDF has also been reported for large electrocaloric effect (Liu et al., 2010; Wang et al., 2011). PVDF is produced by polymerization of vinylidene difluoride monomers. It is a low density fluoropolymer and consists of two chain conformations namely trans (T) and gauche (G). Depending upon the arrangement of conformations, three phases can be obtained. These are alpha (TGTG), beta (TTTT) and gamma (TTTGTTTG) phases. Out of these three, beta phase is capable of exhibiting ferroelectric behavior. PVDF is often co-polymerized with trifluoroethylene (TrFE) and chlorofluoroethylene (CFE) to improve the crystallinity of the polymer. The co-polymers are credited with having improved piezoelectric and pyroelectric response and have been extensively reported in the literature (Bao et al., 2007; Chu et al., 2006; Bauer et al., 2006). Recently, Liu et al. have reported huge room temperature electrocaloric effect in Langmuir–Blodgett P(VDF–TrFE–CFE) thin films (Liu et al., 2010). This particular composition is credited with having high saturation polarization, high dielectric breakdown strength and low dielectric loss. These thin films were prepared using Langmuir–Schaefer horizontal deposition. The films were reported to have a Curie temperature of 390 K (Patel et al., 2014). Thermally deposited aluminum was used as electrodes to form the capacitor structure for the polarization versus electric field (P–E) hysteresis measurement. These P–E loops were used in present study to simulate the performance. 2.1. Energy harvesting using pyroelectric materials Pyroelectric effect can be used to generate electrical energy using time varying   thermal excitations. For a temperature gradient of dT , the generated pyroelectric current dt (IP) can be estimated as:   dT Ip ¼ A  p  ð1Þ dt where A is the surface area of the pyroelectric material (perpendicular to dipole orientation) p is the pyroelectric coefficient and dT is the heating/cooling rate (Nguyen dt et al., 2010). Eq. (1) is only valid for a small temperature change due to nonlinearity in behavior of materials. Regardless, it forms the basis for all forms of pyroelectric

Fig. 1. Electrical circuit for pyroelectric energy harvesting.

conversion systems. This generated current is then supplied to external circuit as shown in Fig. 1 where load resistance and load capacitance are connected in parallel to the material. The value of output voltage generated can be evaluated using Eq. (2). C

dV V þ ¼ IP dt R

ð2Þ

The cumulative capacitance C is the sum of both material capacitance and parallel load capacitance C = CL + Cm where CL is load capacitor and Cm is material capacitance. Similarly the equivalent value of resistance is R1 ¼ R1L þ R1m ; RL and Rm being load and material resistance respectively. Eq. (2) will further be utilized for obtaining power density (Cuadras et al., 2010; Sebald et al., 2009; Dalola et al., 2010). A number of reports have been made on the figure of merits of pyroelectric devices (Whatmore, 1986, 1991; Whatmore et al., 1987; Lee et al., 1998). Furthermore, it has been reported that direct pyroelectric effect could be utilized to harness thermal energy using various thermodynamic-cycles (Olsen et al., 1981). A comparison of pyroelectric harvested energy density was made using Lenoir and Ericsson cycle for PMN-25PT single crystal. It was reported that the Ericsson cycle generated twice the energy (35 mJ cm3) when compared to Lenoir cycle (17 mJ cm3). The efficiency of Ericsson cycle was observed to be around 15% of Carnot cycle. It was concluded that Ericsson cycle is comparatively more efficient for thermal energy harvesting than other cycles (Mohammadi and Khodayari, 2012). In the present study, we have investigated solar energy harvesting possibilities using Olsen/ Ericsson cycle. 2.2. Olsen/Ericsson cycle The P–E hysteresis loops represent the dielectric losses associated with the dipolar switching behavior in ferroelectric materials. This loss is presented in the form of material heating and is indicative of the difference in the energy required to polarize and depolarize a ferroelectric material. It is reported that reversible polarization can be done to trace a clockwise loop between two different temperatures

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and can be used to reverse the process of electricity to heat conversion. This can be effectively used to generate electrical energy from thermal energy. The technique was first reported by Olsen and co-workers and is popularly known as the Olsen or Ericsson cycle (Nguyen et al., 2010; Olsen et al., 1981; Olsen and Evans, 1983; Ryder and Raman, 1992; Olsen et al., 1985). A schematic representation of the same is shown in Fig. 2. The shaded area in Fig. 2, (1–2–3–4–1) gives the harvested energy density per unit volume of the material. Application of unipolar field can substantially increase the harvested energy as the dipolar

