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Thermodynamics Cycle Analysis and Numerical Modeling of Thermoelastic Cooling Systems international journal of refrigeration 56 (2015) 65e80 Available online at www.sciencedirect.com ScienceDirect www.iifiir.org journal homepage: www.elsevier.com/locate/ijrefrig Thermodynamics cycle analysis and numerical modeling of thermoelastic cooling systems Suxin Qian, Jiazhen Ling, Yunho Hwang*, Reinhard Radermacher, Ichiro Takeuchi Center for Environmental Energy Engineering, Department of Mechanical Engineering, University of Maryland, 4164 Glenn L. Martin Hall Bldg., College Park, MD 20742, USA article info abstract Article history: To avoid global warming potential gases emission from vapor compression air- Received 3 October 2014 conditioners and water chillers, alternative cooling technologies have recently garnered Received in revised form more and more attentions. Thermoelastic cooling is among one of the alternative candi- 3 March 2015 dates, and have demonstrated promising performance improvement potential on the Accepted 2 April 2015 material level. However, a thermoelastic cooling system integrated with heat transfer fluid Available online 14 April 2015 loops have not been studied yet. This paper intends to bridge such a gap by introducing the single-stage cycle design options at the beginning. An analytical coefficient of performance Keywords: (COP) equation was then derived for one of the options using reverse Brayton cycle design. Shape memory alloy The equation provides physical insights on how the system performance behaves under Elastocaloric different conditions. The performance of the same thermoelastic cooling cycle using NiTi Efficiency alloy was then evaluated based on a dynamic model developed in this study. It was found Nitinol that the system COP was 1.7 for a baseline case considering both driving motor and Solid-state cooling parasitic pump power consumptions, while COP ranged from 5.2 to 7.7 when estimated with future improvements. © 2015 Elsevier Ltd and IIR. All rights reserved. Analyse de cycle thermodynamique et modelisation numerique des systemes de refroidissement thermoelastique Mots-cles : Alliage am emoire de forme ; Elastocalorique ; Efficacite ; Nitinol ; Refroidissement al 'etat solide (Sharp et al., 2006), magnetic cooling (Sarlah et al., 2006; Vasile 1. Introduction and Muller, 2006; Zimm et al., 2006; Jacobs et al., 2014), elec- trocaloric cooling (Gu et al., 2013; Jia and Yu, 2012), thermoa- Solid-state cooling technologies have been developed rapidly coustic cooling (Reid et al., 1998; Swift et al., 1999; Yazaki et al., during the past few decades, including thermoelectric cooling 2002), and most recently, thermoelastic cooling (Cui et al., * Corresponding author. Tel.: 1 301 405 5247; fax: 1 301 405 2025. þ þ E-mail address: [email protected] (Y. Hwang). http://dx.doi.org/10.1016/j.ijrefrig.2015.04.001 0140-7007/© 2015 Elsevier Ltd and IIR. All rights reserved. 66 international journal of refrigeration 56 (2015) 65e80 1 Nomenclature u fluid mean velocity [m sÀ ] 1 u* internal energy [J gÀ ] 3 1 Symbols V_ volumetric flow rate [m sÀ ] A material constant related to hysteresis energy W work [J] 1 [J gÀ ] W_ work rate [W] 1 Bi Biot number w specific work [J gÀ ] COP coefficient of performance VCC vapor compression cycle 1 1 2 1 cp specific heat [J gÀ KÀ ] a thermal diffusivity [m sÀ ] D mechanical efficiency loss factor d equivalent thickness [m] e strain ε effectiveness 1 e_ strain change rate [sÀ ] s stress [MPa] F cyclic loss factor g non-dimensional latent heat GWP global warming potential h efficiency 3 g000 generation term in energy equation [W mÀ ] k thermal mass factor 3 HR heat recovery r density [kg mÀ ] HTF heat transfer fluid x martensite phase fraction 1 1 Dh latent heat [J gÀ ] x_ martensite phase fraction change rate [sÀ ] 2 1 h heat transfer coefficient [W mÀ KÀ ] D material constant related to strain [ ] À ID internal diameter [m] Subscripts K material constant related to elasticity [MPa] 1 1 ad adiabatic k thermal conductivity [W mÀ KÀ ] AM austenite to martensite L length [m] cyc cycle m mass [kg] 1 f fluid m_ mass flow rate [kg sÀ ] HT heat transfer OD outside diameter [m] init initial Q heat transferred [J] mat material Q_ capacity [W] 1 mot motor q capacity per unit mass [J gÀ ] MA martensite to austenite RHS right hand side 1 1 rec recovery s specific entropy [J gÀ KÀ ] s solid, solid heat exchanger or bed SMA shape memory alloy sat saturation sec second trsm transmission T temperature [C] loading DT adiabatic temperature span [K] þ ad unloading t time, or duration [s] À t* heat recovery coefficient 2012) (a.k.a. elastocaloric cooling). These solid-state cooling the useful cooling/heating effect is the result of the associated systems offer us alternatives to eliminate the emission of latent heat released during the stress-induced martensitic traditional high global warming potential (GWP) halogenated phase change process, which makes the material transits refrigerants used in the vapor compression cycle (VCC) sys- between the martensite phase and austenite phase. As shown tems. Compared with other alternative cooling