Pyroelectric Energy Harvesting: with Thermodynamic-Based Cycles

Hindawi Publishing Corporation Smart Materials Research Volume 2012, Article ID 160956, 5 pages doi:10.1155/2012/160956 Research Article Pyroelectric Energy Harvesting: With Thermodynamic-Based Cycles Saber Mohammadi and Akram Khodayari Mechanical Engineering Department, School of Engineering, Razi University, Kermanshah 67149-67346, Iran Correspondence should be addressed to Saber Mohammadi, [email protected] Received 30 November 2011; Revised 31 January 2012; Accepted 2 February 2012 Academic Editor: Mickael¨ Lallart Copyright © 2012 S. Mohammadi and A. Khodayari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This work deals with energy harvesting from temperature variations using ferroelectric materials as a microgenerator. The previous researches show that direct pyroelectric energy harvesting is not effective, whereas thermodynamic-based cycles give higher energy. Also, at different temperatures some thermodynamic cycles exhibit different behaviours. In this paper pyroelectric energy harvesting using Lenoir and Ericsson thermodynamic cycles has been studied numerically and the two cycles were compared with each other. The material used is the PMN-25 PT single crystal that is a very interesting material in the framework of energy harvesting and sensor applications. 1. Introduction for the systems with limited accessibility such as biomedical implants, structure embedded microsensors, or safety moni- Small, portable, and lightweight power generation systems toring devices. are currently in very high demand in commercial markets, Thermodielectric power generation utilizes the pyroelec- due to a dramatic increase in the use of personal electronics tric effect to convert heat to useful electricity. Pyroelectricity and communication equipments. The simple way to satisfy has been observed in different crystals and ceramics [6]. these demands is to utilize batteries; however, nonrecharge- Materials with high pyroelectric activity or those exhibiting able batteries are becoming useless upon discharging, and a transition can be used for energy harvesting [7, 8]. The rechargeable batteries require portable power generation pyroelectric effect may be used for temperature/heat sensors units to recharge them. Thus, a portable small-scale power or energy harvesting; on the contrary the electrocaloric generation system that can either replace batteries entirely effect may be used for refrigeration devices [9–13]. The or recharge them to extend their lifetime is of considerable pyroelectric effect manifests itself in a polar, capacitive interest. There are several different classes of small-scale power generators currently being researched. The power material that has a temperature-dependent electric polariza- generation technique that is investigated in this study is tion. It occurs when the material is heated or cooled. The the thermodielectric power generation system, which is resulting polarization change forces the material to reject or somewhat similar to thermoelectric power generation [1]. accept electrical charge from its surroundings, based on the Some possible ambient energy sources are thermal energy, direction of temperature change and the orientation of the solar energy, or mechanical energy. Harvesting energy from polarization. Therefore, it can be used in a power generation such renewable sources has stimulated important research system to force electrical charge from the power generating efforts over the past years [2–5]. Thermal energy is a source material (pyroelectric) to an electrical storage device via available everywhere. Also, electronics advances directed heating and cooling. the researchers towards completely autonomous microchips Initial investigations of thermodielectric power genera- embedding their own energy source. Furthermore, propos- tion have been studied to evaluate the energy conversion ing self-powered devices opens new application possibilities properties of various dielectric materials [14–17]. Olsen’s 2 Smart Materials Research group studied various power generation cycles that would P optimize the power density and thermal efficiency [18– 22]. Most recently, Ikura’s experimental investigation [23] implemented one of Olsen’s theoretical operating cycles in a 2 simple thermodielectric converter, demonstrating the ability to generate power with a thermodielectric device. 