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reorientation (hysteresis) losses are reduced. The improved energy harvesting is represented by the shifted loop (10 –2– 3–4–10 ). Thus, Olsen/Ericsson cycle consists of two isoelectric (constant electric field) (2–3; 4–1) and two isothermal (constant temperature) (1–2; 3–4) processes as shown in Figs. 2 and 3. The details of the processes are discussed below: Process 1–2: Electric field is raised from lower value (EL) to higher value (EH), thereby increasing the polarization of the material from 1 to 2. This consumes electrical work of polarization (WP) equivalent to charging a capacitor. This

Fig. 2. Schematic for thermal energy conversion using Ericsson/Olsen cycle.

Fig. 3. Schematic for polarization change in Ericsson/Olsen cycle.

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process is completed at a constant temperature (TC). EH is selected such that saturation polarization is achieved at the temperature of operation. Similarly EL is decided by either the intersection point of the two polarization curves or coercive electric field, whichever is deemed best suited for operation. Process 2–3: Now heat (QS) is supplied to the material causing a thermal depolarization. The drop in polarization (2–3) creates a pyroelectric current which can be harvested for generation and storage of electrical energy. The whole process is carried out at constant electrical field (EH) while the temperature of the material increases to TH. Process 3–4: In the third step, the electric field is lowered to EL at a constant temperature (TH). This causes the induced polarization to fall to (4) and a weak discharge current is generated. The lower value of electric field is required to create the necessary difference of energy between the polarization and depolarization processes. Process 4–1: Lastly, part of repolarization is recovered by cooling the material to its initial temperature. This restores the value of polarization to (1). The heat (QR) rejection is carried out at constant electric field (EL). This restores the material to its original state and completes the cycle. The energy density (ND) per unit volume of the material obtained by the cycle can be estimated as (Nguyen et al., 2010; Olsen et al., 1981): I ð3Þ N D ¼ E  dD Here, E and D represent electric field and electric displacement vector respectively and Eq. (3) gives the surface integral of the E with respect to change in D. Using Eq. (4), the power density (PD) of the cycle can be calculated as: PD ¼ ND  f

ð4Þ

where f is the frequency of the cycle. It has been claimed that energy density of the proposed cycle is dependent on the frequency of operation (Zhu et al., 2009; Lee et al., 2012; McKinley et al., 2012; Ikura, 2002). This dependence stems from the fact that finite amount of time is taken to reach the higher operating temperature extremes. Thus at higher frequencies the operating temperature extremes are difficult to achieve. Hence decreased energy density is obtained for higher frequency of operation. The reported energy density obtained using Olsen/ Ericsson cycle is around 103 times higher than those employing direct pyroelectric effect as the magnitude of change in polarization is significantly larger in the former approach (Bao et al., 2007; Chu et al., 2006). The original experiment performed by Olsen demonstrated the cycle for PZST and P(VDF–TrFE) thin films. Thereafter, many attempts have been made to improve the efficiency of the cycle by design modifications such as cascading (Olsen et al., 1985). Recently, a prototype was fabricated which obtained an operating efficiency 0.55 times Carnot’s efficiency between the same working temperature range (Navid et al., 2010).