methods, in Fig. 1 (a), when the SMA is subjected to an external stress elastocaloric effect has a higher adiabatic temperature span, exceeding the phase change stress ssat, austenite crystal and therefore, it's possible to use a single stage cycle for starts to transform to martensite crystal, and meanwhile re- typical air-conditioning and refrigeration applications. A more leases the latent heat to raise SMA's temperature at the same sophisticated ranking of solid-state materials also indicates time. The cooling effect takes place when the external system that thermoelastic cooling materials are better than materials stress is less than the ssat. As the stress decreases below the used for magnetic cooling (Qian et al., 2015) in terms of the threshold, the material transits back to the “parent” state, the material level performance. Therefore, from thermodynamics austenite state, and absorbs ambient heat. The SMA was perspective, thermoelastic cooling can be easily applied to famous for its unique mechanical property that it “re- cooling systems as compared to its competitive technologies. members” an original “trained” shape, and can return to this Thermoelastic cooling technology uses shape memory pre-deformed shape upon heating above a transitional tem- alloy (SMA), which is a group of metal alloys with significant perature. NiTi alloy and copper based alloys are most widely elastocaloric effect. They can be used for power cycle, or used as engineering functional materials for a variety of ap- applied reversely for thermoelastic cooling/heat pump cycles. plications, including automotive, aerospace, mini actuators In a power cycle, the driving potential is the temperature and sensors, biomedical, and orthopedic surgery (Jani et al., difference. While in a heat pump cycle, the applied stress in- 2014). As the market of SMA grows, the cost of SMA reduces duces the cooling and heating. In a cooling/heat pump cycle, and it is now possible to use them for power generation and international journal of refrigeration 56 (2015) 65e80 67 Fig. 1 e Illustration of martensitic phase change processes. cooling/heat pump systems. Significant theoretical in- models and finite element or finite volume methods have vestigations for SMA heat engines have been carried out (Tong been carried out in the past decade. and Wayman, 1974; Ahler, 1975; Wayman and Tong, 1975; There are two concerns for the current literature of SMA Delaey and Lepeleire, 1976; Cunningham and Ashbee, 1977; heat engines. First, most of the simple equilibrium analysis and Ziolkowski, 1993), and a few prototypes were built (Sato the sophisticated dynamic model used the homogeneity et al., 2008; Kanada, 2008; Kaneko and Enomoto, 2009; assumption, which is in fact quite common in continuum Wakjira, 2001; Schiller, 2002) and simulated (Gil and Planell, mechanics and thermodynamics. However, applying such 1999; Liu, 2004; Zhu et al., 2001a, 2001b) in the past few de- simplification to complicated shape memory alloy phase cades. Existing SMA heat engines were either wire based change could deviate from reality to a significant amount under wheels (Sato et al., 2008; Kanada, 2008; Kaneko and Enomoto, some circumstances (Furst et al., 2012). To avoid complexity in 2009; Wakjira, 2001), or spring-based on twin crank design calculation of the work needed to drive the cooling/heat pump (Schiller, 2002). A common design of SMA heat engine's heat cycle, experimental data were used to fit in a simple one- source is a hot water bath, with an air cooled heat sink, dimensional constitutive model, in order to evaluate the therefore no complicated fluid lines are necessary. The simple loading/unloading energy related to the coefficient of perfor- design reduced the structural complexity, but left no room for mance (COP) for this study. Such a decoupling of stressestrain applying heat regeneration between the cold SMA wire going relation from temperature allows for better understanding of into the hot water bath, and hot SMA wire leaving hot water the system level performance, rather than focusing on all the bath, as indicated by Fig. 2. Besides heat transfer, the work details of the material level performance. This practice will not production is another essential part when it comes to evaluate lose much accuracy on the material level as long as real the power generation efficiency. Early works on deriving the experimental loading/unloading data are applied. analytical efficiency relies on simple equilibrium stresse- Second, for simplicity consideration, neither the previous strain model (Tong and Wayman, 1974; Ahler, 1975; Wayman analytical approach nor the simulation in the literature and Tong, 1975; Delaey and Lepeleire, 1976; Cunningham and considered heat recovery/regeneration process to improve the Ashbee, 1977), where only a single stress-saturation temper- efficiency. Besides, the control volume of the system they ature is needed and the computation of work is simple. Recent considered is only the SMA itself, excluding any heat transfer computation using analytical approach (Ziolkowski, 1993) fluid loops and associated losses.
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