1 When considering energy conversion from heat, it is E necessary to compare efficiencies with the Carnot cycle efficiency, which is the maximum energy that can be 3 converted for a given temperature variation. However, in the case of pyroelectric energy conversion, a Carnot cycle is not realistic because it is difficult to control successive 4 adiabatic and isothermal conditions. As a consequence, other Figure 1: PE thermodynamic Carnot cycle. cycles have to be considered, such as the Ericsson, Olson [9, 22, 23], or Lenoir cycles. The objective of this study is to further present thermodynamic-based cycles of ferroelectric 3. Carnot Cycle harvesting energy as an efficient micro-thermodielectric power generator. Therefore, the Lenoir and Ericsson thermo- The Carnot cycle is defined as two adiabatic and two dynamic cycles are studied and the results compared with isothermal curves on the polarization-electric field (PE) each other numerically. Finally, the thermodynamic cycle cycle (see Figure 1). It is considered as the optimal energy simulation results are tested on PMN-25 PT single crystal harvesting cycle whose efficiency is because of high pyroelectric activity [11, 13, 24]. θ η = − c Carnot 1 θ ,(5) 2. Thermodynamic Cycles h where θc and θh are the cold and hot temperatures, respec- Any device that operates in a thermodynamic cycle absorbs tively. In the first adiabatic increase of the electric field dΓ = thermal energy from a source, rejects a part of it to a sink, 0(path1-2inFigure 1)andfrom(2), and presents the difference between the energy absorbed and energy rejected as work to the surroundings is called a heat dθ p =− dE engine. A heat engine is, thus, a device that produces work. θ c , The mechanism of pyroelectric generator is similar to a heat (6) engine. θh p ln =− EM, When energy is harvested from heat, one should consider θc c at first the classical thermodynamic cycles. What cycle is E efficient and is it realistic? What is their efficiency and which where M is the maximum amplitude of the applied electric parameters are important to optimize the efficiency? field. This equation shows the relation of electric field The governing equations of pyroelectric materials are as amplitude with the temperatures ratio. In the isothermal dθ = follows [7]: decrease of the electric field 0 (path 2-3), dD = εθ dE pdθ dQh 33 + , (1) dΓ = = pdE, θh dθ (7) dΓ = pdE c (2) + θ , Qh =−pθhEM. where D, E, θ,andΓ are electric displacement, electric field, The two following steps are similar and are not detailed here temperature, and entropy, respectively. (path 4-1 is similar to 2-3 and 3-4 is similar to 1-2). The The coefficients that are assumed to be constant are resulting energy conversion ratio gives defined as in θ − θ W = θ − θ δΓ =−pE h c . θ dD dD dΓ dU e ( h c) M (8) ε = , p = = , c = ,(3) θh 33 dE θ dθ dE dθ E In this cycle the conversion ratio does not depend on material and also properties (5). It depends on the temperature variations. dQ δWcycle dΓ = , η = ,(4) θ |Qh| 4. Ericsson Cycle Q W where h and cycle are the heat taken from the hot reservoir The Ericsson cycle is defined as two constant electric field and cycle net work, respectively. and two isothermal processes curves on the (PE) cycle In the following, two different harvesting cycles are (see Figure 2). As it can be seen, the Ericsson cycle starts presented and their efficiencies compared to the Carnot one. with applying electric field E1 at a temperature θc (cold Smart Materials Research 3 P P 2 θc 1 2 3 1 θh 3 4 E Emax E max E Figure 2: PE thermodynamic Ericsson cycle. Figure 3: PE Lenoir cycle. Table 1 P temperature). Polarization subsequently increases to the 2 6 p cE (×10 ) θ Material ε/ε value (path 1-2). Then, temperature is increased to h (hot μC·m−2·K−1 J·m−3·K−1 0 temperature) at constant electric field (path 2-3). Therefore, 111 PMN-25PT the polarization of the single crystal decreases to P .Then, 1790 2.5 961 3 (single crystal) with the decrease of the applied electric field from Emax to 0, the polarization decreases to P4 (path 3-4). Temperature is then finally decreased to its initial value, completing the cycle (PE) cycle (see Figure 3).Thefirstpathistheincreaseof (path 4-1). electric field dD = 0 (path 1-2) and from (1), Eelectrical and thermal energies can be determined for each segment of cycle. Consequently, we can write εdE =−pdθ, (13) dQ = pθdE cdθ EM 12 + , Wcycle =−(θh − θc) pdE. (9) 0 where dQ12 is the input thermal heat. In the isentropic path dΓ = 0 (path 2-3) and from (2), The energy taken from the hot temperature reservoir is dθ p =− dE, (14) EM θ c Qh = c(θh − θc) + pθhdE. (10) 0 We = EdD. (15) Then, the conversion ratio can be expressed as follows, which defined as the ratio of net electric work to the energy taken The electrical work can be harvested in this step (15). In the from the hot temperature reservoir: constant electric field dE = 0 (path 3-1) and from (1) and(2) dθ W EM pdE dD = pdθ, dΓ = c , cycle 0 θ η = = E . (11) (16) Qh c θ / θ − θ M pdE + ( h ( h c)) 0 Q31 = c(θ3 − θ1), ffi With the comparison to the Carnot cycle e ciency (5), we where Q is the outgoing heat from the material. obtain 31 η EM pdE 6. Results and Discussions = 0 . (12) η c θ − θ EM pθ dE Carnot ( h c) + 0 h In this section, we investigate the simulation results of energy harvesting for each cycle as a function of electric field and This ratio decreases with the increase of temperature varia- temperature.

Load more