2.3. Proposed design The system required for uninterrupted energy generation necessitates continuous change in heat transfer rate. For this purpose, a simple structure with glass plate covering the material surface was used. This is similar to those used in solar panels to utilize optimum solar radiation. The ultraviolate radiation gets transmitted from transparent glass to material, and this radiation is absorbed by material and is converted to higher wavelength radiation which is reflected back towards glass plate that does not allow it to escape. Glass plate also minimizes convection losses which further adds to the heat content. To account for this gain, higher glass and material properties are assumed. Cooling has been achieved by two different methods and their effect is investigated in terms of two different cases: Case 1: Heating process is assumed to be completed using natural air convection cooling condition on upper and lower surfaces of glass and material respectively, while cooling process is performed under forced air convection condition with ambient air velocity 3 m/s on both upper and lower surfaces. Case 2: Heating process is assumed with natural air convection cooling condition on upper surface of glass as well as lower surface of material while cooling process is performed with natural air convection condition on upper surface of glass and forced convection (using water flow under gravitational effect) on lower surface of the pyroelectric material. The following assumptions were made for solving the analytical part: Assumptions 1. All walls other than the liquid-material interface and material-glass interface are assumed to be perfect thermal insulators while liquid-material interface is assumed to be electrically insulated only. 2. All material properties (except ferroelectric behavior) are assumed to be temperature invariant. 3. The fluid (water) is assumed to be incompressible. 4. All edge effects are neglected. 5. Fluid flow is assumed to be through natural (gravitational) convection. 6. The flow of fluid is unidirectional on surface/interface. 7. Forced convection air cooling is assumed to be at an ambient air flow of 3 m/s.

2.4. Methodology The intensity of incoming solar radiation and all other ambient conditions are collected from official reports as provided for New Delhi, India by the Meteorological Society (Indian Meteorological Department, 2014). Both types of radiations namely direct and diffused have been considered for heating effects. The direct radiation as incident on the surface has been considered for the latitudinal

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orientation and horizontal orientation of the mounted setup. This intensity can change from maximum (when surface is normal to sun’s rays) to minimum (when surface is parallel to sun’s rays). Direct solar radiation I D on the inclined surface can be calculated as: I D ¼ I n ðcos b cos acosu þ sin bsinuÞ

ð5Þ

where I n is intensity of radiation in normal direction and b: solar altitude angle; ;: surface inclination to the vertical; a: solar azimuth angle. While the diffused radiation I d can be calculated as: I d ¼ I n  F ss

ð6Þ

where Fss = angle factor between surface and sky. Therefore, the combined intensity of radiation falling on the surface of the setup can be calculated as: It ¼ Id þ ID

ð7Þ

The peak intensity of solar radiation is assumed as 1300 W/ m2, which is standard optimum solar radiation intensity falling on the earth’s surface during normal (90°) inclination. However, due to environmental effects and other constraints this value is reduced to 1000 W/m2. Even this value of radiation is not constant and varies with time of the day, from a minimum (in evening) to maximum (during the afternoon). The intensity may vary from 400 W/m2 at 9 am in the morning to 700 W/m2 in peak hours between 12 pm to 3 pm. Thus, typical average values of solar radiation have been considered for calculating the energy conversion using pyroelectric material as a function of time. Heat absorption by the material will cause a rise in its temperature. Due to this increment in body temperature, a combined effect of conduction and convective heat transfer will account for the heat loss from material surface. To minimize this effect, we make use of a transparent glass plate glazing for covering the pyroelectric material (Agrawal and Tiwari, 2011; Prakash, 1994; Zondag et al., 2003). Numerical formulation for both heating and cooling process is given below: 2.4.1. Heating process At 0 6 t 6 th , where t is the heating time duration ranging from 0-th. When air is in contact with the material surface and incoming solar radiation is being used for heating the material, temperature rises from environmental temperature T 0 to its equilibrium temperature. The net heat stored in the material is the difference of the heat absorbed by the material and the heat lost to the environment. The governing equation for this study has been adopted from Krishnan et al. (2013), Chow et al. (2009) and can be represented as: qg cg V g

dT t Tt  T0 ¼ ag Ag I solar   Qr ; dt rg þ rair þ rm

0 6 t 6 th ð8Þ

qm cm V m

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dT t Tg  Tm ¼ eg am Am I solar þ dt rg þ rm Tt  T0   Qr ; 0 6 t 6 t h rg þ rair þ rm

ð9Þ

where Qr ¼ eg rAg ðT 4t  T 40 Þ and rg ¼

hg hm 1 1 ; rm ¼ ; rair ¼ ; rw ¼ ; r ¼ 5:87  108 : h a Ag Ag hw k g Ag KA

where rg: thermal resistance of glass; rm: thermal resistance of material; rair: air thermal resistance and rw: water thermal resistance. These equations are in the form of non-homogeneous first-order differential equation. The complete analysis of the model is based on lumped capacitance system, as the value of Biot number is found to be (0.1). From Eqs. (8) & (9), the value of time required for heating the pyroelectric material can be estimated for given temperature range. Once the thermal equilibrium achieves, there is no change in polarization. To regain the polarization change, cooling of material is required which is achieved by flow of water on the surface of electrically insulated material under gravitational effect through a dielectric surface-plate interface. Cooling through water decreases the cooling time and hence increases cycle frequency and subsequently the power output. Heat transfer during cooling process is mentioned below. 2.4.2. Cooling process From th 6 t 6 t f . In case 1, for forced air cooling, high speed air is flowed from both the top of glass surface and the bottom of material surface (which decreases the convective resistance). While in case 2, for water cooling, the water is in contact with the lower side of electrically insulated material surface. While upper side of glass surface is assumed to have natural air cooling. Owing to the low cooling time and rapid heat transfer rate, the effect of heating due to solar radiation is estimated to be very low during this time. The cooling of material takes place to near environmental temperature. Case 1: qg cg V g

dT t dT t þ qm c m V m ¼ ag Ag I solar dt dt ðT t  T 0 Þ  rairforced þ rm þ rg  Qr ; th < t < tf

for air ð10Þ

Case 2: qg cg V g

dT t dT t ðT t  T 0 Þ þ qm c m V m ¼ ag Ag I solar  rw þ rm þ rg þ rair dt dt  Qr ; th < t < tf

for water ð11Þ

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Value of rair varies with different states of process. For heating process, these values are higher because of air convection and can be calculated based on an assumed air speed corresponding to natural convection. While for cooling in case 1, the value of rair varies with the wind speed, has been calculated as per the assumed wind speed of 3 m/s. Value of ha is calculated separately for heating and cooling processes. While for case 2, rair and rw are total thermal resistance for air and water respectively. The value of rw is very low for high convective coefficient. The flow of water is assumed to be at atmospheric pressure head. Water was flowed through lower surface of the pyroelectric material while keeping its surface electrically insulated. Air cooling (natural convection) is assumed from the upper surface of glass plate. The simulation and obtained results have been discussed in the subsequent sections. 2.5. Simulation The simulation was performed using finite element method for solar radiation based on average value of solar intensity from 9 am to 5 pm. With that solar intensity, the equilibrium temperature of surface of material was measured (keeping in consideration the air mass effect of environment). For these intensities, the values of higher equilibrium temperature were calculated. All the equations described above were used to obtain the results for threedimensional heat diffusion model. A 3-D model geometry was utilized for physical representation of the setup as represented in Fig. 4 (one side kept facing the solar radiation). Assuming model is rotating along with the direction of incident solar radiation using a simple one-directional solar tracker. Time varying (heating and cooling processes) are computed. Discretized finite element model is obtained from equations (Sebald et al., 2009; Fang et al., 2010;

Navid et al., 2010; Chauhan et al., 2014) by substituting finite element approximation for dependent variable T. This approximation is selected so the time dependence variable is separated from spatial variation. Uniform tetrahedral mesh was created for model. In tetrahedral mesh generation, each segment is divided into smaller sub segments. Weight residue based galerkin (finite element method) is used for weak formulation. ZZZ

  2     @T @T 2 @T 2 @T þ qc w k þ þ þ bT  aT dV ¼ 0 @x @y @z @t v

ð12Þ

The elemental matrix equation obtained is given as follows: ½C e fT_ e g þ ½K e fT e g ¼ fQe g  fqe g ð13Þ h i C eij ¼ V qe ce fN ei gfN ej g dV is elemental heat capacity matrix, fN e g is shape function and superscript T is transpose h ofe it. i e e e @N @N @N e @N @N e @N e K ij ¼ v k @xi @xj þ @yi @yj þ @zi @zj þ bfN ei gfN ej g dV is conductivity matrix. {Qe } = ev afN ei gdV is source heat flux vector. {qe } = ev bfN ei gdV heat loss vector due to convection and surface to ambient radiation boundary condition. Dimensions of C and K are n  n, n is number of nodes. Elemental matrices are assembled and boundary conditions are applied. The assembly process adds the entries of each element matrix into the entries of the global matrix. {T_ e } and {T e } are the nodal temperature rate vector and nodal temperature vector. For solving transient problem time discretization is performed using Taylor expansion

fT nþ1 g ¼ fT n g þ DtfT_ nþ1 g

Fig. 4. Schematic for solar energy harvesting using water and air cooling cycles.

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Table 1 Material properties of P(VDF–TrFE–CFE). Properties 3

Density (kg/m ) Thermal conductivity (W/m K) Specific heat capacity (J/kg K) Specific resistivity (ohm cm) Permittivity Pyroelectric coefficient (C/m2 K) Absorption coefficient of radiation Surface emissivity Thickness (mm) Surface area (cm2)

Symbols

Value

qm Km Cpm Rm er P am em hm Am

1760 0.14 1363 2.00E+14 8.85E11 3.00E05 0.6 0.6 0.2 100

Table 2 Material properties of silica glass. Properties 3

Density (kg/m ) Thermal conductivity Specific heat capacity (J/kg K) Specific resistivity (ohm cm) Permittivity Absorption coefficient of radiation Surface emissivity Thickness (mm) Surface area (cm2)

Symbols

Value

qg Kg Cpg Rg er ag eg hg Ag

2230 0.55 750 2E+19 4.1595E11 0.8 0.8 0.1 100

Fig. 5. Temperature variation vs time plot for P(VDF–TrFE–CFE) polymer for water and air cooling cycles.

3. Results and discussions

the temperature of both material surface and glass surface to get uniform higher heating time is considered. Now keeping this temperature range into consideration, the value of output voltage is obtained using Eq. (2). This is further used for obtaining the value of power density of material using pyroelectric effect for an optimized value of load resistance RL (7 MX and 14 MX) and load capacitance CL (2 lF). The value of load resistance is varied from 2 to 60 MX keeping load capacitance constant for finding maximum power density and average power density for both water and air cooling methods. The obtained value of output voltage (Fig. 6) attains a maximum value of 2.37 V and 1.1 V for water and air cooling process respectively. Figs. 7 and 8 display the value of maximum and average power densities respectively for both cooling methods considered under study. The obtained value of peak power density at 7 MX load resistance is 0.437 lW/cm3 for water cooling cycle and 0.2 lW/cm3 for air cooling cycle at 14 MX resistance. Although the value of average

The value of material temperature is obtained by simulating Eqs. (7)–(9) for heating and cooling of pyroelectric material for both air and water cooling cycles. The equilibrium temperature for the material is varied from 300 K to 330 K by changing the time elapsed for different processes. Proceeding on the assumption that the application of electric field is done isothermally, values for power density and energy density can be obtained for this temperature range and cycle time. As shown in Fig. 5, the variation in temperature is obtained in temperature range 300 K to 330 K. The initial value of material temperature is considered as 293 K. The material is allowed to heat till 330 K beyond which cooling process is applied to lower its temperature down to 300 K, using water and forced air cooling cycles. Due to the higher thermal diffusion time required between glass and pyroelectric materials, there is a finite temperature difference between pyroelectric material and glass surfaces for higher frequency of process. To allow

Fig. 6. Output voltage obtained from pyroelectric effect under water and air cooling cycles.

Dt is time increment is each step. A backward difference (BDF) scheme is used for time discretization. Further model was coupled with electrical model for getting electric voltage (Dehghani et al., 2010; McIntosh et al., 2014). All the values for physical properties used in the simulation are mentioned in Tables 1 and 2 (for both glass plate and pyroelectric material). The value of generated current is obtained from Eq. (1). This current can further be used for finding power density generated from the material using direct pyroelectric effect.

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Fig. 7. Plots for peak power density and load resistance.

Fig. 8. Average power density vs load resistance plot.

power densities are 0.044 lW/cm3 and 0.047 lW/cm3 for water and air cooling cycles respectively. Further increase in load resistance will not hike the power density. This is in accordance with the maximum power transfer theorem. As the optimum value of output voltage is attained any further increase in load resistance will only contribute towards increasing losses. As shown in Figs. 7 and 8, the plotted curves for power densities first increases with rise in load resistance attains optimum value of power densities at 7 MX and 14 MX respectively for water and air cooling cycles then start decreasing with further rise in load resistance. The value of peak power density for water and air cooling process due to direct pyroelectric effect is estimated to be 0.437 lW/cm3 and 0.2 lW/cm3 for optimized load resistance of 7 MX and 14 MX while load capacitance of 2 lF. These figures represent an extremely low measure and can only provide valuable contribution in sensor applications. This has been the primary drawback preventing successful

Fig. 9. Energy density vs EL plots for temperature ranges 300–330 K and 300–350 K.

commercialization of pyroelectric harvesting devices. The investigation is now extended to incorporate harvesting possibilities using Olsen/Ericson cycle for the same limit of temperature variation. Surface integrals can be performed on the P–E hysteresis loops for the material under consideration to obtain the value of harvested energy density. This energy density can then be multiplied by the operating frequency to obtain the power density per unit volume of the material. Magnitude of lower electric field (EL) is varied from 50 to 300 MV/m while value for higher electric field EH is kept constant at 350 MV/m, and the energy density is estimated. The values of maximum energy density are shown in Fig. 9 where energy density is calculated for two temperature ranges from 300–330 K and 300–350 K. This is based on the assumption that for extended heating time period, a temperature of 350 K or more is achievable. This can also be accomplished using other means such as solar collectors or concentrators. The obtained value of maximum energy density for 300– 330 K temperature range is 1478 mJ/cm3 (or 1478 kJ/m3) and for 300–350 K range, the value of energy density is 3164 mJ/cm3 (or 3164 kJ/m3) for the operating range of EH = 350 MV/m and EL = 100 MV/m. The obtained cycle frequency for the temperature range of 300–330 K is found to be nearly 0.011 Hz for air cooling and 0.013 Hz for water cooling techniques respectively. Thus, the problem of low energy density can be solved by employing Olsen/Ericsson cycle for solar energy harvesting. Even though the operational frequency of circuits driven on Olsen cycle remain low (<1 Hz), the significantly high energy density can clearly offset this shortcoming. This is especially prominent when compared to linear pyroelectric harvesters. The obtained value of energy density can be used for calculating power density. Fig. 10 represents the power density as a function of EL for both air and water cooling cases in 300–330 K temperature range. In case of water cooling, the observed value of

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at optimized load resistances of 7 MX and 14 MX. In contrast to this, the maximum value of power density obtained for water and air cooling (using Olsen/Ericsson cycle) is found to be 19.65 mW/cm3 and 16.4 mW/cm3 for operational frequencies of 0.013 and 0.011 Hz respectively. These values are substantially higher when compared to the power density of direct pyroelectric effect. Olsen/ Ericsson cycle can prove to be promising method for solar energy conversion. The results also reveal the fact that water cooling is more beneficial for enhanced energy harvesting. Acknowledgements

Fig. 10. Power density vs EL for fixed cooling and heating temperature.

maximum power density is 19.65 mW/cm3 (or 19.65 kW/ m3). While this value is reduced to 16.35 mW/cm3 (or 16.35 kW/m3) for forced air cooling. In both the cases, the value of applied higher electric field is kept constant at EH = 350 MV/m and the value of lower electric field is varied from EL = 50 MV/m to 300 MV/m. It can be observed that the value of energy and power densities increase almost linearly for decreasing value of EL from 300 MV/m to 200 MV/m. The energy density decreases abruptly for lower value of EL due to innate non-linearity of the ferroelectric material. It is also made evident from the observed results that due to decreasing cycle time, the gain in power density for water cooling based cycle is 19.7% more than forced air cooling cycle. Thus, water or liquid cooling can prove to be beneficial. Also the peak value of power density is very high for solar energy harvesting using Oslen/Ericsson cycle as compared to that obtained by direct pyroelectric effect. 4. Conclusions This study attempts to utilize pyroelectric effect for solar energy harvesting using P(VDF–TrFE–CFE) polymer. Two separate methods are undertaken for solar energy harvesting; first case employs direct pyroelectric current for power generation. The second method investigates enhanced energy harvesting using Ericsson cycle in conjunction with forced cooling techniques. Forced cooling techniques help in further increasing the energy density and reduce cycle time. The system used for the study has been designed and simulated using finite-element method. It was observed that the peak value of power density for water cooling and air cooling processes (direct pyroelectric effect) was found to be 0.437 lW/cm3 and 0.2 lW/cm3, respectively. While the average value of power density for water cooling cycle is 0.044 lW/cm3 and for air cooling cycle is 0.047 lW/cm3

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